78 students went on a field trip. They went by van or car. The total number of cars and vans were 10. Each car held 5 students and each van held 12 students. How many cars and how many vans went on the field trip?
Solution:Let the number of cars be "x" and the number of vans be "y".
According to question,
x + y = 10 5x + 12y = 78 -->(ii)
=> 5(x + y) = 10 × 5
=> 5x + 5y = 50 -->(i)
By Elimination method,
Equation (i) - (ii) we get,
(5x + 5y) - (5x + 12y) = 50 - 78
=> 5x + 5y - 5x - 12y = - 28
=> - 7y = - 28
=> 7y = 28
=> y = 28/7
=> y = 4
Putting the value of "y" in Equation (i)
5x + 5y = 50
=> 5x + 5 × 4 = 50
=> 5x + 20 = 50
=> 5x = 50 - 20
=> 5x = 30
=> x = 30/5
=> x = 6
Therefore,The total number of cars went = 6
The total number of vans went = 4
====================================================
Question no.6:168 students went on a field trip. They took a total of 10 vans and buses. Each bus held 42 students, and each van held 6 students. How many vans went on the field trip?
Solution:
Let the number of buses be "x" and the number of vans be "y".
According to question,
x + y = 10 42x + 6y = 168 -->(ii)
=> 42(x + y) = 10 × 42
=> 42x + 42y = 420 -->(i)
By Elimination method,
Equation (i) - (ii)
(42x + 42y) - (42x + 6y) = 420 - 168
=> 42x + 42y - 42x - 6y = 252
=> 36y = 252
=> y = 252/36
=> y = 7
Putting the value of "y" in Equation (ii)
42x + 6y = 168
=> 42x + 6 × 7 = 168
=> 42x + 42 = 168
=> 42x = 168 - 42
=>42x = 126
=> x = 126/42
=> x = 3
Therefore,Total number of buses went = 3
Total number of vans went = 7
Ann opened a savings account with an initial deposit of $250. Which combination will result in a zero balance in Ann's account?
A deposit $20 in the first week and withdraw $270 in the second week
B deposit $270 in the first week and withdraw $20 in the second week
C deposit $20 in the first week and withdraw $250 in the second week
D deposit $250 in the first week and withdraw $20 in the second week
Answer:
The answer is A 250+20 then 270-270=0
solve for x and y please
Answer:
Step-by-step explanation:
The 2 triangles are similar so corresponding sides are in the same ratio.
3/x = 6/16
6x = 48
x = 8.
9/y = 6/16 = 3/8
3y = 72
y = 24.
Answer:
y = 24 mx = 8 musing proportional equation:
[tex]\rightarrow \sf \dfrac{AC}{CE} = \dfrac{DB}{DE}[/tex]
[tex]\hookrightarrow \sf \dfrac{9}{6} = \dfrac{y}{16}[/tex]
[tex]\hookrightarrow \sf 9(16)} = {6y}[/tex]
[tex]\hookrightarrow \sf y = 24[/tex]
====================
[tex]\rightarrow \sf \dfrac{AE}{CE} = \dfrac{EB}{DE}[/tex]
[tex]\hookrightarrow \sf \dfrac{3}{6} = \dfrac{x}{16}[/tex]
[tex]\hookrightarrow \sf 3(16)} = 6x[/tex]
[tex]\hookrightarrow \sf x = 8[/tex]
A triangle has angle measurements of 31°, 10°, and 139º. What kind of triangle is it?
Answer:
Its a Obtuse Angled Triangle
Step-by-step explanation:
This is due to one of the angles being over 90 Degrees
Find the surface area
explain how the model for 3/5 - 1/2 9s is different from the model for 3/5 - 3/10
The model is different because it has different denominator and numerator
What is the surface area for the following shape?
Answer:
The answer is : A 192 in cubic
Step-by-step explanation:
100 % correct
Answer:
208 in^2
Step-by-step explanation:
front: 6x4 = 24
back: 6x4 = 24
right: 6x8 = 48
left: 6x8 = 48
top: 4x8 = 32
bottom: 4x8 = 32
24+24+48+48+32+32 = 208
whats the answer.......
Answer:
up
Step-by-step explanation:
We should go 4 units up from the zero in the coordinate plane.
What is coordinate plane?A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.
Given that, in the ordered pair (3, 4), the value of y is 4.
Here, in the ordered pair (3, 4), 3 is x-coordinate and 4 is y-coordinate.
The perpendicular distance from the x-coordinate 3 and y-axis is 3 units, which is 3 units right to the y-axis.
The perpendicular distance from the y-coordinate 4 and x-axis is 4 units, which is 4 units up to the x-axis.
Hence, we should go 4 units up from the zero in the coordinate plane.
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What is the slope of
the line?
Give your answer as
a fraction in simplest
form.
Answer:
3/5
Step-by-step explanation:
Rhis time we dont have another dot, so we just start from zero. We rise 3 and then run 5.
Hoped this helped!!
A toy boat is bobbing on the water.
Its distance D(t)D(t)D, left parenthesis, t, right parenthesis (in \text{m}mstart text, m, end text) from the floor of the lake as a function of time ttt (in seconds) can be modeled by a sinusoidal expression of the form a\cdot\sin(b\cdot t)+da⋅sin(b⋅t)+da, dot, sine, left parenthesis, b, dot, t, right parenthesis, plus, d.
At t=0t=0t, equals, 0, when the boat is exactly in the middle of its oscillation, it is 1\text{ m}1 m1, start text, space, m, end text above the water's floor. The boat reaches its maximum height of 1.2\text{ m}1.2 m1, point, 2, start text, space, m, end text after \dfrac{\pi}{4}
4
π
start fraction, pi, divided by, 4, end fraction seconds.
Find D(t)D(t)D, left parenthesis, t, right parenthesis.
An equation for a toy boat is bobbing on the water is in the sinusoidal form which we can write as, D(t) = 0.2 sin2t +1
What is an Equation ?
An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, D(t) = acos2t +b
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given information,
Equation of bobbing, D(t) = a sinbt + d
By graph we can say that it is compressed two times,
So, value of b will be, 2
At t =0, height from the floor is 1 m
1 = a sin(2×0) + d
d = 0
At t =π/4, height from the floor is 1.2 m
1.2 = a sin(2×π/4) + 1
a = 0.2
By graph we can say that it is compressed two times,
So, value of b will be 2
Hence, An equation is D(t) = 0.2 sin2t +1
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I WILL GIVE BRAINIEST!!!! Help!!!! 4. A stone nudged off the Royal Gorge Bridge near Cañon City, Colorado, falls 1053 feet before
hitting water. Because its speed increases as it falls, the distance it travels each second
increases. During the first second, it drops 16 feet. During the next second, it drops an
additional 48 feet. During the third second, it drops another 80 feet. The distances traveled
each second form an arithmetic sequence:
16, 48, 80, ...
Part I: How far does the stone fall during the 5th second? Find and use the explicit formula.
a. What is the first term of the sequence?
b. What is d, the common difference?
c. Write the explicit formula in function notation. Use f(n) = f(1) + (n - 1)d, where f(1)
Answer:
First term = a= 16.
Common difference, d, = 32.
Answer for the fifth second is = 144 feet.
Step-by-step explanation:
This question is simply an Arithmetic Progression, AP,.
so, the 1st second represents the first term and so on.
for the common difference, you just subtract the first from the second term and confirm by subtracting the second from the third term and i got 32.
How many quarts is 16000 gallons
64000quarts is 16000gallons
Answer:
64,000 quarts are in 16,000 gallons
Step-by-step explanation:
Formula - Divide the volume by 4
Hope this helps (:
If 5,x,125 are in continued proportion, find valueee of xxxxx.....
Answer:
[tex] \pmb{SOLUTION:-}[/tex]
5,x,125 are in continued proportion,Then,
[tex] \displaystyle{ \frac{5}{x} = \frac{x}{125} }[/tex]
[tex]5 \times 125 = {x}^{2} [/tex]
[tex] {x}^{2} = 625[/tex]
[tex]x = \sqrt{625} [/tex]
[tex]x = 25[/tex]
Answer:
a₂ = ±25Step-by-step explanation:
5, x, and 125 are part of a geometric progressionWhat we know :
a (first term) = 5aₙ (final term) = 125n (number of terms) = 3Finding the common ratio (r)
aₙ = arⁿ⁻¹125 = (5)(r)³⁻¹25 = r²r = ± 5Finding x
x is the 2nd term of the progressiona₂ = ara₂ = 5(±5)a₂ = ±25Peter earns each hour for the first 40 hours he works each week. For every hour, he works after 40 hours he earns $12 each hour last week, Peter earned $444. Which equation could be used to find the number of hours, h, during which Peter earned $12 last week?
Answer:
5
Step-by-step explanation:
I said so THATS WHY
Re-write the quadratic function below in Standard Form
y=2(x+2)(x−4)
Answer:
Standard form:
y=2x^2-4x-16
Help picture below problem 11
Answer:
B) angle B
Step-by-step explanation:
Since the question is telling you that both the triangles are essentially the same, you just have to look to see which letter of triangle ABC is in the same general place as triangle DEF.
In this case angle B is in the same general spot as angle E, so therefore B is your answer.
Hope this helps you :)
For each statement, determine if the statement can be true or if the statement can never be true.
Select the correct choice in each row.
Question 6 of 10
The graph of f(x) -13*-6 is shown below. g(x) is a transformation of f(x).
How would you write the equation for the function g(x)?
10+
9)
5
25-20-15-10
5 10 15 20 25
10-13-6-10-
-15+
O A 9-364-43
OB. 863)-23* +3
OC. 900---13--6
D. g(x) - 3* +2
The graph is attached.
Step-by-step explanation:
This will be an exponential function, which means it will be a smooth curve.
The y-intercept will be 35, since this is the starting population.
Since the population is increasing, the curve will increase as well.
PLEASEEE HELPPPP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
98Step-by-step explanation:
the solution is in the picture
In an invasion game such as Soccer, Football, or Handball, how can you tell which team is offense and which team is defense?
Answer:
The easiest way to determine whose offense or defense would be to check where the players are positioned at. Obviously, the main goals of Soccer or Football are in the back meaning people who are defending the goal are most likely to be behind the teammates who are offensive (common sense).
Step-by-step explanation:
Given: -7x<-21 choose the solution set
Answer:
x > 3
Step-by-step explanation:
The only thing you need to do is just divide both sides by -7
-7x/-7<-21/-7
x>3
I hope this helped!! Good luck (:
In the accompanying diagram, AB is a diameter of circle O, FECA and
FBG are secants, AD, DE, EB = 1:3:2 and BG = 40°. Find the measures of AD,
DE, EB, and AG.
Check the picture below.
so to split 180 in a 1 : 3 : 2 ratio, we'll simply divide 180 by (1 + 3 + 2) and distribute accordingly
[tex]\cfrac{180}{1+3+2}\implies 30\qquad \qquad \stackrel{1}{1(30)}~~:~~\stackrel{3}{3(30)}~~:~~\stackrel{2}{2(30)}\implies 30~:90~:60 \\\\[-0.35em] ~\dotfill\\\\ \widehat{AG}=180+40\implies \widehat{AG}=220[/tex]
a triangular prism is cut parallel from its bases, what is the shape of the cut?
Answer:
a triangle
Step-by-step explanation:
when looking at a triangular prism it is made of 4 triangles, so any way you cut it, it will be a triangle
What is the 15th term of the following sequence? 0.25, 0.5, 1, 2, 4…
4,096
Solution:In this case, we have a geometric sequence.In a geometric sequence, we use multiplication/division in order to get to the next term.In this case, we multiply each term by 2.So these are the terms:0.25, 0.5, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024, 2,048, 4,096Hope it helps.
Do comment if you have any query.
a poker hand consisting of five cards, is dealt from a standard deck of 52 cards. Find the probability that the hand contains five face cards
Answer:
56
Step-by-step explanation:
because is one times 44
How do you know when terms can be combined?
A. They are the same size
B. They have the same exponent
C. They have the same number
D. They have the same variable and exponent
Answer:
C. They have the same number
Let R be the region in the first quadrant bounded above by the graph of y=1−x^2 and below by the graph of y=1−√x, as shown in the figure above. What is the area of the region?
If R be the region in the first quadrant bounded above by the graph of y=1−x² and below by the graph of y=1−√x then area is 1/3.
To find the area of the region bounded by the graphs of y = 1 - x² and y = 1 - √x in the first quadrant.
we need to determine the points of intersection and integrate the difference between the two functions over that interval.
To find the points of intersection, we set the two functions equal to each other:
1 - x²= 1 - √x
x²= √x
Squaring both sides again, we have:
x⁴ = x
x(x³ - 1) = 0
This equation gives us two potential solutions: x = 0 and x = 1.
To determine the limits of integration, we need to find the x-value where the two curves intersect.
Since y = 1 - √x represents the upper curve, we can set the two functions equal to each other and solve for x:
1 - x² = 1 - √x
x² = √x
x⁴ = x
Since we are only interested in the first quadrant, the solution x = 0 is not relevant.
Therefore, the only point of intersection is x = 1.
Integrating the difference between the two functions over the interval [0, 1] will give us the area of the region R:
A = ∫[0, 1] (1 - x²) - (1 - √x) dx
Expanding and simplifying the integrand:
A = ∫[0, 1] 1 - x² - 1 + √x dx
A = ∫[0, 1] -x² + √x dx
Integrating each term separately:
A = [-x³/3 + (2/3)x^(3/2)]|[0, 1]
A = [-(1/3) + (2/3)] - [0]
A = 1/3
Therefore, the area of the region R is 1/3.
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The measure of the arc from A to B that does not pass through C?
A-160
B-140
C-100
D-90
Answer: C
Step-by-step explanation:
choose a random number between 1 and 20 . What is the probability that the number is greater than 5 and less than 15
Answer:
MY RANDOM ANSWER : my answer is 3
Step-by-step explanation:
The probablitiy of that is 9
Two boys san around a track that is 400 meters long. Miguel ran around the track three
times in 240 seconds. Joseph ran around the track three times in 200 seconds. What was the
difference between the speeds of the two boys?
A.
1 meter per second
5 meters per second
B.
C.
6 meters per second
D.
11 meters per second
Using proportions, it is found that the difference between the speeds of the two boys was of:
A. 1 meter per second.
What is a proportion?A proportion is a fraction of a total amount. Following this concept, velocity is distance divided by time.
In this problem, Miguel ran 1 lap = 400 meters each 240/3 = 80 seconds, hence his speed is given by:
sM = 400/80 = 5 m/s.
Joseph ran 400 metters each 200/3 = 66.67 seconds, hence his speed is given by:
sJ = 400/66.67 = 6 m/s.
The difference is given by:
6 m/s - 5 m/s = 1m/s.
Hence, option A is correct.
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Help picture below 3 problems easy will give brainlest
Answer:
7. 64
22. 12.9
12. 22
Step-by-step explanation:
x = 154 154 - 90 = 64
15% of 86 is 12.9
A triangle's angles must all add up to 180.
90 + 68 = 158 180 - 158 = 22