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Tom [10]
3 years ago
12

Please Help! Which description best describes the solution to the following system of equations? y = −x + 4 y = 3x + 3 Line y =

−x + 4 intersects the line y = 3x + 3. Lines y = −x + 4 and y = 3x + 3 intersect the x-axis. Lines y = −x + 4 and y = 3x + 3 intersect the y-axis. Line y = −x + 4 intersects the origin.
Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
7 0

Answer:

Line y = −x + 4 intersects the line y = 3x + 3.

Step-by-step explanation:

Please Help! Which description best describes the solution to the following system of equations?

y = −x + 4

y = 3x + 3

Line y = −x + 4 intersects the line y = 3x + 3.

This is the response because the solution to a system of two equations is represented by the intersection of the equations of the two lines/curves.

Lines y = −x + 4 and y = 3x + 3 intersect the x-axis.

Lines y = −x + 4 and y = 3x + 3 intersect the y-axis.

Line y = −x + 4 intersects the origin.

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Please help!<br> This is mathematics!
Elanso [62]

Answer:

30, 30, 32, 32, 34, 38, 38, 38. Thats how you first need to set it up then what you do is add them all up which would equal to 272. Then you take 272 dived by how many numbers there are (theres 8 numbers) so you do 272/8 which would be 34! So 34 would be your answer.

Step-by-step explanation:

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. You invest £4000 in a fund which earns 11% compound return per year. How much would the fund be worth after 10 years, given th
zmey [24]

Answer: $5,678.85

Step-by-step explanation:

First find out how much the fund was worth after 5 years.

Compound interest formula:

= Investment * (1 + rate) ^ years

= 4,000 * ( 1 + 11%)⁵

= £6,740.23

Half was removed:

= 6,740.23/2

= £3,370.12

Then compound this for the remaining 5 years:

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= $5,678.85

7 0
3 years ago
Two trains leave Cleveland at the same time. One train travels east and the other travels west. The speed of the westbound train
OlgaM077 [116]

Answer:

The eastbound train travels at 92 mph and the westbound train travels at 96 mph.

Step-by-step explanation:

We know that Velocity = distance / time

If the eastbound train travels at x miles per hour, the westbound train travels at x + 4 mph.

After 3.5 hours, they are 658 miles apart. If we solve for distance the formula given above we have: Distance = velocity x time. We have that the total distance between both trains is 658 miles.

Substituting the values of the problem and solving for x we have

658 = 3.5x+3.5(x+4)\\658=3.5x+3.5x+14\\644=7x\\92=x

Thus, the eastbound train travels at 92 mph and the westbound train travels at 96 mph.

6 0
3 years ago
If Upper X overbar equals 62​, Upper S equals 8​, and n equals 36​, and assuming that the population is normally​ distributed, c
marishachu [46]

Answer:

The 99% confidence interval would be given by (58.373;65.627)    

We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X=62 represent the sample mean

\mu population mean (variable of interest)

s=8 represent the sample standard deviation

n=36 represent the sample size  

Part a: Confidence interval

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=36-1=35

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,35)".And we see that t_{\alpha/2}=2.72

Now we have everything in order to replace into formula (1):

62-2.72\frac{8}{\sqrt{36}}=58.373    

62+2.72\frac{8}{\sqrt{36}}=65.627    

So on this case the 99% confidence interval would be given by (58.373;65.627)    

We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.

3 0
3 years ago
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