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Flura [38]
1 year ago
5

Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 12 centimeters, the length of C B is 9.8

centimeters, and the length of A C is 6.9 centimeters.
Which expressions can be used to find m∠BAC? Select three options.

Mathematics
1 answer:
RSB [31]1 year ago
3 0

Answer: We can find angle BAC by using (1) SinA = 9.8/12

(2) CosA = 6.9/12

(3) TanA = 9.8/6.9

Step-by-step explanation: The question indicates that we have a right angled triangle ABC with the right angle at point C (that is, angle ACB is the right angle). Also the three sides have been labeled as AB equals 12 cm, CB equals 9.8 cm and AC equals 6.9 cm. Line AB has been identified as the hypotenuse and angle A (that is, BAC) is the reference angle. If angle A is the reference angle, then line CB facing angle A shall be the opposite side, while line AC is the adjacent (which lies between the reference angle and the right angle). Please see the attached diagram for details.

Having these details available, we can actually find angle A by using any of the three trigonometric ratios, since all three sides are given. Hence,

SinA = opposite/hypotenuse

SinA = 9.8/12

SinA = 0.8167

Checking with your calculator or table of values, A = 54.76 (approximately 55)

Also CosA = adjacent/hypotenuse

CosA = 6.9/12

CosA = 0.5750

Checking with your calculator or table of values A = 54.90 (approximately 55).

Finally TanA = opposite/adjacent

TanA = 9.8/6.9

TanA = 1.4203

Checking with your calculator or table of values A = 54.83 (approximately 55).

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Suppose x follows a continuous uniform distribution from 1 to 5. determine the conditional probability p(x >2.5 | x ≤ 4).
Rainbow [258]
Because the random variable x follows a continuous uniform distribution from x=1 to x=5, therefore
p(x) = 1/4,  x=[1, 5]
The value of p(x) ensures that the total area under the curve = 1.

The conditional probability p(x > 2.5 | x ≤ 4) is the shaded portion of the curve. Its value is
p(x > 2.5 | x ≤4) = (1/4)*(4 - 2.5) = 0.375

Answer: 0.375

8 0
1 year ago
What is the following quotient? sqrt 6 + sqrt 11 / sqrt 5 +sqrt 3
just olya [345]

Answer:

\frac{\sqrt6 +\sqrt{11}}{\sqrt{5} + \sqrt{3}} \times \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}} = \frac{\sqrt{30} - \sqrt{18} + \sqrt{55} - \sqrt{33}}{2}

Step-by-step explanation:

Let's translate what you've written in words to an expression with mathematical symbols.

\frac{\sqrt6 +\sqrt{11}}{\sqrt{5} + \sqrt{3}}

To solve this, you need to multiply both the numerator and denominator with the conjugate of the denominator.

\frac{\sqrt6 +\sqrt{11}}{\sqrt{5} + \sqrt{3}} \times \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}} = \frac{\sqrt{30} - \sqrt{18} + \sqrt{55} - \sqrt{33}}{2}

5 0
2 years ago
Read 2 more answers
A. If a spacecraft was parked on Venus and needed to make a flight to Jupiter, how far would it need to travel? Show your work a
bija089 [108]
A. (Assume both planets are aligned with the sun and are on the same side of the sun.) Show your work and provide your answer in scientific notation. Jupiter = 778,500,000 km from sun. Venus = 108,200,000 km from sun.

778,500,000 – 108,200,000 = 670,300,000
It would need to travel 670,300,000 km/ 6.703 x 10 with a 8 squared km (as shown below)
10 {}^{8}


B.Mercury, Venus, and Earth are the three planets closest to the sun. Would their combined distance from the sun be greater or less than the distance from the sun to Neptune? Show your work and justify your answer. Mercury = 57,909,000 km Venus = 108,200,000 km Earth = 149,600,000 km 57,909,000 + 108,200,000 + 149,600,000 = 315,709,000 Less because 315,709,000 km is less than 4,498,000,000 km

C.If Earth was 10 times farther away from the sun than it is now, which planet would it be closest to? (Assume all the planets are aligned with the sun and are on the same side of the sun.) Compare Earth's new distance to that planet. How far apart would they be in standard notation? How far apart in scientific notation? Show your work. Earth = 149,600,000 km 149,600,000 x 10 = 1,496,000,000 Earth’s new distance = 1,496,000,000 Earth would be closest to Saturn. 1,496,000,000 – 1,429,000,000 = 67,000,000
They would be 67,000,000 km apart
Scientific notation: 6.7 x 10 with a 7 squared km (sorry I can't write this to show this figure but see below as you should write it exactly like how I typed it below followed by km)
10 {}^{7}


D. The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. (Assume both planets are aligned with the sun and are on the same side of the sun.) Show your work. Convert your answer into scientific notation if necessary. Earth = 149,600,000 km
Saturn = 1,429,000,000 km
1,429,000,000 - 149,600,000 = 1,279,400,000
1,279,400,000 km
1,279,400,000 ÷ 28,000 = 45,692.8
Estimated hours it will take the shuttle to reach Saturn from Earth = 45,693
Scientific notation: 4.5693 x 10 with a 4 squared
(same with this one, it should be written as I have it shown below instead of how I first tried to explain it.)
10 {}^{4}






4 0
2 years ago
A scale model of rectangle patio is 6 feet 3 feet wide the actual patio is 15 feet long what is the area of the actual patio
Anuta_ua [19.1K]
The answer is 6 divide 145 into 9 you"ll get the length
7 0
2 years ago
mrs.beluga is driving on a snow covered road with a drag factor of 0.2. she brakes suddenly for a deer. The tires leave a yaw ma
Aneli [31]
First, we are going to find the radius of the yaw mark. To do that we are going to use the formula: r= \frac{c^2}{8m} + \frac{m}{2}
where 
c is the length of the chord 
m is the middle ordinate 
We know from our problem that the tires leave a yaw mark with a 52 foot chord and a middle ornate of 6 feet, so c=52 and m=6. Lets replace those values in our formula:
r= \frac{52^2}{8(6)} + \frac{6}{2}
r= \frac{2704}{48} +3
r= \frac{169}{3} +3
r= \frac{178}{3}

Next, to find the minimum speed, we are going to use the formula: s= \sqrt{15fr}
where
f is <span>drag factor
</span>r is the radius 
We know form our problem that the drag factor is 0.2, so f=0.2. We also know from our previous calculation that the radius is \frac{178}{3}, so r= \frac{178}{3}. Lets replace those values in our formula:
s= \sqrt{(15)(0.2)( \frac{178}{3}) }
s= \sqrt{178}
s=13.34 mph

We can conclude that Mrs. Beluga's minimum speed before she applied the brakes was 13.34 miles per hour. 
8 0
2 years ago
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