The polynomial P(x) = x⁴ + 3x³ + cx² - 7x + 6 is divisible by x+3.
Determine the value of c and factor the polynomial fully.

Answer:

1) 54+2x=5x−6−18x Distributive Property

2) 60=−15x Division Property of Equality

3) −4=x Division Property of Equality

Explanation:

1.) This answer is Distributive Property because the parenthesis in the original equation were removed through the process of distributing.

3(–2 – 6x) was distributed by multiplying 3 • –2 and 3 • –6x to get –6 – 18x

2.) This answer is Division Property of Equality because for all real numbers x, y, and z, if x = y and z ≠ 0, then x/z = y/z. This is true in this equation because of 60/–15 = −15x/–15.

3.) Division is used to get the value of x, which is –4.

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nswer:

Explanation:

) We want to start by drawoing a Venn diagram

We call the set of the married people M and the set of the full-time workers F

We have the Venn diagram represented as follows:

b) We want to get the probability that an employee works full time and is married

We have that as:

P(full-time) OR P(married) -P(Full time and married)

P(full time) = 70/110

P(married) = 60/110

P(full time and married) = 35/110 (since half of the full-time workers are married)

Thus, we have:

:

c) The probability that an employee works full time or is not married

Mathematically, we have that as:

P(full time) OR P(not married) -P(full time and not married)

P(not married) = 1 - P(married)

:

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"d" proportional to }t^2}{ {\Large \begin{array}{llll} d=kt^2 \end{array}}}\qquad \textit{we also know that} \begin{cases} d=80\\ t=4 \end{cases}\implies 80=k(4)^2 \\\\\\ \cfrac{80}{4^2}=k\implies 5=k\hspace{15em}\boxed{d=5t^2} \\\\\\ \textit{when t = 8, what is "d"?}\qquad d=5(8)^2\implies d=640~in[/tex]

The possible values of the number will be -62/4 or -31/2.

Multiplication of numbers may be defined as the tool or arithmetic operation which can be used to increase the count of a number. For example, if there is a number 4, then in order to increase the number it will be multiplied with some other number like 9. Now, the number will be 4×9 = 36. We are given that the product of -4 with a number gives the answer as 62. Let us assume the number as x and form the equation in accordance with the data given in the question.

-4×(x) = 62

Now, to find x we divide -4 on both the sides and we get

x = -62/4

This number can also be simplified by dividing both numerator and denominator with 2 and we get

x = -31/2.

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The value of n is 1/2 and it is not an even number or odd number

From the question, the steps are given as

n + n + 1 = 2n + 1

n + n + 1 = 2n+2-1

n + n + 1 = 2(n+1) -1

Also, from the question, we have the result of the expression to be

2

This means that

n + n + 1 = 2

Substitute n + n + 1 = 2(n+1) -1 in the equation n + n + 1 = 2

So, we have

2(n + 1) - 1 = 2

Add 1 to all sides of the equation

So, we have

2(n + 1) = 3

Divide both sides of the equation by 2

So, we have

n + 1 = 3/2

Subtract 1 from all sides

n = 1/2

The above implies that the number n is neither an even number, nor an odd number

This is so because the result is a fraction

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The weight of the twelve people on the elevator is 1,825 pounds.

And the weight of the thirteen person is given by the inequality:

x ≤ 175

We have an elevator with 12 people in it, such that the weights of these 12 people are:

175, 140, 135, 155, 170, 190, 125, 160, 150, 150, 130, 145

To find the total weight we just need to add these numbers, we will get:

175 + 140 + 135 + 155 + 170 + 190 + 125 + 160 + 150 + 150 + 130 + 145 = 1,825

So the 12 people in the elevator have a total weight of 1,825 pounds.

Now, the weight limit is 2,000 pounds.

So if we define x as te weight of the 13 th person, we can write the inequality:

1,825 + x ≤ 2,000

x ≤ 2,000 - 1,825

x ≤ 175

So the person can weight at mos 175 pounds.

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The amount of money that Ahmed gave to his brother is AED 140.

It is given in the question that Ahmed has AED 180. He gives his brother 0.7  with bar notation of the amount he has.

We have to find the amount given by Ahmed to his brother.

Here, we have to convert a non-terminating but recurring rational number into fraction form.

Let 0.7 bar = x

Multiplying the equation by 10, we get

7.7 bar  = 10x

10x - x = 7.7 bar - 0.7 bar

9x = 7

x = 7/9

Hence, Ahmed gave 7/9 of the amount he had to his brother.

Hence, we can write,

Amount given to Ahmed's brother by Ahmed = (7/9)*180 = AED 140.

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If a cave explorer is at an elevation of −32 feet and the explorer starts moving at a rate of −6 feet per minute. it will take, 9 in minutes for the explorer to reach an elevation deeper than −140 feet.

Elevation of feet =  −32 feet.

Feet per minute =  −6 feet per minute

Elevation deeper than  feet = −140 feet

Let x  represent the time for reach the desired height

Inequality

-32 - 6x = ≤ -140

Substract 32 from both side

12x ≤ 140 -32

12x  ≤ 108

Divide both side by 12x

x ≤ 108/12

x ≤ 9

Therefore we can conclude that the explorer will have to use 9 minutes to get to the elevation.

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Answer:

b

Step-by-step explanation:

because he borrowed $2 everyday and now he owes 10 so b

yw! :)

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Answer:

For example, 7 is a divisor of 84 because 84 ÷ 7 is an even division. However, that also means that 7 × (a number) = 84, so 7 is a factor of 84.

The amount by which an apple is more expensive than a pear is; D: 4p

We are told that  5 apples and 3 pears costs 8p more than 3 apples and 5 pears.

Let the cost of apples be x and let the cost of pears be y. Thus, the equation that represents the sentence is;

5x + 3y = 3x + 5y + 8

Rearrange to get;

5x - 3x + 3y - 5y = 8

2x - 2y = 8

divide both sides by 2 to get;

x - y = 4

Thus;

x = 4 + y

Which means it costs 4p more

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Answer:

0.86

Step-by-step explanation:

Move the decimal point one place to the right

NO. Your friend is incorrect because the solution to the system of equations on the graph is: (4, 3).

The solution to a system of linear equations is the coordinates of the point where the two lines of the linear equations intersect.

The x-coordinate and the y-coordinate of this point lie on each of the lines of the linear equations. This means that, both values of x and y are a solution to each of the linear equation given.

Therefore, the solution to a system of linear equations is usually represented as (x, y) and not just as a single value of x.

The system of linear equations that is graphed above shows that both lines intersect at (4, 3), that is, when x = 4, the value of y = 3.

However, your friend only stated the value of x = 4, as the solution to the system of linear equations that is represented on the graph.

Therefore, your friend is wrong.

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Value of x is 28.5 and y is 14.

An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles created when two rays are in the plane where the rays are located. The intersection of two planes also creates angles. We refer to these as dihedral angles.

Given Data

a = 2x + 3y

b = 4x - y

c = 3x + 2y

∠b = 100° ( corresponding angle)

4x - y = 100

4x - 100 = y

∠a = ∠b ( alternate angle)

2x + 3y = 4x - y

Equating values of y

2x + 3(4x - 100) = 4x - 4x + 100

2x + 12x - 300 = 100

14x = 400

x = [tex]\frac{400}{14}[/tex]

x = 28.5

For the values of y,

4(28.5) -100

114 -100

14

Value of x is 28.5 and y is 14.

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L = lbs lost by Leila

N = lbs lost by Nina

since we know that Leila lost "L" lbs and Nina lost 43lbs more than that, so Nina lost then "L + 43", and we also know their total weight was 95lbs hmmmm so

[tex]\stackrel{Leila's}{L}~~ + ~~\stackrel{Nina's}{(L+43)}~~ = ~~\stackrel{total}{95}\implies 2L+43=95\implies 2L=52 \\\\\\ L=\cfrac{52}{2}\implies L=26\hspace{15em}\underset{Nina~lost}{\stackrel{26~~ + ~~43}{\text{\LARGE 69}~lbs}}[/tex]

Answer:

3.2

Step-by-step explanation:

→ State Pythagoras theorem

x² + y² = z²

→ Substitute in

3² + 1²

→ Simplify

10 = z²

→ Evaluate

√10 = 3.2

Answer:

3.2

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

a = 3

b = 1

[tex]3^{2}[/tex] + [tex]1^{2}[/tex]  = 9 + 1 = 10

[tex]c^{2}[/tex] = 10

c = [tex]\sqrt{10}[/tex]

c = 3.16227766017

Round to the nearest tenth

c = 3.2

No. there is no rigid transformation taking Rectangle A to Rectangle B. See the explanation below.

The type of transformation that is taking place in the attached image from Rectangle A to Rectangle B is a non-rigid transformation. This is is because A rigid transformation (or isometry) is a transformation that DOES NOT change the size or shape of a geometric figure.

As it is easily observed, rectangle A is no longer the same shape and size as B. This means that the change or transformation that has occurred is non-rigid.

It is to be noted that dilation is a transformation that keeps the figure's geometry and orientation but alters its size. A dilation's scale factor is the factor by which each linear measure of the figure (such as a side length) is multiplied.

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The equation of the line that has a slope of -3 and passes through the point (5, -1) is 3x + y = 14.

What is slope ?

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

We know the slope point form,

y - y1 = m( x - x1 )

Where x1 and y1 atre the coordinates of the points and m is the slope.

Putting thew values from the question:

y - (-1) = -3 ( x - 5)

=> y  + 1 = -3x + 15

=> 3x + y = 14

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Answer: $13,713.75

Step-by-step explanation: 10% of $13,250 = $1,325 (the raise given)

$13,250 - $1,325 = $11,925 (original salary)

15% of $11,925 = $1,788.75

$11,925 + $1,788.75 = $13,713.75

Answer:

1.5 hour

Step-by-step explanation:

since 1 hour =70km . Then x hour =105 ÷70=1.5 hour

I just checked it for you. yes it can

Option (B) Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour is correct.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that:

A group of hikers tracked how long it took to hike a 10-mile trail. They hiked 2.5 miles in 2 hours, 7.5 miles in 6 hours, and 8.75 miles in 7 hours.

From the data given:

Ratio = distance/time

2.5 / 2 = 1.25 miles per hour

7.5 / 6 = 1.25 miles per hour

8.75 / 7 = 1.25 miles per hour

Thus, option (B) Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour is correct.

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Answer:

x = 9

Step-by-step explanation:

To solve for x, you must isolate the variable.

First, start by adding 2 to BOTH sides to eliminate the 2.

3=1/3x. then divide each side by 1/3

3÷1/3 = x

3/1 × 3/1 = x

9 = x

Answer: HL

Step-by-step explanation: the diagram compares the two sides, or legs, and the hypotenuse.

Answer:

3.26 time 102

Step-by-step explanation:

Because a square of 10 is 100

3.26 x 100 = 326

We know that the decimal move 2 spots to the right

So the answer is 3.26 x 102

Answer:60°

Step-by-step explanation:the whole thing equals 180° since it is a straight line. 30°+90°=120°   180°-120°=60°

The constant of the proportionality is 5.

Constant of proportionality:

The word constant of proportionality refers the ratio that relates two given values in what is known as a proportional relationship.

Given,

Greg has to find the area of a rectangle. The area can be determined by the equation A=5I, where A is area and I is the length of rectangle.

Here we need to find the constant of proportionality.

Through the given question we know that the area of the rectangle is

A = 5l

Here A represents the area of the rectangle

and the letter "l" denotes the length of the rectangle.

While we compare these with the standard form,

y = mx

Here m represents the constant of proportionality.

While in the given equation the place of m in standard equation number 5 is presented.

Therefore, 5 is the constant of proportionality.

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The least number of visits he needs to make in order to earn a free movie ticket is approximately 15 visits.

Points received for signing up = 85 rewards points

Points received for each visit to the movie theater = 10.5 points

Points needed for a free movie ticket = 240 points

Number of visits = x

85 + 10.5x ≤ 240

10.5x ≤ 240 - 85

10.5x ≤ 155

x ≤ 155 / 10.5

x ≤ 14.761

Approximately,

x ≤ 15 visits

Therefore, Jordan needs at least 15 visits to earn a free movie ticket.

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