What value, entered in the blank below, would make the two expressions equivalent? Expres

Mathematics

1 answer:

malfutka [58]3 years ago

5 0

Answer:

The value is -3

Step-by-step explanation:

Here in this question, we are interested in making the expressions on both sides of the equation equal. But we seek a particular value or number which when placed in front of the quadratic expression on the right hand side makes the equations equal.

To get this done with, we will need to factorize the expression on the left hand side of the equation.

Thus, we can write;

-27x^2 + 9x + 12 as 3(-9x^2 + 3x + 4)

What do we notice? we can see that the now factored quadratic expression resembles what we have on the right hand side asides there fact that we are not there yet in terms of sign.

Thus, we can finally write ;

-27x^2 + 9x + 12 as -3(9x^2 -3x -4)

This exactly gives the expression on the right hand side

Thus the value to place in the blank is -3

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How do you factor number 1 ?

kaheart [24]

What you did is correct.

8 0

3 years ago

Please help! im vv bad at math

aniked [119]

Answer:

Your answer is 36

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3 0

3 years ago

Can someone help me? Please and thank you!

Viefleur [7K]

The perimeter of a rectangle can be found using the formula P = 2l + 2w, where l is the length and w is the width.

Here is what we know of the rectangle:

P = 68 in
l = 3w - 2

To find the length, plug 68 for P into P = 2l + 2w, and plug 3w - 2 for l in the same formula. Then solve algebraically for w.

P = 2l + 2w
68 = 2(3w - 2) + 2w
68 = 6w - 4 + 2w
68 = 8w - 4
72 = 8w
9 = w

Now that we have w, we can plug it into 3w - 2 to find l, length.

3w - 2
3(9) - 2
27 - 2
25

That makes our length 25 inches and our width 9 inches. (Don't forget to write units!) Let's plug everything back into the formula to check our work.

68 = 2(25) + 2(9)
68 = 50 + 18
68 = 68 -- This is true

Answer:
The length of the rectangle is 25 inches.

7 0

4 years ago

The vertices of square RSTV have coordinates R(-1,5), S(-3,1), T(-7,3), and V(-5,7). What is the perimeter of RSTV?

Verizon [17]

The distance between two points (x₁,y₁),(x₂,y₂) = √[(x₂-x₁)² + (y₂-y₁)²]

let the length of the square RSTV = d
So, the perimeter of RSTV = 4 d
d is the distance RS or ST or TV or VR

RS distance between R,S
ST distance between S,T
TV distance between T,V
VR distance between V,R

R(-1,5), S(-3,1), T(-7,3), and V(-5,7)

RS = S - R = √[(-3 - -1)² + (1- 5)²] = √[(-2)² +(-4)² ]= √(4+16) = √20 ≈ 4.472

∴ The perimeter of RSTV = 4 d = 4 * 4.472 = 17.888

The attached figure represents an explanation of the problem.
we should note that:
RS = ST = TV = VR = d ≈ 4.472