Four siblings have a dog walking business. The table shows the hours worked by each sibling. Each sibling earns $25.50 per hour and the total number of hours worked is represented by 10h+15 , where h represents the number of hours Michael worked.

The solution of the given integral [tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]

Given;

To evaluate the value of a given integral;

[tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex]

Let;

[tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]2\cdot \int \left(x^2+4\right)^3xdx[/tex]

Now, assume u = x² + 4

→ [tex]2\cdot \int \left(x^2+4\right)^3xdx[/tex] = [tex]2\cdot \int \frac{u^3}{2}du[/tex]

→ [tex]2\cdot \frac{1}{2}\cdot \frac{u^4}{4}[/tex]

→ [tex]2\cdot \frac{1}{2}\cdot \frac{u^4}{4}[/tex]

→  [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]

By adding constant C;

[tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]+ C

Hence, the solution of the given integral [tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]

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The slope of the line as shown in the diagram is 4/3.

The slope of a line is the ratio of the amount that y increases as x increases some amount.

To calculate the slope from the diagram, we use the formula below.

Formula:

Where:

From the graph,

At  x = 30, y = 20

And at x = 60, y = 60

Therefore,

Substitute these values into equation 1

Hence, the slope of the is 4/3.

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Answer: Give me brainliest or your mean.

Step-by-step explanation: 1/3 jersey 1/2 short. 1/3 x 1/2 = 1/6 possibility.

The number of hours that helena need to work to generate 165 dollars is

33 hours.

Helena has to work hours to earn $165. 33

Algebraic equations are equations with

unknown variables. The alphabet letters are used to represent algebraic equations.

Total $33.00 in her 6 hours she worked.

This question should find out how long it takes her to earn her $165.00 in that job.

let x hours be required work hours to earn $165.00 ..

This can be expressed in algebraic equations as:

x= 6× 165/33

x= 990/33

x= 30

Hence, helna have to work thirty hours to earn $165.00 ..

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Answer:

0.83 repeating 3

Step-by-step explanation:

5 goes in the box and 6 goes outside. you can't put 6 into 5 so you would put a 0 on the top and a decimal point. now you would write a 0 next to the 5 and you would do 6×8=48 and so put 8 next to the 0 and the decimal point. then subtract 50-48 which will be 2. Put another 0 next to the 50 and bring it down. you will have 20 which you do 6×3=18. and so put a 3 next to 0.8 and you will subtract 20-18=2. It will be repeating so put a line at the top of 3 to show that it's repeating.

In the given circle the length of the chord marked x is

We know that the length of the chord is bisected by the perpendicular from the center of the circle.

Therefore the length of the chord is 7 × 2 = 14 units.

Again from the chord properties of a circle we know that, chords that are equidistant from the center are equal.

Since both the chords are at a distance of 9 units hence both chord lengths

Hence the length of the other chord = 14 units.

∴ x = 14

The segment of a line that joins any two points on a circle's circumference is known as the chord. It must be emphasized that its longest chord is its diameter, which runs through the center of the circle.

The circle and its chord are depicted in the diagram below. In the center of the circle, equal-length chords subtend equal angles.

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The graph of this quadratic function (x² + 3x - 108) is shown in the image attached below. Also, the two roots of this quadratic equation (x² + 3x - 108) are -12 and 9, while the axis of symmetry (vertex) is equal to -1.5.

In Mathematics, a quadratic function is a mathematical expression which defines and represent the relationship that exists between two or more variable on a graph.

Mathematically, the graph of every quadratic functions is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function would always form a parabolic curve. For this quadratic function, the graph is a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero.

Next, we would determine the axis of symmetry (vertex) of this quadratic function:

Axis of symmetry (vertex), Xmax = -b/2a

Axis of symmetry (vertex), Xmax = -3/2(1)

Axis of symmetry (vertex), Xmax = -1.5.

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The polynomial function p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 value at x = -2 is -1

given that

polynomial function p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 at x=-2

To find the value of a function at x = -2, put in all the places of  in the function.

Polynomial is made up of two words, poly, and nomial. "Poly" means many, and "nomial" means the term, and hence when they are combined, we can say that polynomials are "algebraic expressions with many terms".

Polynomial functions are expressions that may contain variables of varying degrees, coefficients, positive exponents, and constants.

Here,

p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 put x =-2

p(-2) = 5[tex](-2)^{3}[/tex]+8[tex](-2)^{2}[/tex] - 3(-2)+1

p(-2) = 5(-8) + 8(4) + 6+1

p(-2) = -40+32+6+1

p(-2) = -40+39

p(-2)  =-1

At So, the value of the function at x= -2 is -1

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The linear equation is equal to

y = -3x + 8

m = slope

x = input variable

c = 8

The given equation is linear function or linear equation

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

Definition of variables to suit the problem to be solved

y = output variable

m = slope

x = input variable

c = y intercept

In comparison, to the linear equation given as equal to

y = -3x + 8

m = -3

x = input variable

c = 8

putting the input variables gives out put accordingly

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The probability that no two ants will reach the same vertex is 5/256.

Plane, point B and attention. Ants that move to D can come from either E or C. Ants moving to E can come from either B or D of points A and F of the octahedron. Therefore, there are 2 degrees of freedom to decide which ants move to D, 2 degrees of freedom to decide which ants move to E, and 2 degrees of freedom to decide which ants move to A.

So there are 2× 2× 2=8 ways an ant can move to different points.

There are 8 ways for ants to move to different points.

Points B, there are a total of 8 + 4 + 8 = 16 ways Ant can move to her different points. Aligned the square so that point B is defined as point where the ant moved from point A.

An ant can actually move from point A to 4 different points, so there are a total of 4×20=80 ways an ant can move to different points.

Each ant acts independently and has 4 different points to choose from.

So each ant has a 1/4 chance of moving to the desired location. Since he has 6 ants, the probability of appearance is

= 1/4096

So, the desired answer is 80/4096

= 5/256

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The co-ordinates of J'K'L'M'N' are (0,5), (-2,3), (-3,4), (-4,1), (-1,2)

What is Co-ordinate Geometry?

Coordinate geometry is a field of mathematics that assists in displaying geometric forms on a two-dimensional plane and learning the attributes of these figures.

Solution:

The co-ordinates of J'K'L'M'N' are (0,5), (-2,3), (-3,4), (-4,1), (-1,2)

From the figure it can be clearly observed that

a) L' is located at (-3,4) - True

b) M' is located 4 units left of the y - axis - True

c) The y - co ordinate of zN' is the opposite of the y - co ordinate of N - False

d) J'K' = JK - False

e) M' is located at (-4,1) - True

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Answer:

x=8

No it’s not an equilateral

Step-by-step explanation:

Since side AB is about the same length as BC we can set them equal to each other

x-1=7

 +1 +1

x=8

This is not an equilateral because if you fill in X for the third side you will get 5

8-3=5

Estimate product of (-25.31) (9.61) using compatible numbers is equal to -250.

As given in the question,

Given expression is equal to :

( -25.31 ) ( 9.61 )

Compatible numbers to calculate the estimate product we have,

Compatible number for ( -25.31 ) is equal to ( -25 ) .

-25 > -25.31 > -26

-25.31 is more nearer to -25 .

Now, 9 < 9.61 < 10

Compatible number for 9.61 is equal to 10 as 9.61 is more close to 10.

( -25.31 ) × ( 9.61 )

= ( -25 ) × (10)

= 250

Therefore, estimate product of (-25.31) (9.61) using compatible numbers is equal to -250.

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Answer: 8

[tex]m^{2} = 9+55\\m^{2} = 64\\m=8[/tex]

Answer: m = 8

9 + 55 = 64

[tex]\sqrt{64}[/tex] = 8

[tex]8^{2}[/tex] = 64

Answer:

here you go....

Step-by-step explanation:

The coordinates of the image of reflecting (3, -2) across the line y = 5 are (3, 12)

When we reflect a point (x, y) across a horizontal line of the form:

y = a

The coordinates of the image after the reflection are:

(x, 2a - y)

In this case we have the point (3, -2), and we reflect this across the line y = 5, then the new coordinates are:

(3, 2*5 - (-2))

(3, 10 + 2)

(3, 12)

The coordinates after the image are (3, 12)

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Answer:

2(2x+9)

Step-by-step explanation:

Just break each number up

2 X 2 = 4

2 X 9 = 18

2(2x+9)

Answer:

-4.5

......

......

Answer:

1.5 minutes (or 1 minute and 30 seconds)

Step-by-step explanation:

5 : 40 = x : 12

x = (5 * 12)/40

x = 12/8

x = 1.5 minutes

Answer: 1 min and 50 seconds

Step-by-step explanation:

first, you have to find the unit rate of how many papers the printer can make in a min which is 40 divided by 5 which gets you a unit rate of 8 for every minute then you take your 12 paper and divide it by your unit rate of 8 per minute which gets you how long it would take to print 12 papers which equal 1.5

If the team buys 18 jerseys for a total of (18x-36) dollars then we can conclude that the discount the team has received is $36.

According to the question,

We have the following information:

A soccer team receives a discount on each jersey purchased. The original price of each jersey is x dollars. The team buys 18 jerseys for a total of (18x-36) dollars.

Now, the original price of 18 jerseys will be 18x.

Now, when 36 is subtracted from 18x to find the total cost then it means that this is the discount from the original price.

Hence, if the team buys 18 jerseys for a total of (18x-36) dollars then we can conclude that the discount the team has received is $36.

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It will take 11 years for the canyon floor to have an elevation of −31 feet.

A mathematical statement known as an equation makes two expressions' values equal. It is a mathematical statement that says "this is equivalent to that," in other words. The left side appears to be a mathematical expression, the centre appears to be an equal sign, and the right side is another mathematical expression. The right side of the equation frequently has a value of zero.

Given,

The first step in this situation is to define the variables.

So, we have:

x: the age in years

y: height in feet

The equation used to model the issue is then written.

So, we have:

y = 1.5x - 14.5

Then, at a -31 foot elevation, we have:

-31 = 1.5x - 14.5

For years,

x = -16.5/1.5

x = 11

In 11 years it will take for the canyon floor to have an elevation of −31 feet.

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The statement that describes the account growth is D. The account is growing exponentially at an annual interest rate of 2.00%.

From the information, the table shows the balance of an investment account at the beginning of each year the account was held.

The percentage change for the second year will be:

= (510 - 500) / 500 × 100

= 10/500 × 100

= 2%

The percentage change for the third year will be:

= (520.20 - 510) / 510 × 100

= 10.20/510 × 100

= 2%

Therefore, there's. 2% growth.

The correct option is D.

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Answer:

D

Step-by-step explanation:

Answer:

-0.16

Step-by-step explanation:

Divide the answer :)

Answer:

[tex]\sf n=\cfrac{1}{2}[/tex]

Step-by-step explanation:

[tex]\sf -12=10n-40n+3[/tex]

[tex]\sf 10n-40n+3=-12[/tex]

Combine like terms:-

[tex]\sf \:(10n-40n)=-30n[/tex]

[tex]\sf -30n+3=-12[/tex]

Subtract 3 from both sides:-

[tex]\sf -30n+3-3=-12-3[/tex]

Simplify:-

[tex]\sf -30n=-15[/tex]

Divide both sides by -30:-

[tex]\sf \cfrac{-30n}{-30}=\cfrac{-15}{-30}[/tex]

Simplify:-

[tex]\sf n=\cfrac{1}{2}[/tex]

_________________

Hope this helps!

Have a great day! :)

Answer:

49

Step-by-step explanation:

18/42=21/ED

18 ED=882

ED=49

The simplified terms are 12.504 and 17.76 when the terms are in decimal.

Given that,

The numbers are 13.4-0.896 and 8.6 + 9.16

We have to simplify the terms.

We know that,

When a full number and a fraction are combined, decimals are used. The "." symbol, often known as a decimal point, will be used to demarcate the entire number from the fraction in this instance.

Take the numbers,

13.4-0.896

Subtracting the terms

12.504

Take the numbers,

8.6 + 9.16

Adding the terms

17.76

Therefore, The simplified terms are 12.504 and 17.76 when the terms are in decimal.

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Answer:

10.7

Step-by-step explanation:

The only thing I can think of is 10.7. Because when you do this problem you get 10.6666666667. So I'm assuming you're to round it. There is no other way to solve the problem that wouldn't get you either 10.6666666667 or 10.7.

Answer:

10.66

Step-by-step explanation:

[tex]\frac{24}{9}[/tex] + [tex]\frac{8}{1}[/tex]

[tex]\frac{24}{9}[/tex] + [tex]\frac{72}{9}[/tex]

[tex]\frac{96}{9}[/tex]

10.666...

The slope of the line is -1/2, the coordinates of midpoint is (1,3) and the equation of perpendicular bisector is y = 2x + 1

The slope of a line is a measure of its steepness.

Given that, a line segment has end points = A(-1,4) and B(3,2)

(i) Slope = (y2 - y1)/(x2 - x1) = -1/2

(ii) Coordinates of the midpoint of a line = (Xm, Ym) = (x₁ + x₂)/2, (y₁ + y₂)/2

(Xm, Ym) = (-1+3)/2, (4+2)/2 = (1,3)

(iii) The slope of the two lines perpendicular to each other are negative reciprocal of each other, so, slope of the line perpendicular to the given line is = 2

Standard equation of a line = y = mx + c

Since the line is the perpendicular bisector of AB, it will pass through (1,3)

Solving for c,

3 = 2*1 + c

c = 1

Therefore, the equation of the of line perpendicular to AB is

y = 2x + 1

Hence, the slope of the line is -1/2, the coordinates of midpoint is (1,3) and the equation of perpendicular bisector is y = 2x + 1

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Answer:

Rema receives 90 sweets

Step-by-step explanation:

See attached image

Using the theories of archaeology, we got that date on the coin represents

a terminus post quem if a coin with a date on it is found in a sealed archaeological deposit.

Potassium-argon dating: This absolute dating method was actually developed by the A.E. Douglass, an American astronomer, chiefly from work he conducted at the Pueblos of American Southwest tree-ring dating Layers of the sediments resulting from the melting of ice sheets and deposited in the lakes on an annual basis are known as varves

Hence, if a coin with a date on it is found in a sealed archaeological deposit, and we know that the deposit can be no older than the date on the coin. in that situation the date on the coin represents a terminus post quem.

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