Resources

Resources

Solve equations with variables on both sides

d

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-5d = -8d - 6

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d =

g

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2 + 8g = 10g

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g =

z

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\frac{5}{3}z + 1 = 3 - \frac{2}{3}z

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z =

f

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2 - \frac{1}{4}f = f - \frac{3}{4}f + 3

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f =

Extraneous solutions of equations

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Li Juan solves the equation below by first squaring both sides of the equation.

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\sqrt{3-2 w}=w+6

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What extraneous solution does Li Juan obtain?

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w=

16

. A cone has a surface area of

16 \pi \mathrm{m}^{2}

and a volume of

8 \pi \mathrm{m}^{3}

. If a similar cone has a surface area of

100 \pi \mathrm{m}^{2}

. What is the similarity ratio of the smaller cone to the larger cone? What is the volume of the larger cone?

Giant kelp is one of the fastest-growing organisms on the planet. Desmond told his little brother that kelp grows about

1.38 \times 10^{-2}

feet per minute. What would be the most appropriate unit for Desmond to use instead of feet per minute?

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(A) inches per minute

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(B) feet per second

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(C) feet per hour

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(D) feet per day

Standard to Slope Intercept Form

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1

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Put the following equation of a line into slope-intercept form, simplifying all fractions.

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12 x-20 y=-100

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1

2

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\square

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5

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7

10

2

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10

12

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10

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The table shows the approximate number of ounces of chlorine that should be added to a pool based on the number of gallons it holds.

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Number of Gallons of Water

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x

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4

500

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7

000

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Number of Ounces of Chlorine

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y

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0

585

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0

91

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Find the unit rate for the ounces of chlorine to the gallons of water. Then write an equation to represent the situation.

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\square

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\square

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y= \square

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0

5

8

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7

10

2

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10

12

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10

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The table shows the approximate number of ounces of chlorine that should be added to a pool based on the number of gallons it holds.

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

\newline

\hline Number of Gallons of Water

(\boldsymbol{x})

4

500

7

000

\newline

\hline Number of Ounces of Chlorine

(\boldsymbol{y})

0

585

0

91

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Find the unit rate for the ounces of chlorine to the gallons of water. Then write an equation to represent the situation.

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\square

\square

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y=

\square

classroom.google.com/c/

NTUONTI2NTY

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Inc Student Logins - St. B Apple Music

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tions: Find the value of

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\epsilon

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x=

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y=

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Directions: Find the value of each

v

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1

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x=

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\qquad

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y=

7

-42

X

Y

650

miles apart, Train \#

1

travels from City

X

Y

60

mile/hour. Train \#

2

travels from City

Y

X

70

mile/hour. Train \#

1

8

00

X

2

10

00

am from City Y. What time will the two trains meet?

150

words per minute on average in Hungarian, and

190

words per minute on average in Polish. She once gave cooking instructions in Hungarian, followed by cleaning instructions in Polish. Sakura spent

5

minutes total giving both instructions, and spoke

270

more words in Polish than in Hungarian.

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How long did Sakura speak in Hungarian, and how long did she speak in Polish?

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Sakura spoke for

\square

minutes in Hungarian and for

\square

minutes in Polish.

Vera studies the extinction of the bear population of Siberia over time. The following function gives the number of bears

t

years since Vera started tracking it:

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B(t)=2190 \cdot e^{-0.3 t}

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What is the instantaneous rate of change of the number of bears after

2

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1

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1202

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1202

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-361

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-361

A person stands

12

meters east of an intersection and watches a car driving away from the intersection to the north at

4

meters per second.

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At a certain instant, the car is

9

meters from the intersection.

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What is the rate of change of the distance between the car and the person at that instant (in meters per second)?

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1

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2

4

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4 \sqrt{10}

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15

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\frac{20}{3}

Two cars are driving away from an intersection in perpendicular directions.

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The first car's velocity is

7

meters per second and the second car's velocity is

3

meters per second.

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At a certain instant, the first car is

5

meters from the intersection and the second car is

12

meters from the intersection.

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What is the rate of change of the distance between the cars at that instant (in meters per second)?

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1

\newline

\frac{99}{13}

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\mathbf{1 3}

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\sqrt{58}

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\frac{71}{13}

Two cars are driving away from an intersection in perpendicular directions.

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The first car's velocity is

5

meters per second and the second car's velocity is

8

meters per second.

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At a certain instant, the first car is

15

meters from the intersection and the second car is

20

meters from the intersection.

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What is the rate of change of the distance between the cars at that instant (in meters per second)?

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1

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13

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25

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9

4

\newline

\sqrt{89}

29

-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at

7

meters per minute.

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At a certain instant, the bottom of the ladder is

21

meters from the wall.

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What is the rate of change of the distance between the bottom of the ladder and the wall at that instant (in meters per minute)?

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1

\newline

\frac{20}{3}

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20

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\frac{147}{20}

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7

20

-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at

8

meters per minute.

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At a certain instant, the top of the ladder is

12

meters from the ground.

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What is the rate of change of the distance between the bottom of the ladder and the wall at that instant (in meters per minute)?

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1

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\frac{32}{3}

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8

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24

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6

39

-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at

10

meters per minute.

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At a certain instant, the bottom of the ladder is

\mathbf{3 6}

meters from the wall.

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What is the rate of change of the distance between the top of the ladder and the ground at that instant (in meters per minute)?

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1

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-\frac{25}{6}

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-12

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-\mathbf{1 0}

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-24

A person stands

12

meters east of an intersection and watches a car driving away from the intersection to the north at

4

meters per second.

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At a certain instant, the car is

9

meters from the intersection.

\newline

What is the rate of change of the distance between the car and the person at that instant (in meters per second)?

\newline

1

\newline

\frac{20}{3}

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15

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4 \sqrt{10}

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2

4

Two cars are driving away from an intersection in perpendicular directions.

\newline

The first car's velocity is

7

meters per second and the second car's velocity is

3

meters per second.

\newline

At a certain instant, the first car is

5

meters from the intersection and the second car is

12

meters from the intersection.

\newline

What is the rate of change of the distance between the cars at that instant (in meters per second)?

\newline

1

\newline

\frac{99}{13}

\newline

\frac{71}{13}

\newline

\mathbf{1 3}

\newline

\sqrt{58}

Two cars are driving away from an intersection in perpendicular directions.

\newline

The first car's velocity is

5

meters per second and the second car's velocity is

8

meters per second.

\newline

At a certain instant, the first car is

15

meters from the intersection and the second car is

20

meters from the intersection.

\newline

What is the rate of change of the distance between the cars at that instant (in meters per second)?

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1

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13

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9

4

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25

\newline

\sqrt{89}

25

-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at

3

5

meters per minute.

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At a certain instant, the top of the ladder is

7

meters from the ground.

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What is the rate of change of the distance between the top of the ladder and the ground at that instant (in meters per minute)?

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1

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-3

5

\newline

-12

\newline

-7

\newline

-24

29

-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at

7

meters per minute.

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At a certain instant, the bottom of the ladder is

21

meters from the wall.

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What is the rate of change of the distance between the bottom of the ladder and the wall at that instant (in meters per minute)?

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1

\newline

7

\newline

\frac{147}{20}

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20

\newline

\frac{20}{3}

20

-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at

8

meters per minute.

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At a certain instant, the top of the ladder is

12

meters from the ground.

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What is the rate of change of the distance between the bottom of the ladder and the wall at that instant (in meters per minute)?

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1

\newline

8

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6

\newline

\frac{32}{3}

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24

A person stands

30

meters east of an intersection and watches a car driving away from the intersection to the north at

17

meters per second.

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At a certain instant, the car is

16

meters from the intersection.

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What is the rate of change of the distance between the car and the person at that instant (in meters per second)?

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1

\newline

\sqrt{1189}

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34

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36

125

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8

Khiloe Hoenig e Book Goog

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My OLDEST DAUGHILR IS M

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Assignment Player

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:- bigideasmath.com/MRL/public/app/\#/student/assessment;isPlayerWindow=true;assignmentld=

5419

9

-4016

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10

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M

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15

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MODELING REAL LIFE You are riding on a zip line. Your speed is

15

miles per hour. What is your speed in feet per second?

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\square

feet per second

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7

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8

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9

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10

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11

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12

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13

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14

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15

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16

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support powered b

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CalcChat and CaleV

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8

6-x=9

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9

-x=-12 \quad x=

19

. What is the correlation coefficient based on the scatter plot below?

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-1

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0

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-0

85

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1

x

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\frac{1}{2x}+1=-1x+4

20

feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for

12

minutes, and then flies directly back to the hive at

12

feet per second. It is away from the hive for a total of

17

minutes. What equation can you use to find the distance of the flowerbed from the hive?

Find five Rationd Numbers betwem

3

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2

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r+s

3

Practice) - Unit

8

PQRS

is a trapezoid. Find each measure.

m/\_Q=

m/\_s=

Sfephanic is TWICE as old as hel SisteR Rosa. If Stepharie is

18

years old, How OLDis Rosa?

Stephanie is thice as old as her SisteR ROSa. If Stepharie is

18

years old, How OLD is Rosa?

6

. At a given instant, a cyclist is at a point

A

along a straight path

A P B

. He cycles along

A P

at an average speed of

8 \mathrm{~m} / \mathrm{s}

P Q

at an average speed of

6 \mathrm{~m} / \mathrm{s}

, to reach a point

Q

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A B=90 \mathrm{~m}

B Q=40 \mathrm{~m}

, determine the distance between

A

A P B

0

such that he will be able to reach

Q

in the shortest time.

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Get Al Tutoring New e:

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^{2}

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4

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Google Classroom

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You might need: [igleculator

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What is the area of the region between

2

consecutive polnts where the graphs of

f(x)=\cos (x)

g(x)=-\cos (x)+2

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1

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4

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4 \pi

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2

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2 \pi

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Show Calculator

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Brport a problem

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s^{\prime} \quad

5

19

DeltaMath Student Application

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Desmos | Scientlific Calculator

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3345436

22863483

11367

6

689

6035

83

8

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ReadTheory | Readi...

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Space huggers - Op.

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0 / 20

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1

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Solve the equation for all real solutions in simplest form.

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3 z^{2}-z+5=6

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Answer Attempt y out of

2

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9

) Additional Solution

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z=

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During a mayoral election, candidate A spent

\$960,000

on her campaign, and candidate B spent

\$720,000

on her campaign. What is the ratio of candidate A's campaign spending to candidate B's campaign spending?

x = 7, y = 4.

6x + 8xy - 3y =

P = 4a^2 + 12ab + 9b^2

Q = 4a^2 – 12ab + 9b^2

Effectuez l’opération suivante :

P – Q

Solve for the exact value of

x

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6 \ln (4 x+9)+4=-14

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Solve for the exact value of

x

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2 \ln (6 x+5)-11=-3

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d

\newline

\frac{4}{5}d + 3 = -2 - \frac{1}{5}d

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d =

s

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\frac{5}{8} - \frac{3}{8}s = 2 - s

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s =

A plane and a helicopter are both flying toward Clover City Airport. The plane is

1,200

miles from the airport, and it is flying at a constant speed of

510

miles per hour. The helicopter is

500

miles from the airport, and it is flying at a constant speed of

160

miles per hour.

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Which equation can you use to find

h

, the number of hours it will take for the plane and the helicopter to be the same distance from the airport?

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1,200 - 500h = 510 - 160h

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1,200 - 510h = 500 - 160h

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How many hours will it take for the plane and the helicopter to be the same distance from the airport?

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Simplify any fractions.

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Julia and Lena started reading a science fiction book at the same time. During the first week, Lena read

10

more pages than Julia. The following week, Lena read

14

pages, and Julia read the same number of pages she read the first week. Now they are on the same page.

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Which equation can you use to find

j

, the number of pages Julia read during the first week?

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j + 10 + 14 = j + j

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j + 10 = j + j + 14

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How many pages did Julia read during the first week?

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\_\_\_

A plane and a helicopter are both flying toward Clover City Airport. The plane is

1,200

miles from the airport, and it is flying at a constant speed of

510

miles per hour. The helicopter is

500

miles from the airport, and it is flying at a constant speed of

160

miles per hour.

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Which equation can you use to find

h

, the number of hours it will take for the plane and the helicopter to be the same distance from the airport?

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1,200 - 510h = 500 - 160h

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1,200 - 500h = 510 - 160h

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How many hours will it take for the plane and the helicopter to be the same distance from the airport?

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Simplify any fractions.

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