Answer:
32 adult245 studentStep-by-step explanation:
The given relations between numbers and prices can be used to write a system of equations for the number of each kind of ticket. One equation will describe ticket numbers; the other will describe ticket revenue.
SetupLet x represent the number of adult tickets, and y the number of student tickets. The given relations can be written as the general-form equations ...
8x -y -11 = 0 . . . . . . . . . ticket numbers
5x +3y -895 = 0 . . . . . ticket revenue
SolutionThe setup using general form equations lends itself to solution using the "cross multiplication method." Using this method, we define three numbers used in the solution:
Δ = 8(3) -5(-1) = 24 +5 = 29
Δx = -1(-895) -3(-11) = 895 +33 = 928
Δy = -11(5) -(-895)(8) = -55 +7160 = 7105
And the solutions are ...
x = Δx/Δ = 928/29 = 32
y = Δy/Δ = 7105/29 = 245
32 adult tickets and 245 student tickets were sold.
__
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Find the exact values of the remaining trigonometric functions of satisfying the given conditions. (If an answer is undefined, enter UNDEFINED.)
cos =
24
25
,
tan < 0
The exact values of the remaining trigonometric functions are sin(x) = -7/25 and tan(x)= -7/24
How to solve the trigonometric functions?The function is given as:
cos(x) = 24/25, tan(x) < 0
The sine function is calculated using:
sin^2(x) + cos^2(x) = 1
So, we have:
sin^2(x) + (24/25)^2 = 1
Collect like terms
sin^2(x) = -(24/25)^2 + 1
Evaluate the squares
sin^2(x) = -576/625 + 1
Take the LCM
sin^2(x) = (625-576)/625
Evaluate
sin^2(x) = 49/625
Take the square roots
sin(x) = -7/25 --- sin(x) is negative because tan(x) < 0
The tangent function is calculated using:
tan(x) = sin(x)/cos(x)
This gives
tan(x) = (-7/25) / (24/25)
Evaluate
tan(x)= -7/24
Hence, the exact values of the remaining trigonometric functions are sin(x) = -7/25 and tan(x)= -7/24
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Complete question
Find the exact values of the remaining trigonometric functions of satisfying the given conditions. (If an answer is undefined, enter UNDEFINED.)
cos(x) = 24/25, tan(x)< 0
sin(x) =
tan(x) =
Abby can buy individual songs for $1.00 to download, or she can
download an entire album for $8.00. Abby can spend no more
than a total of $50. She wants to buy at least two albums, and no
more than 30 individual songs.
The following system of inequalities represents this situation,
where x is the number of individual songs and y is the number of
albums.
x + 8y ≤ 50
x ≤ 30
y22
Which yellow shaded region corresponds to Abby's possible
choices?
The solution to the inequalities x + 8y ≤ 50, x ≤ 30, y > 2 is the darker region shown on the graph.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the number of individual songs and y represent the number of albums, hence:
x + 8y ≤ 50 (1)
x ≤ 30 (2)
y > 2 (3)
The solution to the inequalities x + 8y ≤ 50, x ≤ 30, y > 2 is the darker region shown on the graph.
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Equations in Iwo V Solve the system by the addition method. 3x+8y=6 3x-8y=6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. There is exactly one solution. The solution set is ‹› (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. The solution set is {(x,y)|3x + 8y = 6) or ((x,y)|3x - 8y = OC. The solution set is Ø.
Answer:
A. there is exactly one solution. the solution set is {(2, 0)}.
Step-by-step explanation:
3x + 8y = 6
3x - 8y = 6
when we add these 2 equations, we get
6x + 0 = 12
6x = 12
x = 2
now we use one of the original equations to get y :
3×2 + 8y = 6
6 + 8y = 6
8y = 0
y = 0
Cost of a microscope: $149.95
Markup: 30%
Answer:
194.935
Step-by-step explanation:
149.95×30%=44.985
149.95+44.985=194.935 new price
2x-y+z=8
X+2y+2z-6=0
X-2y-z=1
Solve by linear equation
Answer:
68
Step-by-step explanation:
I did it and it was right
112 is the product of 7 and Raj’s score.
Answer: 16
Step-by-step explanation: 112 is equal to the product of 7 and Raj's score. Therefore, Raj's score score is 112 divided by 7 which is 16.
Answer:
Raj´s score = 16
Step-by-step explanation:
112 = 7R
R = Raj´s score
112/7 = R
R = 16
find the area of a triangle whose sides are 5 m, 6 m and 9m,( use root 2 =-1.41 m)
Answer: 14.1 sq meters
Step-by-step explanation:
this question has already been answered
What is the simplified base of the function f(x)=1/4([tex]\sqrt[3]{108} ^{x\\}[/tex])
The simplified function of [tex]f(x) = \frac 14(\sqrt[3]{108^x})[/tex] is [tex]f(x) = \frac {3^x}4(\sqrt[3]{4})^x[/tex]
How to simplify the base function?The function is given as:
[tex]f(x) = \frac 14(\sqrt[3]{108^x})[/tex]
Expand 108
[tex]f(x) = \frac 14(\sqrt[3]{27 * 4})^x[/tex]
Take the cube root of 27
[tex]f(x) = \frac 14 * 3^x(\sqrt[3]{4})^x[/tex]
Evaluate the product
[tex]f(x) = \frac {3^x}4(\sqrt[3]{4})^x[/tex]
Hence, the simplified function of [tex]f(x) = \frac 14(\sqrt[3]{108^x})[/tex] is [tex]f(x) = \frac {3^x}4(\sqrt[3]{4})^x[/tex]
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Match the expression to its simplified form.
The following histogram represents quiz scores and uses the following interval bins: 1-5, 6-10, 11-15, 16-20, 21-25, 26-30, 31- 35, and 36-40. Frequency 15 94°F 10 5 Grades on 40-Question Quizo 8 1-5 8 6-10 13 11-15 9 16-20 3 21-25 Grade on Quiz 4 26-30 Select the true statement for this histogram.
The student that earned a score of 21 or higher on the quiz has a cumulative frequency of 7 and the relative cumulative frequency of 14%
What is a Histogram?
This refers to the pictorial representation of data that is used to show the distribution of numerical data.
From the given image, the histogram shows the quiz scores of students and the frequencies, and the relative cumulative frequency was gotten by dividing the frequency of each interval by the total number of observations
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factorize 3ac-6ad-2bc+4bd
Answer:
(c - 2d) (3a - 2b)
Step-by-step explanation:
if you need the steps just ask me in the comments and I’ll type them lol
You have 660 grams AP apples. What is your EP weight if the yield is 75 percent?
Which of the following is a metric unit for distance?
A. centimeters
B. miles
C. feet
D. kilograms
Answer:
A centimeters.
Step-by-step explanation:
Problem
Using the following image, find the midpoint of the line by completing the problems below.
Solution
The midpoint is ( Answer
, Answer
).
Given the initial point( x₁,y₁) and the final point( x₂,y₂ ), the midpoint of the line is ( 1, 1 ).
What is the midpoint of the line in the graph?From the graph;
Point 1 : ( x₁ = 0, y₁ = 4 )Point 2: ( x₂ = 2, y₂ = -2 )Midpoint = ?Using midpoint formula;
[tex]( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
We substitute in our values
[tex]( \frac{0+2}{2},\frac{4+(-2)}{2}) \\\\( \frac{2}{2},\frac{4-2)}{2}) \\\\( \frac{2}{2},\frac{2}{2}) \\\\( 1, 1 )[/tex]
Given the initial point( x₁,y₁) and the final point( x₂,y₂ ), the midpoint of the line is ( 1, 1 ).
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Three friends start a business and decide to split the profits equally. Susan invests $6,000, John invests $4,000, and Pria invests $7,000. If the profits are $12,000, how much of the profits would Pria receive if the profits were divided proportional to how much each friend invested
Susan investment = $6000
John investement = $4000
Pria investment = $12000
investment proportion of Susan, John and Pria = 6:4:12= 3:2:6
Hence, Pria share in profit = (6/11)*$12000
= $ 6,545.454
Answer:
Pria receives $4941.18 of the profits.
Step-by-step explanation:
• Susan invested $6,000,
• John invested $4000,
• Pria invested $7000.
The ratio of their investments Susan : John : Pria is 6000 : 4000 : 7000 ,
⇒ 6 : 4 : 7
This means that Pria should receive 7/17 th of the total profits.
∴ Pria receives = [tex]\frac{7}{17}[/tex] × $12,000
= $4941.18
Answer This Mathematics (Hard Mode)
522 X 854 = ____
Answer:
445788
Step-by-step explanation:
OMG too difficult man!!
Thanks to my calculator to solve this hard question
The table represents the multiplication of two binomials.
Which letters from the table represent like terms?
A and B
B and C
A and D
B and D
B and C are the letters from the table which have like terms which is denoted as option B.
What is a Binomial?This is referred to a type of polynomial which has two terms and is the sum or difference of a monomial.
From the table we can deduce the following:
A = -2x * 4x = -8x²B = 4x * 3 = 12xC = -2x * 1 = -2xD = 1 * 3 = 3B and C have a degree of 1 which means they are like terms thereby making them the most appropriate choice.
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Answer:
option 2 is correct
Step-by-step explanation:
median mark of 1,2,3,4,5,6,7,8
Answer:
4.5
Step-by-step explanation:
1+2+3+4+5+6+7+8= 36
36/8= 4.5
Renee says that y = mx can be rewritten in the form y = mx + b. Is she right? Explain why or why not
Can I please get a full answer with steps? Thanks a bunch!
The region in the w-plane into which a rectangular region bounded by the lines x=0, y=0, x=1, y=2 in the z-plane is mapped under the transformation w = (1- i)z + (2 - i) is mathematically given as
(u, v)=(2,1)
(v, v)=(3,0)
(u, u)=(3,2)
(v, u)=(2,2)
What is The region in the w-plane into which a rectangular region bounded by the lines x=0, y=0, x=1, y=2..?Generally, the equation for is mathematically given as
[tex]&\quad(1-i) 2+(2+i) \\\\&(1-i)(x+y i)+2+i \\\\\&x-x i+y i-1 y+2+i \\\\\&(-x+y+1) i+(x+2) \\\\\[/tex]
Given - that
[tex]&x=0 \\\\&y=0 \\\\\&x=1 \\\\\&y=2 \\\\\&(0,0): v=(-0+0+1): u(0+1) \Rightarrow(u, v)=(2,1) \\\\\&(1,0): v=(-1+0+1): u(1+2) \Rightarrow(v, v)=(3,0) \\\\&(1,2): v=(-1+2+1): u(1+2) \Rightarrow C u, u)=(3,2) \\\\&(0,2): v=(-0+2+1): u(0+2) \Rightarrow(v, u)=(2,2)\\\[/tex]
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Please help All of these rectangles have an area of 18 square inches. Each square represents 1 square inch.
Which rectangles do not have a perimeter of 18 inches?
Choose each correct answer.
Answer:3
Step-by-step explanation:because listen 3 is 2 for the side then 9 for the top so 9+9 equals 18 right so then 2+2 equals 4 18+4 does not equal 18
Micaela and Chelsea each improved their yards by planting rose bushes and ivy. They bought their supplies
from the same store. Micaela spent $58 on 5 rose bushes, r, and 3 pots of ivy, i. Chelsea spent $100 on 5
rose bushes and 10 pots of ivy. Write equations to represent the scenario. Then, find the cost of one rose
bush and the cost of one pot of ivy.
Answer: A rose bush, r, cost $8; one pot of ivy, i, cost $6;
Step-by-step explanation:
[tex]\left \{ {{5r + 3i =58} \atop {5r+10i=100}} \right.[/tex]
We combine them by minus, we get:
5r + 3i = 58
- 5r + 10i = 100
- 7i = - 42
i = 6
We plug in i = 6 to the first equation, we get:
5r + 3(6) = 58
5r + 18 = 58
5r = 40
r = 8
The cost of one rose bush is $8 and the cost of one pot of ivy is $6.
How to calculate the equationHere are the equations to represent the scenario:
Micaela: 5r + 3i = 58
Chelsea: 5r + 10i = 100
Let's solve the system of equations to find the cost of one rose bush (r) and one pot of ivy (i).
Subtracting the first equation from the second equation, we get:
7i = 42
Dividing both sides by 7 we get:
i = 6
The rose bushes will be:
5r + 3i = 58
5r + 18 = 58
5r = 58 - 18
5r = 40.
r = 8
This means that the cost of one rose bush is $8 and the cost of one pot of ivy is $6.
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Cómo puedo hallar la longitud de un lado de un triángulo usando el teorema del ángulo de 30°
En un triángulo rectángulo con ángulos de 30° -60° -90°, para encontrar la longitud de un lado, debes encontrar la longitud de la hipotenusa.
¿Cómo encontrar la longitud de la hipotenusa?Es necesario encontrar la longitud del cateto opuesto al ángulo de 30°, también conocido como cateto menor, y luego multiplicarlo por 2, descubriendo así el cateto de la hipotenusa, utilizando la fórmula del teorema de Pitágoras:
a²+b²=c²Por lo tanto, puedes usar el teorema de Pitágoras para calcular la longitud del lado que falta en un triángulo rectángulo.
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126. If the marked price of an article is 40% above the cost price. By how much percent cost price is less than the marked price?
The percent that the cost price is less than the marked price will be 40%.
How to illustrate the information?Let the cost price be 100.
Since the marked price of an article is 40% above the cost price, the marked price is 140.
The percent that the cost price is less than the marked price will be:
= 140 - 100
= 40%
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Customers can pick their own pumpkins at The Great Pumpkin Patch. They
pay $4 to enter the patch and $3 per pound for the pumpkins they pick. Write
an equation to model the total cost, y, for x pounds of pumpkins.
A. y = 3x+4
B. y = 3(x+4)
C. y = x(4+3)
D. y = 4x + 3
Answer:
the answer is A
Step-by-step explanation:
the starting point which is the addition part is 4 dollars for entrance and 3 stands for the price per pound and x is the amount of pounds
Find the vertex
f(x) = 2x²-x-10
Answer:
vertex = (1/4 , -81/8)
Step-by-step explanation:
f(x) = y
f(x) = 2x²-x-10
a= 2
b= -1
c = -10
-b/2a
-(-1)/(2(2))
1/4
x = 1/4
f(x) = 2x²-x-10
y = 2x²-x-10
y = 2(1/4)²-(1/4)-10
y = 2/16-1/4-10
y = 2/16-4/16-160/16
y = -2/16-160/16
y = -162/16
y = -81/8
Giving brainliest :)
The system of equation that will represent her situation is as follows:
1.39b + 2.49m = 50.73
1.29b + 2.69m = 51.63
How to represent system of equation?At store A she will pay a total sum of $50.73 for bread and milk.
At store B she will pay a total sum of $51.63 for bread and milk.
Therefore, the system of equation that will represent her situation is as follows:
where
b = number of breadm = number of milkTherefore,
1.39b + 2.49m = 50.73
1.29b + 2.69m = 51.63
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a. In the general education course requirement at a college, a student needs to choose one each from social sciences, humanities, natural sciences, and foreign languages. There are 5 social science courses, 4 humanity courses, 4 natural science courses, and 3 foreign language courses available for general education. How many different ways can a student choose general education courses from these 4 areas?
Using the Fundamental Counting Theorem, there are 240 ways to choose general education courses from these 4 areas.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Considering the number of options for each course, the parameters are given as follows:
[tex]n_1 = 5, n_2 = 4, n_3 = 4, n_4 = 3[/tex].
Hence the number of ways is given by:
N = 5 x 4 x 4 x 3 = 240.
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The swimming pool at Spring Valley High School is a rectangle with a width of 70 meters and a length of 30 meters. Around the perimeter of the pool is a tiled floor that extends w meters from the pool on all sides. Find an expression for the area of the tiled floor.
The expression that can be used to find the area of the tiled floor is 4w² + 200w
Area of rectangleOriginal rectangle:Length = 70 Meters
Width = 30 meters
Area = length × width
= 70 × 30
= 2100
New rectangle(including tiled floor):Length = 70 + 2w meters
Width = 30 + 2w meters
Area = length × width
= (70+2w) (30+2w)
= 2100 + 140w + 60w + 4w²
= 4w² + 200w + 2100
Area of the tiled floor = Area of new rectangle - area of old rectangle
= (4w² + 200w + 2100) - 2100
= 4w² + 200w + 2100 - 2100
= 4w² + 200w
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Find 10 rational numbers between 2/5 and 3/2
[tex] \frac{2}{5} \: \: and \: \: \frac{3}{2} [/tex]
L.C.M. of 5 and 2 = 10
[tex] \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \\ \\ \frac{3 \times 5}{2 \times 5} = \frac{15}{10} [/tex]
[tex] \frac{5}{10} , \frac{6}{10} , \frac{7}{10} , \frac{8}{10} , \frac{9}{10}, \frac{10}{10} , \frac{11}{10} , \frac{12}{10} , \frac{13}{10} , \frac{14}{10} [/tex]
The 10 rationals numbers are :
[tex] \frac{1}{2} , \frac{3}{5} , \frac{7}{10} , \frac{4}{5} , \frac{9}{10} , \frac{1}{1}, \frac{11}{10} , \frac{6}{5} , \frac{13}{10} , \frac{7}{5} .[/tex]