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3 years ago

Brainliest for whoever gets this correct with working out

Mathematics

1 answer:

alukav5142 [94]3 years ago

6 0

Answer:

$\frac{2x - 5}{x + 5}$

Step-by-step explanation:

Firstly, you have to factorize the expressions on the numerator and denorminator :

Numerator :

$2 {x}^{2} - 3x - 5$

$= 2 {x}^{2} + 2x - 5x - 5$

$= 2x(x + 1) - 5(x + 1)$

$= (2x - 5)(x + 1)$

Denorminator :

${x}^{2} + 6x + 5$

$= {x}^{2} + x + 5x + 5$

$= x(x + 1) + 5(x + 1)$

$= (x + 1)(x + 5)$

Next, you have to put the factorized-form in the fraction and cut out the similar expressions :

$\frac{(2x - 5)(x + 1)}{(x + 1)(x + 5)}$

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

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A fire station is to be located along a road of length A, A < q. If fires occur at points uniformly chosen on (0, A), where s

Shtirlitz [24]

Answer:

Step-by-step explanation:

Given that X is uniform in the interval (0,A)

X is continuous since it represents the distance

A fire station is to be located along a road of length A, A < q. If fires occur at points uniformly chosen on (0, A), we should find where the station be located so as to minimize the expected distance from the fire

Distance can be taken as absolute values here as either side is the same.

E(|x-a|] is to be minimum

E(|x-a|)=E(x-a) for 0<x<a

=E(a-x), for a<x<A

Using integral we find this value

$E(|x-a|)=\int\limits^a_0 {x-a} \, dx +=\int\limits^A_a -{x-a} \, dx\\f(a)=\frac{a^2}{2} -\frac{(A-a)^2}{2}$

$f(a)=\frac{a^2}{2} +\frac{(A-a)^2}{2} \\f'(a) = a-(A-a)\\f"(a) =2$

Using calculus we find that f" is positive so when f' =0 we get solution

f'(a) =0 gives

$a=\frac{A}{2}$

Hence fire station to be located at the mid point of 0 and A

8 0

4 years ago

A rectangle has a height of b3 + b2 and a width of b2 + 76 + 4.

zaharov [31]

Answer:

The area is:

${b}^{5} + 8 {b}^{4} + 11 {b}^{3} + 4 {b}^{2}$

Step-by-step explanation:

To find the area of a rectangle, multiply the width by the height (I'll be using x for b, as it is easier when writing the equations):

$a = ({x}^{ 3} + {x}^{2} )( {x}^{2} + 7x + 4) \\ a = {x}^{5} + 7{x}^{4} + 4 {x}^{3} \\ + {x}^{4} + 7 {x}^{3} + 4 {x}^{2} \\ a = {x}^{5} + 8 {x}^{4} + 11 {x}^{3} + 4 {x}^{2}$

3 0

4 years ago

asambeis [7]

Answer:

The sum of 2 and the quotient of 3 and y

Step-by-step explanation:

The expression 2 + 3/y without any parentheses is evaluated as ...

2 + (3/y)

which is a sum. The first contributor to the sum is 2, and the second contributor is the quotient of 3 and y. (Usually, "the quotient of "a" and "b" means "a/b".)

Hence the answer shown above is a good description of the expression.

3 0

3 years ago

If f(x) = 6x – 4, what is f(x) when x = 8?<br> 0.16

kykrilka [37]

$f(8)=6\cdot8-4=48-4=44$