Which of the following is an example of the distributive property?
(3 x 6) x 8 = 3 x(6 x 8)
2 + (9-4) = (2+9) - 4
(4 + 3)2 = (4 + 3)(4 + 3)
5x (7 - 1) = (5 x 7) - (5 x 1)
i

Answer:

third option

Step-by-step explanation:

Given f(x) has zeros x = a, x = b, then

the factors are (x - a), (x - b) and the polynomial is the product of the factors.

Complex zeros occur as conjugate pairs, thus

5 + 4i is a zero then 5 - 4i is a zero

The zeros are x = 3, x = - 13, x = 5 + 4i, x = 5 - 4i, thus the factors are

(x - 3), (x - (- 13)), (x - (5 + 4i)), (x - (5 - 4i)), that is

(x - 3), (x + 13), (x - 5 - 4i), (x - 5 + 4i)

= (x - 3), (x + 13), ((x - 5) - 4i), ((x - 5) + 4i)

The polynomial is the product of the factors

f(x) = (x - 3)(x + 13)((x - 5) - 4i)((x - 5) + 4i) ← expand factors in pairs

     = (x² + 10x - 39)((x - 5)² - 16i²) → i² = - 1

     = (x² + 10x - 39)(x² - 10x + 25 + 16)

     = (x² + 10x - 39)(x² - 10x + 41) ← distribute

     = [tex]x^{4}[/tex] - 10x³ + 41x² + 10x³ - 100x² + 410x - 39x² + 390x - 1599 ← collect terms

     = [tex]x^{4}[/tex] - 98x² + 800x - 1599

Answer:

The third option

Step-by-step explanation:

The small number is 2.

The large number is 3.

Step-by-step explanation:

Let the two consecutive numbers be x and x+1.

The sum of these two consecutive integers = small integer + large integer

The sum of these two consecutive integers is x+x+1 = (2x+1)

It is given that,

Therefore, it can determined that :

(2x+1) = 3x-1

Keeping x term on one side and constants on other side,

3x-2x = 1+1

x = 2

Therefore, the small number is 2 and the large number is x+1 = 3.

Answer:

D

Step-by-step explanation:

1. Find the rate of change of the graph. Which is 4.

2. Because 5 is greater of 4, Object B has the greater speed.

3. To find the factor you must divide 4 from 5.  5 ÷ 4

4. 5 ÷ 4 = 1.25

5. The correct answer is D

Answer:C)Object A by a factor of 1.25

Step-by-step explanation:this is the answer for USA test prep.

Hello There!

The answer to your problem is 10:5 or 2:1

How to get 10:5

To get 10:5 you divide a number that can go into 20 and 10 which is 2. You divide 20/2 and 10/2 and get 10:5.

How to get 2:1

To get 2:1 you divide a number that can go into 10 and 5 which is 5. You divide 10/5 and 5/5 and get 2:1.

Hope This Helps!

The equivalent ratio of 20 : 10 will be 40/20 or 40 : 20.

Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A statement expressing the equality of two ratios A:B and C:D is called a proportion. We can express proportion as -

A : B ∷ C : D

AND

A x D = B x C

Product of extremes equal to product of means.

Given is the ratio 20 : 10

The equivalent ratio of 20 : 10 will be -

20 : 10 = 20/10 = (20 x 2)/(10 x 2) = 40/20 = 40 : 20

Therefore, the equivalent ratio of 20 : 10 will be 40/20 or 40 : 20.

To solve more questions on ratios, visit the link below-

https://brainly.com/question/2462048

#SPJ2

y = 8

hope this helps :)

Answer:

x= 0

Step-by-step explanation:

in order to find the value of x in the 2x - 4(x + 2) = -2X-8

we are going to apply bodmas rule by first opening the bracket

we have,

2x-4x-8 = 2x -8

we proceed to collect the like terms

2x -4x-2x = -8 +8

-4x = 0

divide both sides by -4

-4x/-4 = 0/-4

x= 0

Solution:

Given that,

One of the acute angles in a right triangle has a measure of 34.6°

The sum of the three angles of a triangle is always 180 degrees.

Also, that the measure of a right angle is always 90 degrees

Let "x" be the other acute angle

Therefore,

x + 90 + 34.6 = 180

x + 124.6 = 180

x = 180 - 124.6

x = 55.4

Thus the measure of other acute angle is 55.4 degrees

Answer:

Yes, what the other person said

Step-by-step explanation: basically you subtract 90.0 - 34.6

Answer:

Part a) Alyssa's expectation is equal to $0.33

Part b) Gabriel's expectation is equal to -$0.33

Step-by-step explanation:

we know that

The expected value is the probability of winning multiplied by the value you get when you win, plus the probability of losing multiplied by the value you get when you lose (which is negative as it is a loss).

Part a) Determine​ Alyssa's expectation

we know that

1) If Alyssa rolls a​ 1, 2, or​ 3, Gabriel gives Alyssa ​$4

The probability is 3/6

so

we have

[tex]\frac{3}{6}(4)=\$2[/tex]

2) If Alyssa rolls a​ 4, or​ 5, Gabriel gives Alyssa ​$1

The probability is 2/6

so

we have

[tex]\frac{2}{6}(1)=\$0.33[/tex]

3) if Alyssa rolls a​ 6, she gives Gabriel ​$12

The probability is 1/6

so

we have

[tex]-\frac{1}{6}(12)=-\$2[/tex]  ---> is negative because is a loss

therefore

Alyssa's expectation is equal to

[tex]\$2+\$0.33-\$2=\$0.33[/tex]

Part b) Determine​ Gabriel's expectation

we know that

1) If Alyssa rolls a​ 1, 2, or​ 3, Gabriel gives Alyssa ​$4

Is a loss for Gabriel

The probability is 3/6

so

we have

[tex]-\frac{3}{6}(4)=-\$2[/tex]  ---> is negative because is a loss

2) If Alyssa rolls a​ 4, or​ 5, Gabriel gives Alyssa ​$1

Is a loss for Gabriel

The probability is 2/6

so

we have

[tex]-\frac{2}{6}(1)=-\$0.33[/tex] ---> is negative because is a loss

3) if Alyssa rolls a​ 6, she gives Gabriel ​$12

Is a win for Gabriel

The probability is 1/6

so

we have

[tex]\frac{1}{6}(12)=\$2[/tex]  

therefore

Gabriel's expectation is equal to

[tex]-\$2-\$0.33+\$2=-\$0.33[/tex]

The expected outcomes for both Alyssa and Gabriel from the game are $0. This is calculated using the probabilities of each outcome and their respective gains or losses.

In the game between Alyssa and Gabriel, we are to calculate the expected outcomes for both players. To calculate the expectation, we will weigh the possible outcomes ($4, $1, -$12 for Alyssa and -$4, -$1, $12 for Gabriel) by their probabilities.

The dice has six faces, so the probability for each outcome is determined by the number of corresponding faces divided by six. Let's calculate the expectation for both:

So, both Alyssa and Gabriel have an expected gain of $0 from this game.

https://brainly.com/question/37190983

#SPJ11

Answer:

1 inch : 5⅓ miles

6 inches

Step-by-step explanation:

Map : Actual

4½ : 24

1 : 24/4.5

24 ÷ 9/2 = 24 × 2/9 =

1 inch on map represents an actual distance of 16/3 miles in actual

16/3 = 5⅓ miles

Map : Actual

¼ inch : 1 mile

X inch : 24

¼×24 = 6 inches

Answer:    3/16 inches : 1 mile

                  6 inches

Step-by-step explanation:

[tex]\dfrac{\text{Model}}{\text{Actual}}:\dfrac{4\frac{1}{2}\ inches}{24\ miles}\div\dfrac{24}{24}=\dfrac{\frac{3}{16}}{1}\quad \longrightarrow \quad \large\boxed{\dfrac{3}{16}\ inches:1\ mile}\\[/tex]

[tex]\dfrac{\text{Model}}{\text{Actual}}:\dfrac{\frac{1}{4}\ inches}{1\ mile}=\dfrac{x}{24\ miles}\\\\\\\text{Cross Multiply}:\quad \dfrac{1}{4}\bigg(24\bigg)=x\\\\.\qquad \qquad \qquad \qquad \quad \quad \large\boxed{6=x}[/tex]

Answer:

[tex]f(x) = - (x + 2)(x + 1)(x - 3)[/tex]

Step-by-step explanation:

Let f(x) be the 3rd degree polynomial function.

The roots of this function are:

x=-2, x=-1 and x=3.

The factored form is:

[tex]f(x) = a(x + 2)(x + 1)(x - 3)[/tex]

This equation passes through (2,12)

This implies that;

[tex]a(2 + 2)(2+ 1)(2 - 3) = 12 \\ - 12a = 12 \\ a = - 1[/tex]

The polynomial function is

[tex]f(x) = - (x + 2)(x + 1)(x - 3)[/tex]

Answer:

B

Step-by-step explanation:

B produces the term 12x that cancels out after subtraction.

In order to eliminate one variable by subtracting, you should multiply the top equation by -3 and the bottom equation by 2. In doing so, this will make the coefficients of y equal and opposite, allowing this variable to be eliminated when the two equations are added together.

The question relates to the method of solving a system of linear equations by subtraction. In order to eliminate one variable when subtracting these equations, we would need to manipulate the equations such that the coefficients of one variable are exact opposites. Hence, the objective is to make the coefficients of y, -2 and -3, opposite each other.

To achieve this, the correct answer is C. Multiply the top equation by -3 and the bottom equation by 2.

By performing these multiplications we'll have:
-12x + 6y = -21.
6x - 6y = 30.
Now, if we add these two equations, we'll be able to eliminate the y variable and can proceed to solve for x.

https://brainly.com/question/21620502

#SPJ2

Answer:

The attached picture shows the location of each of the coordinates on the Cartesian plane. Hence, (0, 1) is the coordinate that lies on the y- axis.

Step-by-step explanation:

The solution to the question above is answered thus:

Note that the first value in each bracket is for x while the other is for y. Hence; 0, 7, 6 and 8 are value of x while 1, 0, 8 and 2 are values of y.

Thus:

Coordinate (0, 1) lies on the y - axis.

Coordinate (7, 0) lies on the x - axis.

Coordinates (6, 8) and (8, 2) lie on the 1st quadrant of the Cartesian plane

Coordinates.

Therefore, coordinate (0, 1) is the answer because it lies on the y- axis.

The answer is (0,1)

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Given here: The points  (0,1), (7,0), (6,8), (8,2)

For the point to lie on the y-axis its x-coordinate or abscissa must be zero

Only  (0,1) satisfies this.

Hence, The answer is (0,1)

Learn more about co-ordinate system here:

https://brainly.com/question/27749090

#SPJ5

Answer:5

Step-by-step explanation:

you do it

Answer:

that would be 57,946

Answer: 295.642 (Work is shown below in the image)

Step-by-step explanation:

Answer:

6x

Step-by-step explanation:

x + x + x + 2x + x

Simplify the equation

4x + 2x

6x

Hope this was useful to you!

Answer:

182 miles

Step-by-step explanation:

52 times 3.5=182

The Answer is 182 miles

When multiplying 52 by 3.5 you'll get 182 as the product

Answer:

Hi there!

The correct answer will be 15 yd

Step-by-step explanation:

There are two ways you can go about solving this problem

Method One: Pythagorean Theorem

a^2 + b^2 = c^2 then all you have to do is plug in the values

(12)^2 + (9)^2 = c^2 you should get c^2 = 225 then you square root both sides and you get c = 15

Method Two:  Pythagorean Identities

This triangle represents a 3,4,5 triangle

All the sides just tripled so that means the hypotenuse is 5*3 which equals 15

7/-21=7/4.58=350/229=1whole number 121/224

Answer:

the answer is c

Step-by-step explanation

Answer:

c

Step-by-step explanation:

Answer:

( x - 4)

Step-by-step explanation:

x² + 2x - 24

From here, you must find the two factors of -24 (the first and third terms' coefficients multiplied together) that add up to 2 (the middle terms coefficient)

( x - 4) ( x + 6)

Other factor of x² + 2x - 24 is (x - 4).

Factors and multiples are two related concepts in math. A factor is a number that divides the given number exactly with 0 as the remainder.

Given expression

x² + 2x - 24 has factor (x + 6)

So, the expression should be divisible by (x + 6)

(x² + 2x - 24)/(x + 6)

It can be written as

(x² + 6x - 4x -24)/(x + 6)

Factoring out common factor

(x (x + 6) - 4 (x + 6))/(x + 6)

factoring out common factor

(x + 6)(x - 4)/(x + 6)

Simplifying

= (x - 4).

Hence, (x - 4) is other factor of x² + 2x - 24.

Learn more about factor here:

https://brainly.com/question/19386208

#SPJ6

Answer:

104

Step-by-step explanation:

x+37=141

subtract 37 from both sides

 -37=141-37

x= 104

Step-by-step explanation:

x = First number

x + x + 37 = 141 (Because we know that the 2nd number is 37 more than the first, we can just say x + 37.)

2x + 37 = 141 (Combine like terms.)

2x = 104 (Subtract 37 from both sides.)

x = 52 (Divide 2 from both sides.)

Now we know that the first number is 52. Now we just add the 37 to 52 to find the second number.

37 + 52 = 89 = Second number

Proof: 52 + 89 = 141

Answer:

11

Step-by-step explanation:

i think.............

Answer:

The value of x is equal to 7

Step-by-step explanation:

if -4x + 26 = -2

-4x = -2 - 26

-4x = - 28

Divide both sides by -4, then we will have

x = -28/-4

x = 7

Steps to solve:

-4x + 26 = -2

~Subtract 26 to both sides

-4x + 26 - 26 = -2 - 26

~Simplify

-4x = -28

~Divide -4 to both sides

-4x/-4 = -28/-4

~Simplify

x = 7

Best of Luck!

Answer:

-3.66666666668

Step-by-step explanation:

The zero's you do not have to add because they have to content or value.

-4 5/9 into improper = 31/9 = -4.55555555556

8/9 = 0.88888888888

ADD

[tex]\left\begin{array}{ccc}-4.55555555556\\+\\0.88888888888\end{array}\right\\---------[/tex]

-3.66666666668

Hope this helps you!

Have a good night! :)

Answer:

-3.66666666668

Step-by-step explanation:

Answer:

$16.15

Step-by-step explanation:

The wholesale price:

Selling Price:

Pair of shoes sold for $16.15 in the store

The department store marks up the wholesale price by 90%, equating to $7.65. Adding this to the original wholesale price of $8.50, the retail price of the shoes in the department store is $16.15.

To calculate the retail price of the shoes in the department store, we need to add the markup value to the original wholesale price. The markup is 90% of the wholesale price. Therefore, we calculate 90% of $8.50, and then add that to the original price.

To find 90% of $8.50, we multiply $8.50 by 90/100. This gives us $7.65. This is the markup value.

We then add this markup value to the original wholesale price. So, $8.50 + $7.65 = $16.15.

The price of the pair of shoes in the department store is therefore $16.15.

https://brainly.com/question/34159861

#SPJ3

Answer:

72 lbs

Step-by-step explanation:

t=tail h=head b=body

t = 9

h = t + .5b

b = h + t

Substitute

b = h + 9

h = 9 + .5b

h = 9 + .5h + 4.5

.5h = 13.5

h = 27

b = 36

TOTAL = t + h + b = 27 + 36 + 9 = 72