I need help please solve for x and y rectangles

A new auditorium is begging built for a college the balcony has 200 seats the floor has 25 rows with x seats in each row the num

aliya0001 [1]

Question:

A new auditorium is being built for a college. The balcony has 200 seats. The floor has 25 rows with x seats in each row. The number of people in the auditorium must be under 750 to meet safety regulations. What is the solution of this inequality, and what is its meaning?

Answer:

$200 + 25x < 750$

Number of seats in a row must be less than 22

Step-by-step explanation:

Given

Total = Less than 750

Current Seats = 200

Rows = 25

Seat per row = x

Required

Represent as an inequality

The scenario will be represented as:

$Current\ Seats + Rows * x = Total$

Substitute 200 for Current Seats

$200 + Rows * x = Total$

Substitute 25 for Rows

$200 + 25* x = Total$

$200 + 25x = Total$

Substitute <750 for Total.

The equation then becomes

$200 + 25x < 750$

Solving further:

$25x < 750 - 200$

$25x < 550$

$x < \frac{550}{25}$

$x < 22$

This means that:

Number of seats in a row must be less than 22

3 0

3 years ago

(b) A color printer prints 26 pages in 10 minutes.

sdas [7]

Answer:

Equals to 0.384 seconds (round if needed)

Step-by-step explanation:

10 / 26 = 0.384615385

5 0

3 years ago

Before we can make the mashed potatoes, we need to boil some water. The water starts out at room temperature, 70° F, and increas

Karolina [17]

Answer:

Part a) $y=50t+70$

Part b) $t=2.84\ min$

Step-by-step explanation:

Part a) Create a linear equation

Let

t ----> the time in minutes

y ---> the temperature in °F

we know that

The linear equation in slope intercept form is equal to

$y=mt+b$

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value of the linear equation

In this problem we have

The slope m is equal to

$m=50\° F\ per\ minute$

The y-intercept is

$b=70\° F$

substitute

$y=50t+70$

Part b) How many minutes until the water boils at 212° F?

For y=212° F

substitute in the linear equation and solve for t

$212=50t+70$

$50t=212-70$

$50t=142$

$t=2.84\ min$

6 0

3 years ago

Convert the line integral to an ordinary integral with respect to the parameter and evaluate it. modifyingbelow integral from no

vovangra [49]

Parameterize $C$ by

$\vec r(t)=(1-t)(0,0,0)+t(1,3,6)=(t,3t,6t)$

with $0\le t\le1$ . Then the line integral is

$\displaystyle\int_Cxyz\,\mathrm dS=\int_0^1x(t)y(t)z(t)\left\|\frac{\mathrm d\vec r}{\mathrm dt}\right\|\,\mathrm dt$

$=\displaystyle18\sqrt{91}\int_0^1t^3\,\mathrm dt=\boxed{\frac{9\sqrt{91}}2}$

8 0

4 years ago

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7D%20k%20-%20%28k%20%2B%20%20%5Cfrac%7B1%7D%7B4%7D%29%20%3D%20%20%5Cfrac

VikaD [51]

Firstly, foil -(k + 1/4) (think of the minus sign as -1):

$\frac{2}{3}k-k-\frac{1}{4}=\frac{1}{12}k+\frac{4}{12}$

Next, combine like terms:

$-\frac{1}{3}k-\frac{1}{4}=\frac{1}{12}k+\frac{4}{12}$

Next, we have to add 1/3k on both sides, but first we have to find the LCD, or lowest common denominator, of 3 and 12. To do this, list the multiples of both and the lowest one they share is their LCD. In this case, the LCD is 12. Multiply both sides of -1/3 by 4/4 and 1/12 by 1/1:

$-\frac{1}{3}\times \frac{4}{4}=-\frac{4}{12}\\\\\frac{1}{12}\times \frac{1}{1}=\frac{1}{12}\\\\-\frac{4}{12}k-\frac{1}{4}=\frac{1}{12}k+\frac{4}{12}$

Now add 4/12k on both sides of the equation:

$-\frac{1}{4}=\frac{5}{12}k+\frac{4}{12}$

Next, to subtract 4/12 on both sides we need to find the LCD of 4 and 12. It's the similar process as we did with 12 and 3. This time the LCD is also 12. Multiply both sides of -1/4 by 3/3 and 4/12 by 1/1:

$-\frac{1}{4}\times \frac{3}{3}=-\frac{3}{12}\\\\\frac{4}{12}\times \frac{1}{1}=\frac{4}{12}\\\\-\frac{3}{12}=\frac{5}{12}k+\frac{4}{12}$

Now subtract 4/12 on both sides:

$-\frac{7}{12}=\frac{5}{12}k$

Lastly, multiply both sides by 12/5, and your answer will be:

$-\frac{84}{60}=-\frac{7}{5}=k$

3 0

3 years ago