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4 years ago

Solve for x 2 ( x − 5 ) = 6 x − ( x − 8 )

Mathematics

1 answer:

fredd [130]4 years ago

7 0

Answer:

-6

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2(x−5)=6x−(x−8)

2(x−5)=6x+−1(x−8) (Distribute the Negative Sign)

2(x−5)=6x+−1x+(−1)(−8)

2(x−5)=6x+−x+8

(2)(x)+(2)(−5)=6x+−x+8 (Distribute)

2x+−10=6x+−x+8

2x−10=(6x+−x)+(8) (Combine Like Terms)

2x−10=5x+8

Step 2: Subtract 5x from both sides.

2x−10−5x=5x+8−5x

−3x−10=8

Step 3: Add 10 to both sides.

−3x−10+10=8+10

−3x=18

Step 4: Divide both sides by -3.

−3x

−3

x=−6

Answer:

x=−6

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Question 5 (5 points)

Tpy6a [65]

Answer:

The solution of the system of equations is, (1,-1,2)

Step-by-step explanation:

Given system equation;

x + 5y - 3z = -10

-5x + 6y – 5z = -21

-x + 8y - 8z = -25

Matrix form is written as;

$\left[\begin{array}{ccc}1&5&-3\\-5&6&-5\\-1&8&-8\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}-10\\-21\\-25\end{array}\right] \\\\\\det. = 1\left[\begin{array}{cc}\\6&-5\\8&-8\end{array}\right] -5\left[\begin{array}{cc}\\-5&-5\\-1&-8\end{array}\right] -3\left[\begin{array}{cc}\\-5&6\\-1&8\end{array}\right] \\\\\\det. = 1(-8) -5(35)-3(-34)= -8 - 175+ 102 = -81$

Cofactor;

$First \ row \left[\begin{array}{cc}+\\ 6&-5\\\ 8&-8\end{array}\right \left\begin{array}{cc}-\\ -5&-5\\-1&-8\end{array}\right \left\begin{array}{cc}+\\-5&6\\-1&8\end{array}\right] = [-8 \ \ -35 \ \ -34]\\\\\\\ Second \ row \left[\begin{array}{cc}-\\ 5&-3\\\ 8&-8\end{array}\right \left\begin{array}{cc}+\\ 1&-3\\-1&-8\end{array}\right \left\begin{array}{cc}-\\1&5\\-1&8\end{array}\right] = [16\ \ -11 \ \ -13]\\\\\\$

$Third \ row \left[\begin{array}{cc}+\\ 5&-3\\\ 6&-5\end{array}\right \left\begin{array}{cc}-\\ 1&-3\\-5&-5\end{array}\right \left\begin{array}{cc}+\\1&5\\-5&6\end{array}\right]= [-7 \ \ 20\ \ 31]$

$Cofactor =$ $\left[\begin{array}{ccc}-8&-35&-34\\16&-11&-13\\-7&20&31\end{array}\right]$

$inverse \ matrix =-\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] \\\\\\$

Solution of the matrix:

$\left[\begin{array}{c}x\\y\\z\end{array}\right] = -\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] X \left[\begin{array}{c}-10\\-21\\-25\end{array}\right] = \left[\begin{array}{c}\frac{-8*-10 }{-81 } +\frac{16*-21 }{-81 } + \frac{-7*-25 }{-81 }\\\\\frac{-35*-10 }{-81 } +\frac{-11*-21 }{-81 }+ \frac{20*-25 }{-81 }\\\\\frac{-34*-10 }{-81 }+ \frac{-13*-21 }{-81 }+ \frac{31*-25 }{-81 }\end{array}\right] \\\\\$

$\left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}\frac{-81}{-81} \\\\\frac{81}{-81} \\\\\frac{-162}{-81} \end{array}\right] = \left[\begin{array}{c}1\\-1\\2\end{array}\right]$

Therefore, the correct option is (1,-1,2)

5 0

3 years ago

One cubic centimeter of sand weighs 1.9 grams. Find the amount of sand that the sandcastle bucket can hold.

satela [25.4K]

Answer:

5198.4 grams of sand

Step-by-step explanation:

The bottom cube:

12*12*13= 144*13= 1872

The top pyramid:

144*6= 864

1872+864= 2736 cubic cm

THEN

2736*1.9= 5198.4 g of sand!

Brainliest plsss

4 0

3 years ago

Solve 0.21 x 2 = ________. Use the model to help you find the product. (1 point)

Nadusha1986 [10]

Answer:

0.42

Step-by-step explanation:

3 0

3 years ago

Simplify 25/12th in fraction

Nimfa-mama [501]

25/12 is already simplified. We can however convert it into a mixed number from an improper fraction.

$\frac{25}{12} = \frac{24+1}{12} = \frac{24}{12} + \frac{1}{12} = 2+ \frac{1}{12} =\boxed{\bf{2 \frac{1}{12} }}$

25/12 as a mixed number is 2 1/12.

8 0

3 years ago

If sin 115° ≈ 0.91 and cos 115° = -0.42, then sin -115° =

EastWind [94]

Answer:

sin -115° = -0.91

Step-by-step explanation:

Point A is (cos 115°, sin 115°). Since cos 115° = -0.42 and sin 115° ≈ 0.91, it means that the coordinates at point A is (-0.42, 0.91).

As for point B which was revolved around -115°,

the coordinates will be similar to point A but you just have to change the negative.

B(cos -115°, sin -115°) = B(0.42, -0.91)

3 0

3 years ago