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2 years ago

The graphs below have the same shape. Complete the equation of the blue

Mathematics

1 answer:

NeTakaya2 years ago

8 0

The answer : (x-5)^2 .....................................(x-5)square

For example, for f(x)= x square . For x=1 ,then, y=1 .

But consider the g function. the minimum value that g function has is x is 5. When x is 5, y is 0 . So (x-5)square is the equation of this function.

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Zac and Lynn are each traveling on a trip. So far, Zac has traveled 123.75 miles in 2.25 hours. Lynn leaves half an hour after Z

Savatey [412]

Complete question is;

Zac and Lynn are each traveling on a trip. So far, Zac has traveled 123.75 miles in 2.25 hours. Lynn leaves half an hour after Zac. So far

she has traveled 105 miles in 1.75 hours. Assume Zac and Lynn travel at constant rates.

Let a represent the number of hours that have elapsed since Zac started traveling. Let y represent the number of miles traveled. Write a system of linear equations that represents the distance each of them has traveled since Zac left on his trip.

Assume Zac and Lynn continue to travel at the same constant rates and make no stops.

Determine the solution of the system of linear equations.

Answer:

Zac: y = 55a

Lynn: y = 60(a - ½)

6 hours after Zac started traveling, both Zac and Lynn would have covered 330 miles each.

Step-by-step explanation:

Zac has traveled 123.75 miles in 2.25 hours. Since he travels at constant speed, we can say;

zac's speed = 123.75/2.25 = 55 mi/hr

Similarly, Lynn traveled 105 miles in 1.75 hours. Thus, since she travels at a constant speed;

Lynn's speed = 105/1.75 = 60 mi/hr

Now, we are told that a represents the number of hours that have elapsed since Zac started traveling and y represents the number of miles traveled.

Thus;

a hours after Zac started travelling, his distance covered will be;

Zac: y = 55a

Now,for Lynn, since she started ½ an hour after Zac, it means a hours after Zac started, she had traveled (a - ½) hours.

Thus, Lynn's distance traveled after Zac started = 60(a - ½)

Lynn: y = 60(a - ½)

The solution will be when they have travelled equal distances a hours after Zac started. Thus;

55a = 60(a - ½)

55a = 60a - 30

60a - 55a = 30

5a = 30

a = 30/5

a = 6 hours

Putting 6 for a in y = 55a, we have;

y = 55 × 6

y = 330 miles

5 0

2 years ago

Which graph represents the function f(x) = (x – 5)2 + 3?

goblinko [34]

The function
$f(x)=(x-5)^2+3$
describes a parabola with vertex = (5, 3).

The graph of the function is attached.

4 0

2 years ago

Read 2 more answers

Carl scored 32 on the ACT mathematics Test and 730 on the mathematics portion of the SAT. If the ACT Math Test had a mean score

Shtirlitz [24]

Answer:

Carl's ACT grade had a higher z-score, which means that he earned a better score with respect to his peers on the ACT test.

Step-by-step explanation:

Z-score

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

On which exam did Carl earn a better score with respect to his peers?

On whichever exam he had the higher z-score.

SAT

Scored 730, mean 516, standard deviation 116. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{730 - 516}{116}$

$Z = 1.84$

ACT

Scored 32, mean 21, standard deviation 5.3. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{32 - 21}{5.3}$

$Z = 2.08$

Carl's ACT grade had a higher z-score, which means that he earned a better score with respect to his peers on the ACT test.

4 0

2 years ago

Which of the following equations correctly represents the law of sines?

aev [14]

The Law of Sines may be written as
b/sin(B) = c/sin(C)

Multiply each side by sin(B).
b = (c*sin(B))/sin(C)

The correct answer is C.

Answer: C. (c*sin B)/sin C

5 0

2 years ago

Kiley gathered the data in the table. She found the approximate line of best fit to be y = 1.6x – 4.

mihalych1998 [28]

The difference between the observed value of the dependent variable (y) and the predicted value (ŷ) is called the residual (e). When x is equal to 3, the value of y from the best fit line would be 0.8. Therefore, the residual would be -1 - 0.8 = -1.8. Option A is the correct answer.

7 0

2 years ago

Read 2 more answers