Two trees standing side by side in the sunlight one is 50 feet tall and the other is 20 feet tall if the taller tree casts a 18-foot shadow, what is the length in feet of the shadow of the shorter tree

Answer:

A. a = 10

B. m<FNT = 120°

C. m<KTU = 60°

Step-by-step explanation:

A. (7a + 50)° and (14a - 20)° are corresponding angles. Therefore:

(7a + 50)° = (14a - 20)°

Use this equation to find the value of a

7a + 50 = 14a - 20

Combine like terms

7a - 14a = - 50 - 20

-7a = -70

Divide both sides by -7

-7a/-7 = -70/-7

a = 10

B. m<FNT = (14a - 20)° (alternate interior angles are congruent)

Plug in the value of a

m<FNT = 14(10) - 20

m<FNT = 140 - 20

m<FNT = 120°

C. m<KTU + (14a - 20)° = 180° (linear pair)

Plug in the value of a

m<KTU + 14(10) - 20 = 180

m<KTU + 120 = 180

m<KTU + 120 - 120 = 180 - 120

m<KTU = 60°

Answer: The probability of Dana selecting a hockey card will be a 4/36 or 1/9.

Work:

1.I added all of the cards together.

2.I saw that the number of hockey cards was 4 and divided it by 36 (the total number of cards)

3.Simplified

Answer:

Step-by-step explanation:

Trapezoid 1 with vertices

and

Trapezoid 2 with vertices

It can be observed by comparison that:

and

So the rule of translation is:

Answer:

Step-by-step explanation:

another way is by graphing. (see attached)

the translation is:

   3 units right, 2 units down.

or (x, y) = (x + 3, y - 2)

Answer:

4

Step-by-step explanation:

I am assuming you mean (-2)^2 and not -(2)^2, correct.

If i m wrong in the assumption and its the latter one, then it is -4 since you are taking the - of 4

Answer:

Step-by-step explanation:

[tex]-2^2=-4\ \text{because}\ -2^2=-(2\cdot2)=-4\\\\(-2)^2=4\ \text{because}\ (-2)^2=(-2)(-2)=4[/tex]

The parentheses are very important here.

The same in

[tex]\dfrac{2}{3}^2=\dfrac{4}{3}\\\\\left(\dfrac{2}{3}\right)^2=\dfrac{4}{9}[/tex]

Given parameters:

Length of the suitcase  = 24 inches

Length of the diagonal = 30 inches

Unknown:

Length of zipper required to cover the perimeter  = ?

The length of this zipper is the same as the perimeter of the rectangular suitcase.

  Perimeter of a rectangle  = 2(L + B)

where L is the length and B is the breadth

Now, let us find the find the unknown breadth;

  Using Pythagoras theorem;

           30²  = 24² + Breadth²

            Breadth²  = 30² - 24²  = 324

             Breadth = √324  = 18 inches

Perimeter of the suitcase  = 2(24 + 18)  = 84 inches.

The length of zipper that will cover this suitcase is 84inches.

Answer:

x=1.6

y=4.8

z=9

Step-by-step explanation:

Answer:

X=12.5

Y=3.2

Z=6

Step-by-step explanation:

idek dwjejdjjriiwknansns

Step-by-step explanation:

nmjwjw

Answer:

Step-by-step explanation:

Least to greatest:

7.083, 7.2, 7.21

Greatest to least:

7.2, 7.2, 7.083

Answer:

Step-by-step explanation:

N=503

P=0.7

Sqrt(503×0.7(1-0.7))=10.28

The standard deviation, for the binomial distribution, is 10.28 which has the stated values of n and p; n =503: p=0.7.

It is defined as the measure of data disbursement, It gives an idea about how much the data is spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

We have:

The value of n = 503

The value of p = 0.7

For the binomial distribution:

As we know,

The formula for the standard deviation:

σ = √[p(1 - p)n]

Plug the values of p, and n, we get:

σ = √[0.7(1 - 0.7)503]

σ = √[0.7(0.3)503]

σ = √[0.21x503]

σ = √[105.63]

σ = 10.277 ≈ 10.28

Thus, the standard deviation, for the binomial distribution is 10.28 which has the stated values of n and p; n =503: p=0.7.

Learn more about the standard deviation here:

brainly.com/question/12402189

#SPJ5

Answer:

g+12/4

Step-by-step explanation:

Answer: True

Explanation: The domain of a quadratic function in standard format is always all real numbers, meaning you can substitute any real number for x. The range of a function is the set of all real values of y that you can get by plugging real numbers into x.

Linear function is almost always going to be all real numbers. The range of a non-horizontal linear function is all real numbers no matter how flat the slope might look.

Answer:

16

Step-by-step explanation:

5x + 2y - 7z    

(x = 2, y = 10, z = 2)

First things first you would want to take the letters that the numbers are equal to and replace them with the numbers.

5(2) + 2(10) - 7(2)

Then you multiply the number that's beside the parentheses, 5(2) is the same as 5 x 2.

5(2) = 10

2(10) = 20

7(2) = 14

so now you have

10 + 20 - 14

10 + 20 = 30

30 - 14 = 16

and 16 is your final answer!

Answer:

g+14=64

Step-by-step explanation:

Answer:

64=14+g

Step-by-step explanation:

Sum of two numbers is 64, so that means you put 64 before the equals sign. All that remains is g and 14. It says the sum of 14 and g (gregs height) equals 64, so you know that in the equation they have to be added together.

Answer:

20 m/s

Step-by-step explanation:

560 m/25 s

=22.4 m/s

≈ 20 m/s ( nearest tenth of m/s )

Answer:

22.4

Step-by-step explanation:

Just divide 560 by 25 .

Answer:

In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole

Answer:

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

Answer:

9:5

ratios are just putting the numbers next to each other with ':' in the middle

Step-by-step explanation:

Answer:

ITS B

Step-by-step explanation:

HOPEFULLY THIS WORKS!!!

Answer:  No solutions.

============================================

Work Shown:

4c + 5 < 4c + 3

4c+5-4c < 4c+3-4c ... subtract 4c from both sides

4c-4c+5 < 4c-4c+3

0c+5 < 0c+3

0+5 < 0+3

5 < 3 ... statement is false

Since that statement is false, this means the original inequality is false regardless of what you pick for c.

There are no solutions.

A relation between two variables a and b is a rule that takes some values a from a domain set and returns some value b in the range set.

The table says that, if you give 0, the relation returns 2. If you give 1, you get 6. If you give 4, you get -9. If you give 8, you get 8 back.

The domain is the set of values the relation can take, so here it is the set {0, 1, 4, 8}.

From the given choices, only 0 belongs to the domain.

Answer:

You already know the answers

Step-by-step explanation:

I did the work to show you how i got there. It took a little time to get there, if you don't understand how i got there, then don't be afraid to ask me a question

Answer:

16, 5, 28

Step-by-step explanation:

1 liter is equal to 4 servings

Answer:

B

Explanation: dont got one

Answer:

4 5/8"

Step-by-step explanation:

quizlet will have all the answers btw

Answer:

2\3x60=40

3\5x20=12

12+40=52

60-52=8

Answer:

x=24

Step-by-step explanation:

HE= 1/3(HG)

x-3=1/3(4x-15)

3x-9=4x-15

-x=-24

x=24

Answer:

HE=3

Step-by-step explanation:

Equations

With the data provided, we can set up an equation. Then we need to solve the equation. Finally, we use the just-found value of x to calculate HE.

Data:

HE=1/3 HG

HE=x-3

HG=4x-15

Replacing the last two equations in the first:

x-3=1/3(4x-15)

Multiply both sides by 3:

3(x-3)=4x-15

Operate:

3x-9=4x-15

Moving x's to the left and numbers to the right:

3x-4x=-15+9

Joining like terms:

-x=-6

Multiply by -1:

x=6

Since HE= x-3:

HE=6-3

HE=3

Answer:

x²+4x+3

Step-by-step explanation:

(x+1)(x+3)

x²+3x+1x+3

x²+4x+3