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netineya [11]
3 years ago
11

The first four terms of an arithmetic sequence are -11,-5,1,7. what is the equation for an

Mathematics
1 answer:
mr_godi [17]3 years ago
7 0

Answer:

y = 6x - 11

Step-by-step explanation:

An arithmetic sequence is a linear function. This means it steadily increases or decreases through addition/subtraction by a constant amount. Here the sequence grows by adding 6 each time.

-11 + 6 = -5

-5 + 6 = 1

1 + 6 = 7

etc....

Since this is linear, its equation has the form y = mx + b where m is the slope and b is the y-intercept. The slope is m = 6 and b = -11.

y = 6x - 11

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A polynomial function has a root of –6 with multiplicity 1, a root of –2 with multiplicity 3, a root of 0 with multiplicity 2, a
Temka [501]
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3 years ago
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What is the slope of a line that is perpendicular to the line y = x 4? the slope of the line is .
SIZIF [17.4K]

Answer:-1/4

Step-by-step explanation:

Take the negative of the reciprocal for perpendicular lines. In the case of no slope (y=number) replace y with x

7 0
2 years ago
Help! How would I solve this trig identity?
NeTakaya

Using simpler trigonometric identities, the given identity was proven below.

<h3>How to solve the trigonometric identity?</h3>

Remember that:

sec(x) = \frac{1}{cos(x)} \\\\tan(x) = \frac{sin(x)}{cos(x)}

Then the identity can be rewritten as:

sec^4(x) - sen^2(x) = tan^4(x) + tan^2(x)\\\\\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)}  = \frac{sin^4(x)}{cos^4(x)}  + \frac{sin^2(x)}{cos^2(x)} \\\\

Now we can multiply both sides by cos⁴(x) to get:

\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)}  = \frac{sin^4(x)}{cos^4(x)}  + \frac{sin^2(x)}{cos^2(x)} \\\\\\\\cos^4(x)*(\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)}) = cos^4(x)*( \frac{sin^4(x)}{cos^4(x)}  + \frac{sin^2(x)}{cos^2(x)})\\\\1 - cos^2(x) = sin^4(x) + cos^2(x)*sin^2(x)\\\\1 - cos^2(x) = sin^2(x)*sin^2(x) + cos^2(x)*sin^2(x)

Now we can use the identity:

sin²(x) + cos²(x) = 1

1 - cos^2(x) = sin^2(x)*(sin^2(x) + cos^2(x)) = sin^2(x)\\\\1 = sin^2(x) + cos^2(x) = 1

Thus, the identity was proven.

If you want to learn more about trigonometric identities:

brainly.com/question/7331447

#SPJ1

7 0
1 year ago
4^{3x+2}=<br> 4 <br> 3x+2<br> =<br> \,\,2^{2x-4}<br> 2 <br> 2x−4
aliina [53]

Answer:

Dont know

Step-by-step explanation:

Sorryyyyyyyyyyyyyyyyyyyyy

8 0
3 years ago
A lighthouse is located on an island 200 feet from the shore of the mainland as
Deffense [45]

Answer: Approximately d = 208.72

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

Work Shown:

Make sure your calculator is in radian mode

A quick way to check is to compute cos(pi) and you should get -1

cos(angle) = adjacent/hypotenuse

cos(x) = 200/d

cos(0.29) = 200/d

d*cos(0.29) = 200

d = 200/cos(0.29)

d = 208.715135166392 which is approximate

d = 208.72

I rounded to two decimal places since x is rounded in that manner as well. Round however else you need if your teacher instructs.

4 0
2 years ago
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