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lutik1710 [3]
1 year ago
8

Divide g(x) = x^4 - 2x^3 + X + 3 by x+3

Mathematics
1 answer:
SVEN [57.7K]1 year ago
8 0

Let's first get the coefficients of the numerator: x^4 - 2x^3 + x + 3 = 1, -2, 0, 1, 3

<em>There is no x^2 in the expression, thus, the coefficient for x^2 = 0</em>

Zero of the denominator: x + 3; x = -3

Using synthetic division,

-3 I 1 -2 0 1 3

I_________________

-3 I 1 -2 0 1 3

I_________________

1

-3 I 1 -2 0 1 3

I_____-3___________

1 -5

-3 I 1 -2 0 1 3

I_____-3__15_______

1 -5 15

-3 I 1 -2 0 1 3

I_____-3__15_-45____

1 -5 15 -44

-3 I 1 -2 0 1 3

I_____-3__15_-45____

1 -5 15 -44

-3 I 1 -2 0 1 3

I_____-3__15_-45_132__

1 -5 15 -44 135

The remainder is 135. Which transforms it into 135/x+3.

Thus, the quotient of x^4 - 2x^3 + x + 3 divided by x + 3 ​is:

x-5x^2+15x\text{ - 44 + }\frac{135}{x+3}

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3 years ago
Please help me i need to solve for RS
Sonbull [250]

Answer:

<h2>         RS = 47</h2>

Step-by-step explanation:

RV=VU and SW=WT    ⇒    VW=\dfrac{RS+UT}{2}

So:

3x+5=\dfrac{2x+15+6x-37}{2}\\\\3x+5=\dfrac{8x-22}{2}\\\\3x+5=4x-11\\^{\qquad-5\qquad-5}\\3x=4x-16\\^{-4x\qquad-4x}\\-x=-16\\^{\div(-1)\quad\div(-1)}\\x=16\\\\RS=2x+15=2\cdot16+15=32+15=47

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3 years ago
Write the slope-intercept form of the equation of the line; (-5,-4) and prep. To y equals 5x plus 1
ohaa [14]

Answer:

y=-\frac{1}{5} x-5

Step-by-step explanation:

The given line is defined by:  y=5x+1, where we see that the slope is 5 and the y-intercept 1.

In order to find a line perpendicular to the given one, we need it to have a slope that is the "opposite of the reciprocal" of the given slope.

"Opposite" means it would have its sign inverted (in our case from positive to negative); and "reciprocal means that instead of 5, it would be its reciprocal: \frac{1}{5}.

We can write this new line with such slope, and try to find its y-intercept (b) by using the given condition that requires it to go through the point (-5,-4) on he plane:

y=-\frac{1}{5} x+b

we require then that when x=-5, the value of y=-4.

Therefore: -4=-\frac{1}{5} (-5)+b\\-4=\frac{5}{5} +b\\-4=1+b\\b=-4-1=-5

Then our final answer is that the new line should have the form: y=-\frac{1}{5} x-5

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Answer:

Angle EDC = Angle ADC

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ABD ~ ECD because all angles are congruent

If two are congruent, third one has to be as well since total angle is 180 each

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The cost for a pack of 7 padlocks to $23.80. Find the unit price in dollars per padlock. If necessary, round your answer to the
Galina-37 [17]

It asks to "Find the unit price in dollars per padlock"

The phrasing "dollars per padlock" is the same as "dollars per 1 padlock"

In other words, the teacher wants to know how much 1 padlock costs.

7 padlocks : $23.80

7/7 padlocks : $23.80/7 .... divide both parts by 7

1 padlock : $3.40

We see that 1 padlock costs $3.40, so the unit cost is $3.40 per padlock

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