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3 years ago

Determine the measure of angle UVT

Mathematics

1 answer:

Arte-miy333 [17]3 years ago

8 0

Answer:

$UVT =40$

Step-by-step explanation:

Required

Solve for UVT

First, calculate UTV

$UTV = 180 - UTB$

$UTV = 180 - 20x$

Next:

$UTV + VUT + UVT = 180$ ---- angles in a triangle

So:

$180 - 20x +60+7x+5 = 180$

Collect like terms

$- 20x +7x= 180-180-60-5$

$-13x= -65$

Divide by -13

$x = 5$

$UVT =7x+5$

$UVT =7*5+5$

$UVT =40$

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The number of airline passengers in 1990 was 466 million. The number of passengers traveling by airplane each year has increased

taurus [48]

Answer:

2010.

Step-by-step explanation:

We have been given an exponential growth formula $P(t)=466\cdot 1.035^t$ , which represents number of passengers traveling by airplane since 1990.

To find the year in which 900 million passengers will travel by airline, we will equate the given formula by 900 and solve for t as:

$900=466\cdot 1.035^t$

$\frac{900}{466}=\frac{466\cdot 1.035^t}{466}$ $1.9313304721030043=1.035^t$

Take natural log of both sides:

$\text{ln}(1.9313304721030043)=\text{ln}(1.035^t)$

Using property $\text{ln}(a^b)=b\cdot \text{ln}(a)$ , we will get:

$\text{ln}(1.9313304721030043)=t\cdot \text{ln}(1.035)$

$0.658209129198=t\cdot 0.034401426717$

$\frac{0.658209129198}{0.034401426717}=\frac{t\cdot 0.034401426717}{0.034401426717}$

$19.1331927775=t\\\\t=19.1331927775$

This means that in the 20th year since 1990, 900 million passengers would travel by airline.

$1990+20=2010$

Therefore, 900 million passengers would travel by airline in 2010.

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3 years ago

Factor the following expression. 10x^5 + 5x^3 - 14x^2 - 7

nadezda [96]

(5x^3-7)(2x^2+1 answerrrrrrrrrr

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3 years ago

3x - 5x + 4 = 10 A. -7 B. 7 C. 3 D. -3

Alborosie

$3x-5x+4=10\\\\-2x+4=10\ \ \ |-4\\\\-2x=6\ \ \ |:(-2)\\\\x=-3$
Answer: D. -3

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4 years ago

Read 2 more answers

Mr. Sanchez bought 2 magazines for $9.95 each and 1 book for $14.95. If the sales tax is 6%, what is the total cost of Mr. Sanch

Gennadij [26K]

add up the purchases

2(9.95) + 14.95

19.90 +14.95

34.85

now find the sales tax

34.85 * .06 =2.091 = 2.09 (round to 2 decimal places with money)

add the purchases and the sales tax to get the total amount

34.85 + 2.09

$36.94

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4 years ago

Claire bought just enough fencing to enclose either a rectangular garden or a triangular garden, as shown. The two gardens have

Arte-miy333 [17]

To find the perimeter of the rectangle, you would add all sides or use P=2L+2w (Perimeter = 2 times the length plus 2 times the width)

P= 2(3x-3) + 2(x-3)

P=6x-6+2x-6

P=8x-12

To find the perimeter of the triangle, add all the sides.

P=(2x-1)+2x+(2x-1)

P=6x-2

Now we know that both of the perimeters are the same so we can set them equal to each other.

8x-12 = 6x-2 solve by subtracting 6x from both sides.

2x-12 = -2 then add 12 to both sides

2x=10 last divide by 2 on both sides

x=5

Now replace x with 5 on either the rectangle or the triangle. I will use the triangle.

P=(2x-1)+2x+(2x-1)

P=(2*5-1)+2*5+(2*5-1)

P=28 feet

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4 years ago