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GrogVix [38]
3 years ago
15

Given: m∠V=103°, m∠VRT=71°, RS ∥ VU Find: m∠TRS, m∠U

Mathematics
1 answer:
lawyer [7]3 years ago
5 0

Answer:

m∠U = 103° and m∠TRS = 6°

Step-by-step explanation:

In the given circle O,

Since, RS║VU, and VR is a transverse,

Therefor, m∠V + m∠R = 180° [Consecutive interior angles]

m∠R + 103° = 180° [m∠R = 103° given]

m∠R = 180° - 103°

m∠R = 77°

Since m∠R = m∠VRT + m∠TRS

77° = 71° + m∠TRS

m∠TRS = 77° - 71° = 6°

Quadrilateral RTUV is a cyclic quadrilateral.

Therefore, m∠U + m∠R = 180°

m∠U + 77° = 180°

m∠U = 180° - 77° = 103°

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Simplify each only using positive exponents:<br> 2x^-3 • 4x^2<br> 2x^4 • 4x^-3<br> 2x^3y^-3 • 2x
erica [24]
<h2>Answer:</h2>

\frac{2}{x}

\frac{x}{2}

\frac{4x^4}{y^3}

<h2>Step-by-step explanation:</h2>

a. 2x^-3 • 4x^2

To solve this using only positive exponents, follow these steps:

i. Rewrite the expression in a clearer form

2x⁻³ . 4x²

ii. The position of the term with negative exponent is changed from denominator to numerator or numerator to denominator depending on its initial position. If it is at the numerator, it is moved to the denominator. If otherwise it is at the denominator, it is moved to the numerator. When this is done, the negative exponent is changed to positive.

In our case, the first term has a negative exponent and it is at the numerator. We therefore move it to the denominator and change the negative exponent to  positive as follows;

\frac{1}{2x^3} . 4x^2

iii. We then solve the result as follows;

\frac{1}{2x^3} . 4x^2 = \frac{2}{x}

Therefore, 2x⁻³ . 4x² = \frac{2}{x}

b. 2x^4 • 4x^-3

i. Rewrite as follows;

2x⁴ . 4x⁻³

ii. The second term has a negative exponent, therefore swap its position and change the negative exponent to a positive one.

2x^4 . \frac{1}{4x^3}

iii. Now solve by cancelling out common terms in the numerator and denominator. So we have;

\frac{x}{2}

Therefore, 2x⁴ . 4x⁻³ = \frac{x}{2}

c. 2x^3y^-3 • 2x

i. Rewrite as follows;

2x³y⁻³ . 2x

ii. Change position of terms with negative exponents;

2x^3.\frac{1}{y^3} .2x

iii. Now solve;

\frac{4x^4}{y^3}

Therefore, 2x³y⁻³ . 2x = \frac{4x^4}{y^3}

8 0
3 years ago
Original: $0.95, Markup: 60%
Mademuasel [1]
.57 is your answerrrr
3 0
2 years ago
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10483 people attended a rock festival. if there were 811 more boys than girls, and 2481 fewer adults over 50 years of age than t
Bond [772]

Answer: 4051 girls, 4862 boys and 1570 adults over 50 years of age group attended the festival.

Step-by-step explanation:

Let x denotes the number of girls.

Then, the number of boys = x+811

The number of adults over 50 years of age = x-2481

Now, by considering the given scenario :-

x+x+811+x-2481=10483\\\\\Rightarrow\ 3x-1670=10483\\\\\Rightarrow\ 3x=10483+1670\\\\\Rightarrow\ 3x=12153\\\\\Rightarrow\ x=\dfrac{12153}{3}=4051

Thus, the number of girls attended the festival = 4051,

Then number of boys = 4051+811=4862

Number of adults = 4051-2481=1570

7 0
3 years ago
If you have 3 cups of pineapple juice, how many total cups of lunch can you make?
RideAnS [48]
About 6 that’s what I came up with
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2 years ago
Find the zeroes of the polynomial x2 −
alexgriva [62]

Answer:

Constant = αβ=−5

Step-by-step explanation:

ab is5x

7 0
3 years ago
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