Answer: For the sum of 130
First: $90
Second: $40
Step-by-step explanation:
We write equations for each part of this situation.
<u>The Total Charge</u>
Together they charged 1550. This means 1550 is made up of the first mechanics rate for 15 hours and the second's rate for 5 hours. Lets call the first's rate a, so he charges 15a. The second's let's call b. He charges 5b. We add them together 15a+5b=1550.
<u>The Sum of the Rates</u>
Since the first's rate is a and the second is b, we can write a+b=130 since their sum is 130.
We solve for a and b by substituting one equation into another. Solve for the variable. Then substitute the value into the equation to find the other variable.
For a+b=130, rearrange to b=130-a and substitute into 15a+5b=1550.
15a + 5 (130-a)=1550
15a+650-5a=1550
10a+650-650=1550-650
10a=900
a=$90 was charged by the first mechanic.
We substitute to find the second mechanic's rate.
90+b=130
90-90+b=130-90
b= $40 was charged by the second mechanic
Answer:
<u>-2</u>
Step-by-step explanation:
Find two points which lie on the line :
- Take (-2, -1) and (-1, -3)
Formula for slope (m) :
- m = y₂ - y₁ / x₂ - x₁
- m = -3 + 1 / -1 + 2
- m = -2/1
- m = <u>-2</u>
Compute the derivative dy/dx using the power, product, and chain rules. Given
x³ + y³ = 11xy
differentiate both sides with respect to x to get
3x² + 3y² dy/dx = 11y + 11x dy/dx
Solve for dy/dx :
(3y² - 11x) dy/dx = 11y - 3x²
dy/dx = (11y - 3x²)/(3y² - 11x)
The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when
11y - 3x² = 0
or
y = 3/11 x²
(provided that 3y² - 11x ≠ 0)
Substitute y into into the original equation:
x³ + (3/11 x²)³ = 11x (3/11 x²)
x³ + (3/11)³ x⁶ = 3x³
(3/11)³ x⁶ - 2x³ = 0
x³ ((3/11)³ x³ - 2) = 0
One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with
(3/11)³ x³ - 2 = 0
(3/11 x)³ - 2 = 0
(3/11 x)³ = 2
3/11 x = ³√2
x = (11•³√2)/3
Solving for y gives
y = 3/11 x²
y = 3/11 ((11•³√2)/3)²
y = (11•³√4)/3
So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).
Answer:
1. According to the angle bisector theorem, DAC = BAC
2. Same kind of goes for BC
3. X must be equal in both equations. x= 3
9(3) -7 = 20
4(3) +8 = 20
Hope this helped!
Answer:
-14
Step-by-step explanation:
step 1:
Subtract 11 from both sides.
y+11−11<−3−11
y<−14
