The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x=3.

x=5, y=-4

an equation is y=___

When x=3, y=___

Show work

Answer:

45

Step-by-step explanation:

3 to the 4th power is the same as 3 x 3 x 3 x 3

3 x 3 x 3 x 3 = 81

-6 x -6 = 36 (a negative times a negative is always positive)

81 - 36 = 45

Answer:

21 hot dogs

9 pizza slices

Step-by-step explanation:

Given information:

Define the variables:

Create two equations from the given information:

[tex]\textsf{Equation 1}: \quad x + y = 30[/tex]

[tex]\textsf{Equation 2}: \quad 2.5x+3.25y=81.75[/tex]

Rewrite Equation 1 to make x the subject:

[tex]\implies x=30-y[/tex]

Substitute this into Equation 2 and solve for x:

[tex]\implies 2.5(30-y)+3.25y=81.75[/tex]

[tex]\implies 75-2.5y+3.25y=81.75[/tex]

[tex]\implies 75+0.75y=81.75[/tex]

[tex]\implies 0.75y=6.75[/tex]

[tex]\implies y=9[/tex]

Substitute the found value of y into the rewritten form of Equation 1 and solve for x:

[tex]\implies x=30-9[/tex]

[tex]\implies x=21[/tex]

Solution

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Answer:

Number of hot dogs purchased = 21

Number of pizza slices purchased = 9

Step-by-step explanation:

Let the number of people buying hot dogs be represented by the variable H and the number of people buying pizzas be represented by the variable P

Since H hot dogs were purchased and each hot dog costs $2.50, total amount spent on hot dog purchase = $2.50H

Since P slices of pizza were purchased and each slice of pizza costs $3,25,  total amount spent on hot dog purchase = $3,25P

Total amount spent (in $) = 2.50H + 3.25P and we are given that this total amount is $81.75

So we have an equation in two variables

2.50H + 3.25P = 81.75      (1)

We know the number of people is 30 and that should equal the number of hot dogs and pizza slices purchased

So

H + P = 30     (2)

Multiply Equation (2) on both sides by 2.50
==> 2.50(H + P) = 2.50 x 30

2.50H + 2.50P = 75    (3)

Subtract equation (3) from equation (1) to eliminate the H terms

(1) - (3):

2.50H + 3.25P - (2.50H + 2.50P) = 81.75 -75

2.50H + 3.25P - 2.50H - 2.50P = 6.75

Collect like terms and simplify

==>  (2.50H -2.50H) + (3.25P - 2.50P) = 6.75

==>  0.75P = 6.75

Divide both sides by 0.75

==>  0.75P/0.75 = 6.75/0.75

==>  P = 9

So number of people who bought pizza slices = 9

This is the same as the number of pizza slices that were bought

Substitute for P in Eq (2) H + P = 30
==>  H + 9 = 30

Subtract 9 from both sides

==> H + 9 - 9 = 30 - 9

==>  H = 21

So number of people who bought hot dogs = 21

This is the same as the number of hot dogs purchased

The Area of the trapezoid in the image attached below is: 204 units².

To find the area of a trapezoid, the following formula is used:

Area of trapezoid = 1/2 × (a + b) × h, where h is the height of the trapezoid, and a and b are the length of the two parallel bases of the trapezoid.

Given the trapezoid in the image attached below, we have the following parameters:

a = 10

b = 24

h = 12

Area of trapezoid = 1/2 × (10 + 24) × 12

Area of trapezoid = 1/2 × (34) × 12

Area of trapezoid = 34 × 6

Area of trapezoid = 204 units²

Therefore, the Area of the trapezoid in the image attached below is: 204 units².

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Answer:

Hello,

Step-by-step explanation:

The time they travel is t=6 hours

v is rate of the fastest train

v-2 the slower one.

v*t+(v-20)*t=900

2vt-20t=900

12v-120=900

12v=900+120

v=1020/12

v=85 (mi/h)

v-20=65 (mi/h)

Answer:

i think its 2

Step-by-step explanation:

Answer: 2.

Step-by-step explanation:  Because if you see where the dot of line is you will see that the dot is right next to number 2

The Density of the given plank with dimensions is; 33.82 kg/m³

We are given;

Length of plank = 2.3 meters

Width of plank = 30 cm = 0.3 m

Height of Plank = 3 cm = 0.03 m

Mass of plank = 0.7 kg

Now, formula for density = mass/volume

Volume of the plank is gotten from the formula;

Volume = Length * width * height

V = 2.3 * 0.3 * 0.03

V = 0.0207 m³

Thus;

Density = 0.7/ 0.0207

Density = 33.82 kg/m³

Thus, we can conclude that the Density of the given plank with dimensions is 33.82 kg/m³

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Answer:

It is incorrect. It is supposed to be set at -8 to 9 but instead it is at -8 to 7.

The decimal should go up 2 places higher!

Step-by-step explanation:

Answer:

55.2 miles

Step-by-step explanation:

6.9 x 8 = 55.2

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)

n = 1 is a counterexample for both the given equations.

Here, we are given two equations, let us look at them one by one-

a. (n + 5) / 5 = n + 1

let us take n = 1

the, (1 + 5) / 5 = 1 + 1

6/ 5 = 2

This equation does not hold as 6/5 ≠ 2. Thus, n = 1 doesn't satisfy the given equation and hence is a counterexample.

b. (n + 4)² = n² + 4²

Let us take n = 1

(1 + 4)² = 1² + 4²

5² = 1 + 16

25 = 17

Again, this equation does not hold as 25 ≠ 17. Thus, n = 1 doesn't satisfy the given equation and hence is a counterexample.

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The value of angle A is 60.

In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

We have the angles as:

∠H = 2x + 60

∠T = x + 30

Now, HALT is a parallelogram.

Therefore, angles H and T are supplementary.

So,

∠H + ∠T = 180

2x + 60 + x + 30 = 180

3x + 90 = 180

3x = 180 - 90

3x = 90

x = 90 / 3

x = 30

Substituting the value of x in the angles, we get:

∠H = 2x + 60

∠H = 2(30) + 60

∠H = 60 + 60 =120

∠T = x +30

∠T = 30 + 30

∠T = 60

Now, angles T and A are congruent angles.

Therefore, ∠T = ∠A

∠A = 60

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The length of a rectangle is 6 m longer than its width. of the perimeter of the rectangle is 36 m, its area is  72 m².

Any polygon's area is the amount of space it takes up or encloses. The amount of square units that make up the polygon. Because the area is a two-dimensional object, it has both length and width. Typically, the area is expressed in square meters, square feet, or square inches. Acres, hectares, and square kilometers are used to measure the size of larger shapes like cities and farms.

Let l be the length of the rectangle

And w be the width of the rectangle.

Given, l=6+w

Perimeter,p =36m

We know that, p= 2(l+w)

p =36=2(6+w+w)

36/2= 6 +2w

18-6=2w

w=6m

Therefore, l=6+w

l=12m

Area of rectangle= lw

A = 12×6

A=72 m².

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Answe[tex]10c^{2} +5c+4[/tex]

Step-by-step explanation:

Step 1 -(((6•(c2))-2c)-1)+((22c2+7c)+5)

Step 2-(((2•3c2) -  2c) -  1) +  (4c2 + 7c + 5)

in conclusion, you get [tex]10c^{2} +5c+4[/tex]

I hoped i have helped u have a wonderful day or night !

Answer:

x=0

Step-by-step explanation:

:)

Answer:

[tex]{ \tt{ \frac{3}{2}(6x + 2) = - 3(x - 1) }} \\ \\ { \tt{3(3x + 1) = - 3(x - 1)}} \\ { \tt{3x + 1 = - (x - 1)}} \\ { \tt{3x + 1 = - x + 1}} \\ { \tt{3x + x = 0}} \\ { \tt{x = 0}}[/tex]

By addition of all the exercise and substracting it from 1 hourJavier runs on treadmill on Monday is 0.40 hour.

Now According to the question javier completed 3 repetitions of each exercise so by multiplication time taken by javier to complete each exercise is as follow;

Squats = 0.8*3= 0.24 hour

Crunches = 0.03*3 = 0.09 hour

Lunges = 0.04*3 = 0.12 hour

curls = 0.05*3 = 0.15 hour

we can calculate total time taken to complete all exercise by Addition is,

0.24 + 0.09 + 0.12 + 0.15

0.60 hour

time taken on treadmill by javier;

1 hour - 0.60 hour

0.40 hour

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The equivalent form of the compound inequality -22 > -5x - 7≥-33  is  -22 > -5x - 7 and -5x - 7≥-33

Inequality:

A mathematical phrase in which the sides are not equal is referred to as being inequal. In essence, a comparison of any two values reveals the existence of an inequality when one of the values is less than, larger than, or equal to the value on the opposite side of the equation.

Given inequality is -22 > -5x - 7≥-33

The equivalent inequality is -22 > -5x - 7 and -5x - 7≥-33

Therefore,The equivalent form of the compound inequality -22 > -5x - 7≥-33  is  -22 > -5x - 7 and -5x - 7≥-33.

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The equation of the translated graph is g(x) = |x + 2| + 1

The parent function is given as

f(x)= |x|

From the graph, we can see that the parent function f(x) is translated as follows:

This is represented as

(x, y) = (x + 2, y + 1)

So, we have

g(x) = |x + 2| + 1

Hence, the equation of the translated graph is g(x) = |x + 2| + 1

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The supplied statement indicates that the angle of elevation will be = -75 feet.

The term angle of elevation refers to the angle between the horizontal and an object. The line of sight of an observer would be over the horizontal. The term angle of depression refers to the angle between the horizontal and an item. The line of sight of an observer would fall below the horizontal.

"rise over run" is an easy-to-remember equation for calculating a change in elevation as a decimal, which means the rise (the change in vertical distance) divided by that of the run (the change in horizontal distance). As an example, suppose the increase is two and the run is six. So you'd multiply 2 by 6 (or 2/6) to get.

Given The elevation of a sunken ship =  120 feet

the elevation of a submarine  = 5/8

So,

Your elevation will be given by employing the MULTIPLICATION OPERATION.

(5/8) x -120 feet

= -75 feet

The supplied statement indicates that the angle of elevation will be = -75 feet.

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The correct option for the function in this problem is:

D- An exponential function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was 0.9 times its value 1 year before.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

For this problem, during each 1 -year period after the equipment was purchased, the value of the equipment at the end of the period was 10% less than its value at the beginning of the period, hence r = 0.1 and the equation is:

[tex]A(t) = A(0)(1 - 0.1)^t[/tex]

[tex]A(t) = A(0)(0.9)^t[/tex]

Which means that option D is correct.

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Answer:

Step-by-step explanation:

You want the number of nickels and dimes that make up $13.30 when there are 5 more nickels than dimes.

Let d represent the number of dimes. Then (d+5) is the number of nickels. The total value in cents is ...

  10d +5(d+5) = 1330

Simplifying the equation, we get ...

  15d +25 = 1330

  15d = 1305 . . . . . . . . subtract 25

  d = 87 . . . . . . . . . . . divide by 15

  (d+5) = 92 . . . . . . the number of nickels

[tex]\boxed{\text{There are 92 nickels and 87 dimes in the piggy bank.}}[/tex]

Answer:

7.8 miles

Step-by-step explanation:

5.9 + 1.9 = 7.8miles

Answer: I hope this helps.

Step-by-step explanation:

[tex] \bf \implies \: y \: = \frac{1}{2} p - x[/tex]

Answer:

this is hard , I suggest you see a tutor

The subject of the function is t = w - v

It should be noted that the function that's given is illustrated as:

w = uv + t

Subtract uv from both sides.

w - uv = uv + t - uv.

w - uv = t

Therefore, it can be seen that the subject of the function is t = w - v

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In decreasing size, the slopes of the linear functions are given as follows:

m4, m3, m2, m1.

A linear function is modeled by:

y = mx + b

In which:

Regarding the slope, we have that:

Hence, for the lines in this graph:

Then, we consider the intensity of growth/decay.

Thus the list is given by:

m4, m3, m2, m1.

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Eight thousand two hundred and eighty two

Answer:

±3

Step-by-step explanation:

4 - 1 = 3

1 - 4 = -3

Either way you subtract them, the answer is still 3, whether negative or positive.

The equations that could represent the graph shown are:

A. -4x + 2y = -6

C. y = 3x - 2

The equation of a linear graph, in slope-intercept form, can be written as y = mx + b, where:

Given the graph in the diagram, it would have a positive slope and a negative y-intercept.

A. -4x + 2y = -6

Rewrite in slope-intercept form

2y = 4x - 6

y = 4x/2 - 6/2

y = 2x - 3 [positive slope and negative y-intercept]

B. 2x - 3y = -9

Rewrite in slope-intercept form

-3y = -2x - 9

y = 2/3x + 3 [positive slope and positive y-intercept]

C. y = 3x - 2 [positive slope and negative y-intercept]

D. y = -10 is a horizontal line.

Therefore, the equations that could represent the graph shown are:

A. -4x + 2y = -6

C. y = 3x - 2

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Answer:

Step-by-step explanation: