Sally is 10 years older than one fifth of her mother’s age. If Sally is 20 years old, how old is her mother?

Answer:

657720 ways

Step-by-step explanation:

This is the number pf permutations of 4 from 30:-

=  30! / (30 - 4)!

= 30! / 26!

= 30*29*28*27

The greatest common factor between 10 and 24 is 2.

What is Greatest common factors?

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Given that;

The numbers are;

10 and 24

Now,

The factors of 10 = 1, 2, 5, 10

The factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.

Clearly, The greatest common factor of the number 10 and 24 is highest number which is common in both factors.

Thus, The greatest common factor between 10 and 24 is 2.

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The solution of the system of equations and inequalities, indicates that the solution are;

In order to find the solution of the system of equations by graphing, the lines are graphed on the same coordinate plane and the point at which the two graphs intersect is the solution of the system of equations.

1) y = (1/4)·x - 4, y = (-1/2)·x - 1,

The x-coordinates at the point of intersection, can be found by noting that the y-values of both equations are the same

Please find attached the graph of the system of equations with the point of intersection, (4, -3), which corresponds to x = 4, and y = -3, created with MS Excel

The solution of the system of equations therefore is; x = 4, y = -3

2. 3·x - 2·y = 8

x - 2·y = 4

Making y the subject of both equations, we get;

y = (3/2)·x - 4

y = (1/2)·x - 2

The graph of the above two equations can be plotted on the same coordinate plane using MS Excel, is attached

The point of intersection of the two graphs is (1, -2.5)

The solution of the system of equations is therefore; x = 1, and y = -2.5

3) The solution of the system of inequalities is the feasible region, corresponding to the region that satisfies both inequalities;

Please find attached the graph of the inequalities, showing the positive region that satisfies both inequalities, which is the triangle with vertices, (0.51, 0), (1, 1), and (1.5, 0)

4) The inequalities can be graphed by making y the subject of both inequalities and graphing the equations on the same coordinate plane.

x + y > -2, therefore; y > -2 - x

6·x - y ≥ 3, therefore; y ≤ 6·x - 3

6·x - 3 = -2 - x

The points in the feasible region of the graph are; points below and on the line, y = 6·x - 3, above the line y = -2 - x, and to the right of the point (1/7, -2 1/7)

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Answer:

They make it easier to get your arms through

Rounded to the nearest thousand is 47,000 because the number to the right of it is not 5 or up, so this is the answer.

hope that helps :)

failed to evaluate 9 × - 8

2( - 3x + 1) = 9 × - 8

- 6x + 2 = - 72 ( subtract 2 from both sides )

- 6x = - 74 ( divide both sides by - 6 )

x = [tex]\frac{-74}{-6}[/tex] = [tex]\frac{37}{3}[/tex]

Your answer will turn out to be −4x^2+3x.

Simplify. Distribute -1 to all terms within the second parenthesis

-(6x² + 3x + 5) = -6x² - 3x - 5

Combine like terms

2x² - 6x² = -4x²

6x - 3x = 3x

5 - 5 = 0

-4x² + 3x is your answer

~Rise Above the Ordinary

The exact circumference of the Circle Measurements is 12π yards and the exact area is 36π square yards.

To find the exact area and circumference of the circle, we can use the formulas given:

Circumference of a circle = 2πr

Area of a circle = πr^2

Given that the diameter of the circle is 12 yards, we can find the radius by dividing the diameter by 2: r = 12 / 2 = 6 yards.

Now we can substitute the value of r into the formulas:

Circumference = 2πr = 2π(6) = 12π yards

Area = πr^2 = π(6^2) = 36π square yards

So, the exact circumference of the circle is 12π yards and the exact area is 36π square yards.

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13, paula has 6, myles has 1 more than her that mean he has 7

6+7= 13

Answer:

13

Step-by-step explanation:

We know that Paula has 6 video games and Myles has one more video game than Paula.

So the number of video games Myles has will be equal to 6 + 1 = 7.

Now that we know the number of games that Paula and Myles have, we can find the number of video games in all by simply adding the two numbers:

Total number of video games = 6 + 7 = 13

Therefore, Paula and Myles together have 13 video games.

First, turn the two fractions into decimals : 7/9 = .77777 7/8 = .875

Now, all of the numbers are in common form so you can identify which is largest, etc. : .875, .77777, .7

Now put the values back to fractions : 7/8, 7/9, .7

To compare the ratios 2 to 7 and 5:7 using the circles to model we need to make two circles first.

Then we need to make 7 parts of each circle.

For 2:7 ratio, we need to shade 2 parts of the total 7 parts of the circle.

For 5:7 ratio, we need to shade 5 parts of the total 7 parts of the circle.

So, the first circle represents  2:7 ratio and second circle represents  5:7 ratio.

Answer:

To compare the ratios 2 to 7 and 5:7 using the circles to model we need to make two circles first.

Then we need to make 7 parts of each circle.

For 2:7 ratio, we need to shade 2 parts of the total 7 parts of the circle.

For 5:7 ratio, we need to shade 5 parts of the total 7 parts of the circle.

So, the first circle represents 2:7 ratio and second circle represents 5:7 ratio.

Step-by-step explanation:

Answer:

[tex]V_{E} = -22.5 / 15 = 1.5 miles/minute\\V_{F} = 7.5 / 15 = 0.5 miles/minute[/tex]

Step-by-step explanation:

To answer this problem, we must bear in mind that the express train travels 3 times faster than the freight train.

If we call F the distance that the freight train travels and we call E at the distance that the express train travels, we must have the distance between them after 15 minutes it must be 30 miles.

So

[tex]F + E = 30\\[/tex]

We also know that:

[tex]E = 3F[/tex]

Since the express train travels 3 times faster than the freight train.

So, like both equations, we have to:

[tex]F + 3F = 30\\F = 30/4\\F = 7.5 miles\\[/tex]

Then [tex]E = 7.5*3 = 22.5[/tex] miles in the opposite direction.

This is the distance you traveled in 15 minutes.

Therefore, the speed of the express train ([tex]V_{E}[/tex]) is the distance traveled between the time it did

[tex]V_{E} = -22.5 / 15 = 1.5 miles/minute\\V_{F} = 7.5 / 15 = 0.5 miles/minute[/tex]

[tex]\dfrac{8(4-z)}{7}=-z\\\\8(4-z)=-7z\\\\32-8z=-7z\\\\-7z+8z=32\\\\z=32[/tex]

8(4 - z)/ 7  = -z

8(4 - z) = -7z

32 - 8z = -7z

-8z + 7z = -32

-z = -32

z = 32

Answer:

Step-by-step explanation:

Given that Henry  deposited $420 into a savings account. There is a $5.00 per month service fee on the account. Also, Henry decides he wants to withdraw $25 a week for spending money.

Let us convert everything into days.

30 days a month and 7 days in a week

Service charges for 30 days = 5

withdrawn amount for 7 days = 25

Let x be the total no of days

Then [tex]\frac{25x}{7} +\frac{5x}{30}= 420\\\\750x+35x=420(7)(30)\\785x=420(7)(30)\\x=112.3567[/tex]

i.e. between 3 and 4 months

We can say in 3 months this will be exhausted.

Option A

Set up the equations:

two numbers: a and b

sum: a+b=21

quotient: a/b=2

(the last one means b=a/2)

combine them:

a+a/2=3a/2=21

a=14

and so

b=7

the two numbers are 14 and 7

Final answer:

To find two numbers given their sum and quotient, set up and solve a system of equations. In this case, the numbers are 14 and 7.

Explanation:

The sum of two numbers is 21 and their quotient is 2. To find the two numbers, we can set up a system of equations:

Let the two numbers be x and y. We have the equations x + y = 21 and x/y = 2.

Solve the system by substituting y = 21 - x into the second equation to get x = 14 and y = 7.

Therefore, the two numbers are 14 and 7.

Standard form of non-polynomials is purely to solve them.

10^4 = 10,000

2.1 * 10,000 = 21,000

Answer:

The linear equation for the total combination age is [tex]X+7+(X+4)+7=24[/tex]

Step-by-step explanation:

If Jane is X years old today. And her brother is 4 years older then her brothers age is,

X+4.

Jane's age after 7 years = X+7

Jane's Brothers age after 7 years = (X+4)+7

So after seven years their combined age will be 24, Lets write this in an equation form,

[tex]X+7+(X+4)+7=24[/tex]

So the linear equation for the total combination age is,

[tex]X+7+(X+4)+7=24[/tex]

Answer:

2.72 m/s

Step-by-step explanation:

We are given that

Boy jogs=250 meters

Time taken by boy=110 seconds

We have to find the average speed in m/s

In order to find the average speed then we will divide distance by time

[tex]Average\;Speed=\frac{distance}{time}[/tex]

Using the formula then we get

Average speed=[tex]\frac{250}{110}=2.72 m/s[/tex]

Hence, the average speed=2.72 m/s

Final answer:

To calculate the average speed, the boy's distance jogged (250 meters) is divided by the time taken (110 seconds), yielding an average speed of 2.27 m/s.

Explanation:

The student's question asks how to calculate the average speed of a boy who jogs a certain distance in a given amount of time. To find the average speed, you divide the total distance traveled by the total time taken. In this case, the boy jogs 250 meters in 110 seconds.

The calculation for the average speed (v) would be:

Distance (d) = 250 meters

Time (t) = 110 seconds

Average Speed (v) = d / t

Plugging the values into the equation yields:

Average Speed (v) = 250 m / 110 s = 2.27 m/s

Hence, the boy's average speed is 2.27 meters per second.

Letter D, because the y intercept is on -4 and if you look at the slope and use the method "Rise over Run" you can see that the rise is one and negative a half.

Final answer:

Ally's box has a total surface area of 594 square centimeters, calculated using the surface area formula for a rectangular prism: Surface Area = 2lw + 2lh + 2wh.

Explanation:

The surface area of a box can be calculated by finding the area of all six faces and adding them together. Since the box Ally is designing has dimensions of 12 cm long, 9 cm high, and 9 cm deep, we will have two faces for each dimension. To calculate the surface area of Ally's box, we use the formula:

Surface Area = 2lw + 2lh + 2wh

Where l is the length, w is the width, and h is the height of the box. Now, plugging in Ally's box dimensions:

Surface Area = 2(12 cm)(9 cm) + 2(12 cm)(9 cm) + 2(9 cm)(9 cm)

Surface Area = 2(108 cm2) + 2(108 cm2) + 2(81 cm2)

Surface Area = 216 cm2 + 216 cm2 + 162 cm2

Surface Area = 594 cm2

Therefore, the total surface area of Ally's box is 594 square centimeters.

Answer:

B: 18.9

Step-by-step explanation:

The answer is D because when you insert it into a calculator it gives you D. Yet, if you do it manually you still get the same number .

Answer:

The answer is D

Step-by-step explanation:

Hope I helped!! :)

Marisa had rounded 3.48 to 4 and times it to 7.33 which she rounded to 8

In fact 3.48 is closer to 3 we know this since the .48 of 3.48 s below .50 if it was .50 or above it would round to 4 but it doesn't the same applies to 7.33 so

it should be 3 x 7 = 21

If Marisa is going to estimate, then she needs to round each number. If she rounds to the nearest ones place, then she should have rounded 3.48 to 3 and rounded 7.33 to 7.

3 x 7 = 21

B)The numbers are being divided by 10 repeatedly.

The numbers are:

7000

700

70

.7

.07

.007

(See it now?)

The number that is missing is 7

My conjecture is that 7 can’t be written in scientific notation.

Hope I helped!

Good Luck!

⛈

Answer is: p = [tex]\frac{21}{4}[/tex]