How do you solve
9
x
−
4
=
81
?

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

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:

Gradient of parallel line: 6

Gradient of perpendicular line: -1/6

Step-by-step explanation:

The gradient is the value of m in the equation format y = mx + c.

Parallel lines share the same gradient, with just the y-axis intercept (c value) changing.

The gradient of a line perpendicular to a line is found by taking the negative reciprocal of the original line's gradient. A reciprocal is a essentially fraction flipped over. For example 3/2 becomes 2/3. 6 can be expressed as 6/1 (as every whole number can be divided by 1), so the reciprocal of that is 1/6. The negative version of 1/6 is -1/6.

Answer:

Step-by-step explanation:

h(t)=-5t²+10t+80=-5(t²-2t+1-1)+80

=-5(t²+2t+1)+5+80

=-5(t-1)²+85

maximum height reached=85 ft

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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Answer:

the answer is 12 just =12

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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Step-by-step explanation:

the answer is, if it's correct y=4

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

Answer:

x = 5.4

Step-by-step explanation:

6.3 = 2x-4.5  

2x = 6.3 + 4.5 = 10.8  

x= 5.4

Answer:

5.4is the value if x

Step-by-step explanation:

6.3=2x-4.5

6.3+4.5=2x

10.8=2x

10.8/2=x

5.4=x

So,x=5.4

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 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:

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 :)

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:

7.8 miles

Step-by-step explanation:

5.9 + 1.9 = 7.8miles

Step-by-step explanation:

58 multiple 4

..................

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 !

Eight thousand two hundred and eighty two

Answer:

this is hard , I suggest you see a tutor

Answer:

(-2,-2)

Step-by-step explanation:

For a cartesian plane, the solutions to 2 lines is where the 2 lines intercept.

Where this interception point is put into a coordinate (x,y)

Which in this case, the point of intersection is found to be (-2,-2) (Read from the graph)

Answer:

Step-by-step explanation:

sin2x = cosx + l

This can be written as:

2 sinxcosx = cosx + 1

One way would be to draw graphs of sin2x and cosx + 1 and see where they intersect.

Another way is to use y = tan(x/2),  then sinx = 2y/(y^2+1) and cos x

= (-y^2 + 1) / (y^2 + 1) to substitute into the given equation and solve for y.

The algebra will be pretty challenging in this method.

The value of x if U is between T and V is -7/3

The given parameters are:

U is between T and V,

TU = 7x + 35

UV = 4(x + 7)

TU ≅ UV

The above means that

7x + 35 = 4(x + 7)

Open the brackets

7x + 35 = 4x + 28

Evaluate the like terms

3x = -7

Divide both sides by 3

x = -7/3

Hence, the value of x if U is between T and V is -7/3

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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]

Using proportions, it is found that the weekly amounts are given as follows:

We have to determine for Lucretia these following weekly amounts:

The rates are given as follows:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Lucretia's weekly salary is given as follows:

20 x 18.15 = $363.

The withholding allowance is fixed at $33 for a person earning her amount, while the tax rate is of 37%, as she lives in a state with no income tax, hence she only pays the federal tax rate.

The other amounts are given as follows:

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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]

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 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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Answer:

look at the multiple of 3 and seven and find which number in the 7 multiple equal 14 more.

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:

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: