9514 1404 393
Answer:
A) 5x+12 = -12x-12
D) 5x+12 = -5x-12
Step-by-step explanation:
If you subtract the right side expression from both sides, you will get an equation with something equal to zero. If the 'something' has a variable in it, there is exactly one solution.
A: (5x+12) -(-12x-12) = 17x+24 = 0 . . . one solution
B: (5x+12) -(5x-5) = 17 = 0 . . . . no solutions
C: (5x+12)-(5x+12) = 0 = 0 . . . . infinite solutions
D: (5x+12) -(-5x-12) = 10x +24 = 0 . . . one solution
Answer:
Shorter piece= 4 ft, longer piece= 13 ft
Step-by-step explanation:
If shorter piece is x
Longer pc is 2x + 5
Together they make 17 feet
So x + 2x + 5 = 17
3 x + 5 = 17
3x = 17 - 5 = 12
3x = 12
X = 12/ 3 = 4
So shorter pc is 4 feet
Longer pc is 2 x + 5
= (2 x 4) + 5
= 8 + 5 = 13
<h3>
Answer: Approximately 119.76 meters</h3>
===================================================
Work Shown:
x = starting length of the shadow
y = height of the pole
tan(angle) = opposite/adjacent
tan(58) = y/x
1.6003345 = y/x
1.6003345x = y
x = y/1.6003345
x = (1/1.6003345)y
x = 0.62486936y
-------------------------
When the angle changes, the adjacent side gets 90 meters longer
tan(angle) = opposite/adjacent
tan(36) = y/(x+90)
0.72654253 = y/(0.62486936y+90)
0.72654253(0.62486936y+90) = y
0.453994166y + 65.3888277 = y
65.3888277 = y-0.453994166y
65.3888277 = 0.546005834y
0.546005834y = 65.3888277
y = 65.3888277/0.546005834
y = 119.758478075162
y = 119.76
The height of the pole is about 119.76 meters.
Answer:
Step-by-step explanation:
Let x = gallons consumed by car 1
Let y = gallons consumed by car 2
We set up our equations:
35x+40y = 1850 eq1
x+y = 50 eq2
Substituting eq 2 into eq 1,
35x+40(50-x) = 1850
35x+2000-40x = 1850
-5x+2000 = 1850
-5x = -150
x = 30
Substitute value of x into eq 2.
x+y = 50
30+y = 50
y = 20
Car 1 consumes 30 gallons of gas.
Car 2 consumes 20 gallons of gas.
Answer:
(f · g)(x) = 4x³ + x² - 20x - 5
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra I</u>
- Combining Like Terms
- Expand by FOIL (First Outside Inside Last)
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = 4x + 1
g(x) = x² - 5
(f · g)(x) is f(x)g(x)
<u>Step 2: Find (f · g)(x)</u>
- Substitute: (f · g)(x) = (4x + 1)(x² - 5)
- Expand [FOIL]: (f · g)(x) = 4x³ - 20x + x² - 5
- Combine like terms: (f · g)(x) = 4x³ + x² - 20x - 5
