Please help me it’s for Plato on edmentum! Algebra 1 Quadratic relationships Mastery test

Answer:

Look at the equations:

y

=

−

9

x

−

21

and

y

=

5

x

+

7

Because both equations equal (y), they both equal the same.

If an equations says "

y

=

−

9

x

−

21

" , that means we can replace (y) with

−

9

x

−

21

.

Therefore when i take the equation:

y

=

5

x

+

7

, we can replace (y) to get:

−

9

x

−

21

=

5

x

+

7

Now isolate (x):

−

9

x

−

21

=

5

x

+

7

⇔

−

21

=

14

x

+

7

⇔

−

28

=

14

x

⇔

x

=

−

2

The function of the graph is y = 4(3)^x

The graph is an exponential function with the following points

(x,y)= (0,4) and (1,12)

An exponential function is represented as:

y = ab^x

Substitute (0,4) in the equation

4 = a * b^0

a = 4

Substitute a = 4 in y = ab^x

y = 4b^x

Substitute (1,12) in the equation

12 = 4b^1

12 = 4b

Divide by 4

b = 3

Substitute b = 3 in y = 4b^x

y = 4(3)^x

Hence, the function of the graph is y = 4(3)^x

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Answer:

  dilation by a factor of -1/2 about the center (6, 5)

  (x, y) ⇒ (9 -x/2, 7.5 -b/2)

Step-by-step explanation:

Figure B is half the size of Figure A. It has been rotated, and translated. The single transformation must have all of these effects.

__

The orientation of shape B is the same as that of shape A. The small extension from the rectangle still points counterclockwise relative to the figure's center. However, it points west instead of east, signifying a rotation of 180°. The same 180° rotation can be accomplished by a reflection across a point.

Shape B has half the dimensions of shape A. That means it has been dilated by a factor of 1/2. The reflection across a point can be accomplished by using a negative dilation factor.

The center of the dilation must reside between the two figures in order for "reflection across a point" to be accomplished. Each point on figure A must be twice as far from that center as the corresponding point on figure B.

Corresponding points are (1, 1) on figure A, and (8.5, 7) on figure B. The center of dilation divides the line between these points into the ratio 2:1. That center can be found as ...

  (a, b) = (2(8.5, 7) +(1, 1))/3 = (17+1, 14+1)/3 = (6, 5)

The single transformation that maps figure A to figure B is ...

  dilation by a factor of -1/2 about the center (6, 5)

  (x, y) ⇒ (9 -x/2, 7.5 -b/2)

Answer:

f(-2)=4

Step-by-step explanation:

put -2 where x is

f(x)=2x²+x-2

f(-2)=2(-2)²+(-2)-2

f(-2)=(2*4)-4

f(-2)=8-4

f(-2)=4

Answer:

[tex] \boxed{\rm \: Volume_{(Cylinder)} \approx \: 307.7 \: m {}^{3} } ( \rm \: nearest \: tenth )[/tex]

Step-by-step explanation:

Given:

To Find:

Solution:

Use the formulae of the volume of cylinder:

[tex] \boxed{\rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h}[/tex]

where,

According to the question:

Substitute the values onto the formulae in order to find out the volume:

[tex] \rm \: Volume_{(Cylinder)} = \pi(7) {}^{2} (2)[/tex]

[tex] \rm \: Volume_{(Cylinder)} = \pi(49)(2)[/tex]

[tex]\rm \: Volume_{(Cylinder)} = 98\pi[/tex]

[tex]\rm \: Volume_{(Cylinder)} = \: 98 \times 3.14[/tex]

[tex]\rm \: Volume_{(Cylinder)} = 307.72 \: m {}^{3} \: (exact \: form)[/tex]

[tex] \boxed{\rm \: Volume_{(Cylinder)} \approx \: 307.7 \: m {}^{3} } \: ( \rm nearest \: tenth )[/tex]

Hence,we can conclude that:

The volume of the cylinder is approximately

307.7m³.

[tex]V=lwh=(3)\left(\frac{4}{3} \right) \left(\frac{3}{5} \right)\\\\V=3\left(\frac{12}{15} \right)\\\\V=\frac{36}{15}=\boxed{\frac{12}{5} \text{ cm}^{2}}[/tex]

Answer:

17/8

Step-by-step explanation:

You must type 2* 8 and add 1. That makes 17/8

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to convert 2 1/8 into an improper fraction (a fraction whose numerator is greater than its denominator).

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

These are the steps:

However, we cannot simplify 17/8, so that's our answer.

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Answer: B

Step-by-step explanation:

The angles add to 90 degrees if they are complementary, so:

[tex]x-2+2x+5=90\\3x+3=90\\3x=87\\x=29[/tex]

So, the angles measure 29-2=27 degrees and 2(29)+5=63 degrees.

The angle of depression of the airplane is 39.8°, length of the runway is 45794 ft, and approximate height of the tower is 321 m.

The angle of depression of the airplane is given as follows:

Let the angle of depression be A.

[tex]A= {tan}^{ - 1} ( \frac{15000}{8000} ) = {39.8}^{o} [/tex]

Angle of depression is 39.8°.

If the angle of elevation is 6.8°, the length of the runway l is calculated thus:

horizontal distance of airplane from end of runway = d

length of runway, L = d - 80000 ft

[tex]d = \frac{15000}{tan 6.8°} = 125794 ft[/tex]

L = 125794 - 80000

L = 45794 ft

The length of the runway is 45794 ft

2. Let the height of the tower be H

[tex]H = \tan(69.8) \times 118 = 321m[/tex]

The approximate height of the tower is 321 m

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Answer:

x<_-5

Step-by-step explanation:

-4(x+3)<_-2-2x

-4x-12<_-2-2x

-4x+2x<_-2+12

-2x<_10

-2x/-2<_10/-2

x<_-5

Answer:

Drivers located below mile marker 47 or at mile marker 70 or above never get pulled over.

Step-by-step explanation:

[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{30\% of 45}}{\left( \cfrac{30}{100} \right)45}\implies 13.5~\hfill \underset{final~cost}{\stackrel{45~~ - ~~13.5}{31.5}}[/tex]

Answer:

Step-by-step explanation:

Answer:

0.8p

Step-by-step explanation:

Hello!

As the questions states, 20% of p is 0.2p.

Simplifying the equation:

0.8p is also 80% of p, which can be translated to 100% - 20% of p.

The equivalent expression is 0.8p.

Answer:

8x^2 +6x +36xy^2+27y^2

Step-by-step explanation:

2x * 4x-2x*-3) -9y-^2(-4x)-9y^2(-3)

Answer:

2?

Step-by-step explanation:

2 is the square root of 4 since 2×2=4

Answer:

2

4

Step-by-step explanation:

Because 2 × 2 = 4, we know that 2 is the square root of 4.

√4 = 2

[tex]\begin{array}{r|l}576&2\\288&2\\144&2\\72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}[/tex]

[tex]576=2^6\cdot3^2[/tex]

Therefore

[tex]4\sqrt{576}=4\sqrt{2^6\cdot3^2}[/tex]

Answer:

x = 25

Step-by-step explanation:

the line QC is parallel to BR

Then

x/15 = 40/24

Then

24x = 40×15

Then

24x = 600

Then

x = 600/24

Then

x = 25

No, the cone and the cylinder can't have congruent heights and bases.

The volume of a cylinder of radius R and height H is:

V = pi*R^2*H

And for a cone of radius R and height H is:

V = pi*R^2*H/3

So, for the same dimensions R and H, the cone has 1/3 of the volume of the cylinder.

Here, the cylinder has a volume of 120cm³ and the cone a volume of 360cm³, so the cone has 3 times the volume of the cylinder.

This means that the measures must be different, so the cone and the cylinder can't have congruent heights and bases.

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Answer: Heyaa! ~

When simplifying (2x^2y)3 the answer will be...  6x²y

Step-by-step explanation:

    Multiply the numbers:

Hopefully this helps you! ^^

The net present value is $305.73. The project should be accepted.

Using this formula

Net present value=Cashflow÷(1+Cost of capital)^ time

Let plug in the formula

Net present value=-$2,400+ ($630÷(1+.09)^1) + ($760÷(1+.09)^2) + ($800÷(1+.09)^3) + ($880 ÷(1+.09)^4) + ($380÷(1+.09)^5)

Net present value=-$2,400+ ( $630÷(1.09)^1) + ($760÷(1.09)^2) + ($800÷(1.09)^3) + ($880 ÷(1.09)^4) + ($380÷(1.09)^5)

Net present value=-$2,400+ ($630÷1.09) + ($760÷1.1881) + ($800÷1.295029) + ($880 ÷1.41158161) + ($380÷1.538639549)

Net present value=-$2,400+ $577.98+$639.68+$617.75+623.41+$246.91

Net present value=$305.73

Based on the above calculation the project should be accepted.

Therefore the NPV is $305.73.

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it will print no, because B = 3 and not 2 so it will skip the print yes line.

The given differential equation is not exact, if we convert it to an exact one, we get:

[tex]2ydx + 2*(x - sin(y)^{1/2})*dy = 0[/tex]

A differential equation:

[tex]Ndx + Mdy = C[/tex]

Is exact only if:

[tex]\frac{dM}{dy} = \frac{dN}{dx}[/tex]

In this case, we have:

[tex]2ydx + (x - sin(y)^{1/2})*dy = 0\\\\then:\\\\N = 2y\\M = x - sin(y)^{1/2}[/tex]

If we differentiate, we will get:

[tex]\frac{dN}{dy} = 2\\\\\frac{dM}{dx} = 1[/tex]

So, to convert this to an exact differential equation, we need to add a factor 2 to N, this will give:

[tex]2ydx + 2*(x - sin(y)^{1/2})*dy = 0[/tex]

This is, in fact, an exact differential equation.

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Answer:

9y

Step-by-step explanation:

Mathematicaly, the product of 9 and a number "y" is:

9y

Answer:

These are Vertical angles, adjacent angles are next to each other and make up a whole angle, while vertical angles are across and equal the same thing.

X = 81 because 84 and (x + 3) are the same so 84 minus 3 is 81

Hope that helps

The x-intercept of the function [tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex] is -2

The equation of the function is given as:

[tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex]

The x intercept is the x value when h(x) = 0

So, we have:

[tex]8 * \sqrt[3]{x - 6} + 16 = 0[/tex]

Subtract 16 from both sides

[tex]8 * \sqrt[3]{x - 6} = -16[/tex]

Divide both sides by 8

[tex]\sqrt[3]{x - 6} = -2[/tex]

Take the cube of both sides

x - 6 = -8

Add 6 to both sides

x = -2

Hence, the x-intercept of the function [tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex] is -2

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Answer:

7 years

Step-by-step explanation:

Your equation should read     = 200 * e^(.08 t)  =  350

    solving for t       = 6.99 yrs     ~~ 7 years