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coldgirl [10]
2 years ago
5

How can you Factor:ab^2-ab

Mathematics
1 answer:
NeTakaya2 years ago
3 0

Answer:

ab(b−1)

Step-by-step explanation:

Factor ab out of  ab ^2 − ab

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What is a correct congruence statement for the triangles shown? Enter your answer in the box. ​ △QDJ≅△ ​ A triangle Q D J. The b
almond37 [142]

Answer: The correct congruence statement is \triangle QDJ\cong \triangle MCW.

Explanation:

It is given that A triangle Q D J. The base D J is horizontal and side Q D is vertical. Another triangle M C W is made. The base C W and side M C are neither horizontal nor vertical. Triangle M C W is to the right of triangle Q D J.

The sides Q D and M C are labeled with a single tick mark. The sides D J and C W are labeled with a double tick mark. The sides Q J and M W are labeled with a triple tick mark.

Draw two triangles according to the given information.

From the figure it is noticed that

QD\cong MC

DJ\cong CW

QJ\cong MW

So by SSS rule of congruence we can say that \triangle QDJ\cong \triangle MCW.

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Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 162 square feet
Gnom [1K]

Answer:

The width and length of rectangle is 12.728 m

Step-by-step explanation:

Let the length of the rectangle = L

let the width of the rectangle = W

The subjective function is given by;

F(p) = 2(L + W)

F = 2L + 2W

Area of the rectangle is given by;

A = LW

LW = 162 ft²

L = 162 / W

Substitute in the value of L into subjective function;

f = 2l + 2w\\\\f = 2(\frac{162}{w} )+2w\\\\f = \frac{324}{w} + 2w\\\\\frac{df}{dw} = \frac{-324}{w^2} +2\\\\

Take the second derivative of the function, to check if it will given a minimum perimeter

\frac{d^2f}{dw^2}= \frac{648}{w^3} \\\\Thus, \frac{d^2f}{dw^2}>0, \ since,\frac{648}{w^3} >0 \ (minimum \ function \ verified)

Determine the critical points of the first derivative;

df/dw = 0

\frac{-324}{w^2} +2 = 0\\\\-324 + 2w^2=0\\\\2w^2 = 324\\\\w^2 = \frac{324}{2} \\\\w^2 = 162\\\\w= \sqrt{162}\\\\w = 12.728 \ m

L = 162 / 12.728

L = 12.728 m

Therefore, the width and length of rectangle is 12.728 m

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2 years ago
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