Supergym is a national chain of gyms. This year, its employees sold 10,412 gym memberships, which turns out to be 52% more than they sold last year. How many memberships did they sell last year?

First, any number multiplied by 1 yields the result of itself

Therefore, we can rewrite it as 5/3 x 3.

We do the multiplication : 5/3 x 3 = 5/3 x 3/1 = (5x3)/(3x1) = 15/3 = 5.

Rewrite 5 as 5/1 for a fraction result.

Answer: missing side length = 12.5

Step-by-step explanation:

1. Identify what equation to use

there are 2 side lengths, and no Pythagorean triples present therefore using the Pythagorean theorem a^2+b^2=c^2 would be a good approach

2. plug in numbers

knowing the missing side length is the hypotonus we can plug 6 and 11 for a and b: 6^2+11^2=c^2

3. Solve equation

6^2+11^2=c^2

36+121=c^2

157=c^2

12.52=c | to cancel square (^2) you must square root the number

12.5=c | round

The equation of the line passing through the points (2, 11) and (-8, -18) is y = 29 / 10 x + 26 / 5

The equation of a line can be express as follows:

y = mx + b

where

Therefore, the equation of the line passes through the points (2, 11) and (-8, -18).

Hence,

m = -18 - 11 / -8 - 2

m = - 29 / - 10

m = 29 / 10

Therefore, let's find the y-intercept using (2, 11)

The equation is as follows:

11 = 29 / 10(2) + b

11 = 58 / 10 + b

b = 11 - 58 / 10

b = 110 - 58 / 10

b = 52 / 10 = 26 / 5

Therefore,

y = 29 / 10 x + 26 / 5

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Answer:

[tex]\frac{2}{25}[/tex]

Step-by-step explanation:

There are a total of 15 pieces of fruit.  For the first selection, we want a apple (6) and the second pick we want and orange (3).

[tex]\frac{6}{15}[/tex] x [tex]\frac{3}{15}[/tex] =

Which is the same as

[tex]\frac{2}{5}[/tex] x [tex]\frac{1}{5}[/tex]  if I simplify both fractions which is [tex]\frac{2}{25}[/tex]

By using the method subtraction,

1 quarter is 0.25

1 nickel is 0.05

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

Given that,

Isaac has 18 coins, all quarters and nickels.

The total value of the coins it $3.50.

Let the quarters be x and nickels be y

x+ y= 18

x= 18 - y... equation 1

1 quarter is 0.25

1 nickel is 0.05

So,

0.25x+ 0.05y= 3.50

substitute x value in above equation

0.25(18-y)+0.05 = 3.50

4.5-0.25y+ 0.05 = 3.50

4.55 - 3.50 = 0.25y

1.05= 0.25y

y= 4.2

y in equation 1

x= 18 - y

x= 18-4.2

x= 13.8

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The simplified expression of 5^4 * 5^-6 is 5^-2

The expression is given as

5^4 * (5^-2)^3

Evaluate the product of exponents

So, we have

5^4 * 5^-6

The base of the above expression are the same

i.e. Base = 5

This means that we can apply the law of indices

So, we have

5^4 * 5^-6 = 5^(4 -6)

Evaluate the sum in the above equation

So, we have

5^4 * 5^-6 = 5^(4 -6)

Evaluate the difference in the above equation

So, we have

5^4 * 5^-6 = 5^-2

Hence, the simplified expression of the expression given as 5^4 * 5^-6 is 5^-2

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The area of the rectangle when its width is 3 m is 39m².

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares. The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given Data

A function rule for the area of a rectangle with a length 7 m more than three times its width.

Area of rectangle = Length(Width)

Area of function = (w) (3w+7)

Area of function = 3w² + 7w

If w = 3m

Area of function = 3(3)² +7(3)

Area of function = 3(9) + 21

Area of function = 18 + 21

Area of function = 39

the area of the rectangle when its width is 3 m is 39m².

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The pages read by Luis, Dayja and Michael read all together is 252.

What is Percentage?

A relative value indicating hundredth part of any quantity is called percentage.

Given that;

The conditions is,

Luis read 75% more pages than Dayja, and Dayja read 75% more pages than Michael.

Total pages read by Dayja = 84

Now,

Since,  Luis read 75% more pages than Dayja.

So, The pages for Luis = 75% of 84

                                   = 75/100 × 84

                                   = 6,300 / 100

                                   = 63

Thus, Pages for Luis = 84 + 63

                                 = 147

And, Number of pages read by Michael = 84 - 63

                                                              = 21

Thus,  Number of pages read by Michael = 21

So, Total number of pages read by Luis, Dayja and Michael all together is;

= 84 + 147 + 21

= 252

Therefore,

The pages read by Luis, Dayja and Michael read all together is 252.

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Solution:

The equation of the ellipse in the question is given as

Concept:

The general formula of a hyperbola is

From the above equation by comparing coeficient, we will have

The linear eccentricity c, will be

The vertices of the hyperbola will be calculate using the formula below

The co-vertex are calculated using the formula below

The foci of the hyperbola will be calculated using the formula below

The eccentricity, e is

Hence,

The sketch of the graph is given below as

The foci is represented with the two red dots on the graph

The vertices are represented above by the two coordinates

Answer:

10^22

Step-by-step explanation:

= (10^11)(10^11) -> the bases are the same, add the exponents

= 10^22

The table that represents a proportional relationship between x and y is table 2.

A relationship is proportional if each pair of data values are related in the same way, by multiplying by a factor.

A proportional relationship is one in which two quantities vary directly with each other.

For example,

y = kx

where,

k  = constant of proportionality

You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values.

If those ratios are all the same, the table shows a proportional relationship.

Therefore, let's calculate the ratios of the table

Hence, the table 2 has a proportional relationship.

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The total cost of the meal is 66.045

Given,

The cost of the meal = 64.75

The discount given on that day = 15%

The tip given by Zurn family = 20%

We have to find the total cost of the meal.

First we have to find the total cost including tip before discount is added.

That is,

120% of 64.75

= 64.75 × 120/100

= 6.475 × 12

= 77.7

Here, the total cost including tips before discount is 77.7

Now, we have to deduct the discount.

100 - 15 = 85

That is,

85% of 77.7 will be the total cost of the meal

= 77.7 × 85/100

= 6604.5 / 100

= 66.045

Therefore, the total cost of the meal is 66.045

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The graph of the linear equation, y = -3x - 2, that passes through (-2, 4) is shown in the attachment below.

The linear equation of a line is expressed in slope-intercept form as y = mx + b. The y-intercept of the line, which is the point where the line intercepts the y-axis, is represented as "b" in the equation.

The slope is represented as "m".

Given that the line, y = -3x + b passes through the point A(-2, 4), find the value of the y-intercept of the line, b, by substituting x = -2 and y = 4 into y = -3x + b:

4 = -3(-2) + b

4 = 6 + b

4 - 6 = 6 + b - 6

-2 = b

b = -2

Substitute b = -2 into the equation:

y = -3x - 2

The graph of y = -3x - 2 is given in the attachment.

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Answer:

Step-by-step explanation:

12. We have : angle ABF = angle ABE + angle FBE = 2(w+11) + angle FBE = 8w - 6

-> angle ABE = 8w - 6 - [2(w+11)] = 8w - 6 - 2w - 22 = 6w - 28.

13. As we can see, angle EBA and angle EBC is a linear pair, therefore they're supplementary angles, adding up to 180.

-> 3r + 10 + 2r - 20 = 180

5r - 10 = 180
r = 38.

So, angle EBF = 2r - 20 = 76 - 20 = 56.

(pls just don't blur the question next time cause im very confused why the 2 angles are marked equal)

Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

Answer:

16,25 Pa

Step-by-step explanation:

P=F/A;

650/40 = 16,

Answer: v = 8, 5; The sum of these values would be 13.

∣2v − 13∣ + 6 = 9

Combine like terms, utilizing the properties of equality. Do not forget to follow the order of operations!

∣2v − 13∣ + 6 = 9

Subtract 6 from both sides of the equation.

∣2v − 13∣ = 3

Consider the definition of absolute value (distance from the number zero); the absolute value of x and -x would both be x.

2v − 13 = 3

2v − 13 = −3

Add 13 to both sides of the equation.

2v = 16

2v = 10

Divide both sides of the equation by 2.

v = 8

v = 5

Add the sum of the values.

8 + 5 = 13

Step-by-step explanation:

easy so first you are going to subtract 130 from 180 since any angle that is made on a straight line segment if subtracted you get the answer of the other angle

180-130 =50

I want you to draw this diagram on paper and extend the line S that is 50° since we know the angle SRQ =130

Now you will be able to see a Z formation PQR and the other half of the S is making a Z formation the interior angles of a z formation are always equal to each other

so the interior x =50°

extend the line P or Q out wards that will also be equal to the other side now since it also makes a Z formation

As we know that the angle SRQ is equal 130 we will half it or divide it by 2 the answer will be 65

one angle in R angle will be 65 while the other one will also be 65

Now we know two angles in the triangle PQR and one angle in triangle PRS

applay the formula that all interior angles sum =189

x + 65 + z =180 (name the left unknown angle z)

50 + 65 + z= 180

105+ z =180

z=180-105

z=75

we now all the angles in the triangle x

y angle =65 again apply the z formation to get the answer

Answer:8/5

Step-by-step explanation:

TO find the reciprocal, divide 1 1 by the number given

1/(5/8)

=8/5

Parallel lines l and m are intersected by p and q, which are also parallel. The parallelism of the lines p and q can be inferred.

According to the transitive property, "all the quantities are equal to each other if two quantities are equal to the third quantity."

Given: Line l is parallel to line m.

Angle 1 exists equal to angle 3.

Angles 1 and 3 are shown in the figure as equivalent angles that are equal.

Angle 1 created by line p and line l is equivalent to angle 3 created by lines q and m. Lines l and m are parallel as well. Since p and q form the same angle as two parallel lines, they too should be parallel.

In light of this, it can be said that lines p and q are parallel.

Therefore, it can be concluded that the lines p and q are parallel.

The complete question is:

Given: l || m; ∠1 ∠3 Prove: p || q Complete the missing parts of the paragraph proof. We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because . We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. So, we can conclude that lines p and q are parallel by the

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Answer:

Step-by-step explanation:

As per diagram, the angles BGC and CGF are marked as congruent.

It gives us:

Solve it for x:

Find the angle measures:

To find the measure of ∠BGF consider the angle addition:

Answer:

p = 11, I hope this helps and I hope you can improve your grade.

Step-by-step explanation:

Adjacent Angles = 90 degrees, or a right angle.

90 = (5p + 7) + (3p - 5)

1. Subtract the numbers

90 = 5p + 2 + 3p

2. Combine Like Terms

90 = 5p + 2 + 3p

90 = 8p + 2

3. Subtract 2 from both sides

90 - 2 = 8p + 2 - 2

88 = 8p

4. Divided 8 from both sides

88/8 = 8p/8

p = 11

The surface area of the cylinder is 1733.28 square inches

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you multiply the side lengths to determine the area

The shape is given as

Shape = cylinder

Also, we have

Radius, r = 12 inches/2

r = 6 inches

Height, h = 40 inches

The surface area of the cylinder is calculated as

SA = 2πr² + 2πrh

So, we have:

SA = 2 * 3.14 * 6² + 2 * 3.14 * 6 * 40

Evaluate

SA = 1733.28 square inches

Hence, the area is 1733.28 square inches

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Answer:

8

Step-by-step explanation: