If the perimeter of a right triangle is 42 units and the length of the hypotenuse is 20 units, find the length of the other two sides of the triangle.Can you please show work

Answers

Answer 1

Answer: so
a^2+b^2=c^2
c=hypotenuse
a^2+b^2=20^2=400

if the permiter is 42 then
p=hypotonuse+side+side
42=20+side+side
subtract 20 from both sides
22=side+side

a+b=22
subtract b from both sides
a=22-b
subsitute for a in equation below
a+2+b^2=c^2
(22-b)^2+b^2=400
b^2-44x+484+b^2=400
2b^2-44x+484=400
divide both sides by 2
b^2-22x+242=200
subtract 200 from both sides
b^2-22x+42=0
factor
(b+/-number)(b+/-number)
to find the numbers, find which 2 number multiply to 42 and add to get -22
the numbers must be neative since same signs multiplied=positive and negative+negative=negative
(b-number)(b-number)
facrors of 42=2,3,6,7,14,21
2,21
3,14
6,7
it's hard to find the number, but the numbers are -19.8882 and -2.11181
(b-19.8882)(b-2.11181)=0
if xy=0 then assume that x and y=0

b-19.8882=0
add 19.8882 to both sides
b=19.8882

b-2.11181=0
add 2.11181 to both sides
b=2.11181

the side legnths are 19.8882 units and 2.11181 units

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Katie spent $465 on DVDs and CDs. The CDs cost $15 each, and the DVDs cost $19 each. A total of 27 CDs and DVDs were purchased. How many of each did she buy?(solve by substitution or elimination methods only)

Answers

Answer:

12 CDs and 15 DVDs

Step-by-step explanation:

Let

x----> the number of CDs

y---> the number of DVDs

we know that

x+y=27 -----> x=27-y ----> equation A

15x+19y=465 ----> equation B

Solve by substitution

substitute equation A in equation B and solve for y

15(27-y)+19y=465

405-15y+19y=465

4y=465-405

4y=60

y=15 DVDs

Find the value of x

x=27-y

x=27-15=12 CDs

You are reducing a map of 24 in. by 36 in. to fit onto a piece of paper 8 in. by 10 in. What are the dimensions of the largest possible map that can fit on the page?

Answers

The largest possible map that can fit on the page is 8 in. by 12 in.

What is Ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

We can begin by finding the scale factor by which the map needs to be reduced.

Since the map dimensions are 24 in. by 36 in., and we want to fit it onto a page that is 8 in. by 10 in.

We need to reduce each dimension by the same factor.

Let x be the scale factor:

24/x = 8

36/x = 10

Solving for x, we get:

x = 24/8 = 3

Therefore, we need to reduce the map by a scale factor of 3.

To find the dimensions of the largest possible map that can fit on the page, we divide the original map dimensions by 3:

24/3 = 8

36/3 = 12

Hence, the largest possible map that can fit on the page is 8 in. by 12 in.

To learn more on Ratios click:

brainly.com/question/1504221

#SPJ2

Since 10 in will be the longer side, to find the shorter did
x/10 = 24/36
x/10 = 2/3
x = 10•(2/3)
x = 6 2/3
So the dimensions are
6 2/3 in by 10 in

If a line moves downward from left to right, it has a

Answers

Answer and Step-by-step explanation:

The answer is that the line has a negative slope.

In an equation, the the slope (m) would be a negative number, looking like this:

y = -mx + b

#teamtrees #PAW (Plant And Water)

Answer:

Negative slope

Step-by-step explanation:

You test 8 automobiles of the same make and model and find their mileage ratings to be 27, 27, 28, 29, 32, 33, 34, and 1,000,000 mpg, arranged in order from smallest to largest. If you use inferential statistics (and reject the outlier) to predict what mileage consumers can expect when they buy this type of car, what value would you predict?

Answers

Answer:

it 30 mpg

Step-by-step explanation:

The statement " y varies directly as x ," means that when x increases,y increases by the same factor. In other words, y and x always have the same ratio:

= k

where k is the constant of variation.
We can also express the relationship between x and y as:

y = kx

where k is the constant of variation.

Since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate. For example, if y varies directly as x , and y = 6 when x = 2 , the constant of variation is k = = 3 . Thus, the equation describing this direct variation is y = 3x .

Example 1: If y varies directly as x , and x = 12 when y = 9 , what is the equation that describes this direct variation?

k = =
y = x

Example 2: If y varies directly as x , and the constant of variation is k = , what is y when x = 9 ?

y = x = (9) = 15

As previously stated, k is constant for every point; i.e., the ratio between the y -coordinate of a point and the x -coordinate of a point is constant. Thus, given any two points (x 1, y 1) and (x 2, y 2) that satisfy the equation, = k and = k . Consequently, = for any two points that satisfy the equation.

Example 3: If y varies directly as x , and y = 15 when x = 10 , then what is y when x = 6 ?

=
=
6() = y
y = 9

The time , in hours , it takes to repair an electrical breakdown in a certain factory is represent by a random variable x where repair time follow a normal distribution with mean 5 hour and standard deviation 1 hour , if 5 electrical breakdown ore randomly chosen , Find the probability that ( a all repaired time below 6 hours ( b ) exactly 3 of them repaired below 6 hours

Answers

Answer:

a) 0.4215 = 42.15% probability that all are repaired in less than 6 hours.

b) 0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours

Step-by-step explanation:

To solve this question, we need to understand the normal and the binomial probability distributions.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

In which $C_(n,x)$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_(n,x) = (n!)/(x!(n-x)!)$

And p is the probability of X happening.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Proportion repaired below 6 hours:

Mean 5 hours and standard deviation 1 hour, which means that $\mu = 5, \sigma = 1$