Check all of the polynomial functions that have 2 as a root.
A. h(m) = 8 – m^3
B. f(g) = g^3 – 2g^2 + g
C. f(a) = a^3 – 4a^2 + a + 6
D. f(x) = x^3 – x^2 – 4

2.  KL = LM

3.  Definition of midpoint

4.  L is the midpoint of KM

5. Transitive Property of Congruence

x + 3 < 4x - 12                 or            4x - 12 < 20

-x         -x                                           +12  +12

     3 < 3x - 12                 or           4x        < 32

   +12       +12                               ÷4           ÷4  

    15 < 3x                       or              x        <  8

   ÷3    ÷3

    5 <  x

5 < x < 8

Graph:   5 o---------------o 8

Answer:

5<x<8

Step-by-step explanation:

x + 3 < (4x – 12) < 20

Solve the inequality

x + 3 < 4x – 12 < 20

We break the inequality

x+3<4x-12  and 4x-12<20

solve it separately

x+3<4x-12

subtract 4x on both sides

-3x +3< -12

subtract 3 on both sides

-3x < -15

divide by -3 on both sides

x> 5

4x-12<20

add 12 on both sides

4x <32

divide by 4

x<8

x>5  and x<8

so x lies between 5  and 8, 5<x<8

the graph is attached below

The best graph that best fits your table is graph D.

For number 12, I don't see any graphs, but the graph would look like the graph I have below.

For number 11, A) y = 1/2x - 1 is correct. Here's the proof! (pic #2)

For number 10, the first graph is correct, here's the proof! (pic #3)

Answer:

306 seats

Step-by-step explanation:

The total number of seats in the auditorium is calculated by multiplying the number of rows by the number of seats in each row for both sets of rows, then adding both totals together. The total comes to 306 seats.

This is a mathematics question focused on multiplication and addition, which are key fundamentals in arithmetic, often covered in middle school. To find the total number of seats in the auditorium, you need to multiply the number of rows by the number of seats in each row, then add these numbers together.

For the first part, there are 9 rows with 18 seats in each. By multiplying these numbers (9 * 18), we get 162.
For the second part, there are 6 rows with 24 seats in each. By multiplying these numbers (6 * 24), we get 144.

Then, to find the total number of seats in the auditorium. we add these two numbers together (162 + 144), which equals 306. Therefore, there are 306 seats in the auditorium.

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The complete question is here:

In an auditorium there are 9 rows of seats with 18 seats in each row. There are also 6 rows of seats with 24 seats in each row. How many seats are there in the auditorium?

ANSWER TO QUESTION 1

Given

[tex]f(x)=5x^3+8x^2-7x-6[/tex]

We can use the factor theorem to determine if

[tex]x+2[/tex] is a factor of the polynomial or not.

According to this theorem, if [tex]x+2[/tex] is a factor of [tex]f(x)[/tex], then [tex]f(-2)=0[/tex].

How did we get the [tex]-2[/tex]?

We set [tex]x+2=0[/tex] and then solve to obtain [tex]x=-2[/tex].

So now let us plug in [tex]x=-2[/tex] in to the function to see if it will simplify to zero.

[tex]f(-2)=5(-2)^3+8(-2)^2-7(-2)-6[/tex]

[tex]f(-2)=5(-8)+8(4)+7(2)-6[/tex]

[tex]f(-2)=-40+32+14-6[/tex]

[tex]f(-2)=6-6[/tex]

[tex]f(-2)=0[/tex]

Since the result simplifies to zero, we conclude that

[tex]x+2[/tex] is a factor of

[tex]f(x)=5x^3+8x^2-7x-6[/tex]

ANSWER TO QUESTION 2

We have the function,

[tex]f(x)=5x^3+8x^2-7x-6[/tex]

We can use the remainder theorem to show that

[tex]x+1[/tex] is NOT a factor of the polynomial.

According to this theorem, if [tex]x+1[/tex] is not a factor of [tex]f(x)[/tex], then [tex]f(-1)\ne 0[/tex].

So now let us plug in [tex]x=-1[/tex] in to the function to see if it will simplify to non-zero number.

[tex]f(-1)=5(-1)^3+8(-1)^2-7(-1)-6[/tex]

[tex]f(-1)=5(-1)+8(1)+7(1)-6[/tex]

[tex]f(-1)=-5+8+7-6[/tex]

[tex]f(-1)=4[/tex]

[tex]f(-1)\ne0[/tex]

Since the result simplifies to a non zero number, we conclude that

[tex]x+1[/tex] is NOT a factor of

[tex]f(x)=5x^3+8x^2-7x-6[/tex]

Subtract to find the difference:

2000 - 500 = 1500

Divide the difference by the original population:

1500 / 500 =  3

Multiply that by 100 to get the percentage:

3 x 100 = 300%

The first quartile Q1 shows a partition of the first 25% of the data. In the same way the quartile Q3 shows a partition of 75% of the data.

Then, the difference Q3-Q1, also called the interquartile range shows the central 50% of the data.

Therefore the answer is option C:

The percentage of Best Actress winners (among women) between Q1 = 28 and Q3 = 41 is 50%.

Answer: Option C

Step-by-step explanation: i Just Took The Test

ANSWER

[tex](25\times9)+(75\times9)=9(25+75)[/tex]

[tex](25\times9)+(75\times9)=9(100)[/tex]

[tex](25\times9)+(75\times9)=900[/tex]

EXPLANATION

According to the distributive property,

[tex](a\times b)+(a\times c)=a(b+c)[/tex]

This implies that,

[tex](25\times9)+(75\times9)=9(25+75)[/tex]

[tex](25\times9)+(75\times9)=9(100)[/tex]

The Right Hand Side of the equation now has 2 factors.

We solve now to obtain;

[tex](25\times9)+(75\times9)=900[/tex]

The distributive property allows you to factor out a common factor from both terms in an equation. In this case, you can rewrite the expression (25x9)+(75x9) using the distributive property as 9*(25+75), which simplifies to 9*100 or 900.

The distributive property in mathematics is a property where each term inside a bracket is multiplied by the term outside the bracket. We can use the distributive property to rewrite the given expression (25x9)+(75x9).

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Hi, the answer is this...

Otylia's solution is: Incorrect

Because 4y+y is the same as 4y+1y

4y2 is the same as 4y x y

4y+y simplifies to 5y

Answer:

Otylia's solution is incorrect

Correct solution is 5y

Step-by-step explanation:

Otylia simplifies the expression 4y + y to 4y^2.

LEts simplify the expression 4y+y and check with Otylia's solution

4y and y are like terms

y or 1y are same

4y and 1y are like terms

To combine like terms, we add only the coefficient of y

So 4y + 1y = 5y

Otylia simplifies the expression 4y + y to 4y^2

4y^2 is not correct. So Otylia's solution is incorrect

Answer:

D. Commutative Property of Multiplication

Step-by-step explanation:

Commutative Property of Multiplication states that two numbers can be multiplied in either order.

For this case we have to:

By definition, the commutative property of the multiplication establishes that, the order of the factors does not alter the product, that is to say:

[tex]a * b = b * a\\[/tex]

Therefore the expression given by:

[tex]2*3 = 3*2[/tex] represents:

The commutative property of multiplication

Answer:

Option D

The mode of this set of numbers is 5.

The mode of a set of numbers, is the most common/frequent number within the set. Since there are two 5's but only one of each other number. Thus making 5 the mode.

HE WOULD HAVE 64$ IN TOTAL

Answer:

-64

Step-by-step explanation:

its actually, -64 not 64.

Answer:

It is not direct variation.

Step-by-step explanation:

In a direct variation, each y value divided by its corresponding x-value gives the same quotient, which is the constant of variation. Let's try two y-values and their corresponding x-values.

11/7 = 1.571428...

13/8 = 1.625

Since the two quotients above are different, there is no constant of variation, and the relation is not direct variation.

Answer:

It is not direct variation.

Step-by-step explanation:

In a direct variation, each y value divided by its corresponding x-value gives the same quotient, which is the constant of variation. Let's try two y-values and their corresponding x-values.

11/7 = 1.571428...

13/8 = 1.625

Since the two quotients above are different, there is no constant of variation, and the relation is not direct variation.

Step-by-step explanation:

This makes sense what they put

Final answer:

To find out how many apples Clint picked, we need to first determine how many apples Tim picked. Clint picked 13 apples.

Explanation:

To find out how many apples Clint picked, we need to first determine how many apples Tim picked. It is given in the question that Tim picked 5 fewer apples than Clint.

So, we can subtract 5 from Clint's total apples to get Tim's total apples.

Next, to find Clint's total apples, we can add the number of apples Tim picked to the 5 fewer apples. This will give us Clint's total apples.

Let's solve the problem step-by-step:

Clint picked 13 apples.

Tim picked 5 fewer apples than Clint, which is 13-5 = 8 apples.

Clint's total apples = Tim's apples + 5 fewer apples = 8 apples + 5 apples = 13 apples.

Therefore, Clint picked 13 apples.

Answer:

To construct the Square using a compass and straight edge, you have written the steps not in proper order. I am rearranging the steps for you

1. Construct horizontal ​ H J¯¯¯¯¯

2. ​Construct a circle with point H as the center and a circle with point J as a center with each circle having radius HJ .

3.Label the point of intersection of the two circles above​ ​ HJ¯¯¯¯¯ ​​, point K, and the point of intersection of the two circles below ​ HJ¯¯¯¯¯ ​, point L.

4.Construct KL¯¯¯¯¯ , the perpendicular bisector of ​ HJ¯¯¯¯¯ ​, intersecting​ ​ HJ¯¯¯¯¯ ​ ​​at point M.

5.Construct a circle with point M as the center with radius MJ .

6.Label the point of intersection of circle M and ​ KL¯¯¯¯¯ ​ closest to point K, point N, and the point of intersection of circle M and ​ KL¯¯¯¯¯ ​  closest to point L, point O.

7.Construct HN¯¯¯¯¯¯ , NJ¯¯¯¯¯ , JO¯¯¯¯¯ , and OH¯¯¯¯¯¯ to complete square HNJO .

1. Yes they are congruent. You translate AB to move it over to CD. Specifically, shift 2 units to the right.

2. No, they are not congruent. QR is longer than MN. Congruent segments must be the same length.

3. No, they are not congruent. At first glance, they seem to be congruent after translation and reflection. However, XY is longer than UV, and those legs should be the same length for a pair of congruent triangles to be possible.

4. Yes they are congruent. You translate triangle ABC to move it over to triangle DEF (shift 1 to the left, 3 down).

Answer:

Graph given on the top right side.

Step-by-step explanation:

Nina used 5 L of water from her rain barrel to water her plants every week.

She did this until her rain barrel was empty.

So barrel will be empty in the time = [tex]\frac{75}{5}=15[/tex] weeks.

Nina started watering when rain barrel contained 75L of water.

We draw a graph with water remaining on y-axis and weeks to get the barrel empty on x-axis.

Line representing this process will start from a point (0, 75) on y-axis and will end at x-axis at the point (15, 0).

Therefore, graph given on the top right side of the options is the correct answer.

The correct graph is the graph at the top right of the image given.

From the graph, we see that the water remaining is represented on the y-axis while weeks it will take for the barrel to get empty is represented on the x-axis.

This means that, the first coordinate will be; (0, 75). 0 on the x-axis and 75 on y-axis.

Number of weeks it took for the barrel to be empty = 75/5 = 15 weeks

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Answer: A: Ford should leave the starting pitcher in the game.

I just used the other answer provided and it was wrong, at least on study island it was wrong.

If 60 is 2 more than the product of 5 and N:

The product of 5 and N is when they are multiplied, so 5N is going to be part of the equation.

We know that 60 is 2 more than 5N, so 5N + 2 would be 60.

We can make an equation with this:

60 = 2 + 5N

Therefore, the equation would be 60 = 2 + 5N.

Hope this helps! :)

The equation that can be used to depict the information 60 is 2 more than the product of 5 and N will be 60 = 2 + 5N

From the information given, 60 is 2 more than the product of 5 and N and this will be written as 60 = 2 + 5N.

To further solve the equation, we can solve for N and this will be:

60 = 2 + 5N

Collect like terms

5N = 60 - 2

5N = 58

N = 58/5

N = 11.6

Therefore, the value of N will be 11.6.

In conclusion, 60 is 2 more than the product of 5 and N and this will be written as 60 = 2 + 5N.

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Best Answer:

7.8

Whats an irrational number again?

When you approximate 6 raised to the power of 2.8, you get a result of approximately 177.83 (rounded to two decimal places).

To approximate the number 6 raised to the power of 2.8 using a calculator, follow these steps:

1. Turn on your calculator and make sure it is in standard mode.
2. Enter the base number, which is 6.
3. Look for the exponent key on your calculator, which is usually denoted by the "^" symbol or a button labeled "Exp" or "EE".
4. Enter the exponent value, which is 2.8.
5. Press the equals "=" button to calculate the result.

Now, let's calculate it together:

6^2.8 ≈ 177.827941

Therefore, when you approximate 6 raised to the power of 2.8, you get a result of approximately 177.83 (rounded to two decimal places).

Keep in mind that different calculators may vary slightly in their display of decimal places, so the exact result may differ slightly depending on the calculator you are using.

1/3 of $120.00 is $40.00, therefore the sale price will be $80.00 :-) xxx