The history museum charges a $30 fee plus $12 per student for a field trip.
The aquarium charges a $40 fee plus $10 per student. The lines in the graph
represent the cost of each field trip.
For what number of students will the total cost of each field trip be the same,
and what will that cost be?
Field Trip Costs
y = 40 + 10x
Cost ($)
120
140
100
90
80
70
60
50
40
30
20
10
y = 30 + 12x
1 2 3 4 5 6 7 8 9 10 11 12
Number of students

Answer:

y = -[tex]\frac{5}{3}[/tex]x - -[tex]\frac{23}{3}[/tex]

Step-by-step explanation:

First, let's divide both sides by 5 to get the first equation into the form y = mx + b. We get y = [tex]\frac{3}{5}[/tex]x + 5. The m value, [tex]\frac{3}{5}[/tex], is the slope and the b value, 5, is the y-intercept of this line.

When a line is perpendicular to another line, the slopes must multiply to get -1. In other words, the slopes must be a negative reciprocal of each other. Since the slope of the original line is [tex]\frac{3}{5}[/tex], we know that the slope of the line perpendicular to that is -[tex]\frac{5}{3}[/tex].

Then, since we know x, y, and m of the second equation, we can substitute those three values into the equation, y = mx + b, to find the y-intercept (b).

-1 = (-[tex]\frac{5}{3}[/tex])(-4) + b

-1 = [tex]\frac{20}{3}[/tex] + b

b = -[tex]\frac{23}{3}[/tex]

After plugging in the values of m and b we calculated, we get the equation for the line perpendicular to the original line: y = -[tex]\frac{5}{3}[/tex]x -[tex]\frac{23}{3}[/tex].

The ratio 2 gallons to 27 quarts as a fraction in its simplest form is 4/27

The given ratio is:

2 gallons to 27 quarts

This can also be written as:

2 gallons  :  27 quarts

Convert 27 quarts to gallons so that both items in the ratio can be of equal unit

Note that:

1 quart  =  0.25 gallons

27 quarts = 0.25 x 27

27 quarts = 6.75 gallons

The ratio can therefore be re-written as:

2 gallons :  6.75 gallons

In fraction form:

2 gallons  :  27 quarts = 2/6.75

Multiply the numerator and denominator by 4

2 gallons  :  27 quarts  =  4/27

The ratio 2 gallons to 27 quarts as a fraction in its simplest form is 4/27

Learn more here: https://brainly.com/question/25843849

Answer:

7^-25

Step-by-step explanation:

7^1/5^5

7^5^-1*5

7^5^-5

7^5*-5

7^-25

Answer:

7

Step-by-step explanation:

[tex](7^{\frac{1}{5}})^{5}[/tex]

[tex]7^{\frac{1}{5}*{5}[/tex]  -- simply, (5 cancels)

7¹

7

Answer:

x/3 ≤ 5

I'm not sure if this is what you were looking for. If not, please be more specific in your questions!

Answer:

  AC = 55°

Step-by-step explanation:

In this geometry, arcs AC and BD have the same measure. The sum of the parts of arc CD will total the measure of CD.

  AC + AB + BD = CD

  2AC +80 = 170

  AC = 110/2 = 55

The measure of arc AC is 55°.

Answer:

AC = 55°

Step-by-step explanation:

because the measure is part of CD. Hope this helps!

Answer:

7 ^2 ⋅ 7 ^4 = 49^6

Step-by-step explanation:

7² / 7 ⁻⁴

= 7²⁻⁽⁻⁴⁾

= 7 ⁽²⁺⁴⁾

= 7⁶

= 117649

Remember :-

xᵃ / xᵇ = xᵃ⁻ᵇ

___

Hope it helps ⚜

⁽

Answer:

252 blue sweets

Step-by-step explanation:

red : blue

3 : 7 ( x4 )

12 : 28

blue : green

4 : 5 ( x7 )

28 : 35

red : blue : green

12 : 28 : 35

12 + 28 + 35 = 75

Blue Sweets:

675 x 28/75 = 252

Step-by-step explanation:

h(x) = 4x - 1

given,

h(x) = -9

now,

h(-9) = 4(-9) - 1

→ -36 - 1

→ -37

hope this answer helps you dear, take care!

Answer:

x = - 2

Step-by-step explanation:

Given h(x) = 4x - 1 and h(x) = - 9, then equating right sides gives

4x - 1 = - 9 ( add 1 to both sides )

4x = - 8 ( divide both sides by 4 )

x = - 2

Answer:

1. Answer Is 33

2. Answer Is 25

3. Answer Is 33

Answer:

38%

Step-by-step explanation:

Answer:

the answer is 38%

Step-by-step explanation:

multiply 19 by 2 because 50 is half of 100

Answer:

-13

Step-by-step explanation:

negative 13 = -13

Answer:

32

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

1/125

Step-by-step explanation:

Simply subtract the exponents

in this case 6 - 3 so then its now 5 / 5^3

now just make the numerator a 1

1 / 5^3

5x5x5 = 125

1/125

Answer:

0.008

Step-by-step explanation:

i did 5 to the 3rd power which is 125

Then i did 5 to the 6 power and got 15625

finally I divided the answers and got  0.008   or in 125

3/ 8

of a cup.

Explanation:

You want half of the recipe, so you want half of

3/4

of a cup.

Of means multiplication when it comes to fractions, so multiply

3/4  by 1/2 to get 3/4 ⋅ 1/2 = 3/8

Answer:

-12

Step-by-step explanation:

1-2x+3y

1-2(-2)+ 3(-5)

1-4-9

= -12

Answer:

follow me on the gram (andrewa223) also the answer is a

Step-by-step explanation:

Let

ATQ

[tex]\\ \sf{:}\longrightarrow Area=1800[/tex]

[tex]\\ \sf{:}\longrightarrow Length(Breadth)=1800[/tex]

[tex]\\ \sf{:}\longrightarrow 5x(4x)=1800[/tex]

[tex]\\ \sf{:}\longrightarrow 20x^2=1800[/tex]

[tex]\\ \sf{:}\longrightarrow x^2=900[/tex]

[tex]\\ \sf{:}\longrightarrow x=30[/tex]

[tex]\\ \sf{:}\longrightarrow Perimeter=2(L+B)[/tex]

[tex]\\ \sf{:}\longrightarrow Perimeter=2(150+120)[/tex]

[tex]\\ \sf{:}\longrightarrow Perimeter=2(270)[/tex]

[tex]\\ \sf{:}\longrightarrow Perimeter=540m[/tex]

Answer:

About 29%

Step-by-step explanation:

Answer:

0% chance

Step-by-step explanation:

there are no green marbles

Marbles no

There is no green marbles

So it will never occur(impossible event)

Answer:

5

Step-by-step explanation:

plug in the numbers (-15x9/5)+35 PEMDAS.

Answer: He needs to splash the threes

Step-by-step explanation: He dosent have the vertical so he just needs to have a splashy 3 pointer

Answer:

Obtuse Angles are

1, 3, 5, 7, 9, 11

Acute angles are

2, 4, 6, 8, 10, 12

Step-by-step explanation:

Answer:

A - Exponential

Step-by-step explanation:

Exponential is the best fitting model because there's a $500 raise in salary each year, so $500 is added to the salary of the previous year.

Answer: -2

Step-by-step explanation:

9e-7=7e-11

-7e         -7e

2e-7=-11

   +7  +7

2e=-4

/2   /2

e=-2

Answer: Rogun dam is 335m tall and Nurek dam is 300m tall

Step-by-step explanation:

I will use [tex]r[/tex] to represent the height of the Rogun dam and [tex]n[/tex] to represent the height of the Nurek dam.

The system of equations is as follows:

[tex]r+n=635[/tex]

[tex]r-n=35[/tex]

From the second equation, we can rearange it to be:

[tex]r=35+n[/tex]

Then take this new value of [tex]r[/tex] and plug it into our first equation to find [tex]n[/tex]

[tex](35+n)+n=635[/tex]

[tex]35+2n=635[/tex]

[tex]2n=600[/tex]

[tex]n=300[/tex]

This means that the Nurek dam is 300m tall, and the Rogun dam is 335m tall, found by pluggin the value into our first equation:

[tex]r+300=635[/tex]

[tex]r=335[/tex]

Answer:

6

Step-by-step explanation:

XY = 3x – 1, YZ = 5, and XZ = 5x – 8,

We know that XY + YZ = XZ, so

3x - 1 + 5 = 5x - 8

3x + 4 = 5x - 8

3x + 12 = 5x

12 = 2x

6 = x

The value of x from the given line segment XZ is 6. Therefore, the correct answer is option A.

Given that, X, Y, and Z are collinear and Y is between X and Z.

Collinear points are those that are on the same straight line or in the same plane. In Euclidean geometry, two or more points on a line that are close to or far from each other are said to be collinear.

So, here [tex]XZ=XY+YZ[/tex]

[tex]5x-8=3x-1+5[/tex]

[tex]5x-8=3x+4[/tex]

[tex]5x-3x=4+8[/tex]

[tex]2x=12[/tex]

[tex]x=6[/tex]

Therefore, the correct answer is option A.

To learn more about an collinear points visit;

https://brainly.com/question/5191807.

#SPJ3

Answer:

Step-by-step explanation:

a. addition

b. division

c. given