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Pavlova-9 [17]
3 years ago
12

Your​ school's talent show will feature 12 solo acts and 3 ensemble acts. The show will last 102 minutes. The 6 solo performers

judged best will give a repeat performance at a second 72 minute​ show, which will also feature the 3 ensemble acts. Each solo act lasts x​ minutes, and each ensemble act lasts y minutes
Mathematics
1 answer:
Andrei [34K]3 years ago
3 0

Answer:

each solo act will last 5 minutes and each ensemble act will last 14 minutes

Step-by-step explanation:

In the first show, we are told that there are 12 solo acts and 3 ensemble acts.

Now since each solo act lasts x​ minutes, and each ensemble act lasts y minutes and the show lasts 102 minutes, thus we have;

12x + 3y = 102 - - - - eq1

In the second show which lasts 72 minutes, we are told that there will be 6 solo acts and 3 ensemble acts.

Thus,we have;

6x + 3y = 72 - - - - eq2

Now, let's find x and y by subtracting eq 2 from eq1 to give;

6x = 30

Divide both sides by 6 to give;

x = 5

Put 5 for x in eq2;

6(5) + 3y = 72

30 + 3y = 72

3y = 72 - 30

3y = 42

y = 42/3

y = 14

Thus, each solo act will last 5 minutes and each ensemble act will last 14 minutes

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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
prohojiy [21]

Answer:

2.25

Step-by-step explanation:

(6x^{-2})^2(0.5x)^4\\\\=(6^2(x^{-2})^{2})(0.5^4x^4)\ \ \ \ \ \ \ \ \ \ \ \ \ as\ (ab)^m=a^mb^m\\\\=36\times 0.5^4((x^{-2})^2x^4)\ \ \ \ \ \ \ \ \ \ as\ multiplication\ is\ associative\ a(bc)=(ab)c\\\\=36\times 0.0625(x^{-4}x^4)\ \ \ \ \ \ \ \ \ \ \ as\ (x^m)^n=x^{mn}\\\\=(36\times 0.0625)(x^{-4+4})\ \ \ \ \ \ \ \ \ \ \ as\ x^mx^n=x^{m+n}\\\\=2.25x^0\\\\=2.25\ \ \ \ \ \ \ \ \ \ \ \ as\ x^0=1\\\\(6x^{-2})^2(0.5x)^4=2.25

7 0
3 years ago
Solve 2x+3y=2<br> 5x-y=-29<br> By elimination
Andreyy89

Answer:

\huge\boxed{x=-5,\ y=4\to(-5,\ 4)}

Step-by-step explanation:

\left\{\begin{array}{ccc}2x+3y=2\\5x-y=-29&\text{multiply both sides by 3}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+3y=2\\15x-3y=-87\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad17x=-85\qquad\text{divide both sides by 17}\\.\qquad\dfrac{17x}{17}=\dfrac{-85}{17}\\.\qquad\boxed{x=-5}\\\\\text{Substitute it to the second equation:}\\\\5(-5)-y=-29\\\\-25-y=-29\qquad\text{add 25 to both sides}\\\\-25+25-y=-29+25\\\\-y=-4\qquad\text{change the signs}\\\\\boxed{y=4}

5 0
3 years ago
You try to explain the number of IBM shares traded in the stock market per day in 2005. As an independent variable you choose th
allochka39001 [22]

Answer:

This is an example of

C. simultaneous causality.

Step-by-step explanation:

Simultaneous causality eliminates the conclusion that is often taken for granted to the effect that one variable is a response variable while the other is an explanatory variable because the two variables, the price and the number of shares, influence each other at the same time.  When more shares are traded than demanded in the stock market in any day, the price tends to go down, and vice versa.

4 0
2 years ago
An express train travels 80km/h from Ironton to Wildwood. A local train, traveling at 48km/h, takes 2 hours longer for the same
masha68 [24]

Answer:

They are 240 kilometers apart.

Step-by-step explanation:

This question can be solved using the following relation:

v = \frac{d}{t}

In which v is the velocity, d is the distance and t is the time.

An express train travels 80km/h from Ironton to Wildwood.

Here we have v = 80, t = x. So

v = \frac{d}{t}

80 = \frac{d}{x}

d = 80x

A local train, traveling at 48km/h, takes 2 hours longer for the same trip.

This means that when v = 48, t = x + 2[tex]. So[tex]v = \frac{d}{t}

48 = \frac{d}{x+2}

Since d = 80x

48 = \frac{80x}{x+2}

Applying cross multiplication

80x = 48(x + 2)

80x = 48x + 96

32x = 96

x = \frac{96}{32}

x = 3

So the distance is:

d = 80x = 80*3 = 240

They are 240 kilometers apart.

3 0
3 years ago
I’ll give points + brainalist for correct answer (:
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Answer:

C) 2

Step-by-step explanation:

Emma: Range  = 8

Arianna: Range = 6

The difference in the range is 2 (8-6)

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2 years ago
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