function rule to find f(21)

Answer:

Here is your answer,

Step-by-step explanation:

(c)

x + y = 31 ------ (i)

x - y = 5 ------ (ii)

We have subtract eqn (ii) from eqn (i). Here we get the equation as,

2y = 26

y = 13 ------(iii)

Put eqn (iii) in eqn (i), we get -

=> x + y = 31

=> x = 31 - 13

=> x = 18

Therefore, their present ages of younger brother & older brother is 13 yrs & 18 yrs respectively.

Answer:

The runners will be in a straight line after 1/2 seconds.

To solve this problem, we can set the y-coordinates of each runner equal to each other and solve for t. The y-coordinate represents the lane number, and if the lane numbers are equal, the runners are on a straight line.

Jon: y = 1

Laura: y = 2

Ellis: y = 4

Jon: 3t = 1

Laura: 4t = 2

Ellis: 6t = 4

Solving these equations simultaneously, we find that t = 1/2 seconds. This means that after 1/2 seconds, the runners will be in a straight line.

The image after a dilation with scale factor k=3, then the vertices of triangle X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, the triangle with vertices X(−3, 2), Y(2, 3), and Z(1,−1) and scale factor k=3.

Now, X(-3, 2)→3(-3, 2)→X'(-9, 6)

Y(2, 3)→3(2, 3)→Y'(6, 9)

Z(1,-1)→3(1, -1)→Z'(3, -3)

Vertices of X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).

Therefore, the image after a dilation with scale factor k=3, then the vertices of triangle X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).

To learn more about the scale factor visit:

https://brainly.com/question/22312172.

#SPJ2

Answer:

18

Step-by-step explanation:

If n=9, then plug in 9 for n in the equation and solve. You should get 2•9, which is 18 when you simplify. Hope this helps and please mark brainliest!

According to the given statement Liam is incorrect because average speed is 34.28 miles per hour.

The average scores of a body's speed over a duration of time is its average speed. Because a moving body's speed is not constant over time and fluctuates, the average speed formula is required.

The overall distance the thing travels in a given amount of time is its average speed. A scalar value symbolizes the average speed. It has no direction and therefore is indicated by the magnitude.

Distance covered in first three hours = 40 × 3 = 120 miles

Time taking to covered remaining 120 miles = 120/30

                                                                          = 4 hours

Total time = 4 hours + 3 hours = 7 hours

Total distance = 120 miles + 120 miles

                        = 240 miles

Average speed = total distance /  total time

Average speed = 240 miles / 7 hours = 34.28 miles per hour

To know more about average speed visit:

https://brainly.com/question/25004917

#SPJ1

Answer:

I think multiples of 4

I hope this helps

The work done to empty the tank by pumping the water out of the top of the tank is 3.4 * 10^6 .

Given :

a tank has the shape of an inverted circular cone with height 10 m and base radius 4 m. it is filled with water to a height of 8 m. find the work done to empty the tank by pumping the water out of the top of the tank .

Formula :

[tex]W=\int_a^bpA(y)D(y)dy[/tex]

Using the base radius of 4, I found the equation of the line which was y = 5x / 2 and by solving for x gives us x = 2y / 5 .

Work = [tex]9.8*1000\int_0^{8} (\pi(\frac{2y} 5)^2)(10-y)dy[/tex]

= 3.4 * 10^6

Learn more about the radius here:

https://brainly.com/question/811328

#SPJ4

Answer:4.25

Step-by-step explanation: because it is daddy

Answer: the answers should be B and D

Step-by-step explanation:

so basically, this is just simplifying

B is the correct answer because the numerator 12, when divided by 4 is 3, and the denominator 32, when also diving by 4, is eight. This makes the two fractions equivalent.

Same goes for D, for if you diving the numerator and denominator by 2, you get answer choice D

it’s kind of a trial and error type problem and you have to test out all possibilities

hope this helps!

Answer:

B and D

Step-by-step explanation:

12/32 (if you divide them both by three) does not equal 4/10

12/32 fully simplified is 3/8

12/32 - subtracting is not simplifying, therefore, 10/30 is not correct

12/32 - both divided by two, a common factor, is 6/16, therefore, this answer is correct

12/32 - both of them divided by three equals 4/10.7 (rounded up to the nearest tenth), therefore, 4/9 is not a correct answer

12/32 - both divided by six equals 2/5.3 (rounded down to the nearest tenth), therefore, 2/6 is not a correct answer

Therefore the the best statement that describes this situation is Measurement error has occurred, and the researcher is guilty of unethical statistical practice.

As per the details share in the above question are as follow,

A researcher collected weights of a random sample of children using a scale that she had set to give weights 2.5 kilograms less than the actual weight.

We have to determine the best statement that describes this situation?

It measured precisely 2.5 kg less, which is a systematic inaccuracy, thus there has been a measuring error.

The statistician was guilty because she purposefully gave them less weight in order to support her argument.

For more such question on researcher studying.

https://brainly.com/question/3764906

#SPJ4

The best buy is pack  of 30 .

A cost function is a mathematical formula used to chart how production expenses will change at different output levels.

The general form of the cost function formula is C(x)=F+V(x) C ( x ) = F + V ( x ) , where F is the total fixed costs, V is the variable cost, x is the number of units, and C(x) is the total production cost.

Division is the opposite of multiplication.

A division is a process of splitting a specific amount into equal parts.

Pack A has 30 pencils

sells for $7.50.

pack of 30:

7.97/30 = 0.27 per pencil

Pack B has 12 pencils

costs of $4.25.

pack of 12:

4.77/12 = 0.40 per pencil

The best buy is pack  of 30 because:

0.27 < 0.40

Learn more about cost and division here;

https://brainly.com/question/24215186

#SPJ1

In mile there are 63360 inches.

The number of inches in a mile is equal to the number of inches in a foot times the number of feet in a mile

We multiply 528 by 12 and add one zero to the right of the result.

Use vertical form to perform the multiplication.

So. 12 × 5280=63360

  ∴ 5280/6336

  = 1056

The number of inches in a mile = 12 × 5280

We multiply 528 by 12 and add one zero to the right of the result.

Use vertical form to perform the multiplication:

  528 × 12 = 1056

1056 + 5280 = 6336

So, 12 × 5280 = 63360 miles

Therefore, in mile there are 63360 inches.

To learn more about Yard calculation, Here :

https://brainly.com/question/11781050?referrer=searchResults

1. Reason: Since QA divides ∠PQR into two different parts so it is a bisector∠PQA≅∠RQA.

2. The line which divides an angle into two different angles is known as a bisector.

4. ∠QXA≅∠QYA and they are situated opposites to each other so we can say that right angles are conjugate.

5. Given, Both are situated in the same plan so QA≅QA

6.ΔQXA≅ΔQYA, by the AAS Postulate.

8. Definition of equidistant. XA=XY.

Read more about geometry:

https://brainly.com/question/11583754

Answer:

Step-by-step explanation:

(2, 0), (4, -6)

(-6 -0)/(4 - 2)= -6/2= -3

y - 0 = -3(x - 2)

y = -3x + 6

or

f(x) = -3x + 6

Answer:

Step-by-step explanation:y= -3x + 6

Answer:

y = [tex]\frac{2}{3}[/tex] x + [tex]\frac{26}{3}[/tex]

y = [tex]\frac{-3}{2}[/tex] x

Step-by-step explanation:

y = [tex]\frac{-3}{2}[/tex] x - 6

The slope of this line is -3/2

A perpendicular slope is the opposite reciprocal.  That means you flip it upside down and take the opposite sign.  Since this slope is negative, the perpendicular slope will be positive.  If I turn this fraction upside down it will be 2/3, so the perpendicular slope is 2/3.

For the equation of the line we need the slope (m) and the y intercept.  To find that we will use the point that goes through this line.

m = (2/3)

x  = -4      from the point given (-4, 6)

y = 6        from the point given (-4,6)

y = mx + b

6 = [tex]\frac{2}{3}[/tex] [tex](\frac{-4}{1})[/tex] + b

6 = [tex]\frac{-8}{3}[/tex] + b   Add [tex]\frac{8}{3}[/tex] to both sides

[tex]\frac{6}{1}[/tex] + [tex]\frac{8}{3}[/tex] = b

[tex]\frac{18}{3}[/tex] + [tex]\frac{8}{3}[/tex] = b

[tex]\frac{26}{3}[/tex]

y = [tex]\frac{2}{3}[/tex] x + [tex]\frac{26}{3}[/tex]

Parallel lines have the same slope.

m = [tex]\frac{-3}{2}[/tex]

x = -4   from the point (-4,6)

y = 6   from the point (-4,6)

y = mx + b

6 = [tex]\frac{-3}{2}[/tex][tex](\frac{-4}{1})[/tex] + b

6 = 6 + b  Subtract 6 from both sides

0 = b

y = [tex]\frac{-3}{2}[/tex] x

Answer:

NO

FALSE

Step-by-step explanation:

The diameter divides the circle into two equal part called semi– circles( the image on white)

A sector is the plane figure enclosed by two radii of a circle or ellipse and the arc between them.

( the image that is dark)

i hope this helped

Answer: No, the diameter of a circle divides the circle into two equal halves called semi circle.

Step-by-step explanation:

The line that splits a circle into two identical halves is its diameter. The widest chord that divides the circle in half exactly is called the diameter. Each component is known as a semicircle.

Answer: 7/13 is the y intercept

Answer: His work shows that the answer is an F. E. Which means a False Equation.

Step-by-step explanation:

This happens when an equation cannot be solved. Here is an example of a false equation answer:

Let's say that 3=6, in the equation or expression, all the letters like "x, y, z..." have been undone.

Therefore we can no longer undo, so the answer to your question is a False Equation.

The angle should it have to go straight to its destination is 66° east of north. The correct option is D.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

Given that a ship's destination is 30 miles north and 12 miles east. The angle will be calculated as,

tanθ = 30 / 12

θ = tan⁻¹ ( 30 / 12)

θ = 66°

The angle is θ = 66°

To know more about trigonometry follow

https://brainly.com/question/7045552

#SPJ1

AE(X) = $23,333.33  could John expect to collect in yearly leases for the whole building in a given year.

What is  probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The given table is:

Number of Lease Offices :  0           1         2       3        4         5

Probability                         : 5/18     1/4     1/9    1/18     2/9      1/12

The expected probability is

Expected probability [tex]$=\sum_{i=0}^5 x_i p\left(x_i\right)$[/tex]

Expected probability [tex]$=0 p(0)+1 P(1)+2 P(2)+3 P(3)+4 P(4)+5 P(5)$[/tex]

Expected probability [tex]$=0 \cdot\left(\frac{5}{18}\right)+1 \cdot\left(\frac{1}{4}\right)+2 \cdot\left(\frac{1}{9}\right)+3 \cdot\left(\frac{1}{18}\right)+4 \cdot\left(\frac{2}{9}\right)+5 \cdot\left(\frac{1}{12}\right)=\frac{35}{18}$[/tex]

It is given that the yearly lease [tex]$=\$ 12,000$[/tex].

The yearly leases for the whole building in a given year is

Yearly leases [tex]$=\frac{35}{18} \times 12000=23333.3333333 \approx 23333.33$[/tex]

To learn more about probability  visit:https://brainly.com/question/11234923

#SPJ4

Answer:

x = 20

Step-by-step explanation:

x + 2x + 6x = 9x / 180

x=20

triangles = 180

angle 1 = ?

angle 2 = 160?

angle 3 = 20

The value of x in quadrilateral JKLM is 29

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points. The sum of interior angles of quadrilaterals is always equal to 360 degrees.

The sum of the interior angles in a quadrilateral is 360°

∠J + ∠K + ∠L + ∠M = 360

3X + 90 + 2X + 8 + 4X + 1 = 360

9x + 99 = 360

9x = 360 - 99

9x = 261

x = 261/9

x = 29

In conclusion 29 is the value of x in the quadrilateral.

Learn more about Quadrilateral: https://brainly.com/question/27991523

#SPJ1

The inequality that represents this situation is, (1 + x) > 2.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Ava’s pet pig is older than Izzy’s pet pig, which is 2 years old.

Ava adopted her pig when it was 1 year old, and she has had it for x years.

∴ The inequality that represents this situation is,

(1 + x) > 2.

x > 2 - 1.

x > 1.

Ava adopted her pig for more than one year.

learn more about inequality here :

https://brainly.com/question/28823603

#SPJ1

The simplified form of the given expression, [tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }[/tex] is equal to [tex]4x^{9}[/tex]

What are Exponents?

What is the Product of Powers rule?

In this question, the expression is  [tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }[/tex]  ------(1)

Multiplying the values in the numerator, we get

[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-5} \times x^{-3} }[/tex]

Now, the values in the denominator can be simplified using the Product of Powers rule.

The formula for the Product of Powers rule is given as, [tex]x^{m} \times x^{n} =x^{m+n}[/tex]

Simplifying the given expression using the Product of Powers rule, we get

[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-5+(-3)} }\\\implies \frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-8} }[/tex]     -----(2)

The formula for the Quotient of Powers rule is given as, [tex]\frac{x^{m} }{x^{n} } =x^{m-n}[/tex]

Simplifying the expression in (2) using the Quotient of Powers rule, we get

[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=4x^{1-(-8)} \\\implies \frac{4x \times 1}{x^{-5} \times x^{-3} }=4x^{9}[/tex]

Therefore, the simplified form of the given expression is [tex]4x^{9}[/tex]

To learn more about the Law of Exponents from the given link

https://brainly.com/question/29565624

#SPJ1

Quadratic equation :The maximum height reached by Alonzo's ball will be 9m.

What is a quadratic equation?

The equation whose highest degree of the variable used in the equation is 2 and has 2 roots, is called quadratic equation.

Here the quadratic equation of the path of Chase's ball is given by y = - 4x²+ 5x+ 7
To compare the height of both paths followed by the ball
we have to first calculate the height of the path of Chase's ball.
the path of Chase's ball is f(x)=-4x²+ 5x+ 7
The function will have the highest value when f'(x) will be 0.
f'(x)=-8x+5
f'(x)=0
⇒-8x+5=0
⇒-8x=-5
⇒x=5/8
at x=5/8, function value is
f(x)=-4x²+ 5x+ 7
=-4(5/8)²+ 5(5/8)+ 7
=-4(25/64)+(25/8)+7
=(-25/16)+25/8+7
=8.5625
There maximum value of f(x) is 8.5625.
The maximum height reached by Chase's ball will be 8.5625m.
From the graph of the path of Alonzo's ball, it is clear that
The maximum height reached by Alonzo's ball will be 9m.
As 8.5625m < 9m
Alonzo's baseball will reach greater height.

Learn more about Quadratic equation
here: brainly.com/question/458181
#SPJ1

Complete Question:
Chase and Alonzo stand next to each other and throw baseballs in the air. The path of Chase's ball is described by the equation y = - 4x²+ 5x+ 7. The path of Alonzo's ball is shown by the graph. In each function, x is the horizontal distance the ball travels in meters, and y represents its height. Whose baseball reaches a greater height?
A. Both baseballs reach the same height.
B. Chase's baseball
C. Alonzo's baseball
D) Non of these

Answer:

Alonzo's baseball

whompwhompwhompwhopwhompwhompwhompwhompwhompwhompwhompwhompwhompwhompwhomp

Step-by-step explanation:

For 8% p-value cutoff , Melissa should use 92% confidence interval

A confidence interval calculated for a treatment effect measure shows the range in which the true treatment effect is likely to fall.

A smaller sample size or higher variability will result in a wider confidence interval with a larger margin of error. The interval width is also influenced by the level of confidence. If you want a higher level of certainty, the interval should be wider.

The width of the confidence interval and the size of the p value are related.

The narrower the interval, the smaller the p value. The confidence interval, on the other hand, provides useful information about the likely magnitude of the effect under consideration as well as the accuracy of the estimate.

To know more about Confidence interval here

https://brainly.com/question/24131141

#SPJ4

Answer:

Step-by-step explanation:

a) the opposite angles of a quadrilateral inscribed in a circle are supplementary

70 + angle D = 180

angle D = 180 - 70

angle D = 110 degrees

b) DAB is a semicircle, so angle A and angle C are two circumference angles whose sides passes through the extremes of the diameter.

The centre angle of a semicircle is 180 degrees and its circumference angle is half that measure, so its value is 90 degrees

A = 90 degrees

C = 90 degrees

The solution of the equations 4x + 6y = 21 and 7x - 3y = 3 will be (1.5, 2.5).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The linear equation is given below.

4x + 6y = 21            ...1

7x - 3y = 3              ...2

From equation 2, then we have

7x - 3y = 3

3y = 7x - 3

y = (7/3)x - 1

Put in equation 1, then we have

4x + 6[(7/3)x - 1] = 21

4x + 14x - 6 =  21

18x = 27

x = 3/2

x = 1.5

Then the value of the variable 'y' is calculated as,

y = (7/3)(3/2) - 1

y = 7/2 - 1

y = 3.5 - 1

y = 2.5

The solution of the equations 4x + 6y = 21 and 7x - 3y = 3 will be (1.5, 2.5).

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ1

Answer:

15 ft

Step-by-step explanation:

60 divide by 40 equal 1.5

1.5 x 10 = 15