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Helga [31]
2 years ago
11

Lee has $220 to spend on shirts at $22 each and pants $38 each. what inequality represents the possible number of shirts and pan

ts that he can buy? find atleast three possible solutions. can the solutions include negative numbers?
Mathematics
1 answer:
Viefleur [7K]2 years ago
6 0

The inequality that models the given situation is:

y*$22 + x*$38 ≤ $220

And some solutions are (1, 1), (1, 2), (2, 2).

<h3>Which inequality models the given situation?</h3>

To find the inequality, we first need to define the variables that we will use, the variables are:

  • x = number of pants bought.
  • y = number of shirts bought.

Knowing the price of each individual item, the total cost will be given by:

C = y*$22 + x*$38

And Lee has $220 to spend, so the maximum amount that he can spend is $220, then we have the inequality:

y*$22 + x*$38 ≤ $220

Now, to find solutions you just need to find some values of x and y that make the inequality true, for example, one solution is x = 1 and y = 1.

1*$22 + 1*$38 ≤ $220

$60 ≤ $220

This is true, so (1, 1) is a solution.

Another solutions are (2, 2), (1, 2), (0, 3), etc.

If you want to learn more about inequalities you can read:

brainly.com/question/24372553

#SPJ1

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which of the functions have a range of real numbers greater than or equal to 1 or less than or equal to-1​
lilavasa [31]

The question is incomplete. Here is the complete question:

Which of the functions have a range of all real numbers greater than or equal to 1 or less than or equal to -1? check all that apply.

A. y=\sec x

B. y= \tan x

C. y= \cot x

D. y= \csc x

Answer:

A. y=\sec x

D. y=\csc x

Step-by-step explanation:

Given:

The range is greater than or equal to 1 or less than or equal to -1.

The given choices are:

Choice A: y=\sec x

We know that, the \sec x=\frac{1}{\cos x}

The range of \cos x is from -1 to 1 given as [-1, 1]. So,

|\cos x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\cos x|}\geq 1\\|\sec x|\geq 1

Therefore, on removing the absolute sign, we rewrite the secant function as:

\sec x\leq -1\ or\ \sec x\geq 1\\

Therefore, the range of y=\sec x is all real numbers greater than or equal to 1 or less than or equal to-1​.

Choice B: y= \tan x

We know that, the range of tangent function is all real numbers. So, choice B is incorrect.

Choice C: y= \cot x

We know that, the range of cotangent function is all real numbers. So, choice C is incorrect.

Choice D: y=\csc x

We know that, the \csc x=\frac{1}{\sin x}

The range of \sin x is from -1 to 1 given as [-1, 1]. So,

|\sin x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\sin x|}\geq 1\\|\csc x|\geq 1

Therefore, on removing the absolute sign, we rewrite the cosecant function as:

\csc x\leq -1\ or\ \csc x\geq 1\\

Therefore, the range of y=\csc x is all real numbers greater than or equal to 1 or less than or equal to-1​.

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MA_775_DIABLO [31]

Answer:

y=1/4x-3/4

Step-by-step explanation:

y=mx+b

m=1/4

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3 years ago
If the angle of elevation of the sun is 61.7° when a building casts a shadow of 56.5 feet, what is the height of the building ro
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SOLUTION

Let us use a simple diagram to interprete the question

In the diagram above, the dark stuff below represents the shadow and the rectangular bar represents the building. I have labelled the height of the building as h.

So we will use the right-angled triangle formed to find h

As we can see h represents the opposite side and 56.5 feet represents the adjacent side of the right-angle triangle. So we will use TOA

\text{TOA tan }\theta=\frac{opposite}{\text{adjacent}}

So we have

\begin{gathered} \text{ tan }\theta=\frac{opposite}{\text{adjacent}} \\ \text{ tan }61.7\degree=\frac{h}{56.5} \\ 1.8572015=\frac{h}{56.5} \\ \text{cross multiplying, we have } \\ h=1.8572015\times56.5 \\ h=104.931887 \end{gathered}

Hence the answer is 104.9 feet to the nearest tenth

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Answer:

Step-by-step explanation:

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