Answer:
1. x = 7
2. x = -5
Step-by-step explanation:
1. Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation: 2*x+5*(6*x-9)-(179)=0
Pull out like factors 6x - 9 = 3 • (2x - 3)
(2x + 15 • (2x - 3)) - 179 = 0
Pull out like factors: 32x - 224 = 32 • (x - 7)
Solve: x-7 = 0
Add 7 to both sides of the equation = 7
2. Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation: -40-(6*x-5*(-4*x-18))=0
Pull out like factors: -4x - 18 = -2 • (2x + 9)
-40 - (6x - -10 • (2x + 9)) = 0
Pull out like factors: -26x - 130 = -26 • (x + 5)
-26 • (x + 5) = 0
Solve: x+5 = 0
Subtract 5 from both sides of the equation: x = -5
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Answer:
212 children, and 265 adults
Step-by-step explanation:
To find the number of children and adults, we can set up a systems of equations.
x= number of children
y= number of adults
Equation 1: Price
1.50x+2.25y=914.25
Equation 2: Total number of people
x+y=477
Now, let's solve the equation using substitution.
Rearrange the second equation to solve for one variable.
x+y=477
x=477-y
Now plug x equals into the first equation, and solve for y.
1.50x+2.25y=914.25
1.50(477-y)+2.25y=914.25
715.5-1.50y+2.25y=914.25
715.5+0.75y=914.25
0.75y=198.75
y=265
We just solved for the number of adults. Now let's plug y equals into the second equation to find the number of children.
x+y=477
x+265=477
x=212
Answer:
8. Arithmetic Progression
9. 
Step-by-step explanation:
Given
Solving (8): Arithmetic or Geometric
We start by checking if it is arithmetic by checking for common difference (d).
This gives:
<em>Because the common difference is equal, then it is an arithmetic progression</em>
<em></em>
Solving (8):
To find f(9), we substitute 9 for n
We need to solve for f(8); substitute 8 for n
We need to solve for f(7); substitute 7 for n
We need to solve for f(6); substitute 6 for n
We need to solve for f(5); substitute 6 for n
From the function, f(4) = 25 and f(1) = 55.
So:
W = width
3w + 7 = length
Equation: 3w + 7 + w = 75
Combine like terms: 4w + 7 = 75
Subtract 7 to the other side: 4w = 68
Divide both sides by 4: w = 17
Width = 17
Length = 3(17) + 7, so 58
Gino studied for 5/4 hours in all. To get this, do 3+2 for the numerator and just put 4 as the denominator. (Four just stays the same the denominator is all fours. If you want more details just put it on comments.) Now you have the answer: 5/4 hours.
