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2 years ago

What is the remainder when a^3 - 4 is divided by a+2? a)0 b)-6 c)-2 d)-12

Mathematics

1 answer:

antoniya [11.8K]2 years ago

6 0

Answer:

<em>The remainder is -12. Choice d)</em>

Step-by-step explanation:

<u>The Remainder Theorem</u>

The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-r) is equal to f(r).

We have the polynomial

$P(a)= a^3 - 4$

To evaluate the remainder when P is divided by a+2, we only have to find P(-2):

$P(-2)= (-2)^3 - 4$

$P(-2)= -8 - 4=-12$

The remainder is -12. Choice d)

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A rectangular yard is 20 feet by 15 feet. The yard Is covered with grass except for an 8.5 feet. Square flower garden. How much

stich3 [128]

Answer: $227.75\ ft^2$

Step-by-step explanation:

<h3> The complete exercise is: "A rectangular yard is 20 ft by 15 ft. The yard is cover with grass except for 8.5 feet square flower garden. How much grass is in the yard?"</h3><h3 />

The area of a rectangle can be calculated with the following formula:

$A=lw$

Where "l" is the lenght of the rectangle and "w" is the width.

Based on the data given in the exercise, you can identify tha the length and the width of the rectangular yard are:

$l=20\ ft\\\\w=15\ ft$

Then, you can substitute these values into the formula and then evaluate in order to find the area of the entire yard:

$A_y=(20\ ft)(15\ ft)=\\\\A_y=300\ ft^2$

The area of the flower garden which is an square, can be calculated with this formula:

$A=s^2$

Where "s" is the side length.

In this case you know that:

$s=8.5\ ft$

Then the area of the flower garden is:

$A_g=(8.5\ ft)^2\\\\A_g=72.25\ ft^2$

<em> </em>Since this is not covered with grass, you need to subtract both areas calculated above in order to find the surface covered with grass in the yard.

This is:

$A_g=300\ ft^2-72.25\ ft^2\\\\A_g=227.75\ ft^2$

4 0

3 years ago

Help me with this test in math please!! (questions in images)

irga5000 [103]

Answer:

Step-by-step explanation:

There is no slope because it is a strait vertical line.

8 0

2 years ago

Read 2 more answers

There are 60 feet between the bases on a softball diamond. How far does a catcher throw drone home plate to second base

mixas84 [53]

Answer: $12\sqrt{5}$

Required theorem:

Pythagorean theorem = $a^2 + b^2=c^2$

In other words, one side length squared + another side length squared = the middle lined squared.

Step-by-step explanation:

$60^2+60^2 = c^2\\\\360+360=c^2\\\\720=c^2\\\\\ \sqrt{c^2} =\sqrt{720}\\\\c=+/- 12\sqrt{5}$

We can only have a positive distance so your final answer is :

$12\sqrt{5}$

3 0

1 year ago

Jake’s measures the height of a tree to be 74 3/8

goblinko [34]

I'm assuming the question is asking how tall the tree is if it has grown 2 3/4 inches.

The initial height of the tree is 74 3/8 inches and it grows 2 3/4 inches after six months. We can add these two numbers together to calculate the height of the tree now.

$74\frac{3}{8} + 2\frac{3}{4}$

Since these are both mixed numbers, we must find a common denominator to add our fractions. 8 is the lowest common denominator for 4 and 8. So:

$74\frac{3}{8} + 2\frac{6}{8}$

We can now add our whole numbers up (74 + 2) and add the numerators of the fractions together to get a single fraction ( $\frac{3}{8} + \frac{6}{8}$ ).

74 + 2 = 76

$\frac{3}{8} + \frac{6}{8} = \frac{9}{8}$

Putting these two together, we get $76 \frac{9}{8}$ , which is equal to $77\frac{1}{8}$ .

We can also turn this answer into an improper fraction. This is done by multiplying the whole number by the denominator and adding the numerator. So in this case:

77 x 8 = 616

616 + 1 = 617

The denominator stays the same, so our answer as an improper fraction would be $\frac{617}{8}$ .

So the tree is $77\frac{1}{8}$ inches tall, or $\frac{617}{8}$ inches tall.

7 0

2 years ago

I need help ASAP!!!<br><br><br> g(x) = x2 - 2x2 + x<br> g(3) =

Art [367]

Answer:

-6

Step-by-step explanation:

put the value of x=3 in the equation g(x)

7 0

3 years ago