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Start by writing an equation that represents this hanger diagram.

To determine how the graph of the parent function [tex]y = x^2[/tex] is transformed to create the graph of the new function [tex]y = -(x – 1)^2 – 5[/tex], we need to analyze the individual transformations one by one Therefore the correct option is A.

1. Translation: (x – 1) This term inside the function represents a horizontal translation of the graph. When we subtract 1 from x, the entire graph is shifted to the right by 1 unit. Hence, this function is translated right 1 unit. 2. Reflection: (-) The negative sign outside the function reflects the graph across the x-axis. Thus, the graph opens downward.

3. Vertical Transformation: -5 The term -5 outside the function causes a vertical shift of the graph downward by 5 units. In summary, the graph of the new function [tex]y = -(x – 1)^2 – 5[/tex]  undergoes the following transformations: - Translated right 1 unit due to (x – 1) - Reflected (opens downward) due to the negative sign - Translated down 5 units due to -5 Therefore, the correct answer is A. Translated right 1 and down 5 only

Hence the correct option is A

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 4.80}}{\left( \cfrac{5}{100} \right)4.80}\implies 0.24~\hfill \underset{\textit{price including tax}}{\stackrel{4.80~~ + ~~0.24}{5.04}}[/tex]

Answer:

A

Step-by-step explanation:

It could just be it was dilated (I think thats the word) by 3. 6×3=18, 8×3=24

Step-by-step explanation:

11.

x is sin(60) in a circle with radius of 8.

x = sin(60)×8 = 6.92820323... ≈ 6.9

12.

x is sin(30) in a circle with radius "diagonal length".

6 is cos(30) in the same circle.

6 = cos(30)×r

r = 6/cos(30) = 6.92820323...

x = sin(30)×r = 3.464101615... ≈ 3.5

13.

similar to 12.

but we refer to the angle at the bottom right vertex.

remember, the sum of all angles in a triangle is always 180°.

so, the angle over there at the right is

180 - 90 - 68 = 22°

x = sin(22)×r

25 = cos(22)×r

r = 25/cos(22) = 26.96336857...

x = sin(22)×r = 10.10065565... ≈ 10.1

14.

9 is the sine of the complementary angle of 49 in a circle with radius x.

the complementary angle is the angle that adds up with the original angle to 90° and is therefore

90 - 49 = 41°

9 = sin(41)×x

x = 9/sin(41) = 13.71827778... ≈ 13.7

18.

we use the extended Pythagoras :

c² = a² + b² - 2ab×cos(C)

with c being the side opposite of the angle C.

so we have

LK² = 16² + 24² - 2×16×24×cos(29) =

= 256 + 576 - 768×cos(29) =

= 832 - 671.7079351... = 160.2920649...

LK = 12.66065026... ≈ 12.7

19.

law of sine

a/sin(A) = b/sin(B) = c/sin(C)

with the sides being always opposite to the corresponding angles.

to find the angle at H we need to find the angle at G first, because we don't know GF yet.

so,

28/sin(76) = 18/sin(G)

sin(G) = 18×sin(76)/28 = 0.623761538...

G = 38.59134528...°

remember the 180° rule in triangles.

H = 180 - 76 - G = 65.40865472...° ≈ 65.4°

20.

GF is now calculated using the law of sine again.

28/sin(76) = GF/sin(H)

GF = 28×sin(H)/sin(76) = 26.23980579... ≈ 26.2

Answer:

[tex] \frac{160}{3} [/tex]

Step-by-step explanation:

Step 1: A discount of

[tex] \frac{1}{3} [/tex]

means that the current price is two thirds of the original cost.

Step 2: The total cost is

[tex]80 \times \frac{2}{3} = \frac{160}{3} [/tex]

and the answer follows.

Solution:

Note that:

Simplify the expression.

Lynn will pay $53.33.

Here for 120, the expression for the start root and end root is given  

[tex]\sqrt{120} =2\sqrt{30}[/tex]

Here we need to find [tex]\sqrt{120}[/tex]

By simplifying the given expression, we get:

[tex]120=2\times2\times2\times3\times5[/tex]

[tex]120=(2^{2} )\times3\times5[/tex]

by taking square roots on both sides we get

[tex]\sqrt{120} =2\sqrt{30}[/tex]

Thus for 120, the expression for the start root and end root is given  [tex]\sqrt{120} =2\sqrt{30}[/tex]

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Answer:

2 square root 30x

Step-by-step explanation:

A on Edge

Answer:

.25

Step-by-step explanation:

.25 or 1/4 is one-fourth of 1

You can divide 1 by 4 to get .25

Check the picture below.

[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3}~~ \begin{cases} B=\stackrel{base}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=12.4\\ h=5 \end{cases}\implies V=\cfrac{(12.4)(5)}{3}\implies V=20.\overline{6}~ft^3[/tex]

Answer:

break it down to prime factorization

so the ans will be 2^3 * 3^2 *11

Answer:

[tex]=13a^{437}+12a[/tex]

Step-by-step explanation:

[tex]\left(a^{413}a^{22}a+1\right)\cdot \:13a-2a+1\cdot \:a[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:-2a+1\cdot \:a=-a[/tex]

[tex]=\left(a^{413}a^{22}a+1\right)\cdot \:13a-a[/tex]

[tex]=\left(a^{436}+1\right)\cdot \:13a-a[/tex]

[tex]=13a\left(a^{436}+1\right)-a[/tex]

[tex]=13a^{437}+13a-a[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:13a-a=12a[/tex]

[tex]=13a^{437}+12a[/tex]

Answer:

Step-by-step explanation:

Minimum Amount = circumference of the pond.

Formulas

C = pi * d

Givens

pi = 3.14

d = 30 feet

Solution

C = pi*d             Substitute for the givens.

C = 3.14 * 30      Multiply

C =  94.2

The value of z is equal to 50.28.

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

These numbers are represented by a ratio between two integers numbers ([tex]\frac{a}{b}[/tex]), where b[tex]\neq[/tex]0.  Besides, this ratio can be simplified in decimal form.

For solving this equation, firstly, rewrite the information given:

                                          [tex]y=512x \;(1)\\ \\ z=50.25+x \;(2)\\ \\ y=15.5 \;(3)[/tex]

As the question gives the values for y, you can find x.

                                        [tex]y=512x\\ \\ 15.5=512x\\ \\ x=\frac{15.5}{512} =0.03[/tex]

Applying x=0.03 in the equation (3), you can find z.

                              [tex]z=50.25+x \\ \\ z=50.25+0.03\\ \\ z=50.28[/tex]

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it depends on the original question. here are 2 ways to solve depends on the question

7x³ - x²/2x³

7x³ - 1/2x

but if the problem is

(7x³-x²)/(2x³)

[x²(7x-1)]/(2x³)

(7x-1) / (2x)

36.9 / 60 = 61.5% on shoes and 38.5% on the shirt

Answer:

Area: 24   Perimeter: 20

Step-by-step explanation:

Area (multiply side 1 by side 2):

4×6=24

Perimeter (add all of the sides together):

4+4=8

6+6=12

8+12=20

Answer:

(0.5, -3)

Step-by-step explanation:

(-3, -1) (4, -5)

midpoint formula

(x1 + x2) /2, (y1 + y2) /2

-3 + 4 = 1 / 2 = 0.5

-1 + -5 = -6 / 2 = -3

Answer:

y = 8sqr3,

x = 4sqr3

Step-by-step explanation:

Use SOH CAH TOA, to solve this.

Here I know the opposite, so I could use either SOH either TOA or both to find the 2 unknowns.

To find y, I would use SOH, which is Sin(angle) = opposite/hypotenuse.

When I rearrange it, I get opposite/Sin(angle) = hypotenuse.

Now let's fill in with the values to give:

12/sin(60) = 8sqr3

And then to find x, let's use TOA, which is Tan(angle) = opposite/adjacent.

Rearrange it to get opposite/Tan(angle) = adjacent. This gives us a side x with a value of:

12/tan(60) = 4sqr3

Answer:

Neither

Step-by-step explanation:

To determine if two lines are parallel or perpendicular, you have to look at the slopes. For the line y=kx+b, k is the slope.

For two lines  y=k1x+b1 and y=k2X+b2 ,When K1=K2, two lines are parallel; when K1=-1/k2, two lines are perpendicular. It doesn't matter whatever b1, b2 are. Hence to save time, you only need to calculate  k1 and k2.

To calculate the slope k of any line, you have to change the equation to y=kx+b

For -y=3x-2, k=3/(-1)=-3 (you divide -1 on each side of =, but you don't need to calculate -2/(-1))

For -6X+2y=6, K=6/2=3 (you first move the -6x to right side, it becomes 6x, then divide by 2)

Now you can get the answer: The two lines neither parallel nor perpendicular

Answer:

D. Parallel

Step-by-step explanation:

When Graphed, These two equations bring up lines that are parallel to each other

Answer:

the second one is an example of a rational function

Answer: 43

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

3/9 = 1/3

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: Height = 16.6 ft

Step-by-step explanation:

The area of a trapezoid is (b1+b2)*h/2, where b1 and b2 are the bases and h is the height.

We can plug in the values given:

234.06 ft^2 = (19.2 ft + 9 ft)*h/2

We can multiply both sides by 2 and combine like terms:

468.12 ft^2 = 28.2 ft*h

Divide both sides by 28.2 ft:

Height = 16.6 ft

Answer:

b. -3

Step-by-step explanation:

slope = y2 - y1 / x2 - x1

= 3 - 9 / 0 + 2

= -6 / 2

= -3

Answer:

b

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 9 ) and (x₂, y₂ ) = (0, 3 )

m = [tex]\frac{3-9}{0-(-2)}[/tex] = [tex]\frac{-6}{0+2}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3

Answer:

4p + 4

Step-by-step explanation:

Original expression:

4(p + 3) - 8

Apply the distributive law:  a(b + c) = ab + ac

⇒ 4p + 12 - 8

Subtract 8 from 12:

⇒ 4p + 4

Answer:

Four coordinate pairs that could serve as the other endpoint of the given line segment are given by:

Step-by-step explanation:

One endpoint of (4,-12), length of 5 units.

Four possible pairs:

Answer: 16

Step-by-step explanation: