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saveliy_v [14]
3 years ago
7

Mrs.Manning is making cookies for the bake sale. She jas 3/4 cup of flour and needs 1/3 cup of flour for her chocolate chip cook

ies. What fraction of the flour Mrs.Manning has will be used for her chocolate chip cookies?
Mathematics
1 answer:
Sedbober [7]3 years ago
3 0

Answer:

<em>The fraction of the flour Mrs. Mannng will use for her chocolate chip cookies is 4/9</em>

Step-by-step explanation:

<u>Fraction of Portion</u>

Suppose we have a number n and another number m such as m>n. The portion or fraction of size n of m is given by the quotient n/m.

For example, 3 pieces of cake out of a total of 6 make them a fraction of 3/6 = 1/2 of the whole cake, i.e. half of the total available.

Mrs. Manning needs 1/3 cup of flour to make cookies for the bake sale. She actually has 3/4 cups of flour. Calculate the fraction of needed against the available flour:

\displaystyle \frac{\frac{1}{3}}{\frac{3}{4}}

The division can be easier performed by multiplying by the reciprocal of the denominator:

\displaystyle \frac{1}{3}\cdot \frac{4}{3}=\frac{1*4}{3*3}

\displaystyle =\frac{4}{9}

The fraction of the flour Mrs. Mannng will use for her chocolate chip cookies is 4/9

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ohaa [14]

9514 1404 393

Answer:

  • scale factor: 3
  • rule: (x, y) ⇒ (3x +15, 3y -24)
  • center: (-7.5, 12)

Step-by-step explanation:

The scale factor can be found by comparing the length of CB to the length of RQ.

  B-C = (-2, 8) -(-4, 9) = (2, -1)

  Q-R = (9, 0) -(3, 3) = (6, -3)

The length of RQ is clearly 3 times the length of CB, so the scale factor (k) is ...

  ratio of corresponding differences = 6/2 = -3/-1 = 3 . . . . . scale factor

__

We know that for dilation about a point O, the distance from O is multiplied by the scale factor. For dilation of point B to point Q, this means ...

  k(B -O) = (Q -O)

Solving for Q, we get ...

  Q = kB -kO +O . . . . this is what our dilation rule will look like.

The quantity O-kO can be found by subtracting kB:

  Q -kB = O -kO = O(1 -k)

This is what we need for our dilation rule.

  Q -kB = (9, 0) -3(-2, 8) = (9+6, 0-24) = (15, -24)

So, our dilation rule is ...

  (x, y) ⇒ k(x, y) +(15, -24)

  (x, y) ⇒ (3x +15, 3y -24) . . . . . dilation rule

__

The center of dilation can be found from ...

  (Q -kB)/(1 -k) = O

  O = (15, -24)/(1 -3) = (-7.5, 12)

The center of dilation is (-7.5, 12).

_____

<em>Additional comments</em>

On the graph, the center of dilation can be found by drawing a line through a point and its image. (Points are always dilated along a line through the center of dilation.) The intersection of two such lines is the center of dilation.

On this graph, the center is just above the top edge of the chart, at point (-7.5, 12). You can see this if you carefully draw lines BQ and AP.

You usually have coordinates for two original points and two image points, so finding the scale factor the way we did is not difficult. If you just have one point on the original and the image, the scale factor is found by finding their distances from the center of dilation. Each image point is k times as far as each original point from that center.

7 0
3 years ago
Sumathi says that the area of a triangle PQR is, A=1/2×8×7 CM. rajini says that it is A=1/2×9×7 cm. who is correct? give reason?
Alecsey [184]

Answer:

Rajini is correct, A = 1/2 × 9 × 7

Step-by-step explanation:

A = 1/2 × base × height

base = the leg bisected by the height, in this case leg QD = 9cm

height = 7cm in this case

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ivolga24 [154]

Answer:

5/6

Step-by-step explanation:

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What is the midrange is the following data set 5,11,10,12,4,12,18,18,18
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Answer:

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Step-by-step explanation:

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Determine the center and radius of the following circle equation:
blagie [28]

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Radius: 4

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