Jolie uses the childcare facilities at her gym. Her monthly dues are $32, and childcare is $9 per visit. This month, she does not
wish to spend more than $122 for both dues and childcare. If x represents the number of times she can use childcare services,
which of the following inequalities symbolizes this situation?
A.
$32x+ $9 > $122
B. $32x + $9 < $122
C. $9x + $32> $122
D. $9x + $32 < $122

Answer:

Length is w-5

Area  = length x width

84 = (w-5)w

84 = w^2 - 5w

0 = w^2 - 5w - 84

0 = (  w     -    12 )( w   +     7    )

w + 7 = 0 leads to negative measures.

w-12=0 ---> w = 12

width is 12, length is 5 less, or 7

The dimensions of the rectangle are 12 feet by 7 feet, determined by solving the quadratic equation derived from the relationship between the length and width and the given area of the rectangle.

To find the dimensions of a rectangle where the length is five feet less than its width and the area is 84 square feet, we can set up an equation. Let's define the width of the rectangle as w feet. Then, the length would be w - 5 feet. Since the area of a rectangle is defined as the product of its length and width, we get the following equation:

w times (w - 5) = 84

Expanding the left side gives us:

w^2 - 5w = 84

To solve this quadratic equation, move all terms to one side to set the equation to zero:

w^2 - 5w - 84 = 0

Factoring the quadratic equation, we look for two numbers that multiply to give -84 and add to give -5. These numbers are -12 and +7. So the equation factors as follows:

(w - 12)(w + 7) = 0

The solutions to the equation are w = 12 and w = -7. However, width cannot be negative in this context, so we discard w = -7. Thus, the width is 12 feet and the length is 12 - 5 = 7 feet.

Therefore, the dimensions of the rectangle are 12 feet by 7 feet.

x=14  and y=109

Step-by-step explanation:

Given

y= 5x +39

y= 3.5x +60

5x+39 = 3.5 x+60

5x-3.5x = 60-39

1.5x =21

x= 21/1.5 = 14

Use the value of x = 14 in equation  y=5x+39

y=5*14 +39

y=109

Hence, x=14  and y=109

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Final answer:

To solve the given system of linear equations, we use the elimination method to find the intersection point (14, 109), which is where the two lines represented by the equations meet.

Explanation:

To solve the system of equations:

y = 5x + 39

y = 3.5x + 60

We can use the method of substitution or elimination. In this case, elimination is the straight-forward choice. Since both equations are already solved for y, set them equal to each other and solve for x:

5x + 39 = 3.5x + 60

Now, subtract 3.5x from both sides:

1.5x + 39 = 60

Subtract 39 from both sides:

1.5x = 21

Divide both sides by 1.5:

x = 14

Now, plug the value of x into one of the original equations to solve for y:

y = 5(14) + 39

y = 70 + 39

y = 109

The solution to the system is (14, 109). This represents the point where the two lines intersect on a graph.

Answer:

x=-12

Step-by-step explanation:

2-3/4x=11

3/4x=2-11

3/4x=-9

x=-9/(3/4)

x=(-9/1)(4/3)

x=-36/3

x=-12

Answer:

4

Step-by-step explanation:

The first digit after the decimal point is the tenths place. in this case, it would be 4

Answer:

4 Is in the tenths place

Step-by-step explanation:

7 in the hundreds

2 in the tens

9 in the ones

4 in the tenths

6 in the hundredths

Lets first make it easier.

If you add the 20 minutes to 12:50 it will turn to 1:10.

After this you add the 5 hours.

This will turn 1:10 into 6:10.

Hope this helps :)

Answer:

14

Explanation:

2  l     7

4  l    14

6  l   21

8  l   28

10 l  35

12 l  42

14 l  49

If you noticed the italized, bold, and underlined number fourteen, you would notice that 2 and 7 both have number fourteen as a multiple and it is also the least common multiple.

Answer:

  The equation has a greater constant of variation

Step-by-step explanation:

The graph is of a line through point (0, 0) can be represented by the equation ...

   y = kx

Using the given values for x and y, we see that ...

  3 = k·1

  k = 3 . . . . . the constant of variation for the graph

__

The given fraction can be rewritten as ...

  y = (10/3)x = (3 1/3)x

In this form, the constant of variation is 3 1/3, greater than that of the graph.

Answer:

The equation has a greater constant of variation

Step-by-step explanation:The equation has a greater constant of variation

Final answer:

By calculating and comparing the price per pound of meat for each shopper, it is clear that they paid different prices per pound ($3.29 and $4.19), indicating they did not buy the same kind of meat.

Explanation:

To determine if both shoppers bought the same kind of meat, we need to calculate the price per pound that each shopper paid and compare the results. The first shopper bought 3 pounds for $9.87. To find the price per pound, we divide $9.87 by 3 pounds, which gives us $3.29 per pound.

The second shopper bought 4 pounds for $16.76. Similarly, we divide $16.76 by 4 pounds to get $4.19 per pound. Since the price per pound for each shopper is different, we can deduce that they did not buy the same kind of meat.

Answer:

Shown in the picture

Step-by-step explanation:

A:

Set the value of x to "5" and "30" to find the corresponding values of y (i.e. the altitudes of the plane at 5 or 30 minutes after beginning descent).

B:

Use the the same method to determine the set of coordinates (/ordered pairs) at each of the values for x given in part B of the question.

C:

The initial value is simply the starting value of y, or in other words, the altitude at which the plane begins to descend in this context;

So it will be 0 mins after the beginning of descent of the plane, i.e. when x = 0, therefore the answer is (0, 28000) as an ordered pair or simply 28000 ft.

D:

Rate of change is a fancy or more technical way of referring to the gradient of a function;

In this case of the context of a plane descending, it refers to the change in altitude over time;

This can be calculated using any two ordered pairs (or coordinates as I call them) using the formula of the difference in the y values divided by the difference in the x values.

Answer:

x=14

Step-by-step explanation:

not sure what your asking for???

x-5=9

x=14

Answer:

The answer is [6 18}

Step-by-step explanation:

I just took the test :)

The product of the matrices [4 2] and [-2 5 7 -1] is a 1x4 matrix. The resulting matrix is [-8 -4 20 10].

In order to find the product of two matrices, we need to ensure that the number of columns in the first matrix matches the number of rows in the second matrix. The first matrix, [4 2], has 1 row and 2 columns (1x2), while the second matrix, [-2 5 7 -1], has 2 rows and 4 columns (2x4). Since the number of columns in the first matrix matches the number of rows in the second matrix, we can proceed with matrix multiplication.

To compute the product, we perform the following steps:

Step 1: Take the first row of the first matrix and multiply each element by the corresponding element in the first column of the second matrix.  

- First element: 4 * (-2) = -8  

- Second element: 2 * (-2) = -4

Step 2: Take the first row of the first matrix and multiply each element by the corresponding element in the second column of the second matrix.  

- Third element: 4 * 5 = 20  

- Fourth element: 2 * 5 = 10

Step 3: Now, we have the elements for the first row of the resulting matrix: [-8 -4 20 10].

Step 4: Repeat the above steps for the second row of the first matrix.

Step 5: Combine the results to form the final product matrix: [-8 -4 20 10].

So, the product of the matrices [4 2] and [-2 5 7 -1] is the 1x4 matrix

[-8 -4 20 10].

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Answer:

The system has infinite solutions

Is a consistent dependent system

Step-by-step explanation:

we have

First equation

[tex]\frac{1}{2}x-\frac{1}{3}y=5[/tex]

Isolate the variable y

[tex]\frac{1}{3}y=\frac{1}{2}x-5[/tex]

Multiply by 3 both sides

[tex]y=\frac{3}{2}x-15[/tex] ----> equation A

Second equation

[tex]x=\frac{2}{3}y+10[/tex] -

Isolate the variable y

[tex]\frac{2}{3}y=x-10[/tex]

Multiply by 3/2 both sides

[tex]y=\frac{3}{2}x-15[/tex] ---> equation B

Compare equation A and equation B

The equations are identical

therefore

The system has infinite solutions

Is a consistent dependent system

Answer:

y=-4/3x+2

Step-by-step explanation:

Answer:

810 cubes

Step-by-step explanation:

step 1

Find the volume of the rectangular prism

The volume of the rectangular prism is

[tex]V=LWH[/tex]

we have

[tex]L=2\frac{1}{2}\ in=2+\frac{1}{2}=\frac{5}{2}\ in[/tex]

[tex]W=2\ in\\H=6\ in[/tex]

substitute

[tex]V=(\frac{5}{2})(2)(6)[/tex]

[tex]V=30\ in^3[/tex]

step 2

Find the volume of the cube

The volume of the cube is

[tex]V=b^3[/tex]

where

b is the length side of the cube

we have

[tex]b=\frac{1}{3}\ in[/tex]

substitute

[tex]V=(\frac{1}{3})^3[/tex]

[tex]V=\frac{1}{27}\ in^3[/tex]

step 3

Find out how many unit cubes with edge lengths of 1/3 inch can fit inside the prism

Divide the volume of the prism by the volume of the cube

[tex]30:\frac{1}{27}=30(27)=810\ cubes[/tex]

Missing value is Decreased by 20%

Step-by-step explanation:

We need to find the missing term.

As we can see from the figure we go from Decreased 10% and then decreased 10% to reach the final goal.

If we directly go from starting point to end point the total will be decreased by 20% as (10%+10%= 20%)

So, Missing value is Decreased by 20%

Answer:

-2

Step-by-step explanation:

(–4, 3) (4, –3) (–3, –4) (3, 4)

this is a rather simple yet complex concept the easiest way to solve these is to do the exact opposite.

so in this instance it is refrcted across the y-axiss so we swap ONLY the x value NOT the Y ie (-4,3) would switch to (4,3)

same thing would apply if it reflected across x-axis ex (-4,-3)

If it reflect across orgin you change both signs. ex (4,-3)

ie.

(–4, 3) (4, –3) (–3, –4) (3, 4)

changes to

(4, 3) (-4, –3) (3, –4) (-3, 4)

hope it helps

The coordinates of the image of vertex R after a reflection across the y-axis is (3, 4).

A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state.

Given is a point R = (-3, 4) we need to find the coordinates of the point R after it being reflected over y-axis,

So, we know that,

When dealing with reflection of a line or shape or a figure in the coordinate plane, especially if it is reflected across the y-axis, you just have to give the opposite of the given (original) x- coordinate in order to give a symmetric figure.

The rule of reflection over y-axis is =

(x, y) = (-x, y)

So,

R = (-3, 4), after it being reflected over y-axis =

R' = (3, 4)

Hence the coordinates of the image of vertex R after a reflection across the y-axis is (3, 4).

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Answer:

25Ncm^2

Step-by-step explanation:

Pressure = force/area

Force = 2000N

Area = 80cm^2

Therefore,

Pressure = 2000/80

= 25Ncm^2

Answer:

First add 0.2 to both sides

x = 0.53

Step-by-step explanation:

4x - 0.2 = 1.9

4x - 0.2 + 0.2 = 1.9 + 0.2

4x = 2.1

Divide both sides by 4

4x/4 = 2.1/4

x =0.53

Answer:

Distance in meters D = 167.75 meters

Step-by-step explanation:

Distance covered in 5 seconds is given by:

Distance, D = Speed (S) X Time (T)

Where,

Distance = ?

Speed = 75mph

Time = 5s

Since we are calculating distance in meters, we have to convert 75miles per hour to meters per second

75mph = 75miles/1hr X 1km/0.621miles X 1000m/1km X 1hr/60mins X 1min/60s

            = (75X1000) / (0.621X60X60) meter per second

            = 75000/2235.6 meter per second

            = 33.55 meter per second

∴ Distance D = 33.55 meter per second X 5 seconds

                      = 167.75 meters

Answer:

Length of the ladder used by worker = 17 feet

Step-by-step explanation:

Given:

Height of the window from the ground = 13 ft

Distance of fence from the building = 3 ft

Distance of ladder from the building = (3+8) = 11 ft

We have to find the length of the ladder.

Let the length of the ladder be 'x'

From the diagram we can also say that 'x' is the hypotenuse of the right angled triangle.

Using Pythagoras formula:

⇒ [tex]hypotenuse\ 'x' =\sqrt{(perpendicular)^2+(base)^2}[/tex]

Here base length = 11 ft

Perpendicular = 13 ft

Plugging the values:

⇒ [tex]x=\sqrt{(13)^2+(11)^2}[/tex]

⇒  [tex]x=\sqrt{(169+121)}[/tex]

⇒ [tex]x= \sqrt{290}[/tex]

⇒ [tex]x=17.02[/tex] feet

The length of the ladder = 17 feet to its nearest tenth.

The worker will need a ladder that is approximately 8.5 feet long. This calculation is based on the Pythagorean theorem, considering the ladder's placement 8 feet from the fence and the need to reach a window 13 feet above the ground.

To find the length of the ladder the worker needs, we can use the Pythagorean theorem, as the ladder, the distance from the building, and the distance from the fence form a right triangle.

Let:

L be the length of the ladder.

D be the distance from the building to where the ladder rests (8 ft).

F be the distance from the fence to where the ladder rests (3 ft).

According to the Pythagorean theorem, we have:

[tex]L^2 = D^2 + F^2[/tex]

Substitute the known values:

[tex]L^2 = 8^2 + 3^2[/tex]

[tex]L^2 = 64 + 9[/tex]

[tex]L^2 = 73[/tex]

Now, take the square root of both sides:

L ≈ √73 ≈ 8.54 ft (rounded to the nearest tenth)

So, the worker will need a ladder that is approximately 8.5 feet long to safely reach the window 13 feet above the ground when placed 8 feet from the fence for stability.

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Answer:

Step-by-step explanation:

A square is equal on each side. There are a total of 4 sides so we would take 320 and divide it by four to find the size of one side.

320/4

80

A = lw

A = 80 x 80

A = 6400 m^2

Answer:

Step-by-step explanation:

(17 1/2) / (5/6) =

(35/2) / (5/6) =

35/2 * 6/5 =

105/5 =

21 <===

Answer:

1.067

Step-by-step explanation:

Answer:

  $1299.50

Step-by-step explanation:

It appears that the graph shows the percentage of market value of a 6-year-old car is about 10%. So the value of such a car with an original value of $12,995 would be ...

  $12,995 × 0.10 = $1299.50

The current market value is $1299.50.

The current market value of the car is $1299.50

The original cost is given as:

Original = $12,995.

From the graph, the worth of the car after 6 years is

Rate = 10%

So, the current market value of the car is:

Value = $12,995 * 10%

Evaluate the product

Value = $1299.50

Hence, the current market value of the car is $1299.50

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Answer:

40% decrease

Step-by-step explanation:

6.5*40%=2.6

6.5-2.6=3.9

Answer:

40%

Step-by-step explanation:

Original Mass of the pumpkin = 6.5kg

After carving, the mass of the pumpkin became = 3.9 kg

Decrease in mass = 6.5 — 3.9 = 2.6kg

Therefore, the percentage decrease in mass of the pumpkin = (2.6/6.5)x100 = 40%

Answer:

34+22=56+16=72 100-72=28 feet

Step-by-step explanation:

Solution:

Given that,

Kate wants to build a fence around her garden to prevent her rabbits from eating her vegetables

Given is a square garden

Area = 144 square meter

[tex]Area = (side)^2\\\\144 = (side)^2\\\\Take\ square\ root\ on\ both\ sides\\\\side = 12[/tex]

Thus length of side of square is 12 meter

Perimeter = 4(side)

Perimeter = 4(12)

Perimeter = 48 meter

[tex]Cost = perimeter \times 7.50\\\\Cost = 48 \times 7.50\\\\Cost = 360[/tex]

Thus it costs $ 360 to enclose a square garden with an area of 144 square meter