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Alekssandra [29.7K]
3 years ago
11

John could not decide, but he had 9 dollars he could spend on fruit kabobs that cast 1.75 dollars and smoothies that cost 2.50 d

ollars. He knew he wanted at least one each. What are some combinations he could afford? Show at least three possibilities.
Mathematics
1 answer:
IrinaK [193]3 years ago
5 0

Answer:

One fruit kabob and one smoothie

Two fruits kabobs and two smoothies

Three fruit kabobs and one smoothie

One fruit kabob and two smoothies

Explanation:

In this situation, the basic combination John can afford is simply to buy one fruit kabob and one smoothie ( $1.75 + $ 2.50 = $4.25) because he wants at least one unit of each item. Additionally, it is possible to add more units of each item to create new combinations or possibles, just make sure they do not total more than 9 dollars, which is the money John has. Here are some of the possible combinations:

Two fruit kabobs and two smoothies

Fruit kabobs: $1.75 x 2 = $3.5

Smoothies: $ 2.50 x 2 = $5

Total: $8.5

Three fruit kabobs and one smoothie

Fruit kabobs: $1.75 x 3 = $5.25

Smoothie: $2.50

Total: $7.75

One fruit kabob and two smoothies

Fruit kabob: $1.75

Smoothies: $2.50 x 2 = $5

Total: $6.75

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Which of the following is equivalent to tan2θcos(2θ) for all values of θ for which tan2θcos(2θ) is defined?
Aloiza [94]

Answer:

2sin²θ - tan²θ

Step-by-step explanation:

Given

tan²θcos(2θ)

Required

Simplify

We start by simplifying cos(2θ)

cos(2θ) = cos(θ+θ)

From Cosine formula

cos(A+A) = cosAcosA - sinAsinA

cos(A+A) = cos²A - sin²A

By comparison

cos(2θ) = cos(θ+θ)

cos(2θ) = cos²θ - sin²θ ----- equation 1

Recall that cos²θ + sin²θ = 1

Make sin²θ the subject of formula

sin²θ = 1 - cos²θ

Substitute sin²θ = 1 - cos²θ in equation 1

cos(2θ) = cos²θ - (1 - cos²θ)

cos(2θ) = cos²θ - 1 +cos²θ

cos(2θ) = cos²θ + cos²θ - 1

cos(2θ) = 2cos²θ - 1

Substitute 2cos²θ - 1 for cos(2θ) in the given question

tan²θcos(2θ) becomes

tan²θ(2cos²θ - 1)

Open brackets

2cos²θtan²θ - tan²θ

------------------------

Simplify tan²θ

tan²θ = (tanθ)²

Recall that tanθ =  sinθ/cosθ

So, we have

tan²θ = (sinθ/cosθ)²

tan²θ = sin²θ/cos²θ

------------------------

Substitute sin²θ/cos²θ for tan²θ

2cos²θtan²θ - tan²θ becomes

2cos²θ(sin²θ/cos²θ) - tan²θ

Open bracket (cos²θ will cancel out cos²θ) to give

2(sin²θ) - tan²θ

2sin²θ - tan²θ

Hence, the simplification of tan²θcos(2θ) is 2sin²θ - tan²θ

Option E is correct

7 0
3 years ago
Mai's mother was 28 when Mai was born. Mai is now 12 years old. In how many years will Mai's mother be twice Mai's Age
noname [10]

Answer:

4

Step-by-step explanation:

Let x = the number of years

In x years, Mai's mother's age will be: 28 + x

                         and Mai's age will be:  12 + x

Then,                                      28 + x = 2(12 +   x)

Distribute the 2                      28 + x =    24 + 2x

Subtract 24 from each side     4 + x =            2x

Subtract x from each side             x = 4

In four years, Mai's mother will be twice Mai's age.

<em>Check: </em>

28 + 4 = 2(12 + 4)

   32   = 2 ×  16

   32   =   32

6 0
3 years ago
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Alex777 [14]

Answer:

A

Step-by-step explanation:

6 0
3 years ago
If Claire earns $75 the next week from babysitting and deposits it in her account, what will her balance be then?
nataly862011 [7]
It will be 75$ i guess the question is a bit wrong please recheck
5 0
3 years ago
Read 2 more answers
Show the correct steps to simplify this problem.
KengaRu [80]
Do 12-5 then 6.4 then 2.2 then whatever answer you get for 12-5 multiply it by the answer you get for 6.4 then subtract whatever answer you get for 2.2 hope this helps!
7 0
2 years ago
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