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SpyIntel [72]
2 years ago
11

Last year there were 45 memebers of the tennis club at Marks Middle school. This year although the number of boys increeased by

20%, the number of girls decresed by 20%, the total numbers decresed by 1. Find how many boys anf girls are in the tennis club this year.
Mathematics
1 answer:
Bas_tet [7]2 years ago
3 0

Answer:

24 boys & 20 girls

Step-by-step explanation:

Last year:

Number of boys = x

Total number = 45

Number of girls = 45 - x

An increase of 20% is the same as multiplying by 1.2

A decrease of 10% is the same as multiplying by 0.8

This year:

New number of boys: 1.2x

New number of girls: 0.8(45 - x)

New total number = 45 - 1 = 44

1.2x + 0.8(45 - x) = 44

1.2x + 36 - 0.8x = 44

0.4x + 36 = 44

0.4x = 8

x = 20

Last year there were 20 boys and 25 girls.

This year there are 20 * 1.2 = 24 boys

and 44 - 24 = 20 girls

Answer: 24 boys & 20 girls

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Answer:

A) Distance time graph

B) d(t) = 25t

C) The expression shows the distance more clearly.

Step-by-step explanation:

A) A distance time graph as seen in the attachment provides a representation of the distance travelled.

We are told the car travels at a constant speed of 100 meters per 4 seconds. Which means that 100 m for each 4 hours. So, for 200m, it's 8 hours like seen in the graph and for 300m,it's 12 hours as seen in the graph.

B) And expression for the distance is;

d = vt

Where;

d is distance in metres

v is speed in m/s and t is time

We are told that the car travels at a constant speed of 100 meters per 4 seconds.

Thus, v = 100/4 = 25 m/s

Distance travelled over time is;

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C) Looking at both A and B above, it's obvious that the expression of the distance shows a more clearer way of getting the distance because once we know the time travelled, we will just plug it into the equation and get the distance. Whereas, for the representation form, one will need to longer graphs if the time spent is very long.

6 0
3 years ago
Combine likes terms to create an equivalent expression 1/7 - 3(3/7h -2/7)
Anastasy [175]

\frac{1}{7} -3(\frac{3}{7}h -\frac{2}{7}) = \frac{7-9h}{7}

<em><u>Solution:</u></em>

<em><u>Given expression is:</u></em>

\frac{1}{7} -3(\frac{3}{7}h -\frac{2}{7})

We have to combine the like terms

From given expression,

\frac{1}{7} -3(\frac{3}{7}h -\frac{2}{7})

By distributive property,

The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

a(b + c) = ab + bc

Therefore,

Solve for brackets using distributive property

\frac{1}{7} - (3 \times \frac{3}{7}h) + (3 \times \frac{2}{7})\\\\\frac{1}{7} - \frac{9h}{7} + \frac{6}{7}

Add 1/7 and 6/7

\frac{1}{7} + \frac{6}{7} -\frac{9h}{7}\\\\\frac{1+6}{7} -\frac{9h}{7}\\\\Simplify\\\\\frac{7}{7}-\frac{9h}{7}\\\\1-\frac{9h}{7}\\\\Simplify\\\\\frac{7-9h}{7}

Thus the equivalent expression is found

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