The senior classes at High School A and High School B planned separate trips to the state fair. The senior class at High School A rented and filled 13 vans and 6 buses with 278 students. High School B rented and filled 10 vans and 12 buses with 428 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
Answer:
8 students in van, 29 students in bus
Step-by-step explanation:
To find the number of students in each van and bus, we can use system of equations to solve. Our first step is to create one equation for High School A and B. Let's use x for vans and y for buses, but ultimately, the variables don't matter that much.
High School A: 13x+6y=278
High School B: 10x+12y=428
Let's use elimination method to solve. We would multiply the first equation by 2.
26x+12y=556
10x+12y=428
Now that the 12y is the same in both equations, let's eliminate y by subtracting the 2 equations.
26x+12y=556
-(10x+12y=428)
16x=128
With 16x=128 left, we can just solve for x.
16x=128 [divide both sides by 16]
x=8
Now that we have x=8, we can plug that into the equations above to find y.
13(8)+6y=278 [multiply]
104+6y=278 [subtract both sides by 104]
6y=174 [divide both sides by 6]
y=29
With x=8 and y=29, we know that there are 8 students in each van and 29 students in each bus.
Step-by-step explanation:
Let,
No. of students in vans = x
No. of students in bus = y
In case 1
13x + 6y = 278(1)
In case 2
10x + 12y = 428(2)
On multiplying eq. 1 by 2
2(13x + 6y) = 2(278)
26x + 12y = 556 (3)
On subtracting 2 and 3
26x + 12y - (10x + 12y) = 556 - 428
26x + 12y - 10x - 12y = 128
16x = 128
x = 128/16
x = 8
From 1
13(8) + 6y = 278
104 + 6y = 278
6y = 278 - 104
6y = 174
y = 174/6
y = 29
Write the cubes of 5 natural numbers which are of the form 3n + 1 (eg.4,7,10…)and verify the following
"The cube of a natural number of the form 3n + 1 is a natural number of the
Same form
in when divided by 3 it leaves the remainder 1'
Answer:
yes it is true
Step-by-step explanation:
write the first five elements then write their cubes then write the cubes in the same form
for eg:
4³=16= 3×5+1= 3n+1
7³=49=3×16 +1= 3n + 1
and so on till the fifth element...
Given CH with C(2, 1) and H(-2,-15), find
the coordinates of E if E divides CH three
fourths of the way from C to H.
The coordinate of E will be (1, -3) if the coordinates of E if E divides CH three -fourths of the way from C to H
Midpoint of a line is a point that divides a line into two equal parts.
If the line is divided in the ratio a:b, then the midpoint formula will be expressed as:
[tex]M(X,Y) =(\frac{ax_1+bx_2}{a+b}, \frac{ay_1+by_2}{a+b})\\[/tex]
Given the coordinate points, C(2, 1) and H(-2, 15) divided in the ratio of 3:4
[tex]X = \frac{3(2)+1(-2)}{3+1}\\X= \frac{6-2}{4}\\X=\frac{4}{4}\\X = 1[/tex]
Get the coordinates Y:
[tex]Y = \frac{3(1)+1(-15)}{3+1}\\Y= \frac{3-15}{7}\\Y=\frac{-12}{4}\\Y= -3[/tex]
This shows that the coordinate of E will be (1, -3)
Learn more here: https://brainly.com/question/3510899
Cupcakes Promotion All cupcakes at $2 each !
Buy 8 and get 1 free!
How many cupcakes will Fatimah get if she paid $80 during the promotion?
Answer:
45
Step-by-step explanation:
....................
Hey there! I'm happy to help!
We see that the cupcakes are $2, but for every 8 you buy you get 1 free.
So, if we buy 8 cupcakes, we will be paying $16, but we will actually be receiving 9 donuts, so that means that for every $16 we pay, we get 9 donuts.
Let's see how many times $16 goes into $80.
80/16=5
So, this means that our $16 that gives us 9 donuts was done 5 times, which totals up to 80 dollars. Let's multiply our donuts now.
9*5=45
So, Fatimah will get 45 donuts during the promotion.
Have a wonderful day and keep on learning! :D
Quadrilateral ABCD is a square. What is the length of AC?
Select the best answer from the choices provided.
A. 11
B.15.556
C.19.052
D. 22
one month, ruby worked 6 hours more than isaac, and svetlana worked 4 times as many hors as ruby. together they worked 114 hours. find the number of hours each person worked
Answer:
Ruby = 18+6=24
Isaac = 18
Svetlana = 4*18=72
24+18+72=114
Step-by-step explanation:
Ruby= x+6
Isaac= x
Svetlana = 4x
x+6+x+4x = 114
6x = 114 - 6
x = 108/6
X = 18
felicia went out to dinner with friends. when the check came, she said she would pay the tip. the tip was 10 percent of the total bill for all 4 people was $22.00. what was the total tip she paid?
Answer:
$2.20
Step-by-step explanation:
The tip is 10% of $22, or 0.1 * 22 = 2.2
So $2.20 (we can add a hidden 0 on the end)
Write the equation of the line that passes through the points
(3,-2) and (6, 1).
y=x-5
y = 5x + 1
y = -x + 5
Answer:
It is y = x - 5
Step-by-step explanation:
General equation of a line:
[tex]{ \bf{y = mx + c}}[/tex]
m is the gradient, and c is y-intercept.
For gradient:
[tex]slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1}} [/tex]
substitute:
[tex]slope = \frac{1 - ( - 2)}{6 - 3} \\ \\ = \frac{3}{3} \\ slope \: = 1[/tex]
m = 1
for y-intercept:
consider point (6, 1):
[tex]y = mx + c \\ 1 = (6 \times 1) + c \\ 1 = 6 + c \\ c = 1 - 6 = - 5[/tex]
therefore:
[tex]{ \sf{equation \: is \: \{y = x - 5 \}}}[/tex]
19. A square is divided into a 100-by-100 grid of smaller squares. If 100
squares are shaded in the top row, 99 in the second row, 98 in the third
row, and so on, what is the ratio of the squares shaded to the squares not
shaded? Write the answer as a fraction in simplest form.
Answer:
13:9 with 9 being unshaded
Step-by-step explanation:
i drew a similar grid, shaded them in in the way you specified, then counted the squares on either side. the i put the numbers in a fraction and simplified
What is 2 5/6 + 7/4
A. 2 2/5
B. 3 1/5
C. 3 4/5
D. 4 7/12
Answer:
D
Step-by-step explanation:
2 5/6=2 10/12
7/4=1 3/4= 1 9/12
2 10/12+1 9/12= 4 7/12
you can just change the denominators to the same which is 12. Hope you appreciate it!
. Point C is on line segment AB
so the ratio of AC to CB is 1 to
3. What are the coordinates of
Point ?
Answer:
Using the section formula, if a point (x,y) divides the line joining the points (x
1
,y
1
) and (x
2
,y
2
) in the ratio m:n, then
(x,y)=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
3AC=CB
CB
AC
=
3
1
Since, A(1,1) and B(2,3) & m:n=1:3
Therefore, we have
C(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
(
1+3
(1)(2)+3(1)
,
1+3
(1)(3)+3(1)
)
C→(
4
5
,
2
3
).
if the replacement set for the independent variable of the function f(x)=2x^2+1 is {2,4,6,10} what is the corresponding set for the dependent variable
9514 1404 393
Answer:
{9, 33, 73, 201}
Step-by-step explanation:
Put each of the values in place of the variable and do the arithmetic. For example, ...
f(10) = 2(10)² +1 = 201 . . . . . 201 is in the output set, corresponding to x=10.
__
I find repetitive calculations are done easily by a graphing calculator or spreadsheet.
The corresponding set for the dependent variable is {9, 33, 73, 201}.
help plz i will rate
Solve S = 2trh for h
Answer and Step-by-step explanation:
To solve for h, divide everything from both sides to get h by itself.
[tex]\frac{S}{2tr} =h[/tex] <- This is the answer.
#teamtrees #PAW (Plant And Water
Find an equation of the line L that contains the points (0,0) and (5,3)
Y =
Answer:
y = (3/5)*x
Step-by-step explanation:
First, we can use the slope-intercept form of a line, or y=mx+b
To find the slope, m, we can find
(y₂-y₁)/(x₂-x₁). Denoting (0,0) as (x₁,y₁) and (5,3) as (x₂, y₂) (it is perfectly okay to have (0,0) as (x₂, y₂) and (5,3) as (x₁,y₁) as well), we have
(y₂-y₁)/(x₂-x₁) = (3-0)/(5-0) = 3/5
Therefore, our equation is
y = (3/5)x + b
To solve for b, we can plug any value of (x,y) from the line, e.g. (0,0), and solve from there, resulting in
y = mx + b
0 = (3/5)*0 + b
0 = b
Our equation is therefore
y = (3/5)*x + 0
= (3/5)*x
You are six spaces behind your
opponent in a board game. What integer represents your situation?
+ An Integer less than 0 is represented as
Answer:
9,-9
Step-by-step explanation:
Because your opponent is in the positive while you are in the negative
Solve the following equation for X to find the total number of people who downloaded songs for music site for a certain month.
X= 0.6x + 384
How many people downloaded songs from the site that month?
Answer:
960
Step-by-step explanation:
x=0.6x+384
0.4x=384
960
Answer:
960
Step-by-step explanation:
x = 0.6x + 384
Subtract 0.6x in both sides:
0.4x = 384
Divide both sides by 0.4:
x = 384/0.4
x = 960
Find the surface area of the composite solid below. (2 ft, 2 ft, 2 ft, 3 ft)
Answer:
44 sq. ft
Step-by-step explanation:
5(2^2) = 20
4(3x2) = 24
20+24 = 44
Write the Roman Numeral CLXIV in standard form. Standard Roman Number Numeral 1 1 5 V 10 X 50 100 500 D 1,000 M XJ002 2 A) 169 OB) 166 C) 164
Answer:
C. 164
Step-by-step explanation:
its self explanitory
Estimate 26 to the nearest tenth. Then locate 26 on a number line.
Answer:
30 is the nearest tenth of 26
A square sandbox has an area of 42ft to the power of 2. What is the approximate perimeter of the sandbox to the nearest hundredth?
Solve the following problem. Round to one decimal place if necessary.
Answer:
Sinθ = Opposite/hypotenuse
[tex] \sin(21) = \frac{x}{22} \\ 0.358 = \frac{x}{22} \\ x = 22 \times 0.358 \\ x = 7.88[/tex]
I hope I helped you^_^
Round 55,553.65478 to:
a. hundreds
and
b. thousandths
Answer:
a. hundreds
55,600
b. thousandths
55,553.65500
HELPPPPP!!!!!!!!!!!!!!!!!!!
What is the longest version of pi? Please type the whole thing.
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058038150193511253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955321165344987202755960236480665499119881834797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548161361157352552133475741849468438523323907394143334547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383827967976681454100953883786360950680064225125205117392984896084128488626945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645995813390478027590099465764078951269468398352595709825822620522489407726719478268482601
Segment addition postulate
Find RT
Answer:
RT = 25.5
Step-by-step explanation:
RT = RS + ST = 17 + 8.5 = 25.5
46. Order these numbers from least to greatest:
1/2, 0.4, 1/3, 1/5
Answer:
1/5, 1/3, 0.4, 1/2
Step-by-step explanation:
1/5 = 0.2
1/3 = 0.33
1/2 = 0.5
Can someone answer this? It’s 9th grade algebra
Answer:
C
Step-by-step explanation:
We want to solve the inequality:
[tex]\displaystyle 5.1(3 + 2.2x) > -14.25 - 6(1.7x+4)[/tex]
Distribute:
[tex](15.3+11.22x) > -14.25 + (-10.2x-24)[/tex]
Combine like terms:
[tex]15.3 + 11.22x > -10.2x-38.25[/tex]
We can add 10.2x to both sides:
[tex]15.3 + 21.42x > -38.25[/tex]
Subtract 15.3 from both sides:
[tex]21.42x > -53.55[/tex]
And divide both sides by 21.42. Hence:
[tex]\displaystyle x > -2.5[/tex]
This means all values greater than -2.5. Hence, in interval notation:
[tex](-2.5, \infty)[/tex]
In conclusion, our answer is C.
find the value of' m' if (-m 3) is the solution of equation 4x +9y -3=0
[tex]\\ \qquad\quad\sf\longmapsto 4x+9y-3=0[/tex]
[tex]\\ \qquad\quad\sf\longmapsto 4(-m)+9(3)-3=0[/tex]
[tex]\\ \qquad\quad\sf\longmapsto -4m+27-3=0[/tex]
[tex]\\ \qquad\quad\sf\longmapsto -4m+24=0[/tex]
[tex]\\ \qquad\quad\sf\longmapsto -4m=-24[/tex]
[tex]\\ \qquad\quad\sf\longmapsto m=\dfrac{-24}{-4}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto m=6[/tex]
Pls help a couple more questions left pls.
Answer: Amir Is Right
Step-by-step explanation: 4 seconds and it made 8 clicks
4/8 is 2 and the check if its right you can do 2x4 to get the clicks that were made in 4 seconds.
Answer:
Amir is correct.
Step-by-step explanation:
To find the cps (clicks per second), divide the clicks by the number of seconds.
[tex]\frac{8 clicks}{4 seconds}[/tex]
Simplify the fraction.
[tex]\frac{2 clicks}{1 seconds}[/tex]
Since 2 over 1 is really just 2 and the line of the fraction can be read as "per", we could re-write the above fraction in words as:
2 clicks per second
Therefor, Amir is correct.