21. Transportation A youth group with 26 members is going skiing. Each of the five
chaperones will drive a van or sedan. The vans can seat seven people, and the
sedans can seat five people. Assuming there are no empty seats, how many of each
type of vehicle could transport all 31 people to the ski area in one trip?

Answer:

The side lengths are 5, 12, 13

Step-by-step explanation:

These are the side lengths we know before we have solved the problem.

a= x   b= x+7   c= 13

If we put this into the Pythagorean theorem, we get

[tex]13^{2} = x^{2} +(x+7)^{2}[/tex]

Expand

[tex]169 = 2x^2+14x+49\\[/tex]

Subtract 169 from both sides

[tex]0 =2x^2+14x-120[/tex]

Solve using the quadratic formula

a= 2   b= 14   c= -120

[tex]\frac{-14\pm \sqrt{14^2-4\cdot \:2\left(-120\right)}}{2\cdot \:2}[/tex]

[tex]x= \frac{-14\pm \:34}{2\cdot \:2}[/tex]  

If we separate the solutions we get

[tex]x= \frac{20}{4} = 5[/tex]

and

[tex]x= \frac{-48}{4} = -12[/tex]

Since this is a question about length, we can ignore the negative.

So the longer leg is 12ft and the shorter leg is 5ft

The shorter length is 5feet and the longer length is 12 feet

Let the shorter leg = x

Let the longer leg = x+7

Therefore,

x² + (x+7)² = 13²

x² + x² + 14x + 49 = 169

Collect like terms

2x² + 14x + 49 - 169 = 0

2x² + 14x - 120 = 0.

Divide by 2

x² + 7x - 60

By using quadratic equation

x² + 12x - 5x - 60

x(x + 12) - 5(x + 12)

Therefore, x - 5 = 0

x = 0 + 5.

x = 5

The shorter length is 5ft

Longer length = 5+7 = 12 feet

Read related link on:

https://brainly.com/question/19574344

Answer:

Step-by-step explanation:

B is the answer

Answer:

answer is attached in the figure below hope it helps please mark it as brainlist

Answer: A

Step-by-step explanation:y=2x−2 2.00AM 2°c and rises 2°C each hour for x hours

y=-1/2x +3 it's last one

Answer:

21

Step-by-step explanation:

solved it

Answer:?????

Step-by-step explanation:

what do u need help with/?//???/???

Answer:

9 cm

Step-by-step explanation:

2.5x4=10

Answer:

8 Batches

Step-by-step explanation:

Simple. Since it takes 2/3 of a cup for one batch, we divide 5 1/3 by 2/3, wich equals 8.

Answer:

im guessing it says they give $5 to the father

if that is the case then the answer is c

Step-by-step explanation:

Answer:

So if you take the 12 and add it to the 7 you get 19 then do 19 mines 7 and you get 12 so always add the sum to the number given to get the missing number

Step-by-step explanation:

Have a great day

Answer:

C

Step-by-step explanation:

Texas was not around during George Washington so that cant be correct

Texas was not around during the constitution of 1824

Texas did not want more restaurants lol

So Texans considered themselves  independent from Mexico is correct

Answer:

Step-by-step explanation:Texas was not around during George Washington so that cant be correct Texas was not around during the constitution of 1824 Texas did not want more restaurants So Texans considered themselves  independent from Mexico is correct

took it on edge 2020 and got it write with this

Answer:

[tex]3.10* 10^0[/tex]

Step-by-step explanation:

Given

[tex]3.091403[/tex]

Required

Express in standard form

A number in standard form can be expressed as:

[tex]a * 10^b[/tex]

Where

[tex]1 \leq a \leq 10[/tex]

i.e.

a is between 1 and 10 (inclusive) and preferable, a should be in 2 decimal places

We have that:

[tex]3.091403[/tex] is between 1 and 10.

So, in standard form it is:

[tex]3.091403 * 10^0[/tex]

Approximate to 2 decimal places

[tex]3.10* 10^0[/tex]

Hence, the standard form of [tex]3.091403[/tex] is [tex]3.10* 10^0[/tex]

Answer: 2/1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Line is passing through the points (2, 3) & (5, 9)

Slope = (9 - 3)/ (5 - 2) = 6/3 = 2

Slope of the line is 2.

Answer:

Rotating 180 clockwise would mean that Q is Q if r is r, the coordinates of it pointing to Q would be in your picture , can I see a picture of the problem?

Step-by-step explanation:

Answer:

this is an increasing graph. of y = 30x + b

Step-by-step explanation:

since all that is happening is that people are adding money, the graph just goes up and up

Answer:

2.25

Step-by-step explanation:

1.5 / 0.666 (repeating) = 2.25

Answer:

There are 2 one-quarter cup servings in 1 half cup

In 5.25 cups there are 21 one-quarter cup servings

Step-by-step explanation:

So 21 quarter cup servings divided by 2 quarter cup servings per half cup serving will yield the number of half cup servings.

21/2 is 10.5, so there are ten and half, half cup servings in 5.25 cups

Answer:

-7

Step-by-step explanation:

the full coordinate would be  3,-7. just line up the number directly above it and to the left/right and write it down x,y

Answer: The expected number of spades that you will draw is 0.751 spades

Step-by-step explanation:

The expected value can be calculated as:

∑xₙ*pₙ

Where xₙ is the n-th event, and pₙ is the probability of that event.

First, let's count the possible events and calculate the probability for each one.

x₀ = drawing 0 spades.

Out of 52 cards, we have only 13 spades, then 52 - 13 = 39 are not spades.

Then the probability of not drawing a spade in the first draw is:

p1 = 39/52

In the second draw we will have a card less than before in the deck (so we have 38 cards that are not spades, and 51 cards in total), then the probability of not drawing a spade is:

p2 = 38/51

And with the same reasoning, in the third draw the probability is:

p3 = 37/50

The joint probability for this event will be:

p₀ = p1*p2*p3 = (39/52)*(38/51)*(37/50) = 0.413

Second event:

x₁ = drawing one spade.

Let's suppose that in the first draw we get the spade, the probability will be:

p1 = 13/52

In the second draw, we get no spade, then the probability is:

p2 = 39/51

in the third draw we also get no spade, the probability is:

p3 = 38/50

And we also have the case where the spade is drawn in the second draw, and in the third draw, then we have 3 permutations, this means that the probability of drawing only one spade is:

p₁ = 3*p1*p2*p3 = 3*(13/52)(39/51)*(38/50) = 0.436

third event:

x₂ = drawing two spades:

Let's assume that in the first draw we do not get a spade, then the probabilities are:

p1 = 39/52

p2 = 13/51

p3 = 12/50

And same as before, we will have 3 permutations, because we could not draw a spade in the second draw, or in the third, then the probability for this case is:

p₂ = 3*p1*p2*p3 = 3*( 39/52)*(13/51)*(12/50) = 0.138

And the last event:

x₃ = drawing 3 spades.

The probabilities will be:

p1 = 13/52

p2 = 12/51

p3 = 11/50

And there are no permutations here, so the joint probability is:

p₃ = p1*p2*p3 = (13/52)*(12/51)*(11/50) = 0.013

Now we can calculate the expected value:

EV = 0*0.413 + 1*0.436 + 2*0.138 + 3*0.013 = 0.751

The expected number of spades that you will draw is 0.751 spades

Answer:

$2675

Step-by-step explanation:

Answer:

I got 4x=5y sorry if i'm wrong

Answer:

B

Step-by-step explanation:

The correct statement of the given ones are - the unit rate of best fudge is less than unit rate of candy cane.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept.

Given is a table that shows the cost for fudge at candy lane. The graph represents the cost for similar fudge that best fudge shop sell.

The slope of straight line represented by the table -

m[1] = (16 - 8)/(2 - 1)

m[1] = 8

The slope of the line plotted on graph -

m[2] = (9 - 6)/(3 - 2)

m[2] = 3

The slope is the measure of unit rate. Therefore, the unit rate of best fudge is less than unit rate of candy cane.

The cost 3 pounds of fudge at best fudge shop = 3 x 3 = $9

The cost 1 pound of fudge at candy lane = $8

Hence, cost 3 pounds of fudge at best fudge shop is greater than the cost of a pound of fudge at sweet treats.

Therefore, the correct statement of the given ones are - the unit rate of best fudge is less than unit rate of candy cane.

To solve more questions on straight line graphs, visit the link below-

brainly.com/question/2954112

#SPJ6

[Refer to the image attached for table and graph]

Answer:

Step-by-step explanation:

Coordinate points: (18, -7) and (18,2)

m= rise / run      or    [tex]\frac{ y_2 - y_1} {x_2 - x_1}[/tex]

m = slope

(x1, y1) = coordinates of first point in the line

(x2, y2) = coordinates of second point in the line

So your rise is...

2 - (-7)

and you run is...

18 -18

Rise = 9

Run = 0

Now, do you see the issue...

You can not have a number over 0 (* a great way to remember is N/0 spells no: "N" being number and "0" being zero)

The slope or the equation 9 / 0 (9 divided by 0 or 9 over 0)  is ERROR in the calculator which means the slope of these points are undefined

The line is vertical when this happens

*Side Note: if you were to have 0 as you rise and 9 as your run, 0/9 is ok because that means you have a zero slope meaning that you have a horizontal line

0 divide by 9 is zero

Answer:

Step 3.

Step-by-step explanation:

When 10.2b - 5 = 18.92, you cannot combine the unlike terms together on the left side to get 5.2b. Instead, add 5 to both sides:

10.2b = 18.92 + 5 = 23.92.

Answer: step 3

Step-by-step explanation:

Answer:

-3.5

Step-by-step explanation:

Rise over run