Answer: the length and width are
(x + 8) and (x + 8)
Step-by-step explanation:
The rug has an area represented by the expression
Area = 4x² + 64x + 256.
The factors in the factored expressions represent the length and width of the rug.
Dividing the the equation by 4, it becomes
x² + 16x + 64 = 0
We would find two numbers such that their sum or difference is 16x and their product is 64x^2.
The two numbers are 8x and 8x. Therefore,
x² + 8x + 8x + 64 = 0
x(x + 8) + 8(x + 8) = 0
The factors are
(x + 8)(x + 8)
Answer:
36 millimeters
Step-by-step explanation:
From Pythagoras theorem, the square of the hypotenuse is equal to the sum of the square of the two other legs
In mathematical terms;
a^2 = b^2 + c^2
Let a represent the hypotenuse = 39 mm and the length of one leg, say c, is 15 mm
Slotting in the values of a and b
39^2 = b^2 + 15^2
1521 = b^2 + 225
collect like terms
1521 - 225 = b^2
1296 = b^2
Take the square root of both sides
36 = b
Therefore b = 36 mm
Answer:
450
Step-by-step explanation:
Solution for What is 75 percent of 600:
75 percent * 600 =
(75:100)* 600 =
(75* 600):100 =
45000:100 = 450
Now we have: 75 percent of 600 = 450
Question: What is 75 percent of 600?
Percentage solution with steps:
Step 1: Our output value is 600.
Step 2: We represent the unknown value with $x$x.
Step 3: From step 1 above,$600=100\%$600=100%.
Step 4: Similarly, $x=75\%$x=75%.
Step 5: This results in a pair of simple equations:
$600=100\%(1)$600=100%(1).
$x=75\%(2)$x=75%(2).
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
600
x=
100%
75%
Step 7: Again, the reciprocal of both sides gives
x
600=
75
100
Therefore, $75\%$75% of $600$600 is $450$
Answer:
The correct solution is "4.6".
Step-by-step explanation:
Given:
Interest rate,
r = 6.2%
or,
= 0.062
Amount,
A = 100000
Principle,
P = 76000
As we know,
⇒ 
On substituting the values, we get
⇒ 
⇒ 
On taking log both sides, we get
⇒ 
⇒ 
By putting the values of log, we get
⇒ 
or,
⇒ 
Answer:
((2 x + 1) (4 x^2 - 2 x + 1))/8
Step-by-step explanation:
Factor the following:
x^3 + 1/8
Put each term in x^3 + 1/8 over the common denominator 8: x^3 + 1/8 = (8 x^3)/8 + 1/8:
(8 x^3)/8 + 1/8
(8 x^3)/8 + 1/8 = (8 x^3 + 1)/8:
(8 x^3 + 1)/8
8 x^3 + 1 = (2 x)^3 + 1^3:
((2 x)^3 + 1^3)/8
Factor the sum of two cubes. (2 x)^3 + 1^3 = (2 x + 1) ((2 x)^2 - 2 x + 1^2):
((2 x + 1) ((2 x)^2 - 2 x + 1^2))/8
1^2 = 1:
((2 x + 1) ((2 x)^2 - 2 x + 1))/8
Multiply each exponent in 2 x by 2:
((2 x + 1) (2^2 x^2 - 2 x + 1))/8
2^2 = 4:
Answer: ((2 x + 1) (4 x^2 - 2 x + 1))/8
