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3 years ago

The measure of angle A to the nearest tenth of a degree is: A 18.5 B 19.5 C 20.5

Mathematics

1 answer:

Andrew [12]3 years ago

6 0

Answer:

Step-by-step explanation:

This is a right triangle as shown by the right angle.

The side opposite the right angle is the hypotenuse, which is 9.
The side opposite angle A is 3.

So we have the opposite of A and the hypotenuse.

The trigonometric ratio that relates opposite side to hypotenuse is SINE.

$sin\theta=\frac{opposite}{hypotenuse}$

Since, we need angle A, $\theta$ is A, opposite side is 3, and hypotenuse is 9, we substitute:

$sinA=\frac{3}{9}\\sinA=\frac{1}{3}$

To solve for the angle, we use our calculator and find the inverse sin of $\frac{1}{3}$ :

$A=sin^{-1}(\frac{1}{3})\\A=19.47$

Rounding to nearest tenth of a degree:

$A=19.5$

B is the right choice.

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mezya [45]

Answer:

$52,936

Step-by-step explanation:

1400(.14)(4) + 4(6)(9.75) = 784 + 234 = $1018/week

52(1018) = $52,936

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3 years ago

The value of y varies directly with x. If x =3, then y=21. What is the value of x when y=105?

Goshia [24]

Answer:

x = 15

Step-by-step explanation:

given that y varies directly with x

mathematically we can express this as

y = k x , where k is a constant

step 1: find k

given x = 3 and y = 21

y = k x

21 = k (3)

k = 7

hence the equation becomes

y = 7 x

when y = 105,

105 = 7x

x = 105 / 7 = 15

3 0

3 years ago

If 60 seconds are in a minute, 60 minutes in an hour, and 24 hours in a day, then 86,400 seconds are in a day. What type of reas

Anvisha [2.4K]

Let's define both terms first. Inductive reasoning is a conclusion that you get out of a series of observation. However, this may be true or not. But for deductive reasoning, you reach a conclusion that you get out of a series of observations that are also supported by facts. These are all true.

Since all the statements are based on facts, this is a deductive reasoning.

The answer is B. deductive.

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3 years ago

Find the solution to the system:

Sliva [168]

Answer:

u = 12, v= 15

Step-by-step explanation:

Given the system of simultaneous equation:

1/6 u− 1/3 v=−3... (1)

0.2u+0.1v=3.9...(2)

Rewriting both equation as fraction

1/6 u− 1/3 v=−3

1/5 u + 1/10 v = 39/10

Multiplying equation (1) by 6 and (2) by 10 we have:

u - 2v = -18... (3)

2u + v = 39...(4)

Using elimination method, we will first multiply equation (3) by 2 and (2) by 1 to have:

2u-4v = -36 ...(5)

2u+v = 39...(6)

Subtracting (5) from (6);

-4v-v = -36-39

-5v = -75

v = -75/-5

v = 15

Substituting v = 15 into equation (3) to get u we have:

u - 2(15) = -18

u - 30 = -18

u = -18+30

u = 12

The solution to the system of simultaneous equation are u = 12 and v = 15

7 0

3 years ago

Which points are the verticles of the ellipse? Equations of ellipse

Mashutka [201]

Answer:

This question is solved in detail below. Please refer to the attachment for better understanding of an Ellipse.

Step-by-step explanation:

In this question, there is a spelling mistake. This is vertices not verticles.

So, I have attached a diagram of an ellipse in which it is clearly mentioned where are the vertices of an ellipse.

Vertices of an Ellipse: There are two axes in any ellipse, one is called major axis and other is called minor axis. Where, minor is the shorter axis and major axis is the longer one. The places or points where major axis and minor axis ends are called the vertices of an ellipse. Please refer to the attachment for further clarification.

Equations of an ellipse in its standard form:

$\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1$

This is the case when major axis the longer one is on the x-axis centered at an origin.

$\frac{x^{2} }{b^{2} } + \frac{y^{2} }{a^{2} } = 1$

This is the case when major axis the longer one is on the y-axis centered at an origin.

where major axis length = 2a

and minor axis length = 2b

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3 years ago