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3 years ago

Given QT = SR, QV = SU, and the diagram, prove that triangles QUT and SVR are congruent. Write a paragraph proof.

Mathematics

1 answer:

QveST [7]3 years ago

5 0

Answer:

Triangles QUT and SVR are congruent because the defining two sides and an included angle of triangles QUT and SVR are equal

Step-by-step explanation:

Here we have QT = SR and

QV = SU

Therefore,

QT = √(UT² + QU²)........(1)

RS = √(VS² + RV²)..........(2)

Since QS = QU + SU = QV + VS ∴ QU = VS

Therefore, since SR = QT and QU = VS, then from (1) and (2), we have UT = RV

Hence since we know all sides of the triangles QUT and SVR are equal and we know that the angle in between two congruent sides of the the triangles QUT and SVR that is the angle in between sides QU and UT for triangle QUT and the angle in between the sides RV and VS in triangle SVR are both equal to 90°, therefore triangles QUT and SVR are congruent.

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3 years ago

Simplify negative 4 and 1 over 6 − negative 6 and 1 over 3. Which of the following is correct?

Pavlova-9 [17]

The correct answer is 2 1/6.

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2 years ago

Read 2 more answers

I got the first two can you help me with the last one PLZ

Nat2105 [25]

1. Geometric Sequence

2. $a_n = a_{n-1} * 3$

3. $a_n = 6 * (3)^{n-1}$

Step-by-step explanation:

Given sequence is:

6, 18, 54, 162,....

Here

$a_1 =6\\a_2 = 18\\a_3 = 54$

(a) Is this an arithmetic or geometric sequence?

We can see that the difference between the terms is not same so it cannot be an arithmetic sequence.

We have to check for common ratio (ratio between consecutive terms of a sequence) denoted by r

$r = \frac{a_2}{a_1} = \frac{18}{6}= 3\\r = \frac{a_3}{a_2} = \frac{54}{18} = 3$

As the common ratio is same, the given sequence is a geometric sequence.

(b) How can you find the next number in the sequence?

Recursive formulas are used to find the next number in sequence using previous term

Recursive formula for a geometric sequence is given by:

$a_n = a_{n-1} * r$

In case of given sequence,

$a_n = a_{n-1} * 3$

So to find the 5th term

$a_5 = a_4*3\\a_5 = 162*3\\a_5 = 486$

(c) Give the rule you would use to find the 20th week.

In order to find the pushups for 20th week, explicit formul for sequence will be used.

The general form of explicit formula is given by:

$a_n = a_1 * r^{n-1}$

Putting the values of a_1 and r

$a_n = 6 * (3)^{n-1}$

Hence,

1. Geometric Sequence

2. $a_n = a_{n-1} * 3$

3. $a_n = 6 * (3)^{n-1}$

Keywords: Geometric sequence, common ratio

Learn more about geometric sequence at:

#LearnwithBrainly

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3 years ago

If J is the centroid of cde, de=52, fc=15, he=14, find each missing measure

const2013 [10]

Answer:

$DG = 26$

$GE = 26$

$DF = 15$

$CH = 14$

$CE = 28$

Step-by-step explanation:

The figure has been attached, to complement the question.

$DE = 52$

$FC = 15$

$HE = 14$

Given that J is the centroid, it means that J divides sides CD, DE and CE into two equal parts respectively and as such the following relationship exist:

$DF = FC$