MATHEMATICS HIGH SCHOOL

1. what is the GCF of the terms of 8c^3+12c^2+10c? A.2
B.4
C.2c
D.4c


2. How can the polynomial 6d^4+9d^3-12d^2 be factored l?

Answers

Answer 1
Answer:

Answer:

1. C. 2c

2. 3d^2(2d^2+3d-4)

Step-by-step explanation:

A. We have been given an expression and we are asked to find the GCF of our given expression.

8c^3+12c^2+10c

Let us find factors of each of our given terms.

Factors of c^3 are c*c*c,

Factors of c^2 are c*c,

We can see that c is the greatest common factor of c^3, c^2 and c.

Factors of 8 are: 1, 2, 4, 8.

Factors of 12 are: 1, 2, 3, 4, 6, 12.  

Factors of 10 are: 1, 2, 5, 10.

The greatest common factor of 8,12 and 10 is 2.

So let us factor out 2c from our expression.

2c(4c^2+6c+5)

Therefore, the greatest common factor of our given expression is 2c and option C is the correct choice.

2. We have been given a polynomial and we are asked to factor our given polynomial.

6d^4+9d^3-12d^2

We will pull out the greatest common factor of the terms of our given polynomial.

We can see that GCF of d^4, d^3 and d^2 is d^2.

The GCF of 6, 9 and 12 is 3.

So let us factor out 3d^2 from our polynomial.

3d^2(2d^2+3d-4)

Therefore, the factored form of our given polynomial is 3d^2(2d^2+3d-4).
Answer 2
Answer: If you pay attention 2 goes into 8, 10, & 12 and it looks like they all have one C. So what do you think it is lol?(:

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What is the next term for the given arithmetic sequence?-3, -2.25, -1.5, -0.75, ...

A -0.25

B 0

C 0.75

Answers

the next term is formed by adding 0.75

Answer:

the next term for the given arithmetic sequence would be B) 0

Y varies directly as x , y= 25 when x=5. Determine y when x= 13

Answers

Answer:

y = 65 when x = 13

Step-by-step explanation:

Here we have a proportion problem.

Y varies directly as x means that y equals the product of x and a constant

Let’s say our constant is k

Thus;

y = kx

now, k = y/x

Using the initial values;

k = 25/5 = 5

Now we want to get y when x = 13

Recall; y = kx

Thus using the value of k earlier calculated;

y = 13 * 5

y = 65

6 to the 2nd power ÷ 2(3) + 4

Answers

For this case we have the following expression:
 "6 to the 2nd power ÷ 2(3) + 4"
 Rewriting the expression in algebraic form we have:
 (6^2)/(2(3)+4)
 Rewriting the numerator we have:
 (36)/(2(3)+4)
 Rewriting the denominator we have:
 (36)/(6+4)
 (36)/(10)
 (18)/(5)
 Dividing both numbers we have:
 (18)/(5) = 3.6
 Answer:
 The result of the given expression is: 
 (6^2)/(2(3)+4)=3.6
6 to the second power means 6²

So,

6² ÷ 2 ( 3 ) + 4
 
=36/2(3)+4

=(18)(3)+4

=54+4

=58

Polygon ABCDE is dilated by a scale factor of 3 with the center of dilation at the origin to create polygon A'B'C'D'E'. If the endpoints of BC are B(3, 5) and C(5, 10), what is the slope of B'C'?

Answers

Answer;

slope = 5/2

Solution and Explanation;

-Polygon which is dilated by a scale factor of 3.

The endpoints of BC are B (3,5) and C (5,10) .

The image of B and C under the dilation will be;

B' = 3 (3,5) = (9,15)

C' = 3(5,10) = (15, 30)

The slope is given by change in y divided by change in x

slope = (30-15)/(15-9)

= 15/6

= 5/2
The question or problem ask to calculate the slope of the said dilated polygon which it was dilated by a scale factor of 3. In my own calculation the slope of the BC is 5/2 or -5/-2 and the dilated polygon has a the same slope of the original polygon. I hope this would help 

Find the unknown side length, x. Write your answer in simplest radical form. A. 15 B. 11 square root 2 C. 2 square root 121 D. 15 square root 5

Answers

We have two right isosceles triangles. Hypotenuse of that triangle is a √(2) or you can use the Pythagorean theorem: 11² + 11² = c²
121 + 121 = c²
242 =c²          c= √(242)= √(121*2)=11 √(2) Answer is the same: B) 11 square root 2

Answer:

B

Step-by-step explanation:

3 3\10 divided by 1 4\7

Answers

Answer:

First, let's convert the mixed numbers into improper fractions:

3 3/10 = (3 * 10 + 3)/10 = 33/10

1 4/7 = (1 * 7 + 4)/7 = 11/7

Now, we can divide the two fractions:

33/10 ÷ 11/7

To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 11/7 is 7/11.

So, the division becomes:

33/10 * 7/11

Next, multiply the numerators (top numbers) together and the denominators (bottom numbers) together:

(33 * 7) / (10 * 11) = 231/110

Finally, simplify the fraction, if possible. In this case, we can divide both the numerator and denominator by their greatest common divisor, which is 11:

231/110 = (231 ÷ 11)/(110 ÷ 11) = 21/10

Therefore, 3 3/10 divided by 1 4/7 is equal to 21/10.
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