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3 years ago

How to factor 4(x+5)^3(x-1)^2-(x+5)^4 • 2 (x-1) by grouping?

1 answer:

5 0

$\bf 4(x+5)^3(x-1)^2-(x+5)^4\cdot 2(x-1)
\\\\\\
4(x+5)^3(x-1)^2-2(x-1)(x+5)^4
\\\\\\ \underline{2}\cdot 2\underline{(x+5)^3}(x-1)\underline{(x-1)}~-~\underline{2}\underline{(x-1)}(x+5)\underline{(x+5)^3}\leftarrow 
\begin{array}{llll}
notice~the\\
common\\ \underline{factors}
\end{array}
\\\\\\
2(x+5)^3(x-1)~[~2(x-1)-(x+5)~]
\\\\\\
2(x+5)^3(x-1)~[2x-2-x-5]\implies 2(x+5)^3(x-1)(x-7)$

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Sarah would like to make a 6 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of a mixture that is 80%

weeeeeb [17]

Answer: a. The system that models this situation is,

x + y = 6 , 8 x + 5 y = 36.

b. Solution is x = 2lb and y = 4lb

where x is the quantity of 80% of peanuts mixture mix with y quantity of 50% of peanuts mixture for making 60% of peanuts mixture.

Step-by-step explanation:

Let x quantity of 80% of peanuts mixture mix with y quantity of 50% of peanuts mixture for making 60% of peanuts mixture.

Then According to the question,

x + y = 6 --------- (1)

And, 80 % of x + 50 % of y = 60 % of 6

⇒ 0.8 x + 0.5 y = 3.6

⇒ 8 x + 5 y = 36 --------- (2)

Where equation 1) and equation 2) are the required equation which models the given situation.

Now, 8 × equation 1)

We get, 8 x + 8 y = 48 ----------(3)

equation (3) - equation (2)

we get, 3 y = 12

⇒ y = 4

By putting the value of y in equation (2)

we get, x = 2

Thus, he mixed 2 lb of mixture 80/20 and 4 lb of mixture 50/50 for making 6 lb of 50/50 mixture.

4 0

3 years ago

The circumference of the hub cap of a tire is 83.96 centimeters. Find the area of this hub cap. Use 3.14 for . Use pencil and pa

Bess [88]

Answer:

Area = $561.2485$ square centimeter

If the circumference of the hub cap would have been smaller, then its radius would have been smaller and subsequently its area would also have been less.

Step-by-step explanation:

As we know the circumference of a circle is $2\pi r$

The radius of the hub cap needs to be devised to determine the area

$83.96$ $= 2* 3.14*r$

$r = \frac{83.96}{2*3.14}$

$r = 13.37$ centimeters

Area of the hub cap = $\pi r^{2}$

Substituting the devised value of r in the above equation, we get -

$3.14 * 13.37^2\\$

$561.2485$ square centimeter

If the circumference of the hub cap would have been smaller, then its radius would have been smaller and subsequently its area would also have been less.

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3 years ago

Gloria is an artist. She sets a goal to paint 2 paintings every month. The number of paintings Gloria creates depends on the num

BartSMP [9]

Answer:

we get the all equation of given condition $M = 2P+1$ & $P=2M+1$ Step-by-step explanation: