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evablogger [386]
3 years ago
10

PLEASE HELP ASAP WILL MARK BRAINLIEST.

Mathematics
1 answer:
Nataly [62]3 years ago
6 0

The factor of the expression is 7\left(9y^2+5y+4\right)

Explanation:

The given expression is 63y^2+35y+28

We need to determine the factor of the expression.

The factor of the expression can be determined by simplifying the given expression.

Now, we shall rewrite each term as a multiple of 7.

Thus, rewriting, we have,

63=7\times9

35=7\times5

28=7\times4

Hence, substituting these values in the expression, we get,

(7\times9)y^2+(7\times5)y+(7\times4)

Let us factor out the common term 7, we get,

7\left(9y^2+5y+4\right)

Thus, the factor of the expression is 7\left(9y^2+5y+4\right)

The factor of the expression is determined by taking out the common term 7 from the expression.

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Answer:

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Step-by-step explanation:

Imagine that you have this walkway around the garden, with dimensions 30 by 20 feet. This walkway has a difference of x feet between it's length, and say the dimension 30 feet. In fact it has a difference of x along both dimensions - on either ends. Therefore, the increases length and width should be 30 + 2x, and 20 + 2x, which is with respect to an increases area of 1,000 square feet.

( 30 + 2x ) * ( 20 + 2x ) = 1000 - Expand "( 30 + 2x ) * ( 20 + 2x )"

600 + 100x + 4x^2 = 1000 - Subtract 1000 on either side, making on side = 0

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( Quadratic Equation is as follows ) - x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a},

x=\frac{-100+\sqrt{100^2-4\cdot \:4\left(-400\right)}}{2\cdot \:4}:\quad \frac{5\left(\sqrt{41}-5\right)}{2},

x=\frac{-100-\sqrt{100^2-4\cdot \:4\left(-400\right)}}{2\cdot \:4}:\quad -\frac{5\left(5+\sqrt{41}\right)}{2}

There can't be a negative width of the walkway, hence our solution should be ( in exact terms ) \frac{5\left(\sqrt{41}-5\right)}{2}. The approximated value however is 3.5081...or approximately 3.5 feet.

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