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3 years ago

Solve for x: 2/5 (x - 4) = 2x

1 answer:

6 0

2/5 (x - 4) = 2x
2/5x - 8/5 = 2x
-2x + 2/5x = 8/5
- 8/5x = 8/5
x = -1
answer
−1
--------------------
−ax + 4b > 9
-ax > 9 - 4b
x < (9-4b)/-a
x < (-4b +9)/-a 

answer is
x < (-4b + 9) /-a
---------

$1128 - $72 = $1056

$1056 / $ 43 = 24.55

answer
Maximum 24 video games

24 (first choice)

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The sum of two consecutive odd integers is 244. What is the smaller integer?

x + x + 2 = 244
2x + 2 = 244
2x = 242
x = 121

two consecutive odd integers are 121 and 123

answer
smaller integer is 121

121 (last choice)

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Solve for XX. Assume XX is a 2×22×2 matrix and II denotes the 2×22×2 identity matrix. Do not use decimal numbers in your answer.

sveticcg [70]

The question is incomplete. The complete question is as follows:

Solve for X. Assume X is a 2x2 matrix and I denotes the 2x2 identity matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated.

$\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ · X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ =I.

First, we have to identify the matrix I. As it was said, the matrix is the identiy matrix, which means

I = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

So, $\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ · X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Isolating the X, we have

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ - $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Resolving:

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}2-1&8-0\\-6-0&-9-1\end{array}\right]$

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Now, we have a problem similar to A.X=B. To solve it and because we don't divide matrices, we do X=A⁻¹·B. In this case,

X= $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ ⁻¹· $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Now, a matrix with index -1 is called Inverse Matrix and is calculated as: A . A⁻¹ = I.

So,

$\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ · $\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$ = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

9a - 3b = 1

7a - 6b = 0

9c - 3d = 0

7c - 6d = 1

Resolving these equations, we have a= $\frac{2}{11}$ ; b= $\frac{7}{33}$ ; c= $\frac{-1}{11}$ and d= $\frac{-3}{11}$ . Substituting:

X= $\left[\begin{array}{ccc}\frac{2}{11} &\frac{-1}{11} \\\frac{7}{33}&\frac{-3}{11} \end{array}\right]$ · $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Multiplying the matrices, we have

X= $\left[\begin{array}{ccc}\frac{8}{11} &\frac{26}{11} \\\frac{39}{11}&\frac{198}{11} \end{array}\right]$

6 0

3 years ago

Side lengths: 24 in, 30 in, and 36 in

Sonja [21]

Volume of this is 25920 inches cubed

5 0

3 years ago

8. Solve X=Students & Y=Teachers X+Y=24 X=3Y

Len [333]

Answer:

x=18, y= 6

Step-by-step explanation:

if x+y=24

x= 24- y

in second case

x= 3y

24_ y = 3y

24=4y

y= 6

hence x = 24 _6 = 18

5 0

3 years ago

if a and b are the measures of two first quadrant angles and sin a = 4/9 and sin b = 2/5 find sin (a+b)

Rzqust [24]

38/45. 49+25 =( 4 × 5) + (2 × 9) 9 × 5 = 38/45

8 0

4 years ago

Read 2 more answers

#1: Solve the equation below. 5x + 7 = -3x + 31

svlad2 [7]

Answer:

x=3

Step-by-step explanation:

You can solve by:

5x+7=-3x-31

adding 3x to each side:

8x+7=31

Subtract 7 from each side:

8x=24

Divide each side by 8:

x=3

That is your answer

Hope this helps!

8 0

3 years ago

Read 2 more answers