The constant of variation for a function is 2. Which of the following graphs best represents this situation
Answers
The required graph shows the constant of variation for a function is 2 is A and B. Option A and B is correct.
Given that,
To determine the graphs which show the constant of variation for a function is 2.
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
in the graphs only graph, A and B show the given condition of the constant of variation for a function is 2. Because in both graphs shows that y = 2x and 2y = x.
Thus, the required graph shows the constant of variation for a function is 2 is A and B. Option A and B is correct.
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Related Questions
The first equation in a system is 5x+2y=-4Which equation gives a system with no solution
Answers
System of equations
A system of equations with two variables can have one solution, no solution, or infinitely many solutions.
Each equation corresponds to a line which can be expressed like:
y = mx + b
Where m is the slope and b is the y-intercept
For a system to have one solution, both lines must have different slopes, so they cross each other at one point.
If a system has no solution, both lines are parallel
If a system has infinitely many solutions, both lines are the same line (they coincide)
We have the following equation:
5x + 2y = -4
Let's solve it for y:
2y = - 5x -4
[tex]y=-\frac{5}{2}x-2[/tex]Only one of the lines has the same slope as the given line:
[tex]y=-\frac{5}{2}x-3[/tex]Both lines have the same slope but don't have the same y-intercept, so they are parallel.
Thus, the correct choice is D.
Answer:d
Step-by-step explanation:
Julianne needs 7 yards of string for her kite. She has 5/8 yards. How many more yards does Julianne need for her kite?
Answers
Find out the difference between 7 yards and 5/8 yards
[tex]7-\frac{5}{8}=\frac{8*7-5}{8}=\frac{51}{8}\text{ yd}[/tex]Convert to a mixed number
51/8=(48/8)+(3/8)=6+3/8=6 3/8 yd
therefore
The answer is 6 3/8 ydThe product of a number and 3 is the same as the sun of that number and 6
Answers
Answer: 3x = 6x
Step-by-step explanation: After you move the variable over you will move 6x so the opposite of 6x is -6x after you subtract -6-3 you should get 3. Thus, the final answer would be 3.
homework 7.5 solving radical equations
6=(2x+34)^1/2
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Answer:
x=1
Step-by-step explanation:
The concert lasted two hours. For how many minutes did the chorus perform alone?
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In order to find how many minutes the chorus performed, let's convert the time of 2 hours into minutes.
To do that conversion, we need to know that 1 hour is equal to 60 minutes.
Then, we can write the following rule of three:
[tex]\begin{gathered} \text{hours}\to\text{minutes} \\ 1\text{ hour}\to60\text{ minutes} \\ 2\text{ hours}\to x\text{ minutes} \end{gathered}[/tex]From this rule of three, we can write the following equation and solve it for x:
[tex]\begin{gathered} \frac{1}{2}=\frac{60}{x} \\ 1\cdot x=2\cdot60 \\ x=120 \end{gathered}[/tex]Therefore the chorus performed for 120 minutes.
Richard and Teo have a combined age of 32. Richard is 5 years older than twice Teo's age. How old are Richard and Teo?
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The age of Teo is 9 years and the Age of Richard is 23 years.
What is problem-solving?
Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
Calculation:-
Richard and Teo have a combined age = of 32
Richard is 7 years older than twice Teo's age
Let the age of Teo = X
Age of Richard = 2X + 7
2X + 5+ X = 31
X = 31 - 5 /3
X = 27/3
= 9 years
Therefore the age of Teo is 8 years
Age of Richard = 19 years
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What is x?5x-35=55-xHow do I get like variables together
Answers
hello
this is a simple equation and to solve this, we should first of all collect like terms together
[tex]5x-35=55-x[/tex]step one
collect like terms together
[tex]\begin{gathered} 5x-35=55-x \\ 5x+x=55+35 \\ 6x=90 \end{gathered}[/tex]step two
divide both sides by the coefficient of x
[tex]\begin{gathered} 6x=90 \\ \frac{6x}{6}=\frac{90}{6} \\ x=15 \end{gathered}[/tex]from the calculations above, the value of x is equals to 15
Mark and label the points 1/4 2/4 3/4 and 4/4 on the number line
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We can divide a number line from 0 to 1 into 4 parts as label:
1/4, 2/4, 3/4, and 4/4 (which is 1).
Shown below:
Which to be used to write an inequality?A. C.=D.+
Answers
The symbols > and < can be used to write an inequality. (Options A and B)
Find the area of each figure. 4. & 3 3 S 2 2 8 a square units
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area is
[tex]A=s^2=1^2=1[/tex]and
[tex]\text{Atotal}=1\times11=11[/tex]answer: 11 square units
:) 4 inches of snow in 5 hoursHow much snow fell each hour?
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The amount of snow fell in 5 hours is 4 inches.
To find snow fell in each hour, we divide 4 by 5.
Divide 4 by 5.
[tex]\frac{4}{5}=0.8[/tex]So 0.8 inches of snow fell each hour.
Answer: 0.8 inches
What is the rule for the following dilation? A(-5.8) B(13.65, 12.8) C(-9, -13) D(0, 12) A'(-2.5, 4) B'(6.825, 6.4) C'(-4.5, -6.5) D'(0, 6) O Scale Factor: 1.5 O Scale Factor: 2 O Scale Factor: 5 O Scale Factor: 0.5
Answers
Answer:
(D)Scale Factor: 0.5
Explanation:
The coordinates A,B, C and D are those of the pre-image while A',B',C' and D' are those of the image.
Using the coordinates of A and A'
Let the scale factor = k
On the x-axis:
[tex]\begin{gathered} -5k=-2.5 \\ k=\frac{-2.5}{-5}=0.5 \end{gathered}[/tex]Similarly, on the y-axis
[tex]\begin{gathered} 8k=4 \\ k=\frac{4}{8} \\ k=0.5 \end{gathered}[/tex]We conclude that the scale factor is 0.5
A town's population grows at a rate proportional to itspopulation. If the growth rate is 6.8% per year and thecurrent population is 1627, what will the population be8.5 years from now?a) Write the equationb) Determine the future population of the town.
Answers
Solution:
Given:
[tex]\begin{gathered} P_o=1627 \\ r=6.8\text{ \%}=\frac{6.8}{100}=0.068 \end{gathered}[/tex]The equation of the population can be gotten using the formula;
[tex]P=P_oe^{rt}[/tex]Hence, the equation is:
[tex]P=1627e^{0.068t}[/tex]The population of the town 8.5years from now will be:
[tex]\begin{gathered} when\text{ }t=8.5years \\ \\ Then, \\ P=1627e^{0.068\times8.5} \\ P=1627e^{0.578} \\ P=2900.08 \\ \\ Since\text{ the population must be a whole number,} \\ P=2900 \end{gathered}[/tex]1. select all equations 2. select all equations 3.select all equations
Answers
The correct option C and F
Explanation:x² + 6x = 16
we need to check the other options to find out its equivalence.
a) x² + 6x + 9 = 0
Rewritting the equation above: x² + 6x - 16 = 0
From the above, we can see they are different
b) x² + 6x + 9 = 16
rewritting: x² + 6x + 9 - 16 = 0
x² + 6x - 7 = 0
This is not equivalent to x² + 6x - 16 = 0
c) x² + 6x + 9 = 25
x² + 6x + 9 -25 = 0
x² + 6x -16 = 0
x² + 6x = 16
This is equivalent to x² + 6x = 16
d) (x + 3)² = 0
(x+3)(x+3) = 0
x(x+3)+3(x+3) = 0
x² +3x +3x + 9 = 0
x² + 6x + 9 = 0
This is not equivalent to x² + 6x - 16 = 0
e) (x+3)² = 16
(x+3)(x+3) = 16
x(x+3)+3(x+3) = 16
x² +3x +3x + 9 = 16
x² + 6x + 9 = 16
x² + 6x = 16 - 9
x² + 6x = 7
This is not equivalent to x² + 6x - 16 = 0
f) (x+3)² = 25
(x+3)(x+3) = 25
x(x+3)+3(x+3) = 25
x² +3x +3x + 9 = 25
x² + 6x + 9 = 25
x² + 6x = 25 - 9
x² + 6x = 16
This is equivalent to x² + 6x = 16
The correct option C and FF
x(x+3)+3(x+3) = 16
x² +3x +3x + 9 = 16
x² + 6x + 9 = 0
what value of X makes this equation true?10×-6=3[×+1/2]A=14/15B=13/14C=15/14D=14/13
Answers
10x - 6 = 3 ( x + 1/2)
To find the value of x that make the equation true, we need to solve for x
open the parenthesis
10x - 6 = 3x + 3/2
collect like term
10x - 3x = 3/2 + 6
[tex]7x\text{ =}\frac{3+12}{2}[/tex][tex]7x\text{ =}\frac{15}{2}[/tex]Multiply both-side of the equation by 1/7
[tex]x\text{ =}\frac{15}{2}\times\frac{1}{7}[/tex][tex]x=\frac{15}{14}[/tex]Answer:
x=15/14
Step-by-step explanation:
No explanation
Jada leaves the beach with some seashells. One out of every three of the shells turns out to contain a hermit crab. Write an expression to represent the number of hermit crabs Jada found. Let z represent the total number of seashells she collected.
Answers
The expression to represent the number of hermit crabs Jada found is:
1/3z
Given, Jada leaves the beach with some seashells.
One out of every three of the shells turns out to contain a hermit crab.
we are asked to determine the expression to represent the number of hermit crabs Jada found.
Let z represent the total number of seashells she collected.
Hence the expression is:
z × 1/3
= 1/3z
So the total number of seashells Jada collected are 1/3z.
Hence we get the answer as 1/3z
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Graph the system of linear inequalities and shade in the solution set. If there are no solutions, graph the corresponding lines and do not shade in any region X - y > 2 Y < - 1/3x + 1
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We need to graph the following inequality system:
[tex]\begin{cases}x-y>2 \\ y<-\frac{1}{3}x+1\end{cases}[/tex]Now we need to isolate the y-variable on the left side for the first equation:
[tex]\begin{cases}yNow we have to graph the boundary lines, which are:[tex]\begin{gathered} y=x-2 \\ y=-\frac{1}{3}x+1 \end{gathered}[/tex]We need to points to graph these equations. We will use the points that have x equal to 0 and y = 0.
For the first equation:
[tex]\begin{gathered} y=0-2 \\ y=-2 \end{gathered}[/tex]The first point is (0,-2).
[tex]\begin{gathered} 0=x-2 \\ x=2 \end{gathered}[/tex]The second point is (2, 0).
For the second equation:
[tex]\begin{gathered} y=-\frac{1}{3}\cdot0+1 \\ y=1 \end{gathered}[/tex]The first point (0,1).
[tex]\begin{gathered} 0=-\frac{1}{3}x+1 \\ \frac{1}{3}x+1 \\ x=3 \end{gathered}[/tex]The second point is (3, 0).
Now we can trace both boundary lines:
Finally we can shade the solution set, which is the region that is below both lines, since both have an "<" signal.
log32187 = 7 can be expressed as _______A. 37 = 2187B. 32187 = 7C. 73 = 2187D. 72187 = 3
Answers
Recall the log to exponential rule:
[tex]\begin{gathered} If \\ \log_aN=x \\ then \\ a^x=N \end{gathered}[/tex]Therefore, we can express the log expression given to be:
[tex]\log_32187=7[/tex]in the exponential form as:
[tex]3^7=2187[/tex]OPTION A is correct.
A bag contains 25 cookies. There are 15 chocolate chip cookies, 7 peanut butter cookies, and the rest are oatmeal raisin cookies. What is the probability of randomly choosing a chocolate chip or peanut butter cookie from the bag? (Write your answer as a whole percent)
Answers
SOLUTION:
Case: Probability
Method:
Total= 25 cookies
Chocolate chip (C)= 15
Peanut butter (P)= 7
Oatmeal raisin (O)= 25 - 15 - 7
Oatmeal raisin= 3
The probability of randomly choosing a chocolate chip or peanut butter cookie from the bag.
[tex]\begin{gathered} Pr(CorP)=\frac{15+7}{25} \\ Pr(CorP)=\frac{22}{25} \end{gathered}[/tex]As a percentage, the percentage equivalence is:
[tex]\begin{gathered} Pr(CorP)=\frac{22}{25}\times100 \\ Pr(CorP)=22\times4 \\ Pr(CorP)=88 \end{gathered}[/tex]Final answer:
88%
Parker is playing a game in which the object is to obtain a 0 by adding the points scored during each round. (Graph up top ) Based on the points he scored during the first 4 rounds, what score does Parker need on the 5th round?
Answers
Objective:
Obtain an score of 0 after add all the scores in all the rounds
Info given:
Round 1: -9
Round 2: 3
Round 3: -8
Round 4: 2
And we want to estimate the score in round 5 in order to obtain a 0 so we can do this:
[tex]-9+3-8+2+x=0[/tex]Where x represent the score required for round 5 and solving we got:
[tex]x=9+8-3-2=12[/tex]So then the score required for round 5 is 12
(4k² + 9k + 9) - (k² + 8k + 5)
Answers
we have the expression
(4k² + 9k + 9) - (k² + 8k + 5)
simplify
step 1
group like terms
(4k²-k²) +(9k-8k)+(9-5)
step 2
combine like terms
3k²+k+4hich is equivalent to RootIndex 5 StartRoot 1,215 EndRoot Superscript x?
243x
1,215 Superscript one-fifth x
1,215 Superscript StartFraction 1 Over 5 x EndFraction
243 Superscript StartFraction 1 Over x EndFraction
Answers
The given expression is equivalent to [tex]$(1215)^{x/5}[/tex].
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following equation -
[tex]$(\sqrt[5]{1215})^{x}[/tex]
For [tex]$\sqrt[a]{x} = x^{1/a}[/tex]
Using the rule, we can write -
[tex]$(\sqrt[5]{1215})^{x}[/tex] = [tex]$(1215)^{x/5}[/tex]
Therefore, the given expression is equivalent to [tex]$(1215)^{x/5}[/tex].
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Write an equation of a circle giving its Center and radius or diameter.
Answers
The equation of a circle with center (h,k) and radius r is given as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]From the question, it is given that the center of the circle is (-7,-4) and the diameter is 8.
Since the radius is half the diameter, it follows that the radius is:
[tex]\frac{\text{diameter}}{2}=\frac{8}{2}=4[/tex]So it implies that r=4, h=-7, and k=-4.
Substitute these values into the equation of a circle:
[tex]\begin{gathered} (x-(-7))^2+(y-(-4))^2=4^2 \\ \Rightarrow(x+7)^2+(y+4)^2=16 \end{gathered}[/tex]Hence, the equation of the circle is:
[tex](x+7)^2+(y+4)^2=16[/tex]
A psychology test has personality questions numbered 1,2,3, intelligence questions numbered 1,2,3,4, and attitude questions numbered 1,2. If a single question is picked at random, what is the probability that the question is an intelligence question OR has an odd number?Provide the final answer as a simplified fraction.
Answers
Given:
Personality question = 1,2,3
Intelligence question = 1,2,3,4
Attitude question = 1,2
Find-: what is the probability that the question is an intelligence question OR has an odd number
Sol:
The total number of questions is:
3 Personality, 4 intelligence, and 2 attitudes so the total number of questions is:
[tex]\begin{gathered} =3+4+2 \\ \\ =9 \end{gathered}[/tex]The odd numbers are:
[tex]\begin{gathered} =1,1,1,3,3 \\ \\ \text{ Total 5 questions.} \end{gathered}[/tex]Probability is :
[tex]P=\frac{\text{ Favorable outcome }}{\text{ Total outcome}}[/tex]The probability of an odd number is:
[tex]P=\frac{5}{9}[/tex]The probability of intelligence question of even number is:
[tex]P=\frac{2}{9}[/tex]So required probability is:
[tex]\begin{gathered} =\frac{5}{9}+\frac{2}{9} \\ \\ =\frac{7}{9} \end{gathered}[/tex]Probability is 7/9.
What is the product of -a + 3)(a + 4)?A. a 2-a + 12 B. a 2 - a - 12 C. -a 2 - a - 12 D. -a 2 - a + 12
Answers
The given expression is : (-a +3)(a + 4)
[tex]\begin{gathered} (-a+3)(a+4)=(-a)\times(a+4)+3(a+4)_{}_{} \\ (-a+3)(a+4)=(-a)\times(a)+4\times(-a)+3\times(a)+3\times4 \\ (-a+3)(a+4)=-a^2-4a+3a+12 \\ (-a+3)(a+4)=-a^2-a+12 \end{gathered}[/tex]Answer : D) - a² - a + 12
Find the equation of a line perpendicular to the given line and pass through the given point. Write equation in slope-intercept form Line y= -4/5x + 2 point, (8,9) Graph
Answers
ANSWER
Equation:
[tex]y=\frac{5}{4}x-1[/tex]Graph:
The red line is the graph of the given line and the green line is the graph of the perpendicular line passing through (8, 9).
EXPLANATION
The equation of the line is given in the slope-intercept form,
[tex]y=-\frac{4}{5}x+2[/tex]The slope is -4/5 and the y-intercept is 2.
Two lines are perpendicular if their slopes are opposite reciprocals of each other. Therefore, a perpendicular line to the given line has a slope of 5/4,
[tex]y=\frac{5}{4}x+b[/tex]There is an infinite number of perpendicular lines, but there is only one that passes through the point (8, 9). Replace x and y with the coordinates of this point in the equation above,
[tex]9=\frac{5}{4}\cdot8+b[/tex]And solve for b,
[tex]\begin{gathered} 9=5\cdot2+b \\ 9=10+b \\ 9-10=b \\ -1=b \end{gathered}[/tex]Hence, the equation of the perpendicular line is,
[tex]y=\frac{5}{4}x-1[/tex]which of the following does not show the commutative property of addition 9+x=x+9a+b=b+aab=ba3x+4y=4y+3x
Answers
The commutative property of addition is such that two or more values or numbers when added up ould alays have the same result no matter how the numbers are rearranged.
Options 1, 2 and 4 shows the commutative property of addition, but OPTION 3 DOES NOT.
The correct answer here is option 3, hich is
ab = ba
[tex]7 \sqrt{5 |4| } [/tex]3+6-4÷36×59099m
Answers
Find the value of k that makes f(x) continuous at x = 3
Answers
Given:
The function is,
[tex]f(x)=f(x)=\begin{cases}\frac{x-3}{x^2+2x-15},x\ne3 \\ k,x=3\end{cases}[/tex]As the given function is continous at x= 3 ,
[tex]\begin{gathered} \lim _{x\to3}f(x)=k \\ \lim _{x\to3}(\frac{x-3}{x^2+2x-15})=k \end{gathered}[/tex]Sam is making Apple Pies and Pumpkin Pies for her Pie shop. She sells eachApple Pie for $6 and each Pumpkin Pie for $7. If Sam sells a total of 80 piesone day and makes a total of $512, how many apple pies did she sell?
Answers
Let m represent the number of apple pies Sam is making and
Let n represent the number of pumpkin pies Sam is making
If Sam sells a total of 80 pies, this can be represented by
m + n = 80 ------------------------------equation (1)
If she makes a total of $512 on the same day, this cost can be represented by
6m + 7n = 512 ----------------------------equation (2)
Solving both equations simultaneously
m + n = 80
6m + 7n = 512
from m + n = 80,
m = 80 - n
substitute m = 80 - n into equation (2)
we have
6(80 -n) + 7n = 512
480 - 6n + 7n = 512
480 + n = 512
n = 512 - 480
n = 32
Put n = 32 into m = 80 - n
we have
m = 80 - 32
m = 48
The number of apple pies Sam sell is 48