Graphing proportional relationships
Problem
Graph the line that represents a proportional relationship betweenddd andttt with the property that an increase of 0.20.20, point, 2units intttcorresponds to an increase of1.81.81, point, 8units inddd.
What is the unit rate of change ofdddwith respect tottt? (That is, a change of 111unit intttwill correspond to a change of how many units ind?d?d, question mark)
The unit rate of change is
.
Graph the line.
Answers
a. The unit rate is 9 d per t
b. Find the graph in the attachment
To graph the line, we need to find its gradient or unit rate
a. How to calculate the unit rate of change of d with respect to t?Since t has an increase of 0.20 units in t corresponds to an increase of 1.8 units in d.
The gradient or unit rate of change is m = change in d/change in t
= Δd/Δt
Since
Δd = +1.8 units and Δt = +0.2 unitsSo, substituting the values of the variables into the equation, we have
m = Δd/Δt
= + 1.8 units/+ 0.2 units
= 9 d per t
So, the unit rate is 9 d per t
b. The graph of the line
To graph the function, we need to know the equation of the graph.
So, the equation of a graph in gradient form is
m = (y - y')/(x - x') where (x', y') = (0, 0) since the graphs both start at the origin
Since m = 9, we have
m = (y - y')/(x - x')
9 = (y - 0)/(x - 0)
9 = y/x
y = 9x
So, the equation of the line is y = 9x
Find the graph in the attachment.
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Related Questions
The surface area of an open-top box with length
L
, width
W
, and height
H
can be found using the formula:
A
=
2
L
H
+
2
W
H
+
L
W
Find the surface area of an open-top box with length 4 cm, width 8 cm, and height 5 cm.
Answers
Answer:
Surface Area is equal to 160 cm²
here is your answer
Which of the following is a solution to the equation ¾x-12=-18?
4.5
-22.5
-40
-8
Answers
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above2[/tex]
We have the equation [tex]\large\boldsymbol{\sf{\displaystyle\frac{3}{4}x-12=-18}}[/tex].
First we should add 12 to both sides of the equation.
[tex]\large\boldsymbol{\sf{\displaystyle\frac{3}{4}x=-18+12}}[/tex]. Simplify
[tex]\large\boldsymbol{\sf{\displaystyle\frac{3}{4}x=-6}}[/tex].
This done, let's multiply the equation by 4. You'll see why
[tex]\large\boldsymbol{\sf{\displaystyle\frac{3}{\not4}x\times\not4=-6\times4}}[/tex]
Did you see how on the left, the 4's cancelled? That's
because dividing by 4 and then multiplying the same
number, or the result, by 4, are operations that undo each
other.
This being said, let's finish solving this equation in terms of x
[tex]\large\boldsymbol{\sf{3x=-24}}[/tex]. See how this works?
Now, remember that we ought to use inverse operations
to solve for x. These are operations that undo each other.
So if x is multiplied by 3, we should... divide by 3!
Also, please keep in mind that we can only divide the left side
by 3 if we divide the right side by 3.
[tex]\large\boldsymbol{\sf{\displaystyle\frac{3x}{3}=\displaystyle\frac{-24}{3}}}[/tex]. Once again the 3s on the left cancel, leaving
x. Wait! Isn't that what we wanted? Yepp, sure!
The right side is now -8. Thus,
[tex]\large\boldsymbol{\sf{x=-8}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
Solve the system of equations.
y+4z=0
4x+y-2z=2
-3x-3z=-9
Answers
Step-by-step explanation:
y+4z=0
4x+y-2z=2
-3x-3z=-9
Answer:
x = 7/3y = - 8/3z = 2/3Step-by-step explanation:
y + 4z = 0
4x + y - 2z = 2
____________ -
- 4x + 6z = - 2
- 4x + 6z = - 2 → times 3 → - 12x + 18z = - 6
- 3x - 3z = - 9 → times 4 → - 12x - 12z = - 36
- 12x + 18z = - 16
- 12x - 12z = - 36
______________ -
30z = 20
z = 20/30
z = 2/3
y + 4(2/3) = 0
y + 8/3 = 0
y = - 8/3
- 3x - 3z = - 9
- 3x - 3(2/3) = - 9
- 3x - 6/3 = - 9
- 3x - 2 = - 9
- 3x = - 9 + 2
- 3x = - 7
x = - 7/- 3
x = 7/3
translate the sentence into an equation rhoda's score decreased by 10 is 51 use r to represent rhoda's score
Answers
Answer: r - 10 = 51
Step-by-step explanation:
While researching different companies, she discovers the following standard deviations of one year of daily stock closing prices.
Masterful Pocket Watches: Standard deviation of stock prices =$9.83
Eye Remember Enterprises: Standard deviation of stock prices =$1.15
Based on the data and assuming these trends continue, which company would give Donna a stable long-term investment?
a} eye remember enterprises; the smaller deviation indicates that eye enterprises have less variability in its closing prices than masterful pocket watches.
b}masterful pocket watches; the larger standard deviation indicates that masterful pocket watches have less variability in its closing prices than eye remember enterprises.
c} eye remember the enterprises; the smaller standard deviation indicates that eye remember enterprises has a greater mean closing price than masterful pocket watches.
d}masterful pocket watches; the larger standard deviation indicates that masterful pocket watches have a greater mean closing price than eye remember enterprises.
Answers
The data and assuming shows that the company that would give Donna a stable long-term investment is A. eye remember enterprises; the smaller deviation indicates that eye enterprises have less variability in its closing prices than masterful pocket watches.
How to illustrate the information?It should be noted that the information given implies that Donna needs a stable long term investment.
In this case, it's appropriate that the company that has the less standard deviation should be chosen.
This illustrates that Perfect Plungers has less variability.
In conclusion, the correct option is A.
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Richard wants to purchase a Jeep. The purchase price of the Jeep is $ 42 , 000. The dealership will allow him to pay cash or finance the Jeep with a down payment of $ 4 , 000. and 72 monthly payments of $ 680. Richard chose to finance the jeep.
Answers
Answer:
Good for him for buying a Jeep
Step-by-step explanation:
Linear function model
Answers
Answer:
f(x) = 800 - 75x
Step-by-step explanation:
Rachel took a loan of 800 dollars | Money Owed: f(x) = 800
She pays back 75 dollars a week <-> (x) | Money Owed: f(x) = 800 - 75x
Which of the following is correct based on this picture? A. none of these are correct B. sinZ=61/73 C. cosZ=61/73 D. tanZ=61/73
Answers
Answer:
C.) cosZ=61/73
Step-by-step explanation:
I hope you got the answer
Will give brainliest
A radioactive element has a half-life of 55 days. what percentage of the original sample is left after 115 days? round to 4 decimals when necessary.
Answers
The percentage of the radioactive isotope left is 25.0000%.
What is the half life?The half life of a radioactive isotope is the time that will elapse before only half of the number of original isotopes will remain.
Now;
We are told that;
Half life (t1/2) = 55 days
Time taken (t) = 115 days
Ratio of isotope remaining = N/No
Thus;
N/No = (1/2)^t/t1/2
N/No = (1/2)^115/55
N/No = (1/2)^2
N/No =1/4
Hence, the percentage = 1/4 * 100/1 = 25.0000%
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Find the coefficient of determination, given that the value of the linear correlation coefficient, r, is –0.721.
Answers
The coefficient of determination is calculated as: 0.520.
How to Find the Coefficient of Determination?The coefficient of determination = the square of the correlation coefficient.
Given the following:
Value of the linear correlation coefficient (r) = -0.721
Therefore, we would have:
The coefficient of determination = (-0.721)²
The coefficient of determination = 0.520
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1. a. Determine the equation of a parent function for the parabola that has zeros 1,-5.
Determine the member equation that passes through the point (-2,-36)
Answers
The member equation which passes through the point (-2,-36) is y = 4 ( x-1)(x+5) .
What is a Parabola ?Parabola is a U shaped figure , whose all points are at a fixed distanced from a point called as focus and a line called as Directrix.
It is given that
The zeroes of the parabola is 1,-5.
The equation of the parabola is given by
y = a( x - x')(x-x'')
y = a( x-1)( x+5)
This is the equation for the parent function for the parabola
The parabola passes through the point ( -2 , -36 )
-36 = a( -2 -1)(-2+5)
-36 = (-3) * (3) a
-36 = -9 a
a = 4
y = 4 ( x-1)(x+5)
The member equation which passes through the point (-2,-36) is y = 4 ( x-1)(x+5) .
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how do i find x?? whats the answer?
Answers
Through proportionality theorem.
Therfore [tex] \frac{ 11}{121} = \frac{10}{5x + 10} \\ \\ 11(5x + 10) = 121(10) \\ (5x + 10) = \frac{121(10)}{11} \\ 5x + 10 = 110 \\ 5x = 110 - 10 \\ 5x = 100 \\ \frac{5x}{5} = \frac{100}{5 } \\ x = 20cm[/tex]HOPE THIS HELPS!Select the correct answer.
Consider the graph of function f below.
Y
-8 -4
8+
O
A
O
4
-4-
-8
The function g is a transformation of f. If g has a y-intercept at 4, which of the following functions could represent g?
4 8
O g(x)=f(x) + 4
g(x) = f(x-4)
g(x) = f(x) - 2
Og(x)=f(x + 2)
Answers
Answer:
742
Step-by-step explanation:
4x203
Therefore , the solution of the given problem of function comes out to be g(x) is given by g(x) = (x-4)² + 6
What is function ?A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single, recognized output for each input.
Here, we have,
Given the graph of the original function f(x), whose vertex is at (0, 0), and indeed the graph of the translating function g(x), whose vertex is at (0, 0), (5, 2).
Be aware that the translated function's vertex is 2 units higher and 5 units to the right of the f graph's graph (x).
The function f(x) is then translated 5 units toward the right и 2 units up to arrive at g(x).
Recall that provided a function, f(x), is characterized as a parabola with a vertex at (h, k).
=> f(x) = (x-h)² + k
The outcome of translating a unit to the right with b unit up is
=>f'(x) = (x-h-a)² + k + b
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Which diagram represents rx ◦ RO,180°?
Answers
Answer:
if this is for edge unity the answer is B
A beekeeper’s hives are making honey at a constant rate. The profit from honey can be represented by the equation
P(t) = -16t2 + 2050t + 150, where t is the time in days and P(t) is the profit the beekeeper receives. After how many days should she harvest her honey to maximize profit?
Answers
Using the vertex of a quadratic function, she should harvest her honey after 64 days to maximize profit.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.The profit function is given as follows:
P(t) = -16t² + 2050t + 150.
The coefficients are a = -16 < 0, b = 2050, c = 150, hence the t-value of the vertex is:
[tex]t_v = -\frac{b}{2a} = -\frac{2050}{-32} = 64[/tex]
Hence she should harvest her honey after 64 days to maximize profit.
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3. What is the measure of angle HEK in this figure?
95
55
85
150
Answers
Answer:
95 is the correct answer
Step-by-step explanation:
The initial or beginning side is H. Look on the protractor and you will see the top number is 55 degrees. That is where we start. Now, go to line E, that is where we end. The top number is 150. To find <HEK, we need to subtract 55 from 150 to get 95.
Slope is given by the formula
Answers
Answer:
A
Step-by-step explanation:
Answer
You never add or subtract to get the slope. That makes C and D incorrect. B is the upside down of the answer.
Answer: the answer is A slope = rise / run
Ten copper pennies having a total mass of 25 grams warm up from 23oC to 38oC as you hold in your hand. If the specific heat capacity of copper is 0.39 J/(g *oC), how much energy is absorbed by the pennies?
Answers
The amount of energy absorbed by the pennies made up of copper is 146.25J
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Amount of energy absorbed = mass * temperature change * specific heat capacity
Amount of energy absorbed = 25 * (38 - 23) * 0.39 = 146.25J
The amount of energy absorbed by the pennies made up of copper is 146.25J
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Aisha has a health insurance policy with an 80/20 coinsurance and deductible of $3,200. She has met 45% of her deductible before having
some tests done. Given the cost of her tests below, how much will she pay?
Bill #1- Blood Test = $345.25
Bill #2 - Allergy Test = $175.00
Bill #3- MRI = $920.65
Select one:
O a. $319.10
O b. $1,440.90
O c. $3,200.00
O d. $1,760.00
Answers
The payment for the test based on the information about the insurance will be B. $1440.90.
How to compute the value?The cost for the payment will be:
= Blood test expenses + Allergy test - MRI expenses
= $345.25 + $175.00 + $920.65
= $1440.90
Therefore, the payment for the test based on the information about the insurance will be $1440.90
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the eastern alberta DC transmission like is a project that began construction in 2012. It includes a 500km, 500kv power line from the brooks area to the edmonton area. (the V stands for volts, and SI unit for the electrical potential)
Answers
The number of the required towers based on the information given is 3334.
How to calculate the number?From the information given, it should be noted that the length of power line is 500km
The towers supporting the line are 1.5hm apart. It should be be noted that 1km = 10hm. Therefore, the require towers will be:
= (500 × 10)/1.5
= 3334
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Equation P: a + b = 6
Equation Q: 4a + 2b = 19
Which of the following steps can be used to eliminate the a term?
−1(4a + 2b = 19)
−4(4a + 2b = 19)
−4(a + b = 6)
4(a + b = 6)
Answers
Answer:
-4(a + b = 6)
Step-by-step explanation:
When you multiply equation P by -4, you obtain -4a - 4b = -24. You can then add this equation to equation Q to eliminate the a term.
WHAT IS THE CORRECT ANSWER ANSWER ASAP
Answers
Answer:
d
Step-by-step explanation:
The equation of the line of best fit of a scatter plot is y = 6x − 9. What is the slope of the equation?
Answers
Answer:
6
Step-by-step explanation:
The equation of the line is written in the slope-intercept form:
y = mx +b
where m is the slope and b is the y-intercept.
Matching patternsThe given equation is ...
y = 6x -9
Comparing this to the slope-intercept form, we see that ...
m = 6
b = -9
The slope of the line is m = 6.
2. For the following data, calculate the z-score. (5 points)
a. Sierra wishes to enroll her son in an exclusive academy. Her son must
score an 107 on their aptitude test in order to be accept. Calculate the z-
score for a score of 107 based on the data provided.
Score (Y) = 107
Mean = 95
Standard Deviation = 7.5
hint: Use the z-score formula to convert 107 into a z-score
Answers
The z-score for a score of 107 is 1.6
How to determine the z-score?The given parameters are:
Score (Y) = 107Mean = 95Standard Deviation = 7.5The z-score is calculated using:
[tex]z = \frac{x -\bar x}{\sigma}[/tex]
So, we have:
[tex]z = \frac{107 -95}{7.5}[/tex]
Evaluate the difference
[tex]z = \frac{12}{7.5}[/tex]
Divide
z = 1.6
Hence, the z-score is 1.6
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If
f(x) = 2x² - 5
and
g(x) = 5x + 7
Find
f(g(x)) = [?]x² + [?]x + [?]
Answers
Answer:
f(g(x)) = 50x² + 140x + 93
Step-by-step explanation:
f(g(x)) means that within the f(x) equation, you want to replace all of the x variables with the g(x) equation.
So,
f(g(x)) = 2 (5x+7)² -5
= 2 ( 25x²+ 70x + 49) - 5
= 50x² + 140x + 93
:)
Please help me with this on the picture.
Answers
Answer:
year 7 mean: ≈7.714
year 8 mean: 14
Step-by-step explanation:
mean = sum / number of observations
number of observations = 5, as there are 5 bars for each year
year 7 is the bar on the left for each day
observations for year 7:
5, 8, 9, 13, 19 (left to right)
sum = 5 + 8 + 9 + 13 + 19 = 54 for year 7
mean for year 7 = 54 / 7 ≈ 7.714
observations for year 8 (left to right):
10, 11, 18, 12, 19
sum = 10 + 11 + 18 + 12 + 19 = 70
mean = 70 / 5 = 14
Using a supply and demand graph for gasoline starting at an equilibrium price of $5.00 per gallon and a quantity of 20
gallons, show the effect of a government price ceiling on gasoline of $2.50 a gallon. Is this a binding price ceiling? Why
or wy not? Please explain.
Answers
Yes, to some extent President Biden is right in telling them to lower the price rate because due to the war, a lot of gas companies a using it as a yardstick to inflate their prices and sell above the normal rate they bought it and the oil firms needs to consider the times that people are too.
2. The effect of a government price ceiling on gasoline of $2.50 a gallon is shown in the image attached. There is a binding at $2.00.
3. As price increases, demand also increases in times of gasoline because due to the war, Russia have refuse selling their oil and as such, this has lead to increase demand on the gasolines on ground.
What is Binding Price Ceiling?
A binding price ceiling is one that often takes place if the government are known to have set up a standard price on a good or goods at a specific price that is below equilibrium.
Therefore, to the number one question, we respond Yes, to some extent President Biden is right in telling them to lower the price rate because due to the war, a lot of gas companies a using it as a yardstick to inflate their prices and sell above the normal rate they bought it and the oil firms needs to consider the times that people are too.
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Please solve this question
Answers
Answer:
a) 0.2098
b) 0.036
c) 0.1866
d) 0.9849
Step-by-step explanation:
Image is color coordinated for each part below,
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Solve 10x=3
how do i take logarithms on both sides?
Answers
3/10=x
3/10=0.3
X=0.3
Answer:
x ≅ 0.477.
Step-by-step explanation:
You probably meant:
[tex]10^x = 3.[/tex]
If that is the case, then let's solve it:
[tex]10^x = 3\\\\log\,10^x=log\,3\\\\x = log\,3\\\\x = (approx.)\,\,0.477.[/tex]
Simplify: √36x² if x is less than or equal to 0
Answers
Answer:
[tex]-6x[/tex]
Step-by-step explanation:
[tex]\sqrt{36x^2} = 6\times\sqrt{x^2}\\\\=6\times-x\\\\=-6x[/tex]