In the pulley system shown in this figure, MQ = 30 mm, NP = 10 mm, and QP = 21 mm. Find MN.

To solve any questions relating to ages, I find it easier to make a table, like in the picture below.

See picture for answer and clear diagram.

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Notes/Explanations + answer in written form

Let's say that Halley's age now is:              x

That means that her age in 18 years is:      x + 18

It also means that her age 2 years ago is:   x - 2

In the question, we are told that when Halley is 18 years older than her current age,  she will be 5 times the age she was when she was 2 years younger than her current age

That means:

Halley's current age + 18 years = 5 times (Halley's current age - 2 years)

So we get this equation (which we solve to get the answer) :

x + 18 = 5 * (x -2)                      ( expand the brackets)

x + 18 = 5x - 10                          (subtract x from both sides)

18 = 4x - 10                                 (add 10 to both sides)

28 = 4x                                       (now divide both sides by 4)

7 = x

Therefore, Halley's current age is 7 years

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Note: equation is:   x + 18 = 5 * (x -2)    

Answer:

y = 2/5x.

Step-by-step explanation:

This is the correct answer to this question.

Hope this helps!!!

Kyle.

Y=2/5x is the answer to this graph as the equation

Answer:

the answer to this question is x=3\4

Answer:

1 and 2

Step-by-step explanation:

look this solution :

Answer:

64

Step-by-step explanation:

Just completed this for edge.

Regression equation : Y = 0.44352X - 21.29443

Approximate height of man who wears size 7 shoe = 64 inches

Regression can be defined as a measurement that is used to quantify how the change in one variable will affect another variable. Regression is used to find the cause and effect between two variables.

Given, ordered pairs

(height in inches, men’s shoe size).

(70, 9.5)

(67, 8)

(69, 9)

(72, 11.5)

(68, 7.5)

(60, 6)

(71, 11)

Using regression calculator

Regression equation

Y = 0.44352X - 21.29443

Approximate height of  a man who wears a size 7 shoe

7 = 0.44352X - 21.29443

0.44352X = 28.29443

X = 28.29443/0.44352

X = 63.7951614 ≈ 64

Approximate height = 64 inches

Hence, Y = 0.44352X - 21.29443 is the regression equation,

64 inches is the approximate height of the man wearing size 7 shoe

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Answer: [tex]f^{-1}(x)=\frac{x}{5}[/tex]

Step-by-step explanation:

By definition the domain of an inverse function [tex]f^-1(x)[/tex] is the range of f(x) and the range of the inverse function is equal to the domain of the principal function f(x).

If you have a function [tex]f(x)=5x[/tex], then to find the inverse function, follow these steps:

1. Make [tex]y=f(x)[/tex]

 [tex]f(x)=y=5x[/tex]

 [tex]y=5x[/tex]

2. Solve for the variable "x":

[tex]x=\frac{y}{5}[/tex]

3. Exchange the variable "x" with the variable "y":

[tex]y=\frac{x}{5}[/tex]

4. Exchange "y" with[tex]f^{-1}(x)[/tex]. Then the inverse function is:

[tex]f^{-1}(x)=\frac{x}{5}[/tex]

The inverse of the function [tex]y = 3x^5 - 4[/tex] is [tex]y = \sqrt[5]{\frac{x + 4}{3}}[/tex]

How to determine the inverse of the function

From the question, we have the following parameters that can be used in our computation:

[tex]y = 3x^5 - 4[/tex]

Swap the variabls x and y

So, we have

[tex]x = 3y^5 - 4[/tex]

Add 4 to both sides

This gives

[tex]3y^5 = x + 4[/tex]

Divide through by 3

[tex]y^5 = \frac{x + 4}{3}[/tex]

Take the 5th root of both sides

[tex]y = \sqrt[5]{\frac{x + 4}{3}}[/tex]

hence, the inverse of the function is [tex]y = \sqrt[5]{\frac{x + 4}{3}}[/tex]

Final answer:

To cover the wooden cylinder with carpet, Sandy needs to find the surface area of the cylinder and then cut out a piece of carpet that matches that area.

Explanation:

To cover the wooden cylinder with carpet, Sandy needs to find the surface area of the cylinder and then cut out a piece of carpet that matches that area. The surface area of a cylinder can be found using the formula: SA = 2πr(r+h), where r is the radius of the base and h is the height of the cylinder. In this case, the diameter of the cylinder is 1 ft, so the radius is 1/2 ft. The height of the cylinder is 4 ft. Plugging these values into the formula, we get: SA = 2π(1/2)(1/2 + 4) = 2π(1/2)(9/2) = 9π square ft.

Answer:

C. y = -9, -3, 0, 5, 7

Step-by-step explanation:

The given function is represented by the set of ordered pairs

{(-2,0,) (-4, -3,) (2, -9,) (0,5,) (-5,7)}

The range of this function is the set of all the y-values.

The set of the y-values are:

{-9,-3,0,5,7}

Therefore the range is y = -9, -3, 0, 5, 7

The correct option is C

Answer:

C

Step-by-step explanation:

Given data are :

{1,2,2,2,2,4,4,5,6,6,8,8,8,10}

1 appears only once so there will be 1 point above number 1 in the dot plot.

Then choice B or C or D are possible choices.

2 appears 4 times so there will be 4 points above number 4 in the dot plot.

Then choice B or C or D are possible choices.

4 appears 2 times so there will be 2 points above number 2 in the dot plot.

Then choice C or D are possible choices.

5 appears once once so there will be 1 point above number 5 in the dot plot.

Only choice that satisfies those results is C.

Hence correct answer is C.

Binomial

A monomial is just one term. A binomial is two monomials added or subtracted together. A trinomial is three monomials added or subtracted together.

Answer:

It is a binomial because it has two terms

Answer:X=11/10

Step-by-step explanation:

2x2-10x+7=0

4-10x+7=0

11-10x=0

-10x= -11

Divide both side by -10

-10x/-10.  -11/-10

Answer= 11/10

Answer:

x₁ = 5 + √11

         2

x₂ = 5 - √11

          2

Step-by-step explanation:

quadratic formula is given by

x = -b ±√b² - 4ac

             2a

a = 2, b = -10, c = 7

x = -(-10) ± √-10² - 4*2*7

                  2*2

x = 10 ± √100 - 56

           4  

x = 10 ± √44   = 2(5 ± √11)  = 5 ± √11

             4                   4               2

x₁ = 5 + √11

           2

x₂ = 5 - √11

           2

Answer:

1/2 - 2/6 = 1/6

Step-by-step explanation:

to answer two that are different simply take the lesser up or higher down example: 1/2-2/4 this would be zero because 2 x 1/2 = 2/4

1/2-2/6= 0.16

hope this helps

$ 0.77 or 77 cents

because 77 out 100 is written in decimal form as .77

Hello there!

Answer:

Your answer would be $0.77

Step-by-step explanation:

The reason why $0.77 would be the correct answer is because that represents something that is lower than a dollar, more so you would know it as "cents."

When you look at the question, it says, "77/100 of a dollar." What that means is that there is 77 of a dollar, and a dollar is equivalent to one whole.

The denominator "100" represents a whole, so that means that there is 77 out of a whole.

When you know currencies, cents are lower than a whole, therefore would be represented as a decimal.

77/100 is equivalent to 0.77.

As a money amount, it would be $0.77.

$0.77 should be the CORRECT answer.

Answer:

f(- 1) = 7

Step-by-step explanation:

To evaluate f(- 1) substitute x = - 1 into f(x)

f(- 1) = 5(- 1) + 12 = - 5 + 12 = 7

For this case we have a function of the form[tex]y = f (x)[/tex], where:

[tex]f (x) = 5x + 12[/tex]

We must find the value of the function when x = -1.

That is, [tex]f (-1)[/tex]:

[tex]f (-1) = 5 (-1) +12\\f (-1) = - 5 + 12[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]f (-1) = 7[/tex]

Answer:

[tex]f (-1) = 7[/tex]

Answer:

Part 1) [tex]y+8=3(x+2)^{2}[/tex] -----> [tex]y=-8.08[/tex]

Part 2) [tex]y-14=-(x-3)^{2}[/tex] ---->  [tex]y=14.25[/tex]

Part 3) [tex]y+7.5=2(x+2.5)^{2}[/tex] ---->  [tex]y=-7.625[/tex]

Part 4) [tex]y-17=-(x-3)^{2}[/tex] -----> [tex]y=17.25[/tex]

Part 5) [tex]y+7=(x-4)^{2}[/tex] ----> [tex]y=-7.25[/tex]

Part 6) [tex]y-6=-(x-1)^{2}[/tex] ---->  [tex]y=6.25[/tex]

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y-k=\frac{1}{4p}(x-h)^{2}[/tex]

where

(h,k) is the vertex

The directrix is

[tex]y=k-p[/tex]

case 1) we have

[tex]y+8=3(x+2)^{2}[/tex]

the vertex is the point (-2,-8)  

[tex]\frac{1}{4p}=3[/tex]

[tex]p=\frac{1}{12}[/tex]

The directrix is equal to

[tex]y=-8-\frac{1}{12}=-8.08[/tex]

case 2) we have

[tex]y-14=-(x-3)^{2}[/tex]

the vertex is the point (3,14)  

[tex]\frac{1}{4p}=-1[/tex]

[tex]p=-\frac{1}{4}[/tex]

The directrix is equal to

[tex]y=14+\frac{1}{4}=14.25[/tex]

case 3) we have

[tex]y+7.5=2(x+2.5)^{2}[/tex]

the vertex is the point (-2.5,-7.5)    

[tex]\frac{1}{4p}=2[/tex]

[tex]p=\frac{1}{8}[/tex]    

The directrix is equal to

[tex]y=-7.5-\frac{1}{8}=-7.625[/tex]

case 4) we have

[tex]y-17=-(x-3)^{2}[/tex]

the vertex is the point (3,17)      

[tex]\frac{1}{4p}=-1[/tex]

[tex]p=-\frac{1}{4}[/tex]    

The directrix is equal to

[tex]y=17+\frac{1}{4}=17.25[/tex]

case 5) we have

[tex]y+7=(x-4)^{2}[/tex]

the vertex is the point (4,-7)      

[tex]\frac{1}{4p}=1[/tex]

[tex]p=\frac{1}{4}[/tex]    

The directrix is equal to

[tex]y=-7-\frac{1}{4}=-7.25[/tex]

case 6) we have

[tex]y-6=-(x-1)^{2}[/tex]

the vertex is the point (1,6)      

[tex]\frac{1}{4p}=-1[/tex]

[tex]p=-\frac{1}{4}[/tex]    

The directrix is equal to

[tex]y=6+\frac{1}{4}=6.25[/tex]

The correct matches are: Directrix y = -7.25 → Equation of Parabola: y + 7 = (x - 4)², Directrix y = 6.25 → Equation of Parabola: y - 6 = -(x - 1)², Directrix y = 17.25 → Equation of Parabola: y - 17 = -(x - 3)², Directrix y = 14.25 → Equation of Parabola: y - 14 = -(x - 3)².

To match the equations representing parabolas with their directrixes, it's essential to understand the standard form of a parabola's equation related to its axis of symmetry.

For a vertical parabola, the standard form is y = a(x - h)² + k, where the vertex is at (h, k) and the directrix is y = k - 1/(4a) for a parabola that opens upwards, or y = k + 1/(4a) for a parabola that opens downwards.

For a horizontal parabola, the standard form is x = a(y - k)² + h. In our case, all given equations are in the vertical form where x is squared.

Let's take each equation and find its directrix:

With the directrix found for each equation, the correct matches are:

Answer:

$71

Step-by-step explanation:

First

61.72 times .15= 9.258

Second

61.72+9.258= 70.978

Answer:   5/y

Step-by-step explanation:

Answer:

Equation: x/9 + 2 = 8

Solution: x = 54

Step-by-step explanation:

I'd imagine the question is asking "two more than the quotient of a number and 9 is 8." Let's break this down:

- two more than means we're going to be adding two to the following quantity in the sentence.

- the quotient of a number and 9 we can interpret as a division expression. We don't know what "a number is," so we can give it a label (I'll pick n), and we can now write it is x/9. Taken with that last bullet point, our expression becomes x/9 + 2.

- Finally, we're told that the result of this expression is 8, so we can write the compete equation as x/9 + 2 = 8.

Now, if we want to solve this:

We can start by subtracting 2 from either side, giving us

x/9 = 6

And multiplying either side by 9 gives us the solution

x = 54.

Answer:

Step-by-step explanation:

Keep in mind that this is a polynomial and all odd-powered polynomials start low (read that as "in Quadrant III") and end high ("Quadrant I").  So yes, the fourth answer choice, D, is the correct one.

(D) The graph of the function starts with low and high ends.

Remember that this is a polynomial and that all odd-powered polynomials have a low starting point (read it as "in Quadrant III") and a high ending point ("Quadrant I").

Therefore, the correct answer is (D) the graph of the function starts with low and high ends.

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Answer:

Step-by-step explanation:

29-3(5)

29-15

14

X=14

Answer: Surface area is equal to 200[tex]cm^{2}[/tex]

Volume is equal to 333.33[tex]cm^{3}[/tex]

Step-by-step explanation:

First, let's do surface area.

The surface area of a pyramid is equal to 1/2(perimeter of base)(lateral height) + area of the base

The perimeter of the base is 10(4) = 40; as the base is a square with a side length of 10.

The lateral height is given as 5 cm.

The area of the base is 10(10) = 100.

We can plug those numbers into the equation to get 1/2(40)(5) + 100, which comes out to be 200[tex]cm^{2}[/tex].

Now for volume.

The volume of a pyramid is equal to 1/3(area of the base)(height).

We already have the area of the base, which is 100.

The height is given as 10 cm.

Plugging those numbers into the equation, we get 1/3(100)(10), which is 1000/3 or about 333.33[tex]cm^{3}[/tex].

Hope this helps!

The center of the circle is (-1.5, -2) and the radius is 3.205.

To find the center and radius of the circle, we can use the formula for the distance between two points in a coordinate plane. The two points given are (-3, -4) and the origin (0, 0), which represents the diameter of the circle. The center of the circle is the midpoint of the diameter, which can be found by taking the average of the x-coordinates and the y-coordinates. So, the center is ( (-3+0)/2 , (-4+0)/2 ) = (-1.5, -2). The radius of the circle is half the length of the diameter, which can be found using the distance formula as the distance between the center and one of the endpoints of the diameter. So, the radius is the distance between (-1.5, -2) and (-3, -4), which is √((-3-(-1.5))² + (-4-(-2))²) = √(2.5² + 2²) = √(6.25 + 4) = √10.25 = 3.205.

Answer: -12

x/4=-3

(x/4)(4)=-3(4)

x=-12

Answer:

The correct answer is the amount the average person spends in a month on gasoline.

Step-by-step explanation:

When comparing the amounts spent on the purchase of two items, we must need to see the price difference between the products first, then we will see the consumption of those products. Here the two items that are being compared have different purchase prices. A cup of Coffee is far cheaper than purchasing a tank of gasoline. If coffee is purchased on daily basis, even then the amount spent on purchasing coffee would be much lesser than the amount spent on buying the gasoline. For example, the cup of coffee costs $1 and a tank of gasoline costs $50. If coffee is purchased daily, then monthly amount spent on it will be $30, and if gasoline is purchased twice in a month, the amount spent on it will be $100. So an average person spends more amount on gasoline than on purchasing coffee.

Answer:

1+6i

Step-by-step explanation:

Given:

f(x)=x^4 - 2x^3 + 38x^2 - 2 + 37

zero of f(x) = 1-6i

another zero of function = ?

Conjugate Zero theorem:

As per conjugate zero theorem, if a function f(x) has real coefficients and one of zero is a complex number then the conjugate of that complex number will also be a zero of that function i.e. complex zeroes will occur in complex conjugate pairs.

conjugate of 1-6i is 1+6i

hence another zero of f(x) will be 1+6i !

Answer:

Yes

Step-by-step explanation:

3 x - 2 y = 10

( - 2 , - 8 )

We know that coordinates are put in the form ( x , y ) and from that we can work out that x = -2 and y = -8

Now we just substitute x = -2 and y = -8 into 3 x - 2 y = 10

3 x - 2 y = 10

{ 3 × ( - 2 ) } - { 2 × ( - 8 ) } = 10

{ - 6 } - { - 16 } = 10

- 6 + 16 = 10 True

Answer:

yes

Step-by-step explanation:

To determine if the ordered pair is a solution to the equation.

Substitute the x and y values into the left side of the equation and if equal to the right side then the pair are a solution

3x - 2y = 3(- 2) - 2(- 8) = - 6 + 16 = 10

Hence (- 2, - 8) is a solution to the equation

A: 8,250

B: 22

Step-by-step explanation:

A: 15 * 250 = 3,750 + 4,500 = 8,250

B: 10,000 - 4,500 = 5,500/250 = 22. 22 * 250 + 4,500 = 10,000

Answer:

40°

Step-by-step explanation:

1. Shape of a nonagon: 9 (root non-)

2. Total exterior angle: 360° (constant for all polygons)

3. Given that this polygon is regular, the one exterior angle of an nonagon is 360°/9 = 40°.

Answer:

Step-by-step explanation:

An exterior angle and an interior angle are supplementary angles.

Two Angles are Supplementary when they add up to 180°.

Therefore the measure of exterior angle is equal to different between 180° and an interior angle.

Method 1:

You can use the formula of the measure of interior angle of the regular polygon with n-sides:

[tex]\alpha=\dfrac{180^o(n-2)}{n}[/tex]

We have a nonagon. Therefore n = 9. Substitute:

[tex]\alpha=\dfrac{180^o(9-2)}{9}=(20^o)(7)=140^o[/tex]

[tex]180^o-140^o=40^o[/tex]

Method 2:

Look at the picture.

[tex]\alpha=\dfrac{360^o}{9}=40^o[/tex]

[tex]2\beta[/tex] - it's an interior angle

We know: The sum of measures of these three angles of any triangle is equal to 180°.

Therefore:

[tex]\alpha+2\beta=180^o\to2\beta=180^o-\alpha[/tex]

Substitute:

[tex]2\beta=180^o-40^o=140^o[/tex]

[tex]\theta[/tex] - it's a exterior angle

[tex]2\beta+\theta=180^o\to\theta=180^o-2\beta[/tex]

substitute:

[tex]\theta=180^o-140^o=40^o[/tex]

Answer:

-15625 i think

For this case we must find the value of the following expression:[tex]-5 ^ 6 = -1 * 5 ^ 6[/tex]

This means that we must multiply the 5 six times, and then multiply by -1, that is:

[tex]5 ^ 6 = 5 * 5 * 5 * 5 * 5 * 5 = 15,625[/tex]

Then multiply by -1:

[tex]-15,625[/tex]

Answer:

[tex]-5 ^ 6 = -15,625[/tex]

- The answer is simply ( 1, 3 ) and ( 4, 0 ), Nishishi~

- Ouma

Answer:

c on edge nuity

Step-by-step explanation: