In sondras math class the teacher gives all of the students the digram below where ab is perpendicular to bc and ac is perpendicular to bd. sondra works with her classmates to prove that triangle abc, triangle abd and triangle bdc are all similiar right triangles. based on the similarity of the three right triangles, show (AB)2 + (BC)2 = (AC)2

Answers

Answer 1

Answer: Given the set up of the diagram, AB^2 will equal AC x AD and BC^2 will equal AC x DC. To solve, substitute AB^2 + BC^2 with (AC x AD) + (AC x DC). Then, take out like terms through the distributive property: AC (AD + DC). AD + DC is equal to AC. So, AC x AC = AC^2.

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If each person takes up 2.25 square feet of space, how many people can fit into an area that is 15 feet by 30 feet?A) 17
B) 40
C) 88
D) 200

Answers

D is the answer Multiply 15 times 30 and divide by 2.25

Answer:

Step-by-step explanation:

What is the relationship among proportional relationships lines, rates of change, and slope?

Answers

First of all, let's define some concepts. In mathematics, proportional relationships happen when two values always change by the same multiple. That is, when one doubles, the other doubles as well. So, you can always reduce a proportional relationship to the same equation as follows:

$y=kx \n where \ k \ is \ the \ proportionality \ constant$

This constant is also the slope of the straight line.

On the other hand, the average rate of change between any two points $(x_(1),f(x_(1)) \ and \ (x_(2),f(x_(2))$ is the slope of the line through the two points. The line through the two points is called the secant line and its slope is denoted as $m_(sec)$ , so:

$ARC=(f(x_(2))-f(x_(1)))/(x_(2)-x_(1)) \n \n \therefore ARC=(Change \ in \ y)/(Change \ in \ x)=m_(sec)$

Finally, The slope of a nonvertical line is the number of units the line rises (or falls)vertically for each unit of horizontal change from left to right, so:

$Slope=(change \ in \ y)/(change \ in \ x)=(rise)/(run)$

So, we can say that the relationship of these three concepts is that they all talk about the slope of a curve.

It introduces the relationship between two variables and is called correlation. Proportionality or variation is state of relationship or correlation between two variables It has two types: direct variation or proportion which states both variables are positively correlation. It is when both the variables increase or decrease together. On the contrary, indirect variation or proportion indicates negative relationship or correlation. Elaborately, the opposite of what happens to direct variation. One increases with the other variables, you got it, decreases. This correlations are important to consider because you can determine and identify how two variables relates with one another. Notice x = y (direct), y=1/x (indirect)

3^x : write in terms of base e and simplify! ...?

Answers

The given function is exponential. Meanwhile $<b>change of base</b>$ has something to do with logarithms. So we convert the function to logarithm function, change to the required base and convert back to exponential function.

Let

$y = {3}^(x)$

Writing the above exponential equation as a logarithmic equation, we obtain;

$log_(3)(y) = x$

We can apply the change of base formula to obtain,

$( log_(e)(y) )/( log_(e)(3) ) = x$

Or

$( ln(y) )/(ln(3) ) = x$

We can cross multiply to obtain;

$ln(y) = x ln(3)$

Taking logarithm of both sides to base e, we obtain;

${e}^( ln(y) ) = {e}^(x ln(3) )$

This implies that,

$y= {e}^(x ln(3) )$
But we know that,
$y = {3}^(x)$
Hence
${3}^(x) = {e}^(x ln(3))$

3^x : write in terms of base e would

3x=e^ln3^x

=e^xln3

See image for question.

Answers

Answer:

See below

Step-by-step explanation:

P(A) = 3/8
P(B) = 2/7

(i)

P(A and B) = P(A) * P(B) = 3/8*2/7 = 3/28

(ii)

P(A or B) = P(A) + P(B) - P(A and B) = 3/8 + 2/7 - 3/28 = 1/56(21 + 16 - 6) = 31/56

(iii)

P(not A and not B) = P(not A) * P(not B) = (1 - 3/8)*(1 - 2/7) = 5/8*5/7 = 25/56

Another way:

P(not A and not B) = 1 - P(A or B) = 1 - 31/56 = 25/56

Outcomes with two fair coins: TT, TH, HT, HH

Outcomes with normal dice: 1 to 6

P(odd number) = 3/6 = 1/2

P(two heads and an even number) = 1/4*3/6 = 1/8

P(head and tail) = 1/2
P(prime) = 3/6 = 1/2 (primes are 2, 3 and 5)
P(head, tail and prime) = 1/2*1/2 = 1/4

P(two tails and odd number) = 1/4*3/6 = 1/8

12, 6, 7, 11, 11, 9, 13, 16, 10. What is the interquartile range of the data set?

Answers

first put the numbers in order
6,7,9,10,11,11,12,13,16

Q1 = (7 + 9) / 2 = 16/2 = 8
Q2 (median) = 11
Q3 = (12 + 13) / 2 = 25/2 = 12.50

Interquartile range (IQR) = Q3 - Q1 = 12.50 - 8.00 = 4.5

Jerome is going to draw a marble from the bag shown below, replace it, and then draw another marble. What is the probability that Jerome will get a green or yellow marble on the first draw and a pink on the second draw?

Answers

The answer is 7/50.

To calculate this, a multiplication rule and an addition rule are used.

There are in total 20 marbles:

3 green + 4 yellow + 5 blue + 8 pink = 20 marbles.

The addition rule is used to calculate the probability of one of the events from multiple pathways. If you want that only one of the events happens, you will use the addition rule. We have two events from multiple pathways:

1. The probability that Jerome will get a green marble on the first draw is 3/20:

Of all 20 marbles, 3 of them are green. The probability that Jerome will get a green marble is 3/20.

2. The probability that Jerome will get a yellow marble on the first draw is 4/20:

Of all 20 marbles, 4 of them are yellow. The probability that Jerome will get a green marble is 4/20.

- Using the addition rule, the probability that Jerome will get a green or yellow marble on the first draw is 7/20:

3/20 + 4/20 = 7/20

The multiplication rule calculates the probability that both of two events will occur. In this method, the probabilities of each event are multiplied. Here we have two events:

1. The probability that Jerome will get a green or yellow marble on the first draw is 7/20.

2. The probability that Jerome will get a pink on the second draw is 8/20:

Of all 20 marbles, 8 of them are pink. The probability that Jerome will get a pink marble is 8/20.

- Using the multiplication rule, the probability that Jerome will get a green

or yellow marble on the first draw and a pink on the second draw is 7/50:
7/20 × 8/20 = 56/400 = 7/50

Answer:

he is correct

Step-by-step explanation:

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