The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $48, balcony tickets are $45, and mezzanine tickets are $34. One particular night, sales totaled $65,140. There were 381 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 328 more than 2 times the number of mezzanine tickets sold. How many of each type of ticket were sold?
I already have these equations: 48x+45y+34z=65140, x=y+z+381, y=2x+328, but I can't figure out how to substitute them.
Answer: In this problem, you have three unknowns: broadway tickets for the (1) main floor, (2) balcony and (3) mezzanine. To solve algebraic equations, the total number of unknowns must be the same with the number of independent equations. With that, let's formulate these three equations.
Let the 3 unknowns be
x = number of tickets for the main floor
y = number of tickets for the balcony
z = number of tickets for the mezzanine
The independent equations are:
59x+50y+40z=73,785 --> eq 1
x = y+z+435 --> eq 2
y = 78 + 33 z ---> eq 3
Solve the equations simultaneously. Substitute eq3 to eq 2
x = 78+33z+z+435
x = 513+34z --> eq 4
Substitute eq 4 and eq 3 to eq 1
59(513+34z)+50( 78 + 33 z)+40z=73,785
Solve for z using the calculator: z = 11
Use eq 4 to find x: x = 877
Use eq 2 to find y: y = 432
There were 877 main floor tickets, 432 balcony tickets and 11 mezzanine tickets sold.
Step-by-step explanation:
Answer:
Main floor - 892, balcony - 450, mezzanine- 61Step-by-step explanation:
Main floor - x, balcony - y, mezzanine- zEquations:
48x + 45y + 34z = 65140 ↔ (1)x = 381 + y + z ↔ (2)y = 2z + 328 ↔ (3)Substitute (3) into (2):
x = 381 + 2z + 328 + z ⇒ x = 3z + 709 ↔ (4)Substitute (2) and (4) into (1) and solve for z:
48(3z + 709) + 45(2z + 328) + 34z = 65140144z + 48*709 + 90z + 45*328 + 34z = 65140268z + 34032 + 14760 = 65140268z = 65140 - 48792268z = 16348z = 16348/268z = 61Find x and y:
x = 3z + 709 = 3*61 + 709 = 892y = 2z + 328 = 2*61 + 328 = 450CAN SOMEONE PLZ ANSWER THIS ITS DUE AT 11:59 APRIL 11 2021 AND ILL MARK U BRAINLIST
Answer:
answer is c
Step-by-step explanation:
Answer:
c. 586.2
Step-by-step explanation:
add all areas together:
127.2 for semi circle on right
22x18=396 for middle square
7*9=36 for 2 triangles on left
What is the area of the figure show
• below?
-30 ft-
15 ft
- f
1551
A 315 f12
B 225 fra
C 180 ft2
D 90 fre?
Answer:
315 ft²
Step-by-step explanation:
•Split the shape into a triangle and a square.
•A=bh so 15*15=225 (area of square)
•Since the height of the square is 15, subtract given height of 3 from 15 which is 12 and that is the base of triangle.
• To find the height, subtract 15 since the base is equal to the top side.
•A=1/2bh for triangles so 1/2(15)(12) is 90.
•Add 225 and 90 then boom. 315ft²
The volume of the polyhedron is ______ cm3.
Answer:
Volume = 144 cm³
Step-by-step explanation:
Volume of the polyhedron = volume of triangular prism = ½*b*h*l
Where,
b = 4 cm
h = 6 cm
l = 12 cm
Substitute
Volume = ½*4*6*12
Volume = 144 cm³
Can somebody help me
Answer:
the answer is D because it depends of the velocity
Use △GHJ, where A, B, and C are midpoints of the sides. When AC = 3y−5 and HJ = 4y+2, what is HB?
Use △GHJ, where A, B, and C are midpoints of the sides
HB=14
Given :
Use △GHJ, where A, B, and C are midpoints of the sides
AC = 3y−5 and HJ = 4y+2
Apply mid point theorem
mid segment = half of base
[tex]AC=\frac{1}{2}(HJ)[/tex]
Now we replace AC and HJ
[tex]AC=\frac{1}{2}(HJ)\\3y-5=\frac{1}{2} (4y+2)\\3y-5=2y+1\\Subtract \; 2y\\1y-5=1\\Add \; 5\\1y=1+5\\y=6[/tex]
B is the midpoint . HB is half of HJ
[tex]HB=\frac{1}{2} HJ\\HB=\frac{1}{2}(4y+2)\\x=6\\HB=\frac{1}{2}(4(6)+2)\\\\HB=\frac{1}{2}(28)\\\\HB=14[/tex]
So the value of HB = 14
Learn more : brainly.com/question/23120373
Solve for x.
Question 4 options:
A)
8
B)
–8
C)
9
D)
–9
Answer:
x = -9
Step-by-step explanation:
Given:
BC = x + 19
ST = x + 29
Required:
Value of x
Solution:
Midsegment theorem states that the midsegment of a triangle = ½ of the length of its third side
Thus:
BC = ½(ST)
Substitute
x + 19 = ½(x + 29)
Multiply both sides by 2
2(x + 19) = x + 29
2x + 38 = x + 29
Collect like terms
2x - x = -38 + 29
x = -9
Can someone plz help me with my question I will pAaay you
Answer:
sure what is it
Step-by-step explanation:
Well, it depends on the question!!
(comment it if you need me to answer it)
Solve the following system of inequalities graphically on the set of axes below. State
the coordinates of a point in the solution set.
y > -2x - 1
y > x + 2
Answer:
[tex](x,y) = (-1,1)[/tex]
Step-by-step explanation:
Given
[tex]y>-2x - 1[/tex]
[tex]y>x + 2[/tex]
Required
Solve graphically
See attachment for graph;
The black shade represents [tex]y>-2x - 1[/tex]
While the green, represents [tex]y>x + 2[/tex]
Next, determine the intersection points between the two lines
From the attached graph, we have:
[tex](x,y) = (-1,1)[/tex]
Hence, the solution is:[tex](-1,1)[/tex]
A farm is sold for €457 000, which gives a profit of 19%. Find the profit
Answer:
103453.17
Step-by-step explanation:
19% of 457,000 is 86,830 euros and use conversion rate to get a profit of 103453.17
ZABD and ZDBC are supplementary angles.
What is the measure of x?
x = [?]°
110%
AS
>C
B
Angles are not drawn to scale.
Enter
Answer:
x=70°
Step-by-step explanation:
x+110=180 linear pair
x=180-110=70
Answer:
Solution given:
x+110°=180[supplementary]
x=180-110=70°
x=70°
What is the value of k?
k = 28
k = 29
k = 31
k = 42
Answer:
k=29
Step-by-step explanation:
we know that
-------> by supplementary angles
Solve for k
Combine like terms in the left side
Substract both sides
Divide by both sides
therefore
the answer is the option
B
Point B, located at (-4,-7), is reflected over the y-axis. What are the coordinates of B?
A. (-4, 7)
B. (4, -7)
C. (4, 7)
D. (-4, -7)
Answer:
A
Step-by-step explanation:
Factor out the greatest common factor
යය _|5
1/2 45
How to solve trinomial
Answer:
Identify a, b , and c in the trinomial ax2+bx+c.
Write down all factor pairs of c.
Identify which factor pair from the previous step sum up to b.
Substitute factor pairs into two binomials.
Step-by-step explanation:
Jeremy will roll a number cube, numbered 1–6, twice. What is the probability of rolling an odd number, then a number bigger than 2?
Answer:
1/12
Step-by-step explanation:
The probability of rolling an odd number = 3/6
The probability of rolling 2 after an odd number =
1/6
3/6 x 1/6 = 3/36
3/36 = 1/12 (after simplified)
f(x) = 3x + 5 g(x) = 4x2 – 2 h(x) = x2 – 3x + 1 Find f(x) – g(x) – h(x)
Step-by-step explanation:
this is the answer
hope it helped!!!
can someone pls help me
Answer:
B. 7Step-by-step explanation:
AB is a tangent to circle o
ABO is a right-angled
AO²=AB²+BO²
[tex]BO=\sqrt{AO^{2}-(AB)^{2})\\}\\\\\sqrt{(8.6)^{2}-(5)^{2} } \\\\=\sqrt{73.96-25} \\\\=\sqrt{48.9} \\\\=6.99\\\\Answer=7[/tex]
hope it helps....
have a great day :)
9.3+b=−42 , you would subtract 9.3 to isolate the variable.
Answer:
yeh you are correct so it will be b is equal to minus 42 minus 9.3 that will be equal to -51.3 so that is the value of b
Find the GCF of the terms of the polynomial
Answer:
7z³
Step-by-step explanation:
7z³
[tex]\huge\boxed{Hi\:there!}[/tex]
To find the GCF of the polynomial, all we have to do is spot the common factor of all the terms of the polynomial.
21z⁵-42x⁴+14z³
The common term is
7z³
If we factor 7z³ out, we'll get
z³(3z²-6z+2)
[tex]\huge\boxed{\sf{Hope\:this\:helps!}}\\[/tex]
[tex]\huge\bold{Good\:luck!}[/tex]
[tex]\huge\mathfrak{LoveLastsAllEternity}[/tex]
GIVING BRAINIEST to who ever answers hurry
Answer:
x=10
Step-by-step explanation:
50+x=6x
-x -x
50=5x
/5 /5
x=10
y^4-2y^2+1...........
Answer:
(y²-1)²
Step-by-step explanation:
Given:
y⁴ - 2y² + 1
Find:
Factor of given equation
Computation:
y⁴ - 2y² + 1
Change given equation in quadratic equation.
(y²)² - 2(y)²(1) + (-1)²
We know that
(a)² - 2(a)(b) + (b)²
(a-b)²
So,
(y²)² - 2(y)²(1) + (-1)²
(y²-1)²
Please help me with this answer
Thank you!
The frequency table represents the job status of a number of high school students. A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for job with entries 12, 38, 50. The third column is labeled not looking for a job with entries 28, 72, 100. The fourth column is labeled total with entries 40, 110, 150. Which shows the conditional relative frequency table by column? A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for a job with entries 0.3, nearly equal to 0.33, 1.0. The third column is labeled not looking for job with entries 0.7, nearly equal to 0.65, 1.0. the fourth column is labeled total with entries nearly equal to 0.27, nearly equal to 0.73, 1.0. A 4-column table with 3 rows titled job status. The first column is blank with entries currently employed, not currently employed, total. The second column is labeled Looking for a job with entries 0.12, 0.38, 050. The third column is labeled not looking for a job with entries 0.28, 0.72, 1.00. The fourth column is labeled total with entries 0.4, 1.1, 1.5. A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for a job with entries 0.24, 0.76, 1.0. The third column is labeled not looking for a job with entries 0.28, 0.72, 1.0. The fourth column is labeled total with entries nearly equal to 0.27, nearly equal to 0.73, 1.0. A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for job with entries 0.08, nearly equal to 0.25, nearly equal to 0.33. The third column is labeled not looking for a job with entries nearly equal to 0.19, 0.48, nearly equal to 0.67. The f
Answer:
C on edge
hope this helps
Step-by-step explanation:
The answer was C for me on Edg.
The price of one gallion of heating oil $2.589. Which is this number rounded to the nearest penny A $2.50 a $2.59 c $2.70 $3.00
The students in a typing class have a mean typing rate of 38.2 words per minute. Five randomly selected students have typing rates of 32, 28, 41, 38, and 45 words per minute.
What is the value of μ and x¯ ?
μ = 38.2 wpm, x¯ = 38.0 wpm
μ = 36.8 wpm, x¯ = 38.2 wpm
μ = 38.2 wpm, x¯ = 36.8 wpm
μ = 38.0 wpm, x¯ = 38.2 wpm
Answer:
µ = 38.2 wpm, = 36.8 wpm
What is another way to describe the following expression?
5−(x+y)3
Answer:
How can I help you?
5−(x+y)35-(x+y)3
Simplify
Simplify the expression.
−3x−3y+5-3x-3y+5
Answer:
the difference of 5 and the cube of the sum of x and y
what's a 3 number multiplication that = 1000?
Answer:
1,1, and 1000
Step-by-step explanation:
Answer:
(10 x 10) x 10 = 1000
Step-by-step explanation:
10 x 10 = 100
100 x 10 = 1000
Find all complex solutions of the equation z⁴-1-i=0.
Answer:
Step-by-step explanation:
hello :
z⁴=1+i given : z² = t t is the complex number so : z⁴= (z²)² =t²
solve for t this equation : t² = 1+i
if : t = x+iy t² =(x+iy)² = x²+2xiy+(iy)² =x²-y²+2xyi ...... ( i² = -1)
t² = 1+i means : x²-y²+2xyi = 1+i
you have this system : x²-y² = 1.....(*)
2xy = 1.....(**)
slve for x and y you ca add this equation : ....(***)
( use : t² = 1+i
/t²/ = /1+i/ so :/t/² = /1+i/ .... (√(x²+y²))²=√(1²+1²) =√2 means x²+y² = √2)
the system is : x²-y² = 1.....(*)
2xy = 1.....(**)
x²+y² = √2 ....(***)
add (*) and (***) : 2x²= 1+√2
x² = (√2+1)/2
substrac (*) and (***) you have : y² = (√2-1)/2
use (**) the proudect xy is positif (same sign) so :
x=√( (√2+1)/2) and y = √( (√2-1)/2) so : t1 =√( (√2+1)/2)+i√( (√2-1)/2)
x= -√( (√2+1)/2) and y = -√( (√2-1)/2) so :t2= -t1
same method for equation : z² =t1 ..(2 solution ) and z² = t2..(2 solution )
Shelly invested in a lifetime annuity that begins payments at age 65. Her life
expectancy is 88. Shelly invested $800,000 into the annuity, which earns 4.8%
APR, compounded monthly. With this annuity, what is Shelly's monthly
payment amount?
A. $4756.93
B. $4792.38
C. $4984.72
D. $4897.79
Answer: 4792.38
Step-by-step explanation: just did it
