Answer:
0.857 weeks
Step-by-step explanation:
Using the information provided we can create the following equations for the total amount Mallory (M) and Aimee (A) will save after x number of weeks...
M = 35 + 15x
A = 5 + 50x
Now we would need to make both of these equations equal one another and solve for x to calculate after how many week both Aimee and Mallory will have saved the same amount of money
35 + 15x = 5 + 50x ... subtract 5 and 15x from both sides
30 = 35x ... divide both sides by 35
or 0.857 = x
Finally, we can see that after 0.857 weeks both Mallory and Aimee will have saved the same amount of money.
*** The process provided is correct but I believe that the actual values for Aimees savings should be $50 and plans to save $5 a week, this would make the final result 1.5 weeks which would make more sense***
Answer:
no solution
Step-by-step explanation:
1/2(2-4x)+2x=13
We simplify the equation to the form, which is simple to understand
1/2(2-4x)+2x=13
Simplifying:
+ 0.5*(2-4x)+2x=13
Reorder the terms in parentheses
+(+1-2x)+2x=13
Remove unnecessary parentheses
+1-2x+2x=+13
We move all terms containing x to the left and all other terms to the right.
-2x+2x=+13-1
We simplify left and right side of the equation.
0x=+12
0=12
The left and right sides are not equal, therefore there is no solution. This equation is invalid.
Answer:
Step-by-step explanation:
<u>Let's derive a formula</u> :
⇒ Area (triangle) × 3 = Area (square)
⇒ 1/2(bh) × 3 = a²
∴ But a = h (shown in diagram)
⇒ 3/2(bh) = h²
⇒ <u>h = 3b/2</u>
<u>Now, taking tan θ</u> :
⇒ tan θ = b/h
⇒ tan θ = b/(3b/2)
⇒ tan θ = 2b/3b
⇒ tan θ = 2/3
Answer:
there are no extraneous solutions to the equation
Step-by-step explanation:
Given
= x + 2 ( square both sides )
8x + 9 = (x + 2)² ← expand
8x + 9 = x² + 4x + 4 ( subtract 8x + 9 from both sides )
0 = x² - 4x - 5 ← in standard form
0 = (x - 5)(x + 1) ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 1 = 0 ⇒ x = - 1
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions.
x = 5 : 
= 
= 7
right side = 5 + 2 = 7
left side = right side ⇒ x = 5 is a solution
x = - 1 : 
= 
= 1
right side = - 1 + 2 = 1
left side = right side ⇒ x = - 1 is a solution
There are no extraneous solutions
