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
What are the missing numbers on the two number lines?
Answer:
C is -14, 7, 14, 28
not sure what D is
Step-by-step explanation:
The zoo in Samir's city is building a new habitat for its 7 spider monkeys. The habitat will
have trees, ladders, and vines in a cube-shaped cage that measures 14 meters on each side.
What is the volume of the new monkey cage?
[tex]v = 2744 {m}^{3} [/tex]
Step-by-step explanation:
cube-shaped, 14m on each side.
volume...?
[tex]v = 14 \times 14 \times 14 [/tex]
[tex]v = {14}^{3} [/tex]
[tex]v = 2744 {m}^{3} [/tex]
The volume of the new monkey cage is 2744m^3
How to find the volume of cuboid?Let the three dimensions(height, length, width) be x, y,z units respectively.
Then the volume of the cuboid is given as
[tex]V = x \times y \times z \: \rm unit^3[/tex]
The formula for the volume of cuboid is V = s * s * s;
Where, s= side of the cage
s = 14 meters
V = 14 * 14 * 14
V = 2744 m^3
Therefore, the volume of cuboid will be 2744m^3
Learn more about volume;
https://brainly.com/question/1578538
#SPJ2
Pls help me I’m not very smart
Answer:
39.90
Step-by-step explanation:
multiply 95x42, ur not smart if you think u arent.
I need a step by step correct answer bc i need to get in this college please help :(
Answer:
please mark me brainliest
Step-by-step explanation:
-6÷3×2+3÷3
using Bodmas(bracket of division multiplication addition and subtraction)
-2×2+1
-4+1
-3
if 3/4 part of the distance between two places is 45 km find the distance between the places.
Let distances be x
ATQ
[tex]\\ \rm\hookrightarrow \dfrac{3}{4}x=45[/tex]
[tex]\\ \rm\hookrightarrow \dfrac{3x}{4}=45[/tex]
[tex]\\ \rm\hookrightarrow 3x=45(4)[/tex]
[tex]\\ \rm\hookrightarrow 3x=180[/tex]
[tex]\\ \rm\hookrightarrow x=\dfrac{180}{3}[/tex]
[tex]\\ \rm\hookrightarrow x=60[/tex]
In the figure MX = NY
MX and NY are parallel.
i) Are the sides of ∠MPX equal to the sides of ∠NPY ?
ii) what is the special about the postion of P on MN
Answer:
i) yes
ii) it splits MN in half (bisector)
Step-by-step explanation:
We are given that MX and NY are parallel. This means, due to alternate interior angles, <XMN and <YNM are congruent as well as <MXY and <NYX. We are also given MX = NY. This is enough information to prove ΔMPX is congruent to ΔNPY due to ASA(two angles and a side between them).
(i) Now, because of this, we can say that all the sides of ΔMPX are congruent to those of ΔNPY. And, this means MP = NP. Since the point P divides the segment MN into two equal pieces, it's a bisector of MN(splits it in half).
Answer:
YesPoint of intersectionStep-by-step explanation:
SEE the image for solution.
HOPE it helps
Have a great day
A box of cereal states that there are 90 calories in 3/4 cup serving. How many calories are there in 4 cups of the cereal
Answer:
480
Step-by-step explanation:
Let x be the calories in 4 cups
Set it up
[tex]\frac{90}{\frac{3}{4}}=\frac{x}{4}[/tex]
Step 1: Switch sides
[tex]\frac{x}{4}=\frac{90}{\frac{3}{4}}[/tex]
Step 2: Apply fraction rule
[tex]\frac{x}{4}=\frac{90\cdot \:4}{3}[/tex]
Multiply
[tex]\frac{x}{4}=\frac{360}{3}[/tex]
Divide
[tex]\frac{x}{4}=120[/tex]
Step 3: Multiply both sides by 4
[tex]\frac{4x}{4}=120\cdot \:4\\\\=480[/tex]
There are 480 calories in 4 cups of the cereal.
wats 10 to the 2nd power divied by 5 to the 2nd power
Answer:
4
Step-by-step explanation:
10^2/5^2
Do the exponents first
10 to the 2nd power is 100
5 to the 2nd power is 25
100/25
100 divided by 25 is 4
So the answer is 4
Hope this helps!
calculate a length of a square ground of perimeter 160m
A motorboat travels 275 kilometers in 5 hours going upstream. It travels 405 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Step-by-step explanation:
[tex]275 \times 5 = 1375 [/tex]
The rate of the motorboat on still water is 1375
[tex]405 \times 5 = 2025[/tex]
The current rate of the motorboat is 2025
Please help!
Please explain your answer because I need to learn this!
Find the measure of angle theta.
Answer:
48.2
Step-by-step explanation:
We have a right angle so we can do our three trig ratios,
Sine Cosine Tangent
Remeber SOHCAHTOA.
We are given some angle theta, and we are given a side adjacent to the angle and the hypotenuse. We are going to use the cosine rule.
[tex] \cos(theta) = \frac{36}{54} [/tex]
[tex] \cos(theta) = \frac{2}{3} [/tex]
Take the inverse of both sides
[tex] \cos {}^{ - 1} ( \frac{2}{3} ) = x[/tex]
Theta is equal to
[tex]48.2[/tex]
i need help with atleast 2 of these questions pls
Answer:
Below.
Step-by-step explanation:
(a) Over the first 5 seconds rate of change of speed
= (9-1)/5
= 8/5
= 1.6m/s^2
(b) (21-9)/16-t) = 2
12/16-t = 2
32 - 2t = 12
32 - 12 = 2t
20 = 2t
t = 10 seconds
Step-by-step explanation:
Total Time Taken = 16secs
10a). We're asked to calculate the rate of speed change for the first 5secs.
This is another way of saying "Calculate Acceleration" in the first 5sec of Motion.
Why?
Acceleration is the rate of change of speed or the rate at which speed changes.
acceleration = v - u/t
where v = Final Speed
u = initial Speed.
Looking at the graph
You see that
Initial speed(u) = 1m/s
Final Speed(v) = 9m/s
t = 5secs
Acceleration = 9 - 1/ 5
a = 8/5
a = 1.6m/s².✅
10b)
We're asked to calc "t" from the graph.
Given that the acceleration at "t" untill 16sec(end of motion) is 2m/s².
This simply means that Constant Acceleration was held from "t" to the end of the Motion.
Do not confuse Constant Acceleration for Constant Velocity.
At Constant Velocity... Acceleration is zero(0)
At Constant Acceleration...Velocity Changes Uniformly or at the same rate each second and this is what we're dealing with in this question.
Taking the same step as we used in calculating acceleration above
Given a= 2m/s²
a = v - u/∆t
Where ∆t means time change or difference.
From "t" to 16
The change in time is 16 - "t"
2 = 21 - 9/( 16 - t)
2 = 12/16-t
16-t = 12/2
16 - t = 6
t = 16 - 6
t = 10secs.✅
Have a great Day!.
Which expression is equivalent to 7.90 + 8.5 + 8.60 + 1.3?
O 16.4u + 9.9
0 -0.7u + 9.8
Submit Answer
O 16.54 + 9.8
0 -0.74 + 7.2
о
Answer:
[tex]⚪ \: \: 16.5u + 9.8[/tex]
Step-by-step explanation:
[tex]7.9u + 8.5 + 8.6u + 1.3 \\ = (7.9 + 8.6)u + 8.5 + 1.3 \\ = 16.5u + 9.8[/tex]
60 CHALLENGE The Queen Isabella Memorial Bridge connects South Padre Island, Texas, to
Port Isabel on the mainland. Suppose one crew began building from South Padre Island,
and another crew began building from Port Isabel. The two crews met 6256.5 feet from the
South Padre Island side of the bridge approximately 2.5 years after construction began.
a. Suppose the South Padre Island crew built an average of 208.5 feet per month.
Together the two crews built 12,513 feet of bridge. Determine the average number of
feet built per month by the Port Isabel crew.
307
b. About how many miles of bridge did each crew build?
c. Is this answer reasonable? Explain.
2,513
With some give information, we need to solve some algebraic problems that involve a change of units, lets see step by step how we do that:
A) First, we know that:
The bridge was constructed in 2.5 years
Knowing that 1 year = 12 months, we can rewrite:
2.5 years = (2.5)*(12 montsh) = 28 months
The two crews built, together, 12,513 ft of the bridge.
Now, we know that the South Padre Island crew built an average of 208.5 per month.
Then in the 28 months for the whole construction, they built 28 times that amount:
D = (28 months)*(208.5 per month) = 5,838 ft
Then the rest was constructed by the Port Isabel Crew.
They constructed 12,513 ft - 5,838 ft = 6,675ft
So that crew constructed 6,675 ft in 28 months, then the average number of feet built per month (the quotient between the total amount built and the number of months in which that was built) is:
6,675 ft/28 months = 238.39 ft per month.
b)
South Padre Island crew constructed 5,838 ft
Port Isabel Crew constructed 6,675ft
Now we want to transform these to miles.
Remember that;
1 mille = 5280 ft.
Then to transform from ft to miles, we just need to divide our measures by 5280 ft
Then:
South Padre Island crew constructed 5,838 ft = (5,838ft/5280ft) mi = 1.11 mi
Port Isabel Crew constructed 6,675ft = (6,675ft/5280ft) mi = 1.26 mi
c) Is this answer reasonable?
Mathematically, yes, both crews constructed about the same in about the same time, with a small difference that may be related to the sizes of each crew or something like that.
We could conclude that this would not be reasonable if the monthly rates were dramatically different.
If you want to learn more, you can read:
https://brainly.com/question/15051367
a rectangular field has a length of 485 meters and a width of 155 meters how much would it cost to fence the field at £14 a meter
Answer:
£17920
Step-by-step explanation:
total length of the field = 2(155+485) = 1280m
cost = 1280 * 14 = 17920
geometry help pls
How do you say DE = FG?
can someone explain why
Answer:
first option
Step-by-step explanation:
congruency has its own symbol and it's a ~ top of a = sign. and the expression doesn't have the symbol. so we can eliminate two options out meaning it's a.
The correct answer would be an option (A) the measure of segment DE is equal to the measure of segment FG.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
SSS stands for Side-Side-Side criterion. According to this, two triangles are congruent if three sides of a triangle are equal to the corresponding sides of the other triangle.
SAS stands for Side-Angle-Side criterion. According to this, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.
Given that, DE = FG
Congruency is represented by its own symbol, which is a ~ sign on top.
Here, Segment FG's measure is equal to segment DE's measure.
There is no symbol assigned to the expression. Since two possibilities are no longer an option, it must be Option (A).
Hence, the measure of segment DE is equal to the measure of segment FG
Learn more about of congruent triangles here:
brainly.com/question/4364353
#SPJ5
even more math.......
Answer:
A
Step-by-step explanation:
We don't know the height of the building, and it's changeable because we multiplied it by 1/2, also, the rest of the values are revealed, so the answer is A.
Please help with questions 4,5 and 6!
Answer:
Step-by-step explanation:
4) ∠CTB , ∠PTA are vertical angles
If sum of two angles add up to 90, then they are Complementary angles.
If sum of two angles add up to 180, then they are Supplementary angles.
∠FTA and ∠ATR are supplementary angles
5) ( 1 , 2 ) & (3 , 6)
[tex]Midpoint=\left(\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2}\right)[/tex]
[tex]= \left(\dfrac{1+3}{2},\dfrac{2+6}{2}\right)\\\\=\left(\dfrac{4}{2} \ , \dfrac{8}{2}\right)[/tex]
[tex]\=\left(\dfrac{4}{2},\dfrac{8}{2}\right)[/tex]
= (2 , 4)
6) Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]=\sqrt{(3-1)^{2}+(6-2)^{2}}\\\\=\sqrt{2^{2}+(4)^{2}}\\\\=\sqrt{4+16}\\\\=\sqrt{20}\\\\= 4.47[/tex]
You have to evaluate
3³+11-10÷2×4=w
Answer:
18
Brainliest, please!
Step-by-step explanation:
3^3 + 11 - 10 / 2 x 4 = w
27 + 11 - 10 / 2 x 4 = w
27 + 11 - 5 x 4 = w
27 + 11 - 20 = w
38 - 20 = w
w = 18
I really need help because I’m so confused where to start and it’s due tomorrow :(
Answer:
1. 8t+4v
A.9v+7t+6
S.14v+7t
A rectangular box contain 782 apples. If there are 23 rows in a box, how many columns are there?
Select one:
O a. 23
O b. 34
O c. 35
O d. 40
Answer:
34343434343434343434
Tavon has a gift card for $110 that loses $2.50 for each 30-day period it is not used. He has another gift card for $90 that loses $2 for each 30-day period it is not used.
a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal.
b. What will the value of each card be when they have equal value?
30 day period
The first equation is 50 - 2x (because you start with $50 and subtract 2 for each 30 day period)
The second equation is 40-1.5x
Set them equal to each other: 50 - 2x = 40 - 1.5x
Solve for x:
50 - 2x = 40 - 1.5
+2x +2x
50 = 40 + 0.5 x
-40 -40
-------------------
10 = 0.5 x
20 = x
So there will be 20 30-day periods until the cards will be equal in value.
Check: After 20 periods, 50 - 2(20) = $10 left
40 - 1.5(20) = also $10 left
The equations are y = 110 - 2.5x and y = 90 - 2x. Then the value of each card, when they have equal value, will be $10.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let x be the number of days and y be the value of the card.
Tavon has a gift card for $110 that loses $2.50 for each 30-day period it is not used. He has another gift card for $90 that loses $2 for each 30-day period it is not used. Then the equations will be
y = 110 - 2.5x ...1
y = 90 - 2x ...2
From equations 1 and 2, we have
110 - 2.5x = 90 - 2x
20 = 0.5x
x = 40
And the value of y will be
y = 110 - 2.5(40)
y = 110 - 100
y = $10
The equations are y = 110 - 2.5x and y = 90 - 2x. Then the value of each card, when they have equal value, will be $10.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
The price of a printer is $349.00, plus 6% sales tax. What is the sales tax on this printer in dollars and cents?
The sales tax on this printer is $20.94
What is sales tax?A sales tax is a consumption tax imposed by the government on the sale of goods and services.
Given that, the price of a printer is $349.00 having a 6% sales tax.
Sales tax = 6% of $349.00
$349.00 x 0.06 = $20.94
Hence, the sales tax on this printer is $20.94
For more references on sales tax, click;
https://brainly.com/question/29442509
#SPJ6
halp please???????????
Step-by-step explanation:
[tex]thank \: you[/tex]
What is 5 2/3 in radical form?
what is x when the tangent of 25 equals x over 11?
Answer:
x = 5.12938423
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
which expression is equivalent to 2•2 3 •8
Answer:
2^7
Step-by-step explanation:
2 * 2^3 *8
Rewriting 8
8 = 2^3
2 * 2^3 * 2^3
We know that a^b * a^c = a^(b+c)
2^1 * 2^3*2^3
2^(1+3+3)
2^7
Scils Practice convert the following factions into decimals. You must show your work.
How can I turn the fraction 3/12 into a decimal?
3.1 = k - 1.9 solve for k
What is the segment 7x+5=8
Step-by-step explanation:
7x - 5 = 8
7x = 8 + 5
7x = 13 (divide both sides by 7 to get x)
7x/7 = 13/7
x = 1.85714285714
