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2 years ago

Find the shorter base of a trapezoid if the trapezoid's area is 52, its altitude is 8, and its longer basis 10.

Mathematics

1 answer:

DiKsa [7]2 years ago

8 0

Answer:

The shorter base is 3

Step-by-step explanation:

$a = \frac{(b1 + b2)}{2} \times h$

$52 = \frac{(10 + b2)}{2} \times 8$

$b2 = 3$

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Find the inverse of this matrix.<br> 1 -1 -1<br> -1 2 3 <br> 1 1 4

zheka24 [161]

Let's use Gaussian elimination. Consider the augmented matrix,

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\-1 & 2 & 3 & 0 & 1 & 0\\1 & 1 & 4 & 0 & 0 & 1\end{array}\right]$

• Add row 1 to row 2, and add -1 (row 1) to row 3:

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 2 & 5 & -1 & 0 & 1\end{array}\right]$

• Add -2 (row 2) to row 3:

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]$

• Add -2 (row 3) to row 2:

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]$

• Add row 2 and row 3 to row 1:

$\left[\begin{array}{ccc|ccc}1 & 0 & 0 & 5 & 3 & -1\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]$

So the inverse is

$\begin{bmatrix}1&-1&-1\\-1&2&3\\1&1&4\end{bmatrix}^{-1} = \boxed{\begin{bmatrix}5&3&-1\\7&5&-2\\-3&-2&1\end{bmatrix}}$

3 0

3 years ago

How is shading a grid to show 1/10 different than 1/100

gayaneshka [121]

They are very different 1/10 is equivalent to 10% and also 0.1 but 1/100 is equivalent to 1% and 0.01

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3 years ago

What number decreased by 3.5 equals to 12.7 ?

Snowcat [4.5K]

What number = x

x - 3.5 = 12.7

Isolate the x, add 3.5 from both sides

x - 3.5 (+3.5) = 12.7 (+3.5)

x = 12.7 (+3.5)

x = 16.2

16.2 is your answer

hope this helps

5 0

3 years ago

Read 2 more answers

What does r equal in 4r+5=3r

vekshin1

4r+5=3r can also be written
4r=3r-5
1r=-5

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3 years ago

Line I is parallel to line m.if the maesure of angle 6 is 75 what is the measure of angle 3

devlian [24]

Answer:

105

Step-by-step explanation:

l is parallel m so angle 3+angle 6=180

8 0

3 years ago