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san4es73 [151]
2 years ago
8

Please help I have 15 minutes left for my assessment. Thank you!

Mathematics
1 answer:
posledela2 years ago
3 0

Answer:

57kg

Step-by-step explanation:

We need to find the length of each piece of metal:

We already know that 2 of them are 6m and 8m and this would be the same for the pieces of metal opposite.

So we have four lengths - 6m, 6m, 8m, and 8m

To find the last length, we need to use pythagoras theory

a² + b² = c² where c is the slanted side, or the diagonal

6² + 8² = c²

36 + 64 = 100

c² = 100

c = √100 = 10

So the five lengths are 6m, 6m, 8m, 8m, and 10m and the total is 38m

If:

1m = 1.5kg

38m = ?kg

We have to multiply both sides by 38

1m × 38 = 38m

1.5kg × 38 = 57kg

So, the total weight of metal in the frame is 57kg

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2 years ago
The area of a rectangle is 56 cm. the length is 2 less than x and the width is 5 less than twice of x. solve for x
Nostrana [21]

Answer:

x=\frac{9+\sqrt{449}}{4}

Step-by-step explanation:

The area of a rectangle is:

A=l\cdot w

First let's write both the length and the width in terms of x:

l=x-2

<u>How we obtained the answer</u>:

The question states the length is "2 less than x". In this case, "less" is a keyword that represents subtraction. Therefore, "2 less than x" is "x-2".

w=2x-5

<u>How we obtained the answer</u>:

The question states the width is "5 less than twice of x". First, start by figuring out what "twice of x" is. The keyword is "twice" which represents multiplication. Therefore, "twice of x" can be written as "2x". Then, using the same keyword from before ("less"), "5 less than..." represents "2x-5".

Given:

Area = 56 cm

l=x-2

w=2x-5

Find:

x

A=l\cdot w

56=(x-2)(2x-5)

FOIL (Firsts, outsides, insides, lasts):

56=2x^2-4x-5x+10\\56=2x^2-9x+10

Subtract 10 from both sides:

46=2x^2-9x

Subtract 46 from both sides (forms a quadratic equation):

0=2x^2-9x-46

Use the quadratic formula:

{x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}  where 0=ax^2+bx+c

Therefore:

x=\frac{9\pm\sqrt{81-4(2)(-46)}}{2(2)}\\x=\frac{9\pm\sqrt{81+368}}{4}\\\\x=\frac{9\pm\sqrt{449}}{4}

The answer is:

x=\frac{9+\sqrt{449}}{4}

This is because if we used subtraction, we would get a negative value, and we cannot have a negative length/width.

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Answer:

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Step-by-step explanation:

Given expression,

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By substituting x = 8,

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By subtraction property of equality,

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Division property of equality,

y = \frac{89}{6}

By symmetric property of equality,

\frac{89}{6} = y

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