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3 years ago

Algebra 1:

2 answers:

3 0

The nth term can be expressed as 16n-70.
So, if we solve
122=16n-70
we find n=12.
Thus, 122 is the 12th term in the sequence.

SSSSS [86.1K]3 years ago

3 0

122 is the 12th term in the sequence.

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State whether the lines are parallel, perpendicular,or neither.

cluponka [151]

Answer:

Please check the explanation.

Step-by-step explanation:

Two lines are parallel if their slopes are equal.

Two lines are perpendicular if the product of their slope is -1

We also know that the slope-intercept form of the line equation is

$y=mx+b$

where m is the slope and b is the y-intercept

Given the lines

y = 6х - 3

Comparing with y=mx+b, the slope of y = 6х - 3:

m₁=6

y = - 1/6x + 7

Comparing with y=mx+b, the slope of y = - 1/6x + 7:

m₂=-1/6

m₁ × m₂ = -1

6 × - 1/6 = -1

-1 = -1

Thus, the lines y = 6х - 3 and y = - 1/6x + 7 are perpendicular.

y = 3x + 2

Comparing with y=mx+b, the slope of y = 3x + 2:

m₁=3

2y = 6x - 6

simplifying to write in slope-intercept form

y=3x-3

Comparing with y=mx+b, the slope of y=3x-3:

m₂=3

As the slopes of y = 3x + 2 and 2y = 6x - 6 are equal.

i.e. m₁ = m₂ → 3 = 3

Thus, the lines y = 3x + 2 and 2y = 6x - 6 are paralle.

8x - 2y = 3

simplifying to write in slope-intercept form

y = 4x - 3/2

Comparing with y=mx+b, the slope of y = 4x - 3/2:

m₁=4

x + 4y = - 1

simplifying to write in slope-intercept form

y=-1/4x-1/4

Comparing with y=mx+b, the slope of y=-1/4x-1/4:

m₂=-1/4

m₁ × m₂ = -1

4 × - 1/4 = -1

-1 = -1

Thus, the lines 8x - 2y = 3 and x + 4y = - 1 are perpendicular.

3x+2y = 5

simplifying to write in slope-intercept form

y = -3/2x + 5/2

Comparing with y=mx+b, the slope of y = -3/2x + 5/2:

m₁=-3/2

3y + 2x = - 3

simplifying to write in slope-intercept form

y = -2/3x - 1

Comparing with y=mx+b, the slope of y = -2/3x - 1:

m₂=-2/3

As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.

y - 5 = 6x

simplifying to write in slope-intercept form

y=6x+5

Comparing with y=mx+b, the slope of y=6x+5:

m₁=6

y - 6x = - 1

simplifying to write in slope-intercept form

y=6x-1

Comparing with y=mx+b, the slope of y=6x-1:

m₂=6

As the slopes of y - 5 = 6x and y - 6x = -1 are equal.

i.e. m₁ = m₂ → 6 = 6

Thus, the lines y - 5 = 6x and y - 6x = -1 are paralle.

y = 3х + 9

Comparing with y=mx+b, the slope of y = 3х + 9:

m₁=3

y = -1/3x - 4

Comparing with y=mx+b, the slope of y = 1/3x - 4:

m₂=1/3

As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.

8 0

3 years ago

The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 21 people reveals the mean yearly consum

PIT_PIT [208]

Correct question is;

The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 21 people reveals the mean yearly consumption to be 74 gallons with a standard deviation of 16 gallons.

a. What is the value of the population mean? What is the best estimate of this value?

b. Explain why we need to use the t distribution. What assumption do you need to make?

c. For a 90 percent confidence interval, what is the value of t?

d. Develop the 90 percent confidence interval for the population mean.

e. Would it be reasonable to conclude that the population mean is 68 gallons?

Answer:

A) Best estimate = 74 gallons

B) because the population standard deviation is unknown. The assumption we will make is that the population follows the normal distribution.

C) t = 1.725

D) 90% confidence interval for the population mean is (67.9772, 80.0228) gallons

E) Yes

Step-by-step explanation:

We are given;

Sample mean; x' = 74

Sample population; n = 21

Yearly Standard deviation; s = 16

A) We are not given the population mean.

So the closest estimate to the population mean would be the sample mean which is 74.

B) We are not given the population standard deviation and as such we can't use normal distribution. So what is used when population standard deviation is not known is called t - distribution table. The assumption we will make is that the population follows the normal distribution.

C) At confidence interval of 90% and DF = n - 1 = 21 - 1 = 20

From t-tables, the t = 1.725

D) Formula for the confidence interval is;

x' ± t(s/√n) = 74 ± 1.725(16/√21) = 74 ± 6.0228 = 67.9772 or 80.0228

Thus 90% confidence interval for the population mean is (67.9772, 80.0228) gallons

E) 68 gallons lies within the range of the confidence interval, thus we can say that "Yes, it is reasonable"

8 0

3 years ago

reasoning: if you know that 9 x 20 = 180, how can you use this to find 9 x 24? explain your strategy.

Lostsunrise [7]

9 * 20 = 180

24 has 4 more than that, so multiply 9 to 4 and add it to 180.

9 * 4 = 36

180 + 36 = 216

So 9 * 24 = 216

4 0

3 years ago

Read 2 more answers

If your dog eats 7/8 lb of food in 4 meals,how many meals will take your dog to eat 1 lb of food

Naddik [55]

I would say 5 meals. 7/8 =.875. .875/4=.218. .218+.875=1.09 so the dog would eat 1.09 lb ofdog foodafter 5 meals

8 0

4 years ago

Which is the graph of the system of inequalities

Leni [432]

Answer:

Step-by-step explanation:

Try testing each graph by picking a point on the shaded region or none shaded region.

-1/5 and 6= y-intercept

4/5 and 2= slope

You may notice that it is in y-intercept form. So to find where the shaded region goes, test a coordinate and apply it to the equation, if the answer is false, than half of the line is not where the shaded region goes.

6 0

3 years ago