A group of hikers is progressing steadily along an uphill trail. The graph shows their elevation (or height above sea level), in feet, at each distance from the start of the trail, in miles.

Answer:

x = -5

Step-by-step explanation:

Since these two triangles are similar, the ratio between the corresponding lengths of each triangle will be the same.

This means the ratio between one side of each triangle (e.g. AD and DC) will be the same as the ratio between a different side of each triangle (e.g. BE and BC).

So, to create an equation for the sides which contain the unknown 'x', we must first find the ratio between the two sides by using a different set of sides.

On the right side we are given 9 for AD, and 18 for DC.

9/18 = 0.5

This means that the extra length of the larger triangle from the smaller one (AD) is half the length of the smaller triangle (DC). We can use this to make an equation for x:

If AD/DC = 0.5, then BE/EC will also = 0.5

BE = x+23

EC = x+41

Therefore:

[tex]\frac{x+23}{x+41} = 0.5[/tex]

Now we can solve by multiplying both sides by x+41 to eliminate the fraction:

[tex]x+23=0.5(x+41)[/tex]

Now we multiply out the brackets and move the terms to different sides:

[tex]x+23=0.5x+20.5[/tex]

[tex]0.5x = -2.5[/tex]

[tex]x = -5[/tex]

And if we substitute the -5 into the equations:

-5+23 = 18

-5 + 41 = 36

We will see that -5 does indeed give us the same ratio between the lengths:

18/36 = 0.5

Hope this helped!

Answer:

A

Step-by-step explanation:

did it on edge

Answer:

A. 4(cos(x)-cos^2(x))

Step-by-step explanation:

Did the quiz on edge

The length of the diagonal of the room is approximately 21.2 feet when rounded to the nearest tenth.

Given information:

A square room in Denise's house measures 15 feet by 15 feet.

Since the room is square, the diagonal forms the hypotenuse of a right triangle whose legs are the sides of the square.

Each side of the square measures 15 feet, so we have:

d² = 15² + 15²

Simplifying:

d² = 2(15²)

d² = 2(225)

d² = 450

Taking the square root of both sides:

d ≈ 21.2

To learn more about the square;

https://brainly.com/question/28776767

#SPJ1

Answer:

[tex]-5<x<2[/tex]

Step-by-step explanation:

We have the inequality:

[tex]|2x+3|<7[/tex]

Use the definition of absolute value:

[tex](2x+3)<7\text{ or } -(2x+3)<7[/tex]

Let's evaluate each case individually.

Case 1)

We have:

[tex]2x+3<7[/tex]

Subtract 3 from both sides:

[tex]2x<4[/tex]

Divide both sides by 2:

[tex]x<2\\[/tex]

Case 2)

We have:

[tex]-(2x+3)<7[/tex]

Divide both sides by -1. Since we're dividing by a negative, flip our sign:

[tex]2x+3<-7[/tex]

Subtract 3 from both sides:

[tex]2x<-10[/tex]

Divide both sides by 2:

[tex]x<-5[/tex]

So, our solutions are, from least to greatest:

[tex]\{x|-5, 2\}[/tex]

We can see that our inequality is a greater than.

Remember, when dealing with absolute value:

When our sign is greater than (or equal to), our solution is an "or" inequality with our solutions being all values less than our lesser solution or all values greater than our greater solution.

When our sign is less than (or equal to), our solution is an "and" inequality with our solution being between our two solutions.

Since our inequality is a less than, our solution is all the values between our lesser solution and our greater solution.

Our lesser solution is -5. Our greater solution is 2.

So, the solution to the inequality is all values between -5 and 2. As a compound inequality, this is:

[tex]-5<x<2[/tex]

And we're done!

Answer:

a. –4(5x) = 12; OPEN

b. 4 x 6 = 24; TRUE

c. a + 4 = 6, when a = 2; TRUE

d. 4x = 19, when x equals 5; FALSE

Step-by-step explanation:

a. –4(5x) = 12 [-20x = 12 {Divide -20 from both sides} x = -0.6 So, if x is = -0.6, then it is true, so OPEN.

b. 4 x 6 = 24 [4 x 6 = 24 so TRUE]

c. a + 4 = 6, when a = 2. (Plug 2 in for a) 2 + 4 = 6; 6 = 6; TRUE

d. 4x = 19, when x equals 5. (Plug 5 in for x) 4(5) = 19; 20 is not = 19; FALSE

A is the first letter in the alphabet it makes a ahhhhhh sound and is a very usful letter and is clasafiyed as a vauve

Complete Question

You are measuring walnuts for banana-walnut oatmeal and a spinach and walnut salad. You need 3/4 cup of walnuts for the oatmeal and 7/8 cup of walnuts for the salad. You have a 1/8 -cup scoop. Complete the descriptions of two different ways to find how many scoops of walnuts you will need. Enter all non-whole number answers as mixed numbers in simplest form.

Answer:

13 scoops

Step-by-step explanation:

Description 1

Step 1

3/4 cup of walnuts for the oatmeal

7/8 cup of walnuts for the salad

Total cups of walnuts needed for both salad and oatmeal =

3/4 cups + 7/8 cups

(3/4 + 7/8)

(6 + 7/8)

= 13/8 cups of walnuts

= 1 5/8 cups of walnuts

Step 2

You have a 1/8 -cup scoop

The number of cup scoops of walnuts need is calculated as

1 5/8 cups ÷ 1/8 cup scoop

= 13/8 ÷ 1/8

= 13/8 × 8/1

= 13 scoops

Therefore, 13 scoops of walnuts is needed.

Description 2

3/4 cup of walnuts for the oatmeal

7/8 cup of walnuts for the salad

1/8 cup scoop

Therefore,

(3/4 + 7/8) ÷ 1/8

=(13/8) ÷ 1/8

= 13 scoops of walnuts are needed

Answer:

Total distance = 5.754 km

Step-by-step explanation:

Red lines of the right triangle show the layout of the race course.

Total length of the race course = Perimeter of the triangle

Perimeter of the triangle = Sum of the measures of all three sides

                                         = 1.83 + 1.524 + 2.4

                                         = 5.754 km

Therefore, total distance of the race course is 5.754 km.

Answer:

5.754

Step-by-step explanation:

Answer:

2, 3, 5, 7, 11, 13, 17, 19 and 23,

Step-by-step explanation:

The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19 and 23,

Answer:

True

Step-by-step explanation:

this is because when reduced to their most simple terms they are the same so:

4:8 divide both sides by 4 and get:  1:2

32:64 divide both sides by 32 and get:  1:2 as well

Answer:

Yes, it should work.

Step-by-step explanation:

DC=AB  (because it is a rectangle and they are parallel)

DA=CB (because it is a rectangle and they are parallel)

DB=AC (given)

Those are all sides and gives enough information for us to know that it is congruent.

Answer:

yes

Step-by-step explanation:

Answer:

Slope:-1/4 y-int: 3

Step-by-step explanation:

You can you the formula y1-y2/x1-x1 or you can look at it and find out if that makes sense

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Let absolute variation in the wait time at the bus stop = v

Variation = ±3 minutes

Average bus run through the city = 15 minutes

Hence, the minimum and maximum run values due to the variation can be modeled as:

|variation - average run| = ±3

|v - 15| = ±3

minimum : v = - 3 +. 15 = 12 minutes

Maximum : v = 3 + 15 = 18 minutes

Answer:

Step-by-step explanation:

│x - 3│= 15

This is the answer hope this help

Answer:

Step-by-step explanation:

I need help

Answer:

y=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=0

Step-by-step explanation:

it's it's a photo hope this will help you

Answer:15

Step-by-step explanation: 1st multiple what’s in the parenthesis (3*3= 9 & 4*4= 16

Next write it out 22+(9-16)

Then you subtract 9 from 16 since it’s in parenthesis So it’s 22+(-7) and since you are adding a negative and a positive together you will have to subtract and keep the sign of the larger number so the answer is 15 since u needed to subtract but 22 is the larger number making it positive answer

Answer:

132+180+ 168=480

Step-by-step explanation:

3/8 of 480= 180 (tuna)

35% of 480=168 (beef)

ratio is 132 (ham)

and adds up to 480

Answer: ok i dont really know but ask your teacher for help

Step-by-step explanation:

Answer:

The distance between the two points is [tex]\sqrt{85}[/tex] units

Step-by-step explanation:

Let us revise the rule of the distance between two point [tex](x_{1},y_{1})[/tex] and  [tex](x_{2},y_{2})[/tex]

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

∵ We need to find the distance between the two points (8, -7) and (1, -1)

→ Let [tex]x_{1}[/tex] = 8 and [tex]x_{2}[/tex] = 1

→ Let [tex]y_{1}[/tex] = -7 and [tex]y_{2}[/tex] = -1

→ Substitute their values in the rule above

∴ [tex]d=\sqrt{(1-8)^{2}+(-1--7)^{2}}[/tex]

∴ [tex]d=\sqrt{(-7)^{2}+(-1+7)^{2}}[/tex]

∴ [tex]d=\sqrt{49+36}[/tex]

∴ [tex]d=\sqrt{85}[/tex]

→ Simplify the radical

∵ 85 = 5 × 17

→ Both of them are prime numbers

∴ The simplest form of [tex]\sqrt{85}[/tex] is [tex]\sqrt{85}[/tex]

∴ The distance between the two points is [tex]\sqrt{85}[/tex] units

Answer:

Jim is correct.

Step-by-step explanation:

Given that:

Total people = 100

People who exercise in morning = 35

People who exercise in the afternoon= 45

People who exercise in the evening = 20

Ratio claimed by Tara = 33:55, 48:88, and 20:65

Ratio claimed by Jim = 35:100, 45:100, and 20:100

To find:

who is correct ?

Solution:

Looking at the ratio claimed by Tara, the ratio are number which are not known to us.

Therefore, the ratio claimed by Tara can not be correct.

Now, looking at the ratio claimed by Jim:

35:100, 45:100, and 20:100

35 is the number of people who exercise in morning.

45 is the number of people who exercise in evening.

20 is the number of people who exercise in night.

and 100 is the total number of people.

Therefore, this ratio represents the "Part-to-whole" ratio.

So, Jim is correct.

Answer: 490.63

Step-by-step explanation:

Answer:

C. 15m

Step-by-step explanation:

if ABCD and EFGH are congruent that means that they are equivalent to each other. If side FG is the base of that trapizoid, and side CD is the base with the measurement of 15m, then we are left to believe that side FG is 15m

Answer: Add, subtract, multiply, divide

Step-by-step explanation:

Terms must be like terms in order to add or subtract. Terms do not have to be like if we are multiplying or dividing.

You cant add unlike terms when adding or subtracting, but you can use the exponent rules when multiply or dividing.

Answer:

You have to find out how much of the circle the sector is

Step-by-step explanation:

[tex]\frac{\pi R^{2}}{\frac{P}{360}}[/tex]