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SpyIntel [72]
3 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]3 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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Easy 6th grade math! Please help!
Pie

Answer:

Step-by-step explanation 10 + 2.50d = 850

David starts with $10 and each day he earns $2.50. The d represents a variable and can be any number.

To find d you must solve the equation.

10 + 2.50d = 850

2.50d = 840 (subtract 10 from 850)

d = 336 (divide 840 by 2.50)

It will take David 336 days to save $850.

3 0
4 years ago
Explain how to find the vertex of 2x^2+12x+16
Elina [12.6K]

The vertex form:

y=a(x-h)^2+k\\\\(h,\ k)-vertex

Use (a+b)^2=a^2+2ab+b^2\qquad(*)


2x^2+12x+16=2(x^2+6x)+16=2(x^2+2(x)(3))+16\\\\=2(\underbrace{x^2+2(x)(3)+3^2}_{(*)}-3^2)+16=2((x+3)^2-9)+16\\\\=2(x+3)^2+(2)(-9)+16=2(x+3)^2-18+16\\\\=\boxed{2(x-(-3))^2-2}\to h=-3,\ k=-2

<h3>Answer: (-3, -2).</h3>

Other method:

f(x)=ax^2+bx+c\\\\vertex:(h,\ k)\\\\h=\dfrac{-b}{2a},\ k=f(h)

We have

f(x)=2x^2+12x+16\\\\a=2,\ b=12,\ c=16

Substitute:

h=\dfrac{-12}{(2)(2)}=\dfrac{-12}{4}=-3\\\\k=f(-3)=2(-3)^2+12(-3)+16=2(9)-36+16=18-36+16=-2

<h3>Answer: (-3, -2).</h3>
5 0
4 years ago
Calculate the average rate of change of f(x) = 1 x - x2 - 2 for 3 ≤ x ≤ 6. A) -163 18 B) -18 163 C) 163 18 D) 18 163
larisa86 [58]
To solve this we are going to use the average rate of change formula: A(x)= \frac{f(b)-f(a)}{b-a}
where
A(x) is the average rate of change of the function
f(a) is the position function evaluated at a
f(b) is the position function evaluated at b
a is the first point in the interval
b is the second point in the interval

We can infer for our problem that the first point is 3 and the second point is 6, so a=3 and b=6. Lets replace those values in our formula:
A(x)= \frac{f(b)-f(a)}{b-a}
A(x)= \frac{f(6)-f(3)}{6-3}
A(x)= \frac{6-6^2-2-(3-3^2-2)}{3}
A(x)= \frac{-32-(-8)}{3}
A(x)= \frac{-32+8}{3}
A(x)= \frac{-24}{3}
A(x)=-8

We can conclude that the average rate of change of the function f(x) = 1 x - x2 - 2 for <span>3 ≤ x ≤ 6 is -8</span>
3 0
3 years ago
Read 2 more answers
how many ways can 8 distinguishable books be placed in 5 distinguishable shelves so that each shelf contains one book
musickatia [10]

There are 6720 ways by 8 distinguishable books be placed in 5 shelves.

According to statement

The number of books (n) is 8

The number of shelves (r) is 5

Now, we find the ways by which the 8 books be placed in 5 distinguishable shelves

From Permutation formula

P(n,r) = n! / (n-r)!

Substitute the values then

P(n,r) = 8! / (8-5)!

P(n,r) = (8*7*6*5*4*3*2*1) / (3*2*1)

P(n,r) = 8*7*6*5*4

P(n,r) = 6720

So, there are 6720 ways by 8 distinguishable books be placed in 5 shelves.

Learn more about PERMUTATION here brainly.com/question/11732255

#SPJ4

5 0
2 years ago
Two rational expressions have denominators of 2x + 3 and 3 + 2x. Can you find their sum by simply adding their numerators and pl
horrorfan [7]
Okay i haven't done this years but base on my knowledge it think that the answer is 6 and that because:
(2x+3) + (3-2x)
(2x+2x+3) +(3-2x+2x)      (what ever you to one side you do the next and that why it cancel each other)
3+3=6
that my explanation hope this help


 
4 0
3 years ago
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