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zzz [600]
3 years ago
9

A formula for finding SA, the surface area of a rectangular prism, is

Mathematics
1 answer:
lakkis [162]3 years ago
3 0

Step-by-step explanation:

SA=2*(12*6+12*4+6*4)

SA=2*(72+48+24)

SA=2*144

SA=288

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PLEASEEE EXPLAIN AND HELP
Firdavs [7]

The length of the unknown sides of the triangles are as follows:

CD = 10√2

AC = 10√2

BC =  10

AB = 10

<h3>Triangle ACD</h3>

ΔACD is a right angle triangle. Therefore, Pythagoras theorem can be used to find the sides of the triangle.

  • c² = a² + b²

where

c = hypotenuse side = AD = 20

a and b are the other 2 legs

lets use trigonometric ratio to find CD,

cos 45 = adjacent / hypotenuse

cos 45 = CD / 20

CD = 1 / √2 × 20

CD = 20 / √2 = 20√2 / 2 = 10√2

20² - (10√2)² = AC²

400 - 100(2)  = AC²

AC² = 200

AC = √200 = 10√2

<h3>Triangle ABC</h3>

ΔABC is a right angle triangle too. Therefore,

  • AB² + BC² = AC²

Using trigonometric ratio,

cos 45 = BC / 10√2

BC = 10√2 × cos 45

BC = 10√2 × 1 / √2

BC = 10√2 / √2 =  10

(10√2)² - 10² = AB²

200 - 100 = AB²

AB² = 100

AB = 10

learn more on triangles here: brainly.com/question/24304623?referrer=searchResults

5 0
2 years ago
Ms. Skeen bought 3 pounds of candy for the Christmas party. There was a total of 147 pieces of candy. She wants to divide it amo
ohaa [14]

The 3 lbs of candy is irrelevant, so we can discard that. All you need to do is divide 147 by 26, which is 5.65 pieces of candy. Each student will get 5 pieces, with a few left over.

5 0
2 years ago
A rectangular piece of metal is 25 in longer than it is wide. Squares with sides 5 in long are cut from the four corners and the
Licemer1 [7]

Answer:

The original length was 41 inches and the original width was 16 inches

Step-by-step explanation:

Let

x ----> the original length of the piece of​ metal

y ----> the original width of the piece of​ metal

we know that

When squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an open box

The dimensions of the box are

L=(x-10)\ in\\W=(y-10)\ in\\H=5\ in

The volume of the box is equal to

V=(x-10)(y-10)5

V=930\ in^3

so

930=(x-10)(y-10)5

simplify

186=(x-10)(y-10) -----> equation A

Remember that

The piece of metal is 25 in longer than it is wide

so

x=y+25 ----> equation B

substitute equation B in equation A

186=(y+25-10)(y-10)

solve for y

186=(y+15)(y-10)\\186=y^2-10y+15y-150\\y^2+5y-336=0

Solve the quadratic equation by graphing

using a graphing tool

The solution is y=16

see the attached figure

Find the value of x

x=16+25=41

therefore

The original length was 41 inches and the original width was 16 inches

3 0
3 years ago
The length of a rectangle is 1 foot less than twice the width. If the area is 45 ft2, find the length and width.
STatiana [176]
A) Width = 9/2, length = 10

Rectangle area = length(l)x width(w)

9/2 = 4.5

4.5(l) x 10(w) = 45ft
8 0
2 years ago
Describe the process of rewriting the expression Please Help
Mazyrski [523]

Answer:

x^{\frac{21}{4} }

Step-by-step explanation:

Given expression is:

(\sqrt[8]{x^7} )^{6}

First we will use the rule:

\sqrt[n]{x} = x^{\frac{1}{n} }

So for the given expression:

\sqrt[8]{x^{7}}=(x^{7} )^{\frac{1}{8} }

We will use tha property of multiplication on powers:

=x^{7*\frac{1}{8} }

= x^{\frac{7}{8} }

Applying the outer exponent now

(x^{\frac{7}{8} })^6

= x^{\frac{7}{8}*6 } \\= x^{\frac{42}{8} }\\= x^{\frac{21}{4} }

8 0
2 years ago
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