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ivann1987 [24]
2 years ago
5

Abygail is building a dollhouse. She has boards that are two different lengths. One long board is 10 inches longer than the tota

l length of three of the short boards.
If one of the long boards is 37 inches long, how long is a short board?
Mathematics
1 answer:
nikitadnepr [17]2 years ago
7 0

Answer:

9 in

Step-by-step explanation:

a short bored is 9 in

37-10=27

27÷3=9

So that means a short bored is 9 in

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All the edges of a regular square pyramid have length 8. find the Volume of the pyramid, Lateral area of the pyramid and the Tot
RUDIKE [14]

Answer:

V = 120.6796

LA = 110.8513

SA = 174.8513

Step-by-step explanation:

Let me know if you need more of an explanation for any of these

First we need the height, one way to find that out is to use the diagonal of the  and one of the diagonal edges of the pyramid.  Specifically we will need half of the diagonal of the square.  We will call the diagonal of the square d.

8^2+8^2=d^2\\d=\sqrt{64+64} \\d=\sqrt{128}

Gonna leave it like that for ease of writing.  So then half of the diagonal is \frac{\sqrt{128}}{2}

The height, h, will be (\frac{d}{2})^2+h^2 = 8^2.  Plugging everything in gets us h=\sqrt{32}

last, we need to find slant height, which we will call s.

(\frac{8}{2})^2+h^2 = s^2\\s=\sqrt{48}

s is also the height of the triangles for purposes of finding area.  Now for the volume and areas.

Volume is area of the base times height divided by 3, so V=8^2\frac{\sqrt{32} }{3}  = \frac{64\sqrt{48} }{3} = 120.6796

Lateral area is the sum of the four areas of the triangles, and each of those are \frac{8*h}{2} so the whole lateral area is 4 times that.  So we get 4\frac{8\sqrt{32} }{2} =110.8513

Total surface area is the lateral surface area + the area of the base, so 110.8513 + 64 = 174.8513

6 0
3 years ago
Determine the center and radius: x2 + y2 - 10x + 8y -8 = 0​
Kipish [7]

So our equation currently is ⇒ x^2+y^2-10x+8y-8 = 0

<u>Let's first move all the constant to one side and group 'like variables' together</u>:

      (x^2-10x)+(y^2+8y) = 8

<u>Now lets complete the square of both equations</u>

    (x^2-10x+25)+(y^2+8y +16) = 8 + 25 + 16\\(x-5)^2+(y+4)^2 = 49\\(x-5)^2+(y+4)^2 = 7^2

<u><em>Now we know the circle's general equation format is</em></u>:

   ⇒(x-h)^2+(y-k)^2 = r^2

  • (h, k) ⇒ coordinate of the center of the circle
  • r ⇒ length of radius of circle

<u>Thus the radius of the circle is 7</u>

<u></u>

Hope that helps!

7 0
2 years ago
50 POINTS. A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t)=
Morgarella [4.7K]

Answer:

The domain that makes sense for this function is all values greater than or equal to 0.

Step-by-step explanation:

A ball is thrown into the air from a height of 4 feet at time <em>t</em> = 0. It is modeled by the function:

h(t)=-16t^2+64t+4

The domain of the function is time <em>t</em>. The range of the function is the ball's height in the air <em>h</em>.

Since time is our domain, we must restrict our domain to values equal to or greater than 0 since time cannot be negative.

Therefore, the domain that makes sense for this function is all values greater than or equal to 0.

In interval notation, this is:

[0, \infty)

And as an inequality:

t\geq 0

7 0
3 years ago
Read 2 more answers
F(x)= (x-2)(x-3)(x-5) simplify the right side. What is the equation?
Serga [27]

Answer:

x³ - 10x² + 31x - 30

Step-by-step explanation:

Given

(x - 2)(x - 3)(x - 5) ← expand the second pair of factors using FOIL

= (x - 2)(x² - 8x + 15) ← distribute

= x³ - 8x² + 15x - 2x² + 16x - 30 ← collect like terms

= x³ - 10x² + 31x - 30

5 0
3 years ago
If 15 percent of the sixth graders have blonde hair, and there are 120 sixth graders, how many of them have blonde hair?
Vlada [557]
15/100 = 0.15 x 120 = 18
8 0
3 years ago
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