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3 years ago

WHAT IS THE CORRECT SCALE FACTOR?

Mathematics

1 answer:

topjm [15]3 years ago

3 0

Answer:

3/7

Step-by-step explanation:

To find the scale factor we have to compare the initial points to the final points, we can do this by observing only one corner of the triangle, as it will apply to the entire triangle.

Let's look at C and C'

The coordinates of C are (7,-7)

The coordinates of C' are (3,-3)

To make things simpler let's find the relationship between our x-coordinates, then test it on our y-coordinates

We essentially have to find what 7 is multiplied by to get 3, we'll make an equation

7x=3

Solve for x by dividing both sides by 7

x=3/7 <------- This shows that our scale factor in this case is 3/7

Now we will test this on our y-coordinates

-7(3/7)=-3

$\frac{-7(3)}{7}$ =-3?

The 7's on the top and bottom simplify to -1

-1(3)=-3?

-3=-3 <------- This is true! So we know this is our scale factor for the entire triangle

Hope I could help!

-Kaylyn

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Find all real solutions of the equation. (if there is no real solution, enter no real solution.) 35x2 12x − 36

solmaris [256]

Important: 35x2 12x − 36 is not an equation; to obtain an equation, you must set 35x2 12x − 36 = to 0:

35x^2 + 12x − 36 = 0. Also, "the square of x" must be represented by "x^2," and you must insert either the + or the - sign in front of the term 12x.

I am assuming that you meant 35x^2 + 12x − 36 = 0.

If that is indeed the case, then a = 35, b = 12 and c = -36

and the discriminant is b^2 - 4ac, or (12)^2 - 4(35)(-36) = 5184.

Since the discriminant is positive, this equation has 2 real, unequal solutions. They are
-12 plus or minus sqrt(5184)
x = -----------------------------------------
2(35)

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3 years ago

Expand & simplify: (x + 1)(x + 3)

Sindrei [870]

Answer:

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Step-by-step explanation:

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4 years ago

Read 2 more answers

The realtor and her clients do not know the average home sale price for all of Guelph (500 was actually just a guess). However,

strojnjashka [21]

Answer:

a) The 99% confidence interval would be given by (346.708;453.292)

b) The 99% confidence interval would be given by (338.445;461.555)

Step-by-step explanation:

1) 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".

$\bar X=400$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=80$ represent the population standard deviation

n=15 represent the sample size

2) Part a

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

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: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

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

$400-2.58\frac{80}{\sqrt{15}}=346.708$

$400+2.58\frac{80}{\sqrt{15}}=453.292$

So on this case the 99% confidence interval would be given by (346.708;453.292)

3) Part b

For this case we don't know the population deviation so we need to use the t distribution instead the normal standard distribution.

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

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

We need to find the degrees of freedom first df=n-1=15-1=14

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(0.005,14)".And we see that $t_{\alpha/2}=2.98$

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

$400-2.98\frac{80}{\sqrt{15}}=338.445$

$400+2.98\frac{80}{\sqrt{15}}=461.555$

So on this case the 99% confidence interval would be given by (338.445;461.555)

4 0

3 years ago