Mathematics, 02.04.2020 01:52 jenna3490

A magician’s stage has a rectangle trapdoor which is (x+ 1/2) by 2x ft. The outside rectangle length is (x+ 16) ft.

Part A. The total area (in square feet) of the stage can be represented by x2 + 27x + 176. Write an expression for the width of the stage.

Part B: Write an expression for the perimeter of the stage.

Part C: The area of the trapdoor is 10 square feet. Find the value of x.

Part D: The magician wishes to have the area of the stage be at least 20 times the area of the trapdoor. Does this stage satisfy his requirement? Explain.

Answers: 2

Show answers

Answers

Answer from: LEXIEXO

Part A:- x +11 ft Part B:- (4x+54)ft part C:- x= 2ft

Part D:- Yes it satisfy his requirement

Step-by-step explanation:

Given that,

length and breadth of Trapdoor are $(x+ \frac{1}{2} ) by 2x$ ft.

The Outside length of Rectangle is (x+16 ) ft.

Part A:- Total area (in square feet) of the stage can be represented by

$x^{2} + 27x+ 176$ . Write an expression for the width of stage.

So, Area of rectangle = $length \times breadth$

$x^{2} + 27x+ 176 = (x+16) \times breadth$

$Breadth = \frac{x^{2} + 27x+ 176}{x+16}$

Breadth = x+11 ft. ................(1)

Part B:- Write an expression for the Perimeter of the stage.

Here, Perimeter of Rectangle = 2(L+B)

= 2(x+16 + x +11)

= (4x + 54) ft

Part C:- The area of trapdoor is $10 ft^{2}$ . Find the value of x.

So, Area of trapdoor = $10 ft^{2}$

$(x +\frac{1}{2}) \times 2x =10 ft^{2}$

$2x^{2} +x - 10 = 0$

$x = \frac{-1-9}{4}$ , $\frac{-1+9}{4}$

$x = \frac{-5}{2}$ ,

Hence value of x is 2 ft (Neglecting the negative value because

length cannot be negative).

Part D:- The magician wishes to have the area of the stage be at least 20 times the area of the trapdoor. Does this stage satisfy his requirement? Explain.

So, Length of trapdoor is $(2+\frac{1}{2} ) = \frac{5}{2} ft$

breadth of trapdoor is $2\times 2 = 4ft$

Now, outside length of Rectangle is = 18ft

And outside breadth of rectangle is = 13ft

Here, Area of trapdoor = $\frac{5}{2} \times 4 = 10ft^{2}$ ...................(2)

Area of rectangle = $18 \times 13= 234 ft^{2}$ ....................(3)

Thus comparing Equation (1) & (2) we found that

Area of rectangular stage is 20 times greater than the area of trapdoor.

Answer from: Quest

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

Answer from: Quest

Ap human geography and geometry

Another question on Mathematics

Mathematics, 21.06.2019 19:30

Needmax recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

Which equation expression the relationship between the number of boxes b and the number of cans c and the proportion is 48

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

One number is 4 less than 3 times a second number. if 3 more than two times the first number is decreased by 2 times the second number, the result is 11. use the substitution method. what is the first number?

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

On this question. a hypothermia occurs when a person's body temperature drops below 95 degrees fahrenheit. write and solve an inequality that describes how much lower the body temperature of a person with hypothermia will be than the body temperature of a person with a normal temperature of 98.6 degrees fahrenheit

Answers: 1

Answer

You know the right answer?

A magician’s stage has a rectangle trapdoor which is (x+ 1/2) by 2x ft. The outside rectangle length...

Questions

Mathematics, 07.07.2019 18:00

Determine if each fraction is a terminating decimal or a repeating decimal. write each fraction in the correct box....