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ZanzabumX [31]
3 years ago
12

The ideal width of a safety belt strap for a certain automobile is 5 cm. An actual width can vary by at most 0.35 cm. Write and

solve an absolute value inequality for the range of acceptable widths.
Mathematics
1 answer:
notsponge [240]3 years ago
8 0

Answer:

4.65\leq x\leq 5.35

Step-by-step explanation:

Let the actual width of belt be x

we are given that the ideal width of safety belt strap is 5 cm

So, Difference between actual and ideal = (x-5)cm

We are also given that An actual width can vary by at most 0.35 cm.

So, The difference between actual and ideal width should be less than or equal to 0.35 cm

So, |x-5|\leq 0.35

We know

x-5\leq 0.35 and x-5\geq -0.35

x\leq 0.35+5 and x\geq -0.35+5

x\leq 5.35 and x\geq 4.65

So, 4.65\leq x\leq 5.35

Hence the range of acceptable widths is 4.65\leq x\leq 5.35

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Answer:

\boxed{ \tt\longrightarrow \: Area \:  Of  \: Shaded \:  region  \: =\boxed{ \tt 39  \: in²}}

Step-by-step explanation:

<u>Given:</u>

The Dimensions of Parallelogram are 12 in.(Base) and 7 in.(Height)

<em>And,</em>

The Dimensions of Rectangle are 9 in.(Length) and 5 in.(Breadth).

<u>To Find</u>:

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<u>Solution:</u>

When the dimensions of parallelogram and the dimensions of rectangle are given, we need to find the Shaded region using this formula:

\boxed{\tt \longrightarrow Area  = (Parallelogram  - Rectangle)}

We know that the formula of Parallelogram is base*height[b×h] and the formula of rectangle is length*breadth[l*b] .

\tt\longrightarrow \: Area =B×h-l×b

Put their values accordingly:

\longrightarrow  \tt Area = (12 \times 7 - 9 \times 5)in {}^{2}

<u>Simplify it.</u>

<em>[</em><em>Follow BODMAS Rule strictly while </em><em>simplifying]</em>

\tt\longrightarrow \: Area = (84 - 45 ) in {}^{2}

\tt\longrightarrow \: Area = 39 \:  {in}^{2}

Hence, the Area of Shaded region would be 39 in² or 39 sq. in. .

\rule{225pt}{2pt}

I hope this helps!

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Mr. Johns handle this situation to Agree to meet, listen to their concerns, and then explaining that one component of math is understanding reasonable answers.

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