Algebraic ExpressionsWhich of the following sets of ordered pairs represents a function?

{(-2,1),(-1,3),(2,1),(-2,2)}
{(-1,4),(1,4),(2,4),(-2,4)}
{(-1,3),(-1,4),(-1,5),(-1,6)}
{(2,2),(3,3),(4,4),(2,1)}

Use complete sentences to describe the relationship between sets A and B if A is a subset of or is equal to B.
A = {8}
B = {7, 8, 9}

Which of the following properties is a(b · c) = (a · b)c an example of?
associative property
commutative property
multiplicative identity
distributive property

Given: A = {a, e, i, o, u}, B = {a, l, g, e, b, r}, C = {m, y, t, h}, A ∩ C is
m, a, e, i, o, u, t, h
the empty set
i
a, e, i, o, u, y

If G = {(-1, 7),(-8, 2),(0, 0),(6, 6)}, then the range of G is
{(7, -1),(2, -8),(0, 0),(6, 6)}
{-8, -1, 0, 6}
{0, 2, 6, 7}

Given B = {a, l, g, e, b, r} and C = {m, y, t, h}, find B ∪ C.
{}
{a}
{a, b, e, g, h, l, m, r, t, y}

If A ⊂ B and A ∩ B = θ then which of the following can be concluded about the sets A and B?
Set A has more elements in it than set B.
Set A is the set containing zero.
Set A is the empty set.
Both sets A and B are the empty set.

Given A = {a, e, i, o, u} and B = {a, l, g, e, b, r}, find A ∪ B.
{}
{a,e}
{a, b, e, g, i, l, o, r, u}

Which of the following properties is 5(3 + 2) = 15 + 10 an example of?
associative property
commutative property
multiplicative identity
distributive property

Given f(x) = 3x - 1 and g(x)= -x + 6, find f(-2) + g(5).
-6
6
8

List all of the elements of set A if A = {x|x is an integer and -6 ≤ x <0}
{-6, -5, -4, -3, -2, -1, 0}
{-6, -5, -4, -3, -2, -1}
{-5, -4, -3, -2, -1}

Answer:

Option D) multiply y by 4 in the first equation and subtract the second equation

Step-by-step explanation:

we have

2x+y=-10 ----> first equation

3x+4y=-20 ---> second equation

Verify each case

case A) multiply the first equation by 4 and subtract the second equation

so

(2x+y)*4=-10*4 ------> 8x+4y=-40

[8x+4y=-40]-[3x+4y=-20] -----> 5x=-20 -----> x=-4

This step is correct

case B) multiply the first equation by -4 and add the second equation

so

(2x+y)*-4=-10*-4 ------> -8x-4y=40

[-8x-4y=40]+[3x+4y=-20] ----->-5x=20 -----> x=-4

This step is correct

case C)  add 8 times the first equation and −2 times the second equation

so

(2x+y)*8=-10*8 ------> 16x+8y=-80

(3x+4y)*-2=-20*-2 ----> -6x-8y=40

[16x+8y=-80]+[-6x-8y=40] ----->10x=-40 -----> x=-4

This step is correct

case D) multiply y by 4 in the first equation and subtract the second equation

so

2x+4y=-10

[2x+4y=-10]-[3x+4y=-20] -----> -x=-10+20 -----> x=-10

This step is incorrect

NOT produce a system with the same solution

3(n+5)≥17 is the expression for three times the sum of a number n and 5 is at least 17.

What is an Inequality?

The relationship between two expressions or values that are not equal to each other is called inequality.

Given that three times, the sum of a number n and 5 is at least 17.

According to the question, the expression will be = 3(n+5)≥17

Hence, 3(n+5)≥17 is the expression for three times the sum of a number n and 5 is at least 17.

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Answer:

3(n+5)≥17

Step-by-step explanation:

Answer:

Step-by-step explanation:

prime factors of 20 = 2 * 2 * 5

Final answer:

The denominator of the fraction 7/20 can be written as the product of prime factors: 2 x 2 x 5.

Explanation:

The denominator of the fraction 7/20 can be written as the product of prime factors by finding the prime factorization of 20.

1. Start by dividing 20 by the smallest prime number, which is 2. 20/2 = 10.
2. 2 is a prime factor, so we continue to divide 10 by 2. 10/2 = 5.
3. 5 is a prime number, so we have found the prime factorization of 20: 2 x 2 x 5 = 20.

Therefore, the denominator of the fraction 7/20 can be written as 2 x 2 x 5.

Learn more about Prime Factorization here:

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Answer:  A. 9847.04 cubic meters

Step-by-step explanation:

From the given picture, we have

The diameter of the cone = 28 m

Then the radius of the cone =

Height of the cone = 48 inches

The volume of cone is given by :-

Hence, the volume of the cone =

Answer:

Step-by-step explanation:

Radius

= 28 ÷ 2

= 14 m

Volume

= 1/3 (3.14) (14)²(48)

= 1/3 (3.14) (196)(48)

= 9847.04 m³

For this case we have the following function:

We rewrite the function making distributive property.

We have then:

To find the vertex of the function, we derive:

We equal zero and clear the value of x:

We evaluate the function for the value of x obtained:

Then, the vertice of the parabola is:

Answer:

the vertex of the quadratic function f(x)=(x-6)(x+2) is: