As you haven't specifically stated what exactly the question is, I will be assuming that the question is most likely asking for what the dimensions ( length and width ) of the rectangle is. With this in mind, I will be answering the question so here I go...
STEP-BY-STEP SOLUTION:
Let's solve this problem step-by-step.
Let's first establish the formula for the area of a rectangle as displayed below:
Area = Length × Width
A = lw
From this, we will establish the values for each of the parts in the area formula using the information given in the problem as displayed below:
A = 72cm^2
l = w + 6
w = w
Now, we will substitute these values into the area formula and then make ( w ) the subject as displayed below:
A = lw
72 = ( w + 6 ) ( w )
72 = w ( w + 6 )
72 = w^2 + 6w
0 = w^2 + 6w - 72
0 = w^2 + 12w - 6w - 72
0 = w ( w + 12 ) - 6 ( w + 12 )
0 = ( w + 12 ) ( w - 6 )
w + 12 = 0
w = 0 - 12
w = - 12
w - 6 = 0
w = 0 + 6
w = 6
As the answer must be positive as measurements are always positive, the answer must be the option which is a positive number.
Therefore:
w = 6
Using the equation we made for the length before, we can substitute the value of ( w ) to obtain the value of the length as displayed below:
l = w + 6
l = ( 6 ) + 6
l = 12
FINAL ANSWER:
The dimensions of the rectangle are:
Length = 12cm
Width = 6cm
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Answer:
Kaitlin's account will have 72% of the money initially invested, that is, about $ 6,192.
Step-by-step explanation:
Given that last year Kaitlin opened an investment account with $ 8,600, and at the end of the year, the amount in the account had decreased by 28%, to determine the year-end amount in terms of the original amount both in whole numbers and in decimals, the following calculation must be performed:
100 - 28 = 72
8,600 x 0.72 = X
6.192 = X
Thus, Kaitlin's account will have 72% of the money initially invested, that is, about $ 6,192.
For this case, what we must do is find three times the perimeter of the figure.
The length of the arch is given by:
Where,
r: radius of the circle
alpha: central angle in radians
We have then:
Then, the perimeter of the figure is:
Answer:
If David runs around the field three times, he covers a distance of 648 yards.
<u>Answer:</u>
2
<u>Step-by-step explanation:</u>
• Multiplying two numbers with same bases is the same as adding their powers:
∴ 
⇒ 
⇒ 
• Dividing two numbers with same bases is the same as subtracting their powers:
∴
⇒ 
⇒ 
⇒ 
• Raising anything to the power of 
is the same as square-rooting it:
∴
⇒ 
⇒ 2
Answer:
9a^3b^3.
Step-by-step explanation:
The GCF of 9 and 27 is 9.
For a^4 and a^3 it is a^3.
For b^4 and b^3 it is b^3.
Answer is therefore:
9a^3b^3.
