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jolli1 [7]
3 years ago
7

(99 POINTS) Using similarity solve for x. Show all work

Mathematics
2 answers:
ki77a [65]3 years ago
4 0

General Idea:

In any right triangle,

1. The altitude to the hypotenuse is the geometric mean between the segments into which is separates the hypotenuse.

2. Each leg is a geometric mean of the hypotenuse and the segment of the hypotenuse adjacent of the leg.

Applying the concept:

Step 1: We need to label the given diagram and set up a proportion by comparing the similar triangles as provided in attached figure.

Setting up the proportion, we get...

\frac{Shorter \; Leg}{Hypotenuse}=\frac{AB}{AC}=\frac{AD}{AB}\\\\\frac{x}{9+16}=\frac{9}{x}\\Cross \; Multiplying \; we \; get...\\\\x^2=9(9+16)\\x^2=9(25)\\x^2=225\\Take \; square \; root \; on \; both \; sides\\\\\sqrt{x^2}=\sqrt{225}\\x=15

Conclusion:

x=15 \; cm


viva [34]3 years ago
3 0

Shorter Length/Hypotenuse = ab/ac = ad/ab

x/9+16 = 9/x

x^2 = 9 x (9 + 16)

= 9 x 25

= 225

square root of 225 = 15

x = 15

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Sally has decided to spend some time over two days soving math problems. She figures that on the first day she wil be able to so
erastova [34]

A system of equations for this would be

19x + 11y = 273

and

12x + 17y = 283.

X is the amount of minutes to solve one long division problem and y is the amount of minutes to solve a graphing problem.

How To Solve This System of Equations.

Multiply both by 17 and 11 respectively for them to have the greatest common factor for y. So now both equations are:

323x + 187y= 4641

132x + 187y= 3113.

Subtract both equations and you have left:

191x = 1528.

Divide both sides by 191 and you find x.

X = 8.

Answer

It takes Sally 8 minutes to do one Long Division Problem.


Hope this helped. ;)

6 0
3 years ago
Read 2 more answers
Divide £72 into the ratio 4 : 5.
algol13

Answer:

£32 : £40

Step-by-step explanation:

sum the parts of the ratio, 4 + 5 = 9 parts

Divide the amount by 9 to find the value of one part of the ratio

£72 ÷ 9 = £8 ← value of 1 part of the ratio, then

4 parts = 4 × £8 = £32

5 parts = 5 × £8 = £40

Then

£72 in the ratio 4 : 5 is £32 : £40

4 0
2 years ago
Exponential form of 16807
mylen [45]
<span>It is: 7 to the power of 5 = 16807</span>
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3 years ago
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An elevator has a maximum weight of 300 pounds. Each pallet of boxes weighs 25 pounds. Which of the following number lines best
iren2701 [21]

Answer: C.

Step-by-step explanation:

1. Go

2.Stop

3. Win

Sorry if you didn't understand, we do math here differently in Albania ^^

yes

4 0
2 years ago
An automobile manufacturer finds that 1 in every 2500 automobiles produced has a particular manufacturing defect. ​(a) Use a bin
Advocard [28]

Answer:

a) 0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

b) 0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

Step-by-step explanation:

Binomial 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} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given interval.

To use the Poisson approximation for the binomial, we have that:

\mu = np

1 in every 2500 automobiles produced has a particular manufacturing defect.

This means that p = \frac{1}{2500} = 0.0004

a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 7000 cars.

This is P(X = 4) when n = 7000. So

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

P(X = 4) = C_{7000,4}.(0.0004)^{4}.(0.9996)^{6996} = 0.1558

0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p.

Using the approximation:

\mu = np = 7000*0.0004 = 2.8. So

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 4) = \frac{e^{-2.8}*(2.8)^{4}}{(4)!} = 0.1557

0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

6 0
3 years ago
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