MATHEMATICS HIGH SCHOOL

What is the Gcf of 32 and 72

Answers

Answer 1
Answer: The GCF is 8 it divides both values without a remainder

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Select the correct answer.The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate they variable, and what is the solution for this system?x+3y= 422x - y = 14OA. Multiply the second equation by-3. The solution is x= 12, y=9.OB. Multiply the second equation by -2. The solution is x = 12, y=10.OC. Multiply the second equation by 2. The solution is x = 15, y = 9.OD. Multiply the second equation by 3. The solution is x = 12, y = 10.
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The number b less the quotient of a number k and 5

(X-2)²+(y-1)²=25 how do you do this problem?

Answers

(x-x_c)^2+(y-y_c)^2=r^2\n(x_c,y_c) - \text{center}\n\n(x-2)^2+(y-1)^2=25\n\text{center}=(2,1)\nr=√(25)=5

Each histogram represents a set of data with a median of 29.5. Which set of data most likely has a mean that is closest to 29.5?

Answers

Answer: B

Step-by-step explanation:

The mean and median will be close or the same when the graph is symmetrical

Answer: 30

Step-by-step explanation:

What is the range of possible sizes for side x? it is a triangle with one side having 4.0, and the other having 5.6. picture attached below, thanks in advance :)

Answers

Given:

Given that the two sides of the triangle are x, 4.0 and 5.6

We need to determine the range of possible sizes for the side x.

Range of x:

The range of x can be determined using the triangle inequality theorem.

The triangle inequality theorem states that, "if any side of a triangle must be shorter than the other two sides added together".

Thus, applying the theorem, we have;

x=4.0+5.6

x=9.6

Also, the the triangle inequality theorem states that, "the third side must be also larger than the difference between the other two sides".

Thus, we have;

x=5.6-4.0

x=1.6

Thus, the range of possible values for x are 1.6<x<9.6

Final answer:

In accordance with the triangle inequality theorem, the range for the length of the third side (x) in a triangle with sides of 4.0 and 5.6 is greater than 1.6 but less than 9.6.

Explanation:

In the field of Mathematics, specifically geometry, to find the range of possible lengths of a side of a triangle, you need to understand the triangle inequality theorem. The triangle inequality theorem states that the length of a side of a triangle must be less than the sum of the lengths of the other two sides, but more than the absolute difference.

Given you have two sides, 4.0 and 5.6, the possible length for side x should be less than (4.0 + 5.6 = 9.6) and greater than the absolute difference (5.6 - 4.0 = 1.6). So, the range for side x should be 1.6 < x < 9.6.

Learn more about Triangle Inequality Theorem

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Four people in a room. Each shakes hands with each of the others once. How many handshakes are there? 6
10
12
16
22

Answers

The correct answer is 6.

The clearest way to determine this is by creating a table of possible hand shaking. If we label the people A-D, the following are the ways they can be combined:
AB
AC
AD
BC
BD
CD

There are no other combinations.

There are 6 handshakes betweenfour people in the room.

Further explanation

The probability of an event is defined as the possibility of an event occurring against sample space.

\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }

Permutation ( Arrangement )

Permutation is the number of ways to arrange objects.

\large {\boxed {^nP_r = (n!)/((n - r)!) } }

Combination ( Selection )

Combination is the number of ways to select objects.

\large {\boxed {^nC_r = (n!)/(r! (n - r)!) } }

Let us tackle the problem.

This problem is about Combination.

If there are 4 people in a room , then the number of handshaking between 2 people is analogy as selecting 2 people from 4 people available. We will use combination formula in this problem.

^4C_2 = (4!)/(2! (4-2)!)

^4C_2 = (4!)/(2! 2!)

^4C_2 = (4 * 3 * 2 * 1)/(2 * 1 * 2 * 1)

^4C_2 = ( 24 )/(4)

^4C_2 = \boxed{6}

Learn more

Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation

Put the equation y=x²−14x+40 into the form y=(x-h)²+k y= ____

Answers

Answer:

y = (x - 7)² - 9

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

(h, k ) are the coordinates of the vertex and a is a multiplier

given

y = x² - 14x + 40

to obtain vertex form use the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 14x

y = x² + 2(- 7)x + 49 - 49 + 40

 = (x - 7)² - 49 + 40

 = (x - 7)² - 9 ← in vertex form

For the functions f(x) = 2x − 6 and g(x) = 5x + 1, which composition produces the greatest output? A. Both compositions produce the same output B. Neither composition produces an output. C. f(g(x)) produces the greatest output. D. g(f(x)) produces the greatest output.

Answers

f(g(x)) = 2(5x+1)-6 = 10x+2-6 = 10x-4

g(f(x)) = 5(2x-6)+1 = 10x-30+1 = 10-29

10x-4>10-29 because from f(g(x)) you subtract less quantity. 
The answer to your question is C. I hope that this is the answer that you were looking for and it has helped you.

Answer:

-24

Step-by-step explanation:
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