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3 years ago

What is the solution to this equation ? x + 12 +3x =18 - 2x

Mathematics

2 answers:

s344n2d4d5 [400]3 years ago

6 0

x+12+3x=18-2x

12+4x=18-2x

-12 +2x -12 +2x

_______________

6x=6

__ __

6 6

x=1

olasank [31]3 years ago

3 0

First, you combine like terms: x+3x=4x: 12+4x=18-2x

Second, you add the 2x to each side (inverse operation): 12+6x=18

Third, you subtract 12 from 18 to cancel out the 12 (inverse operation): 6x=6

Fourth, you divide each side by 6 to find the value of x

The answer is x=1

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What is the least common multiple of 12 and 10

gtnhenbr [62]

12 = 2*2*3

10 = 5*2

LCM = 5*3*2*2

= 15*4=60

the least common multiple is 60

4 0

4 years ago

Suppose the coefficient matrix of a linear system of four equations in four variables has a pivot in each column. Explain why th

Veseljchak [2.6K]

If the coefficient matrix has a pivot in each column, it means that it is shaped like this:

$A=\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right]$

So, the correspondant system

$Ax = b$

will look like this:

$\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right]\cdot \left[\begin{array}{c}x_1\\x_2\\x_3\\x_4\end{array}\right] = \left[\begin{array}{c}b_1\\b_2\\b_3\\b_4\end{array}\right]$

This turn into the following system of equations:

$\begin{cases}a_{1,1}x_1+a_{1,2}x_2+a_{1,3}x_3+a_{1,4}x_4=b_1\\a_{2,2}x_2+a_{2,3}x_3+a_{2,4}x_4=b_2\\a_{3,3}x_3+a_{3,4}x_4=b_3\\a_{4,4}x_4=b_4\end{cases}$

The last equation is solvable for $x_4$ : we easily have

$x_4=\dfrac{b_4}{a_{4,4}}$

Once the value for $x_4$ is known, we can solve the third equation for $x_3$ :

$x_3 = \dfrac{b_3-a_{3,4}x_4}{a_{3,3}}$

(recall that $x_4$ is now known)

The pattern should be clear: you can use the last equation to solve for $x_4$ . Once it is known, the third equation involves the only variable $x_3$ . Once

4 0

4 years ago

HELP PLEASE ASAP!!!

Bas_tet [7]

A. It's a composite function, so basically, wherever you see a p, replace it with 5t, because we are given that information. So, your answer is:
$A[p(t)] = 5t \pi 2=10t \pi$

B. Let's use the function we created, and just plug in 2 for t:
$A[p(2)] = 10(2) \pi$
$A[p(2)] = 62.83$

So, your answer is (approximately) 62.83 units².

3 0

3 years ago

Read 2 more answers

What is the equation for the line?

KonstantinChe [14]

Answer:

y=4x

Step-by-step explanation:

The line goes through the points (0, 0) and (2, 8).

You can plug these in to the slope formula, and the slope is 4

Since the line intersects the y-axis at 0, the y-intersect is 0.

Using these two pieces of information, you now know that the equation is

y=4x+0, or y=4x.

Hope this helps!

8 0

3 years ago

Read 2 more answers

PLEASE HELP ME DO THIS

gladu [14]

Answer:

Perimeter = 8x

Step-by-step explanation:

If I can see correctly, the area of the squares are x². Area is just s², so we can find one side by finding the square root of x², which is x. Now that we know that x is one side, we can count the amount of sides and multiply that number by x.

There are 8 sides, so the answer is P = 8x

8 0

3 years ago