Let P(x)=x^{5}-2x^{4}-7x^{3}+x^{2}+20P(x)=x 5 −2x 4 −7x 3 +x 2 +20. Use synthetic division to find P(10) and P(-8).

To find the slope of the curve at t=3, we first need to find the values of x and y at t=3 using the given equations.

x = (3)^5 + 3 = 246

y + 3(3)^5 = 3

y = -1347

Next, we can differentiate both equations with respect to t to get the following:

dx/dt = 5t^4 + 1

dy/dt = -15t^4

At t=3, we get

dx/dt = 5(3)^4 + 1 = 454

dy/dt = -15(3)^4 = -1215

Therefore, the slope of the curve at t=3 is given by dy/dx = (dy/dt)/(dx/dt) = (-1215/454) ≈ -2.68. This means that the curve is decreasing (sloping downwards) at t=3.

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Answer:

Step-by-step explanation:

I believe u have to factorise

(a+3)(a+5)

Answer:

1st one is 6.9 X 10^6

2nd one is 2 x 10^5

Step-by-step explanation:

Answer:

Step-by-step explanation:

32.) We are looking for the values that are in x, z, or both

so 1,2,4,6,8,9

33.) We are looking for the values that are in x and y

so 4

34.) We are looking for the value that are in y,z, or both

so 1,2,3,4,5,6,7,8,9

35.) We are looking for the values that are in y and z

so none

Answer:

x = 7, y = 2

Explanation:

equations given:

x + 7y = 21

x + 4y = 15

make "x" the subject:

x + 7y = 21

x = 21 - 7y .........equation 1

x + 4y = 15

x = 15 - 4y .......equation 2

Solving both the equations simultaneously:

15 - 4y = 21 - 7y

-4y + 7y = 21 - 15

3y = 6

y = 6 ÷ 3

y = 2

If y is 2

Then x = 21 -7y;

x = 21 - 7(2)

x = 21 - 14

x = 7

x + 7y= 21

7 goes to RHS = X+ y = 21/7-3

x + 4y = 15

4 goes to RHS= x+y = 15/4 = 3.75

a. $456 would be the amount a customer could save during the first year by switching from Cable Zone to Super Vision.

b. Super Vision raises the rates 23% after a new customer's first year,  a customer who switched from Super Vision save $180 in the second year.

c. Super Vision raises the rates 18% for the third year compared to the second year, for the third year, Cable Zone would be cheaper.

a. To calculate how much a customer could save during the first year by switching from Cable Zone to Super Vision, we need to compare the costs of the two providers.

Cable Zone charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for monthly cable television. Therefore, the total cost per month with Cable Zone is:

$46 (home phone) + $36 (Internet) + $56 (cable television) = $138

Super Vision, on the other hand, offers all three services for a flat $100 monthly fee. So, the customer would save:

$138 (Cable Zone cost) - $100 (Super Vision cost) = $38 per month

Therefore, during the first year, the customer could save:

$38 (monthly savings) * 12 (number of months) = $456

b. After the first year, Super Vision raises the rates by 23%. The new monthly fee would be:

$100 (original fee) + 23% (rate increase) * $100 (original fee) = $123

To calculate the savings in the second year, we need to compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $123 (Super Vision cost) = $15 per month

Therefore, in the second year, the customer would save:

$15 (monthly savings) * 12 (number of months) = $180

c. If Super Vision raises the rates by 18% for the third year compared to the second year, we need to calculate the new monthly fee. The new Super Vision fee would be:

$123 (second-year fee) + 18% (rate increase) * $123 (second-year fee) = $145.14

To determine which company is cheaper for the third year, we compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $145.14 (Super Vision cost) = -$7.14

In this case, the Super Vision cost is higher than the Cable Zone cost by $7.14 per month. Therefore, for the third year, Cable Zone would be cheaper.

Overall, during the three-year period, the customer would save a total of $456 (first year) + $180 (second year) = $636 by switching to Super Vision.

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Greetings from Brasil...

Isolating S:

B = [(S+Z)/4]·h

B/h = (S + Z)/4

Answer: KL = KN LM=NO=9 Side-Side-Side

Step-by-step explanation:

The required answers to the question is given below.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance. They are in alignment with one another when moved. "≅" is the congruence symbol.

Use the following figure to understand the answer.

The Proof is

1. KM=KO=5 (GIven)

2. MN=3 (Given)

3. KN=KM+MN=8 (because the lengths are equal to the sum of their parts.)

4. KL=8 (Given)

5. KL=KN (from 3,4 substitution)

6. NO=ML=9 (Given)

7. ΔKLM=ΔKNO the congruence criterion used is SSS congruence.

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Answer:

----------------------

Given:

To find the arc measure (θ) in radians, we can use the formula:

Now, plug in the given values:

To solve for θ, divide both sides by 4:

Simplify the expression:

So, the arc measure (θ) is 2π/3 radians

Answer:

Rise/Run (A)

Step-by-step explanation:

The slope of a line measures the steepness of the line. Most of you are probably familiar with associating slope with "rise over run". Rise means how many units you move up or down from point to point. On the graph that would be a change in the y values. Run means how far left or right you move from point to point.

We have 3 operations with results that in your calculator appear in scientific notation, we will solve and transcribe these results in the common decimal form.

These are the answers

For the given exponential function f(x) = abˣ, the value of a and b is given as 7 and 5 respectively.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given function,
f(x) = abˣ

Put x = 2 and f(x) = 175,
175 = ab² - - - - (1)

Put x = 0 and f(x) = 7,
7 = ab⁰
Since b° = 1
a = 7

Put a = 7 in equation 1,
175 = 7b²
b² = 175 / 7
b² = 35
b = 5

Thus, the required simplified value of the a and b is 7 and 5 respectively.

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Answer:

20.92

Step-by-step explanation:

Given the data:

X : 170, 160, 130, 165, 125

Standard deviation (s) :

s = √Σ((X - m)² / n)

m = mean

n = sample size

Mean , m = Σx/n

m = (170 + 160 + 130 + 165 + 125) / 5

m = 750/5

m = 150

((X - m)² / n - 1)

[(170-150)^2 + (160-150)^2 + (130-150)^2 + (165-150)^2 + (125-150)^2] / (5-1)

= 1750 / 4

= 437.5

s = √437.5

s = 20.9165

s = 20.92

\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

Make sure your calculator is in Degree mode.

Answer:

84%

Step-by-step explanation:

Multiply 75.6 by 100% and divide by 90.

75.6 x 100% = 75600

7560%/90 = 84%

She got 84% percent correct.

Answer:

1,519

Step-by-step explanation:

96 ( 32 ÷ n ÷ 2 ) –s –t^r

since n = 4, r = 3, s = 9, and t = 2. we will just substitute for the values like this

96 ( 32 ÷ (4 ÷ 2) ) –9 ( –2³)

96 ( 32 ÷ 2 ) –9 –8

96 ( 16 ) –17

=1,536 –17

=1,519

i hope i helped

The distance between the points A ( -12 ) and B ( -7 ) on the number line is given by distance d = -5

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first point be A ( x₁ )

The value of A ( x₁ ) = A ( -12 )

Let the second point be B ( x₂ )

The value of B ( x₂ ) = B ( -7 )

Let the distance between the two points on the number line be = D

Now , the equation will be

The distance between the points A and B is calculated by

The distance D = B - A

Substituting the values in the equation , we get

The distance D = -12 - ( -7 )

Distance D = -12 + 7

Distance D = -5

Therefore , the value of D is -5

Hence , The distance between the points A ( -12 ) and B ( -7 ) on the number line is given by distance d = -5

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Answer:

75%

Step-by-step explanation:

To find the percent decrease, use the percent change formula:

(difference / original) x 100

8 - 2 = 6, so the difference is 6.

Plug in the difference and original:

(6 / 8) x 100

= 75

So, the percent decrease is 75%

Answer:

factor 4 out of 12-8t

4(3-2t)

Answer:

A

Step-by-step explanation:

57 rounded is 60

19 rounded is 20

60/20

3

The coordinates of point J of parallelogram GBJF are (2, 0), and the correct answer is (A) (2, 0).

What is parallelogram?

A parallelogram is a quadrilateral (a 4-sided polygon) with opposite sides parallel to each other.

We know that the diagonals of a parallelogram bisect each other. Since GBJF is a parallelogram, the diagonals must bisect each other.

Let O be the mid point for diagonals GJ and BF

Using the midpoint formula and the information that O is the midpoint of diagonals GJ and BF, we can find the coordinates of point J.

The midpoint formula states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by:

((x1 + x2)/2, (y1 + y2)/2)

Using this formula, we can find the midpoint of GJ and BF:

Midpoint of GJ = ((-4 + xJ)/2, (1 + yJ)/2)

Midpoint of BF = ((-2 + xJ)/2, (3 + 0)/2)

Since O is the midpoint of these two points, we can set the two formulas equal to each other and solve for xJ and yJ:

((-4 + xJ)/2, (1 + yJ)/2) = ((-2 + xJ)/2, 3/2)

Simplifying, we get:

-4 + xJ = -2 + xJ

1 + yJ = 3

Solving for xJ and yJ, we get:

xJ = 2

yJ = 0

Therefore, the coordinates of point J are (2, 0), and the correct answer is (A) (2, 0).

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A logarithm is an operation used to determine the exponent of a given base number.

What is logarithm?

A logarithm is a mathematical function that describes the relationship between the power to which a number (called the base) must be raised, and the resulting value. The logarithm of a number is the power to which the base must be raised to produce that number.

Start by moving the logarithm to the left-hand side of the equation: log(x²-15) = log(2x)

Next, use the property of logarithms that log(a/b) = log(a) - log(b) to get x²-15 = 2x

then you can simplify the equation by subtracting 2x from both sides x²-2x-15=0

then factor the equation to get (x - 5)(x + 3) = 0

Finally, use the Zero Product Property to solve for x. The solutions will be x = 5 or x = -3

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Problem 4

Explanation:

Draw a horizontal divider line to split the figure into two rectangles.

The rectangle up top is 30 by 30, so it has area 30*30 = 900 square inches.

The rectangle on the bottom has area 50*30 = 1500 square inches.

total = 900+1500 = 2400 square inches

========================================================

Problem 5

Explanation:

Draw a horizontal divider line to split the figure into two rectangles.

A = area of rectangle on top = 2*2 = 4 square inches

B = area of rectangle on bottom = 4*2 = 8 square inches

C = total = A+B = 4+8 = 12 square inches

========================================================

Problem 6

Explanation:

Draw a horizontal divider line to get two rectangles.

A = area of rectangle on top = 36*36 = 1296 square yards

B = area of rectangle on bottom = 72*18 = 1296 square yards

C = total = A+B = 1296+1296 = 2592 square yards.

You have the correct answer. Nice work.

Answer:

4)  2400 in²

5)  12 in²

6)  2592 yd²

Step-by-step explanation:

To calculate the area of each given composite figure, divide the figure into two rectangles and sum the area of the two rectangles.

\(\boxed{\begin{minipage}{5cm}\underline{Area of a rectangle}\\\\$A=w\cdot l$\\\\where:\\ \phantom{ww} $\bullet$ \quad $w$ is the width.\\ \phantom{ww} $\bullet$ \quad $l$ is the length.\\\end{minipage}}\)

Separate the figure into two rectangles by drawing a horizontal line (see attachment).

\(\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&= 30\cdot 30+50\cdot 30\\&=900+1500\\&=2400\; \sf in^2\end{aligned}\)

Separate the figure into two rectangles by drawing a horizontal line (see attachment).

\(\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=2 \cdot 2+ 4\cdot2 \\&=4+8\\&=12\; \sf in^2\end{aligned}\)

Separate the figure into two rectangles by drawing a horizontal line (see attachment).

\(\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=36 \cdot36 +72 \cdot18 \\&=1296+1296\\&=2592 \; \sf yd^2\end{aligned}\)

Answer:

Step-by-step explanation:

In the compound interest formula: A = P(1 + r)^t

A represents the amount of money in the account at the end of the term t, including interest.

P represents the initial principal, or the amount of money invested.

r represents the interest rate, usually expressed as a decimal.

t represents the number of time periods over which the interest is compounded.

In the continuously compounded interest formula: A = Pe^(rt)

A represents the amount of money in the account at the end of the term t, including interest.

P represents the initial principal, or the amount of money invested.

r represents the interest rate, usually expressed as a decimal.

t represents the number of time periods over which the interest is compounded.

So the variables in the formulas and their descriptions are:

A: the amount of money in the account at the end of the term t, including interest

P: the initial principal, or the amount of money invested

r: the interest rate, usually expressed as a decimal

t: the number of time periods over which the interest is compounded.

Answers:

The venn diagram is shown below.

========================================================

Explanation:

M = set of people studying math

C = set of people studying chemistry

P = set of people studying physics

Something like the notation n(C) refers to the count of items in set C, aka the number of people who study chemistry. Similar ideas apply to n(M) and n(P) to refer to the counts of math and physics respectively.

Something like n(C and M) is the number of people who study chemistry and math. Same idea applies to something like n(C and P) or n(M and P)

With all that in mind, we have these 7 facts

We'll start with fact 7. This value goes in the very center of the 3 overlapping circles of the venn diagram. Refer to the diagram below.

Since 9 people study all three subjects, and 16 study chemistry and math, this must mean 16-9 = 7 people study chemistry and math without physics involved. We'll write 7 in the region between circles C and M, but outside of circle P.

Since 9 people study all three subjects, and 14 study math and physics, we know that 14-9 = 5 people study only math and physics without chemistry. We'll write 5 in the region between circles M and P, but outside circle C.

Since 9 people study all three subjects, and 18 study chemistry and physics, we know that 18-9 = 9 people study only chemistry and physics without math. We'll write 9 in the region between circles C and P but outside circle M.

If you're lost, then refer the diagram below. So far, we have filled in the very center "9" and the closest three values surrounding it (the 7, 9 and 5).

-------------------------

Focus your attention on circle M for now. The values in this circle add to: 7+9+5 = 21

Since n(M) = 41, this must mean the missing value must be 20. This goes in circle M but outside the other two circles.

Note how 7+9+5+20 = 41 when we add everything in circle M. This circle is completely filled out. We'll follow a similar path for the other circles.

Move onto circle C. Adding everything in it so far gets us 9+9+7 = 25. We want to get to n(C) = 48 which means we need to have 48-25 = 23 in circle C but outside the other circles. Circle C is now done.

Lastly, focus on circle P. The values we found so far in this circle add to 9+9+5 = 23. The missing value must be 19 because 42-23 = 19, and n(P) = 42.

-------------------------

At this point, all three circles are filled out. The only thing missing is the number outside the circles, but inside the rectangle.

Add up everything in the circles: 23+7+20+9+9+5+19 = 92

This tells us that we have 92 people who studied at least one subject (i.e. one or more subjects). There are 120 people surveyed, meaning that 120-92 = 28 people study neither of these subjects. We write 28 outside the circles.

-------------------------

The venn diagram is done by this point. To address the questions, we'll just read from the diagram (and at most do an addition problem).

To find the number of people who study exactly one subject, we will add up the numbers that are in one circle but not in any other circle. Those values are: 23, 20, and 19. So 23+20+19 = 62 people study exactly one subject.

We already found the number of people who study at least one subject, and that was 92 people. This was when we added every number in the circles.

For the last question, we already found this value as well. This answer is 28 people which is found outside all three circles.

The venn diagram is shown below to visually summarize and organize all of the data. Hopefully it clears up any confusion you may have about the previous steps.

Total number of students who exactly one subject is 62

No of students who study at least one subject is 92

No of students who do not study any subject is 28

let us do this problem by set theory.

in the attached figure

three circles have been drawn representing the number of students studying maths, physics and chemistry.

from the diagram

1) Number of students who study exactly one subject=no of students who study maths + number of students who study chemistry+number of students who study physics- 2*[number of students who study both physics and chemistry-number of students who study both physics and maths-number of students who study both maths and chemistry ]+3*number of students who study all three subjects

from the attached figure,

2) Total number of students who exactly one subject = 20+19+23 = 62

3) No of students who study at least one subject will be the sum of each data in the attached figure i.e union of all three sets.

no of students who study at least one subject = 20+7+5+9+19+9+23=92

no of students who do not study any subject = total students- the union of all three sets.

no of students who do not study any subject = 120-92 = 28

therefore,

total number of students who exactly one subject is 62

no of students who study at least one subject is 92

no of students who do not study any subject is 28

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Answer:

An equation or an inequality that contains at least one variable is called an open sentence. When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.

Answer:

Yes, w=5 is a solution for this inequality.

Step-by-step explanation:

w+11<22

If w=5, this is:

5+11<22

16<22, which is true. So w=5 works as a solution

The likelihood that a random cumulative variable will fall within a specific range of values rather than taking on a single value is specified by the Probability Density Function.

The probability density function (PDF), also known as the density of a continuous random variable, is a function whose value at any specific sample (or point) in the data point (the range of potential values for the random variable) can be understood as having given a relative likelihood that the value of something similar to the random variable would be closer to that sample.

There is no absolute probability that a random variable will take on any specific value because there are an unlimited number of alternative values to begin with. However, the PDF value at two samples can be used to estimate how much more likely it is for the random variable to have that particular value in any given draw.

The Cantor distribution, which although having no discrete component, does not assign positive probabilities to any specific locations, and discrete random variable probability distributions do not all have a density function.

A distribution has a density function if and only if the cumulative distribution function F(x) is fully continuous. In this case, F is typically always differentiable, and its derivative can be used to symbolize the probability density.

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Answer:333R1 or as a mixed fraction 33 1/3. I believe this is right :]

Step-by-step explanation:

Answer:

1/8 is a terminatating fraction.

Step-by-step explanation:

1/8 = 12.5