Resources

Resources

One-step inequalities: word problems

À La Mode Ice Cream Parlor uses the function

f(x)

to calculate its profits. When the parlor sells

x

cones, it makes

f(x)

dollars in profit.

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f(50) = 85

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(A) À La Mode Ice Cream Parlor makes

\$85

50

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(B) À La Mode Ice Cream Parlor makes

\$50

85

Find the zeros of the function. Enter the solutions from least to greatest.

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f(x)=(x+2)^{2}-16

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x= \square

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x= \square

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Get Al Tutoring

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{ }^{\lambda}

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You might need: Calculator

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The price of a train ticket consists of an initial fee of

\$ 5

\$ 2.75

per stop. Julia has

\$ 21

and would like to travel

50

kilometers. She wants to know the largest number of stops she can afford to buy on a ticket.

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S

represent the number of stops that Julia buys.

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1

) Which inequality describes this scenario?

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1

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5+2.75 \cdot S \leq 21

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5+2.75 \cdot S \geq 21

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5+2.75 \cdot S \leq 50

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5+2.75 \cdot S \geq 50

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2

) What is the largest number of stops that Julia can afford?

-2

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SBA Task: Assignment November

2024

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1

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TRUCTIONS AND INFORMATION

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Answer ALL the questions.

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Calculators may be used and ALI calculations must be shown.

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All answers must be rounded off to TWO decimal places, unless otherwise stated.

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1

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Patel and Karen started a business and contributed money in the ratio

5: 4

. The business was started with a capital of R

4

500

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1

1

1

Calculate how much money did Patel contribute to start the business.

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1

1

2

Hence, find how mueh did Karen contribute.

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The business made a profit. Patel and Karen decided to share the profit in the ratio

5: 4

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1

2

1

Determine Patel's share of the profit if Karen received R

1

600

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1

2

2

How much profit did the business make altogether?

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1

2

3

How much more profit does Patel receive than Karen?

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Karen says they are planning to inerease their business capital of R

4500

45 \%

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Calculate the new business capital.

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Patel says it is too risky for them to put a lot of money into the business. So they got other people to contribute equal amounts of money as capital for the business and they will share profits equally.

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\begin{tabular}{|c|c|c|c|c|c|c|}

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\hline \begin{tabular}{c}

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\end{tabular} &

1

2

3

4

18

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\hline \begin{tabular}{c}

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\newline

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\end{tabular} &

\mathrm{R} 6525

\mathrm{R} 3262,50

\mathrm{~A}

\mathrm{R} 1631,25

725

\mathrm{R} 362,50

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1

4

1

Complete the table above.

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1

4

2

Does the relationship represent direct or inverse proportion? Give a reason for your answer.

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1

1

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1

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1

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2

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3

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7

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4

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8

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Draw a shape for the statement. Draw the line or lines of symmetry.

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9

. zero lines of symmetry

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10

1

line of symmetry

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11

2

lines of symmetry

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Does the design have line symmetry? Write yes or no.

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If your answer is yes, draw all lines of symmetry.

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5

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6

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4

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8

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Problem Solving (Real)

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Use the chart for

12

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4

2

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34

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8

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12

. Which number or numbers appear to have lines of symmetry?

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13

. WRITE Math Draw a picture of a figure that has more than

3

lines of symmetry. Drawthe lines of symmetry.

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10

1

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\begin{aligned} g(7) & =\frac{3}{7-2} \\ & =\frac{3}{5} \end{aligned}

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2

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\begin{aligned} h(7) & =9(7) \\ & =63 \end{aligned}

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3

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\begin{aligned} (g \circ h)(7) & =\frac{3}{5} \cdot 63 \\ & =\frac{189}{5} \end{aligned}

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What is the mistake in Danielle's work?

f(x, y)=3 x y

has an absolute maximum value and absolute minimum value subject to the constraint

2 x^{2}+2 y^{2}-3 x y=49

. Use Lagrange multipliers to find these values.

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rina the gradient or

g(x, y)=\angle x+2 y-3 x y-4 y

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abla g(x, y)=\langle 4 x-3 y, 4 y-3 x\rangle

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Write the Lagrange multiplier conditions. Choose the correct answer below.

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3 x=\lambda(4 x-3 y), 3 y=\lambda(4 y-3 x), 3 x y=0

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3 x y=\lambda(4 x-3 y), 3 x y=\lambda(4 y-3 x), 2 x^{2}+2 y^{2}-3 x y-49=0

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3 x=\lambda(4 x-3 y), 3 y=\lambda(4 y-3 x), 2 x^{2}+2 y^{2}-3 x y-49=0

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3 y=\lambda(4 x-3 y), 3 x=\lambda(4 y-3 x), 2 x^{2}+2 y^{2}-3 x y-49=0

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The absolute maximum value is

5

1

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Google Classroom

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h(x)=x^{5}-2 x^{4}+10 x^{2}-10 x

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Below is Omar's attempt to write a formal justification for the fact that there exists a value

c

-2<c<2

h^{\prime}(c)=6

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Is Omar's justification complete? If not, why?

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Omar's justification:

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h(-2)=-4 \text { and } h(2)=20 \text {, so } \frac{h(2)-h(-2)}{2-(-2)}=6 .

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So, according to the mean value theorem, there exists a value

c

somewhere in the interval

-2<c<2

h^{\prime}(c)=6

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1

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3

5

The speed of sound is approximately

768

miles per hour. When an object travels faster than the speed of sound, it creates a sonic boom.

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Write an inequality that desribes the speed at which a moving object creates a sonic boom,

s

2

The table shows Ricky's monthly budget. Ricky earns

\$ 1,200

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\begin{tabular}{|l|c|}

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\hline \multicolumn{

1

}{|c|}{ Expense } & \begin{tabular}{c}

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\end{tabular} \\

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\hline Clothes &

\$ 175

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\$ 425

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\hline Cell phone &

\$ 80

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\hline College savings &

\$ 120

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\hline Car payment &

\$ 300

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\$ 100

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Which statement is NOT supported by the information in the table?

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25 \%

of his monthly budget on his car payment.

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(B) Ricky spends

10 \%

of his monthly budget on college savings.

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(C) Ricky spends

50 \%

of his monthly budget on clothes and food.

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\$ 175

0

of his monthly budget on his cell phone and college savings.

Turkey's government requires at least a

\frac{2}{3}

majority of Parliament members to approve any constitutional changes. There are

550

seats in the Parliament. Of those,

313

of the seats are occupied by members who have pledged to support a particular constitutional change. Which inequality represents the number of additional Parliament members,

m

, who would need to support the constitutional change to achieve the required majority?

7 B+13 F>650

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Sania plays a game in which she pops balloons and slices fruits. She scores

7

points for every balloon she pops and

13

points for every fruit she slices. Sania's goal is to score more than

650

points in the game. In the given inequality,

B

represents the number of balloons Sania pops and

F

represents the number of fruits she slices. If Sania pops

30

balloons in the game, what is the least number of fruits she must slice to reach her goal?

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1

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(A) Sania must slice at least

13

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(B) Sania must slice at least

30

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(C) Sania must slice at least

33

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(D) Sania must slice at least

34

Nick is doing some math exercises on a website called Khon Academy. In Khon Academy, you have to get at least

70\%

of the problems in an exercise right in order to gain proficiency.

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So far, Nick answered one question, and he didn't get it right. Suppose he answers

75\%

of the following

q

questions correctly and gains proficiency in the exercise.

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Write an inequality in terms of

q

that models the situation.

Google Classroom

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450

students traveled to a state park for a field trip. The school allowed

6

students to travel by car, and the rest traveled on

11

buses, each of which held the same number of students. If there were

s

students in each bus, which inequality best represents this situation?

You have \$\(20\) to spend on taxi fare. The ride costs \$\(5\) plus \$\(2\).\(50\) per kilometer. Write an inequality to determine the distance in kilometers, \(d\), you can ride for \$\(20\).

Solve using the addition method.

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\begin{array}{l} 8 a+8 b-c=4 \\ 7 a+4 b+c=-4 \\ 4 a-8 b-6 c=20 \end{array}

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Select the correct choice below and, if necessary, fill in the answer boxes to complete your cho

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A. There is one solution. The solution is (, ). (Simplify your answer.)

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B. The system is dependent. There are infinitely many solutions.

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C. The system is inconsistent. There is no solution.

Apolline is mowing lawns for a summer job. For every mowing job, she charges an initial fee plus a constant fee for each hour of work. Her fee for a

5

-hour job, for instance, is

\$ 42

. Her fee for a

3

\$ 28

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y

represent Apolline's fee (in dollars) for a single job that took

x

hours for her to complete.

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Which of the following information about the graph of the relationship is given?

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1

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x

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y

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(C) Slope and a point that is not an intercept

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x

y

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y

-intercept and a point that is not an intercept

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(F) Two points that are not intercepts

A single die is rolled twice. The

36

equally-likely outcomes âre shown to the right.

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Find the probability of getting two numbers whose sum is

8

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The probability of getting two numbers whose sum is

8

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(1)/(8)

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(Type an integer or a simplified fraction.)

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Get more help .

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3

. Points possible:

3

Unlimited attempts. Score on last attempt:

0

. Score in gradebook:

0

Message instructor about this question For triangle

ABC

, we are given that

m\angle C=93.7^\circ

AC=12.5\,\text{ft}

BC=22.6\,\text{ft}

. We can use the Law of Cosines, Law of Sines, and other properties of triangles to determine all of the missing information. Note that the diagram may not be drawn to scale. Determine all of the missing information about this triangle. a.

AB=

** feet Preview b. Draw the triangle and add the length of

\overline{AB}

to your diagram. c.

m\angle A=

* degrees Preview d.

m\angle B=

degrees Preview Note that this question allows you to use trig functions that evaluate for angle measures in degrees. To remind yourself how to evaluate trig functions for angle measures in degrees in this program, click here. Submit Question

4

. Points possible:

3

Unlimited attempts. Score on last attempt:

0

. Score in gradebook:

0

Message instructor about this question Triangle

ABC

is shown below with all three side lengths known.

Solve by the method of your choice.

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Twenty two people purchase raftle tickets. Three winning tickets are selected at randorn. If first prize is

\$ 1000

, second prize is

\$ 500

, and third prize is

\$ 100

, in how many different ways can the prizes be awarded?

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\square

different ways in which the prizes can be awarded.

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(Simplify your answer.)

Solve by the method of your choice.

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Twenty- two people purchase raflle tickets. Three winning tickets are selected at random. If first prize is

\$ 1000

, second prize is

\$ 500

, and third prize is

\$ 100

, in how many different ways can the prizes be awarded?

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\square

different ways in which the prizes can be awarded.

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(Simplify your answer.)

Ashish tried to evaluate the expression

\left(4^{-3} \cdot 2^{-3}\right)^{0}

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\begin{array}{l} \left(4^{-3} \cdot 2^{-3}\right)^{0} \\ =\left(8^{-3}\right)^{0} \\ \text { Step } 1 \\ =8^{0} \\ \text { Step } 2 \\ =0 \\ \text { Step } 3 \\ \end{array}

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Did Ashish make a mistake? If so, in which step?

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1

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(A) Ashish did not make a mistake.

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(A) Achich mado a mictalo in Ctan

1

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10

10

Creep is the ratio of elongation to original length that occurs in materials over time. For a particular steel structure, for the first

50

days the creep increases by

6\times10^{-6}

per day. After the

50

th day, when the creep is

3\times10^{-4}

, the creep triples every

62

days. After the

236

th day, how much less would the creep be if it had continued to grow linearly after the

50

1

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1.1\times10^{-3}

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1.4\times10^{-3}

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6.7\times10^{-3}

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6\times10^{-6}

0

Solve each compound inequality and state the interval solution.

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6 x-2 \leq 10 \text { and } 10 x>-20

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No answer text provided.

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No answer text provided.

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No answer text provided.

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Get Al Tutoring

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{ }^{x}

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Google Classroom

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Marcus and Isabel are playing a game that involves flipping

2

fair coins to see who gets to be the

www-awu.aleks.com

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VitalSource Bookshelf: Print Reading for Cónstruction

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A ALEKS - Zachary Zawacki - Learn

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Polynomial and Rational Functions

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Word problem involving optimizing area by using a quadratic function

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360

meters of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing.

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As shown below, one of the sides has length

x

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(a) Find a function that gives the area

A(x)

of the garden (in square meters) in terms of

x

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A(x)=

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(b) What side length

x

gives the maximum area that the garden can have?

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x: \square

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(c) What is the maximum area that the garden can have?

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\square

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3

2024

McGraw HIII LLC. All Righits Reserved. Terms of Use

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\frac{1}{4} c+3 d

c=6

d=7

earson.com/Student/PlayerHomework.aspx?homeworkld=

664326915

9

&flushed=false&cld=

7667942

&back=DoAssignments.aspx?view... Veronica Childress

03

20

24

7

28

PM Equations of Lines Question

7

13

5

11

75

18

24

(x)

0

1

Use the slope-intercept form to graph the equation

y = -2x - 4

Use the graphing tool to graph the line Use the slope and y-intercept when drawing the line Click to enlarge graph

The recommended maximum speed for the German Autobahn expressway is

v_{\text{max}}

kilometers per hour. Write an inequality that describes

v

, any speed slower than the recommended maximum speed.

Jenna worked out for more than

25

minutes total. She spent

10

minutes running, and

x

minutes each on

2

stations. How much time could she have spent on each station?

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Write an inequality to represent the situation. Use

x

to represent the minutes spent on each of the stations.

A charity organization had to sell

18

tickets to their fundraiser just to cover necessary production costs. They sold each ticket for

\$45

y

represent the net profit (in dollars) when they have sold

x

tickets. Which of the following information about the graph of the relationship is given?

Marie is leaving her cat, Shadow, with a pet-sitter while she's away on vacation. Marie packs up toys, and a note that says Shadow eats at most

12

ounces of food each day.

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Write an inequality to represent the number of ounces of food that Shadow might eat in a day,

f

Frannie thinks she has raised a prize-winning giant pumpkin. It weighs

324

pounds! In order to get the first place prize, the pumpkins of her competitors can weigh

324

pounds at most.

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Write an inequality to represent the weight, in pounds, of the other pumpkins if Frannie is to win the first place prize,

w

g(x)=8x-5

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Which of the following is equivalent to

g(g(x))

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1

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64x-10

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64x-45

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64x^{2}+25

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64x^{2}-80x+25

The light from the moon, in lux, on the night of the

t^{\text{th}}

2016

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L(t)=0.25-\sin\left(\frac{2\pi(t-2)}{28.5}\right)

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What is the period of the light from the moon? Give an exact answer.

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A chameleon is looking for prey. Let positive numbers represent the elevation of prey above the chameleon and negative numbers represent the elevation of prey below the chameleon.

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The chameleon spots a fly at

4\,\text{m}

and a grasshopper at

-6\,\text{m}

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What does an elevation of

0\,\text{m}

represent in this situation?

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1

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(A) The elevation of the fly

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(B) The elevation of the chameleon

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(C) The elevation of the grasshopper

149\,\text{km}

from the university and drives

95\,\text{km}

closer every hour. Valente is

170\,\text{km}

from the university and drives

110\,\text{km}

closer every hour. Let

t

represent the time, in hours, since Chiamaka and Valente started driving toward the university. Complete the inequality to represent the times when Valente is closer than Chiamaka to the university.

4

Test* This hexagon is regular, the dashed line segments form

30

degree angles. What is the image of line

\overline{OJ}

after a rotation of

180

We have a deck of

10

cards numbered from

1

10

, Some are grey and some are white.

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1

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2

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3

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4

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5

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6

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7

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8

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10

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The cards numbered

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10

1

10

2

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The cards numbered

10

3

10

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A card is drawn at random.

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10

5

be the event that the drawn card is grey, and let

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10

6

be the probability of

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10

5

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Let \(\newline\)eg X be the event that the drawn card is not grey, and let

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10

8

be the probability of \(\newline\)eg X.

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(a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability

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1

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2

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3

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4

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5

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6

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7

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8

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10

2

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10

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1

9

A solid line in the

xy

plane passes through the points

(0, -4)

(1, -1)

(2, 2)

. The line divides the plane into two halves. The top half is shaded. A solid line in the

xy

plane passes through the points

(0, -4)

(1, -1)

(2, 2)

. The line divides the plane into two halves. The top half is shaded. If the shaded region in the graph represents the solution set to an inequality, which of the following could be the inequality?

Line and angle proofs

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Google Classroom

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\overleftrightarrow{AB}

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\overleftrightarrow{CD}

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Complete the proof that the alternate interior angles of transversals of parallel lines are congruent.

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Note: this proof is for the case where

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m\angle1 < 90^\circ

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This proof uses the following theorem: Any point on one parallel line is the same distance from the other line on a perpendicular transversal.

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4

Lena is flying a drone. She is controlling the drone so that it ascends at a constant rate. After ascending for

8

seconds, the drone is

152

meters high. After

31

seconds, the drone is

359

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(a) Choose the statement that best describes how the time and the altitude of the drone are related. Then fill in the blank.

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As time increases, the altitude of the drone decreases.

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The altitude of the drone decreases at a rate of

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oxed{ ext{◻}} meters per second.

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As time increases, the altitude of the drone increases.

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The altitude of the drone increases at a rate of

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oxed{ ext{◻}} meters per second.

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(b) What was the altitude of the drone when it started its ascent?

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x

and graph the solution on the number line below.

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5x < 5

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1

2

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\leq\geq\leq\square

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Inequality Notation:

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3

.) There was a study done on oxygen consumption of snails as a function of

\mathrm{pH}

, and the result was a degree

4

polynomial function whose graph is shown below.

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Which statement about this function is incorrect?

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1

) The degree of the polynomial is even.

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2

) There is a positive leading coefficient.

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3

\mathrm{pH}

values, there is a relative maximum value.

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4

) There are two intervals where the function is decreasing.

Mindy and Troy combined ate

9

pieces of wedding cake. Mindy ate

3

pieces of cake and Troy had

\frac{1}{4}

of the total cake. How many pieces of cake were there in all?

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\square

A standard deck of cards has

52

total cards divided evenly into

4

suits - there are

13

13

13

13

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Ayana and Emil are playing a game that involves drawing

2

cards from a standard deck without replacement to start the game. If neither of the cards are spades, then Ayana goes first. Otherwise, Emil goes first.

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Is this a fair way to decide who goes first? Why or why not?

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1

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(A) No, there is a higher probability that Ayana goes first.

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B No, there is a higher probability that Emil goes first.

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(C) Yes, they both have an equal probability of going first.

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34

35

1

point) | Question Attempt:

1

1

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-=24\quad -=25\quad -=26\quad -=27\quad -=29

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Graph the inequality below on the number line.

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y \leq -8

Mindy and Troy combined ate

9

pieces of wedding cake. Mindy ate

3

pieces of cake and Troy had

\frac{1}{4}

of the total cake. How many pieces of cake were there in all?

Use the disk method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the

x

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y=\frac{1}{\sqrt{1+x^{2}}}, \quad y=0, \quad x=-1, \quad x=1

20

\$

to spend on taxi fare. The ride costs

5

\$

2.50

per kilometer. Write an inequality to determine the distance in kilometers,

d

, you can ride for

20

\$

...