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Lorico [155]
3 years ago
11

Sally's summer punch recipe is a combination of lemonade and fruit punch. Sally uses 6 cups of lemonade for every 8 cups of frui

t punch. August made a recipe with 35 cups of liquid total, 15 of which were lemonade. Explain if August made the recipe using the correct ratios
Mathematics
1 answer:
disa [49]3 years ago
4 0

Answer:

August made the recipe using the correct ratios

Step-by-step explanation:

we know that

Sally uses 6 cups of lemonade for every 8 cups of fruit punch

so

using proportion

Find out the number of cups of fruit punch for 15 cups of lemonade

Let

x ----> the cups of fruit punch

\frac{6}{8}=\frac{15}{x}\\ \\x=8*15/6\\ \\x= 20\ cups\ fruit\ punch

The total cups of liquid is the sum of the cups of lemonade plus the cups of fruit punch

so

15+20=35\ cups

therefore

August made the recipe using the correct ratios

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Find the error in the following sample of work, if one exists.
ch4aika [34]

Answer:

D. There is no mistake.

Step-by-step explanation:

The following lines show the process of factorization by using common factor.

<u>Line 1:</u>

In line 1, the equation is given and is completely fine.

y^{2}+8xy+2y+16x=0

The only thing missing was equate to zero, but the options below talk about correct factors only, therefore this can't be considered as a mistake and can be ignored completely.

<u>Line 2:</u>

In line 2, the terms are grouped, from which we can factor out common terms.

(y^{2}+8xy)+(2y+16x)=0

This is also fine.

<u>Line 3:</u>

In line 3, the common term y is taken out from group 1 and 2 from other group.

y(y+8x)+2(y+8x)=0

which is exactly what is given in line 3.

<u>Line 4:</u>

In line 4 the common factors can be seen and easily split into 2 factors.

(y+2)(y+8x)=0

which is exactly what is given in line 4.

Options:

A. The grouping is correct in line 2. So this option is does not hold.

B. Common factor was factored correctly from group 1. So this option does not hold.

C. Common factor was factored correctly from group 2. So this option does not hold.

D. There is no mistake. This is correct. Thus we choose this option as correct answer.

3 0
3 years ago
A boy throws a ball into the air. The equation h=−16t^2+23t+4 models the path of the ball, where h is the height (in feet) of th
lina2011 [118]

Answer:

0.72secs

Step-by-step explanation:

Given the height of the ball in air modeled by the equation:

h=−16t²+23t+4

Required

Total time it spent in the air

To get this we need to calculate its time at the maximum height

At the maximum height,

v = dh/dt = 0

-32t + 23 = 0

-32t = -23

t = 23/32

t = 0.72secs

<em>Hence the total time it spend in the air will be 0.72secs</em>

8 0
3 years ago
Write an equation for the line parallel to the given line that contains C<br> C(2,6); y= -4x + 7
MrRa [10]

Answer:

y=-4x+14

Step-by-step explanation:

step 1

Find the slope of the given line

we have

y=-4x+7

This is the equation of the given line in slope intercept form

The slope is m=-4

step 2

Find the slope of the line parallel to the given line

we know that

If two lines are parallel, then their slopes are the same

therefore

The slope of the line parallel to to the given line is m=-4

step 3

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=-4

C\ (2,6)

substitute

y-6=-4(x-2)

step 4

Convert to slope intercept form

y-6=-4(x-2)

isolate the variable y

y-6=-4x+8

y=-4x+8+6

y=-4x+14

6 0
3 years ago
The old time train museum is raising the price of tickets for train rides.Tickets used to cost $4.80 each. The new ticket price
SVETLANKA909090 [29]
Only add $4.80 + $1.25
5 0
3 years ago
Read 2 more answers
Find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. Use
Simora [160]

Answer:

the area is 10 feet by 10 feet, 100 feet²

subtract the area of the circle from this.

you get it by A = r² * pi

so 5² * 3.14159...

=78.5398163397

100-78.5398163397

is roughly 21.46 square feet

7 0
3 years ago
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