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3 years ago

Solve each equation. Be sure to check for extraneous solution -7= |a-3|/-2

Mathematics

1 answer:

stepan [7]3 years ago

4 0

Answer:

a = -11, 17.

Step-by-step explanation:

-7 = |a-3| / -2

Multiply both sides by -2:

|a - 3| = 14

So a - 3 = 14

Giving a = 17

a - 3 =- -14

giving a = -11.

Checking these values:

-7 = |17-3| / -2 = 14/-2 = -7

- so a = 17 is a solution.

-7 = |-11-3| / -2 = 14/-2 = -7

so a = -11 is also a solution.

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Question D- If the area of a square is 121 square centimeters, what is its side length?

Ipatiy [6.2K]

The formula for the area of a square is the side squared, or multiplied together.

Basically, if the side length is x, the area is x*x or x^2.

We can use that to set up an equation.

x^2=121
x=square root of 121=11

Hope this helps!

3 0

3 years ago

What is the equation of a line that passes through the point (6,3) and is perpendicular to a line with a slope of -3/2

SCORPION-xisa [38]

Answer:

none of the above

Step-by-step explanation:

The perpendicular line will have a slope that is the negative reciprocal of the given slope, so it is ...

m = -1/(-3/2) = 2/3

The point-slope form of the equation of the line with slope m through point (h, k) can be written ...

y = m(x -h) +k

For this slope and the point (6, 3), the equation of the line is ...

y = (2/3)(x -6) +3

y = 2/3x -4 +3

y = 2/3x -1 . . . . . matches none of the offered choices

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The attached graph shows this equation is the one that goes through the given point.

3 0

4 years ago

Find the values of a and b so that the linear system has the given solution.

Flauer [41]

Answer:

<em>The values are a=6, b=8</em>

Step-by-step explanation:

<u>System of Equations</u>

We are given the system of equations:

ax - by = 4

bx - ay = 10

And it's known the solutions are: x=2, y=1.

Plugging in the solutions:

2a - b = 4 [1]

2b - a = 10 [2]

Now we have to solve the system above. Multiply [1] by 2:

4a - 2b = 8

Now we add with [2]:

3a = 18

a = 18/3 = 6

a = 6

From [2]:

2b - 6 = 10

2b = 16

b = 16/2 = 8

b = 8

The values are a=6, b=8

7 0

3 years ago

What value of s makes the equation true?

azamat

Answer:

-17 =s

Step-by-step explanation:

-8s +4 = -7s +21

Add 8s to each side

-8s+8s +4 = -7s+8s +21

4 = s+21

Subtract 21 from each side

4-21 = s+21-21

-17 =s

5 0

3 years ago

Read 2 more answers

The volume of water and a rectangle swimming pool can be modeled by the function v(x)=x^3+13x-210. If the depth of the pool is g

S_A_V [24]

Answer:

Required,

$L=\frac{3+\sqrt{37}}{2}-\frac{144}{x-3}$

$W=\frac{3-\sqrt{37}}{2}-\frac{144}{x-3}$

Step-by-step explanation:

Given volume and depth respectively,

$V(x)=x^3+13x-210$ and $x-3$

To find length and width of the rectanglular swiming pool we know,

Volume=length $\times$ height $\times$ depth.

Let depth=D=x-3, length=L, width=W, then

$V=DLW$

$x^3+13x-210= LW(x-3)$

$LW=\frac{x^3+13x-210}{x-3}$

After divide we will get $x^2-3x-22$ with remainder -144.

Thus,

$x^3+13x-210=(x^2-3x-22)(x-3)-144=(x-3)LW$

Now to find root of,

$x^2-3x-144=\frac{3\pm\sqrt{9+88}}{2}=\frac{3\pm \sqrt{37}}{2}$

Thus,

$L=\frac{3+\sqrt{37}}{2}-\frac{144}{x-3}$

$W=\frac{3-\sqrt{37}}{2}-\frac{144}{x-3}$

5 0

3 years ago