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2 years ago

Find the values of x and y.

Mathematics

1 answer:

vova2212 [387]2 years ago

4 0

Look at the picture.

We have the equation (1) 12x + 4y = 40.

We know, the sum of the acute angles in a right triangle is 90°.

Therefore we have the equation (2) (12x + 4y) + (17x - y) = 90

Substitute (1) to (2):

40 + 17x - y = 90 <em>subtract 40 from both sides</em>

17x - y = 50 (3)

We have the system of equations:

$\left\{\begin{array}{ccc}12x + 4y = 40&|:4\\17x-y=50\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3x + y = 10\\17x-y=50\end{array}\right}\ \text{add both side of equations}\\.\qquad20x=60\qquad|:20\\.\qquad x=3$

Substitute the value of x to (3)

$17(3)-y=50\\51-y=50\qquad|-51\\-y=-1\to y=1$

Answer: x = 3 and y = 1.

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Suppose an identical ladder was put against a building that was 18 feet high and the ladder reached the top of the building. How

nikdorinn [45]

The distance between the bottom of the ladder be from the base of the building will be 17.32 ft.

<h3>What is the Pythagorean theorem?</h3>

It states that in the right-angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.

As we can see in the figure the length of the ladder is 20 ft and the base of the ladder is 10 ft from the base of the building.

By using the Pythagorean theorem we will calculate the distance between the tip of the ladder and the base of the building.

H² = 20² - 10²

H²= 400 - 300

H² = 300

H = √300

H = 17.32 ft.

Therefore the distance between the bottom of the ladder is from the base of the building will be 17.32 ft.

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2 years ago

Christian is placing photos onto scrapbook paper for his photo album. the scrapbook paper is 12 inches long and 12 inches wide.

GenaCL600 [577]

The answer would be 144 inches, found by multiplying the length of the paper by the width.

4 0

3 years ago

Read 2 more answers

The ratio of red cars to blue cars in a parking lot was 5:3 . If there was 40 red cars , how many blue cars were there ?

Bas_tet [7]

The answer is x equals 24
you set up a proportion new over old
so for red cars 40 over 5
since we don’t know the new for blue cars we’ll use x
so x over 3
we then make them equal to each other
40 x
—- = —-
5 3
cross multiply, then we get
120=5x
isolate the x by dividing 5 from both sides to get 24

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3 years ago

For each of the following binomial random variables, specify n and p. (a) A fair die is rolled 50 times. X = number of times a 5

Keith_Richards [23]

Answer:

a) $n = 50, p = \frac{1}{6}$

b) $n = 16, p = \frac{1}{100}$

c) $n = 26, p = 0.25, \mu = 6.5$

Step-by-step explanation:

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 combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $p$ is the probability of X happening.

(a) A fair die is rolled 50 times. X = number of times a 5 is rolled

The die is rolled 50 times, so $n = 50$ .

Each roll can have 6 outcomes. So the probability that 5 is rolled is $p = \frac{1}{6}$

(b) A company puts a game card in each box of cereal and 1/100 of them are winners. You buy sixteen boxes of cereal, and X = number of times you win.

You buy 16 boxes of cereal, so $n = 16$ .