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ElenaW [278]
2 years ago
10

In triangles GHI and RST, ∠G ≅ ∠R, ∠H ≅ ∠S, and segment GI ≅ segment RT. Is this information sufficient to prove triangles GHI a

nd RST congruent through SSS? Explain your answer.
Mathematics
1 answer:
Nat2105 [25]2 years ago
7 0

The information given is not enough to prove that ΔGH ≅ ΔRST through the SSS congruence theorem.

<h3>What is the Side-side-side Congruence Theorem (SSS)?</h3>

The side-side-side congruence theorem (SSS) states that if two triangles have three pairs of corresponding sides that are congruent to each other, then both triangles are similar to each other.

We are only given that both triangles have:

  • 2 pairs of corresponding congruent angles -  ∠G ≅ ∠R and ∠H ≅ ∠S.
  • 1 pair of corresponding congruent sides - GI ≅ segment RT

Therefore, the information given is not enough to prove that ΔGH ≅ ΔRST through the SSS congruence theorem.

Learn more about the SSS congruence theorem on:

brainly.com/question/2102943

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2 years ago
A driver's education course compared 1,500 students who had not taken the course with 1,850 students who had. Of those students
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Answer:

P-value is less than 0.999995 .

Step-by-step explanation:

We are given that a driver's education course compared 1,500 students who had not taken the course with 1,850 students who had.

Null Hypothesis, H_0 : p_1 = p_2 {means students who took the driver's education course and those who didn't took have same chances to pass the written driver's exam the first time}

Alternate Hypothesis, H_1 : p_1 > p_2 {means students who took the driver's education course were more likely to pass the written driver's exam the first time}

The test statistics used here will be two sample Binomial statistics i.e.;

                             \frac{(\hat p_1 - \hat p_2)-(p_1 - p_2)}{\sqrt{\frac{\hat p_1(1- \hat p_1)}{n_1} + \frac{\hat p_2(1- \hat p_2)}{n_2} } } ~ N(0,1)

Here, \hat p_1 = No. of students passed the exam ÷ No.of Students that had taken the course

 \hat p_1  = \frac{1150}{1850}            Similarly,  \hat p_2 = \frac{1440}{1500}          n_1 = 1,850       n_2 = 1,500

  Test Statistics = \frac{(\frac{1150}{1850} -\frac{1440}{1500})-0}{\sqrt{\frac{\frac{1150}{1850}(1- \frac{1150}{1850})}{1850} + \frac{\frac{1440}{1500}(1- \frac{1440}{1500})}{1500} } } = -27.38

P-value is given by, P(Z > -27.38) = 1 - P(Z > 27.38)

Now, in z table the highest critical value given is 4.4172 which corresponds to the probability value of 0.0005%. Since our test statistics is way higher than this so we can only say that the p-value for an appropriate hypothesis test is less than 0.999995 .

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Step-by-step explanation:

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Answer:

She now needs to borrow $4000

Step-by-step explanation:

Juan is going to a school where tuition is $5,000 per year. He has a scholarship that pays 60% of his tuition. He has a grant for $1,000 per year. How much will Juan need to borrow to pay tuition each year?

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The height h, in feet, of a projectile t seconds after launch is modeled by the equation h = 32t – 16t2. How long after launch d
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3 years ago
Read 2 more answers
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