Roberta sold 30 tickets in total, with 10 adult tickets and 20 student tickets. The cost of a student ticket was $3. Ken collected $200 in total and sold 20 student tickets.
Explanation:To solve this problem, we can set up two equations based on the given information. Let's use variables to represent the unknown quantities.
Let's say the cost of an adult ticket is A dollars. Then the cost of a student ticket would be 3/4 of A dollars, or (3/4)A dollars.
Based on the information given, we can set up the following equations:
Robera sold 10 more student tickets than adult tickets, so let's say she sold X adult tickets and X + 10 student tickets.
The total collected by Roberta was $212.50, so we have the equation:
(A * X) + ((3/4)A * (X + 10)) = $212.50
Ken sold 50 tickets in total, so he sold 50 - (X + 10) student tickets. The total collected by Ken was $200, so we have the equation:
((3/4)A * (50 - (X + 10))) + (A * X) = $200
Now we can solve these equations to find the values of X and A.
Plugging in A = 4, we get X = 10. Therefore, Roberta sold 10 adult tickets and 20 student tickets. The cost of a student ticket was (3/4) * 4 = $3.
In conclusion, Roberta sold 30 tickets in total, with 10 adult tickets and 20 student tickets. The cost of a student ticket was $3. Ken collected $200 in total and sold 20 student tickets.
The sides of a square are 5 2/5 inches long. what is the area of the square?
a. 5 4/5 square inches
b. 5 4/25 square inches
c. 25 4/5 square inches
d. 25 4/25 square inches
Answer:
29 4/25 square inches (not given in the options)
Step-by-step explanation:
A square is a plain 4 sided shape with equal sides. As such, all sides of a square are equal. If the length o a side of a square is s, the area of the square will be s² while the perimeter will be 4s.
Area of square = (5 2/5 inches)²
= (27/5 inches)²
= 729/25 square inches
= 29 4/25 square inches
The sum of the squares of two consecutive even integers is 452. find the integers.
MATH HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. less than ( I gave x a number and did both equations )
2. the equation = 400 which is greater than 35
The graphs of the equations 2x+5y=3 and 2x+5y=7 are parallel lines. Find the equation of the line that is parallel to both lines and lies midway between them.
Decide which of the two points lies on the graph of the line
6x-2y= -4
A, -1, -1
B, -3,-2
given the equation -2x-13=8x+7, which order of operations completely solves for x
Which is an x-intercept of the graphed function?
The x-intercepts of the graphed function are -2, -1, 1, and 2
How to determine the x-intercept?The x-intercept is the point where the graph crosses the x-axis
This means that the point on the x-axis where y = 0
From the graph, we have:
x = -2, -1, 1, and 2 when y = 0
Hence, the x-intercepts of the graphed function are -2, -1, 1, and 2
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Donald baked 77 cookies in the morning and 83 cookies in the afternoon for 14 days how many total cookies did he bake
Write an expression for the quantity 506 000 cm in which it is clear that all zeros are significant
A lamp manufacturer uses 714 meters of electrical cord each week. The cord comes on spools that hold 12 meters each. How many spools of electrical cord does the manufacturer use each week?
divide 714 by 12
714 / 12 = 59.5 spools per week
Alan bowls one game, which consists of 10 frames. The number of pins he knocked down in each frame is 5, 6, 7, 5, 7, 9, 2, 4, 8, and 7. Which measure should Alan use to learn the difference of the greatest and the least number of pins he knocked down?
Answer:
Range.
Step-by-step explanation:
Alan must use the measure called Range, which indicates the dispersion between the extreme values of a variable. It is calculated as the difference between the highest and the lowest value of the variable. It is denoted as R. First the data is sorted, then it is calculated as:
R = x (n) - x (1) where,
x (n): It is the largest value of the variable.
x (1): It is the smallest value of the variable.
In the given case (5, 6, 7, 5, 7, 9, 2, 4, 8, and 7), we sort the data, and get,
2, 4, 5, 5, 6, 7, 7, 7, 8, 9
x (n) = 9
X (1) = 2
R = 9 - 2 = 7
Hope this helps!
50 POINTS!!
What are the missing parts that correctly complete the proof?
Answer:- 2. ∠JKM≅∠LKM
5. MK≅MK
6. AAS congruence postulate.
7. Corresponding parts of congruent triangles are congruent.
8. Definition of equidistant.
Therefore the complete proof will be
Proof :- 1. KM is the line bisector of ∠JKL. [Given]
2. ∠JKM≅∠LKM [Definition of bisector]
3. ∠KXM and ∠KYM are right angles [Given]
4. ∠KXM ≅ ∠KYM [All right angles are congruent]
5. MK≅MK [reflexive property of congruence]
6. ΔKXM ≅ ΔKYM [AAS congruence postulate]
7. MX≅MY [Corresponding parts of congruent triangles are congruent]
8. Point M is equidistant from the sides of ∠JKL [Definition of equidistant]
Hence proved.
Twice the sum of a number and 2 is equal to three times the difference of the number and 8. find the number please help
Answer:
28
Step-by-step explanation:
Let n represent the number.
Twice the sum of the number and 2 is ...
2(n +2)
Three times the difference of the number and 8 is ...
3(n -8)
The problem statement tells us these quantities are equal, so ...
2(n +2) = 3(n -8) . . . . the given quantities are equal
2n +4 = 3n -24 . . . . . use the distributive property to eliminate parentheses
2n +28 = 3n . . . . . . . add 24
28 = n . . . . . . . . . . . . subtract 2n
The number is 28.
_____
Check
The sum of the number and 2 is 30; twice that is 60.
The difference of the number and 8 is 20; three times that is 60--the same number.
Need the calculations please
If i run 5 miles in 38 minutes how many miles can i run in 57
What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x/4+5 ?
in the graph below, point D is reflected across the y axis. what are the coordinates of its image ?
Generally, whenever a point (x,y) is reflected across the y axis, the y coordinate stays the same and the sign of x coordinate changes.
So [tex](x,y)[/tex] changes to [tex](-x,y)[/tex].
Point D in the diagram shown has coordinates [tex](3,-1)[/tex]. According to the rule, the x-coordinate, 3, will change to -3 and the y-coordinate, -1, would stay the same.
Hence, our image of D after the reflection about y-axis would have coordinates [tex](-3,-1)[/tex].
ANSWER: [tex](-3,-1)[/tex]
Answer:
(-3, -1)
Step-by-step explanation:
He ages of mark and adam add up to 28 years total. mark is 20 years older than adam. how many years old is adam
The distributive property to express 48+72
Answer:
24(2+3)=24.2+24.3=48+72
Step-by-step explanation:
Given form of number is 48+72.
we have to apply the distributive property to express the above number.
The distributive property is
a(b+c)=ab+ac
Multiply the common term with the term inside the parentheses
So to express 48+72 we have to take the highest factor outside
Let us take 24 outside, we get
24(2+3)=24.2+24.3=48+72
Hence applied
The required expression is [tex]24(2+3)[/tex] by using the distributive property.
Given:
The given expression is [tex]48+72[/tex].
To find:
The equivalent expression by using the distributive property.
Explanation:
According to the distributive property:
[tex]a(b+c)=ab+ac[/tex]
We have,
[tex]48+72[/tex]
It can be rewritten as:
[tex]48+72=24\times 2+24\times 3[/tex]
Using the distributive property, we get
[tex]48+72=24(2+3)[/tex]
Therefore, the required expression is [tex]24(2+3)[/tex].
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Type an equation of the line that passes through the origin with the slope 3
The required equation of the line is y = 3x which passes through the origin with the slope 3.
What is the slope of the line?The slope of the line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
We have to determine the equation of the line that passes through the origin with slope 3.
Let's assume slope-intercept form:
So required line in the slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept.
In this case, the slope of line m = 3, and the line passes through the origin
So, therefore equation will be:
y = 3x + 0 or
y = 3x
Thus, the required equation of the line is y = 3x which passes through the origin with the slope 3.
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Write an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1 .
an equation of the line passing through point P(0, 0) that is perpendicular to the given line is
[tex]y=\frac{1}{9} x[/tex]
Given :
the line passing through point P(0, 0) that is perpendicular to the line
y = −9x−1
The given equation is in the form of y=mx+b
where m is the slope and b is the y intercept
Find out slope from the given equation y=-9x-1
Slope of the given equation is -9
Slope of perpendicular lines are negative reciprocal of one another
slope of perpendicular line is negative reciprocal of -9 is [tex]\frac{1}{9}[/tex]
slope of perpendicular line m=[tex]\frac{1}{9}[/tex]
The line passes through the point (0,0) that means y intercept is 0
the value of b=0
[tex]m=\frac{1}{9} , b=0\\y=mx+b\\y=\frac{1}{9} x+b\\y=\frac{1}{9} x[/tex]
an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1 is
[tex]y=\frac{1}{9} x[/tex]
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The equation of the line passing through point P(0, 0) and perpendicular to the line y = -9x-1 is y = (1/9)x, with the slope of the line being the negative reciprocal of -9.
Explanation:To write an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1, we first identify the slope of the given line. The slope of the line y = −9x−1 is −9, so the slope of a line perpendicular to it will be the negative reciprocal. Therefore, the perpendicular slope is 1/9.
Since the point P(0, 0) is also the y-intercept, we can directly write the equation of the perpendicular line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Thus, the equation of the line we are looking for is y = (1/9)x.
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. Catie is 3 years older than her brother. The sum of their ages is no more than 31. Write an inequality that can be used to represent this situation, where x represents Catie's brother's age. Don’t combine like terms.
Answer: So, the required inequality that can be used to represent this situation is [tex]2x+3\leq 31[/tex]
Step-by-step explanation:
Let the age of Catie's brother be 'x'.
Let the age of Catie be 'x+3'.
According to question, the sum of their ages is no more than 31.
So, it becomes,
[tex]x+x+3\leq 31\\\\2x+3\leq 31[/tex]
So, the required inequality that can be used to represent this situation is
[tex]2x+3\leq 31[/tex]
Simplify. Express your answer as a single term, without a denominator. t0u/tu
Which is equivalent to 243 2/5 ? 3 6 9 12
Answer:
The answer is [tex]9[/tex]
Step-by-step explanation:
we have
[tex](243)^{\frac{2}{5}}[/tex]
we know that
[tex]a^{\frac{n}{m}}=\sqrt[m]{a^{n}}[/tex]
so
[tex](243)^{\frac{2}{5}}=\sqrt[5]{243^{2}}[/tex]
Remember that
[tex]243=3^{5}[/tex]
Substitute
[tex]\sqrt[5]{243^{2}}=\sqrt[5]{(3^{5})^{2}}\\ \\= \sqrt[5]{(3^{10})}\\ \\=3^{\frac{10}{5}}\\ \\= 3^{2} \\ \\=9[/tex]
Find the Least Common Multiple of these two monomials:
16jk^8m^5 and 20j^9k^4m^6
36j^9k^8m^6
80j^9k^8m^6
4jk^4m^5
80j^10k^12m^11
lcm 16 & 10 = 80
lcm j^8 & j^9 = j^9
lcm k^8 & k^4 = k^8
lcm m^5 & m^6 = m^6
answer is: 80j^9k^8m^6
PLEASE HELP ASAP!! Will give brainliest!
How many 12ths are equivalent to 1/3?
How does doubling the side lengths of a triangle affect its area?
Bill earns $87.50 per week and Jack earns $70.00 per week. What percent of Bill's salary is Jack's?
Answer:
80%
Step-by-step explanation:
Let us suppose x percent of Bill's salary is equal to Jacks's salary.
Thus, we can write
x% of 87.50 = 70
Mathematically, we can write this as
[tex]0.0x\times87.50=70[/tex]
Solve the equation for x
[tex]0.0x=\frac{70}{87.50}\\\\x=\frac{70}{87.50}\times100\\\\x=80[/tex]
Therefore, Jack's salary is 80% of Bill's salary
The measures of two complementary angles are 3x+1 and 5x-y. Find x
A: 8
B: 12
C: 14
D: 23