Lyra and Donna are testing the two-way radios they built for their high school science project. Lyra goes to the top of a building that is 22 meters high with one of the radios and stands directly above the building’s entrance. Donna walks out of the entrance, perpendicular to the building, with the other radio. If Donna is more than 50 meters from the entrance, the connection between the radios breaks. What is the range of communication for the two radios to the nearest meter?

Answers

Answer 1

Answer: We use the Pythagorean Theorem: c^2=a^2+b^2. In this case :
c-nearest range between two radios
a=22 m ( height of a building)
b=50 m ( distance from an entrance)
c^2=22^2+50^2˝=484+2500=2984
Finally: c=sqrt(2984) (square root of 2984)=54.626 m
Answer: The range of communication for the two radios is 54.626 meters.

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Courtney reads around 110 words per minute. She procrastinated and now has less than a week to finish her reading assignment. If the book she needs to finish has another 820 pages left and each page has around 350 words, how many hours should she set aside to complete her assignment? Show your work to receive full credit. (10 points)

Answers

First we figure out how many words in total she has to read.
This would be the (number of pages) times (number of words per page).

820 * 350 = 287000
so she has to read 287000 words

we divide this by 110 to get how long it would take for her to finish (in minutes)
287000 / 110 = 2609.09090909....

then since there are 60 minutes in an hour, we divide that number by 60
2609.09090909... / 60 = 43.48484848...

Therefore it would take her about 43.5 hours to complete her assignment.

Answer:

43.5 hours

Step-by-step explanation:

Courtney needs to set aside at least 43.5 hours. We need to figure out many words she needs to read in total.So we need to do 820 * 350287000.We then need to divide by 110 so we can the time in minutes. 2609.09090909....Then we divide the number 60 since the question is asking us for hours. Therefore it would take her about 43.5 hours to complete her assignment

1.a.)In a two-digit number, the units digit is twice the tens digit. If the number is doubled, it will be 12 more than the reversed number. Find the number.
b.)Eight times the sum of the digits of a certain two-digit number exceeds this number by 19. The tens digit is two less than the units digit. Find the number.
c.)In a two-digit number, the units digit is twice the tens digit. If the number is doubled, it will be 9 more than the number reversed. Find the number.
ALL DUE IN 7 MIN! HELP NOW OR NEVER

Answers

x: the unit digit
y: the tens digit

The unit digit is twice the tens digit so:
x=2y

The two digit number:
10y+x

The two digit number doubled:
2(10y+x)

The reversed number:
10x+y

So:
2(10y+x)=10x+y+12

substitute x for 2y

2(10y+2y)=10(2y)+y+12

24y=21y + 12

3y=12
y=4

x=2y=2*4=8

So the number is 48.

xy is the number

a.
unit digit is y
tens is x
units is twice tens digit
y=2x
if it is doubled, it will be 12 more than reversed
20x+2y=12+10y+x
20x+4x=12+20x+x
3x=12
x=4
y=2x
y=2(4)
y=8
48 is the number

b. 8 times sum of digis is bigger than that number by 19
8(x+y)=19+10x+y
x=y-2

8(y-2+y)=19+10(y-2)+y
16y-16=19+10-20+y
y=3
x=y-2
x=3-2
x=1
the number is 13

c.
y=2x
2(10x+y)=9+10y+x
2(10x+2x)=9+20x+x
x=3
y=2x
y=3(3)
y=6

the number is 36

a. 48
b. 13
c. 36

Scores on an AP Exam at a local high school are recorded in the table. What was the average score? A) 0.234 B) 3 C) 3.5 D) 4.266

Answers

we need the scores in order to find the answer

Slope for -8,18 and -14,-3

Answers

$(\stackrel{x_1}{-8}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{-14}~,~\stackrel{y_2}{-3}) \n\n\n \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-3}-\stackrel{y1}{18}}}{\underset{\textit{\large run}} {\underset{x_2}{-14}-\underset{x_1}{(-8)}}} \implies \cfrac{ -21 }{-14 +8} \implies \cfrac{ -21 }{ -6 } \implies \cfrac{7}{2}$

The length and a quarter of the width of a rectangle add up to 7 in, while the length and the width add up to 10 in. What are the rectangle's length and width?