The very busy Freshman class is selling tickets for an upcoming field hockey game. The class sells 20 more student tickets than adult tickets. The adult tickets cost $4 and the student tickets cost $2. The class made a total of $280 from ticket sales. How many of each type of ticket did they sell? Elaborate and clarify your reasoning.
1a. Define the variables in this system
b. Create equations to describe the relationships in this system between the variables
Answer:
60 student tickets and 40 adult tickets were sold
Step-by-step explanation:
Let s represent student tickets and a adult tickets, then the system of equations can be written as
s - a = 20 →(1)
2s + 4a = 280 → (2)
Multiply (1) by 4 and add to (2) to eliminate a
4s - 4a = 80 → (3)
Add (2) and (3) term by term
6s = 360 ( divide both sides by 6 )
s = 60
Substitute s = 60 into (1)
60 - a = 20 ( subtract 60 from both sides )
- a = - 40 ( multiply both sides by - 1 )
a = 40
Thus
60 student and 40 adult tickets were sold.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
A rectangular prism has dimensions of 2x, 3x, and 5x.
Write an expression for the total surface area of the prism.
Answer:
46
Step-by-step explanation:
Determine the approximate ordered pair for f(x) = g(x). the graph of two linear functions negative 4 times x plus 15 times y equals negative 300 and 20 times x plus 4 times y equals negative 20
Answer:
(x, y) ≈ (2.848, -19.241)
Step-by-step explanation:
I find it much easier to work with the problem statement when math expressions are written using numbers and symbols. We assume you have ...
-4x +15y = -300
20x +4y = -20
Dividing the second equation by 4 and subtracting the x-term gives ...
y = -5-5x
Substituting that into the first equation, we get ...
-4x +15(-5-5x) = -300
-79x -75 = -300
x = -225/-79 = 2 67/79 ≈ 2.8481
Substituting this into the equation for y gives ...
y = -5(x +1) = -5(3 67/79) = -19 19/79 ≈ -19.2405
The approximate solution is ...
(x, y) = (2.8481, -19.2405)
Answer:
The answer is (3,-19)
because you see on the graph that's where they intersect f(x) = 3 and g(x) = -19.
Step-by-step explanation:
can i get brainiest pleaseeeeeeeeeeeeeeeeeeeeeeeeeee
Katelynn bought a used car and it was 5 years old. She purchased it for 10,250, after two years the Kelly Blue book value for her car is $8,075. Determine how much the car was worth when it was first bought by the original owners and determine what the depreciation rate is. Hint: Remember these are exponential equations of the form y=abx.
Answer:
a) rate of depreciation is 11.24%
b) original price of car = $18605.33
Step-by-step explanation:
The formula to apply is;
current price= original price *(1-r)^n where r is the rate of depreciation as a decimal and n is the time period
a) Find the rate of depreciation given that ;
The car was bought at $10,250 when it was 5 years old
After 2 years, the value was $8,075
Apply the formula ;
current price= original price *(1-r)^n
8,075=10,250* (1-r)²
8,075/10250 = (1-r)²
0.78780487804 =(1-r)²
√0.78780487804 =(1-r)
0.88758373016 = 1-r
r=1-0.88758373016
r=0.11241626983 ⇒ 11.24%
b) When the car was first bought, the price was;
Apply the formula;
current price= original price *(1-r)^n
10,250 =original price * (1-0.1124)⁵
10,250=O.P *(0.5509)
10,250/0.5509 = original price
$18605.33= original price
A right triangle has an area of 33 mm² and a height of 11 mm.
How long is the base of the triangle?
Enter your answer in the box.
mm
Answer:
6mm
Step-by-step explanation:
Answer:
6 mm
Step-by-step explanation:
I took the quiz
how do I do this pls help It's due in 30 minutes!!!! tanθ=5/12
Answer:
Step-by-step explanat
Pls mark Brainliest.
Answer:
sin θ = 5/13
cos θ = 12/13
Step-by-step explanation:
We know that tan θ = 5/12 which indicates that the adjacent side relative to θ is 12 and the opposite side relative to θ is 5. The hypotenuse is missing which can be figured out using the Pythagorean Theorem.
a² + b² = c²
c = √(5² + 12²)
c = √(169)
c = 13
The hypotenuse is 13, and we know that the opposite and adjacent sides measure 5 and 12, respectively.
sin θ = opposite/hypotenuse
sin θ = 5/13
cos θ = adjacent/hypotenuse
cos θ = 12/13
PLEASE HELP ASAP!!!
Using the data below, determine the percentage of people who prefer cats?
A. 36%
B. 10%
C. 5%
D. 18%
Answer:
A. 36%.
Step-by-step explanation:
Total number of pets = 24 + 18 + 5 + 3
= 50,
So the percentage who prefer cats
= 18/50 * 100
= 18 * 2
= 36%.
Pleaseee helppp with my online school
Answer:
it can be a triangle and a rectangle
Step-by-step explanation:
Answer:
triangle and an rectangle
Step-by-step explanation:
What is the name of the relationship between 1 and 4?
Two horizontal parallel lines cut by a diagonal transversal. Angles 1 and 3 are on the left-hand side of the transversal and the interior of the parallel lines. Angles 2 and 4 are on the right-hand side of the transversal and the interior of the parallel lines.
Answer:
Angles 1 & 4 are alternate interior angles.
The correct name for the relationship between angles 1 and 4 in the given scenario is that they are corresponding angles.
When two parallel lines are cut by a transversal, the following relationships exist between the angles formed:
1. Corresponding angles are equal. These are the angles that are in the same relative position at each intersection where a straight line crosses two others. In this case, angle 1 corresponds to angle 4 because they are both above the parallel lines and on the same side of the transversal.
2. Alternate interior angles are equal. These are the angles that are inside the parallel lines and on opposite sides of the transversal. Angle 3 would be the alternate interior angle to angle 1, not angle 4.
3. Alternate exterior angles are equal. These are the angles that are outside the parallel lines and on opposite sides of the transversal.
4. Consecutive interior angles (also known as same-side interior angles) are supplementary. These are the angles that are on the same side of the transversal and inside the parallel lines.
Since angle 1 and angle 4 are in the same relative position at each intersection (both are above the parallel lines and on the same side of the transversal), they are corresponding angles. Therefore, if the lines are parallel, angle 1 is equal to angle 4.
What is the solution of
X-4 +5=2?
O x=-17
O x=13
x = 53
no solution
The solution of the Equation is x = 1.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have the Equation:
x - 4 + 5 = 2
Now, solving for x we get
x + 1= 2
Now, subtract 1 from both side we get
x+ 1 -1 = 2 - 1
x = 1
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Anouk has two dispensers that can each hold 1.25 liters. She fills them with liquid hand soap from a store that charges $0.19 for every 50 milliliters of soap.
How much does it cost Anouk to fill both of her dispensers with hand soap?
Enter your answer in the box.
Answer:
$4.75
Step-by-step explanation:
1milliliter = 1mL = 1.0*10^-3L
50mL = 50*10^-3L = 0.05L.
But 0.05L costs $0.19 to refill,
How much will 1.25L cost?
0.05L = 0.19
1.25 = x
X = (1.25*0.19) / 0.05
X = $4.75
It will cost her $4.75 to refill 1.25L of soap
Answer:
$9.5
Step-by-step explanation:
Each dispenser holds 1.25 liters, so we have a total of 1.25*2 = 2.5 liters to be filled.
Each 50 milliliters of soap, that is, 0.05 liters, costs $0.19, so we can solve now using a rule of three:
0.05 liters of soap -> $0.19
2.5 liters of soap -> X
0.05/2.5 = 0.19/X
X = 2.5*0.19/0.05 = $9.5
It will cost $9.5 to fill both dispensers with soap.
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 30% salt and Solution B is 70% salt. She wants to obtain 120 ounces of a mixture that is 65% salt. How many ounces of each solution should she use?
Answer:
Solution A: 15 ounces
Solution B: 105 ounces
Step-by-step explanation:
A + B = 120
A = 120 - B
0.3A + 0.7B = 0.65(120)
0.3A + 0.7B = 78
0.3(120 - B) + 0.7B = 78
36 - 0.3B + 0.7B = 78
0.4B = 42
B = 105
A = 120 - 105
A = 15
Answer:
15 ounces solution A
105 ounces solution B
Step-by-step explanation:
Let x be the amount of solution A
We need a total of 120 ounces of solution
Therefore we need
120-x ounces of solution B
Take the ounces of solution A times the percentage salt + the ounces of solution B times the percentage salt and this should equal the total ounces time the percentage sale
.3 x + (120-x) *.7 = 120 * .65
Distribute
.3x +84 -.7x = 78
Combine like terms
-.4x = -6
Divide each side by -.4
-.4x/-.4 = -6/-.4
x =15
We need 15 ounce of solution A
We need 120 ounces total
120-15 =105 ounces of solution B
The generator of a cone forms a 20⁰ angle with the central axis. At what angle could a plane intersect the central axis of the cone to form an ellipse?
10⁰
20⁰
40⁰
90⁰
Answer:
40
Step-by-step explanation:
Find the inequality represented by the graph.
Answer:
y is less then or equal to 5/2x+5
Step-by-step explanation:
It is plus 5 because the line crosses the y-intercept at 5. And 5/2 because that is the calculated slope between the two places.
18 - 5 · 3 =
please help
Answer:
3
Step-by-step explanation:
18 - 5 · 3
PEMDAS says we multiply and divide first
18 - 15
Then add and subtract
3
Answer:
3
Step-by-step explanation:
Solve according to PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)
First, multiply 5 and 3
18 - 5 · 3
18-15
Subtract 15 from 18
3
What is the minimum value
3.0
0
4.7
2.3
Hurry
Help
Answer:
3.0 i think
Step-by-step explanation:
It would be 0. (Choice B)
Step-by-step explanation:This is because it is the lowest point on the box and whiskers plot.
Classify the following triangle. Check all that apply.
9.8 120° 5.2
2040
13.2
A. Scalene
O
B. Isosceles
O
C. Obtuse
o
D. Right
E. Equilateral
O
F. Acute
SUBMIT
The given triangle is a scalene triangle and also an obtuse triangle.
What is a triangle?A triangle is a two-dimensional geometrical figure that has three sides, three interior angles and three vertices.
For the given triangle, three sides are 9.8, 13.2, 5.2.
Three angles are 120°, 40°, 20°.
Therefore, the given triangle is a scalene triangle and also an obtuse triangle.
Since three sides of the given triangle are different.
Therefore, it is neither a isosceles triangle nor an equilateral triangle.
None of the angles is a right-angle.
Hence, it is not a right-angle triangle.
One of three angles of the given triangle is 120°.
Hence, it is not an acute triangle.
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Mandy built a pyramid for her project on Egypt with a
volume of 48 * in. Find the area of the base of the
pyramid. Check all that apply
Use the formula V
Bh to solve the problem
The volume of the pyramid is 48
in
The height of the pyramid is 5 inches
Substitute the values for V and into the formula
and then solve for B
The area of the base of the pyramid is 8 in2
The area of the base of the pyramid is 242
Answer:
The area of the base of the pyramid is 9.6 square inches.
Step-by-step explanation:
Given : Mandy built a pyramid for her project on Egypt with a volume of 48 in.
To find : The area of the base of the pyramid ?
Solution :
The formula of volume of pyramid is
[tex]V=Bh[/tex]
where, B is the area of the base
and h is the height
The volume is [tex]48\ in^3[/tex].
The height is 5 inches.
Substitute the value,
[tex]48=B\times 5[/tex]
[tex]B=\frac{48}{5}[/tex]
[tex]B=9.6[/tex]
Therefore, the area of the base of the pyramid is 9.6 square inches.
Answer:
A )Use the formula V = one-third B h to solve the problem.
B )The volume of the pyramid is 48 and three-fourths in.3
C) The height of the pyramid is 6 inches.
D) Substitute the values for V and h into the formula, and then solve for B
F) The area of the base of the pyramid is 24 and StartFraction 3 over 8 EndFraction in.2
HOPE IT HELPED
What is the length of ED in the given cube? Round to the nearest tenth of an inch if necessary. in.
Answer: 12 in
Step-by-step explanation:hope this helps
Answer:
12
Step-by-step explanation:
Choose the term described.
a string stretched across a doorway
Select the correct answer.
angle
line segment
ray
Mark is pitching a tent he ties a rope from a nail to the top of the tent what is the length of the rope between the nail and the top of the tent
6
7
12
14
The base and height of a parallelogram must be perpendicular.
True
False
Answer:
True because no matter what angle or what parallelogram they are equal
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
3.24 as a simplified fraction with 4 repeating
3.24 as a simplified fraction with 4 repeating is 146/45.
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts.
Let x represent the value of the number.
So,
x= 3.2[tex]\bar4[/tex]
Multiplying both side by 10 we get
10x = 32.44...
Subtracting both above equations
10x -x = 32.44..-3.244..
9x= 29.2
x= 29.2/ 9
x= 146/45
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Final answer:
3.24 with the digit 4 repeating can be converted into the simplified fraction ⅔, which is equivalent to 3 ½.
Explanation:
The student is asking how to express the decimal 3.24 with the digit 4 repeating as a simplified fraction. The repeating decimal can be represented as 3.244444... or 3.24 bar.
To convert this repeating decimal to a fraction, we first denote x = 3.24. To eliminate the repeating part, we can multiply x by 100 to shift the decimal two places to the right, getting 100x = 324.44. Then, we subtract the original equation from this new equation (100x - x) to remove the repeating decimal. This results in 99x = 321, which simplifies to x = ⅔ or x = 3 ½ in fraction form. Therefore, 3.24 bar as a simplified fraction is ⅔.
true or false: the diagonals of a parallelogram intersect to form perpendicular lines
Answer:
false
Step-by-step explanation:
im a little unsure but i think false
Answer:
It is true that a parallelogram has symmetry with respect to the point of intersection of its diagonals.
Step-by-step explanation:
Suruchi is reading a book that is 333 pages long. So far, she has read 5/9 of the book. How many pages does Suruchi have left to
read?
Final answer:
Suruchi has read 5/9 of a 333-page book, which equates to approximately 185 pages. Therefore, she has 148 pages left to read.
Explanation:
The student is asking how many pages Suruchi has left to read from a book that is 333 pages long given that she has already read 5/9 of the book. To find the number of pages read, we multiply 5/9 by the total number of pages:
Pages read = (5/9) imes 333After calculating, Suruchi has read 185 pages since 5/9 of 333 is approximately 185. Therefore, the number of pages she has left to read is:
Pages left = Total pages - Pages readPages left = 333 - 185 = 148So, Suruchi has 148 pages left to read.
Jason empties his piggy bank and counted out exactly $10 in nickels, dimes and quarters. There were twice as many dimes as Nickels. There were twice as many quarters as dimes. How many nickels did they have ?
Answer:
8 nickels
Step-by-step explanation:
Total Amount of Money owned by Jason=$10
1 nickel =$0.05
1 dime=$0.10
1 quarter =$0.25
Let the number of dimes =dLet the number of nickels =nLet the number of quarters =qIf there were twice as many dimes as Nickels, then:
d=2nAlso, there were twice as many quarters as dimes.
q=2dTherefore:
0.1d+0.05n+0.25q=100
Substituting d=2n and q=2d into the above relations
0.1(2n)+0.05n+0.25(2d)=10
0.2n+0.05n+0.25(2(2n))=10
0.2n+0.05n+1n=10
1.25n=10
n=8
q=2d=2X16=32
d=2n=2X8=16
Jason had 8 nickels
Find the area of the trapezoid.
A trapezoid has a base of 8 meters, a height of 6 meters, and a top side length of 4 meters.
The trapezoid has an area of
m2.
Answer:
36 [tex]m^{2}[/tex]
Step-by-step explanation:
A =[tex]\frac{a+b}{2}[/tex]h
that is the formula for area of a triangle so when you insert all those numbers you get 36
:)
Area of the trapezoid is, 36 m²
What is mean by Multiplication?Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.
Given that;
A trapezoid has a base of 8 meters, a height of 6 meters, and a top side length of 4 meters.
Now, We know that;
Area of trapezoid = (a + b) h / 2
Here, We have;
a = 4 meters
b = 8 meters
h = 6 meters
Substitute all the values, we get;
Area of trapezoid = (a + b) h / 2
Area of trapezoid = (4 + 8) × 6 / 2
Area of trapezoid = 12 × 3
Area of trapezoid = 36 m²
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Choose the correct answer
Distance between 2 airports = 1,450 miles
Average speed of airplane = 350 mph
Travel time by bus after arrival at airport = 20 minutes
Total travel time = ??? hours
The choices are:
A) 4.47
B) 3.56
C) 3.97
Answer:
4.14
Step-by-step explanation:
If x + 3y = 7 and y = 2, then x equals
Answer:
I think the answer is x=1
Step-by-step explanation
Well since y=2 then I would multiply 2 with 3. And that is 6. Lastly, I would subtract 7 with 6 and you'll get 1 left over.
The value of x equals 1.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given equation is,
x + 3y = 7
We have to substitute the value of y = 2.
x + (3 × 2) = 7
x + 6 = 7
Subtracting 6 from both sides,
x = 7 - 6 = 1
Hence the value of x is 1.
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How do I justify my answer?
a) The value of x as calculated in the image is 45 degrees.
b) For the lines AD and BC to be parallel in a quadrilateral, the opposite angles need to be supplementary (i.e., their sum should be 180 degrees).
In this case, angle A is:
2x = 245 = 90 degrees
and angle D is:
3x = 345 = 135 degrees.
Since 90 + 135 = 225 degrees, which is not equal to 180 degrees, the lines AD and BC would not be parallel when ABCD is drawn to scale.