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adelina 88 [10]
3 years ago
15

Point b is the midpoint of ac-. if ab= 4x+2 and ac=10x-6, find the length of ac

Mathematics
1 answer:
Natasha2012 [34]3 years ago
3 0

let's bear in mind that B is the midpoint and thus it cuts a segment into two equal halves.

\bf \underset{\leftarrow \qquad \textit{\large 10x-6}\qquad \to }{\boxed{A}\stackrel{4x+2}{\rule[0.35em]{10em}{0.25pt}} B\stackrel{\underline{4x+2}}{\rule[0.35em]{10em}{0.25pt}\boxed{C}}} \\\\\\ AC=AB+BC\implies 10x-6=(4x+2)+(4x+2)\implies 10x-6=8x+4 \\\\\\ 2x-6=4\implies 2x=10\implies x=\cfrac{10}{2}\implies x= 5 \\\\[-0.35em] ~\dotfill\\\\ AC=(4x+2)+(4x+2)\implies AC=[4(5)+2]+[4(5)+2] \\\\\\ AC=22+22\implies AC=44

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The polynomial for the perimeter starts from the formula for the perimeter of a rectangle as written below:

Perimeter = 2L + 2W = 2( L + W)
Perimeter = 2(4A + 3B + 3A - 2B)
Perimeter = 2(7A - B)
Let perimeter be P,
P = 14A - 2B  --> this would be the polynomial

Let's substitute A=12 to the polynomial:
P = 14(12) - 2B = 168 - 2B
To determine the minimum P, set it to 0.0001.
0.0001 = 168 - 2B
B = 83.999 or 84

Thus, the minimum perimeter is achieved if the value of B approached to 84.

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3 years ago
9) Which solution is correct? Be sure to check for extraneous solutions.
shutvik [7]

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3 years ago
Nathan is buying a cell phone for his business. The regular price of the cell phone is $179. If he buys the phone in the next 2
m_a_m_a [10]
20% off
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3 years ago
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Ostrovityanka [42]
Split the trapezium into a rectangle and a triangle and work out the areas of them.
4x6=24
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Area of trapezium= 28
There are 2 trapeziums, which makes 56.
The back of the shape is 4x14=56.
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The underside of the shape is 8x14=112.
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As them all together= 56+56+84+112+62.58=370.58.

Total surface area=370.58.

Hope this helps :)
4 0
3 years ago
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1 3/8 divided by 5/8 show work.
nata0808 [166]

Answer:

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Step-by-step explanation:

The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.

To convert a Decimal to a Fraction follow these steps:

Step 1: Write down the decimal divided by 1, like this: decimal 1.

Step 2: Multiply both top and bottom by 10 for every number after the decimal point. ...

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