Find the perimeter of the image

Mathematics

1 answer:

goblinko [34]3 years ago

3 0

Answer:

4x³ + 14x² + 8x + 6

Step-by-step explanation:

Perimeter = 2(L + W) = 2(7x² + 4x + 3 + 2x³) = 14x² + 8x + 6 + 4x³

4x³ + 14x² + 8x + 6

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Find the distance between the points ( 5, -2) and (-1, -8)

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Step-by-step explanation:

the expression could help you find the distance between A(x; y) and B(x',y')is:

AB = √((x-x')²+(y-y')²)

in this exercise : x = 5

x' = - 1

y =-2

y' = -8

continue .......

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What is the volume of this prism??

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3 years ago

How do i solve this ?

Murljashka [212]

You can choose a couple of the x-values and plug each into all of the x's in each equation on the right. Then see which equations give the y-values equal to the y's adjacent to the 3 x-values you used. I chose x=-4 and x=8. Only the 2nd, 3rd, and 5th equations matched with both.

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3 years ago

1. The prism-shaped roof has equilateral triangular bases. Create an equation that models the height of one of the roof's triang

Mandarinka [93]

1. Check picture 1. Let the one side of the triangle be a, drop one perpendicular, CD. Then triangle ADB is a right triangle, with hypothenuse a and one side equal to 1/2a. By the Pythegorean theorem, as shown in the picture, the height is $\frac{ \sqrt{3} }{2} a$

2. if a a=25 ft, then the height is $\frac{ \sqrt{3} }{2} a=\frac{ \sqrt{3} }{2} *25= \frac{1.732}{2}*25= 21. 7$ (ft)

3. consider picture 2. Let the length of the roof be l feet.

one side of the prism (the roof) is a rectangle with dimensions a and l, so the area of one side is a*l
the lateral Area of the roof is 3a*l

the area of the equilateral surfaces is $2*( \frac{1}{2} *a* \frac{ \sqrt{3} }{2}a )=\frac{ \sqrt{3} }{2} a^{2}$

so the total area of the roof is $\frac{ \sqrt{3} }{2} a^{2} +3al$

4. The total area was the 2 triangular surfaces + the 3 equal lateral rectangular surfaces. Now instead of 3 lateral triangular surfaces, we have 2.
So the total area found previously will be decreased by al

5. so the area now is $\frac{ \sqrt{3} }{2} a^{2} +2al$

6. now a=25 and l=2a=50

Area= $\frac{ \sqrt{3} }{2} a^{2} +2al=\frac{ \sqrt{3} }{2} * 25^{2}+2*25*50=25 ^{2} (\frac{ \sqrt{3} }{2} +4)=625*4.866$

=3041.3 (ft squared)