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3 years ago

How do i solve this?

Mathematics

1 answer:

Alina [70]3 years ago

8 0

Answer:

m∠R = 60°

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Trigonometry

[Right Triangles Only] SOHCAHTOA
[Right Triangles Only] sinθ = opposite over hypotenuse

Step-by-step explanation:

Step 1: Identify

Angle θ = ∠R

Opposite Leg of ∠R = 10√3

Hypotenuse = 20

Step 2: Solve

Substitute in variables [sine]: $\displaystyle sin(R^\circ) = \frac{10\sqrt{3}}{20}$
[Equality Property] Trig inverse: $\displaystyle R^\circ = sin^{-1}(\frac{10\sqrt{3}}{20})$
Evaluate trig: $\displaystyle R = 60^\circ$

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sory i dont now spanish but try this

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3 years ago

Solutions: <4 + <1 = ______

Tom [10]

Answer:

1 ..>5

2.. 30(1)

3.. Sorry

I don't know properly 3 answer

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3 years ago

Scientists discover two planets orbiting a distant star. The average distance from the star to Planet A is 4 AU, and it takes 43

Kitty [74]

Answer:

Option C - 9 AU

Step-by-step explanation:

To find : What is the average distance from Planet B to the star?

Solution :

According to kepler's law,

The squares of the sidereal periods (of revolution) of the planets are directly proportional to the cubes of their mean distances from the Sun.

i.e. $P^2\propto S^3$

We have given,

The average distance from the star to Planet A is $S_1=4$ AU.

It takes 432 Earth days for Planet A to orbit the star i.e. $P_1=432$

It takes 1,460 days for Planet B to complete an orbit i.e. $P_2=1460$

Substitute the values in $(\frac{P_1}{P_2})^2=(\frac{S_1}{S_2})^3$

$(\frac{432}{1460})^2=(\frac{4}{S_2})^3$

$0.0875=(\frac{4}{S_2})^3$

Taking root cube both side,

$\sqrt[3]{0.0875}=\frac{4}{S_2}$

$0.444=\frac{4}{S_2}$

$S_2=\frac{4}{0.444}$

$S_2=9.00$

The average distance from Planet B to the star is 9 AU.

Therefore, Option C is correct.

5 0

3 years ago

8. A paper bag contains one pink crayon, four yellow crayons, three black crayons and two red crayons. What is the probability o

vivado [14]

Answer:

C 1/2

Add all the crayons together and then see how many red and black crayons there are. which in this case it's half. That is the probability

8 0

3 years ago

Use the graph of f at the right to complete each of the parts (a) through (h)

Maru [420]

Answers:

a. The domain of f is ]-∞ , ∞[

b. The range of f is [-4 , ∞[

c. f(1) = 5

d. The vales of x for which f(x) is -3 are 7 and 9

e. The points at which the graph crosses the x-axis are (6,0) and (10,0)

f. The point where the graph of f crosses the y-axis is (0,5)

g. The values of x for which f(x) < 0 are ]6 , 10[

h. f(-7) is positive

Explanation:

Part a:

The domain of the function refers to all the possible x-values that can be used as an input for this function.

Taking a look at the graph, we can see that the graph extends endlessly from both ends of the x-axis. This means that all x-values can be used as a domain for the function. In other words, the domain of the function is all the real numbers.

In interval notation, this is written as:

Domain = ]-∞ , ∞[

Part b:

The range of the function refers to all the possible y-values that can be used as an output for the function.

From the graph, we can note that the function extends endlessly in the direction of the positive y-axis while it stops at a value of -4 in the direction of the negative y-axis.

This means that the range of the function starts from -4 (included) and extends to positive infinity.

In interval notation, this is written as:

R = [-4 , ∞[

Part c:

f(1) means that we are looking for the output (the value of y) for which the input (the value of x) is 1.

From the graph, we start by searching for x=1 (first square edge after the origin) and then move vertically till we intersect the graph.

Doing this, we will find that the value of y at x=1 is 5

Therefore:

f(1) = 5

Part d:

f(x) = -3 means that the output value (the value of the y) for the certain input (value of x) is -3

To get the value of x, we go y=-3 and move horizontally till we intersect the graph.

Doing this, we will find that the value of y is -3 at x = 7 and x = 9

Part e:

The points where the graph crosses the x-axis are the points that have y-value equal to 0

Checking the graph, we can note that the function crosses the x-axis at two points which are (6,0) and (10,0)

Part f:

The point where the graph crosses the y-axis is the point that has x-value equal to 0

Checking the graph, we can note that the function crosses the y-axis at only one point which is (0,5)

Part g:

f(x) < 0 means that the output of the function (the y-value) is less than 0 (0 is not included)

Taking a look at the graph, we can note that the function has negative output on the interval from 6 (excluded) to 10 (excluded)

In interval notation, this is written as ]6 , 10[

Part h:

f(-7) means the output of the function (the y-value) at input (x-vale) equal to -7

From the graph, we can note that the function has a constant value of 5 starting from x=5 till -∞

This means that, at x=-7, the value of y is 5 which is a positive value

Hope this helps :)

6 0

4 years ago

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