Answer:
The number is 72.
Step-by-step explanation:
Let the digits be x and x - 5 where x is the first digit.
(As the number reversed = 3/8 of the original number the first digit must be the largest),
Consider the reverse digit number:
The original number = 10x + (x - 5) so the reverse number is 10(x - 5) + x and
10(x - 5) + x = 3/8(10x + (x - 5))
11x - 50 = 3/8(11x - 5)
11x - 50 = 33/8 x - 15/8 Multiply through by 8:
88x - 400 = 33x - 15
55x = 385
x = 7
and x-5 = 2.
Answer:
B. 24:48
Step-by-step explanation:
3:6 is equivalent to 1:2 which is also equivalent to 24:48.
3. g(x) = (x-3)^2 -5
Replace g(x) with y
y = (x-3)^2 -5
Switch the x and the Y:
x = (y-3)^2 -5
Solve for y:
Add 5 to both sides:
x + 5 = (y-3)^2
Take the square root of both sides:
+ /- SQRT(x+5) = y -3
Add 3 to both sides:
y = +/- SQRT(x +5) +3
The solution is both the positive and negative:
SQRT(x +5) +3 and -SQRT(x+5) +3
7. Following the same steps as 3
The answer is SQRT(x-2) -6 and -SQRT(X-2) -6
9. Following thw same steps as 3.
The answer is SQRT(2(x+4)) +2 and - SQRT(2(x+4))
Answer: x = 5, y = 2; Solution = (5, 2)
Step-by-step explanation:
Substitution
2x + y = 12
x + 2y = 9
x + 2y = 9
Subtract 2y from both sides
x = 9 - 2y
Now, substitute x for (9 - 2y) in the first equation
2x + y = 12
2 (9 - 2y) + y = 12
Distribute 2
18 - 4y + y = 12
18 - 3y = 12
Subtract 18 from both sides
-3y = -6
Divide both sides by -3
<em>y = 2</em>
Now to find x, substitute 2 for y in (x = 9 - 2y)
x = 9 - 2y
x = 9 - 2(2)
x = 9 - 4
<em>x = 5</em>
Solution: (5, 2)
Elimination
2x + y = 12
x + 2y = 9
Multiply the second equation by -2 to find y
2x + y = 12
(x + 2y = 9) -2
2x + y = 12
-2x - 4y = -18
Add both equations
2x and -2x are cancelled out
You get:
-3y = -6
Divide both sides by -3
<em>y = 2</em>
Substitute 2 for y in any of the equations to find x
I chose x + 2y = 9
x + 2y = 9
x + 2 (2) = 9
x + 4 = 9
Subtract both sides by 4
<em>x = 5</em>
Solution = (5, 2)
Btw you can use any of these methods, I used both so you could know that you get the same answer no matter the method.
Hope I helped!
