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3 years ago

How do I prove the corresponding angles theorem?

1 answer:

8 0

The Corresponding Angles Theorem states: If two parallel lines<span> are cut by a </span>transversal<span>, then the </span>pairs<span> of corresponding angles are </span>congruent.
A theorem is aproven<span> statement or an </span>accepted<span> idea that has been shown to be true.</span>

You might be interested in

If a Tyrannosaurus rex ate 3 dinosaurs each week, how many would he eat in 9 weeks?

Dafna11 [192]

Answer:

Step-by-step explanation:

3/1=x/9

cross multiply, or its just a ratio actually. 1:3 is equal to 9:27

8 0

3 years ago

Answer if u know both plzz help

NARA [144]

4) Answer is D.
Irrational numbers cannot be classified as rational numbers

5) Answer is B.
Every irrational number is a real number

4 0

3 years ago

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customer

AlladinOne [14]

Answer:

$4-2.326\frac{1}{\sqrt{100}}=3.767$

$4+2.326\frac{1}{\sqrt{100}}=4.233$

So on this case the 98% confidence interval would be given by (3.767;4.233)

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".

$\bar X=4$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=1$ represent the population standard deviation

n=100 represent the sample size

Solution to the problem

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 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that $z_{\alpha/2}=2.326$

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

$4-2.326\frac{1}{\sqrt{100}}=3.767$

$4+2.326\frac{1}{\sqrt{100}}=4.233$

So on this case the 98% confidence interval would be given by (3.767;4.233)

4 0

3 years ago

The book store is having a sale where all hardcover books are 20% off. Jamie also has a coupon for 15% off any fiction book. Jam

scoray [572]

You can use the fact that both 20% and 15% discounts will be merged to reduce 35% of the price of the book that Jamie buys.

By buying the book on sale and using the coupon, Jamie will save

Option B: $11.55

<h3>
How are discounts calculated for the case when its sale and we've got discount coupons too?</h3>

Suppose the sale gives p% off.

And the discount coupon provides q% off.

Then we have total discount applied on the cost of the object bought as

(p+q)%

<h3>How to find the percentage from the total value?</h3>

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

$\dfrac{a}{100} \times b$

<h3>Using the above fact to calculate the amount that Jamie saved </h3>

Since the sale offers 20% discount and Jamie has got 15% discount coupon for any fiction book, thus, total 35% will be discounted if Jamie buys fiction book.

Since the price of the fiction book that Jamie brought is $32.99, thus,

Saved amount = 35% of $32.99 = $\dfrac{32.99}{100} \times 35 = 0.3299 \times 35 \approx \$11.55$

Thus,

By buying the book on sale and using the coupon, Jamie will save

Option B: $11.55

<h3 />

Learn more about percentage here:

brainly.com/question/11549320

5 0

2 years ago

Good strategy for using slope formula

Fantom [35]

I personally use y2-y1 over x2-x1 because it's simple. Plot two y values and two x values. The first ones you plotted are x1 and y1, the others are x2 y2. Now subtract y2-y1 and x2-x1. Afterwards, divide the y value by the x value, that will give you slope.

3 0

3 years ago