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3 years ago

Find the exact value for x leaving your answer as a surd with a rational denominator where appropriate :

Mathematics

1 answer:

lesya [120]3 years ago

3 0

Answer:

x = 10 $\sqrt{3}$

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin60° = $\frac{\sqrt{3} }{2}$ , then

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{x}{20}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2x = 20 $\sqrt{3}$ ( divide both sides by 2 )

x = 10 $\sqrt{3}$

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The angle measures associated with which set of ordered pairs share the same reference angle? (Negative StartFraction StartRoot

Katarina [22]

Answer:

$(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)$

Step-by-step explanation:

The reference angle is the angle that the given angle makes with the x-axis.

For an ordered pair to share the same reference angle, the x and y coordinates must be the same or a factor of each other.

From the given options:

$(A)\left(-\dfrac{\sqrt{3} }{2} ,-\dfrac{1 }{2}\right)$ and \left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)\\\\(B)\left(\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(-\dfrac{\sqrt{3} }{2}, \dfrac{1 }{2}\right)\\\\(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)\\\\(D)\left(\dfrac{\sqrt{3} }{2},\dfrac{1 }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)$

We observe that only the pair in option C has the same x and y coordinate with the second set of points being a negative factor of the first term. Therefore, they have the same reference angle.

5 0

3 years ago

Read 2 more answers

Many gas stations give a discount for using cash instead of a credit card. A gas station gives a discount of 10 cents per gallon

Lostsunrise [7]

Answer:

2.33 $

Step-by-step explanation:

10x14=140 cents / 2.33$

4 0

3 years ago

A house has decreased in value by 34% since it was purchased. If the current value is $231,000, what was the value when it was p

GenaCL600 [577]

Answer:

309,540

Step-by-step explanation:

231,000 + 34%

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3 years ago

The graph of a function f(x) is shown. What is the value of x where f(x) = -5? And f(0)?

max2010maxim [7]

Answer:

x = -3 when f(x) = -5

f(0) = 3

Step-by-step explanation:

When f(x) = -5, that means they have told you the y value. When y = -5, x = -3.

If the number is in the parentheses of the function, they are giving you the x value. When x = 0, y = 3

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2 years ago

Plot a point on the coordinate plane to represent each of the ratio values in the table.

Crank

Answer:

U almost got it right I posted the right answer below.

Step-by-step explanation:

The answer should be like this:

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3 years ago