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3 years ago

What is the remainder when 3 is synthetically divided into the polynomial -x^2+5x-9

Mathematics

2 answers:

Maurinko [17]3 years ago

8 0

-3 is the remainder when you synthetically divide

nata0808 [166]3 years ago

8 0

Answer:

REmainder is -3

Step-by-step explanation:

find remainder when 3 is synthetically divided into the polynomial -x^2+5x-9

In synthetic division we write all the coefficient of the polynomial and divide by 3

3 -1 5 -9

0 -3 6

-------------------------------

-1 2 -3 ----> Remainder

So the remainder is -3

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In the figure, angle D measures 31° and angle A measures 27

patriot [66]

The acute angles of a right triangle are complementary, so:

$m\angle B=90-27=\boxed{63^{\circ}}\\m\angle F=90-31=\boxed{59^{\circ}}$

3 0

2 years ago

What is 28- 12.5% decrease???

OLEGan [10]

Ok so I assume
28 and decreased by 12.5%

percent means partst out of 100 so
12.5%=12.5/100=0.125
first find 12.5% of 28 then subtract
0.125 times 28=3.5
decrease
28-3.5=24.5

answer is 24.5

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3 years ago

5. The combined perimeter of a circle and a square is 16. Find the dimensions of the circle and square

Tanya [424]

The dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively

Represent the side length of the square with s, and the radius of the circle with r.

So, the perimeter (P) and the area (A) of the shape are:

$P =4s + 2\pi r$

$A =s^2 + \pi r^2$

The perimeter is 16. So, we have:

$4s + 2\pi r = 16$

Divide through by 4

$s + 0.5\pi r = 4$

Make s the subject

$s = 4 - 0.5\pi r$

Substitute $s = 4 - 0.5\pi r$ in $A =s^2 + \pi r^2$

$A = (4 - 0.5\pi r )^2 + \pi r^2$

Expand

$A = 16 - 4\pi r + 0.25(\pi r)^2 + \pi r^2$

This gives

$A = 16 - 4\pi r + (0.25\pi^2 + \pi )r^2$

Differentiate with respect to r

$A' = 0 - 4\pi + 2(0.25\pi^2 + \pi )r$

$A' = - 4\pi + 2(0.25\pi^2 + \pi )r$

Set to 0

$- 4\pi + 2(0.25\pi^2 + \pi )r =0$

Add 4pi to both sides

$2(0.25\pi^2 + \pi )r =4\pi$

Divide both sides by 2

$(0.25\pi^2 + \pi )r =2\pi$

Make r the subject

$r =\frac{2\pi}{(0.25\pi^2 + \pi )}\\$

Factor out pi

$r =\frac{2\pi}{\pi(0.25\pi + 1 )}$

Cancel out the common factors

$r =\frac{2}{0.25\pi + 1 }$

Express pi as 3.14

$r =\frac{2}{0.25\times 3.14 + 1 }$

$r =\frac{2}{1.785}$

Divide

$r =1.12$

Recall that:

$s = 4 - 0.5\pi r$

This gives

$s =4 -0.5 \times \pi \times 1.12$

This gives

$s =4 -0.5 \times 3.14 \times 1.12$

$s =2.24$

Hence, the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively

Read more about minimum areas at:

brainly.com/question/6427280

5 0

3 years ago

Dave receives a salary of $200 a week plus a commission of 10% of his weekly sales. An equation y=mx+b represents Dave’s weekly

eduard

Answer:
Dave makes $350

Explanation:
In order to find this answer, we must first establish the equation for his earnings.
We use slope intercept form:
y = mx + b,
where m = slope and b = y-intercept.

Since the problem states that his commission percentage is the slope and his base salary is the y-intercept, we can use them in the equation to get the following: 
y = 0.1x + 200.

Now knowing that the x is the amount he sells, we can use the $1500 as x to find his total pay for the week:.
y = 0.1(1500) + 200,
y = 150 + 200,
y = 350.

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3 years ago

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Given the point (5,6) and the slope of 5, find y when x=21

TEA [102]

If slope is 5, 5.(x-5)=y-6 so 5x-y-19=0. When x=21, y=86.

4 0

3 years ago

Read 2 more answers