Your school band is performing a concert. Tickets cost $3 for students and $5 for adults. A total of 125 people attended the concert for a total ticket sales of $475. Write and solve a system of equations to find the number of students and adults that attended the concert. Make sure to write your answer in a complete sentence.
Given :
Tickets cost $3 for students and $5 for adults.
A total of 125 people attended the concert for a total ticket sales of $475.
To Find :
The number of students and adults that attended the concert.
Solution :
Let, number of students and adults that attended the concert is x and y.
Mathematical equation of given conditions :
x + y = 125 ....1)
3x + 5y = 425 ....2)
Putting value of x from 1 to equation 2 is :
3( 125 - y ) + 5y = 425
375 - 3y + 5y = 425
2y = 50
y = 25
x = 125 - 25
x = 100
Therefore, number of students and adults that attended the concert is 100 ans 25 respectively.
Hence, this is the required solution.
______ terms are also expressions. (fill in the blank)
A. No
B. All
C. Some
Alex bought 3 tacos for $4.00. How much would she have to pay for 10 tacos at this rate?
There is 1500 ft of fencing available to make 6 identical pens. Find the maximum area for EACH pen (meaning maximum of one pen).
Answer:
The maximum area is therefore is 93750 ft²
Step-by-step explanation:
The given parameter are;
The a]length of fencing available = 1500 ft.
The perimeter of the figure = 9·x + 4·y
Therefore, 9·x + 4·y = 1500 ft.
The area of the figure = 6 × (x × y) = 3·x × 2·y
From the equation for the perimeter, we have;
9·x + 4·y = 1500
y = 1500/4 - 9/4·x = 375 - 9/4·x
y = 375 - 9/4·x
Substituting the value of y in the equation for the area gives;
Area = 3·x × 2·y = 3·x × 2·(375 - 9/4·x) = 2250·x - 27/2·x²
Area = 2250·x - 27/2·x²
The maximum area is found by taking the derivative and equating to zero as follows;
d(2250·x - 27/2·x²)/dx = 0
2250 - 27·x = 0
x = 2250/27 = 250/3
x = 250/3
y = 375 - 9/4·x = 375 - 9/4×250/3 = 187.5
The maximum area is therefore, 3·x × 2·y = 3 × 250/3 × 2 × 187.5 = 93750 ft²
The maximum area is therefore = 93750 ft.²
The table list the profits of some of the worlds largest corporations in 2013. List the companies in order from greatest to least amount of profit
Answer:
C
Step-by-step explanation:
Jordan created a scale drawing of a rectangular room. The drawing is 8 inches long by 6 inches wide. He used a scale of 1 inch equals 3 ft. What is the area, in the square feet, of the room?
Answer: 432 ft^2
Step-by-step explanation:
If 1"=3', and the box is 8"x6", then we can simply multiply the 8 and 6 by three. You would get 24 by 18.
Follow this up by the equation a=w*l to get
a=24*18 = 432 ft^2.
24. Seven tenths of a number plus 14 is less than forty-nine.
Answer:
50. ☺️☺️
Step-by-step explanation:
I'm going to assume you need this inequality solved.
First, write it as numbers, not words.
7/10n + 14 < 49
where "n" is the unknown number.
Second, if I were you, I'd change that fraction into a decimal, as it'll make life easier later on.
7/10 = 0.7
Now, solve it like you would any other equation.
0.7n + 14 < 49
0.7n +14 - 14 < 49 - 14
0.7n < 35
0.7n ÷ 0.7 < 35 ÷ 0.7
n < 50
The answer is n < 50
Answer: 50
Step-by-step explanation:
49 - 14 = 35
35/7 = 5
10 x 5 = 50
Since, 35 is Seven tenths of a number, One tenth is 5 and there are ten tenths, One tenth which is 5 times ten since there are ten tenths equals to 50 (5 x 10 = 50).
What value of x is in the solution set of 9(2x + 1) < 9x – 18?
Answer:
-3 > x
Step-by-step explanation:
Multiply 2x and 1 by 9. You have 18x + 9 < 9x - 18.Add 18 to 9. You are adding because it is the opposite of subtraction, so it cancels out. You now have 18x + 27 < 9x.Subtract 18x from 9. There is no addition sign in front of the 18x, but it's basically implied. You now have 27 < -9x.Divide both sides by -9. When you divide by a negative, the inequality sign flips. You now have -3 > x.can someone help me answer this question please?
Answer:
A
Step-by-step explanation:
f(x) = (x + 3)(x + 2)(x - 3)
The three roots are going to give - 18 so only A and D can be correct. Why minus? because at some point 3 and 2 and - 3 will all be multiplied together. When they are, the result is - 18
So why did I write x + 2 rather than x - 2? Because the roots turn an equation into 0. You are looking for a way to make x + 2 = 0. It will do that when x = - 2
which is what you were given.
Now to get the answer
(x - 3)(x + 3) = x^2 - 9
(x^2 - 9)(x + 2) = x^3 + 2x^2 - 9x - 18 = f(x)
please help meee i’m abt to failllllllllllll
Answer:
stop cheating boi
Step-by-step explanation:
50% of 320 is equal to 80% of what number?
Answer:
128
Step-by-step explanation:
Solve the equation for y , (REDUCE IF POSSIBLE, AND WRITE YOUR ANSWER IN THIS FORM; y=mx+b).
−6x+y=18
Answer:
y=6x+18
Step-by-step explanation:
add the -6x to the other side to get y alone
Answer:
-6x + y = 18 reduced is -2x + y = 2
Step-by-step explanation:
it is called the Hamber Pickering Formula according to STUIPDPEDIA LOL!
using the same application you used in part f, reflect the line segment across the x-axis. then, rotate it 90° clockwise. Finally. translate it down 2 units. what is the relationship between the original line segment and the transformed segment ? if you transform a line segment with a seweurnce of reflections, to stations, or translations, is it still a line segment ?
Answer:
non
Step-by-step explanation:
I have something to say- Brainly your users are very rude like im failing bEcAuSe YoU pEoPlE! but like yu history people r like saving my life-
Sincerely - Miha~
Answer:
thank you. someone had to say it
Step-by-step explanation:
Answer:
Omg ik what you mean i feel you
Step-by-step explanation:
What is the definition of scale factor
Answer:
The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure. Example: Here, XYUV=123=4 . So, the scale factor is 4 .
Step-by-step explanation:
:D
Will give brainliest if correct.
Answer:
The equation is y = 3x + 15.
The second equation is y = 3 * 50 + 15
If you have a value of 50 berries picked, you would make 165 dollars.
A circuit overloads at 1800 watts of electricity you plug in a toaster that uses 800 watts of electricity write and solve an inequality that represents how many watts you can add to the circuit without overloading it.
Answer:
x ≤ 1000 W
Step-by-step explanation:
Since the circuit becomes overloaded when the load exceeds 1800W and the toaster uses 800 W.
Let the additional watts be x
Therefore;
800 + x ≤ 1800
x ≤ 1800 -800
x ≤ 1000 W
How do you solve this problem?
9=-y it is equations and inequalities
PLEASE HELP
Noa was paid a 25 percent commission for selling a used car.
Percents
Total
100%
If she was paid $1,631.24, what was the selling price of the car?
$4,078.10
$6,524.96
$8,156.20
$40,781.00
Answer:
$6,524.96
Step-by-step explanation:
His quarter commission times four is the awnser
Answer:
BHOPE THIS HELPSWhat figure models 6 divided by 3/2?
(6 divided by 3/2 equals 4)
NEEDS HELP NOW!
BRAINLIEST!
Write an equation that could be used to find three consecutive odd integers whose sum is -3
Answer:
2x+1 + 2x+3 + 2x+5 = -3Step-by-step explanation:
2x+1 - the first odd integer
2 x+1 + 2 = 2x+3 - the next odd integer consecutive to 2x+1
2x+3+2 = 2x+5 - the odd integer consecutive to 2x+3 (the third consecutive odd integer)
2x+1 + 2x+3 + 2x+5 - the sum of three consecutive odd integers
therefore the equation:
2x+1 + 2x+3 + 2x+5 = -3
6x + 9 = -3
6x = -12
x = -2
2x+1=2(-2)+1=-3
2x+3=2(-2)+3=-1
2x+5=2(-2)+5=1
the three consecutive odd integers whose sum is -3 are: -3,-1,1
The maximum speed possible on a length of railroad track is directly proportional to the cube root of the amount of money spent ob maintaining the track. Suppose that a maximum speed of 25 km/hr is possible on a stretch for which 450,000 was spend on maintence, find the maximum speed if the amount spent on maintence is increased to $1,750,000 Pls help me show steps please
Answer:
[tex]39.29\ \text{km/h}[/tex]
Step-by-step explanation:
s = Speed of the train
m = Money spent on maintanence
[tex]s\propto m^{\dfrac{1}{3}}[/tex]
Let k be the constant of proportionality so
[tex]s=k (m)^{\dfrac{1}{3}}[/tex]
Now a case is given where 25 km/hr is possible on a stretch for which 450,000 is spent so
s = 25
m = 450000
[tex]s=k (m)^{\dfrac{1}{3}}\\\Rightarrow k=\dfrac{s}{m^{\dfrac{1}{3}}}\\\Rightarrow k=\dfrac{25}{450000^{\dfrac{1}{3}}}\\\Rightarrow k=0.326[/tex]
Now when m = 1750000
[tex]s=k (m)^{\dfrac{1}{3}}\\\Rightarrow s=0.326\times 1750000^{\dfrac{1}{3}}\\\Rightarrow s=39.29\ \text{km/h}[/tex]
The maximum speed of the train would be [tex]39.29\ \text{km/h}[/tex].
Help plz:))) I’ll mark u brainliest
Nadia charges $5.50 an hour for babysitting. She babysits 19.50 hours the first week of the month and 19 hours the second week of the month. Suppose Nadia raises her rate by $0.55 an hour. How many hours would she need to work to earn the same amount of money she made in the first two weeks of the month? Complete the explanation and give your answer. Nadia's new hourly rate is $ . She would need to work hours in the next two weeks to make the same amount she made in the first two weeks.
Answer:
Step-by-step explanation:
ind her earnings for the first two weeks of the month at the $5.50 an hour rate.
5.50 × (18 + 20.50) = 5.50 × 38.5
= 211.75
She earned $211.75 the first two weeks of the month.
Find her new hourly rate, if she raises her rate by $0.55.
5.50 + 0.55 = 6.05
Her new hourly rate is $6.05.
Find how many hours she would need to work at $6.05 an hour in order to earn $211.75.
211.75 ÷ 6.05 = 35
She would need to work 35 hours.
Find the product: a) (5 – 2h) (3 + h) b)4p ^2 q ^2 (p ^2 – q ^2)
Answer:
A.) -8h
Step-by-step explanation:
a.) . (5 – 2h) (3 + h)
a.) (5 – 2h) (3 + h)
(5+3) (h-2h)
8(-h)
-8h
Find the area of a square with side length x when x is equal to the given value. Are the area of a square and the length of its side directly proportional? Justify your answer. x=10 in.
Step-by-step explanation:
The formula for calculating the area of a square is expressed as;
A = x² where;
x is the length of one side of the square
Given
x = 10in
A = 10²
A = 10 * 10
A = 100in²
Area of the square with side length 10in is 100in²
From the equation A = x², we can see that as the value of x increases, the value of the area also increases and vice versa. This means that the area of the square is directky proportional to its length. Hence we can say YES, the area of a square and the length of its side directly proportional
Answer:
100 sq in
Step-by-step explanation:
No, not proportional
Emie read that the movie made 25,992,412.50 in its third week he also read that the average ticket price for this week was 8.35how many people saw the movie this week
Given :
Collection in third week, C = $25,992,412.50 .
Average ticket price, T = $8.35 .
To Find :
Number of people who saw movie in week.
Solution :
Let, number of people are x.
[tex]\text{Number of people }=\dfrac{\text{Total amount }}{\text{Average price}}\\\\= \dfrac{25,992,412.50 }{8.35}\\\\[/tex]
≈ 3112864
Therefore, around 3112864 people saw the movie this week.
Hence, this is the required solution.
What is the slope of this graph?
O
5
3
o
3
O
-3
Answer:
where is the graph?
Step-by-step explanation:
A cleaning mixture requires 5 cups of water for every 2 cups of solution which ratio of cups of water to cups of solution will make the same cleaning mixture?
a. 15:6
b. 8 :20
c. 60;18
d. 20:14
Answer:
a.15.6
Step-by-step explanation:
simplify all the ratios to their simplest forms.
15/3:6/3
5:2
Help!
What is one and sixty-seven hundredths added to fifteen and nine tenths?