Since y = x - 2, replace the y in 8x + 13y = 2 with x - 2:
8x + 13(x - 2) = 2
Simplify the equation by multiplying 13 by (x - 2):
8x + 13x - 26 = 2
Add 26 on each side:
8x + 13x = 28
Add like terms:
21x = 28
Divide by 21 on each side:
x = 28/21
Simplify the fraction:
x = 4/3
Now that we have solved for x we can now use it to plug into one of the equations to solve for y. Plug in 4/3 for x in y = x - 2:
y = (4/3) - 2
Subtract:
y = -2/3
Let's check the work to make sure it is right:
8(4/3) + 13(-2/3) = 2
32/3 + -26/3 = 2
6/3 = 2
2 = 2
As you can see the system of equations has been solved correctly.
Answer:
<-8.60, -12.29>
Step-by-step explanation:
Pictuas shown in the attached image to represent the direction 35 west of south of the vector velocity and understand which trig function to use for its components. See the actual vector velocity as the hypotenuse of a right angle triangle.
The vertical component would be pointing down, and its magnitude would result from the use of the cosine of the angle (since it involves the adjacent side to the angle):
15 * cos (35) = 12.29
the horizontal component is pointing left, and its magnitude would be the result of the use of the sine of the angle (it involves the opposite side to the angle):
15 * (sin*35) = 8.60.
Using the fact that the components are pointing down and pointing left, we need to include a negative sign to both.
Therefore the component form of the vector is: <-8.60, -12.29>
Answer:
18
Step-by-step explanation:
Answer:
It'll take 6.97 minutes to have only 1 package remaining.
Step-by-step explanation:
This problem can be interpreted as a compounded interest problem, where the initial amount is 172 packages the interest is 52% and the final amount is 1 package. The formula for compounded interest is:
M = C*(1 - r)^(t)
Where M is the final amount, C is the initial amount, r is the interest rate and t is time elapsed. So we have:
1 = 172*(1 - 0.52)^(t)
1 = 172*(0.48)^t
1/172 = 0.48^t
0.48^t = 0.006
log(0.48^t) = log(0.006)
t*log(0.48) = log(0.006)
-0.734*t = -5.116
t = 6.97
It'll take 6.97 minutes to have only 1 package remaining.
Answer:
Step-by-step explanation:
<u>Formula for area of rectangle:</u>
= length × width
<u>Area of the smaller rectangle:</u>
length = 7
width = 6
= 7 × 6
= 42
<u>Area of the larger rectangle:</u>
length = 7 + 4 = 11
width = 6 + 2 = 8
= 11 × 8
= 88
<u>Area of the shaded region:</u>
= Area of the larger rectangle - Area of the smaller rectangle
= 88 - 42
= 46
Hope this helped!
<h3>~AH1807</h3>