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icang [17]
3 years ago
14

A large rectangular movie screen in an IMAX theater has an area of 10,800 square feet. Find the dimensions of the screen if it i

s 30 feet longer than it is wide. length ft width ft
Mathematics
1 answer:
icang [17]3 years ago
3 0

Answer:

Let x be the width of the screen and

x + 30 be the length of the screen

Area of the screen = 10384 square feet

=>x(x+30) = 10384

x^2 + 30x = 10384

x^2 + 30x - 10384 = 0

Splitting-

x2+118x - 88x -10384 = 0

x(x+118) -88(x+118) = 0

(x+118)(x-88) = 0

x=-118,88

Since width should be positive,

width = 88 feet

length = 118 feet

Step-by-step explanation:

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Answer:

dimensions = 10.8  X 4

Step-by-step explanation:

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29.6/2 = 6.8 + 2x

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8 = 2x

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4=x

Length of room =  6.8 + x = 6.8 + 4 = 10.8 m

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8 0
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Step-by-step explanation:

943-481

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3 years ago
( I REALLY NEED HELP I WILL GIVE BRILLIANT) If you divide 78 by 34, will the quotient be greater than or less than 34?
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If (x^2 - 1) is a factor of ax^4 + bx^3 + cx^2 + dx + e, show that a + c + e = b + d = 0
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If x²-1 is a factor of the polynomial, both x-1 and x+1 are factors of it.

According to the remainder theorem, if a binomial x-a is a factor of a polynomial p(x), then p(a)=0.

If x-1 and x+1 are factors of the polynomial p(x)=ax⁴+bx³+cx²+dx+e, then p(1)=0 and p(-1)=0.

p(1)=a \times 1^4+b \times 1^3 + c \times 1^2+ d \times 1+e \\
p(-1)=a \times (-1)^4 + b \times (-1)^3 + c \times (-1)^2 + d \times (-1)+e \\ \\
p(1)=a+b+c+d+e \\
p(-1)=a-b+c-d+e \\ \\
p(1)=0 \\
p(-1)=0 \\ \\ \hbox{add both equations:} \\
a+b+c+d+e=0 \\
\underline{a-b+c-d+e=0} \\
2a+2c+2e=0 \\
2(a+c+e)=0 \\
a+c+e=0 \\ \\
\hbox{substitute 0 for a+c+e in the first equation:} \\
a+b+c+d+e=0 \\
(a+c+e)+b+d=0 \\
0+b+d=0 \\
b+d=0 \\ \\
\boxed{a+c+e=b+d=0} \\
\hbox{proved } \checkmark
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