If the two legs of a right triangle are 15 and 20, how long is the hypotenuse?

Problem 1

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Explanation:

The notation A U B means we're applying a union between A and B. This will form a larger set in which items from A or B are thrown into A U B. Think of "union" as in getting married, and person A's stuff is combined with person B's stuff to form a larger set. Any duplicates are tossed. It's often helpful to sort from smallest to largest.

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Problem 2

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Explanation:

Set C is defined as the set of prime numbers less than or equal to 20. The roster form is C = {2,3,5,7,11,13,17,19} which basically lists every item that fits the description earlier. Note how the value 1 is not prime, so it's not in the set C.

From here, we simply count out the values in set C to find there are 8 values. Therefore, n(C) = 8.

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Problem 3

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Explanation:

Let's consider a real world example of set vs subset. Consider the set of all animals and consider the subset of all dogs. Let's say

A = all animals

B = all dogs

We can see that set A is clearly larger than B. Also, any member of set B is also in set A, but not the other way around. In other words, if something is a dog, then they are also an animal. However, this doesn't work the other way around. For instance, we could have a cat in set A that wouldn't be in set B.

Let's return to the problem at hand. Since B is a subset of A, this must mean everything in B = {2,12,x,9} is found in set A. Sure enough, the 2, 12 and 9 are all in set A. The x must also be a value in set A so we could have

x = 3

x = 4

x = 5

x = 6

x = 7

as our possible answers. I'm not listing x = 2, x = 9 or x = 12 as they have been taken care of. I'm assuming that your teacher wants {2,12,x,9} to list unique items (ie it's after the duplicates are tossed out).

The transformation that maps the pre-image to the image is given as follows:

Dilation.

The four types of transformation listed in this problem cause these following changes:

From the image, we get that the side lengths were doubled, while the angle measures remained constant, meaning that the transformation is a dilation and the first option is the correct option.

More can be learned about transformations at https://brainly.com/question/28792248

#SPJ1

Answer:

dilation

Step-by-step explanation:

took the test

By using the corresponding angles theorem we can see that (6x - 5)° and (x - 25)° are supplementary angles, so they add up to 180°.

This means that:

(6x - 5) + (x - 25) = 180

7x - 30 = 180

7x = 210

x = 30

If you want to find the exact values of the angles, just plug x = 30 into the angle values! :)

Answer:

y = 3x + 7

Step-by-step explanation:

When lines are parallel, the slope is the same but the y-intercept is not

The blue line is the graph for y = 3x + 2

The slope for the line is 3/1

So the slope for the line containing (-2,1) should be 3/1

I plotted (-2,1) and used the Rise/Sun (3/1) to find a point on the y-axis, the teal point.

I graphed the line in yellow

In y=mx + b, b = 7, and mx = 3x

So the equation is y = 3x + 7

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

not possible because the area of a square is always a square of it's length and a square cannot be a prime number

Answer:

No

Step-by-step explanation:

Because the area of a square is always a square of its length and a square can't be prime.

Answer:

Cos Z = 7/25

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos Z = 14/50

Cos Z = 7/25

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

As the [tex]\triangle\sf{XYZ}[/tex] is a right angle traingle.

we know that,

[tex]\boxed{\underline{\sf{cos\blue{\theta}=\dfrac{adjacent}{hypertension} }}}[/tex] 

According to the question,

[tex]cosZ=\dfrac{adjacent}{hypertension}\\\\cosZ=\dfrac{14}{50}\\\\\pmb{\green{\sf{cosZ}=\frak{\dfrac{7}{25}}}}[/tex] 

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

the students took math and physics = 55

Answer:

2 [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

5 ÷ 4 = 1 [tex]\frac{1}{4}[/tex]

1 [tex]\frac{1}{4}[/tex] × 2 = 2 [tex]\frac{2}{4}[/tex] = 2 [tex]\frac{1}{2}[/tex]

5 - 2 [tex]\frac{1}{2}[/tex] = 2 [tex]\frac{1}{2}[/tex]

respuesta: 2 [tex]\frac{1}{2}[/tex]

Answer:

We know he spent 5 sixths which is 50 minutes

Ten percent of 50 is 5

This means he spent 3 quarters of an hour in the office

Answer:

Sam spent 50 minutes at the office, and 1/10 (or 5 minutes) in the waiting room.

So, he spent 3/4 of an hour at the office but not in the waiting room.

Let me know if this helps!

Answer:

0.8716 = 87.16% probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they order a nonalcoholic beverage, or they order an alcoholic beverage. The probability of a customer ordering a nonalcoholic beverage is independent of any other customer, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

At a Noodle & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 0.43.

This means that [tex]p = 0.43[/tex]

Find the probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.

This is:

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{7,0}.(0.43)^{0}.(0.57)^{7} = 0.0195[/tex]

[tex]P(X = 1) = C_{7,1}.(0.43)^{1}.(0.57)^{6} = 0.1032[/tex]

[tex]P(X = 2) = C_{7,2}.(0.43)^{2}.(0.57)^{5} = 0.2336[/tex]

[tex]P(X = 3) = C_{7,3}.(0.43)^{3}.(0.57)^{4} = 0.2937[/tex]

[tex]P(X = 4) = C_{7,4}.(0.43)^{4}.(0.57)^{3} = 0.2216[/tex]

Then

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0195 + 0.1032 + 0.2336 + 0.2937 + 0.2216 = 0.8716[/tex]

0.8716 = 87.16% probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.

Answer:

Each dog has 2 ears (unless a dog had genetic disorder)

So-

14 x 2

= 28

So she counted of 28 Ears of total

(honestly that's a weird thing to do but ok)

Answer:

14 x 2 = 28

Step-by-step explanation:

Each dog has 2 ears

14 dogs has 28 ears

Answer:

(x-5)(x+2)(x+4)

Step-by-step explanation:

I just did It

Answer:

First find the coordinates of the vertices. A=(-8,8), B=(-8,3) and C=(-4, 4). Next apply transformation, A'=(2, 2), B=(2, - 3) and C=(6, - 2). Next map this and join them to get the required triangle

Answer:

One of the scenarios:

Answer:

14. x=16, 15. x=9

Step-by-step explanation:

14.

4x+4=7x-44 by alternate exterior angles

3x=48

x=16

15.

15x-26=12x+1 by alternate exterior angles

3x=27

x=9

Answer:

The final solution is 2.

y ÷ 2 + x ; use x = 1 and y = 2

(2) ÷ 2 + (1)  -----> divide 2 by 2

1 + 1 ----> add the quotient of 2/2 to 1

2 ---> answer

Answer:

2

Step-by-step explanation:

(To make this easier I will put this in steps)

Step 1 : Substitute

As you can see we are given the amount the variable stands for so we can simply just substitute them out...

y / 2 + x  OR  2 / 2 + 1

Step 2 : Solve

Now that there are no variables this should now be pretty simple to solve.

2/2 = 1 so...

1 + 1

Then you would add them and get 2

y / 2 + x = 2

Hope this helps :)

Answer:

40 feets

Step-by-step explanation:

Given that :

Person's height = 5feet 6 inches ;

Person's height in inches ;

1 foot = 12 inches ;

5 feets = (12 * 5) = 60 inches

Person's height = 60 + 6 = 66 inches

Height of person's shadow = 16.5 inches

Height of post shadow = 120 inches

Height of goal post = x

(Height of goal post / height of post shadow) = (person's height / person's shadow)

x / 120 = 66 / 16.5

Cross multiply :

16.5x = 120 * 66

16.5x = 7920

x = 7920 / 16.5

x = 480 inches

To feets ;

1 foot = 12 inches

480 inches = 480/12 feets = 40 feets

Answer:

here,

3x-3x=

[tex] {x}^{2} - {x}^{2} [/tex]

x=0

Answer: The missing number is 73

Step-by-step explanation:

Given:

4, 6, 9, 14, 23, 40, ?, 138, 266

Solve:

First, we try arithmetic patterns.

6 - 4 = 2

9 - 6 = 3

14 - 9 = 5

23 - 14 = 9

40 - 23 = 17

Clearly, there aren't arithmetic patterns.

Then, try through multiplication, exponents, and combination.

Finally, the pattern is multiplied by 2 on each number, then subtract 2 starting with 4 and add 1 for each increasing number.

4×2-2=6

6×2-3=9

9×2-4=14

As it goes on, the missing number would be:

40×2-7=73

Hope this helps!! :)

Please let me know if you have any questions

Area = pi x r^2

R = 7/2 = 3.5

Area = 3.14 x 3.5^2

Area = 38.5 m^2

(3x/6) + 2 = 8

=> 3x/6 = 8 - 2

=> 3x/6 = 6

=> 3x = 6 × 6

=> 3x = 36

=> x = 36/3

=> x = 12

Answer:

x=12

Step-by-step explanation:

3x/6+2=8

3x/6=8-2

      =6

3x/6(6)=6(6)

3x=36

x=12

Answer:

MO, NO, MN

Step-by-step explanation:

First, we can identify this triangle as a right triangle, as given by the square next to the O. Next, we know that a right angle is equal to 90 degrees, and the sum of the angles of a triangle is equal to 180 degrees.

Therefore,

∠M + ∠O + ∠N (the angles of the triangle) = 180

49 + 90 + ∠N = 180

139 + ∠N = 180

subtract both sides by 139 to isolate the variable

∠N = 41

Therefore, ∠N is 41 degrees.

In a triangle, given the angles, we know that the side opposite the smallest angle is the side with the smallest length and so on.

Our angle lengths are

41, 49, and 90 degrees in order.

Therefore, the side opposite the largest angle (90 degrees, or ∠O) is the longest side. This is MN. Similarly, ∠N is the smallest angle, and the side opposite of that (MO) is the shortest side. This leaves NO to be in the middle

Answer:

x=19°

Step-by-step explanation:

Line n and l form a right angle. We know that because line m and l are parallel to each other and line n crosses through them as a vertical line.

Right angles always add up to 90°.

So, Angle 1 add Angle 2 equals 90°.

4x+9+x-14=90°

Collect the like terms:

Like terms are terms with the same variables and powers.

4x+x=5x

9-14= -5

Form an equation:

5x-5=90°

Do inverse operations to isolate x.

90+5=95°

95÷5=19° (We divide by 5 because, in algebra, when a number is next to a letter, it means times, so we have to do the opposite and divide).

So, x=19°

Hope this helps :)

Answer:

$84.60

Step-by-step explanation:

$84.60 is what david will earn in 9 hours becuz 9.40 times 9 is 84 dollars and 60 cents

Answer:

50m

Step-by-step explanation:

speed (m/s2) = distance (m) ÷ time (s)

distance = speed (m/s2) x time (s)

1x20 =20m.

30s = 30m because they do 1 meter per second (every second)

50m in total if not counting the constant for half a hour.

Answer:

[tex]{ \sf{ {(x - 2)}^{2} + {(y + 8)}^{2} = 4}}[/tex]

Answer:

Center is (2, -8) and radius =2

h = 2 and k = -8

Filling in this equation:

(x -h)² + (y -k)² = radius²  we get:

(x - 2)^2 + (y--8)^2 = 2^2 which equals

(x-2)^2 + (y +8)^2 = 4

Source: http://www.1728.org/circleqn.htm

Step-by-step explanation:

Answer:

0.04

Step-by-step explanation:

2 / 50 is the same as 1 / 25.

1 / 25 = 0.04

Answer:

0.04

Step-by-step explanation:

When a line is rotated, it is rotated about a fixed point to its new position. Line AB must turn 180 degrees about point A to coincide with line AE.

The complete question is that we determine the angle which AB will turn to, about point A to align with AE (see attachment for the figure)

Line AB and AE form a straight line. This means that the angle between these two lines on either side of point A is [tex]180^o[/tex]

So for line AB to coincides with line AE, the line AB must turn 180 degrees about point A.

Hence, option (B) is correct.

Read more about rotation of points at:

https://brainly.com/question/22363471

Answer:

The forms are:

Given:

Use point slope form:

Convert it to slope-intercept form:

Convert it to standard form:

Answer:

3x-28 = 80

3x = 108

x = 36

Let me know if this helps!