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Vikentia [17]
3 years ago
14

Margaret uses 1 3/4 teaspoon of vanilla to make 12 vanilla cupcakes. She wants to make 30 cupcakes. How much vanilla will Margar

et use?
Mathematics
2 answers:
Dimas [21]3 years ago
6 0
4 3/8
or
35/8
................
Vinil7 [7]3 years ago
5 0

Answer:

4\frac{3}{8} teaspoon vanilla

Step-by-step explanation:

Margaret uses 1\frac{3}{4} teaspoon of vanilla to make 12 vanilla cupcakes.

First we change mixed fraction to fraction

1\frac{3}{4}\Rightarrow \dfrac{7}{4}

For 12 cupcakes of vanilla = \frac{7}{4} teaspoon vanilla

For 1 cupcakes of vanilla = \frac{7}{4}\div 12=\frac{7}{48} teaspoon vanilla

For 30 cupcakes of vanilla = \frac{7}{48}\times 30 teaspoon vanilla

                                          = \frac{35}{8}  teaspoon vanilla

                                          = 4\frac{3}{8}  teaspoon vanilla

Hence, Margaret uses  4\frac{3}{8}  teaspoon vanilla for 30 cupcakes

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In △PKQ, PK = KQ = 12, m∠P = 35º. Find PQ.
Neporo4naja [7]

The length of PQ is 19.66 units

Step-by-step explanation:

The given is:

1. PK = KQ = 12

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We need to find the length pf PQ

∵ PK = KQ

∴ m∠P = m∠Q

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The sum of measures of the angles of a triangle is 180°

∴ m∠P + m∠Q + m∠K = 180°

∴ 35 + 35 + m∠K = 180

∴ 70 + m∠K = 180

- Subtract 70 from both sides

∴ m∠K = 110°

Let us use cosine rule to find the length of PQ

∵ PQ = \sqrt{(KP)^{2}+(KQ)^{2}-2(KP)(KQ)cos(K)}

∵ PK = 12 , KQ = 12 , m∠K = 110°

- Substitute these values in the rule

∴ PQ = \sqrt{(12)^{2}+(12)^{2}-2(12)(12)cos(110)}

∴ PQ = 19.66

The length of PQ is 19.66 units

Learn more:

You can learn more about triangle in brainly.com/question/12985572

#LearnwithBrainly

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