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aksik [14]
3 years ago
15

A pyramid has a rectangular base with edges of length 10 and 24. The vertex of the pyramid is directly 13 units above the center

of the base. What is the surface area?
Mathematics
1 answer:
laiz [17]3 years ago
3 0

Answer:

Step-by-step explanation:

It is given that  A pyramid has a rectangular base with edges of length 10 and 24. The vertex of the pyramid is directly 13 units above the center of the base.. then The total surface area = area of rectangular base + area of 2 isosceles triangles with a base of 24 units + area of 2 isosceles triangles with a base of 10 units.

Area of rectangular base = 24{\times}10=240 sq units

The slant height of isosceles triangles with a base of 24 units =(\frac{10}{2})^{2}+(13)^{2})^\frac{1}{2}=(25+169)^{\frac{1}{2}}=13.928units.

The area of 2 isosceles triangles with a base of 24 units=\frac{2{\times}24{\times}13.928}{2}=334.281 sq units

The slant height of isosceles triangles with a base of 10 units =((12)^{2}+(13)^{2})^\frac{1}{2}=(144+169)^\frac{1}{2}=17.691 units

The area of 2 isosceles triangles with a base of 10 units=\frac{2{\times}10{\times}17.691}{2}=176.918 sq units

The total surface area of the pyramid = 240 + 334.281 + 176.918 = 591.97 sq units.

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9x−4=−1 how do i show my work for this?
AnnZ [28]

Answer:

x = 1/3

Step-by-step explanation:

9x - 4 = -1

9x = -1 + 4

9x = 3

8 0
3 years ago
Use the discriminate to determine the number and the nature of the solutions of the giving equation.
PolarNik [594]

Answer:

Since b^2 -4ac = 256 we have 2 real distinct root roots

Step-by-step explanation:

4x^2+12x=7

We need to subtract 7 to get it in the proper form

4x^2+12x-7=7-7

4x^2+12x-7=0

The discriminant is b^2 -4ac

when the equation is ax^2 +bx+c

so a =4   b=12 and c=-7

(12)^2 - 4(4)(-7)

144 +112

256

If b^2 -4ac > 0 we have 2 real distinct roots

If b^2 -4ac = 0 we have one real root

If b^2 -4ac < 0 we have two complex root

Since b^2 -4ac = 256 we have 2 real distinct root roots

7 0
3 years ago
How do I simplify these expressions?<br> 5(x+8)+3<br> 3.6x-7-5.1x<br> 4+8x+2.2-10x
Aleks04 [339]

Answer:

1. 5x +43

2. -1.5x - 7

3. 6.2 - 2x

Step-by-step explanation:

<u />

<u>Equation 1:</u>

5 (x+8) +3

First, we can distribute the 5 to the (x+8) and get 5x + 40. Distributing is when we multiply the 5 by the first number (x) and then by the second number (8) Because they aren't like terms (don't both have x's) we cannot combine then and must keep them separated by a subtraction sign

Now we have: 5x + 40 + 3

Next, we can combine the like terms. This means that any that have the same variable can be combined. So, the 5x has no other x's so he has to stay how he is. The 40 and the 3, however, can be added together to get 43.

Our finished equation is: 5x + 43

<u />

<u>Equation 2:</u>

3.6x - 7 - 5.1x

First, we can combine like terms as we learned in the last problem. This would be our x's since we have multiple.

We can add 3.6x and -5.1x and get -1.5x

Now we have: -1.5x - 7

<u />

<u>Equation 3:</u>

4 + 8x + 2.2 - 10x

We can start with either the numbers with x's or without but I'll just do the x's. So we have 8x and -10x. Adding these together would get us -2x.

Next, we can combine 4 and 2.2 and get 6.2.

Now, putting these back into our equation would look like this:

6.2 - 2x

I'm not sure how much my explanations helped, but I hope you understand!!

8 0
3 years ago
I really need help on this
Naya [18.7K]

Answer:

armani

Step-by-step explanation:

every number in the first column times 1.50 will be the number in the second column

4 0
3 years ago
A triangle has a perimeter of 24m. All 3 sides are the same length. What is the length of one side of the triangle?
Alex
The answer is 8meters
4 0
3 years ago
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