Cross multiply so 27*4 = (x+2)^3
Then cube root 108 = x+2
(cube root 108)-2= x
Answers:
It costs $15 for one adult
It costs $10 for one child
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Work Shown:
x = cost for one adult ticket (in dollars)
y = cost for one child ticket (in dollars)
"it costs $35 for one adult and two children" so the first equation is x+2y = 35. Solve for x to get x = -2y+35 (subtract 2y from both sides). We'll use this equation later. See the "replacement" step below.
"it costs $60 for two adults and three children" so the other equation to set up is 2x+3y = 60
Use the substitution rule to get rid of the x (replace it with something equivalent in terms of y) then isolate y
2x+3y = 60
2( x )+3y = 60
2( -2y+35 )+3y = 60 ... replace x with -2y+35
2(-2y)+2(35)+3y = 60
-4y+70+3y = 60
-y+70 = 60
-y+70-70 = 60-70
-y = -10
y = 10
Since y = 10, it costs $10 for one kid to get a ticket.
If y = 10, then x must be...
x = -2y+35
x = -2*10+35 ... replace y with 10
x = -20+35
x = 15
Since x = 15, it costs $15 for one adult ticket.
Answer:
75 pages
Step-by-step explanation:
Answer:
( 2,1) is the center of dilation and -2 is the scale factor
Step-by-step explanation:
We can use the formula
A' = k( x-a) +a, k( y-b)+b where ( a,b) is the center of dilation and k is the scale factor
(0,0) becomes (6,3)
( 6,3) = k( 0-a) +a, k( 0-b)+b
6 = -ka+a
3 = -kb+b
We also have
(4,0) becomes (-2,3)
( -2,3) = k( 4-a) +a, k( 0-b)+b
-2 =4k -ka+a
3 = -kb+b
Using these two equations
6 = -ka+a
-2 =4k -ka+a
Subtracting the top from the bottom
-2 =4k -ka+a
-6 = ka -a
-------------------
-8 = 4k
Divide by 4
-8/4 = 4k/4
-2 = k
Now solving for a
6 = -ka +a
6 = - (-2)a +a
6 = 2a+a
6 = 3a
Divide by 3
6/3 =3a/3
2=a
Now finding b
3 = -kb+b
3 = -(-2)b+b
3 = 2b+b
3 = 3b
b=1
Answer:
x = 12
Step-by-step explanation:
Step 1: Define
f(x) = 4x + 6
f(x) = 54
Step 2: Substitute variables
54 = 4x + 6
Step 3: Solve for <em>x</em>
<u>Subtract 6 on both sides:</u> 48 = 4x
<u>Divide both sides by 4:</u> 12 = x
Step 4: Check
<em>Plug in x to verify it is a solution.</em>
f(12) = 4(12) + 6
f(12) = 48 + 6
f(12) = 54
