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4 years ago

Point Z is equidistant from the vertices of ΔTUV.

Mathematics

2 answers:

stealth61 [152]4 years ago

8 0

Answer:

(C)

Step-by-step explanation:

It is given that Point Z is equidistant from the vertices of ΔTUV, therefore ZT=ZU=ZV.

Now, from ΔBTZ and ΔBUZ, we have

ZT=ZU (Given)

BZ=ZB (common)

therefore, by RHS rule of congruency,

ΔBTZ≅ΔBUZ

Thus, by corresponding parts of congruent triangles, we have

∠BTZ=∠BUZ

Thus, option C is correct.

Also, it is not necessary that TA=TB and AZ=BZ because there is no information given regarding these equalities.

Zepler [3.9K]4 years ago

5 0

Consider right triangles BTZ and BUZ.

ZB = ZB (Common)

ZT = ZU (Given)

Therefore, ΔBTZ ≅ ΔBUZ (By RHS theorem)

Hence, by CPCTC,

∠BTZ = ∠BUZ

You might be interested in

If the sum of a number and its square is 182, what is the number ?

vivado [14]

Answer:

-14 or 13

Step-by-step explanation:

x + x^2 = 182

x^2 + x - 182 = 0

rearrange and solve by completing the square

x^2 + x = 182

x^2 + x + 1/4 = 182.25

(x + 1/2)(x + 1/2) = 182.25

(x + 1/2)^2 = 182.25

x + 1/2 = root 182.25

x = + or - root 182.25 - 0.5

x = + or - 13.5 - 0.5

x = 13 or x = - 14

5 0

3 years ago

Read 2 more answers

Mathematics achievement test scores for 300 students were found to have a mean and a variance equal to 600 and 3600, respectivel

Zina [86]

Answer:

(a) Approximately 205 students scored between 540 and 660.

(b) Approximately 287 students scored between 480 and 720.

Step-by-step explanation:

A mound-shaped distribution is a normal distribution since the shape of a normal curve is mound-shaped.

Let <em>X</em> = test score of a student.

It is provided that $X\sim N(\mu = 600, \sigma^{2} = 3600)$ .

(a)

The probability of scores between 540 and 660 as follows:

$P(540\leq X\leq 660)=P(\frac{540-600}{\sqrt{3600} }\leq \frac{X-600}{\sqrt{3600} }\leq \frac{660-600}{\sqrt{3600} })\\=P(-1 \leq Z\leq 1)\\= P(Z\leq 1)-P(Z\leq -1)\\=0.8413-0.1587\\=0.6826$

Use the standard normal table for the probabilities.

The number of students who scored between 540 and 660 is:

300 × 0.6826 = 204.78 ≈ 205

Thus, approximately 205 students scored between 540 and 660.

(b)

The probability of scores between 480 and 720 as follows:

$P(480\leq X\leq 720)=P(\frac{480-600}{\sqrt{3600} }\leq \frac{X-600}{\sqrt{3600} }\leq \frac{720-600}{\sqrt{3600} })\\=P(-2 \leq Z\leq 2)\\= P(Z\leq 2)-P(Z\leq -2)\\=0.9772-0.0228\\=0.9544$

Use the standard normal table for the probabilities.

The number of students who scored between 480 and 720 is:

300 × 0.9544 = 286.32 ≈ 287

Thus, approximately 287 students scored between 480 and 720.

3 0

3 years ago

On a road trip, you drive about 70 miles per hour and your friend drives about 60 miles per hour. The plan is to drive less than

lord [1]

Answer: The answer is 0 hours and 10 hours.

Step-by-step explanation: Given that me and my friend are on a road trip. My speed is 70 miles per hour and my friend's speed is 60 miles per hour. Our plan is to drive less than 15 hours and at least 600 miles each day.

Also, my friend will drive more hours than me.

Let, 'x' and 'y' be the number of hours drove by me and my friend respectively. Then, according to the given information, we have the following inequalities.

$y>x,\\\\x+y$

When we plot these inequalities in a graph paper, we can see in the attached figure, where the common shaded region gives the solution set, one of the solution is point 'P', given by

x = 0 and y = 10.

This solution satisfy all the three conditions given above.

Thus, one of the solution is - I will drive for 0 hours and my friend will drive for 10 hours.