Resources

Resources

Transformations of quadratic functions

Given the function

f

f(-1), f(0), f(2)

f(4)

\newline

f(x)=\left\{\begin{array}{cc} x^{2}-3 & \text { if } x<2 \\ 4+|x-6| & \text { if } x \geq 2 \end{array}\right.

\newline

\begin{aligned} f(-1) & =\ \\ f(0) & =\ \\ f(2) & =\ \\ f(4) & =\\ \end{aligned}

Use the midpoint rule to estimate- the value of

\iint\left(x^{2}-y^{2}\right) d A

R=\{(x, y) \mid-4 \leq x \leq 2,0 \leq y \leq 2\}

using three rectangles of equal area

Rewrite the function

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

f(x)=a x^{2}+b x+c

\newline

f(x)=

1

) The angles of a triangle measure

104^{\circ}, 51^{\circ}

25^{\circ}

. The perimeter of the triangle is

10 \mathrm{~m}

. Find, rounded to

2

decimal places, the length of each side of the triangle.

\newline

12

\bar{A} \cap \bar{B}

\newline

5

U=

\{set of actual numbers from I to from

1

12

\}

P=\{

p

alse present from

1

12

\}, O=\{

set of odd numbers from sets and also present then numbers from

1

\newline

\bar{E}

\newline

\overline{\mathrm{O}}

\newline

\overline{\mathrm{P}}

\newline

(E \cup P)

\newline

U=

0

\newline

U=

1

\newline

U=

2

\newline

U=

3

\newline

U=

4

\newline

U=

5

obert are each trying to solve the equation

x^{2}-10 x+26=0

\mathrm{kn}

0 x^{2}=-1

i

-i

, but they are not sure how to use this informat

and Robert are each trying to solve the equation

\newline

x^{2}-\sqrt{10x+26}=0

\newline

x^{2}=-1

\newline

i

\newline

-i

, but they are not sure how to use this

7

) The product of two numbers is the greatest

2

-digit number. If one of the numbers is

-11

, find the othen number.

\newline

-8016

x

, the answer obtained is

-16

. Find the value of integer

x

\newline

Evaluate the following.

\newline

9

49 \times 89 \times(-107) \times 0 \times 412

\newline

1

(-8) \times(-16)

\newline

[12+9] \div[-9 \div 3]

\newline

\sqrt{[9+6-12-3] \div(-48)}

The product of two numbers is the greatest

2

-digit number. If one of the numbers is

-11

, find the other number. On dividing

-8016

x

, the answer obtained is

-16

. Find the value of integer

x

. Evaluate the following.

(2)

49 \times 89 \times (-107)\times 0\times 412

(c)

48\div(-16)

{:＂ (1) ＂inline_latex_10,\[＂ d. ＂inline_latex_11:}

4

.) The product of two numbers is the greatest

2

-digit number. If one of the numbers is

-11

, find the other number.

\newline

-8016

x

, the answer obtained is

-16

. Find the value of integer

x

\newline

Evaluate the following.

\newline

2

49 \times 89 \times(-107) \times 0 \times 412

\newline

48 \div(-16)

\newline

\begin{array}{l} \text { (C) }(-8) \times(-16) \\ {[12+9] \div[-9 \div 3]} \end{array}

6

\newline

The points A , B , C ,D and E lie on a circle.

\mathrm{AE}

\mathrm{CD}

\newline

\angle \mathrm{EAC}=70^{\circ} ; \angle \mathrm{ABC}=120^{\circ}

\newline

\angle \mathrm{AEC}=

\qquad

\newline

\angle \mathrm{EDC}=

\qquad

\newline

\angle \mathrm{ECD}=

\qquad

\newline

\angle \mathrm{CED}=

\qquad

In the circle below,

\overline{I K}

is a diameter. Suppose m \overparen{J K}=102^{\circ} and

m \angle K J L=54^{\circ}

. Find the following.

\newline

m \angle I J L=

\newline

m \angle I K J=

Use synthetic division to find the quotient and remainder when

-x^{\prime}+4 x^{\prime \prime}-8

x-2

by completing the parts below.

\newline

(a) Complete this synthetic division table.

\newline

2

\begin{array}{llll}-1 \quad 4 & 0 & -8\end{array}

\newline

\square \square \square

\newline

\square \square \square \square

\newline

(b) Write your answer in the following form: Quotient

+\frac{\text { Remainder }}{x-2}

\newline

\frac{-x^{3}+4 x^{2}-8}{x-2}=\square+\frac{\square}{x-2}

\newline

f(x)= \frac{4x-k}{2}

g(x)=4x-1

f(g(x))=8x

, what is the value of

k

\newline

-4

\newline

0

\newline

2

\newline

4

14y^{3}

(7y^{2})(2y)

. Bilal factored

14y^{3}

(10y)(4y^{2})

. Which of them factored

14y^{3}

\newline

1

\newline

\newline

\newline

(C) Both Hiro and Bilal

\newline

(D) Neither Hiro nor Bilal

KLM

ML = (9x-3)

m

Joint equation of two lines, through

(2, -3)

, perpendicular to two lines

3x^{2}+xy-2y^{2}=0

38 \mathrm{ABC}

est un triangle équilatéral de sens direct, inscrit dans le cercle (

{ }^{C}

[\mathrm{AD}]

\newline

1

. Démontrer que la transformation

f

\mathrm{f}=\mathrm{s}_{(\mathrm{BD})}

\mathrm{s}_{(\mathrm{AC})}

est une rotation, dont on précisera le centre I et l'angle.

\newline

2

. Démontrer que la transformation

g

g=s_{(C D)}

s_{(A B)}

est une rotation, dont on précisera le centre

J

\newline

3

. Démontrer que le triangle AIJ est équilatéral. Déterminer la nature et les éléments caractéristiques des transformations

g

f

{ }^{C}

2

A=\{1,2,3,4\},B=\{3,4,5,6\}, U=\{1,2,3,4,5,6\}

then prove De Morgan's law.

\newline

De Morgan's law: first Law:

(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}

(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}

13

A=\{1,2,3,4\}, B=\{3,4,5,6\}

U=\{1,2,3,4,5,6\}

then prove De Mlorgan: law.

\newline

De Morgan's law:

\newline

(A \cup B)^{\prime}=A^{\prime} \cap B^{\prime}

\newline

(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}

a,b,c,k

be rational numbers such that

k

is not a perfect cube.

\newline

a+bk^{\frac{1}{3}}+ck^{\frac{2}{3}}

then prove that

a=b=c=0

4

Emilio is given the triangle shown below.

\newline

Emilio represents the perimeter of the triangle with the equation

(5 w-13)+(2 w+6)+2(5 w+15)=P

P

is the perimeter of the triangle.

\newline

Which equation is correctly solved for

w

\newline

w=\frac{P-23}{17}

\newline

w=\frac{P+49}{17}

In the figure below,

m \angle 2=45^{\circ}

m \angle X W Y=133^{\circ}

\newline

m \angle 1

\newline

m \angle 1=\square \text { 。 }

z=1+4 i

\newline

\theta

(in degrees) that

z

makes in the complex plane.

\newline

Round your answer, if necessary, to the nearest tenth. Express

\theta

-180^{\circ}

180^{\circ}

\newline

\theta=

\newline

\square

R

be the reglon enclosed by the line

y=-1

x=2

y=x^{2}-1

\newline

A solid is generated by rotating

R

y=-1

\newline

Which one of the definite integrals gives the volume of the solid?

\newline

1

\newline

\pi \int_{0}^{2} x^{4} d x

\newline

\pi \int_{-1}^{3}\left(x^{2}-1\right)^{2} d x

\newline

\pi \int_{-1}^{3} x^{4} d x

\newline

\pi \int_{0}^{2}\left(x^{2}-1\right)^{2} d x

9

. The sum of two integers is

116

. If one of them is

-79

, find the other integers.

\newline

10

. Write five pair of integers

(m, n)

m \div n=-3

. One of such pair is

(-6,2

\newline

11

. What number should be added to the sum of

345

67

to make it equal to the

3

\newline

12

. Verify the following:

\newline

(-22) \times[(-4)+(-5)]=[(-22) \times(-4)]+[(-22) \times(-5)]

A=\left(\begin{array}{cc}4 & 2 \\ -1 & 3\end{array}\right), B=\left(\begin{array}{cc}2 & -1 \\ 1 & 3\end{array}\right)

C

C=A B

\operatorname{det} C=

\newline

8

\newline

18

\newline

12

\newline

22

\newline

15

1

\newline

KUIS Pengantar Bisnis

1

\newline

elearning.ut.ac.id/mod/forum/view.php?id=

24867701

\newline

16

2024,11: 48

\newline

Silakan mengerjakan diskusi

1

\newline

Diketahui tiga buah himpunan sebagai berikut: himpunan

A=\{0,1,3,5,6,8\}

B=\{1,2,4,5,6,7,9\}

C=\{0,1,2,3,4,5,6,7\}

\newline

1

A \cap(B \cap C)

\newline

2

A \cup(B \cap C)

\newline

3

A \cap(B \cup C)

g(x)=x^{5}+3 x

h

be the inverse function of

g

g(1)=4

\newline

h^{\prime}(4)=

h(x)=\frac{1}{4} x^{3}+2 x-1

g

be the inverse function of

h

h(2)=5

\newline

g^{\prime}(5)=

h(x)=7-x-2 x^{5}

f

be the inverse function of

h

h(-1)=10

\newline

f^{\prime}(10)=

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

g

be the inverse function of

f

f(2)=11

\newline

g^{\prime}(11)=

h(x)=5-x-x^{3}

f

be the inverse function of

h

h(-1)=7

\newline

f^{\prime}(7)=

f(x)=\frac{1}{2} x^{3}+3 x-4

h

be the inverse function of

f

f(-2)=-14

\newline

h^{\prime}(-14)=

Chun was asked whether the following equation is an identity:

\newline

3(2 x-1)^{2}+27=36 x^{2}-36 x+36

\newline

He performed the following steps:

\newline

3(2 x-1)^{2}+27

\newline

\stackrel{\text { Step } 1}{\hookrightarrow}=3(2 x-1)(2 x-1)+27

\newline

\stackrel{\text { Step } 2}{\hookrightarrow}=(6 x-3)(6 x-3)+27

\newline

\stackrel{\text { Step } 3}{\hookrightarrow}=36 x^{2}-18 x-18 x+9+27

\newline

\stackrel{\text { Step } 4}{\hookrightarrow}=36 x^{2}-36 x+36

\newline

For this reason, Chun stated that the equation is a true identity.

\newline

Is Chun correct? If not, in which step did he make a mistake?

\newline

1

\newline

(A) Chun is correct.

\newline

(B) Chun is incorrect. He made a mistake in step

2

\newline

(C) Chun is incorrect. He made a mistake in step

3

\newline

(D) Chun is incorrect. He made a mistake in step

4

Mustafa was asked whether the following equation is an identity:

\newline

x(9 x+3)+3(x+3)=9(x+1)^{2}

\newline

He performed the following steps:

\newline

x(9 x+3)+3(x+3)

\newline

\stackrel{\text { Step } 1}{\hookrightarrow}=9 x^{2}+6 x+9

\newline

\stackrel{\text { Step } 2}{\hookrightarrow}=(3 x+3)^{2}

\newline

\stackrel{\text { Step } 3}{\hookrightarrow}=(3(x+1))^{2}

\newline

\stackrel{\text { Step } 4}{\hookrightarrow}=9(x+1)^{2}

\newline

For this reason, Mustafa stated that the equation is a true identity.

\newline

Is Mustafa correct? If not, in which step did he make a mistake?

\newline

1

\newline

(A) Mustafa is correct.

\newline

(B) Mustafa is incorrect. He made a mistake in step

1

\newline

(C) Mustafa is incorrect. He made a mistake in step

2

\newline

(D) Mustafa is incorrect. He made a mistake in step

4

Mabel was asked whether the following equation is an identity:

\newline

(4 x-3)(x-2)^{2}=4 x^{3}-19 x^{2}+4 x-12

\newline

She performed the following steps:

\newline

(4 x-3)(x-2)^{2}

\newline

\stackrel{\text { Step } 1}{\hookrightarrow}=(4 x-3)(x-2)(x-2)

\newline

\stackrel{\text { Step } 2}{\hookrightarrow}=(4 x-3)\left(x^{2}-2 x-2 x+4\right)

\newline

\stackrel{\text { Step } 3}{\hookrightarrow}=(4 x-3)\left(x^{2}-4 x+4\right)

\newline

\stackrel{\text { Step } 4}{\hookrightarrow}=4 x^{3}-16 x^{2}+16 x-3 x^{2}-12 x-12

\newline

\stackrel{\text { Step } 5}{\hookrightarrow}=4 x^{3}-19 x^{2}+4 x-12

\newline

For this reason, Mabel stated that the equation is a true identity.

\newline

Is Mabel correct? If not, in which step did she make a mistake?

\newline

1

\newline

(A) Mabel is correct.

\newline

(B) Mabel is incorrect. She made a mistake in step

2

\newline

(C) Mabel is incorrect. She made a mistake in step

3

\newline

(D) Mabel is incorrect. She made a mistake in step

4

4 x-x^{2} y+y^{3}=10

\newline

Find the value of

\frac{d y}{d x}

(1,2)

\newline

1

\newline

0

\newline

\frac{2}{3}

\newline

-1

\newline

-4

y=(x-5)^{2}+1

\newline

Plot five points on the parabola: the vertex, two points to button.

6

Write a quadratic function in verte

\newline

y=4 x^{2}-12 x+13

. Write the equati

\newline

integers or simplified proper or improper fra

f(x)=\left\{\begin{array}{cl}-\frac{1}{2} x-4 & \text { |f } x<-1 \\ (x-2)^{2} & \text { if }-1 \leq x<3 \\ |x-5|-3 & \text { if } x \geq 3\end{array}\right.

y

z

независимой переменной

x

заданы системой уравнений

x^2 + y^2 - z^2 = 0

x^2 + 2y^2 + 3z^2 = 1

dy

dz

d^{2}y

d^{2}z

\begin{aligned} A B & =\sqrt{\left(4-(-1)^{2}+(-3-9)^{2}\right.} \\ & =\sqrt{147} \\ & =12.12 \end{aligned}

\newline

\begin{aligned} C D & =\sqrt{(-1-6)^{2}+\left(5-(-4)^{2}\right.} \\ & =\sqrt{38} \\ & =6.16 \end{aligned}

\newline

The diagram shows the points

A(0,-1), B(p, p)

C(p, q)

\newline

(a) Given that the length of

A B

5

units, find the value of

p

\newline

(b) Given that angle

B A C=

B C A

, find the value of

q

f(x)=4 x^{2}+64 x+262

\newline

g

g(x)=f(x+5)

. For what value of

x

g(x)

reach its minimum?

\newline

-13

\newline

-8

\newline

-5

\newline

-3

Cameron wants to prove the Alternate Interior Angles Theorem. In the diagram,

\overleftrightarrow{P Q} \| \overleftrightarrow{R S}

\newline

Complete Cameron's proof that alternate interior angles

\angle P V W

\angle V W S

\newline

Construct the midpoint

M

\overline{W V}

\overleftrightarrow{P Q}, \overleftrightarrow{R S}

\overleftrightarrow{T U} 180^{\circ}

M

\overleftrightarrow{P^{\prime} Q^{\prime}}, \overleftrightarrow{R^{\prime} S^{\prime}}

\overleftrightarrow{T^{\prime} U^{\prime}}

M

\angle P V W

1

and the rotation is

\angle P V W

2

\angle P V W

3

are equidistant from

M

\angle P V W

1

\angle P V W

6

\angle P V W

7

\angle P V W

8

\angle P V W

3

\newline

\angle V W S

0

rotation of a line is a parallel line, and the only line parallel to

\angle V W S

1

that passes through

\angle P V W

7

\angle P V W

3

\angle P V W

3

\angle V W S

5

\angle V W S

6

coincide. So, the rotation maps

\angle P V W

3

\newline

\angle P V W

3

\angle V W S

9

\begin{array}{l}=\frac{3 x^{2}}{1} \\ \text { Question } 11=3 x^{2} \\ \text { Simplify }\left(7 x^{2} y\right)^{0} \div\left(4 x^{3}\right)^{-1} \\ \left(7 x^{2} y\right)^{0} \div\left(4 x^{3}\right)^{-1}=\end{array}

For the rotation

670^{\circ}

, find the coterminal angle from

0^{\circ} \leq \theta<360^{\circ}

, the quadrant, and the reference angle.

\newline

The coterminal angle is

\square^{\circ}

, which lies in Quadrant

\square

, with a reference angle of

\square^{\circ}

For the rotation

804^{\circ}

, find the coterminal angle from

0^{\circ} \leq \theta<360^{\circ}

, the quadrant, and the reference angle.

\newline

The coterminal angle is

\square^{\circ}

, which lies in Quadrant

\square

, with a reference angle of

\square^{\circ}

For the rotation

965^{\circ}

, find the coterminal angle from

0^{\circ} \leq \theta<360^{\circ}

, the quadrant, and the reference angle.

\newline

The coterminal angle is

\square^{\circ}

, which lies in Quadrant

\square

, with a reference angle of

\square^{\circ}

For the rotation

417^{\circ}

, find the coterminal angle from

0^{\circ} \leq \theta<360^{\circ}

, the quadrant, and the reference angle.

\newline

The coterminal angle is

\square^{\circ}

, which lies in Quadrant

\square

, with a reference angle of

\square^{\circ}

...