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amm1812
3 years ago
10

Dimitri is helping to plan the school talent show. Each performer for the talent show has 666 minutes for his or her performance

, which includes transition time between performances. If the introduction for the talent show is 242424 minutes long and the entire show, including the introduction, will last 150150150 minutes, how many different performances can the talent show accommodate?
Mathematics
1 answer:
strojnjashka [21]3 years ago
7 0

We can find the answer by taking the total count of time, 150, and subtract 24 from it. This is because the 24 minute introduction is not part of the performances, so it is not part of our equation.  After we subtract the two numbers to get 126, we divide the remaining number by 6. This is because each performance lasts 6 minutes, so by dividing it from 126, we get the total amount of performances. The answer is 21.

Hope this helps!


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Philip made a total of 9 bracelets and necklaces from 120 inches of cord. He used 8 inches of cord for each bracelet and 20 inch
Viktor [21]

Answer:

So Philip made 5 bracelets and 4 necklaces.

Step-by-step explanation:

Let x = number of bracelets and y = number of necklaces.

Since we have a total of 9 bracelets and necklaces,

x + y = 9 (1)

Also, we have 8 inches of cord for each bracelet and 20 inches of cord for each necklace, then the total length for the bracelet is 8x and that for the necklace is 20y.

So, the total length for both is 8x + 20y. Since the total length of cord used is 120 inches,

8x + 20y = 120 (2)

Simplifying it we have

2x + 5y = 30  (3).

Writing equations (1) and (3) in matrix form, we have

\left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}9\\30\end{array}\right]

Using Cramer's rule to solve for x and y,

x = det \left[\begin{array}{ccc}9&1\\30&5\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\

x = (9 × 5 - 30 × 1) ÷ (1 × 5 - 1 × 2)

x = (45 - 30) ÷ (5 - 2)

x = 15 ÷ 3

x = 5

y = det \left[\begin{array}{ccc}1&9\\2&30\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\

y = (30 × 1 - 9 × 2) ÷ (1 × 5 - 1 × 2)

y = (30 - 18) ÷ (5 - 2)

y = 12 ÷ 3

y = 4

So Philip made 5 bracelets and 4 necklaces.

3 0
3 years ago
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Answer:

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Step-by-step explanation:

6 0
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Misha Larkins [42]

Answer:

Step-by-step explanation:

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6 0
3 years ago
Triangles E F G and K L M are shown. Angles E F G and K L M are congruent. The length of side K L is 6, the length of side M L i
Masteriza [31]

Answer:

The Answer is C: Yes, △EFG~ △KLM by SSS or SAS

Step-by-step explanation:

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SAS is for side-angle-side

Both triangles have one angle measurement given, and two side lengths given, therefore we can also use the SAS similarity theorem to prove the two triangles are similar.  

Since both SSS and SAS work to prove the triangles are similar, the correct answer is C: Yes, △EFG~ △KLM by SSS or SAS

(I also just answered this question on the assignment and got it correct)

3 0
3 years ago
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The index number representing the price level changes from 109 to 113 in one year. The inflation rate during the year is _____ p
Dima020 [189]

First, get the difference between the price level changes.

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Then, divide it by the initial price level, which is 109.

\frac{4}{109}=0.0367

Multiply by 100 to get its percent.

0.0367\times100=3.67

Thefore, the inflation rate during the year is 3.67 percent.

8 0
1 year ago
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