Answer:
The dimensions are 6 by 5 feet.
Length = 6 feet.
Width = 5 feet.
Step-by-step explanation:
Let the length = L
Let the width = W
Perimeter of a rectangle = 2L + 2W
Translating the word problem into an algebraic equation, we have;
L = 2W - 4 ........equation 1
22 = 2L + 2W .......equation 2
Substituting the value of "L" into equation 2, we have;
22 = 2(2W - 4) + 2W
22 = 4W - 8 + 2W
22 + 8 = 6W
30 = 6W
W = 30/6
Width, W = 5 feet.
To find the length, L
Substituting the value of "W" into equation 1, we have;
L = 2W - 4
L = 2(5) - 4
L = 10-4
Length, L =6 feet
Therefore, the dimensions of the garden are 6 by 5 feet.
Answer:
The given Divisor = 21 and Dividend = 91403
43522191403847463110105534211
The Quotient is 4352 and the Remainder is 11
Answer:
3/6 and 5/10
Explanation:
Given the fraction 1/2:
(a)Multiply the numerator and denominator by 3
An equivalent fraction is 3/6.
(b)Multiply the numerator and denominator by 5:
An equivalent fraction is 5/10.
Answer:
or 
Step-by-step explanation:
The opposite of 
is 
Convert decimal number −0.75 to fraction 
.
Reduce the fraction to lowest terms by extracting and canceling out 25.
Least common multiple of 4 and 5 is 20. Convert 
and to fractions with denominator 20.
Since 
and 
have the same denominator, add them by adding their numerators.
Add -15 and 8 to get -7
Convert decimal number 0.4 to fraction 
. Reduce the fraction to lowest terms by extracting and canceling out 2.
Least common multiple of 20 and 5 is 20. Convert 
and to fractions with denominator 20.
Since and have the same denominator, add them by adding their numerators.
Add -7 and 8 to get 1.
Least common multiple of 20 and 4 is 20. Convert 
and 
to fractions with denominator 20.
Since and 
have the same denominator, subtract them by subtracting their numerators.
Subtract 15 from 1 to get -14.
Reduce the fraction 
to lowest terms by extracting and canceling out 2.
or
Hope this helps! Brainliest would be much appreciated! Have a great day! :)
Step-by-step explanation:
The value of sin(2x) is \sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−
8
15
How to determine the value of sin(2x)
The cosine ratio is given as:
\cos(x) = -\frac 14cos(x)=−
4
1
Calculate sine(x) using the following identity equation
\sin^2(x) + \cos^2(x) = 1sin
2
(x)+cos
2
(x)=1
So we have:
\sin^2(x) + (1/4)^2 = 1sin
2
(x)+(1/4)
2
=1
\sin^2(x) + 1/16= 1sin
2
(x)+1/16=1
Subtract 1/16 from both sides
\sin^2(x) = 15/16sin
2
(x)=15/16
Take the square root of both sides
\sin(x) = \pm \sqrt{15/16
Given that
tan(x) < 0
It means that:
sin(x) < 0
So, we have:
\sin(x) = -\sqrt{15/16
Simplify
\sin(x) = \sqrt{15}/4sin(x)=
15
/4
sin(2x) is then calculated as:
\sin(2x) = 2\sin(x)\cos(x)sin(2x)=2sin(x)cos(x)
So, we have:
\sin(2x) = -2 * \frac{\sqrt{15}}{4} * \frac 14sin(2x)=−2∗
4
15
∗
4
1
This gives
\sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−
8
15
