If f(x)= x³ - 5x² - 22x - 16 and x + 2 is a factor of f(x), then find all of the
zeros of f(x) algebraically.

The expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed is [tex]\frac{3^{6} }{9^{15} }[/tex]

Nine raised to the negative third power = [tex]9^{-3}[/tex]

Three raised to the negative second power times nine squared = [tex](3x^{-2})(9^{2} )[/tex]

The expression is [tex](\frac{9^{-3} }{(3^{-2})(9^{2} ) } )^{3}[/tex]

=[tex]\frac{9^{(-3)(3)} }{(3^{(-2)(3)})(9^{(2)(3)} }[/tex]

=[tex]\frac{9^{-9} }{(3^{-6})(9^{6}) }[/tex]

= [tex]\frac{3^{6} }{(9^{9})(9^{6}) }[/tex]

= [tex]\frac{3^{6} }{9^{15} }[/tex]

Hence, the expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed is [tex]\frac{3^{6} }{9^{15} }[/tex]

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Answer:

I'm sure it's 1.2506407mm

Step-by-step explanation:

By using the method of trigonometry,

(1)sin B=P/H=AD/AB=12/13

(2)sec B=H/B=AB/BD=13/5

(3)cot B=B/P=BD/AD=5/12

(4)cos C=B/H=CD/AC=16/20=4/5

(5)cosec C=H/P=AC/AD=20/12=5/3

(6)tan C =P/B=AD/DC=12/16=3/4

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are the trigonometric functions (sometimes known as the circle functions) that make up trigonometry. The unit circle is the most straight forward way to define the trigonometric functions. Let theta represent an angle that is calculated along a circle's arc counterclockwise from the x-axis.

Given that,

[tex]AD^{2}= AB^{2}- BD^{2}= 13^{2}- 5^{2}= 169-25= 144[/tex]

=>AD=12cm

(1)sin B=P/H=AD/AB=12/13

(2)sec B=H/B=AB/BD=13/5

(3)cot B=B/P=BD/AD=5/12

[tex]AC^{2}= AD^{2}+ DC^{2}= 12^{2}+ 16^{2}= 144+ 256= 400[/tex]

=>AC=20cm

(4)cos C=B/H=CD/AC=16/20=4/5

(5)cosec C=H/P=AC/AD=20/12=5/3

(6)tan C =P/B=AD/DC=12/16=3/4

note: P=perpendicular

B=base

H=hypotenuse

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The sale price of the magazine subscription is $11.55

From the question, the given parameters are:

Subscription = $35

Discount = 67% off

The sale price of the magazine subscription is then calculated as

Sales price = Subscription x (1 - Discount)

Substitute the known values in the above equation

So, we have the following equation

Sales price = 35 x (1 - 67%)

Evaluate the product

Sales price = 11.55

Hence, the sales price is $11.55

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Answer:

y=-3x-2

Step-by-step explanation:

y=mx+b; adjust b value --> y=-3x-2

If CA and CE are opposite rays, CH bisects ∠ GCD, and GC bisects ∠ BGD. If m ∠ BGC = (7x - 2)° and m ∠ CGF = (8x - 8)°, then the value of m ∠ BGF exists 80°.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The two rays are called the sides of an angle, and the common endpoint is called the vertex.

If CA and CE are opposite rays, CH bisects ∠ GCD, and GC bisects ∠ BGD.

Given: m ∠ BGC = (7x - 2)° and m ∠ CGF = (8x - 8)°,

m ∠ BGC = m ∠ CGF

7x - 8 = 8x - 8

substracting 2 from both sides of the equation, we get

7x - 8 = 8x - 8 - 8

7x - 8 = 8x

simplifying the above equation, we get

x = 6

Therefore, the value of x = 6.

⇒ m ∠ BGC = m ∠ C G F = 40°

Therefore, the value of m ∠ BGF = 2(40)° = 80°

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The value of x is 11.7.

The angles CAB, ACB, and ABC are 43.1°, 69°, and 68.2° respectively.

Given angles are:

A = (3x+8)°

B= (6x-2)°

C = 69°

Using the Angle sum property we get,

(3x+8)° + (6x-2)° + 69° = 180°

9x + 75° = 180°

9x = 180°- 75°

x = 11.7

CAB = (3 × 11.7 + 8)° = 43.1°

ACB = 69°

ABC = (6 ×11.7 - 2) = 68.2°

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When a scale factor of 1 inch to 6 feet is used, the length is 9 inches.

From the information illustrated, a scale factor of 1 inch to 6 feet is used. In this situation, an object in real life is 55 feet long.

The number of inches that should be in the scale drawing will be:

= Number of feet / Scale used

= 55 / 6

= 9.17 inches

The length that should be in the scale is 9 inches.

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A scale factor of 1 inch to 6 feet is used. An object in real life is 55 feet long. How many inches long should it be in the scale drawing?

Answer:

1. 6x+18 2. 5y-20 3. -7m+7

Step-by-step explanation:

1. 6(x+3) 2. 5(y-4) 3. -7(m-1)

6x+24. 5y-20. -7m+7 <--- - times - = +

Answer:

92 men

Step-by-step explanation:

First, since they give you the total employees, you need to add the ratios together to get a total.

4 + 7 = 11

Next, setup a proportion using men to total employees.

[tex]\frac{4}{11}=\frac{m}{253}[/tex]

The left side is the ratio and the right side is the actual. m will represent the total number of men employed.

Cross multiply then divide.

4 x 253 = 1012

11 x m = 11m

11m = 1012

11m/11 = 1012/11

m = 92

There are thing we must already know:

From this, we must know that:

The scientis needs 0.25kilograms. From this we calculate:

The equation of the line that contains the point P(-4,6) and has slope 4 is  y=4x+22 .

The equation of line passing through the point (x₁,y₁) with slope (m) is given by the formula

(y-y₁)=m(x-x₁)

In the question ,

it is given that

the required line passes through the point P(-4,6) and has slope 4

So, x₁= -4 , y₁=6 and m = 4

Substituting the values of x₁, y₁ and m in the equation of line formula , we get

y-6=4(x-(-4))

y-6=4(x+4)

y-6=4x+16

y=4x+16+6

y=4x+22

Therefore , the equation of the line that contains the point P(-4,6) and has slope 4 is  y=4x+22 .

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Sum of APs 2+5+8+........ as far as the 18th term is 495.

Sum of n terms of A.P.

[tex]S_{n} = \frac{n}{2}[2a+(n-1)d][/tex]

where,

[tex]S_{n}[/tex] = sum of n terms of A.P.

a = first term of A.P.

d = Common difference.

Given,

d=5−2=3

a=2

[tex]S_{11}[/tex]=[tex]\frac{18}{2}[/tex][4+(18-1)×3]

=[tex]\frac{18}{2}\\[/tex][4+51]

=[tex]\frac{18}{2}[/tex]×55

=495

An arithmetic progression, or arithmetic sequence, is a sequence of numbers in which the difference between successive members is constant. Here is the AP formula for AP a, a + d, a + 2d, a + 3d, . . . a + (n - 1) d. The formula for finding the nth term is [tex]a_{n}[/tex] = a + (n – 1) × d.

Then the formula for finding the sum of the arithmetic progressions is:[tex]S_{n} = \frac{n}{2}[2a+(n-1)d][/tex] where a = first term in arithmetic progression, n = number of terms in arithmetic progression, and d = total difference.

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Answer:

y=4/3-5

Step-by-step explanation:

Y=mx+c

mx=gradient which is 4/3

c is y intercept which is -5

On average, the bear's weight change per month was 8.6 pounds.

The average is the mean value in a data set.

We compute the average by adding the data values and dividing by the number of items in the data set.

In this scenario, the average weight loss per month offers an idea of the weight change the bear experienced during the 7¹/₂ months.

The number of months during hibernation = 7¹/₂ or 7.5 months

The total weight loss = 64.5 pounds

The average weight change per month = 8.6 pounds (64.5/7.5)

Thus, we can conclude that, on average, the bear experienced a weight loss of 8.6 pounds per month and reduced by a total of 64.5 pounds in 7¹/₂ months.

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During 7 1/2months of hibernation, a black bear experienced a weight loss of 64.5 pounds.

(a) The probability distribution table is provided in the attachment.

(b) The probability distribution of X is discrete.

Let X = number of hours a service calls take.

(a)The probability of an event E is:

P(E)=n(E)/N

Here,

n (E) = number of favorable outcomes

N = total number of outcomes.

The probability distribution table is provided in the attachment.

(b)For a discrete probability distribution:

f(x) >= 0

summation f(x)= 1

Check that the probability distribution of X is discrete as follows:

The value of f (x) for all values of x is greater than 0.

The sum of all f (x) is 1.

Thus, the probability distribution of X is discrete.

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There are 10 students in a class, 6 of them wear glasses. If a student is chosen at random from the class, then the probability that they do not wear glass is 2/5

Total number of Students = 10

Students who wear glasses = 6

Students who don't wear glasses = 4

Probability is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as,

P(E) = (Number of favorable outcomes) ÷ (Total favorable outcomes).

The probability of a student not wearing glasses is,

Probability = Students who don't wear glasses/Total number of Students

Probability = 4/10 i.e., 2/5

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Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

The value of x is 4 , the correct option is (C)4 .

In the question ,

it is given that AD and BE are diameters , hence they are straight lines .

From the figure shown below , we can see that

∠AOE and ∠BOD are vertically opposite angles ,

the property of vertically opposite angle states that " the vertically opposite angles are equal in measure ."

So,

substituting the values of ∠AOE and ∠BOD from the figure , we get

36x-4 = 92+(11x+4)

36x-11x = 92+4+4

25x = 100

x=4

Therefore , the value of x = 4, the correct option is (C)4 .

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Answer:

- 8n -4 +n+7

like terms (-8n, n) and (-4, 7)

so; -8n+n-4+7

    = -7n+3

Answer:

-7n + 3

Step-by-step explanation:

   Like terms are terms that have same variable with same power.

-8n and n are like terms.  subtract or add the coefficient of the like terms.

(-8) and 1. So, subtract and it is -7n

(-4) and 7 are like terms(constants).

-8n - 4 + n + 7 = -8n + n - 4 + 7

                        = -7n + 3

Answer:If 104 items were sold and 32 if these are cookies, to get number of brownies sold subtract 32 from 104.  This gives 72 brownies sold.  

A ratio is a fraction.  If we want the ratio of brownies to cookies it would look like

    brownies            72

   ________     =  _____

     cookies             32

This ratio could be reduced by dividing both parts of the fraction by the greatest common factor of 8.

This gives a reduced ratio of     9

                                             _____

                                                4

Step-by-step explanation:

Answer:I think 82 or 56

Step-by-step explanation:

Answer:

We will get that the distance is 3.22.

The expressions that represent Bruce's score at the end of the game will be 5(10x) + 30(5) = 150 + 50x.

From the information, Bruce completed all 5 levels of his favorite video game, Extreme Treasure Hunter and in the game, you can earn points by collecting gemstones or finding pieces of the treasure map.

The expression to illustrate the number of points will be:

= 5(10x) + 30(5)

where c = number of points per gemstone

= 50x + 150

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$7.99 is the constant of proportionality in this relationship.

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well. An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.

Given Data

The cost for 6 months is $47.94.

x = number of months

x = 6

y =  total amount of money they have paid for the subscription

y = 47.94

Constant of proportionality = [tex]\frac{47.94}{6}[/tex]

Constant of proportionality = 7.99

$7.99 is the constant of proportionality in this relationship.

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If QR = 6x, RS = 10 and QS = 5x+13, then the length of the line QS is 28 units.

The length of the line QR = 6x

The length of the line RS = 10

The length of the line QS = 5x+13

We know

The length of the line QS = The length of the line QR + The length of the line RS

Substitute the values in the equation

5x+13 = 6x + 10

Move the 6x to the left hand side of the equation and move 13 to the right hand side of the equation

5x-6x = 10-13

Subtract the terms

(5-6)x = 10-13

-1x = -3

x = 3

Then the length of the QS = 5x+13

Substitute the value of x in the equation

The length of the line QS = 5×3+13

= 15+13

= 28 units

Hence, if QR = 6x, RS = 10 and QS = 5x+13, then the length of the line QS is 28 units

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Answer: move the base and exponent to the other side of the fraction line and change the exponent to positive: 1/(24)

The question is testing knowledge on subsets. The application of combinations is used to sum up. Consider prime factors between 1 and 11. They are{1,2,3,4,5,6,7,8,9,10,11}.

The prime factors in the set are {2,3,5,7,11}. This set has 5 elements.

Apply combinations to obtain the total subsets.

The subsets with 1 element is 5C1 = 5 subsets

The subsets with 2 elements is 5C2= 10 subsets

The subsets with 3 elements is 5C3= 10 subsets

The subsets with 4 elements is 5C4= 5 subsets

The subsets with 5 elements is 5C5= 1 subset

The total non-empty subsets are 5+10+10+5+1 = 31 subsets.

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The ratio of consonants to vowels is 21:5.

What is ratio?

A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4), while the ratio of oranges to overall fruit is 8:14. (or 4:7).

No. of consonants = 21

No. of vowels = 5

(A) Ratio of consonant to vowels = 21/5 = 21:5

(B) Fraction of vowels = 5/26

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We will add 1 to 2/3 to make sum of [tex]1\frac{2}{3}\\[/tex] of an integer and a fraction.

What is integer?

What is fraction?

- [tex]1\frac{2}{3}[/tex]  = _ + (2/3)

we will add 1 to 2/3 to make sum of [tex]1\frac{2}{3}\\[/tex] of an integer and a fraction.

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