17.02.2022 the following question

Shane and abha earned a team badge that required their team to collect no less than 2000 cans for recycling. abha collected 178 more cans than shane did. write an inequality to determine the number of cans, s, that shane could have collected. what is the solution set of the inequality?

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Step-by-step answer

17.02.2022, solved by verified expert
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Shane could have collected more than 911 Cans

Step-by-step explanation:

We are asked to write an inequality to find the number of cans, S that Shane could have collected:

Cans collected by Shane and Abha > 2000

S + A > 2000

Abha collected 178 more cans than Shane did.

A  = 178 + S

Put value of A in the above inequality

S + 178 + S > 2000

2S + 178 > 2000

2S > 2000 - 178

2S > 1822

S > 911

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Mathematics
Step-by-step answer
P Answered by PhD

2S+178\ge 2,000,

[911,\infty).

Step-by-step explanation:

Let S be the number of cans that Shane had collected.

Abha had collected 178 more cans than Shane did, then Abha had collected S+178 cans.

Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling, this means that

S+S+178\ge 2,000,\\ \\2S+178\ge 2,000.

Solve this inequality:

1. Divide it by 2:

S+89\ge 1,000.

2. Now

S\ge 1,000-89,\\ \\S\ge 911.

The solution set is [911,\infty).

Mathematics
Step-by-step answer
P Answered by PhD

[911,∞)


Step-by-step explanation:

Given: S be the number of cans collected by Shane.

Since,  Abha collected 178 more cans than Shane did.

Then, the number of cans collected by Abha = S+178

Also, Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.

So, S+178+S\geq2000

\\\Rightarrow\ 2S\geq2000-178\\\Rightarrow2S\geq1822\\\Rightarrow\ S\geq911

Hence, the solution set of the inequality will be [911,∞)

Mathematics
Step-by-step answer
P Answered by Specialist

2x+178\geq 2000

Step-by-step explanation:

Let, the number of cans collected by Shane = x.

So, the number of cans collected by Abha = x + 178.

Since, at least 2000 cans are required to be collected.

Thus, we have the inequality,

Number of cans by Shane + Number of cans by Abha ≥ 2000.

i.e. x+(x+178)\geq 2000

i.e. 2x+178\geq 2000

Thus, the required inequality is 2x+178\geq 2000.

Mathematics
Step-by-step answer
P Answered by Specialist

Inequality is 2x+178\geq 2000.

Solution set is x\geq 911.

Step-by-step explanation:

Let the number of cans collected by Shane = x and the number of cans collected by Abha = y.

It is given that, Abha collected 178 cans more than Shane.

So, we have, y=x+178.

Since, they both have to collect cans no less than 2000 i.e. greater than or equal to 2000.

So, the equation representing the situation is,

Shane + Abha ≥ 2000

i.e. y + x ≥ 2000

i.e. x+178+x\geq 2000

i.e. 2x+178\geq 2000

i.e. 2x\geq 2000-178

i.e. 2x\geq 1822

i.e. x\geq 911

Thus, we have,

Inequality for the number of cans Shane collected is 2x+178\geq 2000.

Solution set of the inequality is x\geq 911.

Mathematics
Step-by-step answer
P Answered by Specialist

Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.

This means a minimum of 2000 cans are needed.

Abha collected 178 more cans than Shane did.

Let us suppose that the cans collected by Shane = S

So, Abha collected = S+178

The inequality to determine the cans Shane collected can be given by :

S+S+178\geq 2000

= 2S+178\geq 2000

2S\geq 2000-178

2S\geq 1822

S\geq 911

Mathematics
Step-by-step answer
P Answered by Master

Let number of cans collected by Shane =S

Number of cans collected by Abha=S+178

As, it is given that ,Abha collected 178 more cans than Shane did.

Also, the statement about inequality is

Both Shane and Abha have to collect no less than 2000 cans for recycling.

Writing the statement in terms of inequality

S +S+178 ≥ 2000

2 S ≥ 2000 - 178

2 S ≥ 1822

Dividing both sides by 2, we get

S≥ 911

So, Shane must have collected At least 911 cans.

Mathematics
Step-by-step answer
P Answered by PhD

When we multiply two polynomials, like (x+4)(x-4), we use the distributive property to expand the expression. This would give: (x+4)(x-4) = x(x-4) + 4(x-4) = x^2 - 4x + 4x - 16

The constant term of this expression is -16. It's not zero.

Mathematics
Step-by-step answer
P Answered by PhD
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