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Vanyuwa [196]
3 years ago
12

Ind an equation for the nth term of the arithmetic sequence. a14 = -33, a15 = 9

Mathematics
1 answer:
marin [14]3 years ago
5 0

Answer:

a_n=42n-621

Step-by-step explanation:

This is arithmetic sequence so you should go to linear equations in your head.

Think of the question asking you to find the equation of line going through the points:

(14,-33) and (15,9).

First, let's find the slope.

You need to compute y's change over x's change.

The way I like to do that is line up the points vertically, subtract them, and then put 2nd difference over first.

Like this:

(  15  ,   9)

-(  14  ,  -33)

------------------

   1         42

So the slope is 42/1=42.

(The slope is our common difference.)

Now point slope form is:

y-y1=m(x-x1) where m is the slope and (x1,y1) is a point you know on the line.

So we have m=42 and (x1,y1)=(15,9).  (You could have chose the other point.)

y-9=42(x-15)

I'm going to put in slope-intercept form.  Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

y-9=42(x-15)

Solve for y by adding 9 on both sides:

y=42(x-15)+9

Distribute 42 to terms in the ( ) :

y=42x-42(15)+9

y=42x-630+9

y=42x-621

So we can which back to n now:

a_n=42n-621

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Semenov [28]

Answer:

Yes, because m<UVW is congruent to m<XVY and m<VUW is congruent to m<VXY

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

so

In this problem

we know that

m< VUW=55\°

the measure of angle VXY is equal to

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m

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Remember that

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therefore

Triangles VUW and VXY are similar by AAA Similarity Theorem ( the three angles are congruent)

3 0
3 years ago
The resting heart rates for a sample of individuals are normally distributed with a mean of 70 and a standard deviation of 15. U
Liono4ka [1.6K]

Answer:

84%

Step-by-step explanation:

The empirical rule states that 68% values are within 1 standard deviation of mean, i.e,

70

±

15

or from 55 to 85. Since normal distribution is symmetric, we must have (32%) outside this range, and 32/2=16% on the right if this range. Hence below 85 we have (100-16) % = 84%

7 0
3 years ago
What is the equation to a graph with the vertex -1,3 and zeros -4 and -2
Mashutka [201]

Answer:

f(x)=x^2+6x+8

Step-by-step explanation:

We are given zeros as x=-4, x=-2

so, we can set up function as

f(x)=a(x+4)(x+2)

Vertex is at (-1,3)

It means that graph passes through point (-1,3)

so, we can plug x=-1 and f(x)=3

and then we can solve for 'a'

3=a(-1+4)(-1+2)

we get

a=1

now, we can plug it back

and we get

f(x)=1(x+4)(x+2)

now, we can simplify it

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5 0
3 years ago
They take 5 days to drive 679 miles to Seattle, how many miles will they drive each day?
Kisachek [45]

If they take 5 days to drive 679 miles to Seattle. Then the number of miles that they drive each day will be 135.8 miles per day.

<h3>What is speed?</h3>

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

They take 5 days to drive 679 miles to Seattle.

Then the number of miles that they drive each day will be

→ 679 / 5

→ 135.8 miles per day.

More about the speed link is given below.

brainly.com/question/7359669

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8 0
2 years ago
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Y = 1/3x + 2<br> y = -2/3 x + 5
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Answer:

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Step-by-step explanation:

4 0
3 years ago
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