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3 years ago

What is the length of a diagonal brace that could be used for a wall 9 feet high and 12 feet long

1 answer:

5 0

You use the pythagorean theorem to solve this problem. The theorem is a^2+b^2=c^2, where c^2 is the length of the hypotenuse of the triangle, or the side that's the longest and is opposite the right angle of the right triangle. Note that this theorem is applicable because a wall has right angles and it is assumed that the diagonal brace would form a right triangle (the diagonal brace is the hypotenuse). Next, you substitute the values of 9 and 12 for a and b, and then you proceed to solve this algebraically to get c after taking the square roots of both sides of the equation to get c from c^2.

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2. Solve the system of equations. Write your answer in parametric vector notation. X, +5x2 + 4x3 + 3x4 +9xs = 18 2x, +6x2 + 4x3

ratelena [41]

Answer:

The system is inconsistent.

Step-by-step explanation:

The system is

$x_1+5x_2+4x_3+3x_4+9x_5=18\\2x_1+6x_2+4x_3+6x_4+6x_5=28\\3x_1+7x_2+4x_3+10x_4+x_5=41\\4x_1+6x_2+2x_3+7x_4+4x_5=29$

The associated matrix to the system is

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\2&6&4&6&6&28\\3&7&4&10&1&41\\4&6&2&7&4&29\end{array}\right]$

Now we use row operations to find the echelon form of the matrix:

1. We substract to row 2, two times the row 1.

We substract to row 3, three times the row 1.

We substract to row 4, four times the row 1 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&-4&-4&0&-12&-8\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

2. We multiply the second row of the preview step by -1/4. We obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

We add to row 3, eight times the row 2.

We add to row 4, fourtheen times the row 2 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&-5&10&-155\end{array}\right]$

4. We add to row 4 of the preview step, five times the row 3 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&0&0&-140\end{array}\right]$

Using backward substitution we have that

$0x_5=-140$ , then $0=-140$ and this is absurd. Then The system is inconsistent.

4 0

4 years ago

The chorus has 30 members. What expression represents the number of ways a group of 6 members can be chosen to do a special perf

RoseWind [281]

The problem uses the concept of Combination where there are number of members chosen from a group and there order is not important. Thus, the expression that would best describe the given above is 30C6 which means the combination of 30 taken 6. The numerical value for this is 593775.

8 0

3 years ago

Read 2 more answers

And rates: word problems ZB9

asambeis [7]

Answer:

10 mins

Explanation:

Because it takes 2 minutes to fill a 30 gal pool, and 150/30=5, 2 x 5 = 10 giving you the answer of 10 mins to fill a 150 gal pool.

6 0

3 years ago

Simplify 8x - 3 (4x -2)

mash [69]

Answer:

-4x+5

Step-by-step explanation:

use FOIL

3 0

3 years ago

PO<br> What is the slope of a line that goes through the following 2 points?<br> (-12,-5) (0, -8)

balandron [24]

Answer:

-1/4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-8-(-5))/(0-(-12))

m=(-8+5)/(0+12)

m=-3/12

simplify

m=-1/4

Please mark me as Brainliest if you're satisfied with the answer.

3 0

3 years ago