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zaharov [31]
3 years ago
9

-3y+10=-14 Explain How To Solve The Answer.

Mathematics
2 answers:
Sonja [21]3 years ago
6 0
You want to isolate the variable 'y'.

\sf -3y+10=-14

Subtract 10 to both sides:

\sf -3y=-24

Divide -3 to both sides:

\sf y=\boxed{\sf 8}
amid [387]3 years ago
5 0
To solve -3y+10=-14, isolate variable y

In order to isolate y, move everything from the left side of the equation to the right side of the equal sign. This can be done by performing the opposite math operation than the one listed. The variable will not be transferred over to the other side.

 -3y+10=-14

Subtract 10 from the left and right side

 -3y=-24

Divide -3 from both sides in order to isolate y

 y=8


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Step-by-step explanation:

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marissa [1.9K]

Answer:

2. Eunju is right

3. x^2+5x+6 is a factor of x^4+5x^3+2x^2-20x-24.

Step-by-step explanation:

<u>Polynomial Remainder Theorem</u>

The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).

As a consequence, if a polynomial is divisible by x-a, f(a)=0.

Part 1:

Let's make:

f(x)=(x+b)^3+(x+c)^2-(b-c)

To find out if x+b is a factor of f(x), we find f(-b):

f(-b)=(-b+b)^3+(-b+c)^2-(b-c)

Operating:

f(-b)=(-b+c)^2-(b-c)

The value of f(-b) is not zero. This means Eunju is right, x+b is not a factor of f(x).

Part 2:

We must find out if x^2+5x+6 is a factor of x^4+5x^3+2x^2-20x-24 without using long division or synthetic division.

We can use the polynomial remainder theorem again, but since the factor is not in the form (x-a), we can factor it as follows:

x^2+5x+6 =(x+2)(x+3)

Now we just apply the theorem twice. If both remainders are zero, then the assumption is true.

Let's make:

f(x)=x^4+5x^3+2x^2-20x-24

Find f(-2):

f(-2)=(-2)^4+5(-2)^3+2(-2)^2-20(-2)-24

f(-2)=16-5*8+2*4+40-24 =16-40+8+40-24=0

Find f(-3):

f(-3)=(-3)^4+5(-3)^3+2(-3)^2-20(-3)-24

f(-3)=81-5*27+2*9+60-24

f(-3)=81-135+18+60-24 =0

Since both f(-2) and f(-3) are zero, x^2+5x+6 is a factor of x^4+5x^3+2x^2-20x-24.

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3 years ago
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Answer:

\sqrt{57}  = 7.5

\sqrt{26}  = 5.1

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3 years ago
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