What is the distance between the y-intercepts of the lines? Adding a picture please help

Answer:

Part a) The polynomial for the area including the frame is

[tex](4x^{2}+72x+320)\ ft^{2}[/tex]

Part b) The polynomial for the perimeter including the frame is

[tex](72+8x)\ ft[/tex]

Part c) The perimeter of the picture including the frame when the width of the frame is 2 inches is equal to [tex]88\ ft[/tex]

Part d) The area of the picture including the frame when the width of the frame is 2 inches is equal to [tex]480\ ft^{2}[/tex]

Step-by-step explanation:

Let

x-----> the width of the frame

L-----> the length of the picture

W-----> the width of the picture

Part a) What is a polynomial for the area including the frame?

we have

The dimensions of the picture are

[tex]L=20\ in[/tex]

[tex]W=16\ in[/tex]

The area including the frame is equal to

[tex]A=(20+2x)(16+2x)\\ \\A=320+40x+32x+4x^{2}\\ \\A=(4x^{2}+72x+320)\ ft^{2}[/tex]

Part b) What is a polynomial for the perimeter including the frame?

we have

The dimensions of the picture are

[tex]L=20\ in[/tex]

[tex]W=16\ in[/tex]

The perimeter including the frame is equal to

[tex]P=2[(20+2x)+(16+2x)]\\ \\P=2[36+4x]\\ \\P=(72+8x)\ ft[/tex]

Part c) What is the perimeter of the picture including the frame when the width of the frame is 2 inches

we have

[tex]P=(72+8x)\ ft[/tex]

For x=2 in

substitute

[tex]P=72+8(2)=88\ ft[/tex]

Part d) What is the area of the picture including the frame when the width of the frame is 2 inches

we have

[tex]A=(4x^{2}+72x+320)\ ft^{2}[/tex]

For x=2 in

substitute

[tex]A=(4(2)^{2}+72(2)+320)=480\ ft^{2}[/tex]

The perimeter of a two-dimensional figure is the distance covered around it.

The polynomial for the area including the frame is [tex]\rm 4x^2+72x +320[/tex].

The polynomial for the perimeter including frame is [tex]\rm 72+8x[/tex].

The perimeter of the picture including the frame when the width of the frame is 2 inches is 88 feet.

The area of the picture including the frame when the width of the frame is 2 inches is 480 feet.

You are framing a picture with a frame of equal width on each side.

The width of the frame is 2 inches.

The length is 20 inches and the width is 16 inches.

The width of the frame is 2 inches.

The perimeter of a two-dimensional figure is the distance covered around it.

Let the width of the frame be x.

The length of the picture be L.

The width of the picture is W.

1. What is a polynomial for the area including the frame?

[tex]\rm Area \ of \ the \ frame = length \times width\\\\ Area \ of \ the \ frame = (20+2x) (16+2x)\\\\ Area \ of \ the \ frame = 320+40x+32x+4x^2\\\\ Area \ of \ the \ frame = 4x^2+72x +320[/tex]

The polynomial for the area including the frame is [tex]\rm 4x^2+72x +320[/tex].

2. What is a polynomial for the perimeter including the frame?

[tex]\rm Perimeter \ of \ the \ picture = 2 (length + width)\\\\ Perimeter \ of \ the \ picture = 2(20+2x+16+2x)\\\\ Perimeter \ of \ the \ picture = 2(36+4x)\\\\ Perimeter \ of \ the \ picture = 72+8x[/tex]

The polynomial for the perimeter including frame is [tex]\rm 72+8x[/tex].

3. What is the perimeter of the picture including the frame when the width of the frame is 2 inches.

[tex]\rm Perimeter \ of \ the \ picture = 72+8x\\\\Perimeter \ of \ the \ picture = 72+8(2)\\\\ Perimeter \ of \ the \ picture = 72+16\\\\Perimeter \ of \ the \ picture = 88\\\\[/tex]

The perimeter of the picture including the frame when the width of the frame is 2 inches is 88 feet.

4. What is the area of the picture including the frame when the width of the frame is 2 inches.

[tex]\rm Area \ of \ the \ frame = 4x^2+72x +320\\\\ Area \ of \ the \ frame = 4(2)^2+72(2)+320\\\\ Area \ of \ the \ frame=480[/tex]

The area of the picture including the frame when the width of the frame is 2 inches is 480 feet.

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Answer:

b.

Step-by-step explanation:

x-intercepts are found by factoring.  We will use standard factoring here since this one is straightforeward and has real zeros as its solutions.  

In our equation,

a = 2

b = 2

c = -4

The rules are to take a * c and then find the factors that number, determine which combination of those factors will give you the linear term (the term with the single x on it), and rearrange those signs accordingly.  Let's start with that:

Our a * c is 2 * -4 = -8.

We need the factors of |-8|:  1,8 and 2,4

Some combination of those factors needs to give us a +2x.  2,4 will work as long as the 4 is positive and the 2 is negative.

Now we put them back into the equation, the absolute value of the larger number first:

[tex]2x^2+4x-2x-4=0[/tex]

Now group the terms in sets of 2 without moving any of them around:

[tex](2x^2+4x)-(2x-4)=0[/tex]

In each set of parenthesis, pull out what is common to both terms.  In the first set, the 2x is common, and in the second set, the 2 is common:

[tex]2x(x+2)-2(x+2)[/tex]

Now what is common between both terms is the (x + 2), so pull that out, grouping what is remaining in its own set of parenthesis:

[tex](x+2)(2x-2)=0[/tex]

To find the zeros, remember that the Zero Product Property tells us that for that equation above to equal zero, one of those factors has to equal zero, so:

x + 2 = 0 or 2x - 2 = 0.  Solve both for x:

x = -2 so the coordinate is (-2, 0)

2x - 2 = 0 and

2x = 2 so

x = 1 so the coordinate is (1, 0)

3.75 miles or 3 3/4 would be your answer

Answer:

0.3

Step-by-step explanation:

To calculate the dilation factor of two similar figures, you simply need to establish the ratio of the dilated figure (in our case PQRS) to the original figure (ABCD) using the same relative side.  

In our case, we'll take the longest of the sides provided in each figure.

So, we divide 12.6 by 42 to know the dilation factor of the longest side, it will be the same for all other sides:

d = 12.6 / 42 = 0.3

Is there more to the question,

Answer:

1. 90 sq. cm

2. 96 sq. cm

3. 72 sq. cm

4. 72 sq. cm

5. 92 sq. cm

6. 68 sq. cm

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Congruent means the same. Translating it just moves it somewhere else.

Answer: D) The two triangles are congruent because a translation does not change size and shape.

Step-by-step explanation:

Since all rigid motions create congruent figures , it means it do not change the shape and size of the figure.

So, translation does not change size and shape.

If a triangle is drawn and then translated, then they are congruent because a translation does not change size and shape.

Answer:

  Equation 3: y = 12x + 17

Step-by-step explanation:

Only a linear equation (degree 1) will have a graph that is a straight line.

The degree of the equation is the highest power of any of the variables. If different variables are in the same term, it is the sum of the powers of those variables.

Answer:

Equation 3: y = 12x + 17

Step-by-step explanation:

It is the answer because all of the variables have an exponent of 1.

Answer:

B. g(x) = 3x^3.

Step-by-step explanation:

In general   a f(x)  stretches vertically the graph of f(x) by a factor a.

The new function after a vertical stretch of the cubic function F(x) = x^3 is G(x) = 3x³, which multiplies the output of the original function by 3.

When you apply a vertical stretch to the cubic function F(x) = x³, you multiply the output of the function, not the input. A vertical stretch by a factor of 3 would mean that each output value is tripled. Therefore, the correct equation for the new function would be G(x) = 3x³.

Option A is incorrect because (1/3x)³ represents a horizontal stretch by a factor of 3. Option C, (3x)³, represents a horizontal shrink by a factor of 1/3, and results in steeper slopes than the original function, which is the opposite effect of a vertical stretch. Option D, 1/3x³, would be a vertical compression by a factor of 1/3, not a stretch.

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Answer:

D. 5000 kg

Step-by-step explanation:

We assume the second train was standing still and that momentum is conserved. The the product of mass and velocity before the collision is

(5000 kg)·(100 m/s) = 500,000 kg·m/s.

After the collision, where M is the mass of the second train, the momentum is ...

((5000+M) kg)·(50 m/s) = 500,000 kg·m/s

Dividing by 50 m/s and subtracting 5000 kg, we have ...

(5000 +M) kg = 10,000 kg

M kg = 5000 kg

The mass of the second train is 5000 kg.

Answer:

D. 5000 kg

Step-by-step explanation:

Answer:

It is D

Step-by-step explanation:

Answer:

It is the last one. It is clearly less than 90 degrees.

Step-by-step explanation:

Answer:

x = 31

Step-by-step explanation:

The sides of an isosceles trapezoid are the same length, so ...

5x -32 = 2x +61

3x = 93 . . . . . . . . add 32-2x

x = 31 . . . . . . . . . . divide by 3

let's use engineering notation for the sake of brevity.

1 trillion is 1,000,000,000,000, or just 1E12, twelve zeros.

1 million is then 1E6, six zeros.

we know the discharge for one day is 3E12 gallons, and that'd do just fine for country A for 5 months.  How many gallons in 1 month only?

[tex]\bf \begin{array}{ccll} gallons&months\\ \cline{1-2} 3E12&5\\ x&1 \end{array}\implies \cfrac{3E12}{x}=\cfrac{5}{1}\implies 3E12=5x \\\\\\ \cfrac{3E12}{5}=x\implies 6E11=x\implies 600000000000=x[/tex]

if there are 200million inhabitants in A, namely 200E6 or 2E8 inhabitants, how many gallons per inhabitant from all those 6E11 gallons?

[tex]\bf \begin{array}{ccll} gallons&households\\ \cline{1-2} 6E11&2E8\\ x&1 \end{array}\implies \cfrac{6E11}{x}=\cfrac{2E8}{1}\implies 6E11=2E8x \\\\\\ \cfrac{6E11}{2E8}=x\implies \cfrac{600000000000}{200000000}=x\implies 3000=x[/tex]

Answer:

15%

Step-by-step explanation:

29,400-25,000 = 4,400

4,400/29,400 =0.14965

0.14965 x 100 = 14.965%

or round up to 15%

Final answer:

The rate of depreciation for Hugo's car is approximately 14.97%, calculated using the formula for the rate of depreciation and the given values of the original and the selling price.

Explanation:

To solve for the rate of depreciation of Hugo's car, we can use the following equation:

R = ((P - S) / P) × 100

Where:
R = rate of depreciation (%)
P = original price of the car
S = selling price of the car after one year

Given:
P = $29,400
S = $25,000

Substituting the values into the equation:

R = (($29,400 - $25,000) / $29,400) × 100

R = ($4,400 / $29,400) × 100

R = 0.14966 × 100

R = 14.966%

Hence, the annual rate of depreciation for Hugo's car is approximately 14.97%.

Answer:

  a) monthly payment: $177.50

  b) total amount paid: $31,950

  c) toward principal: $17,500; toward interest: $14,450

Step-by-step explanation:

a) The amount of the monthly payment (A) is computed from the principal (P), the annual interest rate (r) and the number of years (n) using the formula ...

  A = P·(r/12)/(1 -(1 +r/12)^(-12n))

Filling in your numbers, we can use r/12 = 0.09/12 = 0.0075, and 12n = 12·15 = 180:

  A = $17500·0.0075/(1 - 1.0075^-180) ≈ $177.50

__

b) The total payment over the term of the loan is 180 of these monthly payments:

  180·$177.50 = $31,950

__

c) $17,500 is paid toward the principal.

 $14,450 is paid toward interest.

Answer:

10 friends

Step-by-step explanation:

we know that

The formula of the sum is equal to

[tex]sum=\frac{n}{2}[2a1+(n-1)d][/tex]

where

a1 is the first term

n is the number of terms (number of friends)

d is the common difference in the arithmetic sequence

In this problem we have

[tex]sum=275\ stickers[/tex]

[tex]a1=5\ stickers[/tex]

[tex]d=5[/tex] ----> the common difference

substitute in the formula and solve for n

[tex]275=\frac{n}{2}[2(5)+(n-1)(5)][/tex]

[tex]550=n[10+5n-5]\\ \\550=10n+5n^{2} -5n\\ \\5n^{2}+5n-550=0[/tex]

Solve the quadratic equation by graphing

The solution is n=10

see the attached figure

therefore

She had 10 friends who got stickers

Answer:

[tex]14\ candles[/tex]

Step-by-step explanation:

step 1

Find the volume of the cylindrical mold

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=3.4\ cm[/tex]

[tex]h=6\ cm[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=(3.14)(3.4)^{2}(6)[/tex]

[tex]V=217.79\ cm^{3}[/tex]

step 2

Find the volume of the wax

The volume is equal to

[tex]V=(15)(12)(18)[/tex]

[tex]V=3,240\ cm^{3}[/tex]

step 3

Divide the volume of the wax by the volume of the cylindrical mold, to calculate the number of candles

[tex]3,240/217.79=14.9\ candles[/tex]

Round down

[tex]14\ candles[/tex]

Answer:

21x^2 - 41x + 10

Step-by-step explanation:

The area of a rectange is length x width.

L = 7x-2

W = 3x-5

So, you would do (7x-2)x(3x-5).

To do this, you can do FOIL.

F (first times first) - (7x)(3x)=21x^2

O (outside times outside) - (7x)(-5)= -35x

I (inside times inside) - (-2)(3x)= -6x

L (last times last) - (-2)(-5) = 10

So, it is 21x^2 - 35x - 6x +10

Then you combine like terms giving you:

21x^2 - 41x + 10

Answer: 21x^2 - 41x + 10

Step-by-step explanation: If the lengths are even then the number would be angle.

Answer:

Option D. $1 million

Step-by-step explanation:

we know that

Reserve Ratio, it is the percentage of deposits which commercial banks are required to keep as cash

Find the 20% of $5 million

20%=20/100=0.20

0.20*5,000,000=$1,000,000

so

$1 million

The required reserve ratio is what banks must keep from a deposit. Given a 20% reserve ratio and a $5 million deposit, banks must reserve $1 million. Using the money multiplier formula, the remaining funds could theoretically create as much as $25 million in money supply.

The required reserve ratio is the percentage of deposits that a bank must hold as reserves. In this case, the required reserve ratio is 20 percent. The rest of the deposit (80 percent) can be loaned out or invested by the bank, which will create additional deposits and thus increase the money supply.

If a commercial bank receives a $5 million deposit and the required reserve ratio is 20 percent, the bank must keep $1 million (20 percent of $5 million) as reserve. The rest, $4 million, can be loaned out or invested.

However, this doesn't simply stop at $4 million. This loaned money will eventually be deposited back into the banking system (let's assume to another bank), which can then loan out 80% of that deposited money, and this cycle can continue. In an extremely simplified scenario, you can continue this process until the banks can no longer lend out money.

To simplify this scenario, the money multiplier formula can be used. The money multiplier formula is 1 divided by the reserve ratio. In this case, it's 1 / 0.20 = 5.  Therefore, a $5 million deposit can potentially lead to a $25 million increase in the money supply, so the answer is (a) $25 million.

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Answer:

A. The graph of the function increases and decreases over its domain.

Step-by-step explanation:

The graph is attached. Some places, it has positive slope (is increasing); other places it has negative slope (is decreasing).

Answer:

3 feet long

Step-by-step explanation:

Answer: Brad's shadow is 3 feet long

Answer:

541.8 cm³

Step-by-step explanation:

Volume of a prism is the height times the area of the base.

V = hA

Area of a rectangle is width times length, so:

V = hwl

Given h = 8.8 cm, w = 4.7 cm, and l = 13.1 cm:

V = (8.8 cm) (4.7 cm) (13.1 cm)

V = 541.8 cm³

Answer:

[tex]541.8cm^{3}[/tex]

Step-by-step explanation:

V = Bh or V = lwh

substitute given measurements, then simplify.[tex]13.1cm * 4.7cm * 8.8cm = 541.8cm^{3}[/tex]

Answer:

#3. (x-7)(x-4)   #5. (2k+7)(k-2)

Step-by-step explanation:

For #3 you have to first get all the terms on one side of the equals sign and set it equal to 0.  So that gives us

[tex]x^{2} -11x+28=0[/tex].

Our a value is 1 and our c value is 28, so the product of those is 28.  Find the factors of 28 and the combination of those factors that add up to equal the linear term -11x is the combination we need for our problem.  The factors of 28 are:  1, 28; 2, 14; 4, 7.  4 and 7 give us 11 when we add them, but since we need a -11, we have to use the negative of both the factors since -7 + -4 = -11.  Set up your equation now using the -7 and the -4, "larger" number first (the absolute value which makes the 7 larger):

[tex]x^{2} -7x-4x+28[/tex].  This is the pattern that you will use to factor the next problem, as well.

Group the terms in groups of 2 to get:

[tex](x^{2} -7x)-(4x-28)=0[/tex].  Notice the sign change in front of the 28 in the second set of parenthesis.  This is because if I distribute the negative infront of the parenthesis back in, negative times a negative will give us the +28 in the original problem.  The same will apply again in #5 when we get there.

Now factor out whatever is common from each set of parenthesis:

[tex]x(x-7)-4(x-7)=0[/tex].

Now the common term is the factor (x-7) so that can be factored out now, leaving behind:

(x-7)(x-4).  That's the answer for #3.

Now for #5:

We will start by getting everything on one side (I am changing the k's to x's):

[tex]2x^{2} +3x-14=0[/tex].

The product of our a value and c value is again 28.  Find the combination of the factors of 28 that will add to give us the middle (linear) term of 3:  That is again 7 and 4, with the 7 needing to be positive and the 4 needing to be negative since 7 - 4 = 3.  Set up our expanded quadratic as follows, "larger" number (the absolute value of) first:

[tex]2x^{2} +7x-4x-14=0[/tex].

Group them into groups of 2 again:

[tex](2x^{2} +7x)-(4x+14)=0[/tex]

Again, notice the necessary sign change so when we distribute the negative back into the parenthesis we get the -14 we started with in the original problem.

Now factor out what is common from each set of parenthesis:

[tex]x(2x+7)-2(2x+7)=0[/tex].

What's common now is the factor (2x+7) so that can be factored out leaving behind

(2x+7)(x-2)=0

And you're done!!!

Answer:

y=1/4x-1

Step-by-step explanation:

First step to determine the equation of a line is is to determine its slope.

We see the line passes through points (4,0) and (0,-1), that means its slope is:

S = (0 - -1) / (4 - 0) = 1/4

Since there's only one choice with a slope of 1/4, the choice is easy :-)

But we can also verify the equation by checking if it validates the given points. So, what's the value of y if x = 0?

y = (1/4)0 - 1 = 0 - 1 = -1  Validated.

And when x = 4?

y = (1/4)4 - 1 = 1 - 1 = 0  Validated too.

Answer:

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

Step-by-step explanation:

The given function passes through: (4,0) and (0,-1).

The equation is of the form;

y=mx+b

where b=-1 is the y-intercept.

The equation now becomes:

y=mx-1

We substitute the point (4,0) into the function to obtain;

0=m(4)-1

0+1=4m

1=4m

[tex]m=\frac{1}{4}[/tex]

Therefore the equation is:

[tex]y=\frac{1}{4}x-1[/tex]

Multiply through by 4 to get;

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

The equation in standard form is;

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

Answer:

x=2

Step-by-step explanation:

Could you please elaborate? Is there an equation?

Answer: What do you need to know?

Step-by-step explanation:

Answer:

D. An exponential function, because exponential functions increase at a nonconstant rate

Step-by-step explanation:

Each month Tai's brother grows more than he grew the previous month.

We can't model his growth by a linear function, because linear functions increase at a constant rate.

The model must be an exponential function.

For example, if the boy's height at Month 0 were 100 units, a model like h = 100(1.1)ⁿ would give the following results.

[tex]\begin{array}{ccc}\textbf{Month} & \textbf{Height} & \textbf{Diff.}\\0 & 100 & \\1 & 110 & 10\\2 & 121 & 11\\3 & 133 & 12\\4 & 146 & 13\\\end{array}[/tex]

An [tex]\boxed{\textbf{ exponential function }}[/tex] is consistent with a monthly change in height that increases each month.

Answer:

The length of the field is 84 yards

Step-by-step explanation:

Since the area of a rectangle is width times the length, we can write a simple equation.

Let w be the width

Let l be the length

W*L = 4284

Since we know the width of the rectangle is 51 yards, we can plug it in.

51L = 4284

Dividing 51 on both sides,

L = 84

Answer:

156.25% =P

Step-by-step explanation:

Is means equals and of means multiply

50 = P * 32

Divide each side by 32

50/32 = 32P/32

1.5625= P

Now we need to change it to percent form by multiplying by 100%

1.5625 * 100% = P

156.25% =P