X=4
Step 1: Simplify both sides of the equation.
1.5(x+4)-3=4.5(x-2)
(1.5)(x)+(1.5)(4)+ -3 =(4.5)(x)+(4.5)(-2)
(1.5x) + ( 6+-3) =4.5x - 9
(Combine like terms)
1.5x+3=4.5x-9
Step 2: Subtract 4.5x from both sides.
1.5x +3 -4.5x =4.5x=-9-4.5x-3x+3=-9
Step 3: Subtract 3 from both sides.
-3x+3-3=-9-3
-3x=12
Step 4: Divide both by -3
-3x/-3=-12/-3
X=4
Answer:
y=6.2 and x=0.4 or (0.4,6.2)
Step-by-step explanation:
Since both expressions are equal to y, we can set them equal to each other and solve for x:
3x+5=8x+3
5=5x+3
2=5x
2/5=x
0.4=x
Now to solve y:
y=8(2/5)+3
y=16/5+3
y=3.2+3
y=6.2
Check answers:
6.2=3(0.4)+5
6.2=1.2+5
6.2=6.2
6.2=8(0.4)+3
6.2=3.2+3
6.2=6.2
Answers work, so y=6.2 and x=0.4 or (0.4,6.2) as an ordered pair
For this case we have the following equation:
r = 9 sin (θ)
In addition, we have the following change of variables:
y = r * sine (θ)
Rewriting the equation we have:
r = 9 sin (θ)
r = 9 (y / r)
r ^ 2 = 9y
On the other hand:
r ^ 2 = x ^ 2 + y ^ 2
Substituting values:
x ^ 2 + y ^ 2 = 9y
Rewriting:
x ^ 2 + y ^ 2 - 9y = 0
Completing squares:
x ^ 2 + y ^ 2 - 9y + (-9/2) ^ 2 = (-9/2) ^ 2
Rewriting:
x ^ 2 + 1/4 (2y-9) ^ 2 = 81/4
4x ^ 2 + (2y-9) ^ 2 = 81
Answer:
The Cartesian equation is:
4x ^ 2 + (2y-9) ^ 2 = 81
Answer:
He must win 11 more matches to qualify for the bonus.
Step-by-step explanation:
24/36 * 100 = 67% (to the nearest %) - This is the current percentage of what the Tennis player has won.
If we add 14 more matches on to the 36 the player has already played, we know that the Tennis player plays 50 matches in total.
Let's say the Tennis player was playing 100 matches, they would need to win 70 or more to qualify for the bonus. Because the player is playing half this amount of matches, we half the amount of games they have to win...
35/50 games or more must be won to qualify for the bonus. The Tennis player has already won 24 matches, so must win 11 more matches to qualify for the bonus.
Hope that helps!
