Maria made two batches of fruit punch. The table at the right shows how many quarts of juice she used for each batch. Write an equation that relates the proportional quantities. Convince Me! How does the equation change if the amount of grape juice is the independent variable, x, and the amount of apple juice is the dependent variable, y? A table with Apple Juice (x), Grape Juice (y) and Grape Juice/Apple Juice (y/x). The first row has x as 5 and y as 8. The second row has x as 10 and y as 16. In each row, the ratio of Grape Juice to Apple Juice is a blank to be filled. The constant of proportionality is . An equation that represents this proportional relationship is =
Answer/Step-by-step explanation:
The equation that relates the proportional quantities would take the following form ---› [tex] y = kx [/tex], where,
y = amount of Grape juice (dependent variable)
x = amount of Apple juice (independent variable)
k = constant of proportionality (y/x)
✔️Using any of the given pair, say, (5, 8),
Constant of proportionality = [tex] k = \frac{y}{x} = \frac{8}{5} = 1.6 [/tex]
Substitute k = 1.6 in [tex] y = kx [/tex].
An equation that represents the proportional relationship would be:
[tex] y = 1.6x [/tex]
Or
[tex] y = \frac{8}{5}x [/tex]
How the equation would change if:
y = amount of Apple juice (dependent variable)
x = amount of Grape juice (independent variable)
The constant of proportionality would change, that is using a pair, say, (8, 5),
[tex] k = \frac{y}{x} = \frac{5}{8} = 0.625 [/tex]
Substitute k = 0.625 in [tex] y = kx [/tex].
The equation would now be:
[tex] y = 0.625x [/tex].
Or
[tex] y = \frac{5}{8}x [/tex]
Paul was making some brownies and cupcakes for his school fundraiser. If the brownies needed 4.8 cups of sugar and the cupcakes needed 5.2 cups, how much sugar would he need altogether?
Answer:
10 cups in total.
Step-by-step explanation:
4.8+5.2= 10.00
add the .2 to the 4.8 you get get 5 then add 5.0+5.0
Which phrase best describes the translation from the graph y = 2x^2 to the graph of y= 2x^2 + 5?
O5 units up
O5 units down
O 5units right
O5 units left
Answer:
05 units up and down
Step-by-step explanation:
hope this hepled luv!
The phrase that best describes the translation from the graph y = 2x^2 to the graph of y = 2x^2 + 5 is "5 units up".
What is transformation on the graphs?Let the functions f(x) and g(x) be two real functions.
And g (x) = f (x) + k, where k is real numbers.
The function can be sketched by shifting f (x), k units vertically.
The direction of shift can be found by the value of k:
if k > 0, the base graph shifts k units up, and
if k < 0, the base graph shifts k units down.
Adding a constant term to a function vertically shifts its graph up or down, depending on the sign of the constant.
In this case, the constant term is positive (+5), which means that the graph of y = 2x² + 5 is shifted upward by 5 units compared to the graph of y = 2x².
Therefore, the correct phrase is "5 units up".
To learn more about the transformation on the graphs;
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Answer:
obtuse triangle because the angle is larger than 90 degrees.
Step-by-step explanation:
Answer:
obtuse
Step-by-step explanation:
Put the following numbers in order from least to greatest.
1/4 1/8 1/2
Answer:
1/8 1/4 1/2
Step-by-step explanation:
i hope it will help you
Step-by-step explanation:
1\8 1\4 1 \2
which expression is undefined?
A.0 ÷ 5
B.(3 - 3)
_____
7
C. 8
_____
(-2+2)
D. (0 - 12)
_____
-6
Answer: C
Work: So, after you simplify that equation, it's 8/0. You Cannot divide zero like that. You can divide 0/8, but you can't with 8/0. I hope this wasn't to confusing, and Happy Holidays! :)
How could you find the product 19. 14 in your head?
I need the answer ASAP
Answer:
like this do 4x9 4x1 then move down and add a zero then do 1x9 1x1 and then add 76 +190 and get 266 all in your head.
Step-by-step explanation:
19
x 14
_______
76
+ 190
______
266
last year raina biked 421 miles this year she biked k miles using k write an expression for the total number of miles she biked
Answer:
i dont know sadly im trying to figure his out too..
Step-by-step explanation: hi
What is the equation of a line with a slope of -2 which goes through the point (3, -1)?
Answer:
Step-by-step explanation:
y+1 = -2(x-3)
y = -2x + 6 - 1
y = -2x + 5
The length of a rectangle deck is 3 times its width. If the deck's perimeter is 16 ft, what is the deck's area?
Answer:12
Step-by-step explanation:
3x+3x+x+x=16
8x=16 so x =2
2*3=6 6*2=12
Answer:
12 sq ft
Step-by-step explanation:
let w = width
let 3w = length
w + w + 3w + 3w = 16
8w = 16
x = 2
Area = 3(2) x 2
A = 6 x 2
Please answer quickly, thanks. :) 35 points and if you answer there are more so you can get 250 points
Answer:
11 cars/day
Step-by-step explanation:
What we know:
After two days, Car-Mart has 43 cars left. After 3 days, it is 32. After five, 10 cars.
Saying that, subtract 32 from 43 to get your rate of 11 cars sold a day.
I can further deduce they started with 76 cars. On day 1 they had 65 cars. On day 4 they had 21 cars. They will have sold all of their cars after day 6.
how to solve
[tex] \sqrt{4} x {}^{2} = x + 2[/tex]
Answer:
➩ [tex]x=2,-\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{4x^2}=x+2[/tex]
➨ We can also solve by completing both squares, however. Since we can pull out the square root.
[tex]\sqrt{4x^2}=|2x|[/tex] ➩ Define of Absolute Value/Square Root
➩ [tex]\sqrt{x^2}=|x|[/tex]
Thus, our new equation is ➩ [tex]|2x|=x+2[/tex]
To solve an absolute-value equation, let there be two conditions.
➨ Where x ≥ 0
[tex]2x=x+2\\[/tex]
Move x to another side
[tex]2x-x=2\\x=2[/tex]
➨ Where x < 0
[tex]-2x=x+2\\-2x-x=2\\-3x=2\\x=\frac{2}{-3}\\x=-\frac{2}{3}[/tex]
Cindy used 6feet of ribbon to wrap 10 gifts . How much ribbon will she use to wrap 25/gifts ? ( all the gifts are the same size)
Answer:
15ft
Step-by-step explanation:
if she used 6ft for 10 gifts, you would multiply 6 by 2 equalling 12.
then multiply 6 by .5, 3. add 3 and 12
the answers 15 sorry i couldnt explain better but ya
pleaSe mark brainliest
its not math but I still need helppppp
Answer:
T
Step-by-step explanation:
Q1. The speed limit on a road is 40km/h. A scooter drives 9
kilometers in 15 minutes. Is the scooter breaking the speed limit?
step by step explanation plz
What is the value of k?
k=
m
Done
Intro
DOOODDOOO
9514 1404 393
Answer:
k = 2
Step-by-step explanation:
All of the triangles are similar, so the ratio of short side to long side is the same for all.
4/8 = k/4
k = 16/8 = 2 . . . . multiply by 4 and simplify
The value of k is 2.
_____
Additional comment
By similar reasoning or by the Pythagorean theorem, ...
l = √20 = 2√5
m = √80 = 4√5
Every day after dinner, a child is to put his plate in the sink. Which formula calculates percent of occurrences?
Answer:
Percent of occurrences= (Numbers of behavior/Numbers of opportunities)*100
Step-by-step explanation:
Based on the information given if a child is to put his/her plate in the sink everyday after having dinner the formula that will be use to calculates percent of occurrences is :
Percent of occurrences=( Numbers of behavior/Numbers of opportunities)*100
Where:
Numbers of behavior represent the Numbers of times the plate was put in the sink by child everday
Numbers of opportunities represent the Numbers of dinners the child had everyday
Which is the graph of f(x) = RootIndex 3 StartRoot x EndRoot – 4?
Answer:
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Answer:
multiple choice?
Step-by-step explanation:
During hibernation, a garter snake’s body temperature never goes below 3 °C. Write an inequality that represents this situation.
Answer:
x ≥ 3*C
Step-by-step explanation:
Please answer correctly will mark brainliest and follow thank you ;)
Answer:
76m
Step-by-step explanation:
Solve perimeter of both rectangles and add
Answer:
238 meters
Step-by-step explanation:
Perimeter? The equation is P = 2 ( l * w )
So lets cut this irregular shape into 2 rectangles.
I added a picture to show you.
So on rectangle is 7 by 11 and the other is 7 by 6.
So lets find the perimeter of the larger rectangle first.
P = 2 ( 11 * 7 )
P = 2 ( 77 )
P = 154
Now the smaller one
P = 2 ( 7 * 6 )
P = 2 ( 42 )
P = 84
Now to find the full perimeter, add both perimeters together
P = 154 + 84
P = 238
238 meters
Don't be afraid to reach out with further questions! Hope this helps!
What is the average rate of change for [-1,2]?
Answer:
Step-by-step explanation:
The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.
Lillian and Jacob work at a dry cleaners ironing shirts. Lillian can iron 25 shirts per hour, and Jacob can iron 20 shirts per hour. Lillian and Jacob worked a combined 13 hours and ironed 295 shirts. Determine the number of hours Lillian worked and the number of hours Jacob worked.
Answer:
x=7 y=6
Step-by-step explanation:
x = 7 hous worked by Lillian
y = 6 hours worked by Jacob
Step-by-step explanation:
Let call " x " and " y " numbers of hours Lillian and Jacob worked respectively, then according to problem statement we have:
They both combined a total of 13 hours, therefore
x + y = 13 ⇒ y = 13 - x
And the number of ironed shirts was 295 then we have
25*x + 20*y = 295
We need to solve that system of equations for x and y then
25*x + 20 * ( 13 - x ) = 295
25*x + 260 - 20*x = 295
5*x = 295 - 260
5*x = 35
x = 35/5
x = 7
And y = 13 - x ⇒ y = 13 - 7
y = 6
Solve for u.
1- u = 235
Answer:
-234
Step-by-step explanation:
1-235=-234
Answer:
Step-by-step explanation:
1-u=235 subtract the 1 from both sides
-u=234 divide by -1
u= -234
What is the location of the second endpoint if the first endpoint is at (5,2) and
the midpoint is at (-5,5)?
Use the diagram below to answer the question. There is a small building that is 24 feet tallThe fire fighter is standing 7 feet away from the building.
Answer:
24- 7 = 17
Step-by-step explanation:
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Answer:
Square root of 56 so in simplest radical form 4 root 4
Step-by-step explanation:
The graph of y=2x^2 is shifted 8 units down on a coordinate grid.
What are the roots of the equation that correspond to the new graph?
A. x=-2 and =2
B. x=-2 and x=4
C. x=-4 and x=2
D. x=-4 and x=4
Answer
x = 2 or x = -2
Option A
Step-by-step explanation:
By shifting it down(we are going 8 units below the origin on the y-axis), we have the equation as;
y = 2x^2 - 8
To find the root, we equate zero
0 = 2x^2 - 8
2x^2 = 8
x^2 = 8/2
x^2 = 4
x = square root of 4
x = +2 or -2
Answer: is A x=y=-2 and x=2
Step-by-step explanation:
Rita is planting saplings along her garden fence. When she started, she had x packages of saplings with 5 saplings per package. She planted 15 saplings and has at most 20 left. How many packages of saplings did she start with? What would the solution look like on a number line graph?
When Rita started, she had
packages of saplings. The solution can be represented as
with an arrow to the
.
Answer:
If we represent x (number of packages of saplings) on a number line graph, it will start on number 4 (number of packages Rita still has) then moves to the right to number 7, that is the number of packages when Rita started to plant.
Step-by-step explanation:
A grocery store sells a bag 7 oranges for $2.66. if alexandra spent $3.42 on oranges how many did she buy
Answer:
9 oranges
Step-by-step explanation:
7 for 2.66 is 38c for 1
Step-by-step explanation:
if 7 gives 2.66
so 3.42×7÷2.66 gives 9 orange