Resources

Resources

Transformations of functions

U = \{(x, y, z) \in \mathbb{R}^3 : 3x - 2y + z = 0\}

W = \{(x, y, z) \in \mathbb{R}^3 : -x + 2y + 2z = 0\}

U \cap W

\text{dim}(U \cap W)

It is given that the constant term in the expansion of

\left(2+\frac{1}{x}\right)^{2}(1-3 x)^{n}

67

n

is a positive integer. Find the value of

n

Use synthetic division to find the quotient and remainder when

f(x)=5 x^{4}-6 x^{3}-5 x^{2}-4 x-3

g(x)=x+9

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Under the sun' note.

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1

2

3

Qulz: Adding and Subtracting Polynomials

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6

10

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Which polynomial represents the sum below?

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\begin{array}{r} 3 x^{2}+4 x+3 \\ +\quad 3 x^{2}+6 x \\ \hline \end{array}

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9 x^{2}+10 x+3

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6 x^{2}+24 x+3

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6 x^{2}+10 x+3

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9 x^{2}+24 x+3

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Home | Schoology

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Under the sun' note.

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1

2

3

Qulz: Adding and Subtracting Polynomials

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6

10

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Which polynomial represents the sum below?

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3x^{2}+4x+3+3x^{2}+6x

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9x^{2}+10x+3

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6x^{2}+24x+3

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6x^{2}+10x+3

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9x^{2}+24x+3

(Get the variable on a side by itself)

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there are addition or subtraction signs, add oppos ite to both sides of equation to get the variable erm by itself.

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1

x+6=9

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2

x-3=8

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3

4+x=-8

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-6

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4

-5=x+8

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5

3+t=21

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6

-9.7=-4.7+y

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there is a coefficient (number) on the variable, divide both sides of the equation by that coefficiel number) to get the variable by itself.

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1

\underline{2 x}=\underline{6}

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2

3 x=-9

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3

-4 \mathrm{x}=-16

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4

.8 \mathrm{x}=.16

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22

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\mathrm{x}=3

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5

x-3=8

0

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6

x-3=8

1

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7

x-3=8

2

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7

x-3=8

3

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8

x-3=8

4

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9

x-3=8

5

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10

x-3=8

6

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11

x-3=8

7

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Mixed Practice. Solve these equations by using the two steps:

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1

. If there are addition or subtraction signs, add oppos te to both sides of

\quad

ing statement is true.

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\left(x^{2}-16 x\right)-17\left(y^{2}+6 y\right)=20

, complete th mplete the square on

y

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Which half-reaction equation represents the reduction of an iron(II) ion?

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1

\mathrm{Fe}^{2+} \longrightarrow \mathrm{Fe}^{3+}+\mathrm{e}^{-}

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3

\mathrm{Fe}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2+}

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2

\mathrm{Fe}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Fe}

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4

\mathrm{Fe} \longrightarrow \mathrm{Fe}^{2+}+2 \mathrm{e}^{-}

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1

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2

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3

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4

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Clear selection

6

\angle 1

\angle 2

are omplementary angles. If m

\angle 1=(7 x+16)^{\circ}

\mathrm{m} \angle 2=(4 x-3)^{\circ}

, then find the measure of

\angle 2

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\rightarrow(7 x+16)+(4 x-3)

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Copyright DeltaMath

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-3

6

\angle 1

\angle 2

11+4=90

0.1=(7 x+16)^{\circ} \mathrm{mdm} \mathrm{m} / 2=(4 x-3)^{\circ}

, then find the mesure of

\angle 2

\quad x=\pi

find the measure of

\angle 2

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7(7 x+16)+(4 x-3)

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(-3)

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Find using distributivity

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\left[\frac{7}{5} \times\left(\frac{-3}{12}\right)\right]+\left[\frac{7}{5} \times \frac{5}{12}\right]

\left[\mathrm{K}^{+}\right]

\left[\mathrm{NO}_{3}^{-}\right]

1

. (Hint: the ratio of

\mathrm{K}^{+}

\mathrm{NO}_{3}^{-}

1

1

) Provide answers for

2

5

on your data sheet.

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Excercises: Determine the antiderivativ

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1

f(x)=(x+1)^{100}

8

\sqrt{2}=1.414 \& \sqrt{3}=1.732

, find the value of

\frac{4}{3 \sqrt{3}-2 \sqrt{2}}

11

Triangie Proportionality Theorem

6

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5 T

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S T=

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\times 12

5.544 \mathrm{~cm}^{2}

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42 \mathrm{~cm}

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60

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2.772 \mathrm{~cm}^{2}

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1.386 \mathrm{~cm}^{2}

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693 \mathrm{~cm}^{2}

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b=\sqrt{144}

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b=12

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23

. Kania akan mengirim paket sebanyak

300

buah berbentuk kubus yang tingginya

4 \mathrm{~cm}

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Kania memasukkan paket ke dalam kardus sampai penuh. Ternyata ada paket yang tidak dapat dimasukkan kardus. Kania kemudian mencari kardus berbentuk balok yang dapat digunakan untuk mengemas paket dengan ukuran yang pas.

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Ukuran kardus berbentuk balok untuk mengemas paket yang tepat adalah

\qquad

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12

16

5.544 \mathrm{~cm}^{2}

0

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16

12

5.544 \mathrm{~cm}^{2}

1

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12

15

5.544 \mathrm{~cm}^{2}

2

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16

8

5.544 \mathrm{~cm}^{2}

3

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24

. Kolam ikan berbentuk balok. Bagian dalam kolam berukuran panjang

5.544 \mathrm{~cm}^{2}

4

5.544 \mathrm{~cm}^{2}

5

5.544 \mathrm{~cm}^{2}

6

. Bagian dalam kolam dicat agar tidak bocor. Biaya pengecatan kolam Rp

30

000

00

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Biaya pengecatan kolam ada

\qquad

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5.544 \mathrm{~cm}^{2}

8

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8

1

350

000

00

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5.544 \mathrm{~cm}^{2}

9

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1

890

000

00

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25

. Dimas memiliki cat di dalam kaleng seperti gambar.

\frac{3 x-4}{7 x-1}=2 \frac{1}{2}

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\frac{2 y-3}{2}-\frac{y+4}{3}=\frac{5 y-1}{6}

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Solve the equation

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

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\frac{3 a+2 b}{7 a-b}=\frac{2}{3}

, find the value of

\frac{2 b}{3 a}

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2(x+4 y)=5(5 x-3 y)

, find the value of

\frac{2 x}{y}

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Sarah is one and a half times older than her da

\angle 1

\angle 2

are supplementary angles. If

\mathrm{m} \angle 1=(4 x-16)^{\circ}

\mathrm{m} \angle 2=(x+1)^{\circ}

, then find the measure of

\angle 2

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y=\pm\frac{16}{14}(x)

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Find the common ratio of the geometric sequence

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\{a_{n}\}_{n=1}^{\infty}

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\begin{align*}\(\newline&\left\{\begin{array}{l}

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-\frac{1}{4}=a_{1}+d \quad d=-\frac{1}{4}-a_{1},(\newline\)a_{2}=-\frac{1}{4},(\newline\)a_{6}=-\frac{12}{243}

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\end{array}\right.

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Find the common ratio of the geometric sequence

\left\{a_{n}\right\}_{n=1}^{\infty}

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\begin{array}{ll} a_{2}=-\frac{1}{4} \\ a_{6}=-\frac{12}{2 / 3}\end{array}

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1

1

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\frac{5x^{2}}{x}=5x

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6(2x+y-7xy)-3(5x-2y+5xy)

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x(x^{2}+2xy+y^{2})+4y(x^{2}+3xy+9y^{2})

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4(2x-3y+xy)-5

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Find the product:

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2\mid03

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(\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+\(\newline\)y)

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(x^{3}-xy+y^{3})(x^{3}+xy+y:}

4

f(x)=-x+3

g(x)=\frac{1}{2} x^{2}-1

, which is a solution to

f(x)=g(x)

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-2

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-1

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1

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2

\mathrm{H}=(x, y, z) \in \mathbb{R}^{3} \mid x+2 y=0

is a subspace of

\mathbb{R}^{3}

\mathrm{H}=(x, y, z) \in \mathbb{R}^{3} \mid x+2 y=0

is a subspace of

\mathbb{R}^{3}

20-2

Consider the function

f(x)=-\frac{1}{3}(x-2)^{2}+1

. Algebraically determine which of the following are the zeros for

f(x)

. Select all correct answers below.

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0

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3+\sqrt{2}

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4

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2+\sqrt{3}

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3-\sqrt{2}

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2-\sqrt{3}

f(x) = \int_{1}^{u} \cos^2 t \, dt

u=\ln(x^2 +x-1)

3

x^{2}-2 x y+y^{2}=25

x-y=

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25

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-5

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5

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\pm 5

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10

ClassLink | Identity \& Access MaI

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Christ the King

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https://www.ixl.com/m=

4

-1

/factor-polynomials

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1>

9

Factor polynomials TAH

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Factor completely.

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4 f^{2}+7 f+3

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44

X - Problem Set

21

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1

-4

, use the direct comparison test to determine if the given series converges or diverges. Your work must indicate the series to which you are comparing the given series and the inequality of the two series (call the

n

a_{n}

b_{n}

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1

\sum_{n=1}^{\infty} \frac{3}{2+5^{n}}

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2

\sum_{n=1}^{\infty} \frac{2}{\sqrt{n+10}}

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3

\sum_{n=1}^{\infty} \frac{n+2}{(n+4) 8^{n}}

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4

\sum_{n=3}^{\infty} \frac{2^{n} \sin ^{2}(5 n)}{4^{n}+\cos ^{2}(n)}

Twice one number added to three times another number equals

-3

. If the first number is tripled and subtracted from

8

and the result is divided by

2

, then the second number is obtained. Find the two numbers.

Twice one number added to thee limes another number equals

3

. If the firat number is tripled and subtracted from

8

and the result is divided by

2

, then the second number is obtained. Find the two numbers.

Find the derivative of

-7 x^{2} y^{4}-4 x y^{3}=x+3

using implicit differentiation.

If the product of

t^{2}+kt-5

2t-3

2t^{3}-11t^{2}+2t+15

, then what is the value of

k

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-5

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-4

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2

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3

3

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The sum of a finite of a geometric series can be found by

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S_n = \frac{a_1(1-r^n)}{1-r}

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Derive the formula for the sum of a finite geometric series.

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a) Start with the general geometric series

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S_n = a_1 + a_1r + a_1r^2 + a_1r^3 + \dots + a_1r^{n-1}

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with common ratio

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r

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b) Multiply both sides of this equation by

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-r

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c) Add the results of

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b. and then do some algebraic rearranging.]

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11

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S_{10}

for the geometric series with

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a_1=5

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r=3

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166

x

-intercept of the graph of

y=(x-5)^{2}

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1

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-25

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-5

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5

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25

f(x)=\frac{-x^{2}-2}{7 x}

, what is the value of

f(8)

, to the nearest tenth (if necessary)?

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What is the discriminant of the quadratic equation

5 x^{2}-8 x+9=0

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-244

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244

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116

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-116

What is the discriminant of the quadratic equation

3 x^{2}-3 x-7=0

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93

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-75

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-93

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75

What is the discriminant of the quadratic equation

4 x^{2}-3 x-5=0

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-71

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-89

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89

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71

What is the discriminant of the quadratic equation

2 x^{2}-9 x-8=0

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-17

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145

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17

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-145

What is the discriminant of the quadratic equation

-x^{2}+8 x-8=0

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32

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96

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-96

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-32

What is the discriminant of the quadratic equation

-5 x^{2}-6 x-9=0

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144

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216

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-144

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-216

For the following quadratic equation, find the discriminant.

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-6 x^{2}-8 x+29=-7 x^{2}-4

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For the following quadratic equation, find the discriminant.

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-11 x^{2}+90 x-160=-6 x^{2}

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For the following quadratic equation, find the discriminant.

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-6 x^{2}-18 x+102=-7 x^{2}+2 x+2

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For the following quadratic equation, find the discriminant.

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-7 x^{2}+54 x-231=-4 x^{2}

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For the following quadratic equation, find the discriminant.

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5 x^{2}-78 x+471=-8 x-4

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For the following quadratic equation, find the discriminant.

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12 x^{2}-16 x-16=8 x^{2}

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For the following quadratic equation, find the discriminant.

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-9 x^{2}-70 x-245=-4 x^{2}

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