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2 years ago

Find the distance between the two points. (-6, – 7), (0,0)

Mathematics

1 answer:

Elden [556K]2 years ago

8 0

Answer:

√85

Step-by-step explanation:

for this, you will probably need to draw a graph. Plot the points, and then you will notice that you can draw a triangle with one side being the x-axis ( go on to (-6,0) then drop down unitll you hit the point (-6;-7)

// use the pythagoream theorem to find the length

the distance of the leg on the x-axis is 6 (calculate 0-(-6))

the distance of the leg that is dropping down is -7 (calculate 0-(-7))

then we have 2 legs and need to find the hypotenuse.

Pythagorean theorem a^2 + b^2 = c^2

substitute :

6^2 + 7^2 = c^2

36+49 = 85

c= √85

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Cheryl is buying lace for her dance costume. One foot of lace costs 3 dollars. How much does each amount cost?

NemiM [27]

Answer:

3/4 of a foot will cost $2.25.

Step-by-step explanation:

This question is solved by rule of three, due to proportions.

One foot of lace costs 3 dollars. How much is 3/4 of a foot going to cost?

1 foot - 3 dollars

3/4 foot - x dollars

$x = 3 \times \frac{3}{4} = \frac{9}{4} = 2.25$

3/4 of a foot will cost $2.25.

7 0

2 years ago

Factor the expression completely over the complex numbers. y^4+12y^2+36

Brums [2.3K]

Y⁴ + 12y² + 36
Now factorize the expression
y⁴ + 6y² + 6y² + 36
= y²(y² + 6) + 6(y² + 6)
= (y² + 6) (y² + 6)
Now 6 is not the perfect square and according to rule, binomial can not be factored as the difference of two perfect squares.
so multiply both.
(y² + 6)² is the answer.

7 0

2 years ago

Read 2 more answers

It costs John $13.50 to take Mary out for the evening. Sixty percent of this total was for theater tickets. What was the cost of

masya89 [10]

4.05 dollars for one ticket.

8 0

2 years ago

Someone help please

Alla [95]

Answer: Choice A

$\tan(\alpha)*\cot^2(\alpha)\\\\$

============================================================

Explanation:

Recall that $\tan(x) = \frac{\sin(x)}{\cos(x)}$ and $\cot(x) = \frac{\cos(x)}{\sin(x)}$ . The connection between tangent and cotangent is simply involving the reciprocal

From this, we can say,

$\tan(\alpha)*\cot^2(\alpha)\\\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\left(\frac{\cos(\alpha)}{\sin(\alpha)}\right)^2\\\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\frac{\cos^2(\alpha)}{\sin^2(\alpha)}\\\\\\\frac{\sin(\alpha)*\cos^2(\alpha)}{\cos(\alpha)*\sin^2(\alpha)}\\\\\\\frac{\cos^2(\alpha)}{\cos(\alpha)*\sin(\alpha)}\\\\\\\frac{\cos(\alpha)}{\sin(\alpha)}\\\\$

In the second to last step, a pair of sine terms cancel. In the last step, a pair of cosine terms cancel.

All of this shows why $\tan(\alpha)*\cot^2(\alpha)\\\\$ is identical to $\frac{\cos(\alpha)}{\sin(\alpha)}\\\\$

Therefore, $\tan(\alpha)*\cot^2(\alpha)=\frac{\cos(\alpha)}{\sin(\alpha)}\\\\$ is an identity. In mathematics, an identity is when both sides are the same thing for any allowed input in the domain.

You can visually confirm that $\tan(\alpha)*\cot^2(\alpha)\\\\$ is the same as $\frac{\cos(\alpha)}{\sin(\alpha)}\\\\$ by graphing each function (use x instead of alpha). You should note that both curves use the exact same set of points to form them. In other words, one curve is perfectly on top of the other. I recommend making the curves different colors so you can distinguish them a bit better.

6 0

2 years ago

See attached file for question

Leto [7]

Answer:

1/6

Step-by-step explanation:

1/3 + 1/2= 1/6. so 1/6 is the answer

4 0

2 years ago