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3 years ago

PLEASE HELP ASAP Create a matrix for this linear system

Mathematics

2 answers:

slavikrds [6]3 years ago

8 0

Answer: A. ( $(\frac{-10}{7} ,\frac{40}{7} ,\frac{36}{7} )$ )

Step-by-step explanation: I got this right on Edmentum.

11Alexandr11 [23.1K]3 years ago

4 0

In matrix form, the system can be expressed as

$\begin{bmatrix}1&3&2\\1&-3&4\\2&1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}26\\2\\8\end{bmatrix}$

Quick way to solve this: notice that adding the first two equations eliminates y, leaving you with

(x + 3y + 2z) + (x - 3y + 4z) = 26 + 2

2x + 6z = 28

x + 3z = 14

From the given answer choices, x has 2 possible values:

• If x = -10/7, we have

-10/7 + 3z = 14

3z = 108/7

z = 36/7 (so A is the correct answer)

• If x = -5/7, then

-6/7 + 3z = 14

3z = 104/7

z = 104/21 (which is not listed)

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What is .238 in word form

sweet-ann [11.9K]

Two hundred thirty eight thousandths. I had to seriously confirm that with multiple people (who also had only a rough idea) because you don't even use that very often if at all past elementary (unless your teacher is super strict). XD

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4 years ago

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A right triangle has leg lengths of x units and 3(x + 1) units. Its hypotenuse measures 25 units. Find the leg lengths. URGENT!

bearhunter [10]

You get the hypothenuse by doing √a²+b² = c

So....

$\sqrt{x^2+[3(x+1)]^2} = 25$

Square both terms

x² + (3x+3)² = 625

x² + 9x² + 18x + 9 - 625 = 0

10x² + 18x - 616 = 0

x₁,₂ = (-b±√Δ)/2a

Δ = b²-4ac

You call a 10, b 18 and c -616

x1,2 = (-18±√18²-4*10*-616)/2*10

x1,2 = (-18±√324+24640)/20

x1,2 = (-18±√24964)/20

x1,2 = (-18±158)/20

x1 = -18+158/20 = 140/20 = 7

x2 = (-18-158)/20 = -176/20 = -44/5

Pick the first solution

So one leg is 7 and the other is 3(7+1) = 3(8) = 24

Let's verify √24²+7² = √576+49 = √625 = 25

6 0

3 years ago

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The perimeter of a triangle is 510 feet and the sides are in the ratio of 11:16:24. Find the area of the triangle

Nutka1998 [239]

If the sides are in the ratio of 11:16:24, it means that they are all multiples of a same number x, according to these factors.

So, the shorter side is 11x feet long, the middle one is 16x feet long, and the longest side is 24x feet long.

This means that the perimeter is

$11x+16x+24x = 51x$ feet long. But we know that this is 510 feet, so we have

$51x = 510 \implies x = \cfrac{510}{51} = 10$ .

So, the three sides are 110, 160 and 240 feet long.

To find the area of a triangle knowing its three sides, you can use Heron's formula, which states that, if $s$ is half the perimeter of the triangle whose sides are $a,b,c$ , the area $A$ is given by

$A = \sqrt{s(s-a)(s-b)(s-c)}$

In our case, $s = 255, a = 110, b = 160, c = 240$ so the formula becomes

$A = \sqrt{255(255-110)(255-160)(255-240)} = \sqrt{255(145)(95)(15)} = \sqrt{52689375} \approx 7258.74$

5 0

4 years ago

How to solve number 4

s2008m [1.1K]

Find the first semicircle area
Area semicircle can be determined by dividing the full area of circle by 2.
The first semicircle radius is 5 cm
semicircle area = 1/2 circle area
semicircle area = 1/2 × π × r²
semicircle area = 1/2 × 3.14 × 5²
semicircle area = 1/2 × 3.14 × 25
semicircle area = 39.25 cm²

Find the second semicircle area
Because the dimension of the second semicircle is congruent to the first semicircle, they have similar area measurement, 39.25 cm².

Find the quarter circle area
The area of quarter circle can be determined by dividing the full area of a circle by 4.
q circle = 1/4 × area of circle
q circle = 1/4 × π × r²
q circle = 1/4 × 3.14 × 10²
q circle = 1/4 × 314
q circle = 78.5 cm²

To find the entire area, add the area above together
area = first semicircle + second semicircle + q circle
area = 39.25 + 39.25 + 78.5
area = 157

The area of shaded region is 157 cm²

4 0

4 years ago

A line is drawn through (–7, 11) and (8, –9). The equation y – 11 = y minus 11 equals StartFraction negative 4 Over 3 EndFractio

yaroslaw [1]

⇒Given equation of line Passing through (–7, 11) and (8, –9) is given by

$y-11= \frac{-4}{3}(x+7)$

⇒Equation of line Passing through (–7, 11) and (8, –9) is given by

$\rightarrow \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\rightarrow \frac{y-11}{x-(-7)}=\frac{-9-11}{8-(-7)}\\\\\rightarrow \frac{y-11}{x+7}=\frac{-20}{15}\\\\\rightarrow \frac{y-11}{x+7}=\frac{-4}{3}\\\\\rightarrow 3y-33=-4x-28\\\\\rightarrow 4x+3y=33-28\\\\ \rightarrow 4x+3y=5$

Option C

4x+3y=5

6 0

3 years ago

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