MATHEMATICS HIGH SCHOOL

A candle is 17 in. tall after burning for 3 hours. After 5 hours, it is 15 in. tall. Write a linear equation to model the relationship between heigh h of the candle and time t. Predict how tall the candle will be after 8 hours.

Answers

Answer 1

Answer:

Let

x------> the time in hours

y------> the height in inches

$A(3,17)\nB(5,15)$

Step $1$

Find the slope m of the linear equation between points A and B

we know that

The formula to calculate the slope between two points is equal to

$m=((y2-y1))/((x2-x1))$

substitutes the values

$m=((15-17))/((5-3))$

$m=((-2))/((2))$

$m=-1$

Step $2$

Find the equation of the line

we know that

the equation of the line in the point-slope form is

$y-y1=m*(x-x1)$

we have

$m=-1$

$A(3,17)$

substitute in the equation

$y-17=-1*(x-3)$

$y=-x+20$ --------> this is the linear equation that model the relationship between height h of the candle and time t

Step $3$

Find the height for $x=8$ hours

substitute the value of x in the linear equation

$y=-8+20$

$y=12\ inches$

The height of the candle will be $12\ inches$ after $8\ hours$

Answer 2

Answer: For the linear equation you have two points (3, 17) and (5, 15) so the equation is: h-17=(15-17)/(5-3)*(t-3), solve for h= -t+20.
For predicting, only replace t=8 into you equation (h= -t+20) and you will get h=-8+20=12

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Please use tree diagram to explain.

Answers

q2—_-___-_-__—-__-_-_-___—-__-__—-__-_

A family has three children. The oldest child is 4 years older than themiddle child, and the youngest child is 2 years younger than the
middle child. The sum of the ages of the children is 26.
R
How many years old is the youngest child?
years old
Q

Answers

Answer:6 years

Step-by-step explanation:

Given

A family has 3 children

Suppose the age of middle child is $x$

According to the question, Age of oldest child is $=x+4$

Eldest child age $=x-2$

Sum of the ages of children is $26$

$x+4+x+x-2=26$

$3x+2=26$

$3x=24$

$x=8$

Therefore age of youngest child is $x-2=8-2=6\ years$

There are ten questions on Jack's science quiz: six multiple choice questions with four choices each and four true/false questions. How many ways can he answer the question?

Answers

Questions with multiple choice can be answered: 4^6 = 4096 ways
True/false questions can be answered: 2^4 = 16 ways

The total number of ways to answer all questions = 4096*16 =65,536 ways

If you have 6 pieces of plywoodthat are 4'x8', how many total
1xl pieces can you get out if
you use all of them?

Answers

Answer:192

Step-by-step explanation:

Calculate the area l*w or s*s

Divide the two areas to get the number of 1*1 from 1 plywood then multiply by their number which is 6 here

4*8=32/1=32*6=192

Final answer:

You can get a total of 192 pieces of 1'x1' plywood from six 4'x8' pieces.

Explanation:

To find the total number of 1'x1' pieces that can be cut from the 4'x8' plywood pieces, we need to find the total area of plywood available and then divide it by the area of the desired pieces.

First, calculate the area of one piece of plywood: 4 feet x 8 feet = 32 square feet.

Since there are 6 pieces, the total area of plywood is 6 x 32 square feet = 192 square feet.

Since each 1'x1' piece has an area of 1 square foot, you can get 192 1'x1' piecesout of all the plywood.

Learn more about Area Calculation here:

brainly.com/question/34380164

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Say you have a warranty on your laptop computer. Which of these situations is most likely to be covered by that warranty?a.
The laptop is stolen.
b.
You short out the hard drive by installing a bigger power supply.
c.
The graphics system fails due to faulty wiring.
d.
The screen cracks when you drop the laptop.

Answers

Option c denotes the laptop warranty.

The information regarding warranty is as follows:

The warranty is provided at the time of delivering the goods.
In the laptop, one -year warranty is given. If there is any defective so it can be replaced by the company.
In the given case, the graphic system fails because of the faulty wiring so this represent the warranty.

Therefore we can conclude that Option c denotes the laptop warranty.

Learn more: brainly.com/question/13549064

Answer:

Say you have a warranty on your laptop computer. Which of these situations is most likely to be covered by that warranty?

a. The laptop is stolen.

b. You short out the hard drive by installing a bigger power supply.

c. The graphics system fails due to faulty wiring.

d. The screen cracks when you drop the laptop.

The answer is C

Determine the constant of variation for the direct variation given.R varies directly with S. When S is 16, R is 80.
1/5
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16