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2 years ago

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The outside of a rectangular picture frame has length 4x + 5 centimeters and width 2x + 3 centimeters. The picture window inside

the frame is a rectangle that is 4x - 2 centimeters long and x + 1 centimeters wide.
a. Write a polynomial to describe the area (in square centimeters) of the picture window.
b. The picture frame, not including the window, is made of flat pieces of wood. Write a polynomial that describes the area (in square centimeters) of the wooden part of the frame. Explain your reasoning

1 answer:

Salsk061 [2.6K]2 years ago

7 0

The area of the wooden part of the frame is 4x² +20x +17 sq.cm , Area of a Rectangle is 4x² +2x-2 sq.cm .

<h3>What is a Rectangle ?</h3>

A rectangle is a polygon with four sides . The opposite sides are parallel and equal.

It is given that the outside length and breadth is 4x + 5 centimeters and width 2x + 3 centimeters.

inside the frame has length and breadth 4x - 2 centimeters long and x + 1 centimeters wide.

The polynomial to describe the area of the picture window

The dimension of the inner picture frame is the dimension of the picture window

Area of a Rectangle = Length * Breadth

Area of a Rectangle = (4x-2) (x+1) = 4x² +4x -2x-2 = 4x² +2x-2 sq.cm

The picture frame area without the window =

Area of the total picture frame - Area of the inner picture frame

= (4x+5)(2x+3) - (4x-2)(x+1)

= 8x² + 12x +10x+15 -4x²-2x +2

= 4x² +20x +17

The area of the wooden part of the frame is 4x² +20x +17 .

To know more about Rectangle

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kow [346]

The value of h(t) when $t=\frac{15}{32}$ is 10.02.

Solution:

Given function $h(t)=-16t^2+15t+6.5$

To find the value of h(t) when $t=\frac{15}{32}$ :

$h(t)=-16t^2+15t+6.5$

Substitute $t=\frac{15}{32}$ in the given function.

$$h\left(\frac{15}{32} \right)=-16\left(\frac{15}{32} \right)^2+15\left(\frac{15}{32} \right)+6.5$

$$=-16\left(\frac{225}{1024} \right)+15\left(\frac{15}{32} \right)+6.5$

Now multiply the common terms into inside the bracket.

$$=-\left(\frac{3600}{1024} \right)+\left(\frac{225}{32} \right)+6.5$

Now, in the first term, the numerator and denominator both have common factor 16. So reduce the first term into the lowest term.

$$=-\left(\frac{225}{64} \right)+\left(\frac{225}{32} \right)+6.5$

To make the denominator same, take LCM of the denominators.

LCM of 64 and 32 = 64

$$=-\left(\frac{225}{64} \right)+\left(\frac{225\times2}{32\times2} \right)+6.5\times\frac{64}{64}$

$$=-\frac{225}{64} +\frac{450}{64}+\frac{416}{64}$

$$=\frac{-225+450+416}{64}$

$$=\frac{641}{64}$

= 10.02

$$h\left(\frac{15}{32} \right)=10.02$

Hence the value of h(t) when $t=\frac{15}{32}$ is 10.02.

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3 years ago

If the output number y is -52 (y=5x-2) what is the input number? SHOW WORK

nordsb [41]

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Step-by-step explanation:

output is always y

input is always x

so instead of y, put -52

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