Answer: x° = 20
Steps:
100 + x + 3x = 180
x + 3x = 80
4x = 80
x = 80/4
x = 20
Check:
100 + x + 3x = 180
100 + 20 + 3(20) = 180
100 + 20 + 60 = 180
180 = 180 ✅
Answer:
x = ± 4
y = - 2
Step-by-step explanation:
y = 0.5x² - 10 ------------------------(I)
y = -x² + 14 ------------------------(II)
Substitute the y value in equation (II)
0.5x² - 10 = -x² + 14 {Add x² to both sides}
0.5x² + x² -10 = 14 {combine like terms}
1.5x² - 10 = 14 {Add 10 to both sides}
1.5x² = 14 + 10
1.5x² = 24 {Divide both sides by 1.5}
1.5x²/1.5 = 24/1.5
x² = 16
x = ±4
Substitute x = 4 in (I)
y = 0.5 * 4² - 10
= 0.5*16 - 10
= 8- 10
y = -2
Substitute x = -4 in (I)
y = 0.5 * (-4)² - 10
= 0.5*16 - 10
= 8- 10
y = -2
5x = 6x-7
subtract 6x from each side
-x=-7
x=7
Answer:
The length of the lights is 2088 inches
Step-by-step explanation:
<em>The question is mixed up with another (See comment for correct question)</em>
Given
Required
The perimeter of the deck (this is what the question implies)
The perimeter (P) is:
Answer:
x = 10
Step-by-step explanation:
Solve for x:
-8 (8 - x) = (4 (x + 10))/5
Multiply both sides by 5:
-8×5 (8 - x) = (5×4 (x + 10))/5
(5×4 (x + 10))/5 = 5/5×4 (x + 10) = 4 (x + 10):
-8×5 (8 - x) = 4 (x + 10)
5 (-8) = -40:
-40 (8 - x) = 4 (x + 10)
Expand out terms of the left hand side:
40 x - 320 = 4 (x + 10)
Expand out terms of the right hand side:
40 x - 320 = 4 x + 40
Subtract 4 x from both sides:
(40 x - 4 x) - 320 = (4 x - 4 x) + 40
40 x - 4 x = 36 x:
36 x - 320 = (4 x - 4 x) + 40
4 x - 4 x = 0:
36 x - 320 = 40
Add 320 to both sides:
36 x + (320 - 320) = 320 + 40
320 - 320 = 0:
36 x = 40 + 320
40 + 320 = 360:
36 x = 360
Divide both sides of 36 x = 360 by 36:
(36 x)/36 = 360/36
36/36 = 1:
x = 360/36
The gcd of 360 and 36 is 36, so 360/36 = (36×10)/(36×1) = 36/36×10 = 10:
Answer: x = 10
