The table is an illustration of a proportional relationship. and can be modeled by the function rule y = 12x
The entries of the table is given as:
Hours Earnings
4 48
6 72
10 120
20 240
Start by calculating the rate (m) of the function
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{72 - 48}{6-4}[/tex]
[tex]m = \frac{24}{2}[/tex]
[tex]m = 12[/tex]
The equation of the table is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = 12(x - 4) + 48[/tex]
[tex]y = 12x - 48 + 48[/tex]
[tex]y = 12x[/tex]
[tex]y = 12x[/tex] means that, the following statements are true:
The rate of change for the data is $12 per hour. $12 is also the constant of proportionalityIf you graph the data, it would pass through the origin (0,0) The data represent a direct variation and can be modeled by the function rule y = 12xRead more about proportional equations at:
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HELP PLEASE TAKING A TEST RIGHT NOW
the graph shows a system of equations
what is the solution to the system of equations?
a. -3, 2
b. 3, -2
c. 3, 2
d. -3, -2
The counting number ABAB is a multiple of 36. If different letters represent different digits, what is the greatest value ABAB can have? PLS HELP ONLY 10 minutes
The greatest value ABAB can have is 7272.
The given parameters:
Counting number ABAB = multiple of 36The counting number can be expanded as follows;
ABAB = 100 x AB + AB
= AB00 + AB
= AB(100 + 1)
= AB(101)
101 is a prime factor of AB and has only two factors.
The prime factor of 101 = 1 x 2
Since 101 is prime, the counting number AB must 2-digits multiples of 36.
The greatest value ABAB can have is calculated as follows;
ABAB = (36 x 2)(36 x 2)
ABAB = 7272
Thus, the greatest value ABAB can have is 7272.
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I need help on these functions questions
Answer:
see explanation
Step-by-step explanation:
(a)
Substitute x = - 1 into f(x)
f(- 1) = 6 - 2(- 1) = 6 + 2 = 8
(b)
Substitute x = [tex]\frac{1}{3}[/tex] into g(x)
g([tex]\frac{1}{3}[/tex] ) = [tex]\frac{9}{\frac{1}{3} }[/tex] = 9 × 3 = 27
(c)
Substitute x = f(x) into h(x)
h(6 - 2x)
= 6 + (6 - 2x)² ← expand using FOIL
= 6 + 36 - 24x + 4x² ← collect like terms
= 4x² - 24x + 42
(d)
Substitute x = f(x) into g(x)
g(6 - 2x)
= [tex]\frac{9}{6-2x}[/tex]
(e)
Evaluate g(12) then substitute value obtained into f(x)
g(12) = [tex]\frac{9}{12}[/tex] = [tex]\frac{3}{4}[/tex] , then
f([tex]\frac{3}{4}[/tex] ) = 6 - (2 × [tex]\frac{3}{4}[/tex] ) = 6 - [tex]\frac{3}{2}[/tex] = [tex]\frac{9}{2}[/tex]
(f)
Evaluate f(- 9) then substitute the value obtained into h(x)
f(- 9) = 6 - 2(- 9) = 6 + 18 = 24 , then
h(24) = 6 + 24² = 6 + 576 = 582
Evaluate "four dollars less than the cost
of a sweater" if a sweater costs $22
a
a
The question says to evaluate the cost of four dollars less than the cost of a sweater.
To do this, what we have to do is to create a mathematical equation of it.
Less than always insinuates that we are to subtract, and as such, we are going to subtract four dollars from the cost of the sweater to get our final answer.
Four dollars less than the cost of a sweater that costs $22 is
22 - 4 = $18
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Convert 62% into a fraction
Answer:
62% = 31 / 50
Step-by-step explanation:
62/100
if you need to simplify then it would be 31/50
How to find the derivative???
Answer:
[tex]y'= \dfrac{2}{3}e^{2x + e^{2x}/3}[/tex]
Step-by-step explanation:
We have [tex]e^{2x} = \ln(y^3)[/tex] and we want the implicit differentiation [tex]\dfrac{dy}{dx}f(x) = y'[/tex]
Therefore, we want to separate the [tex]y[/tex] from the equation.
[tex]\ln(y^3) =e^{2x} \implies 3 \ln(y) = e^{2x} \implies \ln(y) = \dfrac{e^{2x} }{3}[/tex]
[tex]\implies e^{\ln(y)} = e^{e^{2x}/3} \implies \boxed{y = e^{e^{2x}/3}}[/tex]
Now we can calculate the derivative. By the chain rule,
[tex]y' = \dfrac{d}{dx}\left(e^{e^{2x}/3}\right) = e^{e^{2x}/3}\dfrac{d}{dx}\left(\dfrac{e^{2x}}{3}\right)[/tex]
Now
[tex]\dfrac{d}{dx}\left(\dfrac{e^{2x}}{3}\right) =\dfrac{1}{3}\dfrac{d}{dx}\left(e^{2x}\right) = \dfrac{2}{3}e^{2x}[/tex]
Therefore
[tex]y' = e^{e^{2x}/3}\cdot \dfrac{2}{3}e^{2x} = \dfrac{2}{3}e^{2x + e^{2x}/3}[/tex]
Birdseed costs $0.57 a pound and sunflower seeds cost $0.87 a pound. Angela Leinenbachs' pet store wishes to make a 30 pound mixture of birdseed and sunflower seeds that sells for $0.81 per pound. How many pounds of each type of seed should she use?
Step-by-step explanation:
x = pounds birdseed
y = pounds sunflower seeds
x + y = 30
0.57x + 0.87y = 30×0.81
with this last trick (to calculate the full cost of the whole 30 pounds based on the targeted individual price per pound) we bring both constraints into the play.
from the first equation we get
x = 30 - y
and we use that in the second equation :
0.57×(30-y) + 0.87y = 30×0.81 = $24.30
17.1 - 0.57y + 0.87y = 24.3
0.3y = 7.2
y = 24
x = 30 - y = 30 - 24 = 6
she uses 6 pounds of birdseed and 24 pounds of sunflower seeds.
Help helphep help help math straightforward
Step-by-step explanation:
when a line cuts through 2 parallel lines, it does the exact same thing to both lines. it has to. because they are parallel, they act as if they are identical. only their placement is different, but this has no impact on the angles between the lines.
now, imagine a circle with the center at one of the crossing points. this circle is cut in half by the central line.
you know how many degrees a full circle has ?
360 degrees.
now, how many degrees are represented by the half- circle above or below the center line ?
of course, half of the degrees of the full circle. that means 180 degrees.
so, all the angles around a single point on one side of a line must have how many degrees together ?
right, these half-circle 180 degrees again.
because of everything we said up there, the angle 4x+6 is the same as the angle right of the 7x-2 angle.
so, 7x-2 and 4x+6 must be 180 degrees together.
that is called "supplementary angles".
7x - 2 + 4x + 6 = 180
11x = 176
x = 16
PLEASE HELP WILL MARK BRAINIEST!!!!!
Answer:
c. copy an angle.
there's no angle in this as far as I can see.
QUESTION 16 PLEASE HELP ME ASAPP
Answer: changes over time
Step-by-step explanation: it is always decreasing
add r to s, double the result, then multiply what you have by t
Answer:
(rs2) x t
Step-by-step explanation:
r+s=rs
rsx2=rs2
(rs2)xt
Answer:
2t(s+r)
Step-by-step explanation:
Add r to s
s+r
Double the result
2(s+r)
Multiply what you have by t
2t(s+r)
correct?`````````````````````````
Answer:
It's $5 for a ticket
Step-by-step explanation:
Hope this helps
MAy I get Braineist pls?
Please write in full sentences.
Brainliest and 100 points.
If you don't know then don't answer.
Answer:
no because there is a 10 which make it not proportional
Step-by-step explanation:
hope that helps.
Answer: No they are not proportional because the last row has -10 which obstructs the whole relationship.
Please help me solve this
Step-by-step explanation:
first line multiplied with first column. then with second column. and then third.
then the same for the second line and then the third line.
BA11 = 5×3 + 7×3 + 3×2 = 38
BA12 = 5×1 + 7×6 + 3×-1 = 44
BA13 = 5×2 + 7×-4 + 3×-3 = -27
BA21 = -2×3 + -1×3 + 9×2 = 9
BA22 = -2×1 + -1×6 + 9×-1 = -17
BA23 = -2×2 + -1×-4 + 9×-3 = -27
BA31 = 4×3 + 3×3 + 1×2 = 23
BA32 = 4×1 + 3×6 + 1×-1 = 21
BA33 = 4×2 + 3×-4 + 1×-3 = -7
Which of these is a ratio table?
A
1
2.
3
o ono
WON
B.
5
6
7
A
1
2
3
chAUD
B
4
5
7
WN
B
A
1
2
3
COA
4
9
А
1
2
3
B
2.
4
6
ANUD
INI
Answer:
The last one
Step-by-step explanation:
A ratio table means that each number in the first column is multiplied by the same number to get the answer in the 2nd column
Perform the indicated operations/solutions.
1. 12-7+45÷15x11=
2. 16x2+12-18÷9-4=
PLEASE ANSWER!!!
Boris Drove to the mountains last week. There was heavy traffic on the way there, and the trip took 10 hours. When Boris drove home, there was no traffic and the trip only took seven hours. If his average rate was 18 mph faster on the trip home, how far away does Boris live from the mountains?
Answer:
Step-by-step explanation:
Answer:
Let +d+ = the one-way distance to the mountains in miles
Let +s+ = his speed going to the mountains in mi/hr
+s+%2B+27+ = his speed on the trip home in mi/hr
equation for going to the mountains:
(1) +d+=+s%2A7+
Step-by-step explanation:
I hope this helps mark as brainliest if correct
Using the table find then relative frequency of each color, to 3 decimal places
Explanation:
For each row, divide the color counts over the total. For example, we have 9 red in bag one out of 61 total. This leads to a relative frequency of 9/61 = 0.1475 which rounds to 0.148; so approximately 14.8% of the items in bag one are red. This represents the top left corner of the table.
As another example, we have 5 brown out of 60 total in bag ten. That leads to a relative frequency of 5/60 = 0.0833 = 0.083 (see the bottom right corner of the table).
Take note that for any given row, adding up the relative frequencies will yield the value of 1 (though there might be some slight rounding error along the way).
Geoff works at a warehouse , earning $17.50 per hour plus a $200 what’s the equation?
Answer:
P = 17.50x + 200
Step-by-step explanation:
x is the number of hours worked
P is how much money Geoff earns
as the schools sign language interpreter kiran gets paid 35.50 for every parent-teacher conference that he attends. He also gets paid $42 per schhol-related assembly that he attends as an interpreter. If kiran earns $991 for 27 paid events how many parent teacher conferences and how many school related assemblies did he attend write a system of equations describe each variable and solve
Answer:
x= 22 (number of parent teacher conferences) y=5 (number of school related assemblies)
Step-by-step explanation:
This word problem creates the following system of equations for x = number of parent-teacher conferences and y = number of school related assemblies.
x+y = 27 means that the number of parent teacher conferences plus the number of school related assemblies equals a total of 27 paid events.
35.50x + 42y = 991 means that $35.50 multiplied by a certain number of parent teacher conferences, plus $42 multiplied by a certain number of school related assemblies equals his total earnings of $991.
This sets up the following system
x+y=27
35.50x+42y=991
To solve this, we first need to take the first equation and solve for y.
y=27-x
plug in to the second equation and solve for x.
35.50x+42(27-x)=991
35.50x-42x+1134=991
Collect like terms
-6.5x=-143
divide both sides by -6.5 to solve for x.
x=22
Back substitute into other original equation to solve for y.
22+y=27
y=5
The interpreter attended 22 parent-teacher conference and 5 school related assembly
To solve this problem, we would write out two set of linear equations.
The data given on this problem are
parent-teacher conference = $35.50school related assembly = $42The total number of engagements = 27Let x represent the number of parent-teacher conference
let y represent the number of school related conference
Equations[tex]x+y = 27...equation (i)\\35.50(x)+42y=991...equation(ii)[/tex]From equation (i)
[tex]x+y = 27\\x = 27-y...equation(iii)\\[/tex]
Put equation(iii) into equation (ii)
[tex]35.50x+42y=991\\35.50(27-y)+42y=991\\958.50-35.50y+42y=991\\6.50y=991-958.50\\y=5[/tex]
Put y = 5 into equation 1
[tex]x+y=27\\y = 5\\x+5=27\\x=27-5\\x=22[/tex]
From the above calculations, he attended 22 parent-teacher conference and 5 school related assembly.
Learn more on linear equations here;
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Write the equation in standard form y=-x+1
Answer:
x+y=1
Step-by-step explanation:
The Linear Equation Standard Form is = ax+by=c.
Given y=-x+1, we will use Algebra to convert the equation from slope-intercept form to standard form:
x+y=-x+x+1
We added x to both sides to cancel out and move the -x.
x+y=1 is the answer.
need help with this problem
Answer:
x = 6
Step-by-step explanation:
Answer:
Step-by-step explanation:
tan30 = x/12
x = 12tan30
x = 12(sin30/cos30)
x = 12(½ / ½√3)
x = 12/√3
x = (12/3)√3
x = 4√3
A middle school took all of its 6th grade students on a field trip to see a play. The students filled 1917 seats, which was 45% of the total number of seats in the theater. How many total seats were in the theater?
Answer:
4260 seats in the theater
Step-by-step explanation:
We write the equation 0.45x=1917, with x representing the total number of seats.
Multiply both sides by 100, we get 45x=191700.
Divide both sides by 45, we get x=191700/45
x=4260.
There are 4260 seats in the theater.
The total number of seats is the theater is 4,260.
Percentage:
The percentage is a ratio or fraction of 100 and can be calculated with the formula
Percentage = [tex]\frac{parts}{whole}.100[/tex]
How to calculate percentage?Here we have given that the 1917 seats is 45% of the total seats
Let the total number of seats available in theater is = x
Then 45 % of x = 1917
0.45 x = 1917
Multiply both the sides by 100 we have
45 x = 1917x100
x = [tex]\frac{191700}{45}=4260[/tex]
The final answer is 4,260 seats
Learn more about Percentage here-
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At Buffalo Wild Wings, you order a meal that costs $15.86. You leave an 18% tip (on the pre-tax amount).
The sales tax is 8%. What is the total cost of the meal?
Answer:
round to cent 20.59
Step-by-step explanation:
The temperature was -1°F at noon and dropped to -14°F by the evening.
What was the change in temperature?
13°F
-13°F
-15°F
15°F
Answer:
-13°F is the change in temperature.
Step-by-step explanation:
The change in temperature is,
→ -1 + x = -14
→ x = -14 + 1
→ [ x = -13 ]
Hence, -13°F is the change.
Amanda went to the Farmer’s market with her family. She had $5.00 to spend and decided she wanted to spend it on peaches. Each peach cost 68 cents. How many peaches could she buy ?
The length of a pool is twice its width. What is the ratio of the length to the width of the pool?
Answer:
2:1 OR as a fraction, 2/1
Step-by-step explanation:
We don't know the actual length or width of this pool, like we don't know a number, as in exactly how many feet or meters long or wide this pool is. For this question, we don't need to know. "Twice" means 2 times. So if we consider the width (which we don't know) and call it w, then the length, (which we also don't know) which is two times as long, would be 2w
Width = w
Length = 2w
Ratio of Length to Width is
2w:w or as a fraction 2w/w
This can be simplified to
2:1 or as a fraction 2/1
How would you find the average rate of change between two points
on a curve?
Answer:
For a function, it is the change in the y-value divided by the change in the x-value for two distinct points on the graph
Step-by-step explanation:
Answer:
i think that you can find the average rate of change between 2 points on a curve by dividi the change in the output value (Y) by the change in the input value (X)
Step-by-step explanation:
Solve for x:
4x-3Divided by 2 =5/3
Answer:
x=19/12
Step-by-step explanation:
(4x-3)/2 = 5/3
4x-3 = 10/3
3 = 9/3
4x = 10/3 + 9/3 = 19/3
x = 19/12
Hey there!
4x - 3/2 = 5/3
ADD 3/2 to BOTH SIDES
4x - 3/2 + 3/2 = 5/3 + 3/2
CANCEL out: -3/2 + 3/2 because it gives you 1
KEEP: 5/3 + 3/2 because it helps solve for the x-value.
NEW EQUATION: 4x = 5/3 + 3/2
SIMPLIFY IT!
4x = 19/6
DIVIDE 4 to BOTH SIDES
4x ÷ 4 = 19/6 ÷ 4
CANCEL out: 4 ÷ 4 because it gives you 1
KEEP: 19/6 ÷ 4 because it helps solve for the x-value
NEW EQUATION: x = 19/6 ÷ 4
SIMPLIFY IT!
x = 19/24
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
can someone help plz I need help ASAP!
Answer:
[tex]y= \frac{1}{3}x -9[/tex]
Step-by-step explanation:
First you must substract -5 to both sides
-5-4= -9
[tex]y= \frac{1}{3}x -9[/tex]