Picture is here for A framing company is putting out a new product this summer. The width of the frame will be uniform all the way around. The designed frame will be cut out of a piece of steel, and to keep the weight down, the final area of the frame alone should be 100 cm2. The inside of the frame has to be 10 cm by 8 cm. What should the width x of the metal be?

Step-by-step explanation:

The shape of the frame(both inner and outer) is rectangular in nature.

Area of a rectangle = Length *Breadth

Since the width of the metal is x and the width of the frame will be uniform all the way around, then the length of the outer frame will be (x+8+x)cm and the breadth of the outer frame is (x+10+x)cm. Given the area of the outer frame to be 100cm², substituting this given parameters into the formula we have;

100 = (x+8+x) * (x+10+x)

100 = (2x+8)(2x+10)

100 = 4x²+20x+16x+80

4x²+36x-20 =0

Dividing through by 4 we have;

x²+9x-5 = 0

Using the general formula where a=1, b = 9, c = -5

x = -b±√b²-4ac/2a

x = -9±√9²-4(1)(-5)/2(1)

x = -9±√81+20/2

x = -9±√101/2

x = -9±10.05/2

x = -9+10.05/2 and -9-10.05/2

x = 1.05/2 and -19.05/2

x = 0.525 and -9.525

Choosing the positive width

x = 0.525cm

x ≈ 0.5cm

no, the equation would be invalid since they are both not equal.

step-by-step explanation:

here you got

4y-6+4y 2-9

first, you would simplify the equation on the form.

4y-6+4y 2-9

then, move all the terms that contains a y to the left and all the other terms to the right.

+4y-4y+-9-6

finally, you will simplify the left and the right side of the equation.

y=-3

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,