Answers
Answer:
60
Step-by-step explanation:
<H + <T = 180
2x+ 60 + x + 30 = 180
3x + 90 = 180
3x = 90
x = 30
<T = x + 30 = 30 + 30 = 60
Answer
<T = 60
Related Questions
6)
Q:
A:
Lynn has one red, one blue, and one yellow shirt to choose from. She also has one blue and one yellow necklace to choose from. Lynn chooses a random shirt and necklace for work today. Are these events dependent or independent? Give a reason.
A) Dependent. These primary colors mix together to make secondary colors.
B) Dependent. After Lynn chooses a shirt, there are only two more shirts to choose from.
C) Independent. The wardrobe is not large enough for one thing to affect something else.
D) Independent. Randomly selecting a shirt does not affect randomly selecting a necklace.
Answers
i would pick D as the answer.
The events of Lynn choosing a shirt and choosing a necklace are independent. The choice of one item does not affect the choice of the other. The correct answer is D) Independent - Randomly selecting a shirt does not affect randomly selecting a necklace.
Explanation:The question asks whether the events of Lynn choosing a shirt and necklace are dependent or independent. In general, events are called independent if the outcome of one does not affect the outcome of another. In this scenario, picking a shirt does not change the options of necklaces and vice versa. Thus, the selection of a shirt has no effect on the selection of a necklace.
The correct answer is therefore: Independent. Randomly selecting a shirt does not affect randomly selecting a necklace. Even if Lynn picked a red, blue, or yellow shirt first, it wouldn't affect her choice of necklace. She will still have the same two necklaces to choose from regardless of what shirt she picks.
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Tai notices that although his little brother is not growing by the same amount each month, there is a pattern in how quickly he is growing. Tai determines that each month his brother grows more than he grew the previous month. What type of function could represent Tai's brother's growth? Select one: A. A linear function, because linear functions increase at a constant rate B. A linear function, because linear functions increase at a nonconstant rate C. An exponential function, because exponential functions increase at a constant rate D. An exponential function, because exponential functions increase at a nonconstant rate
Answers
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.
find the x-intercepts for the parabola defined by the equation below.
y= 2^2 + 2x - 4
a. -4,0 and 2,0
b. -2,0 and 1,0
c. 0,-2 and 0,1
d. 0,-4 and 0,2
Answers
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)
Sandra has a cylindrical mold for making candles with a radius of 3.4 cm and a height of 6 cm. If Sandra uses a rectangular block of wax measuring 15 cm by 12 cm by 18 cm, about how many candles can she make after melting the block of wax?
Answers
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]
Which angle appears to be acute?
Answers
Answer:
It is the last one. It is clearly less than 90 degrees.
Step-by-step explanation:
The area of a rectangular field is 4284 yd. If the width of the field is 51 yards, what is its length?
Answers
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
What is the equation of the line that is perpendicular to the given line and passes through the point (2, 6)?
x = 2
x = 6
y = 2
y = 6
Answers
Answer:
x=2
Step-by-step explanation:
one days discharge at its mouth, 3 trillion gallons, could supply all of country A’s household for 5 months. how much water an average household uses each month. assume there are 200 million households
Answers
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]
miranda has cubes that measure 4 inches on each side
Answers
Could you please elaborate? Is there an equation?
Answer: What do you need to know?
Step-by-step explanation:
Jane had 275 stickers, which she gave to her friends. Each friend got five more stickers than the friend before. If the first friend got 5 stickers, how many friends got stickers from Jane?
Answers
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
Solve the equation of exponential decay. Hugo sold his car after one year for $25,000. He bought it new for $29,400. What was the rate of depreciation?
Answers
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%.
Suppose the required reserve ratio is 20 percent. A $5 million deposit allows commercial banks to create as much as
a) $25 million.
b) $5 million.
c) $10 million.
d) $1 million.
Answers
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.
Explanation: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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help please
must show work
problem 3 and problem 5
Answers
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!!!
If you vertically stretch the cubic function, F(x)=x^3, what is the equation of the new function?
A. J(x)=(1/3x)^3
B. G(x)=3x^3
C. H(x)=(3x)^3
D. K(x)=1/3x^3
Answers
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.
Explanation: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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Thanks for helping me out
Answers
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
Find the value of x in the isosceles trapezoid below?
Answers
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
What is the volume of the given prism? Round the answer to the nearest tenth of a centimeter. The figure is not drawn to scale.
NEED HELP ASAP!!!!!!!!!!!!!!!!!
Answers
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]
a tree 24 feet tall casts a shadow 12 feet long. Brad is 6 feet tall. How long is Brad's shadow? draw a diagram and solve
Answers
Answer:
3 feet long
Step-by-step explanation:
Answer: Brad's shadow is 3 feet long
Which of the following has a graph that is a straight line? Equation 1: y = 5x2 + 41 Equation 2: y = 14x5 − 4 Equation 3: y = 12x + 17 Equation 4: y4 = 2x − 1
Answers
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.
Equation 1: degree 2Equation 2: degree 5Equation 3: degree 1Equation 4: degree 4The 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.
Zach and Roger spent a total of 69 hours building a treehouse. Roger worked 9 hours less than twice the number of hours Zach worked. Which system of equations can be used to determine the number of hours Zach worked, x, and the number of hours Roger worked, y?
A.
x + y = 69
2x + y = 9
B.
x - y = 69
y = 2x + 9
C.
x + y = 69
y = 9x - 2
D.
x + y = 69
y = 2x - 9
Answers
Answer:
It is D
Step-by-step explanation:
9. A 5,000 kg train is traveling at a velocity of 100 m/s and hits another train. The two trains stick together, and the new velocity is 50 m/s. What is the mass of the second train? A. 15,000 kg B. 8,000 kg C. 10,000 kg D. 5,000 kg
Answers
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:
A triangle is drawn and then translated as shown in the diagram. Which statement is true?
A) The two triangles are congruent because all rectangles are congruent.
B) The two triangles are not congruent because a translation changes side length.
C) The two triangles are not congruent because a translation changes angle measures.
D) The two triangles are congruent because a translation does not change size and shape.
Answers
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:
A translation is a kind of rigid motions that moves a geometric figure on a xy plane by some distance in a particular direction .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.
Melinda walked 9/12 mile each day for 5 days. What was the total distance , in miles, she walked in the 5 days?
Answers
3.75 miles or 3 3/4 would be your answer
Write a polynomial that represents the area of a rectangle with side lengths of 7x-2 and 3x-5
Answers
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.
140 is decreased to 273
Answers
Is there more to the question,
Consider a student loan of $17 comma 500 at a fixed APR of 9% for 15 years.
a. The monthly payment is $_____
(round to the nearest cent as needed.)
b. The total payment over the term of the loan is $______
(Round to the nearest cent as needed.)
c. Of the total payment over the term of the loan, _____% is paid toward the principal and _____% is paid toward interest.
(Round to the nearest tenth as needed.)
Answers
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.
50 is what percent of 32?
Answers
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
Which of the following correctly describes the graph of this function?
Answers
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).
area of composite figures
68 sq. cm
92 sq. cm
72 sq. cm
96 sq. cm
72 sq. cm
90 sq. cm
Answers
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:
You are framing a picture with a frame of equal width on each side. Find the perimeter and the area of the picture including the frame when 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. what is a polynomial for the area and the perimeter. Also what is the perimeter and the area of the picture including the frame when the width of the frame is 2 inches.
Answers
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.
Given thatYou 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.
What is the perimeter?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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