Constant of variation for the direct function is y = [tex]\frac{2 x}5}[/tex]
What is Direct Variation?Direct variation in mathematics is the general form of formula y = k x where x and y are variables (numbers that change) and k is a constant
Convert to slope intercept form
2x -5y =0
Add 5y to both sides
2x-5y +5y =5y
2x=5y
divide both sides by 5
[tex]\frac{2x}{5}[/tex] =[tex]\frac{5y}{5}[/tex]
Cross multiply to solve for y
5(2x) =5(5y)
y = [tex]\frac{2 x}5}[/tex]
Therefore, the constant of variation y = [tex]\frac{2 x}5}[/tex]
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A positive integer is 6 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is frac(5,9), then find the two integers.
The two integers are equal to 1 and 7 respectively.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Let x represent the smaller number. Then the given relationships say ...
1/x + 2/(x+6) = 9/7
Multiplying by 7x(x+6), we have ...
7(x+6) +14x = 9x(x+6)
9x² +54x = 21x +42 . . . . .eliminate parentheses, swap sides
9x² +33x = 42 . . . . . . . . ...subtract 21x
3x² +11 -14 = 0 . . . . . . . . . .subtract 42 and divide by 3
(3x +14)(x -1) = 0 . . . . . . . . factor
Values of x that make this true are x = 1 and x = -14/3. Then for the positive integer x=1, the other integer is x+6=7.
Therefore, the two integers are equal to 1 and 7 respectively.
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Kelly earns $96 in 12 hours. At this rate, how many dollars will she earn in 20
hours?
OA. $160
OB. $240
O C. $200
O D. $80
96/12 = x/20
Solve it and get the answer.
What is the midpoint of AB?
Answer:h
Step-by-step explanation:
8+-6=2
PLEASE HELP WILL GIVE BRAINLIST -3(0.5+3p)=-6(p-5.9) show ur full work in liner questions form i will get my alt and answer to get u brainliST
50 POINTS!!
Answer:
p = - 123/10 = -123/10 = -12.3
Step-by-step explanation:
-3(0.5 + 3p) = -6(p - 5.9)
Use the distributive property to multiply -3 by 0.5 + 3p
-1.5 - 9p = -6 (p - 5.9)
Use the distributive property to multiply -6 by p - 5.9
-1.5 - 9p = -6p + 35.4
Add 6p to both sides
-1.5 - 3p = 35.4
Add 1.5 to both sides
-3p = 35.4 + 1.5
Add 35.4 and 1.5 to get 36.9
-3p = 36.9
Divide both sides by -3
p = 36.9/-3
Expand 36.9/-3 by multiplying both numerator and the denominator by 10.
p = 369/-30
Reduce the fraction 369/-30 to lowest terms by extracting and canceling out 3.
p = -123/10
Can someone please help me with my math homework (m^2+2m-8)/(m+4) thanks and have a good day/night/evening.
Answer:
Below
Step-by-step explanation:
The numerator factors , so you have this:
(m+4)(m-2) / (m+4) the (m+4) 's cancel and you are left with (m-2)
HELP ME OUT THANSKSSSSS SO MUCH
Answer:
10.59
Step-by-step explanation:
If 9 cows can fit in a field, how many fields are necessary to make sure 65 cows are all in a field?
Answer:
7.2 field or 7 field
Step-by-step explanation:
9 cows=1 field
65 cows=x field
cross multiply
9x=65×1
x=65÷9
x=7.2/7 field
I need help with this please help me
Answer: A
Step-by-step explanation:
The three angles in a triangle add to [tex]180^{\circ}[/tex]. Therefore, each angle measures [tex]\frac{180^{\circ}}{3}=60^{\circ}[/tex].
Three verticies of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex. (please helpp!!)
Answer:
AE=19
EAD=34
Step-by-step explanation:
Look at the image for step by step help.
-Hope this helped
SOLVE FOR FF
10f+10=9f
F=
Answer:
-10
Step-by-step explanation:
I would explain it but my keyboard won't let me type certain things.
Please give brainlist T-T
Dance lessons are offered at two studios. The cost of dance lessons at each studio is shown. • Studio Q charges a $30 registration fee plus $80 per month. . Studio R charges a $105 registration fee plus $65 per month. after how many months will the total cost of the dance lessons be equal at the two studios? What will the cost be?
Answer:
5 months and the cost is $430
Step-by-step explanation:
Let's start by figuring out the equations for both dance studios.
Q : 30 registration fee plus 80 per month.
R : 105 registration fee plus 65 per month.
We can use the variable m for months.
Registration is a flat fee, so that will be it's own term. Plus the costs per month. We will multiply the costs per month times months, m.
Q : 30 + 80m
R : 105 + 65m
Now, if we want to find out how many lessons until the costs are equal, we need to make the two equations equal to each other.
80m + 30 = 65m + 105
Now, we work backwards to find out what m is.
Subtract 30 on both sides.
80m = 65m + 75
Subtract 65m on both sides
15m = 75
Divide by 15 on both sides to isolate m.
m = 5
After 5 months, the total cost of the dance lessons will be equal at the two studios. To find out the cost, we must multiply the months back in. We can substitute 5 in for any of the equations as they are equal. I will use 80m + 30.
80(5) + 30 = ?
400 + 30 = ?
430 = ?
The cost for both studios will be equal at 5 months, with a cost of $430.
SOLVE FOR N
3/2 -1/2n= 2n+3
N =
Answer: n= -3/5 OR n= -0.6
Step-by-step explanation:
exact form and decimal form
What does the term rhetorical situation refer to?
• A. Ideals
that a speaker uses to guide a speech no matter who the
audience is
• B. A specific occurrence in ancient Greece when politicians bullied
the people
• C. The relationship between the speaker, the speaker's style of
address, and the audience's expectations
• D. Parents, teachers, and other adults who are on social networking
sites
Answer:
Step-by-step explanation:
This term refers to any set of circumstances that involves at least one person using some sort of communication to modify the perspective of at least one other person.
Answer: c
Step-by-step explanation:
j took the quiz on apex
Consider the curve given by the equation y² - 6y - 9x² - 144x = 576. It can be shown that dy/dx=
9(x + 8)/ Y-3
Find the x-coordinate of the point where the line tangent to the curve is the x-axis.
The x-coordinate of the point where the line tangent to the curve is the x-axis is; x = -8
How to Interpret the tangent line to a curve?To get he x-coordinate of the point that the line tangent to the curve is the x-axis, what we will do is to equate the numerator of the derivative to zero.
Now, we are given the equation of the curve as;
y² - 6y - 9x² - 144x = 576.
We are told that It can be shown that;
dy/dx = 9(x + 8)/(y - 3)
From our earlier definition, the x-coordinate will be at;
9(x + 8) = 0
divide both sides by 9 to get;
x + 8 = 0
x = -8
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Will mark brainliest :)
Answer:
hope it helps!
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
8y ≤ 10x Divide both sides by 8
y ≤ 5/4x Simplified
See the attached picture. This is crossing the y axis at 0. If you start at (0,0) and go up 5 and to the right 4. You will see the second point graphed. This demonstrates the slope of the line. ≤ tells us that we are including everything below the line.
You should check out Desmos. It is a free graphing program. It is cool.
Sergio buys 684 red stickers and
729 blue stickers for his 24 classmates
Each classmate receives the same
number of stickers. Sergio gives the
leftover stickers to his younger brother.
How many stickers does Sergio give to
his younger brother?
Hence, Sergio give to his younger brother is [tex]58[/tex].
What is the division?
Division is the opposite of multiplication. If three groups of four make twelve in multiplication, twelve divided into [tex]13[/tex] equal groups give four in each group in division.
Here given that,
Sergio buys [tex]684[/tex] red stickers and [tex]729[/tex] blue stickers for his [tex]24[/tex] classmates.
Each classmate receives the same number of stickers.
Total number of stickers are
[tex]684+729=1413[/tex]
So, the Sergio give to his younger brother is
[tex]\frac{14131}{24}=58[/tex]
Hence, Sergio give to his younger brother is [tex]58[/tex].
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What does the slope tell you?
◄ 0.25 ounce of salad costs $1.
25 ounces of salad costs $1.
A salad costs $0.25 per ounce.
A salad costs $25 per ounce.
Answer: what is the answer?
Step-by-step explanation:
a salad costs $0.25 per ounce!:)
The dinner bill comes to $30, and you want to leave a 20% tip. What is the total cost of the bill?
Answer:
$36
Step-by-step explanation:
First, let us make an expression to solve this using the given information.
For that let the total cost be x.
Amount of the bill tip total cost
100 ⇒ 20 ⇒ 120
30 ⇒ 20 ⇒ x
Accordingly,
100 ⇒ 120
30 ⇒ x
Use cross multiplication and solve for x.
100x = 120 × 30
100x = 3600
Divide both sides by 100.
x = $ 36
Suppose that 16 inches of wire costs 80 cents. At the same rate, how many inches of wire can be bought for 45 cents?
Solve the system of equations using any method
y = x^2 + 4
y = 2x + 4
The solution of the system of equation is as follows;
x = 2y = 8How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Let's solve the system of equation using substitution method as follows:
y = x² + 4
y = 2x + 4
Therefore,
2x + 4 = x² + 4
x² - 2x = 0
x² = 2x
x = 2
Let's find y
y = 2x + 4
y = 2(2) + 4
y = 4 + 4
y = 8
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NO LINKS!! You have 4 contestants in the second heat of the big race:
The equations for the contestants are:
1. Mr. Pace: y= 3/4x + 4
2. Mr. Glintz: y= 2/3x + 7
3. Ms. Liskey: y= 3x
4. Mr. Brininger: y= 1/2x + 10
Answer:
Part (c):
1st Place: Ms. Liskey2nd Place: Mr. Glintz3rd Place: Mr. Pace4th Place: Mr. BriningerPart (d):
1st Pass: Mr Pace Time: 1.78 s (2 d.p.)2nd Pass: Mr Glintz Time: 3 s3rd Pass: Mr Brininger Time: 4 sPart (e):
y = 3x + 2Step-by-step explanation:
Given equations:
[tex]\textsf{1.\;\;Mr.\;Pace}: \quad y = \dfrac{3}{4}x + 4[/tex]
[tex]\textsf{2.\;\;Mr.\;Glintz}: \quad y = \dfrac{2}{3}x + 7[/tex]
[tex]\textsf{3.\;\;Ms.\;Liskey}: \quad y = 3x[/tex]
[tex]\textsf{4.\;\;Mr.\;Brininger}: \quad y = \dfrac{1}{2} + 10[/tex]
Plot the lines on the given coordinate plane.
(See attachment).
Draw a line at y = 25 to represent the distance at the finish line.
Find the points of intersection of the linear equation of each contestant and the finish line equation y =25. The point with the smallest x-value is the contestant who is first place.
Mr Pace
[tex]\begin{aligned}\implies 25&= \dfrac{3}{4}x + 4\\\dfrac{3}{4}x&=21\\x&=28\; \sf seconds\end{aligned}[/tex]
Mr Glintz
[tex]\begin{aligned}\implies 25&= \dfrac{2}{3}x + 7\\\dfrac{2}{3}x&=18\\x&=27\; \sf seconds\end{aligned}[/tex]
Mr Liskey
[tex]\begin{aligned}\implies 25&= 3x\\x&=8.33\; \sf seconds\;(2\;d.p.)\end{aligned}[/tex]
Mr Brininger
[tex]\begin{aligned}\implies 25&= \dfrac{1}{2}x + 10\\\dfrac{1}{2}x&=15\\x&=30\; \sf seconds\end{aligned}[/tex]
Therefore, the order in which the contestants reached the finish line is:
1st Place: Ms. Liskey2nd Place: Mr. Glintz3rd Place: Mr. Pace4th Place: Mr. BriningerFrom inspection of the attached graph, Ms Liskey (red line) passes all three contestants. To find the time at which she passes the other contestants, substitute her equation into the contestant's equation and solve for x.
Mr Pace
[tex]\begin{aligned}\implies 3x&= \dfrac{3}{4}x + 4\\\dfrac{9}{4}x&=4\\x&=1.78\; \sf seconds\;(2\;d.p.)\end{aligned}[/tex]
Mr Glintz
[tex]\begin{aligned}\implies 3x&= \dfrac{2}{3}x + 7\\\dfrac{7}{3}x&=7\\x&=3\; \sf seconds\end{aligned}[/tex]
Mr Brininger
[tex]\begin{aligned}\implies 3x&= \dfrac{1}{2}x + 10\\\dfrac{5}{2}x&=10\\x&=4\; \sf seconds\end{aligned}[/tex]
Therefore:
1st Pass: Mr Pace Time: 1.78 s (2 d.p.)2nd Pass: Mr Glintz Time: 3 s3rd Pass: Mr Brininger Time: 4 sIf you want to win the race, either:
increase the slope of Ms Liskey's equation: y = 4xor add a value to Ms Liskey's equation: y = 3x + 2Solve the following quadratic
function by factoring:
f(x)=x²-10x+9
Enter the number that belongs in the green box.
x = 9; x = [?]
Answer:
1
Step-by-step explanation:
x²-10x+9 = 0
(x-9)(x-1) = 0
x-9 = 0 => x=9
x-1 = 0 => x=1
Lena buys a 32-oz package of cheese. Does she have enough cheese to make 2 batches of mac-and-cheese and 3 pizzas? Explain.
Answer:
how much oz does it take to make mac and cheese and pizza? will edit when get answer
Step-by-step explanation:
Edna bought a cube-shaped jewelry box that has 7-inch sides. The volume of a cube with side s is s3. What is the volume of the jewelry box?
The volume of the jewelry box will be;
⇒ 343 inch³
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Edna bought a cube-shaped jewelry box that has 7-inch sides.
And, The volume of a cube with side s is s³.
Now,
Since, Edna bought a cube-shaped jewelry box that has 7-inch sides.
Hence, The volume of the jewelry box = 7³
= 7 × 7 × 7
= 343 inch³
Thus, The volume of the jewelry box will be;
⇒ 343 inch³
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Graph the linear equation y = –2x + 6 on the coordinate plane.
The graph of the function y = - 2x + 6 is plotted and attached.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have the following equation of line -
y = - 2x + 6
Given is the following equation of line as -
y = - 2x + 6
The slope of the line would be [- 2] and the [y] intercept would be [6].
Refer to the graph attached.
Therefore, the graph of the function y = - 2x + 6 is plotted and attached.
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Length (cm): Length (m)
100: 1
250: 2.5
78.2: .782
123.9: 1.239
y: ? I need to know what goes next to the y
Write an equation for the proportional relationship. Let x represent a length measured in meters and y represent the same length measured in centimeters. I don't know what would be the equation.
The equation for the proportional relationship is x=y×(1/100) where x represents length in meters and y represents same length in centimeters.
What is meant by proportionality?The phrase proportionality refers to any relationship that always has the same ratio. The quantity of apples in a crop, for example, is proportionate to the number of trees in the orchard, with the ratio of proportionality being the average number of apples per tree.
In mathematics, two sequences of numbers, generally experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is known as the coefficient of proportionality or proportionality constant.
Given,
Length(cm): Length(m)
100 : 1
250 : 2.5
78.2 : 782
123.9 : 1.239
The value that goes next to y is,
y: y×(1/100)
Therefore, x=y×(1/100)
The equation for the proportional relationship is x=y×(1/100)
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Given the function R(x) = x-7/x+2 find the values of a that make the function less than or equal to zero. Write the solution in interval notation
The solution for the function R(x) = x - 7 / x + 2 ≤ 0 is −2<x≤7 or x (-2, 7].
What is function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
The function R(x) = x - 7 / x + 2
The given condition x - 7 / x + 2 ≤ 0
Solve the inequality as shown below
Here, the critical points are x = 7 and x = -2
Check the denominator for the critical point, x = -2 will not be suitable for the function as it becomes undefined,
Thus
−2<x≤7 or x (-2, 7]
Therefore, the solution for the function R(x) = x - 7 / x + 2 ≤ 0 is −2<x≤7 or x (-2, 7].
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If a person weighs 290 lbs, how much of a dosage should they get every 4 hours if they need to be
administered 11.9 mg/kg? Round to 1 decimal.
290 lbs is the same as 131.542 kg.
So, they should be administeted (131.542)(11.9) mg, which is about 15.65 mg.
Please Help!! It's really simple and I've done half already but I REALLY need help on the other half!!!! My assignment is on the first page and the first half that I've done is on the second page.
The equation of asked line is y = x/3+3
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
The equation of a line passing through two points (x1, y1) and (x2, y2) is
y-y1 = (y2-y1)/(x2-x1)*(x-x1)
The two points are (6, 5) and (3, 1)
Equation =
y-5 = -4/-3*(x-6)
y-5 = 4/3*(x-6)
3y - 15 = x-6
3y = x+9
y = x/3+3
Hence, the required equation is y = x/3+3
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Which set of rational numbers is arranged from least to greatest? (4 points) a −3.5, negative 1 over 4 , 2, 1 over 3 b −3.5, negative 1 over 4 , 1 over 3 , 2 c 2, 1 over 3 , negative 1 over 4 , −3.5 d negative 1 over 4 , 1 over 3 , 2, −3.5
The set of rational numbers arranged from least to greatest is -3.5, -1/4, 1/3, 2, which is option (b).
What is a rational number?Any number that can be represented as the ratio of two integers and where the denominator is not zero is referred to as rational.
The given sets of rational numbers are:
(a) -3.5, -1/4, 2, 1/3
(b) -3.5, -1/4, 1/3, 2
(c) 2, 1/3, -1/4, -3.5
(d) -1/4, 1/3, 2, -3.5
Note that 1/4 = 0.25 and 1/3= 0.33
Therefore, the set of rational numbers arranged from least to greatest is -3.5, -1/4, 1/3, 2, which is option(b).
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