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3 years ago

What is the remainder when (x3 − 7x2 − 18x + 42) is divided by (x + 3)?

Mathematics

2 answers:

sertanlavr [38]3 years ago

7 0

Answer:

Step-by-step explanation:

You can use Ruffini's rule to divide x^3 − 7x^2 − 18^x + 42 by x + 3 as follows :

| 1 -7 -18 | 42

-3 | -3 30 | -36

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

| 1 -10 12 | 6

Then (x^3 − 7x^2 − 18^x + 42) : (x + 3) = (x^2 - 10x +12)*(x + 3) + 6

Vitek1552 [10]3 years ago

3 0

Look at the picture.
The remainder is 6.

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A bolt has 16-1/2 turns per inch. How many bolts would be in 2-1/2 inches?

ohaa [14]

Answer:

41 1/4

Step-by-step explanation:

Change 16 1/2 to a mixed number

16 1/2 = (2*16+1)/2 = 33/2

Change 2 1/2 to a mixed number = (2*2+1)/2 = 5/2

Multiply the turns per inch by the inches

33/2 * 5/2 =165/4

Change this back to a mixed number

4 goes into 165 41 times

41*4 = 164 there is 1 left over

41 1/4

6 0

3 years ago

Read 2 more answers

7w+5=3w-15 what is the answer

dem82 [27]

7w+5=3w-15

7w-3w=-15-5

4w=-20

w=-5

4 0

3 years ago

This question is from the similarity chapter. It would be really kind of you if you would answer this question.

katen-ka-za [31]

Answer:

a) 1650 m

b) 1677.05 m

Step-by-step explanation:

Hi there!

1) Determine what is required for the answers

For part A, we're asked for solve for the horizontal distance in which the road will rise 300 m. In other words, we're solving for the distance from point A to point C, point C being the third vertex of the triangle.

For part B, we're asked to solve for the length of the road, or the length of AB.

2) Prove similarity

In the diagram, we can see that there are two similar triangles: Triangle AXY and ABC (please refer to the image attached).

How do we know they're similar?

Angles AYX and ACB are corresponding and they both measure 90 degrees
Both triangles share angle A

Therefore, the two triangles are similar because of AA~ (angle-angle similarity).

3) Solve for part A

Recall that we need to find the length of AC.

First, set up a proportion. XY corresponds to BC and AY corresponds to AC:

$\frac{XY}{BC}=\frac{AY}{AC}$

Plug in known values

$\frac{2}{300}=\frac{11}{AC}$

Cross-multiply

$2AC=11*300\\2AC=3300\\AC=1650$

Therefore, the road will rise 300 m over a horizontal distance of 1650 m.

4) Solve for part B

To find the length of AB, we can use the Pythagorean theorem:

$a^2+b^2=c^2$ where c is the hypotenuse of a right triangle and a and b are the other sides

Plug in 300 and 1650 as the legs (we are solving for the longest side)

$300^2+1650^2=c^2\\300^2+1650^2=c^2\\2812500=c^2\\1677.05=c$

Therefore, the length of the road is approximately 1677.05 m.

I hope this helps!

3 0

3 years ago

Using the concepts of marginal social benefit and marginal social cost, explain how the optimal combination of goods can be dete

PtichkaEL [24]

Answer:

Optimal combination of goods can be determined in an economy that produces only two goods, with production of extra units of the two goods at a minimal marginal social cost. The consumption of the additional units of the two goods being produced will be benefitted by the consumers. This is known as marginal social benefit.

Step-by-step explanation:

Marginal social cost is the change in society's total cost brought about by the production of an additional unit of a good or service. It includes both marginal private cost and marginal external cost.

Marginal social benefit is the change in benefits associated with the consumption of an additional unit of a good or service. It is measured by the amount people are willing to pay for the additional unit of a good or service.

6 0

3 years ago

Samuel took out a personal loan of $13,000 at 7% simple interest. a. How much interest will he pay after 4 years? Show your work

Scorpion4ik [409]

Do 13,000x0.07=910 then do 910x4=3,640

4 0

3 years ago