Each girl scored 9 points
Each boy scored 7 points
Step-by-step explanation:
Let the number of points each girl scored = a
Let the number of points each boy scored = b
7 girls and 6 boys scored a total of 105 points.
7a + 6b = 105......... Equation 1
The difference between the number of points scored by the 7 girls and the number of points scored by the 6 boys is 21
7a - 6b = 21........... Equation 2
7a + 6b = 105......... Equation 1
7a - 6b = 21........... Equation 2
Subtract Equation 2 from Equation 1
12b = 84
b = 84/12
b = 7
Therefore, each boy scored 7 points
7a + 6b = 105......... Equation 1
b = 7
7a+ 6b = 105
7a + 6(7) = 105
7a + 42 = 105
7a = 105 - 42
7a = 63
a = 63/7
a = 9
Therefore, each girl scored 9 points.
find values of x where the horizontal asymptote cross the graph of function f(x)=x^2-1/x^3
The rational function should be set to p and x should be solved if there is a horizontal asymptote,
How do you determine the location where a graph reaches a horizontal asymptote?The rational function should be set to p and x should be solved if there is a horizontal asymptote, such as y=p. In the event that x is a real number, the line crosses the horizontal asymptote at (x,p).
Although your function ultimately reaches for the H.A., it doesn't mean it never touches the line. Set the equation equal to that value and solve to determine which values of x, if any, allow the function to touch the H.A. to determine if it does.
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There are no values of x where the horizontal asymptote crosses the graph of the function.
How do you determine the location where a graph reaches a horizontal asymptote?The rational function should be set to p and x should be solved if there is a horizontal asymptote, such as y=p. In the event that x is a real number, the line crosses the horizontal asymptote at (x,p).
A horizontal asymptote occurs when the function approaches a constant value as the input goes towards positive or negative infinity.
For the graph of the function f(x) = x² - 1/x³, there are no horizontal asymptotes.
A horizontal asymptote would occur if the highest power of x in the numerator of f(x) was equal to the highest power of x in the denominator, but the denominator of f(x) doesn't have any powers of x, so there is no horizontal asymptote.
Therefore, there are no values of x where the horizontal asymptote crosses the graph of the function.
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Zoe is designing an exhibit of her paintings and has at most 315 square feet of wall
space on which to display them. Her paintings take up 22 square feet each. She must
also have a sign from the gallery posted on her wall. The sign is 9 square feet. Which
inequality can be used to solve for how many x paintings can be displayed?
O22x +9 315
O22x +92 315
9x+22315
O22z+9 315
Answer:
The inequality that can be used to solve for how many x paintings can be displayed is 22x + 9 <= 315
Step-by-step explanation:
This inequality states that the total square footage of the paintings and the sign must be less than or equal to 315 square feet. Each painting takes up 22 square feet, and the sign takes up 9 square feet, so the total square footage is represented by the expression 22x + 9.
The inequality states that 22x + 9 <= 315 which means for any number of paintings she displays it should be less than or equal to 315 sq.ft.
The other options:
22x + 9 315: the inequality is less than instead of less than or equal to, which means that the total cost should be less than 315 sq.ft which is not always the case.
22x + 92 315: the coefficient of x is 22 instead of 22 and the 92 is placed in a wrong position.
9x+22 315: the coefficient of x is 9 instead of 22 and the 22 is placed in a wrong position.
22z + 9 315: the variable used is z instead of x
A new van is priced at $19,500. If the buyer chooses to finance, they will pay $5,000 as a down payment and $375 per month. After how many months will the buyer have paid more that $10,000 toward the van?
A. 19,500 — 375x < 10,000
B. 5,000x + 375 > 10,000
C. 19,500 — 5000x > 10,000
D. 5,000 + 375 > 10,000
The inequality that represents the situation is . 5,000x + 375 > 10,000
(option b)
What is the the inequality?
The inequality that can be used to determine after how many months he would have paid more than $10,000 has this form:
down payment + (monthly payment x number of months) > $10,000
$5,000 + ($375 x m) > $10,000
$5,000 + $375m > $10,000
In order to determine the value of m, take the following steps:
Combine similar terms together:
375m > 10,000 - 5,000
Add similar terms together:
375m > $5000
Divide both sides of the equation by 375
m > 5000 / 375
m > 13.3 days
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At noon, a 36 foot building casts a 20 foot shadow. Find the shadow cast by a 6 foot tree. Set up a proportion and solve. Be sure to show all your work!
Answer:
3 1/3 ft
Step-by-step explanation:
Let SHADOW and HEIGHT pertain to the building, and let shadow and height pertain to the tree.
The proportion is:
HEIGHT/SHADOW = height/shadow
Now we fill in with the numbers we know, and "shadow" for the shadow of the tree.
(36 ft)/(20 ft) = (6 ft)/(shadow)
Cross multiply.
36 × shadow = 6 × 20
36 × shadow = 120
shadow = 120/36 = 10/3
shadow = 3 1/3
Answer: 3 1/3 ft
Find the sum of the first 5 terms of a G.P whose first term is 3 and its common ration ¼ to four Significant figure.
Answer:85
Step-by-step explanation:
Finding the Reflection Line On a coordinate plane, triangle 1 is reflected across the x-axis to form triangle 4, is reflected across a diagonal to form triangle 3, is reflected across the y-axis to form triangle 2. Use the figure to complete the statements. Triangle 1 is the image of triangle 2 reflected over the . Triangle 2 is the image of triangle 3 reflected over the . Reflecting triangle 4 over the y-axis results in triangle .
The statements are Triangle 1 is the image of triangle 2 reflected over the Y axis, Triangle 2 is the image of triangle 3 reflected over the X axis and Reflecting triangle 4 over the y-axis results in triangle 3.
What is Reflection?Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.
We have four triangles in the figure given.
So reflection of a figure results in the mirror image of the figure.
Line of reflection is the line through which a figure is reflected.
Line of reflection of the triangles 1 and 2 is the Y axis.
So Triangle 1 is the image of triangle 2 reflected over the Y axis.
Line of reflection of triangles 2 and 3 is X axis.
So Triangle 2 is the image of triangle 3 reflected over the X axis.
Also line of reflection is y axis for triangles 4 and 3.
So Reflecting triangle 4 over the y-axis results in triangle 3.
Hence using the concept of line of reflections, Triangle 1 is the image of triangle 2 reflected over the Y axis, Triangle 2 is the image of triangle 3 reflected over the X axis and Reflecting triangle 4 over the y-axis results in triangle 3.
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Which of the following quadratics would have the roots of 1+ or 1- ^2.
The quadratic equation for the given roots is x²-2x-1=0. Therefore, option 4 is the correct answer.
What is the solution of a quadratic equation?The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The roots of the quadratic equation are 1±√2.
Here, x=1+√2 and x=1-√2
x-1-√2=0 and x-1+√2=0
Now, (x-1-√2)(x-1+√2)=0
= x(x-1+√2)-1(x-1+√2)-√2(x-1+√2)=0
= x²-x+√2x-x+1-√2-√2x+√2-2=0
= x²-2x-1=0
Therefore, option 4 is the correct answer.
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36. Find the value that would be in the 15th percentile for the following data set:
{6, 10, 7, 2, 9, 8, 7, 3, 5)
a. 7
b. 6
c. 2
d. 3
Answer:
Step-by-step explanation:
Answer: a. 7
Work Shown:
Given set = {6, 10, 7, 2, 9, 8, 7, 3, 5}
Sorted set = {2, 3, 5, 6, 7, 7, 8, 9, 10}
P = 15 = percentile value
n = 9 = sample size, i.e. number of values in the set
R = index rank
R = (P/100)*(n + 1)
R = (15/100)*(9+1)
R = 1.5
This rounds to R = 2 when rounding to the nearest integer.
This R value tells us to look at the 2nd slot of the sorted data set. The value "3" is in the 2nd slot.
This is why the answer is choice D
A and B are two cities.
a) Measure the bearing of B from A.
b) Measure the bearing of A from B.
Ax to Bx
a) Measure the bearing of B from A = 030
b) Measure the bearing of A from B = 210
What is bearing angle?The term bearing is used in the navigation. The bearing is the horizontal angle which is made between the direction of an object to the another object.
This angle is measure in the clockwise direction from the north direction.
To measure bearing of two cities:
Draw a straight line between point A and B upward. Now draw 2 lines vertically up going through both points as shown in attached image. Now measure the angle between the vertical line and the diagonal line. It's 030.
Hence, measure the bearing of B from A is 030.
To measure the bearing of A from B add 180 to the 030.
we get 210.
Hence, measure the bearing of A from B is 210.
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Use point-slope form to write the equation of a line that passes through the point
Answer:
y + 13 = - [tex]\frac{2}{3}[/tex] (x + 11)
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - [tex]\frac{2}{3}[/tex] and (a, b ) = ( - 11, - 13 ) , then
y - (- 13) = - [tex]\frac{2}{3}[/tex] (x - (- 11) ) , that is
y + 13 = - [tex]\frac{2}{3}[/tex] (x + 11)
The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 600 people. By selling tickets, the members would like to raise $3,900 every night to cover all expenses. Let x represent the number of adult tickets sold at $8.50. Let y represent the number of student tickets sold at $5.50 each. If all 600 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise exactly $3,900? At one performance there were times as many student tickets sold as adult tickets. If there were 400 tickets sold at that performance, how much below the goal of $3,900 did ticket sales fall?
By using simultaneous linear equation, it can be calculated that 200 adult tickets and 400 student tickets were sold and the ticket sale falls $1320 below the goal of $3300.
What is simultaneous linear equation?Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation. Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
The simultaneous linear equation needs to be solved
Let d represents the number of adult tickets and s represents the number of student tickets
Their auditorium holds 600 people
d + s = 600 ..... (1)
Price of adult ticket = $7.50
Price of student ticket = $4.50
Total price = $(7.50d + 4.50s)
Therefore,
7.50d + 4.50s = 3300
5d + 3s = 2200 ..... (2)
Multiplying (1) by 3
3d + 3s = 1800.... (3)
Subtracting (3) from (2)
2d = 400
d = 200
Putting the value of d in (1)
200 + s = 600
s = 600 - 200
s = 400
Now, Total tickets sold = d + 2d = 3d
d = 120
s = 240
Number of student ticket sold = 240
Number of adult ticket sold = 120
Total cost = 240 4.50 + 120 7.50
= $1980
Fall in ticket sale = $(3300 - 1980) = $1320
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If the exchange rate is 1 U.S. dollar to 81 Japanese yen, how many yen would you spend to purchase something that costs 50 dollars?
Answer:
¥4050
Step-by-step explanation:
The exchange rate given is ¥81 to 1 US dollar.
1 US = ¥81.
You are trying to solve for the amount of yen it will cost if the equivalent is $50.
Multiply $50 US, with ¥81 (as it is the exchange rate):
$50 * (¥81/$1) = ¥4050
¥4050 is your answer.
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Mr.Lee can paint 20 chairs in t hours. He uses 3 liters of paint for every 12 chairs that he painted.
Answer:
Assuming the question is how many l of paint he needs the answer would be 5L
Step-by-step explanation:
1L- 4 chairs
?L- 20 chairs
Therefore 5L- 20 chairs
The floor of a round hut has a diameter of 4 yards. What is the floor's area?
Step-by-step explanation:
The floor of a round hut has a diameter of 4 yards. What is the floor's area?
Answer:
12.56637 or 4 pi hope this helps
Victor bought a pencil for $1. He also bought some notebooks for $3 each. Victor did not spend more than $13 on pencils and notebooks. Write an inequality that can be used to find n, the number of notebooks that Victor could have bought.
Victor spent $1 on a pencil. Additionally, he spent $3 on some notebooks. Buying pencils and notebooks cost Victor no more than $13. 4 <= 13 equals the inequality.
How do you define inequality?[tex]$$1+3 \leq 13:\left[\begin{array}{cc}\text { Solution: } & \text { True } \\\text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$$[/tex]
Steps
[tex]$$1+3 \leq 13$$[/tex]
Simplify 1+3: 4
[tex]$4 \leq 13$[/tex]
The attribute of being unequal or uneven, such as social disparity, disparity of distribution or opportunity, or lack of evenness A key idea in social justice theories is inequality, which is the state of not being equal, particularly in terms of status, rights, and opportunities1. Due to the fact that it frequently has diverse meanings to different people, it can become confusing in public discourse. However, some differences are typical.
Related concepts include lifetime inequality (inequality in incomes over a person's lifetime), inequality of wealth (distribution of wealth across households or individuals at a particular point in time), and inequality of opportunity (impact on income of circumstances over which an individual has no control). According to experts, inequality hinders economic growth and promotes political dysfunction.
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Are these two lines parallel?
Answer:
yes parallel is when two lines directly line up together like this ----
----
5 tan x -3 = 1 solve this equation for 0° ≤ x ≤ 360° make a sketch of the graph and indicate all the solutions.
Answer: 38.66 degrees and 218.66 degrees
Step-by-step explanation:
Larry and Donna bought a sofa at the sale price of $1,152. The original price of the sofa was $1,920.
Find the amount of discount in dollars.
The discount in dollars is $768.
This is a question of simple subtraction.
A sale price is the discounted price at which goods or services are being sold. This price is usually offered for a limited period of time
Discounted Amount means an amount equal to the sum of the Offer Discount, Volume Discount and Payment Discount, applied to the List Price of all Eligible Products ordered by the Customer under these Terms.
Larry and Donna bought a sofa at the sale price of $1152.
The original price of the sofa was $1920.
So, Discounted amount of the sofa= (Original price of the sofa- Sale price of the sofa)
i.e, ($1920-$1152)= $768.
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Please helpppp I’m sooo confusedddddd
We can simplify the expression to get:
2³ + 3*(2) + 14/2 = 21
The correct option is E.
How to simplify the expression?Here we want to simplify the expression below:
2³ + 3*(2) + 14/2
The additions are the last thing we need to do, we can replace:
2³ = 8
3*(2) = 6
14/2 = 7
Replacing that in the expression we will get:
2³ + 3*(2) + 14/2 = 8 + 6 + 7
8 + 6 + 7 = 21
So the correct option is E.
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The sum of the present ages of Kathy and Samantha is 60 years. In 8 years, Kathy will be 5 years older than 3 times as old as Samantha was 3 years ago. How old are they now? Write it in a equation
Answer:
Kathy is 48 years old and Samantha is 12.
Step-by-step explanation:
This is a challenging question that requires some interpretation. Let K and S stand for the current ages of Kathy and Samatha.
We are told that: K+S = 60
And, in 8 years: K+8 and S+8
"Kathy will be 5 years older than 3 times as old as Samantha was 3 years ago" ["3 years ago:" from now or in 8 years. I'll interpret it as from now, or (S-3)]
(K+8) = 3(S+8-3)+5 ["5 years older than 3 times as old as Samantha was 3 years ago"]
(K+8) = 3(S+5)+5
K+8 = 3S+20
K = 3S+12
---
Rearrange the firts equation to isolate K
K = 60-S
Now use this definition of K in the previous equation:
K = 3S+12
60-S = 3S+12
4S = 48
S = 12
K+S = 60
K+12 = 60
K = 48
=====
CHECK
Does K + S = 60? 48+12 = 60 YES
In 8 years, will Kathy will be 5 years older than 3 times as old as Samantha was 3 years ago?
K = 48+8 = 56
S = 12+8 = 20
Three years ago S was 9.
(K+8) = 3(S+8-3)+5
(K+8) = 3(12+8-3)+5
K + 8 = 3(17)+5
K = 48
===
Kathy is 48 years old and Samantha is 12.
Trigonometry (Law of Sines)
The measures, using the Law of Sines, are given as follows:
m < B = 119º. BC = 20.13.AC = 41.62.What is the law of sines?The law of sines states that the ratio between the sine of each angle and the side length opposite to this angle has to be equal for all the angles in the problem.
The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle B is given as follows:
m < B + 25 + 36 = 180
m < B = 180 - (25 + 36)
m < B = 119º.
Then the length BC is obtained as follows:
sin(25º)/BC = sin(36º)/28
BC = 28 x sin(25º)/sin(36º)
BC = 20.13.
The length AC is obtained as follows:
sin(119º)/AC = sin(36º)/28
AC = 28 x sin(119º)/sin(36º)
AC = 41.62.
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Is the point (-1, 6) on the lines below? y = 5x + 3 y = 2x + 4
The point (-1, 6) is on the lines y = 5x + 3 and y = 2x + 4
How to determine if the points is on the lineFrom the question, we have the following parameters that can be used in our computation:
Point = (-1, 6)
Also, we have
y = 5x + 3
y = 2x + 4
Substitute the known values in the above equation, so, we have the following representation
6 = 5(-1) + 3 = -2 -- false
6 = 2(-1) + 4 = 2 --- false
Hence, the point is not one the line
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how do you find the factors of 3 1/2 using a table (proportionality unit rate)
For example:
Numerator Denominator3 1/21 3/2-3 -1/2-1 -3/2We can observe that the factors of 3 1/2 are 3, 1, -3, and -1, with the corresponding fractional factors being 1/2, 3/2, -1/2, and -3/2 respectively. These values can be verified by multiplying the numerator and denominator of each factor and ensuring that the product is equal to 3 1/2.
At a college, the ratio of teachers to students is 1 to 11. The ratio of female students to the total number of students is 4 to 9. If there are 264 female students, then how many teachers are there
Answer:
We know that the ratio of female students to the total number of students is 4 to 9.
That means that for every 4 female students, there are 9 students in total.
So, we can set up the proportion:
4/9 = x/264
where x is the total number of students.
Solving for x, we get:
x = (4/9)*264 = 96
Since the ratio of teachers to students is 1 to 11, then for every 11 students there is 1 teacher, we can set up the proportion:
1/11 = y/96
where y is the total number of teachers.
Solving for y, we get:
y = (1/11)*96 = 8.72 ≈ 8
So, there are 8 teachers in the college.
Step-by-step explanation:
Forest managers plant trees in a triangular section of a state park. The managers
model the area on grid paper. Each grid square represents 1 km². What is the area
of the section that the forest managers plant with trees? Show your work.
10 Km² is the area of the triangular section that the forest managers plant with trees.
What is a sector or segment?A sector is the area between any two circle radii and any arcs that connect them. Segment: A line segment in geometry is a section of a line that has two clearly defined end points and includes every point on the line in between them.
Firstly count how many cells are there
First line = 6
Second line = 1
Last line = 3
So the area of the section that the forest managers plant with tree is
6 + 1 + 3 = 10 Km²
( count more than half a grid or not count )
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Find the value of x that makes the quadrilateral a parallelogram 2x + 3x+7? Someone help me please:(
The value of x = 4 makes the quadrilateral a parallelogram.
What is parallelogram?A special form of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.
Given:
The shape is a quadrilateral.
The opposite sides are parallel.
To show that the given quadrilateral is a parallelogram :
The opposite sides of the parallelogram are equal.
So,
2x + 3 = x + 7
2x - x = 7 - 3
x = 4
Therefore, the value of x is 4.
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The complete question is given in the attached image.
ANYONE GOOD AT MATH PLEASE HELP! SHOW YOUR WORK TOO PLEASE I BEG OF U
A hot air ballon is hovering 104 meters above the ground and begins to assend at a rate of 11 meters per second. Let
y be the height of the balloon in meters x seconds after it begins to assend.
Write an equation in slope-intercept form that models the height of the balloon.
How high is the balloon after 19 seconds?
Answer: The height of the balloon in meters x seconds after it begins to ascend can be represented by the equation y = mx + b, where m is the slope (the rate of change in height) and b is the y-intercept (the initial height of the balloon).
Given that the balloon is hovering 104 meters above the ground and begins to ascend at a rate of 11 meters per second, we can substitute these values into the equation:
y = 11x + 104
This equation is in slope-intercept form, the slope (m) is 11 and the y-intercept (b) is 104. This equation represents the height of the balloon in meters x seconds after it begins to ascend.
To find the height of the balloon after 19 seconds, we can substitute x = 19 into the equation:
y = 11(19) + 104 = 209 meters
So the hot air balloon is 209 meters high after 19 seconds.
Step-by-step explanation:
PLEASE HELP I NEED WORK SHOWN DONT UNDERSTAND
3. A radio station has a tower that is 25 miles east and 32 miles north of downtown Squirrel
Hills. The tower emits a signal that reaches receivers that are within 45 miles of its
location.
A) Write an equation in general form that describes the locations within the receiving
distance of the tower.
B) Determine if Squirrel Hills is within the receiving distance of the signal.
I
An equation in general form that describes the locations within the receiving distance of the tower is (x - 25)² + (y - 32)² = (45)².
And Squirrel Hills is within the receiving distance of the signal.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.
And the general formula of the circle,
(x – h)²+ (y - k)² = r²,
where (h, k) is the center and r is the radius of the circle.
Given:
A radio station has a tower that is 25 miles east and 32 miles north of downtown Squirrel Hills.
The tower emits a signal that reaches receivers that are within 45 miles of its location.
From the attached image,
(25, 32) is the location of the tower.
And (0, 0) is the location of Hill.
So, equation,
(x - 25)² + (y - 32)² = (45)²
To determine if Squirrel Hills is within the receiving distance of the signal:
That means,
when (x, y) = (0, 0),
(0 - 25)² + (0 - 32)² = (45)²
1649 < 2025
That means, the Squirrel Hills is within the receiving distance of the signal.
Therefore, the Squirrel Hills is within the receiving distance of the signal.
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Show each inequality on a number line and then write all the one-digit integers that satisfy it. k ≥0
The one-digit integers that satisfy the inequality k>0 are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
What is a number line?A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R."
It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
A number is a line that is made up of positive and negative numbers with the distance between the preceding and succeeding unit to be 1.
The negative values on the number line are -1, -2, -3...-9 while the value greater than zero are 1, 2, 3, 4,...9
Hence the one-digit integers that satisfy the inequality k>0 are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
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