MATHEMATICS HIGH SCHOOL

Express 8 as a product of prime factors in index form

Answers

Answer 1
Answer:

Answer:

8 = 2^3

Step-by-step explanation:

8 = 4*2

    4 is not a prime number so we break 4 into 2*2 and replace it

8 = 2*2*2

All of these are prime

We see there are three 2's multiplied together, that means 2 is the base and 3 is the exponent

8 = 2^3

2^3 is index form

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What is the product of (x+1) and (2x^2+3x-1)?

Answers

(x+1)\cdot (2x^2+3x-1)=2x^3+3x^2-x+2x^2+3x-1=\n \n=2x^3+5x^2+2x-1
(x+1)(2x^2+3x-1)
x(2x^2)+x(3x)+x(-1)+1(2x^2)+1(3x)+1(-1)
2x^3+3x^2-1x+2x^2+3x-1
2x^3+5x^2+2x-1

Two sides of a triangle have lengths 10 and 15. What must be true about the length of the third side? less than 25 / less than or equal to 25 /equal to 25/ more than 25

Answers

The length of the third side of a triangle is always less than the sum of the other two legs. Therefore if we add the two legs we obtain,

leg 1 + leg 2

10 + 15 = 25

Since the sum of the legs is 25, thus, the third leg should be less than 25. 

Answer:

A. Less than 25.

Step-by-step explanation:

Let x represent 3rd side of triangle.

We have been given hat two sides of a triangle have lengths 10 and 15.

We will use triangle inequality theorem to find the 3rd side of the triangle. Triangle inequality theorem states that 3rd side of a triangle must be less than the sum of other two sides of triangle.

Using triangle inequality theorem, we can set following inequalities:

x+10>15

x+10-10>15-10

x>5

Therefore, the length of third side should be greater than 5.

10+15>x

25>x

x<25

Therefore, the length of third side should be less than 25 and option A is the correct choice.

A triangle with two congruent sides is always a(n)_______________ triangle.a. right
b. scalene
c. isosceles
d. equilateral

Answers

Scalene triangle → Different length, therefore no congurent sides.
Isosceles triangle → Same length, therefore it has two congurent sides.
Equilateral triangle → All length are comparable, it has three congurent sides.
Right triangle → Measures 90°, in some cases, it has two congurent sides.

Congurent defination → Same shape and same size.

Answer → C) Isosceles triangle.

To convert 0.9 to a fraction, Lauren wrote n=0.9 as her first step. For her second step, what should she multiply both sides of that equation by? A) 10
B) 100
C) 1000
d) 10,000

Answers

The number should be multiply is 10.

What is multiplication?

In math, to multiply means to add equal groups. When we multiply, the number of things in the group increases. The twofactors and the product are parts of a multiplication problem.

Given:

n=0.9

Now, there is one number behind decimal point.

So, we have to multiply it by 10 to convert it into fraction from decimal.

Thus,

10n = 0.9*10

10n = 9

n = 9/10

Hence, the number must be multiplied is 10

Learn more about multiplication here:

brainly.com/question/5992872

#SPJ2
answer is a to ur question

What are the measurements???

Answers

Answer:

angle 4 is 31

angle 5 is 59.

Step-by-step explanation:

M<4 and M<5 add up to a  right angle which is 90 degrees . so you put it in a equation form.

2x-5+4x-13=90

rearrange it

2x+4x-5-13=90

6x-18=90

add 18 on both sides

6x=108

divide 6 from both sides

and you get x= 18

Plug in x for angle 4 =2(18)-5 =  31

plug in x for angle 5 = 4(18)-13 = 59

Pls help me with this question!!!!!

Answers

Answer:

D

3,6,9,12,15,18,21,24,27,30,10,20,25
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