When sales of a particular hybrid automobile reach 60,000 units, federal income tax credits begin to phase out. One year after reaching this threshold, buyers are still eligible for 25% of the original $3000 credit. What tax credit would buyers receive if they purchased the vehicle at this time.

Answer:

The answer for both linear equations is A. x = 2, y = 7

Step-by-step explanation:

First start by plugging in the variables with the given numbers (2,7). We'll start with 6x + 3y = 33.

6x + 3y = 33

6 (2) + 3 (7 )= 33 <--- This is the equation after the numbers are plugged in.

12 + 10 = 33

33 = 33 <---- This statement is true, therefore it is the correct pair.

Now we are not done, to confirm that this pair works with both equations we need to solve for 4x + y = 15 to see if it works. Linear Equations must have the variables work on both equations.

4x + y = 15 <----- We are going to do the exact same thing to this equation.

4(2) + 7 = 15

8 + 7 = 15

15 = 15  <-- 15=15 is a true statement therefore this pair works for this equation.

Therefore,

A. x = 2, y = 7 is the correct answer

Sorry this is a day late, I hope it helps.

step by step explanation:

[tex]\mathfrak{x}^{2}+{y}^{2}+16=0[/tex]

=[x2+16=0x26]

=[2x{y}^2{16}~0]

=[4×{y}^0{16}]

=[32x{y}^x]

Answer:

y = 65 + 20x

Step-by-step explanation:

Okay, when you're talking about linear equations try to find the fixed value, and then the changing one.

The fixed value will be by itself

The value that varies will have a variable next to it (x, y, z, whatever)

Then, the answer has to be

y = 65 + 20x

Answer:

1. D. 1

2. B. y=a³/x

3. A. y=1/x

Step-by-step explanation:

too long to give te explanations but they're there in the attachments

Answer:

h=2

Step-by-step explanation:

f is translated right 2 units (so h=2) and up 2 units (so k=2)

The value of h is 2.

Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.

There are horizontal translation and vertical translation of functions.

A function f(x) when translated horizontally leads to the function g(x) which is equal to g(x) = f(x ± k) where k is the units to which the function is translated.

And the vertical translation leads to the function g(x) = f(x) ± k, where k is the units to which the function is translated.

Here the original function is, f(x) = 3ˣ.

The point corresponding to x = 0 in f(x) is x = 2 in g(x).

That is (0, 1) is translated to (2, 3).

f(x) is horizontally translated to the right.

3ˣ translates to 3ˣ⁻².

Hence the value of h is 2.

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Answer:

4/25.

Step-by-step explanation:

We need to have the 2 values in the same unit so:

converting minutes to seconds:

5 mins = 5*60 = 300 seconds.

The require fraction =

48/300              

The GCF of 48 and 300 is 12 so we have:

48/12 / 300/12  

= 4/25

The required fraction of 48 seconds to 5 minutes is  4 / 5 minutes.

Given that,
To express the ratio as a fraction in its lowest terms.48s to 5 minutes​.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
60 second = 1 minute
1 second = 1 / 60 minute
multiply both sides by 48
48 second = 48 / 60 minute
48 second = 4 / 5 minute

Thus, the required fraction of 48 seconds to 5 minutes is  4 / 5 minutes.

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Answer:

[tex]v = \frac{1}{3}bh[/tex]

since base is pi r^2

[tex]v = \frac{1}{3} \pi \: r {}^{2} h[/tex]

it's given that h=4r

[tex]v = \frac{1}{3} \pi \: r^{2} (4r) = \frac{4}{3} \pi \: {r}^{3} [/tex]

now find derivative

[tex] \frac{dv}{dt} = 4\pi \: r {}^{2} [/tex] × dr/dt

r=8 , dv/dt = 3

dv/dt = 4pi (8)^2 ×3 = 768pi

Answer:

768 pi in^3/min

Step-by-step explanation:

Volume of cone=1/3 pi×r^2×h

Differentiating this gives:

dV/dt=1/3×pi×2r dr/dt×h+1/3×pi×r^2×dh/dt

We are given the following:

dr/dt = 3 in./min.

h=4r when r = 8 inches

If h=4r then dh/dt=4dr/dt=4(3 in/min)=12 in/min

If h=4r and r=8 in, then h=4(8)=32 in for that particular time.

Plug in:

dV/dt=1/3×pi×2r dr/dt×h+1/3×pi×r^2×dh/dt

dV/dt=1/3×pi×2(8)(3)×32+1/3×pi×(8)^2×12

dV/dt=pi×2(8)(32)+pi×(8)^2(4)

dV/dt=pi(256×2)+pi(64×4)

dV/dt=pi(512)+pi(256)

dV/dt=pi(768)

dV/dt=768pi

dV/dt=768/pi in^3/min

Answer:

Joe's wife must drive at a rate of 45km/hour.

Step-by-step explanation:

We are given that Joe leaves home and bikes at a speed of 30km/hour. Joe's wife leaves home five minutes later by car, and we want to determine her speed in order for her to catch up to Joe in 10 minutes.

Since Joe bikes at a speed of 30km/hour, he bikes at the equivalent rate of 0.5km/min.

Then after five minutes, when his wife leaves, Joe is 5(0.5) or 2.5 km from the house. He will still be traveling at a rate of 0.5km/min, so his distance from the house can be given by:

[tex]2.5+0.5t[/tex]

Where t represents the time in minutes after his wife left the house.

And since we want to catch up in 10 minutes, Joe's distance from the house 10 minutes after his wife left will be:

[tex]2.5+0.5(10)=7.5\text{ km}[/tex]

Let s represent the wife's speed in km/min. So, her speed times 10 minutes must total 7.5 km:

[tex]10s=7.5[/tex]

Solve for s:

[tex]\displaystye s=0.75\text{ km/min}[/tex]

Thus, Joe's wife must drive at a rate of 0.75km/min, or 45km/hour.

Answer:

1300

Step-by-step explanation:

Given that :

Number of sections = 8

Number of seats per section, x ;

150 ≤ x ≤ 200

The possible Number of seats in the auditorium :

Number of seats per section * number of sections

150 * 8 ≤ x ≤ 200 * 8

1200 ≤ x ≤ 1600

The possible Number of seats will lie within 1200 and 1600

From the options, only 1300 lie within this range

Answer:

Yes, it is appropriate

Step-by-step explanation:

Given

See attachment for pie chart

Required

Is the pie chart appropriate

The attached pie chart displays the distribution of each of the 4 genre. The partition occupied represents the measure of each genre.

Answer:

Part 1)

1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.

2) Dylan is perfectly correct.

3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.

Part 2)

Only Skyler's approach was incorrect. When Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.

Step-by-step explanation:

Part 1)

We want to simplify the expression:

[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7}[/tex]

We can divide. Recall that xᵃ / xᵇ = xᵃ ⁻ ᵇ. Hence:

[tex]\displaystyle =0.88\times 10^{-11-7}=0.88\times 10^{-18}[/tex]

In scientific notation, the coefficient is always between 1 or 10.

So, we can multiply 0.88 by 10. To keep the equality, we need to divide 10⁻¹⁸ by 10. Hence:

[tex]\displaystyle =0.88(10)\times \frac{10^{-18}}{10}[/tex]

(You can see that the 10s can cancel out, giving us our original expression.)

Simplify. Thus:

[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7} = 8.8\times 10^{-19}[/tex]

Therefore, as we can see:

1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.

2) Dylan is perfectly correct.

3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.

Part 2)

Reviewing their work, we can see that only Skyler's approach was incorrect.

729 is indeed 3⁶. However, when Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.

Both Robert and Kevin are correct, having set each exponent equal to each other after their bases are equivalent and solving for x.

Answer:

it's H. 1/2 in.=1,000 ft

[tex]{hope 8 helps}}[/tex]

Answer:

Step-by-step explanation:

Consider the below figure attached with this question.

Given:

The transformation is:

[tex]f(x,y)=(-2x,-3y+1)[/tex]

The range is (4,-2), (2, −5), (−6, 4).

To find:

The domain of the transformation.

Solution:

We have,

[tex]f(x,y)=(-2x,-3y+1)[/tex]

For the point (4,-2),

[tex](-2x,-3y+1)=(4,-2)[/tex]

On comparing both sides, we get

[tex]-2x=4[/tex]

[tex]x=\dfrac{4}{-2}[/tex]

[tex]x=-2[/tex]

And,

[tex]-3y+1=-2[/tex]

[tex]-3y=-2-1[/tex]

[tex]-3y=-3[/tex]

[tex]y=\dfrac{-3}{-3}[/tex]

[tex]y=1[/tex]

So, the domain of (4,-2) is (-2,1).

Similarly,

For the point (2,-5),

[tex](-2x,-3y+1)=(2,-5)[/tex]

On comparing both sides, we get [tex]x=-1,y=2[/tex]. So, the domain of (2,-5) is (-1,2).

For the point (-6,4),

[tex](-2x,-3y+1)=(-6,4)[/tex]

On comparing both sides, we get [tex]x=3,y=-1[/tex]. So, the domain of (-6,4) is (3,-1).

So, the domain of the given transformation is (-2, 1), (-1, 2), (3, -1).

Therefore, the correct option is A.

Answer:

[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]

Step-by-step explanation:

Given

[tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex] -- the correct expression

Required

[tex]\cos(\theta)[/tex]

We know that:

[tex]\sin^2(\theta) + \cos^2(\theta)= 1[/tex]

Make [tex]\cos^2(\theta)[/tex] the subject

[tex]\cos^2(\theta)= 1 - \sin^2(\theta)[/tex]

Substitute: [tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex]

[tex]\cos^2(\theta)= 1 - (-\frac{4}{\sqrt{29}})^2[/tex]

Evaluate all squares

[tex]\cos^2(\theta)= 1 - (\frac{16}{29})[/tex]

Take LCM

[tex]\cos^2(\theta)= \frac{29 - 16}{29}[/tex]

[tex]\cos^2(\theta)= \frac{13}{29}[/tex]

Take square roots of both sides

[tex]\cos(\theta)= \±\sqrt{\frac{13}{29}}[/tex]

cosine is positive in the 4th quadrant;

So:

[tex]\cos(\theta)= \sqrt{\frac{13}{29}}[/tex]

Split

[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}}[/tex]

Rationalize

[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}} * \frac{\sqrt{29}}{\sqrt{29}}[/tex]

[tex]\cos(\theta)= \frac{\sqrt{13*29}}{29}[/tex]

[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]

Answer:

400 + .03(250,000) = $7900

Step-by-step explanation:

Answer:

Extrapolation

Step-by-step explanation:

From the linear regression plot created in the picture given, se could see that Tha percentage of student covered by the the plot is just above 16%. Therefore, to predict the percentage of the number of juvenile violent crime arrests would be in a state if 25% of children are not in school or in the labor force will require us to assume that the current trend continues into the future. Hence, we use the information and indications we have at present to make prediction into the future based on the assumption that we the current trend will remain relevant and applicable. This assumption into the future based on current trend is called EXTRAPOLATION.

Answer:

7-i

Step-by-step explanation:

It is asking for the product of the given complex numbers.

Z1Z2 means Z1 times Z2

(1+i)(3-4i)

You can do the whole foil thing here since we are multiplying a pair of binomials. But all you are doing when you do that is multiplying every term in the first ( ) to every term in the second ( ).

1(3)+1(-4i)+i(3)+i(-4i)

Simplify each term. That is, perform the multiplication in each term:

3-4i+3i-4i^2

Combine like terms and also replace i^2 with (-1):

3-1i-4(-1)

Multiplication identity property used:

3-i+4

Combine like terms:

7-i

Answer:

Step-by-step explanation:

> the equation given is x-y =0

> three points that will solve the equation could be

if x= -2 , y = -2 then x-y = 0 is -2 -(-2) =0 so it works point (-2,-2)

if x=1, y = 1 then x-y = 0 is 1-1 =0 is true so we have point (1, 1)

if x=2 ,y= 2 then x-y = 0 is 2-2 =0 is true so we have point (2, 2)

Answer:

μ = 6500

μx= 6500

σx= 76

σ= 450

n= 35

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The average game is attended by 6,500 fans, with a standard deviation of 450 people.

This means that [tex]\mu = 6500, \sigma = 450[/tex]

35 games:

This means that [tex]n = 35[/tex]

Distribution of the sample mean:

By the Central Limit Theorem, we have [tex]\mu_x = \mu = 6500[/tex] and the standard deviation is:

[tex]\sigma_x = \frac{450}{\sqrt{35}} = 76[/tex]

Answer:

It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.

Step-by-step explanation:

We can write a half-life function to model our function.

A half-life function has the form:

[tex]\displaystyle A=A_0\left(\frac{1}{2}\right)^{t/d}[/tex]

Where A₀ is the initial amount, t is the time that has passes (in this case seconds), d is the half-life, and A is the amount after t seconds.

Since the half-life of the element is 30 seconds, d = 30. Our initial sample has nine grams, so A₀ is 9. Substitute:

[tex]\displaystyle A=9\left(\frac{1}{2}\right)^{t/30}[/tex]

We want to find the time it will take for the element to decay to 0.72 grams. So, we can let A = 0.72 and solve for t:

[tex]\displaystyle 0.72=9\left(\frac{1}{2}\right)^{t/30}[/tex]

Divide both sides by 9:

[tex]\displaystyle 0.08=\left(\frac{1}{2}\right)^{t/30}[/tex]

We can take the natural log of both sides:

[tex]\displaystyle \ln(0.08)=\ln\left(\left(\frac{1}{2}\right)^{t/30}\right)[/tex]

By logarithm properties:

[tex]\displaystyle \ln(0.08)=\frac{t}{30}\ln(0.5)[/tex]

Solve for t:

[tex]\displaystyle t=\frac{30\ln(0.08)}{\ln(0.5)}\approx109.3\text{ seconds}[/tex]

So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.

Answer:

F(x) moved right 2 units to become G(X).

According to graph transformations, that means G(X) = F(X - 2) = [tex](X-2)^{3}[/tex].

I think that's how you do it :\

Answer:

64 is a composite number, and it is 8 squared. 64 = 1 x 64, 2 x 32, 4 x 16, or 8 x 8. Factors of 64: 1, 2, 4, 8, 16, 32, 64. Prime factorization: 64 = 2 x 2 x 2 x 2 x 2 x 2, which can also be written 64 = 2⁶.

For now, I'll focus on the figure in the bottom left.

Mark the point E at the base of the dashed line. So point E is on segment AB.

If you apply the pythagorean theorem for triangle ABC, you'll find that the hypotenuse is

a^2+b^2 = c^2

c = sqrt(a^2+b^2)

c = sqrt((8.4)^2+(8.4)^2)

c = 11.879393923934

which is approximate. Squaring both sides gets us to

c^2 = 141.12

So we know that AB = 11.879393923934 approximately which leads to (AB)^2 = 141.12

------------------------------------

Now focus on triangle CEB. This is a right triangle with legs CE and EB, and hypotenuse CB.

EB is half that of AB, so EB is roughly AB/2 = (11.879393923934)/2 = 5.939696961967 units long. This squares to 35.28

In short, (EB)^2 = 35.28 exactly. Also, (CB)^2 = (8.4)^2 = 70.56

Applying another round of pythagorean theorem gets us

a^2+b^2 = c^2

b = sqrt(c^2 - a^2)

CE = sqrt( (CB)^2 - (EB)^2 )

CE = sqrt( 70.56 - 35.28 )

CE = 5.939696961967

It turns out that CE and EB are the same length, ie triangle CEB is isosceles. This is because triangle ABC isosceles as well.

Notice how CB = CE*sqrt(2) and how CB = EB*sqrt(2)

------------------------------------

Now let's focus on triangle CED

We just found that CE = 5.939696961967 is one of the legs. We know that CD = 8.4 based on what the diagram says.

We'll use the pythagorean theorem once more

c = sqrt(a^2 + b^2)

ED = sqrt( (CE)^2 + (CD)^2 )

ED = sqrt( 35.28 + 70.56 )

ED = 10.2878569196893

This rounds to 10.3 when rounding to one decimal place (aka nearest tenth).

==============================================================

Now I'm moving onto the figure in the bottom right corner.

Draw a segment connecting B to D. Focus on triangle BCD.

We have the two legs BC = 3.7 and CD = 3.7, and we need to find the length of the hypotenuse BD.

Like before, we'll turn to the pythagorean theorem.

a^2 + b^2 = c^2

c = sqrt( a^2 + b^2 )

BD = sqrt( (BC)^2 + (CD)^2 )

BD = sqrt( (3.7)^2 + (3.7)^2 )

BD = 5.23259018078046

Which is approximate. If we squared both sides, then we would get (BD)^2 = 27.38 which will be useful in the next round of pythagorean theorem as discussed below. This time however, we'll focus on triangle BDE

a^2 + b^2 = c^2

b = sqrt( c^2 - a^2 )

ED = sqrt( (EB)^2 - (BD)^2 )

x = sqrt( (5.9)^2 - (5.23259018078046)^2 )

x = sqrt( 34.81 - 27.38 )

x = sqrt( 7.43 )

x = 2.7258026340878

x = 2.7

--------------------------

As an alternative, we could use the 3D version of the pythagorean theorem (similar to what you did in the first problem in the upper left corner)

The 3D version of the pythagorean theorem is

a^2 + b^2 + c^2 = d^2

where a,b,c are the sides of the 3D block and d is the length of the diagonal. In this case, a = 3.7, b = 3.7, c = x, d = 5.9

So we get the following

a^2 + b^2 + c^2 = d^2

c = sqrt( d^2 - a^2 - b^2 )

x = sqrt( (5.9)^2 - (3.7)^2 - (3.7)^2 )

x = 2.7258026340878

x = 2.7

Either way, we get the same result as before. While this method is shorter, I think it's not as convincing to see why it works compared to breaking it down as done in the previous section.

Answer:

Qu 2    =  10.3 cm

Qu 3.   = 2.7cm

Step-by-step explanation:

Qu 2. Shape corner of a cube

We naturally look at sides for slant, but with corner f cubes we also need the base of x and same answer is found as it is the same multiple of 8.4^2+8/4^2 for hypotenuse.

8.4 ^2 + 8.4^2 = sq rt 141.42 = 11.8920141 = 11.9cm

BD = AB =  11.9 cm  Base of cube.

To find height x we split into right angles

formula slant (base/2 )^2 x slope^2  = 11.8920141^2 - 5.94600705^2 =  sq rt 106.065

= 10.2987863

height therefore is x = 10.3 cm

EB = 5.9cm

BC = 3.7cm

CE^2  = 5.9^2 - 3.7^2  = sqrt 21.12 = 4.59565012 = 4.6cm

2nd triangle ED = EC- CD

= 4.59565012^2- 3.7^2 = sq rt 7.43000003 =2.72580264

ED = 2.7cm

x = 2.7cm

Answer:

Step-by-step explanation:

-2x +38 = 2(3 + 3x)

-2x + 38 = 2*3 + 2*3x

-2x + 38 = 6 + 6x

Add 2x to both sides

38 = 6 + 6x + 2x  

Combine like terms

38 = 6 + 8x

Subtract 8  from both sides

38 - 6 = 8x

8x = 32

Divide both sides by 8

x = 32/8

x = 4

Answer:

x = 4

Step-by-step explanation:

Use distributive property to multiply 2 by 3 and 3x

subtract 6x from both side

combine -2x and -6x to get -8x

subtract 38 from both side

subtract 38 from 6 to get -32

divide both side by -8

[tex] \small \sf \frac{-8x}{ -8} = \frac{-32}{-8} \\ \\ \small \sf x = \frac{- 32}{-8}[/tex]

divide -32 by -8 to get 4

9514 1404 393

Answer:

  6

Step-by-step explanation:

Work backward.

If he has 24 after adding 6, he had 18 before that addition.

If he had 18 after tripling his collection, he had 18/3 = 6 cards to start with.

__

Note that this is the same process you would use if you started with an equation.

  3c +6 = 24 . . . . where c is the number of cards Johnny started with

  3c = 24 -6 = 18 . . . . . subtract 6 from the final number

  c = 18/3 = 6 . . . . . . . . divide the tripled value by 3 to see the original value

Johnny started with 6 cards.

Step-by-step explanation:

s+u

Add t: You will need to introduce brackets

(s+u) + t

Add v: Introduce another v

((s/u) + t) + v

Answer:

58.80

Step-by-step explanation:

84 x .7(70%) =58.80