Answer:
C
Step-by-step explanation:
Answer:
Division expression 13 ÷ 33
Fraction 13 / 33
Step-by-step explanation:
Answer:
Step-by-step explanation:
We know that the system of equations
a
1
x+b
1
y=c
1
a
2
x+b
2
y=c
2
has infinitely many solutions, if
a
2
a
1
=
b
2
b
1
=
c
2
c
1
Here, a
1
=2,b
1
=3,c
1
=4,a
2
=k+2,b
2
=6,c
2
=3k+2.
Therefore, the given system of equations will have infinitely many solutions, if
k+2
2
=
6
3
=
3k+2
4
⇒
k+2
2
=
6
3
and
6
3
=
3k+2
4
⇒
k+2
2
=
2
1
and
2
1
=
3k+2
4
⇒k+2=4 and 3k+2=8
⇒k=2 and k=2
⇒k=2
Hence, the given system of equations will have infinitely many solutions, if k=2.
The blue mines X. the answer would be 1.
Answer:
The equation that matches this situation is y = 8.34x + 25 ⇒ B
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
- m is the slope (rate of change)
- b is the y-intercept (initial value)
The rule of the slope is m = Δy/Δx, where
∵ Lisa collects rainwater in a barrel that weighs 25 pounds
∴ The initial value of the weight is 25 pounds
∴ b = 25
∵ When there are 10 gallons of water in the barrel, the total weight
of the barrel and the water is 108.4 pounds
∴ At x = 10, y = 108.4
∵ When there are 20 gallons of water, the total weight is 191.8 pounds
∴ At x = 20, y = 191.8
→ Find Δx and Δy
∵ Δx = 20 - 10 = 10
∵ Δy = 191.8 - 108.4 = 83.4
→ Substitute them in the rule of the slope above
∴ m =
∴ m = 8.34
→ Substitute the values of m and b in the form of the equation above
∵ y = 8.34x + 25
∴ The equation that matches this situation is y = 8.34x + 25