Is (x + 7) a factor of f(x) = x3 − 3x2 + 2x − 8? Explain your reasoning.

Answer: -7

Step-by-step explanation:

7 ÷ (-9 - -8)³

(-9 - -8)³ = -1

7 ÷ -1 = -7

Answer:

-7

Step-by-step explanation:

We have to solve this according to the B O D M A S theorem.

That is:

B ⇒ Brackets

O ⇒ Of

D ⇒ Division

M ⇒ Multiplication

A ⇒ Addition

S ⇒ Subtraction

Also, we know that,

( + ) × ( + )  = ( + )

( - ) × ( - ) = ( + )

( + ) × ( - ) = ( - )

Let us solve it now.

7 ÷ ( - 9 - ( - 8 ) )³

7 ÷ ( - 9 + 8 )³

7 ÷ ( - 1 )³

7 ÷ ( - 1 )

- 7

BD ≅ CE is proved and is shown below.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given are two triangles as shown in the figure.

Triangles ΔMPN and ΔSTU are congruent. We can write -

2x - y = 13

2x - 50 = 24

Now -

2x - 50 = 24

2x = 74

x = 3The measurements of [x] and [y] are 37 and 61 respectively.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is isosceles △ABC with legs AB and AC, BD ⊥DC and CE ⊥ BE.

In △BDC and △CEB, we can write -

∠D = ∠E = 90°

BC = BC {Common}

∠B = ∠C  {Angles opposite to equal sides are equal}

By SAS criteria △BDC ≅ △CEB.

So, we can write -

BD ≅ CE

Therefore, BD ≅ CE is proved and is shown above.

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The time taken by the Reagan to cover the distance of 28 meters will be 7 seconds.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that Reagan is running toward school twice as fast as her brother. If her brother is running at 2 meters per second.

The time taken to cover the distance of 28 meters will be calculated as,

R = 2B

Brother's speed = 2 m / s

Reagan's speed = 2 x 2 = 4 m/s

The time will be,

T = Distance / Speed

T = 28 / 4

T = 7 seconds

Therefore, the time taken by Reagan to cover the distance of 28 meters will be 7 seconds.

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Answer:

22

Step-by-step explanation:

If larry and Donna bought a sofa at the sale price of $1,344. The original price of the sofa was $1,920. Then the discount rate is 30%.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

larry and Donna bought a sofa at the sale price of $1,344.

original price of the sofa was $1,920

We need to find the original rate

1920-1344/1920

576/1920

0.3

Now we have to multiply with 100 as it it hundredth part

0.3×100

30

Hence, the discount rate of sofa is 30%.

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The minutes when Anjam travel from Sheffield at 10.15am and arrived in Watford 3.55pm in minutes is 320 minutes.

It is important to note that the question is simply about the calculation of the time involved. Based on this situation, it should be noted that:

60 minutes = 1 hour.

Given that due to road works and a diversion, Anjam's drive from Sheffield to Watford took a lot longer than planned. He left Sheffield at 10.15am and arrived in Watford 3.55pm in minutes.

The time for the journey will be:

= 3.35pm - 10.15am

= 5.20 hours.

We will change this to minutes:

= (5 × 60) + 20

= 320 minutes

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Answer: 20

Step-by-step explanation:

Use 1 as the denominator to convert any number to a fraction:

24/1

The fraction 5/6 and our new fraction, 24/1, are now side by side, and we can multiply those two fractions to find the answer now that we have converted 24 into a fraction.

Multiply the numerators and denominators after converting the entire number to a fraction.

5*24/6*1 = 120/6

In this instance, it is possible to further simplify our new fraction. To do that, we must determine the two numbers' highest common factor.

So. GCF is 6.

We can now divide both the new numerator and the denominator by 6 to simplify this fraction down to its lowest terms.

120/6 = 20.

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Answer:

Step-by-step explanation:

what is the 5/6 of 24?

we can solve by multiplying 5/6 by 24

5/6 × 24 =

20

Haha ITS MATHXL

Anyways, constant rate of +90 and currently has 1560.

Say y will be the amount of students, and x is how many years later.

y=90x+1560

So for a), the answer is y=90x+1560

For b), plug in 3 for x, since 2017 is 3 years after 2014.

y=90(3)+1560
y=270+1560
y=1830

Amount of students in 2017: 1830

For c), plug in 2010 for y.

2010=90x+1560
Subtract 1560 both sides
450=90x

Divide both sides by 90
x=5

Answers

a) y=90x+1560
b) 1830
c) 5 Years Later, or 2019

Hope this helps!

Answer:

C. 6x + 15

Step-by-step explanation:

1. Distribute

3(2x + 5)

6x + 15

(We get this answer by multiplying the number outside the parentheses, which is 3, by the numbers in the parentheses. As in, 3 x 2x = 6x. And 3 x 5 = 15. So, we get 6x + 15).

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By means of trigonometric functions and trigonometric formulas, the trigonometric equation sec α · (1 - cos² 2α) is equivalent to 4 · cos α - 4 · cos³ α.

In this problem we find the case of a trigonometric equation that must be simplified by definitions of trigonometric functions and trigonometric formulas. First, write the trigonometric equation:

sec α · (1 - cos² 2α)

Second, use the fundamental trigonometric formula:

sec α · sin² 2α

Third, use the definition of secant and the formula for the sine of the double angle:

(1 / cos α) · (2 · sin α · cos α)²

4 · sin² α · cos α

Fourth, use the fundamental trigonometric formula:

4 · (1 - cos² α) · cos α

4 · cos α - 4 · cos³ α

None of the options given are equivalent to the trigonometric equation.

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The domain of the function f(t) is best described as 608 ≤ t ≤ 620

From the question, we have the following parameters that can be used in our computation:

Rate = 2.5 kilograms per hour

Mass of the car (including the fuel) = 1550 kg

Mass of the car (not including the fuel) = 1520 kg

Calculate the times using the rate and the masses above

So, we have the following representations

Time 1 = 1550/2.5

Time 1 = 620

Time 2 = 1520/2.5

Time 2 = 608

Express as an interval

608 ≤ t ≤ 620

Hence, the domain is 608 ≤ t ≤ 620

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Answer:

Step-by-step explanation:

Used  (0,0) and (-2,4)

(4-0)/(-2-0)= m

m= 4/-2 = -2

The amount of blood that the human heart circulates every year is represented by the following compound inequality: 770,000 < x < 1,600,000, where x is in gallons of blood.

Herein we must determine the compound inequality, that is, a simultaneous inequality of the form a < x < b, where a and b are the limits of the inequality. According to the statement, the human heart circulates every year at least 770,000 gallons of blood and at most 1,600,000 gallons of blood. Then, the compound inequality that represents the situation is:

770,000 < x < 1,600,000, where x is in gallons of blood.

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Answer:

3 and 9

Step-by-step explanation:

The factors of 45 are 1, 3, 5, 9, 15, 4.

3x9=45

3+9=14

Answer:

y=6

Step-by-step explanation:

75-3.5y-4y=4y+6

Combine like terms on each side

75-7.5y=4y+6

Add 7.5y to both sides since it is the inverse of subtraction

75-7.5y=4y+6

   +7.5y. +7.5y

75=11.5y+6

Isolate y on one side by subtracting 6 from both sides

75=11.5y+6

-6.          -6

69=11.5y

Divide both sides by 11.5

69=11.5y

/11.5. /11.5

6=y

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There 1540 teams  can be formed.

A combination is a combination of n things taken k at a time without repetition.

Given that, A company has 11 male and 8 female employees, and needs to nominate 2 men and 2 women for the company bowling team.

The formula for a combination of choosing r unique ways from n possibilities is:

nCr  = n!/r!(n - r)!

2 men out of 11 men = 11C2 = 11!/2!(11-2)! = 55

2 women out of 8 men = 8C2 = 8!/2!(8-2)! = 28

Number of teams = 55*28 = 1540

Hence, There 1540 teams  can be formed.

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Answer: 27 pizzas

Step-by-step explanation:

Total ounces available = 4 jars x 24.44 ounces/jar = 97.76 ounces

(97.76 ounces) x (1 pizza/3.5 ounces) = 27.93 pizzas

You can make 27 whole pizzas (the 28th pizza will be short on the sauce)

Answer:

n = 44

Step-by-step explanation:

the 'dashes ' through the 2 legs of the triangle indicate they are congruent.

then n = 44 mm

The profit that Vaughn would make if he charges $3.80 per bag is $27.20.

The first step is to determine the total pieces of candy that Vaughn plans to sell.

Total pieces of candy = number of pieces in each bag x total number of bags

Total pieces of candy = 24 x 15 = 360

The second step is to determine the total number of bags he has to buy.

Number of bags he is going to buy = total pieces of candy he is going to sell / number of pieces in each bag

Number of bags he is going to buy = 360 / 18 = 20 bags

The third step is to determine the total cost of buying 20 bags

Total cost = number of bags he is going to buy x cost per bag

Total cost = 20 x $3.20

Total cost = $64

The next step is to determine the total revenue from making 24 bags.

Total revenue = price per bag x total number of bags

Total revenue = $3.80 x 24

Total revenue = $91.20

Profit = revenue - cost

$91.20 - $64 = $27.20

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The probability that exactly 2 of the brussel-spout-with-turnip-chips cookies is picked at random is 0.05 approximately to two decimal place.

To calculate the probability of an event, we identify an event of the required outcome result and the total number of results or possible outcomes that can occur, and thus divide the number of required outcomes by the total number of possible outcomes.

The total possible outcomes = 20

probability of picking a chocolate-chip cookies = 13/20

probability of picking brussel-spout-with-turnip-chips cookies = 7/20

probability of getting exactly 2 brussel-spout-with-turnip-chips cookies when 4 cookies are picked at random considering the they are not replaced after each pick is calculated as follows;

(13/20) × (13/20) × (7/20) × (7/20)

8281/160000

0.0518.

Hence, from our calculations by simplification the probability of getting exactly 2 brussel-spout-with-turnip-chips cookies when 4 cookies are picked at random is 0.05 approximately to two decimal place.

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The value of 375 grams of a 12% solution is 45 grams.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Based on the information given, it should be noted that in order to calculate the value of the grams, we simply need to multiply the value of the percentage that's is given by the number of grams that's given.

In this case, the value of the gram will be:

= Percentage given × Total grams

= 12% × 375 grams

= 0.12 × 375 grams

= 45 grams.

Therefore, the value will simply be 45 grams.

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Answer:

45

Step-by-step explanation:

375*0.12=45

The daughter's age is 7 years old.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a parent is 20 years older than twice his daughter's age, and he was half of his present age 17 years back.

Let the age of the parent be x,

He/she was half of the age 17 years back, then,

x/2 = x-17

x = 34

Therefore, parent's present age is 34 years.

He is  20 years older than twice his daughter's age,

Let his daughter's age be y,

2y+20 = 34

2y = 14

y = 7

Hence, his daughter's age is 7 years old.

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Answer:

-2

Step-by-step explanation:

use the formula

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

Answer is he run with 11m/s.

Answer:

[tex]\frac{7}{24}[/tex] x + 16

Step-by-step explanation:

[tex]\frac{5}{8}[/tex] x + [tex]\frac{2}{3}[/tex] ( - [tex]\frac{1}{2}[/tex] x + 24) ← distribute parenthesis

= [tex]\frac{5}{8}[/tex] x - [tex]\frac{1}{3}[/tex] x + 16 ( express fractions with common denominator 24 )

= [tex]\frac{15}{24}[/tex] x - [tex]\frac{8}{24}[/tex] x + 16

= [tex]\frac{7}{24}[/tex] x + 16

Answer:

[tex]x = wy - wz[/tex]

Step-by-step explanation:

this equation looks like this

[tex]w = \frac{x}{y - z}[/tex]

to solve for x you can multiply both sides by y - z

this would cancel out the y - z on the bottom

this would make it

[tex]w(y - z) = x[/tex]

now you must distribute and switch the x to the other side

[tex]wy - wz = x[/tex]

[tex]x = wy - wz[/tex]

Answer:

(0,7)

Step-by-step explanation:

Answer:

Step-by-step explanation:

to find x;

-4x - 2 -1 =8

-4x + 3 = 8

+4  + 3 = +4

x + 3 = 12

   -3 + -3

    x  =  10

to find y;

y = x2 - 3

y = (10)2 - 3

y = 20 - 3

y = 17

Answer:

Mikhail is 49 years old.

Step-by-step explanation:

39+49=88

Answer:

(0, 1) and (-3, -2)

Step-by-step explanation:

The solutions are the points of intersection of the two graphs.

We can read the points off the graph.

Answer: (0, 1) and (-3, -2)