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bazaltina [42]
3 years ago
15

A new club sent out 288 coupons to boost sales for next year's memberships. They provided 5 times as many to potential members t

han to existing members. How many coupons did they send to existing members?
A.
6
B.
5
C.
53
D.
48
Mathematics
1 answer:
Aliun [14]3 years ago
7 0

Answer:

D. 48

Step-by-step explanation:

We don't know the numbers of coupons sent to existing members and to potential members, but we know a relationship between the number.

They sent 5 times as many coupons to potential members as they did to existing members.

Let x = number of coupons sent to existing members.

Then 5x = number of coupons sent to potential members.

The total number of coupons sent was x + 5x = 6x

The total number of coupons sent was 288.

Therefore, 6x must equal 288 giving us an equation with a single variable.

6x = 288

x = 48

Answer: 48

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NeTakaya

Using simpler trigonometric identities, the given identity was proven below.

<h3>How to solve the trigonometric identity?</h3>

Remember that:

sec(x) = \frac{1}{cos(x)} \\\\tan(x) = \frac{sin(x)}{cos(x)}

Then the identity can be rewritten as:

sec^4(x) - sen^2(x) = tan^4(x) + tan^2(x)\\\\\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)}  = \frac{sin^4(x)}{cos^4(x)}  + \frac{sin^2(x)}{cos^2(x)} \\\\

Now we can multiply both sides by cos⁴(x) to get:

\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)}  = \frac{sin^4(x)}{cos^4(x)}  + \frac{sin^2(x)}{cos^2(x)} \\\\\\\\cos^4(x)*(\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)}) = cos^4(x)*( \frac{sin^4(x)}{cos^4(x)}  + \frac{sin^2(x)}{cos^2(x)})\\\\1 - cos^2(x) = sin^4(x) + cos^2(x)*sin^2(x)\\\\1 - cos^2(x) = sin^2(x)*sin^2(x) + cos^2(x)*sin^2(x)

Now we can use the identity:

sin²(x) + cos²(x) = 1

1 - cos^2(x) = sin^2(x)*(sin^2(x) + cos^2(x)) = sin^2(x)\\\\1 = sin^2(x) + cos^2(x) = 1

Thus, the identity was proven.

If you want to learn more about trigonometric identities:

brainly.com/question/7331447

#SPJ1

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1 year ago
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scoray [572]
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Step-by-step explanation:

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3 years ago
Find the circumference and area of each. Round to nearest tenth:
patriot [66]

№1. Given: r=8 ft, π≈3.14

C=2×π×r=2×3.14×8=50.24=50.2 ft

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Answer: 50.2 ft; 201 ft²

№2. Given: D=11 cm, π≈3.14

d=2r or r=2/d, so if d is 11 cm, then r is 11÷2=5.5 cm

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8 0
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A company charger shipping fee that is 4.5% of the purchase price for all items it ships. What is the fe to ship an item that co
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Answer:

This is an percentage change question, by any chance you have a maths textbook, look for units that contains the topic: Percentage Change. Now, let's get solving! :)

Step-by-step explanation:

Firstly, you must multiply 4.5% with 56. That is: shipping fees x purchase price

That gives ($) 2.52 (this is your answer)

No addition/totaling needed as the question asked ONLY for the shipping fees.

Stay safe and Merry Christmas! :)

3 0
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