Write a System of Equations to solve the following problem:
The county fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 13 vans and 2 buses with 211 students. High School B rented and filled 4 vans
and 4 buses with 268 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.
#students each VAN can carry:
#students each BUS can carry:
Answer:
each van carries 7 students
each bus carries 60 students
Step-by-step explanation:
let v = # students in a van
let b = # students in a bus
system of equations:
13v + 2b = 211
4v + 4b = 268
I multiplied the 1st equation by -2 to eliminate the 'b' terms
-26v - 4b = -422
+ 4v + 4b = 268
-22v = -154
v = 7
substitute '7' for 'v':
4(7) + 4b = 268
28 + 4b = 268
4b = 240
b = 60
Answer:
13v + 2b = 211
4v + 4b = 268
#students each VAN can carry: 7
#students each BUS can carry: 60
Step-by-step explanation:
Let v = number of students in each van.
Let b = number of students in each bus.
High School A:
13v + 2b = 211
High School B:
4v + 4b = 268
The system of equations is
13v + 2b = 211
4v + 4b = 268
We will solve this system of equation with the addition method.
Write the first equation as it is. Divide both sides of the first equation by 2 and write it below the first equation. Then add the equations.
13v + 2b = 211
(+) -2v - 2b = -134
----------------------------
11v = 77
Divide both sides by 11.
v = 7
Substitute 7 for v in the first original equation and solve for b.
13v + 2b = 211
13(7) + 2b = 211
91 + 2b = 211
Subtract 91 from both sides.
2b = 120
Divide both sides by 2.
b = 60
Answer:
13v + 2b = 211
4v + 4b = 268
#students each VAN can carry: 7
#students each BUS can carry: 60
Yuki concluded:
"It's not possible to map AABC onto AFED using a sequence of rigid transformations, so the triangles
are not congruent."
What error did Yuki make in her conclusion?
Answer:
One more transformation — a rotation — would map △ABC onto △FED So the triangles are congruent.
Step-by-step explanation:
Yup
please solve this for me
Answer:
its A
Step-by-step explanation:
TRUST!
Mrs. Gilbert is interested in determining how many students spend 4 or more hours doing homework each week. She asks every student who earned Honor Roll for the first semester. Is her survey biased or unbiased?
A. biased, because she didn't ask random students
B. unbiased, because she asked every student on honor roll
C. biased, because she only asked students on honor roll
D. unbiased, because first semester is over
Answer:
C. Biased, because she only asked students on honor roll.
Step-by-step explanation:
Since Mrs. Gilbert's goal was to find how many students that spent >4 hours and not how many students that earned Honor Roll that spent >4 hours, the data is biased. Choose C.
A box has the following dimensions: length = x +7, width = x - 4, height = 2x-6. Find the volume of the box if x is 5
Consider the equation: x^2+10x+22=13
Need help asap!!!!
this is due in a hour!
Answer:
(x + 5)^2 = (5 - 3)^2
Step-by-step explanation:
Given the equation;
x^2 + 10x + 22 = 13
We have;
x^2 + 10x = 13 - 22
x^2 + 10x = -9
Adding half of 10 to both sides and completing the square as usual, we have;
(x + 5)^2 = 5^2 + (-9)
(x + 5)^2 = (5 - 3)^2
What is 20.30 - 19.70 and what are the solving steps?
Answer
0.6
Step-by-step explanation:
here is the working out! Can i get brainliest
Answer:
Look at the image!!
Step-by-step explanation:
Hope this helps!!
Sorry for the bad righting XD
If you want to learn more search Mathisfun.com!!
Write each power as a product of the same factor. Then find the value. 7^2
Answer:
49
Step-by-step explanation:
7^2=49
Consider the following formula y−p/2=e. Rearrange the formula to solve for "p":
Answer:
p = 2y - 2e
Step-by-step explanation:
Eliminate the fraction by multiplying all terms by 2:
2( y−p/2=e) = 2y - p = 2e
Now subtract 2e from both sides, obtaining: 2y - 2e = 0.
Finally, add p to both sides: p = 2y - 2e
PLZ PLZ PLZ I NEED HELP!!!!
Answer:
The answer is B
Step-by-step explanation:
Divide the distance by the time.
Find two acute angles that satisfy the equation sin(2x + 8) = cos(x + 28). Check that your answers make sense.
The smaller angle is
°.
The larger angle is
Step-by-step explanation:
why is my brainly sux lol due dude.ex
Mike collects trading cards. His favorites are baseball and football cards. For every 3 basebali cards he owns, Mike has 5 football cards. What is the ratio of baseball cards to football cards in his collection ?
Answer:
56 cards
Step-by-step explanation:
If 5 baseball cards multiplied by 8 is 40, then you multiply the 7 football cards by 8 as well.
7x8=56
56 is the answer because if 5 baseball cards multiplied by 8 is 40, then you multiply the 7 football cards by 8 as well.
In ΔQRS, q = 370 cm, r = 910 cm and ∠S=31°. Find the length of s, to the nearest centimeter.
Answer:623
Step-by-step explanation:
0.6h=13.02 show work
Answer:
21.7
Step-by-step explanation:
0.6h=13.02
h=13.02/0.6
h=21.7
Answer:
21.7
Step-by-step explanation:
0.6h=13.02
h=13.02/0.6
h=21.7
How do I draw and determine the equation of a trend line on a scatterplot
Step-by-step explanation:
Step 1: Draw your trend line.
You begin by drawing your trend line. You want your trend line to follow your data. You want to have roughly half your data above the line and the other half below the line, like this:
trend line equation
Step 2: Locate two points on the line.
Your next step is to locate two points on the trend line. Look carefully at your trend line and look for two easy to figure out points on the line. Ideally, these are points where the trend line crosses a clearly identifiable location.
For the trend line that we just drew, we can see these two easily identifiable points.
trend line equation
We can easily identify these two points as (3, 3) and (12, 6).
Step 3: Plug these two points into the formula for slope.
The formula for slope is this one:
trend line equation
We can label our first point as (x1,y1), and our second point as (x2,y2). So our x1 is 3, our y1 is 3, our x2 is 12, and our y2 is 6. Plugging these values into the equation for slope and evaluating, we get this:
trend line equation
So our slope is 1/3.
An airplane company is determining the difference in selling price if rows of first-class seats are added to a new design. Using the average selling price of $1,000 per first-class seat, the total selling price for one new row is
f(r) = 4,000r. Each row in first class eliminates two rows of economy seats. Using the average selling price of $150 per economy seat, the total price for each pair of removed rows is e(r) = 1,800r.
Which is d(r), the profit or loss for adding r rows of first class seats?
A. d(r) = 2,200r
B. d(r) = 5,800r
C. d(r) = –2,200r
D. d(r) = –5,800r
Step-by-step explanation:
From the original question, we can rewrite this as:
An airplane company is determining the difference in selling price if rows of first-class seats are added to a new design. The total selling price for one new row is f(r) = 4,000r. Each row in first class eliminates a pair of rows of economy seats. The total price for each pair of removed rows is e(r) = 1,800r. Which is d(r), the profit or loss for adding r rows of first class seats?
f(r) = 4000r
e(r) = 1800r
d(r) = ? (profit or loss)
Assuming we had added a row of first class seats,
+ f(r) = 4000r
But we had to remove a pair or rows from the economy seats,
- e(r) = 1800r
Translating these into one equation:
d(r) = f(r) - e(r) = 4000r - 1800r = 2200r
Therefore, OPTION A.) d(r) = 2200r
The value of d(r) will be 2200r. The correct option is A.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Assuming we had added a row of first-class seats,
+ f(r) = 4000r
But we had to remove a pair or rows from the economy seats,
- e(r) = 1800r
Translating these into one equation:
d(r) = f(r) - e(r) = 4000r - 1800r = 2200r
Therefore, the value of d(r) will be 2200r. The correct option is A.
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help the pictures underneath
Answer:
Step-by-step explanation:
I believe the correct answer is A, but im not sure. Hope it helps! <3
Answer:
a
Step-by-step explanation:
it takes a long time for a river to carve a path through rock. for example it took the grand canyon 5-6 million years to form by way of river erosion
factor tree 50 and 75 math
Answer:
2 x 25 (50)
3 x 25 (75)
Step-by-step explanation:
Help please
what is 61x18x4x487?
Answer:
2138904
Step-by-step explanation:
yep
Answer:
61x18x4x487=2138904is your answer
Miguel baked 42 cookies for a charity bake sale. He made packages with 3 cookies in each. What equation can be used to find how many packages, p, of cookies Miguel made?
Answer:3p=42 (p=14)
Step-by-step explanation:
Since there are 3 cookies in each pack you would need to divide.
I WILL GIVE BRAINLIEST IF CORRECT
Answer:
Vertical compression
Step-by-step explanation:
g(x)=0.25f(x), if you substitute for f(x) you get B
Simplify to create an equivalent expression. 8(10-6q)+3(-7q-2)}8(10−6q)+3(−7q−2)
Answer:
-69q+74
Step-by-step explanation:
Distribute:
80-48q-21q-6
Simplify:
74-69q
SOMEONE HELP PLEASE!! ITS DUE AT 16:00 UK TIME ILL GIVE YOU BRAINLIEST IF ITS RIGHT!!!
Answer:
From left column to right
Left Right
1. 23a+18 1. 7a-6
2. 23a-6 2. 7a-18
3. 23a-18 3. 7a+6
4. 0a+4 4. 0a+0
Step-by-step explanation:
The first example you distribute by doing 3 x 5a plus 3 x 2 + 4 x 2a + 4 x 3
Answer is 15a+6+8a+12=
23a+18
Hope this helped :)
Rebecca ran 21 miles in 5 hours. If she ran at a constant speed, how many miles did she run in 2 hours? 8.4 miles 42 miles 4.2 miles 1.2 miles
Answer: 8.4 miles
Step-by-step explanation:
d = rt
Solve for her rate
21 = 5r
r = 21/5
r = 4.2
Solve for if the time is 2 hours and rate (solved previously) is 4.2
d = 4.2*2
d = 8.4
The distance traveled by Rebecca in 2 hours is given by d = 8.4 miles and the speed is S = 4.2 miles / hour
What is Speed?Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the total distance ran by Rebecca be D = 21 miles
The time taken by her to travel 21 miles T = 5 hours
So , the speed of Rebecca S = D / T
On simplifying , we get
S = 21/5
S = 4.2 miles per hour
Therefore , the speed of Rebecca is 4.2 miles / hour
Now , let the time taken be T₂ = 2 hours
So , the distance traveled in 2 hours , D = ST₂
D = 4.2 x 2
D = 8.4 miles
Hence , the distance traveled is 8.4 miles
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In this diagram, the measure of
Answer:
2x - 60 = 180
Step-by-step explanation:
Angles RQS and PQS form a linear pair, so they are supplementary.
The sum of their measure is 180°.
Both angle measures are unknow, so let's use x for the measure of <PQS.
The measure of angle RQS is 60° less than the measure of <RQS, so it is
x - 60
Now we add the measures and set the sum equal to 180.
x + x - 60 = 180
Combine like terms on the left side.
2x - 60 = 180
Answer: 2x - 60 = 180
Rome had to pay yearly
tribute to Carthage..
Is this true or false
Answer:
True
Step-by-step explanation:
At least that's what wiki says
Lengths
Can be side lengths
of a triangle
Cannot be side
lengths of a triangle
9.5, 14.5, 4.5
3, 18,9
5, 15,8
27, 8,7
Answer:
9.5 14.5 and 4.5
Step-by-step explanation:
That’s correct
Simplify Please and Thank you!
Answer:
[tex]2\sqrt{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{24} \\= \sqrt{4} * \sqrt{6}\\= 2\sqrt{6}[/tex]
what did you put for #3?
Answer:
huh
Step-by-step explanation:
all values of x
5 ( x + 10 )^2 − 30 = − 5
Plzzzz