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Nata [24]
3 years ago
8

Mikaela placed a frame around a print that measures 10 inches by 10 inches. The area of just the frame itself is 69 square inche

s. What is the width of the frame?

Mathematics
1 answer:
olchik [2.2K]3 years ago
3 0

Answer:

1.5 in

Step-by-step explanation:

Let x be the width of the frame.

Side of print=10 in

Area of frame=69 square in

We have to find the width of the frame.

Side of frame=10+x+x=10+2x

Area of square=(side)^2

By using the formula

Area of print=10\times 10=100in^2

Area of frame with print=(10+2x)^2

Area of frame=Area of frame with print-Area of print

69=(10+2x)^2-100

(10+2x)^2=69+100=169

(10+2x)=\sqrt{169}=\pm 13

10+2x=13

Because Side is always positive.

2x=13-10=3

x=\frac{3}{2}=1.5

Hence, width of frame=1.5 in

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no it's an acute triangle

Step-by-step explanation:

why? because any angle below 90 degrees is considered an acute triangle which in your case 20,24, and 36 are all very far from being a right triangle

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Belle and Mabel are both 8-week-old puppies of different breeds. Belle has a mass of 12
balandron [24]

Answer:

3:1

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Take the fraction and simplify it:

12/4 = 3/1

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What is the solution of the equation?<br><br> 35√(x+2)3+3=27
Arte-miy333 [17]

Use this rule: <em>(x^a)^b = x^ab</em>

3(x + 2)^3/5 + 2 = 27

Subtract 3 from both sides

3(x + 2)^3/5 = 27 - 3

Simplify 27 - 3 to 24

3(x + 2)^3/5 = 24

Divide both sides by 3

(x + 2)^3/5 = 24/3

Simplify 24/3 to 8

(x + 2)^3/5 = 8

Take the cube root of both sides

x + 2 = 3/5√8

Invert and multiply

x + 2 = 8^5/3

Calculate

x + 2 = 2^5

Simplify 2^5 to 32

x + 2 = 32

Subtract 2 from both sides

x = 32 - 2

Simplify 32 - 3 to 30

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4 0
3 years ago
Find the area of the figure.
mariarad [96]

Answer:25

Step-by-step explanation:Count all the wholes then put all the halves and there is 25

5 0
3 years ago
Read 2 more answers
Solve dis attachment and show all work ( I got it all wrong and I want to know how to solve it )
DedPeter [7]
(a) First find the intersections of y=e^{2x-x^2} and y=2:

2=e^{2x-x^2}\implies \ln2=2x-x^2\implies x=1\pm\sqrt{1-\ln2}

So the area of R is given by

\displaystyle\int_{1-\sqrt{1-\ln2}}^{1+\sqrt{1-\ln2}}\left(e^{2x-x^2}-2\right)\,\mathrm dx

If you're not familiar with the error function \mathrm{erf}(x), then you will not be able to find an exact answer. Fortunately, I see this is a question on a calculator based exam, so you can use whatever built-in function you have on your calculator to evaluate the integral. You should get something around 0.5141.

(b) Find the intersections of the line y=1 with y=e^{2x-x^2}.

1=e^{2x-x^2}\implies 0=2x-x^2\implies x=0,x=2

So the area of S is given by

\displaystyle\int_0^{1-\sqrt{1-\ln2}}\left(e^{2x-x^2}-1\right)\,\mathrm dx+\int_{1-\sqrt{1-\ln2}}^{1+\sqrt{1-\ln2}}(2-1)\,\mathrm dx+\int_{1+\sqrt{1-\ln2}}^2\left(e^{2x-x^2}-1\right)\,\mathrm dx
\displaystyle=2\int_0^{1-\sqrt{1-\ln2}}\left(e^{2x-x^2}-1\right)\,\mathrm dx+\int_{1-\sqrt{1-\ln2}}^{1+\sqrt{1-\ln2}}\mathrm dx

which is approximately 1.546.

(c) The easiest method for finding the volume of the solid of revolution is via the disk method. Each cross-section of the solid is a circle with radius perpendicular to the x-axis, determined by the vertical distance from the curve y=e^{2x-x^2} and the line y=1, or e^{2x-x^2}-1. The area of any such circle is \pi times the square of its radius. Since the curve intersects the axis of revolution at x=0 and x=2, the volume would be given by

\displaystyle\pi\int_0^2\left(e^{2x-x^2}-1\right)^2\,\mathrm dx
5 0
3 years ago
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