The tables/graphs with their equations are
Table (a): y = 3x - 5Table (b): y = -12x + 2Graph (c): y = 5/4x - 5Graph (d): y = -6x + 3How to match the tables and graphs with their equationsFrom the question, we have the following parameters that can be used in our computation:
Tables, Graphs and equations
Table (a)
Here, we notice that:
The output is the 5 less than three times the input
This is represented as
y = 3x - 5
Table (b)
Here, we notice that:
The output is the 2 more than negative 12 times the input
This is represented as
y = -12x + 2
Graph (c)
Here, we have the following points
(4, 0) and (0, -5)
A linear function is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx - 5
Using the other point, we have
0 = 4m - 5
This gives
m = 5/4
So, we have
y = 5/4x - 5
Graph (d)
Here, we have the following points
(0.5, 0) and (0, 3)
A linear function is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx + 3
Using the other point, we have
0 = 0.5m + 3
This gives
m = -6
So, we have
y = -6x + 3
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A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $80, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
The total amount y collected from x students is y = 10x.
The graph is given below.
What is an expression?An expression contains terms with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The club is charging $10 per student that attends.
This means,
Number of students = x
The total amount y collected from x students.
y = 10x
The graph is given below.
Thus,
y = 10x is the total amount y collected from x students is
The graph is given below.
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asuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametricaly opposite a woman
There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.
In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.
Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.
To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.
So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.
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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?
Han spent 60 minutes practicing the piano over the weekend. Priya practiced the violin for 75% as much time as Han practiced the piano. How long did she practice?
By using the unitary method to find out that Priya practiced the violin for 45 minutes, which is 75% of the time Han spent practicing the piano.
Unitary method is a method that involves finding the value of one unit and then using that value to find the value of multiple units. This method is particularly useful in solving problems that involve proportions, ratios, and rates.
Now let's apply the unitary method to the given problem. We know that Han practiced the piano for 60 minutes over the weekend. We also know that Priya practiced the violin for 75% as much time as Han practiced the piano. To find out how long Priya practiced, we need to first find out how long 75% of Han's practice time is.
To do this, we can use the following equation:
75% of Han's practice time = 75/100 x 60 minutes
= 45 minutes
So Priya practiced the violin for 45 minutes over the weekend.
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how to graph y=-2x+2 and y=-2x+1(will give branliest)
A graph of the system of linear equations y = -2x + 2 and y = -2x + 1 is shown in the image attached below.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.
Based on the graph (see attachment), we can logically deduce that the given system of equations has no solution because both lines have the same slope and are parallel.
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Change 33.4 metres to centimetres.
The value of 33.4 meters to centimeters is 3340 centimeters
How to convert the units
Conversion of units is described as the conversion between different units of measurement for the same quantity, and it is done mostly through multiplicative conversion factors.
It also involves multiple steps of multiplication or division by a numerical factor or, a conversion factor.
From the information given, we have to convert meters to centimeters
Note that;
100 centimeter = 1 meter
Then x centimeters = 33.4 meters
cross multiply
x = 100(33.4)
multiply the values
x = 3340 centimeters
Hence, the value is 3340 centimeters
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What is the percent increase from 70 to 100?
Answer:
30%
Step-by-step explanation:
100-70=30
a person eating at a cafeteria must choose 3 of the 19 vegetables on offer. calculate the number of elements in the sample space for this experiment.
The number of elements in the sample space for this experiment are 969 by combination formula.
In an experiment where a person eating at a cafeteria choose 3 out of the 19 vegetables on offer, the number of elements in the sample space is 969.
A sample space of an experiment is the set of all possible outcomes of a random experiment. So the number of elements in a sample space is the total number of possible outcomes of the experiment.
Here the experiment is choosing 3 vegetables from a set of 19 vegetables offered. The total number of ways to choose 3 out of 19 distinct vegetables = [tex]^{19}C_{3}[/tex]
= [tex]\frac{19!}{3!\times16!}[/tex]
= 969
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question 3
pls help me as soon as possible
i'm being timed i only have a hour
The measure of arc FE in the figure is 100 degrees
How to determine the measure of arc FEFrom the question, we have the following parameters that can be used in our computation:
The circle and the intersecting chords
The value of arc FE represented by x is then calculated as
80 = 1/2(x + 60)
Cross multiply the equation
This gives
x + 60 = 160
Subtract 60 from both sides
x = 100
Hence, the measure of x is 100 degrees
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HELP
WHICH IS NOT A PROPIETY OF PARALLELOGRAM
According to the given information Congruent diagonals is not a property of parallelogram.
Why not? A kite is not a parallelogram.A kite's opposing forces aren't always parallel, just like not every kite is just a parallelogram. Trapezoids are quadrilaterals having a single pair of parallel sides. The parallel sides make up the bases. If somehow the foundation angles are equal, the trapezoid is said to be an isosceles trapezoid.
Do parallelograms count as diamonds?Since a diamond has four slanted, equal-length sides, it is an example of a rhombus. They are also both parallelograms since a parallelogram is indeed a rhombus and a diamond is one as well.
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how many pattern block trapezoids would create 3 hexagons
Answer:
Step-by-step explanation:
How many pattern block trapezoids would create for hexagons?
2 trapezoids compose a hexagon using equal-size shapes: 2 trapezoids, 6 triangles, or 3 blue rhombuses. compose hexagons using different shapes. So 2 trapezoids create 1 hexagon. This means 6 trapezoids make 3 hexagons.
The exact number of trapezoids needed to create three hexagons depends on the size and shape of the hexagons.
However, in general, you would need at least 18 trapezoids.
What is Hexagon?An hexagon is a six-sided polygon. It is made up of six equilateral triangles and six trapezoids.
If you are looking to create larger hexagons you will need more trapezoids.
Depending on the size and shape, you could need as many as 24 or more trapezoids.
An hexagon is a six-sided polygon. It is made up of six equilateral triangles and six trapezoids.
Hence, To create an hexagon using pattern blocks, you need 10 equilateral triangles and 20 trapezoids.
Therefore, to create 5 hexagons.
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tyler drove 138miles, and brittney drove 116miles. what is the ratio of tyler's miles to brittney's miles? write your answer as a simplified fraction.
Tyler drove 138miles, and brittney drove 116miles, the ratio of tyler's miles to brittney's miles is 69/58.
The ratio of Tyler's miles to Brittney's miles can be found by dividing Tyler's miles by Brittney's miles.
Ratio of Tyler's miles to Brittney's miles = Tyler's miles / Brittney's miles
Ratio of Tyler's miles to Brittney's miles = 138 miles / 116 miles
Simplifying the ratio by dividing both numbers by their greatest common factor, which is 2, we get:
Hence,
Ratio of Tyler's miles to Brittney's miles = 69/58
This means that for every 69 miles Tyler drove, Brittney drove 58 miles.
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which trig function do you use cos, tan, sin and how it is solved
We can use the sine ratio to solve this problem and the value of x would be 8.604.
What are trigonometric ratios?
Trigonometric ratios are ratios of the side lengths of a right triangle with respect to its acute angles.
Sine (sin) ratio: The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In the given figure, we have given the hypotenuse of the triangle, and an angle is given which is opposite to 35 degree, so we can use the sine ratio to find the value of x
sin35°= x/15
To solve for x, we can use the following steps:
Multiply both sides of the equation by 15 to isolate x:
sin 35° = x/15
15 * sin 35° = x
Use a calculator to approximate sin 35°:
sin 35° ≈ 0.5736
Substitute the approximation into the equation and solve for x:
x = 15 * 0.5736
x ≈ 8.604
Therefore, x is approximately equal to 8.604.
Hence, we can use the sine ratio to solve this problem and the value of x would be 8.604.
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Problem Combine the like terms to create an equivalent expression: − 5 r + 8 r + 5
Answer: -5r+8r+5=3r+5
Step-by-step explanation:
First add like terms, so -5r and 8r. For a second lets pretend the r doesn't exist. So, what is -5 + 8, 3, so 3r. Since 3r and 5 cannot be combined, the equivalent expression is 3r+5.
Pleas help with this homework
Using substitution method, the value of x and y are -13/3 and 2/3 respectively
What is system of linear equationA system of linear equations is a set of two or more linear equations with the same variables. The solution to the system is the set of values for the variables that satisfies all of the equations simultaneously. The variables represent unknown values that we are trying to solve for, and each equation provides a constraint on those variables.
To find the value of x and y, we can use substitution method.
4x + 8y = 12 ...eq(i)
x + 2y = -3 ...eq(ii)
From eq(ii)
x = -3 + 2y ...eq(iii)
Put eq(iii) into eq(i)
4(-3 + 2y) + 8y = 12
-12 + 8y + 8y = 12
-12 + 16y = 12
16y = 24
y = 2/3
Put y = 2/3 in eq(ii)
x + 2(2/3) = - 3
x + 4/3 = -3
x = -13/3
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If area of a rectangle is 20m^10n^4 and the length is 5m^3n what is the width
The width of the rectangle is 4*m⁷*n³
How to find the width of the rectangle?Remember that for a rectangle of length L and width W the area is given by the formula:
A = W*L
Here we know that:
A = 20*m¹⁰*n⁴
L = 5*m³*n
Then we can write:
20*m¹⁰*n⁴ = (5*m³*n)*W
Now we can solve that for W.
(20/5)*(m¹⁰/m³)*(n⁴/n) = W
4*m¹⁰⁻³*n⁴⁻¹ = W
4*m⁷*n³ = W
That is the width.
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need help asap
how to explain the answer
By the property of SAS criterion,
ΔKMN is similar to ΔKJL.
What are similar triangles?Those triangles look the same but are different in size.
And in similar triangles,
the corresponding sides are proportionate, and the corresponding angles are equal.
Given:
In ΔJKL,
MN is parallel to JL.
That means MN and JL are equally spaced.
So,
JM/MK = LN/NK
∠KMN ≅ ∠KJL {By corresponding angles}
ΔKMN is similar to ΔKJL. {By the SAS criterion}
Therefore, ΔKMN is similar to ΔKJL.
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Find the length of the unknown side of the triangle.
10 ft
5 ft
The length of the unknown side of the triangle is?
Answer:
The length of the unknown side of the triangle is
[tex]5 \sqrt{5} [/tex]
Select all the equations that have 9 as a solution. j + 8 = 72 m × 3 = 27 b + 4 = 13 p – 5 = 4 q ÷ 3 = 27
Yen takes her pomeranian kiwii to the dog park once inside the fence kiwii runs across the filed in 10 seconds his path is shown on the graph belowwhat is the average velocity 4 to 8 seconds
The average velocity from 4 to 8 seconds is given as follows:
v = [position at 8 seconds - position at 4 seconds]/4.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
The change in the distance from 4 to 8 seconds is given as follows:
position at 8 seconds - position at 4 seconds
The change in the time from 4 to 8 seconds is given as follows:
8 - 4 = 4 seconds.
Hence the velocity is of:
v = [position at 8 seconds - position at 4 seconds]/4.
Missing InformationThe problem is incomplete, hence the general procedure to obtain the average velocity was presented.
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Type the correct answer in each box. Use numerals instead of words.
Solve the equation by completing the square. x2 + 20x + 82 = 7
The solutions, in order from least to greatest, are x = and x = .
By completing the square, the equation. x2 + 20x + 82 = 7. The solutions are x = -15 and x = -5, going from least to largest.
What is meant by constant?In expression, a constant is a value or number that is consistently the same. Multiple meanings can be derived from the word "constant." Its meanings as a noun and an adjective, respectively, are non-variance and two: an unchanging integer or other non-changing mathematical entity that is fixed and well-defined. The value of a constant is fixed and does not alter over time. A shoe's, a piece of clothing's, or any other item of clothing's size, for instance, will never alter. Because 8 is a constant number and cannot be modified in an algebraic equation, x+y = 8 is a valid solution.The square of half the x-coefficient must equal the constant on the left:
(20/2)^2 = 100
To get it to that value, we can add 18 to both sides of the equation:
x^2 + 20x + 100 = 25 . . . add 18 to both sides of the equation
(x + 10)^2 = 25 . . . . . . . . write the left side as a square
x + 10 = ±√25 = ±5 . . . . . take the square root
x = - 10 ± 5 = {-15, -5}
The solutions are x = -15 and x = -5.
The attached graph shows the solutions to ...
x^2 + 20x + 82 -7 = 0 . . . . . the result of subtracting 7 from both sides
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12.
Rihana measured the length of her dining room. Her percent error was
-5%. The actual length of her dining room is 120 inches.
Part A What length, in inches, did Rihana measure?
Answer
Part B Explain how you got your answer
Part B Explain how you found your answer.
Answer:
114 inchesStep-by-step explanation:
Part A:
The actual length of the dining room is 120 inches and the percent error is -5%, which means that Rihana's measurement was too short. To find the length she measured, we need to add 5% to the actual length:
120 inches * (1 + (-5%)/100) = 120 inches * (1 - 0.05) = 120 inches * 0.95 = 114 inches
So Rihana measured the length of her dining room as 114 inches.
Part B:
To find the length that Rihana measured, we used the formula for calculating percent error:
measured length = actual length * (1 + (percent error)/100)
Since the percent error was negative (-5%), this means that Rihana's measurement was too short, so we subtracted the percent error from 100%. To do this, we added the negative percent error to 100%:
100% + (-5%) = 100% - 5% = 95%
So the measured length was 120 inches * 95% = 114 inches.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
The length of the dining room measured by Rihana with a -5% percent error is 114 inches.
What is a percent error?
The percent error is the distinction between the estimated value and the actual value in relation to the actual value. In other words, the relative error is multiplied by 100 to calculate the percent error.
A) Given the percent error as -5%.
The actual length = 120inches
Now error in measurement = 5% of 120 inches = 6 inches.
Since there is a negative sign in percent error, the measured value is 6 inches less than actual value.
Therefore the measured value = 120 - 6 = 114 inches.
B) We are given the actual length as 120 inches.
There is a -5% error in the measured value.
This means that the measured value is (5% of 120) inches less than actual value. It is identified as less because of the negative sign.
So the measured value is = 120 - 0.05*120 = 114 inches.
Therefore the length of the dining room measured by Rihana with a -5% percent error is 114 inches.
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A tractor and a scooter are in a race.
Write expressions, in terms of t, for each vehicle so that
the vehicles start separated and meet at 10 seconds.
Tractor Position Expression
Try It
Scooter Position
Expression
The expressions, in terms of t, for each vehicle so that the vehicles start separated and meet at 10 seconds is:
Tractor's position = Vt * t
Scooter's position = Vs * t
What is the expression?Let's assume that the starting point for both the tractor and the scooter is at "0". We can then write the expressions for their positions in terms of time "t" as follows:
For the tractor:
Tractor's speed = Vt
Tractor's position = Vt * t
For the scooter:
Scooter's speed = Vs
Scooter's position = Vs * t
Now, as both the vehicles meet at 10 seconds, we can write the equation:
Vt * 10 = Vs * 10
The above equation represents the position of both the vehicles at 10 seconds. If we assume the speed of the tractor and the scooter to be constant, then the equation gives us the relationship between their speeds.
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I need help on this please
A cross-country sprint skier keeps track of how his practice times compare to a
qualifying time for a race. A negative number means he skied faster than the qualifying
time. His results are shown in the table.
Practice Run
1
2
3
st
4
5
6
Difference between Practice Time
and Qualifying Time (seconds)
1.25
-5.38
-0.92
2.19
-6.74
-2.46
1 of 5
What is the mean difference between the skier's practice times and the qualifying
time?
Use the number pad to enter your answer in the box.
second(s)
Finish Later
Submit
The mean difference between the skier's practice times and the qualifying time is given as follows:
-2.01 seconds.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
The observations for this problem are given as follows:
1.25, -5.38, -0.92, 2.19, -6.74, -2.46.
The sum of these six observations is of:
1.25 - 5.38 - 0.92 + 2.19 - 6.74 - 2.46 = -12.06.
Hence the mean is of:
Mean = -12.06/6
Mean = -2.01 seconds.
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Graph the line of best fit.
The line of the best fit of the scatter plot is added as an attachment
How to determine the line of best fitThe missing graph is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The graph
A good line of best fit would have equal number of points on either sides
To plot the graph, we draw a line that divides the points on the graph evenly
This line when drawn on the scattered points divided the points approximately evenly
Hence, the line of the best fit is attached
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can u help me thx
if u can i would be very happy if u cant its fine but hopefully u can ms/mr
Step-by-step explanation:
h represents the number of hours
15 represents the initial price for bike rentals
0.75h represents that for every hour, the price of bike rentals increases by 0.75
ANSWER ATTACHED!
Enter a recursive rule for the geometric sequence. 10,−80,640,−5120....
P.s. If you're going to answer.. don't type random stuff, put the answer I gave you
The recursive rule for the geometric sequence 10, -80, 640, -5120, is a(1) = 10 (the first term) For n > 1, a(n) = -8*a(n-1) (each term is -8 times the previous term).
What does the term "recursive" in math mean?Recursive definitions of objects are those in which they are defined in terms of other objects of the same kind. The whole class of objects can then be built from a small set of initial values and a few of rules by utilising a recurrence relation of some sort. The most typical way to define the Fibonacci numbers is recursively.
geometric sequence 10, -80, 640, -5120
a(1) = 10 (the first term)
For n > 1, a(n) = -8*a(n-1) (each term is -8 times the previous term).
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32% of the 384 students in the eighth grade walk to school, about how many eighth graders walk to school?
Answer: 123 students
32 % of 384 is 122.88. Since a percent of a person can't walk to school, we should round up. This means 123 students in the eighth grade walk to school each day.
I hope this helps and good luck <3!!
A system of inequalities is shown.
The graph shows a dashed upward opening parabola with a vertex at negative 1 comma negative 4, with shading inside the parabola. It also shows a dashed line passing through the points negative 2 comma negative 1 and 0 comma 3, with shading above the line.
Which system is represented in the graph?
The system that is represented in the graph include:
y > x² – 2x – 3
y > 3x + 4
How to explain the graphThe study of graphs, which are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this case, a graph consists of vertices connected by edges.
The graph shows a dashed upward opening parabola with a vertex at negative 1 comma negative 4, with shading inside the parabola. It also shows a dashed line passing through the points negative 2 comma negative 1 and 0 comma 3, with shading above the line.
This depicts y > x² – 2x – 3 and y > 3x + 4.
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Which system is represented in the graph?
y ≥ x2 – 2x – 3
y ≤ 3x + 4
y < x2 –2x – 3
y > 3x + 4
y < x2 – 2x – 3
y > 3x + 4
y > x2 – 2x – 3
y > 3x + 4
a circular table is painted yellow with a red square in the middle. the radious of the tabletop is 6x. the side length of the red square is 3x. what is the area of the yellow part of the tabletop.