Find the remainder for the quotient using either substitution or synthetic division.
x - 5 is a factor of the polynomial

f(x) = x^3 - x^2 - 17x - 15)
(The answer must include what the remainder value is and what it indicates.)

The simplified value of the exponential expression 3³ is 27

An equation is an expression that can be used to show the relationship between numbers and variables.

Exponent simply mean raising a number to a power. It is also called power or indices. It is given as:

a² = a * a;

a³ = a * a * a

Given the expression:

3³

Applying the law of exponents:

3³ = 3 * 3 * 3 = 27

3³ is 27

The simplified value of the exponential expression 3³ is 27

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If the temperature in the morning and noon is -14.8 degrees and 6.2 degrees Fahrenheit the temperature change will be 21°F.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.

It is given that  At 5:00 am in the morning, the temperature was -14.8 degrees Fahrenheit. By noon, the temperature increased to 6.2 degrees Fahrenheit.

First, the temperature is changed from -14.8 degrees to 0 degrees Fahrenheit and then from 0 degrees Fahrenheit to 6.2 degrees Fahrenheit.

The overall temperature change is,

ΔT =T₂ - T₁

ΔT =6.2° F - (-14.8°F)

ΔT =21°F

Thus, if the temperature in the morning and noon is -14.8 degrees and 6.2 degrees Fahrenheit the temperature change will be 21°F.

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Answer:

the answer is 60

Step-by-step explanation:

When first differences are the same it's a linear equation. First differences are equal to the slope, m. General equation is f(x) = mx + b

To see if a table of values represents a linear function, check to see if there's a constant rate of change. If there is, you're looking at a linear function.

How can one locate an equation?

determine a line's equation from two points:

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The line has a slope of 1 is L, and the line has a slope of 2 is K, slope of line is  [tex]y = (\frac{1}{3} )x[/tex].

Suppose a small grid represents a unit, from the graph,.

We can know,

For line L : When adding a unit horizontally, a unit is also added vertically.

Hence,

The slope of L : 1/1 = 1

For line K : When adding a unit horizontally, a two units are also added vertically.

Hence,

The slope of K : 2/1 = 2

A graph a line whose slope is 1/3, label the line a.

'a' line whole slope is 1/3

Suppose the line 'a' is,

[tex]y = (\frac{1}{3} )x[/tex]

x       0        3

y       0        1

Therefore,

The line has a slope of 1 is L, and the line has a slope of 2 is K, slope of line is  [tex]y = (\frac{1}{3} )x[/tex].

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Answer:

[tex]f(x)=x^{2} +13x+30[/tex]

Step-by-step explanation:

1. Whenever you write a quadratic function with zeros, you want to put it into a formula like this:

[tex]f(x)= (x-p) (x-q)[/tex]

p and q are the zeros

2. Your zeros are (-3) and (-10). When plugging in the zeros, you always flip the sign on the number. Because you would plug it in as: [tex]f(x) = (x-(-3)) (x-(-10))[/tex]

Two negative signs equal positive signs, so the equation will look like this:

[tex]f(x)=(x+3)(x+10)[/tex]

3. Solve the equation:

a. Use the foil method:  [tex](a+b)(c+d)=ac+ad+bc+bd[/tex]

[tex]f(x)=x^{2} +10x+3x+30[/tex]

b. Collect like terms

[tex]f(x)=x^{2} +(10x+3x)+30[/tex]

c. Simplify

[tex]f(x)=x^{2} +13x+30[/tex]

Hope that helps!

Answer: I have listed each part below

Step-by-step explanation:

a. The ratio of dogs to cats is 6 to 5

b. The ratio of cats to dogs is 5 to 6

c. For every 6 dogs there are 5 cats

d. The ratio of cats to dogs is 5:6

Answer:

1. 922x81=74,682

2. 783x14=10,962

3. 684x15=10,260

4. 650x22=14,300

5. 2525x37= 93,425

6. 615x41=25,215

Step-by-step explanation:

Answer:

? = 56 m

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{?}{8}[/tex] = [tex]\frac{21}{3}[/tex] = 7 ( multiply both sides by 8 to clear the fraction )

? = 7 × 8 = 56 m

Answer:

Step-by-step explanation:

Light takes approximately 8 minutes to reach the earth from Sun.

We orbit the Sun at a distance of about 150 million km. Light moves at 300,000 kilometers/second. Divide these and you get 500 seconds, or 8 minutes and 20 seconds. The distance between the Earth's orbit and the Sun's center is between 147 million and 152 million kilometers. Sunlight only needs 490 seconds to reach Earth from its closest point. Finally, it takes 507 seconds for sunlight to reach the farthest location.

Distance = 1.5 x 10^8 km

               = 1.5 x 10^11 m

Velocity  = 3 x 10^8

Time       = (1.5 x 10^11)/(3 x 10^8

              = 0.5 x 10^3

              = 500 s

              = 8 1/3 min

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When students in both the classes will know how to write the same number of letters, At that point they will know 7 letters

What is point of intersection?

Point of intersection is the point where two lines intersect.

Initially Mr. Sloan has taught his class 3 letters

and Ms. Estrada has taught her class 5 letters.

Now, Mr. Sloan is planning to teach his class 2 letters per week and Ms. Estrada is planning to teach her class 1 letter per week

By this rate after one week Mr. Sloan's class would know 5 letters and Ms. Estrada's class would know 6 letters.

In the second week, Mr. Sloan's class would know 7 letters and Ms. Estrada would know 7 letters.

The graph can be given as below

In the graph the black line represents the letters learned by Mr. Sloan's class and blue line represents the letters learned by Ms. Estrada's class

Also on the x-axis we put the number of weeks and on the y-axis we put the number of letters learned.

Both lines intersect at the coordinate (2,7) Which means that in the second week both the classes would have learned 7 letters

Hence student from both the classes would know 7 letters at the end of 2nd week

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a) The down payment of $60,000 is 30% for a studio apartment of $200,000 purchase price

b) The  down payment of $90,000 is 45% for a studio apartment of $200,000 purchase price.

Given,

The purchase price for the studio apartment = $200,000

The down payment they paid = $60,000

a) We have to find the percentage of down payment to purchase price.

Here,

Percentage = (down payment x 100) / purchase price

= (60,000 x 100) / 200,000

= 60/2

= 30

That is,

The down payment of $60,000 is 30% for a studio apartment of $200,000 purchase price.

b) We have to find the percentage to purchase price if the down payment is $90,000

Here,

Percentage = (down payment x 100) / purchase price

= (90,000 x 100) / 200,000

= 90/2

= 45

That is,

The  down payment of $90,000 is 45% for a studio apartment of $200,000 purchase price.

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Answer:

v = 61

Step-by-step explanation:

Hello, of course! These are vertical angles, which means they're equal to each other, so let's set up an equation, shall we? (:

Knowing that they're equal to each other, both sides of the equation should be equal to each other as well, so...

2v + 1 = 123

Now, that we have the equation, we must solve for the variable v!

2v + 1 = 123
     - 1      - 1

2v = 122

2v = 122
2        2

v = 61

Therefore, v is 61. Once again, vertical angles are equal to each other, so you set up the equation, where both sides are equal. Hope this helped and best of luck with the rest of your work! <3

Answer:

The equation is y = (5/2)x + 9

Step-by-step explanation:

We look for an equation with the form y = mx + b, where m is the slope and b the y-intercept.

We're given the slope, (5/2) which we can use for m:

y = (5/2)x + b

We are told the line goes through (8,29).  We need a value of b that will move the line to include this point.  Do that by substituting the values:

  x = 8, and y=29

y = (5/2)x + b

29 = (5/2)*8 + b

29 = (20) + b

9 =   b

The equation is y = (5/2)x + 9

See the attached graph.

Answer: All real numbers; (−∞ ,∞) ; infinite solutions

Step-by-step explanation:

[tex]-(8x +4)-1=-7x- (x + 5)[/tex]

You want to distribute the (-) in (-(8x +4)) and (- (x + 5))

[tex](-8x - 4) - 1 = -7x (-x - 5)[/tex]

Combine like Terms on Both sides:

[tex]-8x - 5= -8x - 5\\\\\\[/tex]

Add 5 to the right, and Add 8x to the left. (you want to cancel)

[tex]-8x - 5 = -8x -5\\+8x +5 \ \ +8x +5\\\\[/tex]

You are left with: [tex]0 = 0[/tex]

If you are end with 0=0, that means both equations are equal regardless of the variables. Therefore the answer is all real numbers; (−∞ ,∞) ; infinite solutions. You could check by substituting any values, and getting the same answers on both sides.

Using the slope and y-intercept, the linear function that model this problem is c = 10d + 12

A linear function is a mathematical function that graphs as a straight line. It is a polynomial of degree one and can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

In this problem, we can represent or model the given problem with a set or system of linear equation.

let;

Using y = mx + c and modeling it to suit our given parameter;

m = slope and c = y - intercept

We can take two the two given point and solve for the slope and y - intercept.

m = c₂ - c₁ / d₂ - d₁

m = 122 - 82 / 11 - 7

m = 10

Taking the slope and one point, we can solve for the y - intercept

y = mx + c

82 = 10(7) + c

82 = 70 + c

c = 82 - 70

c = 12

The equation can be written as c = 10d + 12

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The simplified forms of the radical expressions:

In this question we find five cases of addition of radical expressions that must be simplified into a single radical expression, that is, a radical expression of the form a√b. The simplification can be done by using algebra properties. The complete procedure is shown below:

Case 1

- 3√18 + 10√2

- 3 · (√9 × √2) + 10√2

- 3 · 3 · √2 + 10√2

- 9√2 + 10√2

√2

Case 2

- 2∛24 - 5∛3

- 2 · (∛8 × ∛3) - 5∛3

- 2 · 2 · ∛3 - 5∛3

- 4∛3 - 5∛3

- 9∛3

Case 3

5√12 - 2√27

5 · (√3 × √4) - 2 · (√3 × √9)

5 · 2 · √3 - 2 · 3 · √3

10√3 - 6√3

4√3

Case 4

5∛16 + 11∛2

5 · (∛8 × ∛2) + 11∛2

5 · 2 · ∛2 + 11∛2

10∛2 + 11∛2

21∛2

Case 5

3√54 - 21√24

3 · (√6 × √9) - 21 · (√6 × √4)

3 · 3 · √6 - 21 · 2 · √6

9√6 - 42√6

- 31√6

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Answer:

f(X1) = 17 f(X2) = 11

Step-by-step explanation:

f(x1) = -2(0) + 17

f(x1) = 17

f(x2) = -2(3) + 17

f(x2) = -6 + 17

f(x2) = 11

If each machine makes popcorn for 10 minutes, there will be enough popcorn as machine A and machine B make 87.5 ounces in 10 minutes.

According to the question,

We have the following information:

Machine A makes 12.75 ounces of popcorn in 3 minutes.

So, we will find the ounces of popcorn in 1 minute:

3 minutes = 12.75 ounces

1 minute = 12.75/3 ounces

1 minute = 4.25 ounces

So, in 10 minutes machine A will make:

10 minutes = (4.25*10) ounces

10 minutes = 42.5 ounces

Machine B makes 18 ounces of popcorn in 4 minutes.

So, we will find the ounces of popcorn in 1 minute made by machine B:

4 minutes = 18 ounces

1 minute = 18/4 ounces

1 minute = 4.5 ounces

So, in 10 minutes machine B will make:

10 minutes = (4.5*10) ounces

10 minutes = 45 ounces

Now, the total amount of popcorn made by both the machines will be:

Popcorn made by machine A in 10 minutes + Popcorn made by machine B in 10 minutes

42.5 + 45

87.5 ounces

Now, the eight 9-ounce bags mean that there will be 72 ounces of popcorn.

So, we have:

87.5 ounces is greater than 72 ounces.

Hence, the correct option is B.

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In any triangle, the segment joining the mid-points of two sides is parallel to the third side and equal to half its length

B is the mid-point of RS

C is the mid-point of RT

BC = 1/2 ST

BC = x + 19

ST = x + 29

x + 19 = 0.5(x + 29)

x + 19 = 0.5(x) + 0.5(29)

x + 19 = 0.5x + 14.5

Subtract 0.5x from both sides

x - 0.5x + 19 = 0.5x - 0.5x + 14.5

0.5x + 19 = 14.5

Subtract 19 from both sides

0.5x + 19 - 19 = 14.5 - 19

0.5x = -4.5

Divide both sides by 0.5

The answer is D

x = -9

A rate ratio  two groups' incidence, person-time, or mortality rates. The two groups are often distinguished by demographic traits or by exposure to a suspected causal agent, similar to how the risk ratio distinguishes them.

The jar contains nine quarters, three dimes, and one nickel, for a ratio of nine to three to one. As a result, the ratio of pennies to quarters is 6: 7. c. Sum up the pennies to quarters ratio. The amount of dime coins to all the coins should be written down.

How should a rate ratio be written?

A ratio can be expressed as a fraction 35, 3:5, or with a colon. In contrast, a rate is a comparison of two quantities that may have several units. A rate might be, for instance, 5 miles every 3 hours or 34 dollars per square foot.

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Michael should use 2.1 cups of boiling water with 3 lemons.

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Answer:

[tex]\sf y = \dfrac{-2}{5}x+1[/tex]

Step-by-step explanation:

Where m is the slope and b is y-intercept.

      (5, -1)  & (-5, 3 )

    [tex]\sf \boxed{Slope=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

               [tex]\sf =\dfrac{3-[-1]}{-5-5}\\\\=\dfrac{3+1}{-10}\\\\=\dfrac{-4}{10}\\\\=\dfrac{-2}{5}[/tex]

  Substitute m = (-2/5) in the equation,

           [tex]\sf y = \dfrac{-2}{5}x+b\\\\Now, substitute \ any \ point \ in \ the \ above \ equation \ and find \ 'b',\\\\(5,-1)\\\\ -1 = \dfrac{-2}{5}*5+b\\\\-1=-2+b\\[/tex]

        -1 + 2 = b

                [tex]\sf \boxed{b = 1}\\\\\bf The \ equation \ of \ the \ line, \\\\ \ y =\dfrac{-2}{5}x+1[/tex]

Answer

n = 5

Explanation

We need to solve for n in the equation given

7n - 4 = 31

Add 4 to both sides

7n - 4 + 4 = 31 + 4

7n = 35

Divide both sides by 7

(7n/7) = (35/7)

n = 5

Hope this Helps!!!

If y varies directly with x and y = 12 when x = 3, then the direct linear variation equation for the relationship is y = 4x

y varies directly with x

y ∝ x

The directly proportional mean the value of the one variable will varies with the variation in other variable. That means one variable will be dependent variable and other variable will be independent variable

Here

y ∝ x
y = kx

Where y is the dependent variable

x is the independent variable

k is the constant

The values are

y = 12

x = 3

Substitute the values in the equation and find the value of k

12 = k×3

k = 12/3

k = 4

Substitute the value of k in the equation

y = 4x

Hence, if y varies directly with x and y = 12 when x = 3, then the direct linear variation equation for the relationship is y = 4x

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Answer:

k<=-2

Step-by-step explanation:

-3k≥6

3k<=-6 ==> when dividing by negative numbers switch the sign of the inequality

3k/3<=-6/3

k<=-2

In the congruent triangles both triangle are same . In this triangle 2.3.3 congruent triangle image given below to understand better.

According to the question, given that

2.3.3 congruent triangle under congruence triangle are explain:

Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle. We can see from the examples PQR and XYZ that PQ = XY, PR = XZ, and QR = YZ, and thus P = X, Q = Y, and R = Z. Then, we can state that XYZ and PQR.

To be congruent, the two triangles must be the same size and shape. It is necessary for both triangles to be superimposed on one another. A triangle appears to be in a different place or have a different look as we rotate, reflect, and/or translate it.

Two triangles must meet five requirements in order to be congruent. The congruence properties are SSS, SAS, ASA, AAS, and RHS.

SSS Congruence Criteria

Side-Side-Side criterion is referred to as the SSS criterion. According to this standard, two triangles are congruent if their respective triangles' three sides are equal to one another.

The three angles of BAC must be identical to the corresponding angles of XYZ if, according to the SSS condition, BAC XYZ.

SAS Congruence Criteria

Side-Angle-Side criterion is referred to as the SAS criterion. According to this standard, two triangles are said to be congruent if their matching sides and included angles are the same on each side of each other.

The third side (AB) and the other two angles of ABC must be identical to the equivalent side (XY) and the angles of XYZ if ABC XYZ under the SAS condition.

ASA Congruence Criteria

Angle-Side-Angle criterion is also known as ASA criterion. According to the ASA criterion, two triangles are congruent if any two of their included sides and related angles are equivalent in size to those of the other triangle.

AAS Congruence Criteria

Angle-Angle-Side criterion is also known as the AAS criterion. Two triangles are said to be congruent according to the AAS criterion if any two angles and the non-included side of one triangle match the corresponding angles and side of the second triangle.

RHS Congruence Criteria

Right angle-hypotenuse-side congruence is referred to as the RHS criterion. If the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, then two triangles are said to be congruent according to this criterion.

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Answer:

4979

Step-by-step explanation: