An angle measures 120°less than the measure if its supplementary angle. What is the measure of each angle

Find the value of the variable and GH if H is between G and I. GI = 5b + 2, HI = 4b – 5, HI = 3

Katen [24]

Answer:

b = 2, GH = 9

Step-by-step explanation:

The last two equations tell you ...

HI = 3 = 4b -5

8 = 4b . . . . . . . . . add 5

2 = b . . . . . . . . . . divide by 4

Then ...

GI = 5·2 +2 = 12

So ...

GI/HI = 12/3 = 4 = G/H . . . . use the found value for GI and the given HI

G = 4H . . . . . . . multiply by H

GH = 4H² . . . . . multiply by H again

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At this point, it can be useful to try the offered solutions to see what works.

GH = 4H² = 9

H = ±√(9/4) = ±3/2

G = 4H = ±6

Then ...

I = 3/H = 3/(±3/2) = ±2 . . . . matching the sign of H

We want values of G and H such that H is between G and I.

positive H: (G, H, I) = (6, 3/2, 2/3) . . . . yes, H is between G and I

negative H: (G, H, I) = (-6, -3/2, -2/3) . . yes, H is between G and I

The solution b=2, GH=9 satisfies problem requirements.

__

GH = 4H² = 12

H = ±√(12/4) = ±√3

G = 4H = ±4√3

I = 3/H = 3/±√3 = ±√3 . . . . sign matches H

Then (G, H, I) = (4√3, √3, √3) . . . . . H = I; is not "between" G and I

or (G, H, I) = (-4√3, -√3, -√3) . . . . . . H = I; is not "between" G and I

The solution b=2, GH=12 will only satisfy the problem requirements if you interpret "between G and I" to allow that H = I.

6 0

3 years ago

If you have apples 14 banana And 20 potatoes, Find The:

sattari [20]

Step-by-step explanation:

Firs prime factorisation then we will find their GCF and it is 2

7 0

2 years ago

Read 2 more answers

James uses 1 1/2 cups of milk and 2 1/4 cups of flour for his favorite cookie recipe. This makes 60 cookies. How much milk and f

Scrat [10]

Answer:

to get you answer you would have to add 1 1/2 and 2 1/4, then your equation would be 60 ÷ 3 3/4 , then whatever your total is, multiply that by 40 and that would be your answer

8 0

2 years ago

Need help with this math problem

zheka24 [161]

Answer:

m<1 = 51

m<2 = 61

m<3 = 29

Step-by-step explanation:

three angles of a triangle = 180

so knowing that add 68 + 61 to get 129

now subtract cause the last angle will = 180-129 = 51

for angle two is 61 cause their congruent

now we have one angle = 90 and another 61

add them 90+61= 151

now subtract 180-151 = 29

6 0

2 years ago

You take a quiz with 6 multiple choice questions. After you studied your estimated that you would have about an 80 % chance of g

Arada [10]

Answer:

1.15%

Step-by-step explanation:

To get the probability of m independent events you multiply the individual probability of each event. In this case we have m independent events, each one with the same probability, therefore:

$p^{m}$

$0.8^{20} = 1.15\%$

This is a particlar scenario of binomial distribution problem. So the binomial distribution questions are about the number of success of m independent events, where every individual event has the same p probability. In the question we have 20 events and each event has a probability of 80%. The binomial distribution formula is:

$\binom{n}{k} * p^{k} * (1-p)^{n-k}$

n is the number of events

k is the number of success

p is the probability of each individual event

$\binom{n}{k}$ is the binomial coefficient

the binomial coefficient allows to find the subsets of k elements in a set of n elements. In this case there is only one subset possible since the only way to get 20 of 20 correct questions is to getting right all questions (for getting 19 of 20 questions there are many ways, for example getting the first question wrong and all the other questions right, or getting second questions wrong and all the other questions right, etc).

$\binom{n}{k} = \frac{n!}{k!(n-k)!}$

therefore, for this questions we have:

$\frac{20!}{20!(20-20)!} * 0.8^{20} * (1-0.8)^{0} = 1.15\%$

4 0

2 years ago