The graph shows membership costs at a gym. How much was the initial membership fee?

The solutions of the system of inequalities are the points on the purple region, one example of a solution is (-2, -2)

When we have a system of inequalties (so we have 2 or more inequalities) the solutions are the points (x, y) that are solutions of both inequalities at the same time.

Here we can see the graph of a system, such that the solution set of one of the inequalities is represented by the red shaded area, and the solution set of the other inequality is represented by the blue shaded area.

The solution set of the system is represented by the intersection between the areas, which is the purple area.

So any point on that region is a solution to the system, for example, the point (-2, -2) is a solution.

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This is an example of a descriptive quantitative research study.

Descriptive quantitative research involves collecting and analyzing data to describe the characteristics of a population or phenomenon. In this case, the nurse administrator is gathering and analyzing data about the employees on the units they supervise, such as work shift, number of years employed, age, gender, educational preparation, certifications, work history, and professional accomplishments. Statistical techniques such as mean, median, and mode are used to analyze the data, allowing the nurse administrator to compare the characteristics of the employees across various dimensions. This type of research is used to develop an understanding of a given population or phenomenon, allowing for informed decision-making.

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The volume is increasing at a rate of 784 * pi cubic inches per second.

The volume of a sphere is given by the formula V = (4/3) * pi * r^3, where r is the radius of the sphere.

We can find the rate of change of the volume with respect to time by taking the derivative of V with respect to time.

dV/dt = (4/3) * pi * 3r^2 * dr/dt

Given that the radius is increasing at a rate of 2 in/sec, we can substitute this value into the equation and find the rate at which the volume is increasing:

dV/dt = (4/3) * pi * 3 * 9^2 * 2 in^3/sec = 784 * pi in^3/sec

So, when the radius of the snowball is 9 inches, the volume is increasing at a rate of 784 * pi cubic inches per second.

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The triangle proportionality theorem, used to evaluate the figures indicates that we get;

8. [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex]

9. [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex]

10. [tex]\overline{ST}[/tex] ∦ [tex]\overline{PR}[/tex]

11. x = 57.6

12. x = 27.3

13. x = 11

14. x = 10

15. x = 5

16. x = 17

The triangle proportionality theorem states that, in a triangle, a line drawn parallel to one of the sides of a triangle and intersects the other two sides at two different points, then the ratio in which the other two sides are divided by the line are the same.

8. The triangle proportionality theorem indicates, if  [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] are parallel,   [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex], we get; QS/SP = QT/TR

QS/SP = 7/11.2 = 0.625

QT/TR = 10/16 = 0.625

9. Where [tex]\overline{ST}[/tex] and [tex]\overline{PR}[/tex] are parallel,   [tex]\overline{ST}[/tex] ║ [tex]\overline{PR}[/tex], we get;

PS/SQ = RT/TQ

PS = 102 - 45 = 57

PS/SQ = 57/45 = 1.2[tex]\overline{6}[/tex]

RT/TQ = 41.8/33 = 1.2[tex]\overline{6}[/tex]

10. Where [tex]\overline{ST}[/tex] is parallel to [tex]\overline{PR}[/tex], we get;

QS/SP = QT/TR

QS/SP = 19/38 = 0.5

QT/TR =  24/52 = 6/13 ≠ 0.5

11. The triangle proportionality theorem, indicates that we get;

48/25 = x/30

x/30 = 48/25

x = (48/25) × 30 = 57.6

12. Making use of the triangle triangle proportionality theorem, we get;

(49 - 28)/28 = x/36.4

x/36.4 = (49 - 28)/28

x = ((49 - 28)/28) × 36.4 = 27.3

13. 32/60 = (2·x + 6)/52.5

(2·x + 6)/52.5 = 32/60

(2·x + 6) = (32/60) × 52.5 = 28

(2·x + 6) = 28

2·x = 28 - 6 = 22

x = 22/2 = 11

14. (x - 3)/21 = (x - 1)/27

27 × (x - 3)= 21 × (x - 1)

27·x - 27 × 3 = 21·x - 21

27·x - 21·x = -21 + 27 × 3 = 60

6·x = 60

x = 60/6 = 10

15. (7·x - 11)/(4·x - 2) = 20/(35 - 20)

(7·x - 11)/(4·x - 2) = 20/(35 - 20) = 20/15

(7·x - 11)/(4·x - 2) = 20/15

15 × (7·x - 11) = (4·x - 2) × 20

105·x - 165 = 80·x - 40

105·x - 80·x = 25·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

16. 35/(x - 3) = (x - 7)/4

35 × 4 = (x - 3) × (x - 7)

140 = x² - 10·x + 21

x² - 10·x + 21 - 140 = 0

x² - 10·x - 119 = 0

x² - 10·x - 7 × 17 = 0

x² + 7·x - 17·x - 17 × 7 = 0

x·(x + 7) - 17·(x + 7) = 0

(x + 7)·(x - 17) = 0

x = -7, or x = 17

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Answer:

128π in.² ≈ 402.1 in.²

Step-by-step explanation:

The rod can be cut into two equal sized pieces in different ways, so there are different answers to this question. I assume the question is asking when the rod's length is cut in half, so now there are two rods, each one being a cylinder with 4 inch height.

We need the area of the original rod and then add two more base areas.

C = 8π in.

r = 4 in.

total surface area = lateral area + 4 × area of base

SA = 8 in. × 8π in. + 4 × π × (4 in.)²

SA = 64π in.² + 64π in.²

SA = 128π in.² ≈ 402.1 in.²

Answer:

401.9

Step-by-step explanation:

I got this question wrong on my quiz

Answer: Volume of a right prism = BH where B is the area of the base and H is its height.

So Volume = 16 × 12 = 192 cm^3

Step-by-step explanation:

The value of {z} is equivalent to 13.

Given is that SX = z, TW = 6z - 76 and UV = 3z - 24.

We can write -

{z} + {6z - 76} = {3z - 24}

7z - 76 = 3z - 24

7z - 3z = - 24 + 76

4z = 52

z = 13

Therefore, the value of {z} is equivalent to 13.

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The distance of Naudia from starting point based on distance travelled is 13 miles.

The distance travelled by Naudia and distance from starting point will form right triangle. Distance between Naudia and her final destination is the straight line or hypotenuse.

So, the expression will be -

Distance of South² + distance of East² = Distance from starting point

Distance form starting point = 2² + 3²

Distance form starting point = 4 + 9

Distance form starting point = 13 miles

Thus, the required distance is 13 miles.

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Answer:

Equation is   x-5 = 37

Reason:

x = starting temperature

We start with x degrees, and decrease by 5 degrees.

We go from x to x-5

The x-5 is now 37 degrees

Therefore, we arrive at the equation x-5 = 37

To solve this equation, add 5 to both sides and you'll get x = 42

Nice work on getting the correct value of 42.

The values of n for the given expression such that -15< 3n < 6 is -5 < n < 2.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The given expression is:

-15< 3n < 6

Divide all the sides of the equation with 3 to isolate the value of n.

-15 / 3 < 3n/3 < 6/3

-5 < n < 2

Hence, the values of n for the given expression such that -15< 3n < 6 is -5 < n < 2.

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The length of the diagonal support lumber is given as follows:

161.5 inches.

The figure is a rectangle, hence the diagonals have equal measure, and thus the value of x can be obtained as follows:

15x + 13.25 = 17x + 4.5.

2x = 9

x = 4.5.

Hence the length of the  diagonal support lumber is obtained as follows:

2 x (15 x 4.5 + 13.25) = 161.5 inches.

We multiply by 2 as we are given half the length of the diagonal.

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Answer:

1.  5 inches in 2 days

2.  y = (5/2)x. where y is rainfall and x is days.

3.  Yes

4.  (5/2)

5.  2.5"/day

6.  37.5 Inches

Step-by-step explanation:

See attached worksheet

.

Ratio of apple juice to water will make the same recipe is  42.60

Ratios are used to compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This signifies that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.

Add the elements of the ratio together to get the total number of shares.

Subtract the total value from the total number of shares.

Multiply by the number of necessary shares.

A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to one.

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4/5 + 5/6

24+25/30

49/30

hope it will help you

can you talk with me?

The ordered pair could represent the image of point C(5, 2) after the dilation is (2.5, 1)

If we have a general point (x, y) and we apply a dilation with the origin as the center of a scale factor k, then the coordinates of the image after the dilation is (k*x, k*y)

Here we want to see which point can be the image of (5, 2) after the dilation, it will must have the form (k*5, k*2)

The only point that has this form is the one on the third option, where we can write:

(2.5, 1) = (k*5, k*2)

Then we have two equations:

2.5 = k*5

1 = k*2

Solving these we should get the same value of k.

2.5/5 = k = 0.5

1/2 = k = 0.5

so that is the correct option.

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The area of the walkway around swimming pool is 78 square feet.

The outer sides of the walkway will have a length of 12 feet and the breadth will be 11 feet.

The area of the pool along without the walkway will be 12 X 11 = 132 square feet.

The outer sides of the walkway will have a length of 15 feet and the breadth will be 14 feet after the owner create the walkway.

The area of the pool along with the walkway will be 15 X 14 = 210 square feet.

Therefore ,

area of the walkway will be:-

= 210 - 132

= 78 square feet.

so, the area of the walkway around swimming pool is 78 square feet.

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Answer:

400 pounds equal to 0.2 tons

The table that represents the proportional relationship would be table A. Option A

In this table we can see that in option A, there is a constant for which the values of the y are gotten. This is common on all of the values in A

For instance 2² = 4

3² = 9

4² = 16

0² = 0

The power of 2 is the constant that when applied on the values it gives the corresponding solution.

This shows the constant proportional relationship that is in existence between the values in x and the y solution

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The graph of a line passing through the points (2, -4) and (0, 0). The correct answer would be an option (A).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The table represents a linear relationship.

x: −1   0    1    2

y:  2   0  −2  −4

As per the points, the graph has been attached below

Here we can see that the shown graph of a line passing through the points (2, -4) and (0, 0)

So the attached graph shows this relationship.

Hence, the correct answer would be option (A).

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The expression 4× 4 × 5 × 10 = 800 in the field of math.

Algebra is a branch of mathematics that is used to manipulate symbols and equations in order to solve problems. Algebra helps to solve problems involving unknown quantities and to develop relationships between different variables. It is a powerful tool that can be used to solve and analyze a variety of mathematical problems and equations.

Algebra can be used to solve equations, simplify expressions, and find solutions to linear and quadratic equations. Through algebra, we can also find the slope of a line, the area of a triangle, and the volume of a cube. Algebra is an invaluable tool that is useful in many areas of mathematics and science.

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The square root of 224 in long division is 14.96

The term square root in math is defined as  a factor of a number that, when multiplied by itself, gives the original number

Here we know that we need to find the square root of √224.

In order to solve this one we have to do the following steps,

Here we have to start dividing the digits from the right side into pairs of two by drawing a line on top of them. In the case of 224, then we have two pairs 24 and 2.

And then we have to find a number(z) whose square is ≤ 2.

Then the value of z will be 1 as 1 × 1 = 1 ≤ 2.

Here we get the value of quotient and the remainder as 1 and now we have to add the divisor z with itself and get the new divisor 2z (2).

And then we have to drag down the next pair and find a number (n) such that 2n × n ≤ 124 here we have the value of n comes out to be 4.

Finally we have to add a decimal in the dividend (224) and quotient (14) simultaneously.

Here we have to add 2 pairs of zero in the dividend after the decimal  and repeat the above step for the remaining three pairs of zero.

Complete Question:

Finale the square root of √224 and go step by step to reduce the radical.

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Answer: x=14°

Step-by-step explanation:

All angles of a triangle added together is 180°. So we can add the angles together.

7x-11+5x-2+2x-3=180           [combine like terms]

14x-16=180                             [add both sides by 16]

14x=196                                  [divide both sides by 14]

x=14

Therefore, x=14°.

Throughout the solar system, solar energy is continuously emitted by the sun. The Earth is warmed by solar energy, which also affects the weather, the wind, and the survival of plant and animal life. Electromagnetic radiation, which is a kind of energy, heat, and light, is released from the sun (EMR).

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The expression of the statement is 3x² - 8

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

A mathematical statement

The mathematical statement is given as

Three times the square of a number minus eight

Represent the number with x

So, we have

Three times the square of x minus eight

Express as squares and numbers

This gives

3 * x² minus 8

So, we have

3x² - 8

hence. the expression is 3x² - 8

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Answer:

518.4 cm²

Step-by-step explanation:

We have two triangles so

2 × (9×10/2) = 90

We have a base so

14 × 10  = 140

We have two other rectangles so

2 × 14 × 10.3 = 288.2

Now we add it all together

288.4 + 140 + 90 = 518.4

The light travels 3.784 x 10 ^13 kilometers in 4 years .As Given that, light travels 1 meter in 1/299,772,458 of a second.

In 4 years how many kilometers it will travel?

covert 4 years into seconds.

since it is given that 1 year = 365.25 days.

           4 years in seconds = 4 x 365.25 x 24 x 60 x 60

                                            = 126230400 sec

          1 m in 1/299,772,458 sec

          x km in 126230400 sec

(let x be the distance travelled)

          x = 126230400 x 299,772,458

             = 3.784 x [tex]10^13\\[/tex] km.

Therefore , The light travels 3.784 x 10 ^13 kilometers in 4 years .

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The complete question :

if light travels exactly 1 meter in 1/299,772,458 of a second, how many kilometers does it travel in 4.00 years? for this question,

1 year = 365.25 days.

his loan will be $37,234 in the year 2022.

ax2+bx+c=0, with a not equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given, David took out a 20-year $70,000 loan from his bank in 2010.

The quadratic equation that approximates the year/loan balance relationship is y = -98*x^2 - 1,531x + 69,718,

where x is the number of years and

y is the balance

Since the Loan balance is given $37,234.

Thus to calculate the year

$37,234 = -98*x^2 - 1,531x + 69,718,

98 x² + 1534x - 32484 = 0

Comparing with the general form of the quadratic equation.

ax² + bx + c = 0

The discriminant b² - 4ac > 0 thus it has Two real roots.

using the Quadratic Formula

x = [tex]\frac{-b +- \sqrt{b^{2} - 4ac } }{2a}[/tex]

x = -27.62

and

x = 12

Thus year = 2010 + 12 = 2022

Therefore, In the year 2022, his loan will be $37,234.

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The point of intersection with x - axis is (5/3,0) and the point of intersection with y - axis is (0,5).  

Any point on AB's perpendicular bisector, P(x,y), shall be considered. Then, PA = PB.

√(x-3)²+(y-6)² = √(x+3)²+(y-4)²

(x-3)²+(y-6)² = (x+3)²+(y-4)²

x² -6x+ 9 + y²- 12y + 36 = x² +6x+ 9 + y²- 8y + 16

12x + 4y -20 = 0

3x+ y-5 =0 ---(1)  

Consequently, 3x+y-5=0 is the equation for the perpendicular bisector of AB.

We know that the coordinates of any point on x-axis are of the form (x,0). In other words, any point on the x-axis has a y-coordinate of zero. Thus, if we enter y = 0 in (1), we get

3x -5 = 0

x = 5/3

Thus, the x-axis is cut by the perpendicular bisector of AB at (5/3, 0).

(ii) Any point's y-axis coordinates have the following format: (0,y). When we enter x = 0 in (1), we obtain

y − 5 = 0

⇒ y = 5

Thus, the y-axis is where the perpendicular bisector of AB intersects (0,5).

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The ordered pair that is a solution of given two expressions is (3,0) .

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expressions,

4x + 3y < 12

-x + 3y < -3

First find where the 2 lines intersect

4x + 3y = 12

-x + 3y = -3

Subtract :

5x = 15

x = 3

and y = -3 + 3 / 3 = 0

So they intersect at the point (3,0).

Therefore , The ordered pair that is a solution of given two expressions is (3,0) .

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Answer:

there is 30 ways

Step-by-step explanation:

There are 6 people who can be president x 5 other people who can be vice president. so there is 30 ways