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4 years ago

Which two lines are parallel?

1 answer:

8 0

The answer must be "a. II and III" Trust me.
This is because the two linear equations have both the same coefficients of x and y, respectively.

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Find the exact values of the remaining five trigonometric functions of theta, suppose theta is an angle in the standard position

nexus9112 [7]

Answer:

$\sin(\theta)=60/61\text{ and } \csc(\theta)=61/60\\\cos(\theta)=11/61\text{ and } \sec(\theta)=61/11\\\tan(\theta)=60/11\text{ and } \cot(\theta)=11/60$

Step-by-step explanation:

So, we know that:

$\tan(\theta)=60/11\text{ and } 90\textdegree$

Since θ is in QI, this means that all of our trig ratios will be positive. Recall All Students Take Calculus. Since it's QI, we refer to A in All. The A tells us that all the ratios will be positive.

Now, let's figure out the remaining ratios knowing that all of them is positive. First, let's find the hypotenuse. Recall that tangent is the ratio of the opposite side to the adjacent side. So, we can use the Pythagorean Theorem to find the hypotenuse. So:

$a^2+b^2=c^2$

Substitute 60 for a and 11 for b:

$60^2+11^2=c^2$

Solve for c. Square both numbers:

$3600+121=c^2$

Add:

$c^2=3721$

Take the square root of both sides:

$c=61$

Therefore, the hypotenuse is 61.

So, our side lengths are: Opposite=60; Adjacent=11; and Hypotenuse=61.

Now that we know the lengths, we can find the other trig ratios:

Sine and Cosecant:

$\sin(\theta)=opp/hyp$

Substitute 60 for Opp and 61 for Hyp:

$\sin(\theta)=60/61$

Cosecant is the reciprocal of sine. So:

$\csc(\theta)=61/60$

Cosine and Secant:

$\cos(\theta)=adj/hyp$

Substitute 11 for Adj and 61 for Hyp:

$\cos(\theta)=11/61$

Secant is the reciprocal of cosine. So:

$\sec(\theta)=61/11$

Tangent and Cotangent:

We are already given that tangent is:

$\tan(\theta)=60/11$

Cotangent is the reciprocal of tangent. So:

$\cot(\theta)=11/60$

4 0

4 years ago

FIND THE EQUATION OF THE LINE!!! USE EXACT NUMBERS EXAMPLE! y= ( )x + ( )

Korvikt [17]

Answer:

y=mx+b is the form to write this equation. M is the slope and B is the y intercept. therefore:

y=4x-9

Step-by-step explanation:

3 0

3 years ago

What is the unit rate of 1/2 dozen pencils in 1/3 box

maw [93]

(1/2)/(1/3) is the answer for you sir! I think...

7 0

4 years ago

n a group of 40 people, 10 people are healthy. The 30 unhealthy people have either high blood pressure, high cholesterol, or bot

aalyn [17]

Answer:

If a person is randomly selected from this group, the probability that they have both high blood pressure and high cholesterol is P=0.25.

Step-by-step explanation:

We can calculate the number of people from the sample that has both high blood pressure (HBP) and high cholesterol (HC) using this identity:

$N(\text{HBP or HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP and HC})\\\\\\ N(\text{HBP and HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP or HC})\\\\\\ N(\text{HBP and HC})=15+25-30=10$

We can calculate the probability that a random person has both high blood pressure and high cholesterol as:

$P(\text{HBP and HC})=\dfrac{10}{40}=0.25$

3 0

3 years ago

What is the equation in slope-intercept form for the line that passes through the points

LekaFEV [45]

Answer:

Step-by-step explanation:

5 0

3 years ago