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2 years ago

Find the Quotient and Remainder. 5x^3 - 6x^2 + x + 7 divided by x^2

Mathematics

1 answer:

12345 [234]2 years ago

5 0

Step-by-step explanation:

Solution

According to remainder theorem, when f(x) is divided by (x+2), Remainder =f(−2)

f(x)=5x3+2x2−6x+12

f(−2)=5(−2)3+2(−2)2−6(−2)+12

=5×−8+2×4+12+12

=−40+32=−8

∴ Remainder=−8

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3 years ago

consider the graph of the following qudratic equation. y= -x^2 -10x + 24.What is the y-value of the vertex?

3241004551 [841]

Given that the quadratic equation is $y=-x^{2}-10 x+24$

We need to determine the y - value of the vertex.

<u>The x - value of the vertex:</u>

The x - value of the vertex can be determined using the formula,

$x=-\frac{b}{2 a}$

where $a=-1, b=-10, c=24$

Substituting these values, we get;

$x=-\frac{(-10)}{2(-1)}$

Simplifying the terms, we get;

$x=-\frac{-10}{-2}$

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Thus, the x - value of the vertex is -5.

<u>The y - value of the vertex:</u>

The y - value of the vertex can be determined by substituting the x - value of the vertex ( x = -5) in the equation $y=-x^{2}-10 x+24$

Thus, we get;

$y=-(-5)^{2}-10(-5)+24$

Simplifying the values, we have;

$y=-25+50+24$

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Thus, the y - value of the vertex is 49.

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2 years ago

Find the sum: (x + 3) + (4x - 1)

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2 years ago

1. Which would be a more helpful for solving the system: adding the two equations or subtracting

ira [324]

Answer:

1) Subtracting one from the other

2) x = 0.375 and y = 0.125

Step-by-step explanation:

Equation 1 :

$\frac{2x+1}{2y}=7\\\\$

Equation 2:

$\frac{6x-1}{2y}=5$

To solve these equations by the Elimination method we multiply equation 1 with 6 and multiply equation 2 with 2 so now,

$\frac{2x+1}{2y} =7\\\\2x+1=14y\\\\Multiplying\ Equation\ 1\ with\ 6\\\\12x+6=84y$

Now for the second equation:

$\frac{6x-1}{2y}=5\\\\6x-1=10y\\\\Multiplying\ equation\ 2\ with\ 2 \\\\12x-2=20y$

Now subtracting equation 2 from equation 1

$12x+6=84y\\\\12x-2=20y\\\\Subtracting\ leads\ to\\12x-12x+6-(-2)=84y-20y\\0+8=64y\\8=64y\\8/64=y\\0.125=y$

now insert this value of y into any equation

lets insert it into equation 1

$\frac{2x+1}{2y} =7\\\\2x+1=14y\\2x+1=14(0.125)\\2x+1=1.75\\2x=1.75-1\\2x=0.75\\x=0.75/2\\x-0.375$

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3 years ago