Write the letter of the correct answer on your answer sheet. If your answer is not found among

the choices, write the correct answer.

For items 1-5, refer to the graph at the right.

____1. Which of the following could be the equation of the parabola?

A. = ( − 2)2 + 1 C. = ( + 1)2 + 2

B. = ( + 2)2 + 1 D. = ( − 1)2 + 2

____2. Determine the y- intercept of the graph?

A. = −5

C. = 5

B. = −3

D. = 3

____3. What is the range of the parabola?

A. {:≥1}

C. {:≥ -1}

B. {:≤1}

D. {:≤ -1}

____4. What is the axis of symmetry of the graph?

A. x = 2

C. y = 2

B. x = 1

D. y = 1

____5. What is the vertex of the parabola?

A. (-2, -1)

C. (2, 1)

B. (-2, 1)

D. (2, -1)

____6. Describe the graph of () = −2 + 6 − 24

A. Opens to the right

C. Opens to the left

B. Opens upward

D. Opens downward

____7. What is the y-intercept of the parabola defined by the equation = ( + 2)2?

A. -4

B. -2

C. 2

D. 4

____8. What is the minimum value of the graph of the quadratic function = 2 + 4?

A. -4

B. -2

C. 2

D. 4

____9. What is the vertex of the parabola having the equation y = (x – 3)2 + 1?

A. (3, -1)

B. (-1, 3)

C. (1, 3)

D. (3, 1)

____10. What is the vertex form of the equation =2−4+7?

A. =(−2)2−3

C. =(+2)2−3

B. =(−2)2+3

D. =(+2)2+3

____11. The equation of the axis of symmetry of the function = −22 + 5 is____.

A. x = 5

C. − 4

3

B. x= -2

D. 5

4

____12. Which of the following equations of parabola has a wider opening? A. y = 1

4

2

C. y = 3x2 B. y = 1

2

2

D. y = 5x2

____13. Determine the equation of the resulting graph when the parabola with the equation

y = x2 + 3, is shifted 4 units downward.

A. y = x2 – 4

C. y = x2 + 1

B. y = x2 – 1

D. y = x2 + 7

For items 14-15, refer to the graph at the right.

____14. Which of the following could be the equation of the parabola?

A. = −2 + 5

C. = 2

2

+ 5

B. = − 2

2

= 5

D. = 2 + 5

____15. What is the vertex of the parabola?

A. V(-5, 0)

C. V(0, 5)

B. V(0, -5)

D. V(5, 0)​

Answer:

1st and 3rd are functions, 2nd and 4th are not functions

Step-by-step explanation:

Answer:

Function : 1 , 3

Not a Function : 2 , 4

Step-by-step explanation:

Using the vertical line test for the first two, and the last two you are able to tell because each input (x) can only have one output (y).

Answer:

The coordinates of P are (12,9)

Step-by-step explanation:

Equations

We are given the endpoints of the segment AB: A(10,8) B(18,12).

It's required to find the coordinates of point P(x,y) along the segment AB such that:

[tex]\displaystyle \frac{AP}{PB}=\frac{1}{3}[/tex]

The ratio of the distances is the same as the ratio of their respective coordinates:

[tex]\displaystyle \frac{x_{AP}}{x_{PB}}=\frac{1}{3}[/tex]

[tex]\displaystyle \frac{y_{AP}}{y_{PB}}=\frac{1}{3}[/tex]

Since

[tex]x_{AP}=x_P-x_A=x-10[/tex]

[tex]x_{PB}=x_B-x_P=18-x[/tex]

Then:

[tex]\displaystyle \frac{x-10}{18-x}=\frac{1}{3}[/tex]

Multiplying by 3 (18-x):

3( x - 10 )= 18 - x

3x - 30 = 18 - x

Adding x and 30:

4x = 48

x = 12

Similarly:

[tex]\displaystyle \frac{y-8}{12-y}=\frac{1}{3}[/tex]

Multiplying by 3 (12-y):

3( y - 8 ) = 12 - y

3y - 24 = 12 - y

Adding y and 24:

4y = 36

y = 9

The coordinates of P are (12,9)

Answer:

1st is 26.376 2nd is n

Step-by-step explanation:

2pie X r so. 2 X3.14X4.2

Answer:

26.376 cm

4 is the constant

Step-by-step explanation:

C = [tex]2\pi r[/tex]

To find the circumference, we first need to find the radius. The radius of a circle is half the diameter, so divide 84 by 2:

84/2 = 42

The radius is 42. Now we can solve for the circumference:

C = 2[tex]\pi[/tex](42)

C = 84[tex]\pi[/tex]

C = 263.89

The circumference is approximately 263.89 mm. Now we need to convert the millimeters to centimeters. There are 10 millimeters in 1 centimeter, so divide the circumference by 10:

263.89/10 = 26.389

The circumference is approximately 26.389 cm. The answer choice that our answer is closest to is the first answer choice.

4 + 2n

The constant in an expression is the value that doesn't change. After 2 and n are multiplied, that value will be different, so their values aren't constant. So, in this expression, 2 is the coefficient, n is the variable, and 4 is the constant.

Hope this helps :)

Answer:

47 reams of paper were used

Step-by-step explanation:

23,500 divided by 500 equals 47

Answer:

47 reams

Step-by-step explanation:

23,500 sheets were made, then you divide by 500, bc each ream has 500. And you get 47 reams of paper :)

Answer:

lets see every 2kg bag its 15.98 so every 4kg its 31.96 and for every 6kg its 47.94 so if every 1kg its 7.99 so add 47.94 + 7.99 you get 55.93

Step-by-step explanation:

Answer:

The missing value in the solution to

the equation will be:

Step-by-step explanation:

Given the equation

[tex]y+2\:=-3\left(x\:-\:4\right)[/tex]

As the value of y = -2 is given.

so substituting the value y = -2 in the equation to find the missing value

[tex]\left(-2\right)+2\:=-3\left(x\:-\:4\right)[/tex]

switch the sides

[tex]-3\left(x-4\right)=\left(-2\right)+2[/tex]

[tex]\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a[/tex]

[tex]-3\left(x-4\right)=-2+2[/tex]

[tex]-3\left(x-4\right)=0[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-3[/tex]

[tex]\frac{-3\left(x-4\right)}{-3}=\frac{0}{-3}[/tex]

[tex]x-4=0[/tex]

[tex]x=4[/tex]

Therefore, the missing value in the solution to

the equation will be:

Answer:

Yes, its a function

Step-by-step explanation:

Answer:

x= 4+5i

Step-by-step explanation:

The values of x in the given quadratic equation, x²-8x+41 = 0 are x = 4+5i or x = 4-5i

A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.

Given is a quadratic equation, x²-8x+41 = 0, we need to find the values of x,

Since, 41 is a prime number, which can not be factorized so, we will use quadratic formula,

x = [-b ± √(b²-4ac)] / 2a

Here, a = 1, b = -8, c = 41

Therefore,

x = [8 ± √(8²-4(41))] / 2

= [8 ± √(64-164)] / 2

= [8 ± √(-100)] / 2

= [8 ± 10i] / 2

= [4 ± 5i]

Therefore, x = 4+5i or x = 4-5i

Hence, the values of x in the given quadratic equation, x²-8x+41 = 0 are x = 4+5i or x = 4-5i

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Answer:

Option (C) is correct.

Step-by-step explanation:

Given that z = 0.3(cos(31°) + i sin(31°)) and 20(cos(18°) + i sin(18°)).

The product of both the complex number is

zw = [0.3(cos(31°) + i sin(31°))] x [20(cos(18°) + i sin(18°))]

=(0.3x20)[cos(31°) x cos(18°) + cos(31°) x i sin(18°) + i sin(31°) x cos(31°)+ i sin(31°) x i sin(18°)]

Here, (0.3x20)=6, is the magnitude of zw, which is stretching of 0.3 by 20.

zw=6[cos(31°) x cos(18°) + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)}+ i² sin(31°)x sin(18°)]

As i²= -1, So

zw=6[cos(31°) x cos(18°) + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)} - sin(31°)x sin(18°)]

=6[{cos(31°) x cos(18°)- sin(31°)x sin(18°)} + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)}]

As cosAcosB - sin A sin B = cos (A+B) and cosAsinB + sin A sos B = sin (A+B), so

zw=6[cos(31°+18°) + i{sin(31°+18°)]

Note that, initially the argument of z is 31° and after rotation of 18° in counterclockwise direction, the argument od zw is 31°+18°= 49°. i.e

zw=6(cos(49°) + isin(49°)).

So, zw can be determined by stretching z by a factor of 20, then rotating by 18° counterclockwise.

Hence, option (C) is correct.

Answer:

C: Stretch z by a factor of 20, then rotate 18° counterclockwise.

Step-by-step explanation:

Took the quiz.

Answer:

134

Step-by-step explanation:

Its 134, i did the math and my old answer had the explanation, but someone deleted it.

Answer:

c

Step-by-step explanation:

c is the one that divides and a fraction is just division

Answer:

8 walls

Step-by-step explanation:

While painting the interior of a large house, Gene is going to transfer some paint in a large 5 gallon container to a smaller bucket. Unfortunately he slips and spills 2 gallons of paint all over the floor.

The remaining amount of paint is

= 5 gallons - 2 gallons

= 3 gallons

If each wall in the house takes 9/24 of a gallon to paint, how many walls can he paint with what he has left?

Hence:

9/24 gallon = 1 Wall

3 gallons = x wall

Cross Multiply

9/24 × x = 3 × 1

x= 3 ÷ 9/24

x = 3 × 24/9

x = 8 walls

He can paint 8 walls with what is left.

Answer:

Third Option

Step-by-step explanation:

Lets use process of elimination to find the answer to this question. It's not the first option because a scribes job was mainly in the government district as writers/record keepers meaning they don't really protect the kingdom from invasion. It's not the second options because Merchants were traders, meaning they don't make up the Pharaohs police force because all they do is sell goods to Egyptians. Then it's not fourth option because farmers, servants, and slaves make up way more then 20% of ancient Egypt. Leaving the third option meaning it's your answer.

Hope this helps.

Answer:

The first one

Step-by-step explanation:

since you're subtracting 12, it will be -8

the -8/4 = -2

Answer:

It is the first answer choice b<4 or b>-2

Step-by-step explanation:

Solve the first inequality like so

6b<24

divide by 6 on both sides

b<4

Now for the second inequality solve like so

4b+12>4

Subtract 12 on both sides

4b>-8

Divide on both sides by 4

b>-2

This leaves us with only one answer choice which is A -

b<4 or b>-2

If you can please make my answer the brainliest that would be much appreciated. Thanks!

Answer:

there is no slope. y = 4, the line is horizontal

Answer:

C

Step-by-step explanation:

rounding

Answer:

- 7n ≤ 77

Step-by-step explanation:

- 7n ≤ 77

n ≥ - 11

Answer:

2m + 20

Step-by-step explanation:

Given that:

Cost per meal = m

Tip left = $10

Total cost for each person :

m + 10

Total amount spent by the two :

2(m + 10)

2m + 20

Answer:

y=28

Step-by-step explanation:

Answer:

The equation for this line in slope-intercept form (y = mx + b) is y = [tex]\frac{5}{4}[/tex]x + 2, because the rise (5) over the run (4) is the slope aka 'm', and the line touches the y-axis at the point (0,2) In this ordered pair the y-value is 2, so the y-intercept, or 'b', is equal to 2.

Answer:

14/61 cm per day

Step-by-step explanation:

Use the slope formula  [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

Plug it in [tex]\frac{16-2}{61-0}[/tex]

Simplify [tex]\frac{14}{61}[/tex]

If the graph shows the height of a plant over a 2-month growth period. The rate of change per day will be 14/61.

It is defined as the change in values of a dependent variable with respect to the independent variables. Analyze the points first, then calculate the y-values for each interval. After that, subtract the input and output values. Divide and then simplify the differences to determine the rate of change.

It is given that, the graph shows the height of a plant over a 2-month growth period

The kind of graph must be considered when calculating the rate of change. Finding the ratio between the change in output values and the change in their corresponding input values is how linear graphs with constant rates of change are determined. Look at the following linear graph.

The slope of a linear function represents the pace of change. We have two points to determine the slope,

The rate of change per day is found as,

=y₂-y₁/x₂-x₁

=16-2/61-0

=14/61

Thus, if the graph shows the height of a plant over a 2-month growth period. The rate of change per day will be 14/61.

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Answer:

Your answer is 38 degrees.

Step-by-step explanation:

The question was solved through the properties of a circle. The angle subtended at the center is double the angle subtended at the circumference.

Hope I helped, happy schooling!!

The measure of <C is 38°. The answer is the first option 38°

From the question, we are to determine the measure of <C.

In the diagram, <C is an angle on a part of the circumference.

From the given information, the angle subtended by arc AB at the center of the circle is 76°

From one of the circle theorems we have that

The angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle's circumference

Therefore,

2 × <C = 78°

<C = 76° ÷ 2

<C = 38°

Hence, the measure of <C is 38°. The answer is the first option 38°

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Answer:

-26 × -1 = 26

This is your answer , pls mark me the brainliest!!

Answer:

-1

Step-by-step explanation:

1 x 26 is  like that , -1 x -26 = 26. Hope this helps!

Answer:

A) a²-2a+2a-4 the a is correct check my explanation to understand the answer.

Step-by-step explanation:

(a+2)(a-2)= a²-2a+2a-4

Answer:

$1,320

Step-by-step explanation:

First you divide $2.640 with 2 and tah da

Answer:

a) She did mistake in Step 2

b) when she take -3y common then the term should be: -3y(x+5) instead she wrote -3y(x-5)

Step-by-step explanation:

We need to find problem in Ms J solution.

Ms J solution:

[tex]Step \ 1: 4x^2 + 20x - 3xy - 15y\\Step \ 2: 4x(x + 5) - 3y(x - 5)\\Step \ 3: (x+5)(4x - 3y)[/tex]

She did mistake in Step 2 when she take -3y common then the term should be: -3y(x+5) instead she wrote -3y(x-5)

Correcting the mistake:

[tex]Step \ 1: 4x^2 + 20x - 3xy - 15y\\Step \ 2: 4x(x + 5)\mathbf{- 3y(x +5)}\\Step \ 3: (x+5)(4x - 3y)[/tex]

Answer:315

Step-by-step explanation:

Answer:

hi! the slope formula is y2-y1 / x2-x1 ! so (-6,0) (2,-2)

your x1 is -6 and y1 is 0 and x2 is 2 and y2 is -2!

using the formula, -2-0/2--6 is 4

so your slope is 4!

the y intercept is solved by

the slope intercept formula y= mx+b

I hope you've memorized both formulas!

b is your y intercept so let's set the equation up!

pick a point it can be either point we'll do (-6,0)!

now y=mx + b

m is your slope and y is the y coordinate of the point (-6,0) that we chose!

b is what we will solve

so! 0=4(-6)+b

0= -24 + b

now it's basic algebra!

24= b

I hope this helps!

In conclusion, slope is 4 and y intercept is 24

memorize slope formula and slope intercept formula and you can do this!