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2 years ago

11

Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer

in descending powers of x.
(12x ^4 + 17x^ 3 + 8x - 40) ÷ (x + 2)

1 answer:

Alika [10]2 years ago

8 0

Answer:

12x^3 -7x^2 +14x -20

Step-by-step explanation:

See below for the synthetic division tableau.

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1-i need to mix 25% mineral spirits to the varnish i am using what ratio of spirit to varnish am i using? 2-if i use 240 ml of v

Ad libitum [116K]

Answer: (a) The ratio of spirit to varnish is 1 : 3

(b) You will need 80 ml of mineral spirits

(c) Ratio = 3 : 2

Step-by-step explanation: (a) If you have to mix 25% mineral spirit to the varnish as required in the question, then the whole solution would effectively contain 25 percent spirit and 75 percent varnish, giving you a hundred percent solution. To express both quantities in ratio can be done as follows;

Ratio = Spirit : Varnish

Ratio = 25 : 75

Ratio = 1 : 3

(b) Next, if you use 240 ml of varnish, this quantity would constitute 75 percent or ratio 3 out of 4 of your total solution. Therefore 240 ml of varnish can be expressed as follows;

240 : x = 3 : 4

Where x is the total solution and the right hand side (3 : 4) expresses the ratio of varnish in relation to the total solution. Hence,

240/x = 3/4

By cross multiplication you now have,

3x = 240 * 4

x = 960/3

x = 320

If x is the total solution which is 320 ml, and varnish constitutes 240 ml, then spirit equals,

Spirit = Total solution - varnish

Spirit = 320 - 240

Spirit = 80.

Therefore, you would need 80 ml of mineral spirits.

(c) Robson's tapestries all measure 1.5 m by 1 m. This can be expressed in whole numbers by first eliminating the decimal. Multiplying both dimensions by 10 results in,

1.5 (10) x 1 (10)

15 x 10

If both measurements can also be expressed as 15 m by 10 m, then reducing to the least terms would result in 3 by 2. That is,

15/5 by 10/5

3 by 2

Expressed as a ratio, this now becomes

Ratio = 3 : 2

6 0

3 years ago

Joseph needs to calculate how much grass seed he needs to cover his lawn. A diagram of his lawn is shown below. One pound of see

viktelen [127]

L x W = Area
40 x 15 = 600 square ft
So you would need 6 bags of feed
600/ 100 = 6

4 0

2 years ago

What is the measure of one angle of a regular convex 20-gon

Contact [7]

Answer:

The measure of one angle of a regular convex 20-gon is 162°

Step-by-step explanation:

* Lets explain how to solve the problem

- A convex polygon is a polygon with all the measures of its interior

angles less than 180°

- In any polygon the number of its angles equal the number of its sides

- A regular polygon is a polygon that is all angles are equal in measure

and all sides are equal in length

- The rule of the measure of an angle of a regular polygon is

$m=\frac{(n-2)180}{n}$ , where m is the measure of each interior

angle in the polygon and n is the numbers of the sides or the angles

of the polygon

* Lets solve the problem

- The polygon is convex polygon of 20 sides (20 angles)

- The polygon is regular polygon

∵ The number of the sides of the polygon is 20 sides

∴ n = 20

∵ The polygon is regular

∴ All angles are equal in measures

∵ The measure of each angle is $m=\frac{(n-2)180}{n}$

∴ $m=\frac{(20-2)180}{20}$

∴ $m=\frac{(18)180}{20}$

∴ $m=\frac{3240}{20}$

∴ m = 162

∴ The measure of one angle of a regular convex 20-gon is 162°

5 0

3 years ago

Which expression is equivalent to (5^4)^2<br> A. 25^8<br> B. 20^2<br> C. 5^8<br> D. 5^6

Yuliya22 [10]

Answer:

C. 5^8

to raise a power to another power, multiply the exponents

then multiply thr numbers

then u get 5^8

6 0

3 years ago

the initial term of arithmetic sequence is 5. The eleventh term is 125. what is the common difference of the arithmetic sequence

kap26 [50]

An arithmetic sequence starts with one number and you add the common difference to the previous term to get the current term
So...
f(x)=mx+b
m=common difference
b=starting point
f(11)=125=11m+b
-
f(1)=5=1m+b
--------
120=10m
Divide both sides by 10
12=m
Your common difference is 12.

4 0

2 years ago