-70y^2+90x^3+100yx^2-63xyfactor by grouping

1 answer:

4 0

The idea of grouping is to get the terms in groups that allow you to factor out from each group something that becomes a factor in itself, leaving two factors behind that are alike. Like this: rearrange those terms so they are in this order:
(-70y^2 - 63xy) + (90x^3 + 100yx^2). Now out of the first set we are going to factor out a -7y, and out of the second set we are going to factor out a 10x^2. When we do this, this is what we get: -7y(10y + 9x) + 10x^2(9x + 10y). As you can see, what's inside both sets of parenthesis is the same, just in a different order. We can factor that out now, leaving (9x + 10y)(10x^2 - 7y). And that is factored by grouping.

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Find the value of pq - r/4 when p= -8 and q= -3 and r= 68

andrey2020 [161]

Answer:

Step-by-step explanation:

pq - r/4

(-8)(-3) - 68/4

-8 x -3 = 24 (2 negatives equal a positive)

24 - 68/4

68/4 = 17

24-17 = 7

6 0

4 years ago

The length of a rectangle is twice its width. Find its area, if its perimeter is 7 and 1/3 cm.

laila [671]

Answer:

2.99 cm²

Step-by-step explanation:

<em>(The "..." at the end of the decimal means that number is repeating)</em>

The perimeter of a rectangle is the length around the shape. The equation for a rectangle's perimeter is L + W × 2, with L and W representing length and width, respectively (You multiply the length and width by two because the shape is four-sided, so it has two length sides and two width sides). To find the area of the rectangle, you need to know the individual length and width, so you'll solve for that first.

Since you're only given the perimeter and you know the length is double the width, you'll need to work backwards with this equation. To do this, first divide the perimeter (7 $\frac{1}{3}$ , also written as 7.33...) by 2; this equals 3 $\frac{2}{3\\}$ , also written as 3.66...

Next, you can find the length and width by determining what two numbers multiply to equal 3.66..., with one number being two times larger than the other number. The way I tend to think of this is that if one number is double the other, then the smaller number is one third of the sum of the two numbers (since the smaller number represents one part of the sum, and the other represents two parts of the sum, which is double the smaller number).

Since the length and width combine to be the divided perimeter, 3.66..., that means two thirds of 3.66... is the longer side (the length), and then the one third of 3.66... is the shorter side (the width). This means the length is 2.44... and the width is 1.22...

Finally, you can solve for the perimeter by dividing the perimeter by two and then subtracting the length squared. The written equation looks like this:

A = P $\frac{1}{2}$ - L²