please answerrr this is a college course im taking
Mrs. Hartley gave her students a choice
board with 16 projects in which they each
had to pick three. How many ways could a
student choose three projects?
A. 560
C. 2,304
D. 3,360
B. 48

Answer:

Step-by-step explanation:

We know that the angle of elevation is 8 degrees.

We know that the height of the opposite side of the angle is 3 feet.

We want to know the adjacent side (the side from the start of the ramp to the bottom of the opposite side)

We can do this with tangent

[tex]tan(8) = \frac{3}{adj} \\adj = \frac{3}{tan(8)} \\adj = 21.34611 feet[/tex]

The distance between the ramp and the door can be calculated using the principle of Pythagoras, Hence, the distance should be 21.34 feets

Using SOHCAHTOA :

Tanθ = Opposite / Adjacent

Tan(8°) = 3 / d

0.1405408 = 3 / d

0.1405408d = 3

Divide both sides by 0.1405408 to isolate d

0.1405408d / 0.1405408 = 3 / 0.1405408

d = 21.34 feets

Therefore, the distance of the ramp from the door should be 21.34 feets

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Answer:y=28

Step-by-step explanation:

40+3y+2y=180

Subtract 40

3y+2y=140

Combine like terms

5y=140

Divide

y=28

Answer: 1433.65

Step-by-step explanation:

315.83+412.60 +412.60 +412.60 -40 -40 -40= 1433.65

Answer:

√33

Step-by-step explanation:

In the image .

The expression (6 + √3) (6 - √3) / √33 upon  rationalizing the denominator gives √33.

Square root of a number is the value such that upon multiplying the value by itself twice gives the original number.

The given expression is (6 + √3) (6 - √3) / √33

We have the identity,

(a + b) (a - b) = a² - b²

∴ (6 + √3) (6 - √3) / 33 = 6² - (√3)² / √33

                                     = (36 - 3) / √33

                                     = 33 /√33

Multiplying numerator and denominator by √33,

(6 + √3) (6 - √3) / 33 = (33 × √33)  / (√33 × √33)

                                   = 33√33 / 33

                                   = √33

Hence upon rationalizing the denominator in the expression (6 + √3) (6 - √3) / 33 yields √33.

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Answer:

r = 16

Step-by-step explanation:

Cross multiply:

4 x 20 = r x 5

Simplifying

4 x 20 = r x 5

Multiply 4 x 20

80 = r x 5

Reorder the terms for easier multiplication:

80 = 5r

Solve

80 = 5r

Solve for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-5r' to each side of the equation.

80 + -5r = 5r + -5r

Combine like terms: 5r + -5r = 0

80 + -5r = 0

Add '-80' to each side of the equation.

80 + -80 + -5r = 0 + -80

Combine like terms: 80 + -80 = 0

0 + -5r = 0 + -80

-5r = 0 + -80

Combine like terms: 0 + -80 = -80

-5r = -80

Divide each side by '-5'.

r = 16

Simplify

r = 16

Answer:

7x-117

Step-by-step explanation:

1. Distribute the 5 to the terms in parentheses.

5x-120+2x+3

2. Combine like terms.

7x-117

Hi there!

[tex]\large\boxed{f(4) = 33}[/tex]

f(x) = -3x² + 11x + 37

Substitute in 4 for x to find f(4):

f(4) = -3(4)² + 11(4) + 37

f(4) = -3(16) + 44 + 37

f(4) = -48 + 44 + 37

f(4) = 33

Answer:

Step-by-step explanation:

I don't understand what the numbers before the language mean. I will answer the questions that have a definite language.

12 = 2 * 2 * 3

16 = 2 * 2 * 2 * 2

The answer is going to require you have 4 fours and one 3

2 * 2 * 2 * 2 * 3 = 48

24 = 2 * 2 * 2 * 3

36 = 2 * 2 * 3 * 3

The answer is going to require two threes and three 2s

2 * 2 * 2 * 3 * 3 = 72

What is this word  numharthotic

26 = 2 * 13

49 = 7 * 7

The smallest number that can be divided by both with no remainder is

2 * 7 *7 * 13 = 1276

Answer:

yes

Step-by-step explanation:

l,l,;,;,;,;l,;,;

Step-by-step explanation:

x intercept is when y = 0 and y intercept is when x = 0 hence, x intercept is : x = -56 hence (-56, 0) and y intercept is: 4y = -56 y = -14 hence (0, -14)

Topic: coordinate geometry

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

Answer:

y = -7x + 26

I checked it on Desmos

Answer: 3(5x+27)

Step-by-step explanation:

15 and 81 are both divisible by 3.

Answer:

-5.4

Step-by-step explanation:

x= -81/15= -5.4

Answer:

should be -4

Step-by-step explanation:

Answer: Length of shorter tree = 7.2 feet .

Step-by-step explanation:

Given : Height of two trees as 50 feet and 20 feet.

At same time the angle made by sun rays would be same for both trees.

Both trees are vertical to the ground making right angle so triangles made by both triangles must be similar.

Corresponding sides of similar triangles are proportional.

So [tex]\dfrac{\text{length of the shadow of the shorter tree}}{\text{height of shorter tree}}=\dfrac{\text{length of the shadow of the bigger tree}}{\text{height of bigger tree}}\\\\=\dfrac{\text{length of the shadow of the shorter tree}}{20}=\dfrac{18}{50}\\\\\Rightarrow\ \text{length of the shadow of the shorter tree}=\dfrac{18}{50}\times20\\\\\Rightarrow\ \text{length of the shadow of the shorter tree} = 7.2[/tex]

So, Length of shorter tree = 7.2 feet .

Answer:

10.357

Step-by-step explanation:

h=145 =10.357

14

hope this helps:)

Answer:

it is D

(1.5-6)/-2-4 =0.75

Answer: I need to see the picture of the work first to tell u

Step-by-step explanation:

Answer:

Slope: -1/4, y-intercept: -2.

Step-by-step explanation:

The line intersects the y-axis at -2. This means that the y-intercept is -2. The slope is -1/4 because since the slope is rise over run, you go up one and then to the left 4 from the y-intercept. When you do this you see that from both A to B, you will end up on the same line.

Hope this helps!

Answer:

C

Step-by-step explanation:

slope = -1/4

y-intercept = -2

Answer:

No this is not arithmetic this is geometric

Step-by-step explanation:

10 to 15 is a increase of 5

15 to 21 is a increase of 6

21 to 28 is a increase of 7 arithmetic have to have steady increases

Answer:

Hola!

Step-by-step explanation:

Answer:

This graph is not a function.

Step-by-step explanation:

For every x value, it has more than one y value. The graph also doesn't pass the vertical line test.

Answer:

Not a function

Step-by-step explanation:

It fails the vertical line test. 2 points can not cross on this test

Answer: 15

Step-by-step explanation:

suppose;  three consecutive odd integers are x; x + 2; x+ 4 (x is a odd integer)

because Five times the second of three consecutive odd integers is thirteen less than three times the sum of the first and third integers

=> 5(x + 2) = 3( x +x +4) - 13

<=> 5x + 10 = 6x + 12 - 13

<=>6x - 5x = 10 + 13 - 12

<=> x = 11

=> the largest odd number is 11 + 4 = 15

The largest of the three consecutive odd integers which could be written as a, a+2 and a + 4 is 15

Let the integers be : a, a + 2, a + 4

Creating a mathematical equation using the scenario given.

5(a + 2) = 3(a + (a + 4)) - 13

Open the bracket bracket

5a + 10 = 3(2a + 4) - 13

5a + 10 = 6a + 12 - 13

5a + 10 = 6a - 1

Collect like terms

5a - 6a = - 1 - 10

-a = - 11

a = 11

The largest integer = a + 4 ; 11 + 4 = 15

Therefore, the largest of the consecutive odd integers is 15

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Answer:   The scale is 5/4

Step-by-step explanation:

To determine the scale factor, you have to locate which sides are similar to each other .

the side length with 20 is congruent to 16

15 is similar to 12    and 10 is similar to 8.

And to get from triangle A to triangle B of any side length, we need to multiply by a certain number which is the scale factor.

And to  find that number we will divide the side length of any side in triangle A  by the similar side to it in triangle B.

20/ 16 = 5/4

15/ 12 =  5 / 4

10 / 8 = 5/4

Answer:

Step-by-step explanation:

Answer:

b= (0,3)

m= 2/3

inequality= y < 2/3x+3

Step-by-step explanation:

b is the y-intercept. the way to find the y-intercept is looking where the line ends up on the y line. m is the slope. the trick to finding the slope is to choose two points and go up then go to the side where the point is. it forms a triangle. count how much it went up and how much you went to the side. then make it rise over run. the inequality works that way since y is 2/3 of x.

Answer:

Debbie's Deals has the better deal with a price of $0.19 per ounce compared to Bill's Bargains at $0.21 per ounce.

Step-by-step explanation:

Divide $3.36 by 16 = $0.21

Divide $7.60 by 40 = $0.19

Debbie's Deals sells the Circle O's cereal for a cheaper per ounce price thus it's the better price and the better deal.

Good luck!

Answer:

37.3°

Step-by-step explanation:

sin β = [tex]\frac{20}{33}[/tex] ⇒ β = arcsin [tex]\frac{20}{33}[/tex] = 37.3°