The state fair is a popular field trip destination. This year the senior class at High School A and the
senior class at High School B both planned trips there. The senior class at High School A rented and
filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54
students. Every van had the same number of students in it as did the buses. Find the number of students
in each van and in each bus.

Answer:

[tex]2(4 + 7) = 22[/tex]

[tex]3(\frac{1}{3} - p) = 1 - 3 p[/tex]

Step-by-step explanation:

Given

1 & 2

Required

Rewrite and simplify

[tex]1.\ 2(4 + 7)[/tex]

Apply distributive property

[tex]2(4 + 7) = 2 * 4 + 2 * 7[/tex]

[tex]2(4 + 7) = 8 + 14[/tex]

[tex]2(4 + 7) = 22[/tex]

[tex]2.\ 3(\frac{1}{3} - p)[/tex]

Apply distributive property

[tex]3(\frac{1}{3} - p) = 3*\frac{1}{3} - 3 * p[/tex]

[tex]3(\frac{1}{3} - p) = \frac{3}{3} - 3 * p[/tex]

[tex]3(\frac{1}{3} - p) = 1 - 3 * p[/tex]

[tex]3(\frac{1}{3} - p) = 1 - 3 p[/tex]

Answer:

Volume of the prism =  280 ft^3

Step-by-step explanation:

Recall that the volume of a prism is given by the  following formula:

Volume = B * H

where B is the area of the base (in our case a right angle triangle), and H is the prism's height (in our case 16 ft)

Then we estimate the area of the triangle at the base as base* height/2 :

Area triangle = 5 * 7 / 2 = 35/2 ft^2

and multiply by the prism's height to get its volume:

Volume = 35/2 * 16 = 280 ft^3

Answer:

y = ⅓x - 3

Step-by-step explanation:

First, find the slope using two points on the line, say (0, -3) and (6, 0):

[tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-3)}{6 - 0} = \frac{3}{6} = \frac{1}{3} [/tex]

Slope (m) = ⅓

Find the y-intercept (b):

The line intercepts the y-axis at y = -3. So b = -3

Next, substitute m = ⅓ and b = -3 into y = mx + b (slope-intercept form):

y = ⅓(x) + (-3)

y = ⅓x - 3

by the Angle sum property of triangle,

55+75+(-6+7x) = 180

=> 130 +(-6+7x) = 180

=> (-6+7x) = 180-130

=> (-6+7x) = 50

=> 7x = 50+6

=> 7x = 56

=> x= 56/7

=> x = 8

Answer:

80 gallons and a leaking problem.

Step-by-step explanation:

please mark brainliest, give a thanks, and rate a five stars if this helped! feel free to ask anymore questions if you need any more help! thanks!

(lol optional): add my sc: tealyn337

Answer:

Using the point (-2,-4) it would be:

y + 4 = 1/3(x + 2)

Using the point (4,-2) it would be:

y + 2 = 1/2 (x - 4)

Step-by-step explanation:

hope this helps :)

Answer:

A

Step-by-step explanation:

It is letter A I got 100!

Answer:

A

Step-by-step explanation:

EDGE 2021

Answer:

x = 15 cm

Step-by-step explanation:

Triangle area:

[tex] area = \frac{(20)(15)}{2} = \frac{300}{2} = 150 \: cm[/tex]

Then rectangle area:

[tex]area = (10)(x) \\ 150 = 10x \\ x = \frac{150}{10} \\ x = 15 \: cm[/tex]

Answer:

208

Step-by-step explanation:

this is what I did. 348×.6

60% of 580 is 348 is the answer you're looking for

If you divide .6 by 348 you get 580.

To check your answer, you can do .4 (40%) multiplied by 580 to get 232

232+348=250 which is 100%

Answer:

2

Step-by-step explanation:

the answer is K it's parallel

Step-by-step explanation:

the answer is A

Answer:

A

Step-by-step explanation:

We are given a right triangle with a base of x feet and a height of h feet, where x is constant and h changes with respect to time t.

The angle in radians is defined by:

[tex]\displaystyle \tan(\theta)=\frac{h}{x}[/tex]

And we want to find the relationship that describes dθ/dt and dh/dt.

So, we will differentiate both sides with respect to t where x is a constant:

[tex]\displaystyle \frac{d}{dt}[\tan(\theta)]=\frac{d}{dt}\Big[\frac{h}{x}\Big][/tex]

Differentiate. Apply the chain rule on the left. Again, remember that x is just a constant, so we can move it outside the derivative operator. Therefore:

[tex]\displaystyle \sec^2(\theta)\frac{d\theta}{dt}=\frac{1}{x}\frac{dh}{dt}[/tex]

Since we know that tan(θ)=h/x, h is the opposite side of our triangle and x is the adjacent. Therefore, by the Pythagorean Theorem, our hypotenuse will be:

[tex]\text{Hypotenuse}=\sqrt{h^2+x^2}[/tex]

Since secant is the ratio of the hypotenuse to adjacent:

[tex]\displaystyle \sec(\theta)=\frac{\sqrt{h^2+x^2}}{x}[/tex]

So:

[tex]\displaystyle \sec^2(\theta)=\frac{x^2+h^2}{x^2}[/tex]

By substitution, we have:

[tex]\displaystyle \Big(\frac{x^2+h^2}{x^2}\Big)\frac{d\theta}{dt}=\frac{1}{x}\frac{dh}{dt}[/tex]

By multiplying both sides by the reciprocal of the term on the left:

[tex]\displaystyle \frac{d\theta}{dt}=\frac{1}{x}\Big(\frac{x^2}{x^2+h^2}\Big)\frac{dh}{dt}[/tex]

Therefore:

[tex]\displaystyle \frac{d\theta}{dt}=\frac{x}{x^2+h^2}\frac{dh}{dt}[/tex]

Our answer is A.

This is not the correct answer.

1. 2.30 is not even close to the point given in the number line.

2. My guess for the correct answer would be 0.23 because in between 0.2 and 0.3 is 0.25, so the best answer would be 0.23.

Answer:

x

Step-by-step explanation:

The definition of a variable is an unknown quantity, usually represented by a letter.

The variable in the algebraic expression 5x + 13 will be 'x'.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

⇒ 5x + 13

Now,

Since, The algebraic expression is,

⇒ 5x + 13

Hence, The variable of the algebraic expression = x

Therefore, The variable in the algebraic expression 5x + 13 = x

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

Answer

always

Step-by-step explanation:

Answer:

if you mean the power of these letters then the answer is

x^2,y^2 and z

as they are common in both lists

Answer:

(29x + 9)

Step-by-step explanation:

Perimeter of a polygon = Sum of measures of all sides of the polygon

Therefore, Perimeter of the given polygon = (9 + 12x + 2x + 2x + 12x + x)

                                                                       = (9 + 29x)

Expression (29x + 9) will represent the perimeter of the polygon.

Answer: 8x^2 - 10x - 3

Step-by-step explanation:

first, we multiply the parentheses.

2x x 4x + 2x - 3 x 4x - 3

then, we calculate all of that junk.

8x^2 + 2x - 12x - 3

finally, we collect the like terms.

8x^2 - 10x - 3

Answer:

8x^2-10x3

Step-by-step explanation:

8x^(add the 2 upbove the x)-10x-3

Answer:

c=64.2

Step-by-step explanation:

Answer:

hope this hlp u

Step-by-step explanation:

the last one shows the radius

Answer:

figure 4 shows the radius

Answer:

-12

Step-by-step explanation:

-8ab = ?

Plug in the values for a and b.

-8(1/4)(6)

Multiply.

-2(6)

= -12