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creativ13 [48]
3 years ago
8

Duane is making cookies. The recipe calls for two times as many cups of sugar as butter, two times as many cups of oats as sugar

, and two times as many cups of flour as oats. If Duane puts in one cup of butter, how many cups of flour does he need to add? (also this is from MobyMax)
Mathematics
1 answer:
Ronch [10]3 years ago
7 0

Answer:

Step-by-step explanation:

Let b represent the number of cups of butter needed.

Let s represent the number of cups of sugar needed.

Let o represent the number of cups of oat needed.

Let f represent the number of cups of flour needed.

The recipe calls for two times as many cups of sugar as butter. It means that

s = 2b

Two times as many cups of oats as sugar. It means that

o = 2s

Two times as many cups of flour as oats. It means that

f = 2o

If Duane puts in one cup of butter, it means that b = 1

Therefore,

s = 2 × 1 = 2 cups

o = 2s = 2 × 2 = 4 cups

f = 2o = 2 × 4 = 8 cups

Therefore, he needs to add 8 cups of flour

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What is the volume of a pyramid with a base of 22 and a height of 24
larisa86 [58]

Answer:3872

Step-by-step explanation: If base length and base width equal 22, and pyramid height is 24 then you multiply those and divide by three.

V= \frac{22x22x24}{3}

8 0
3 years ago
On the last day of a Shakespeare class, an English teacher asked her students which play they liked most. Out of the 18 students
Vika [28.1K]

Answer:

1/3

Step-by-step explanation:

There were 18 students and six liked Much Ado About Nothing. So, you could write this as 6/18 which simplifies to 1/3.

7 0
3 years ago
Please Help Quicly The equation 8x - 4y = 5 is dilated by a scale factor of 8 centered at the origin. What is the new slope and
Rzqust [24]

For new line, slope m=2 and y-intercept c=(-10)

Step-by-step explanation:

<em>Note : Figure given is for reference to understand better.</em>

<em>Where redline is for given line and blueline for new line</em>

<em />

The equation of given line 8x-4y=5 and it is dilated by a scale factor of 8 centered at the origin.

Step 1 : Find two points on given line.

When x=0, y=?

8x-4y=5

8(0)-4y=5

y=\frac{-5}{4}

When y=0, x=?

8x-4y=5

8x-4(0)=5

x=\frac{5}{8}

We get points A(0,\frac{-5}{4}), B(\frac{5}{8},0)

Step 2: Find distance from centered and scale it.

Now, It is said that line 8x-4y=5 dilated by a scale factor of 8 centered at the origin and point A and point B is on same.

So that point A and point B  will also get dilated by a scale factor of 8 centered at the origin or distance of points from origin will be scaled by 8.

For point A:

Distance of point A(0,\frac{-5}{4}) from origin is ( \frac{-5}{4})  unit in x-direction and zero \frac{-5}{4})  unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is A'(0,-10)

For point B:

Distance of point B(\frac{5}{8},0) from origin is (\frac{5}{8}) unit in x-direction and zero unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is B'(5,0)

Step 3: Find Equation of new line.

Points A'(0,-10) and B'(5,0) make a new line

The equation of given as

\frac{y-Y1}{x-X1} = \frac{Y2-Y1}{X2-X1}

\frac{y-(-10)}{x-0} = \frac{0-(-10)}{5-0}

\frac{y+(10)}{x} = 2

\frac{y+(10)}{x} = 2

y+10= 2x

y= 2x-10

Now, Comparing with the equation of the line : y=mx + c

Where m=slope and c is the y-intercept

We get, Slope m=2 and y-intercept c=(-10)

8 0
3 years ago
If y varies inversely as x, and y=1 as x=2 find y for the x- value of -1
Lina20 [59]
Inverse variation is of the form y=k/x  (direct variation is of the form y=kx)

We are given that x=2 when y=1 so using the inverse form y=k/x we can solve for the constant of variation...

1=k/2

k=2

so the equation is:

y=2/x  now they want us to find y when x=-1 so

y=2/-1

y=-2
3 0
3 years ago
In a school there are 542 girls and boys. how many pupils are there in that school?
DaniilM [7]

Answer:

There are 1084 pupils in that school.

Step-by-step explanation:

If there are 542 girls and boys then you would have to double 542 to get the total number of people. So, there are 1084 people in that school.

Hope this helps!

6 0
2 years ago
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