Answer:
The answer is B.
Step-by-step explanation:
From the interval -6 < x < 0, the line is straight which is linear equation. The line shows its going down so it will be decreasing gradient.
Answer:
C) 4
Step-by-step explanation:
Answer:
It cannot be further simplified
Step-by-step explanation:
11 is a prime number, so there are no numbers that can go into 14 and 11 (besides 1 and 1 would not simplify the problem)
Answer:
Coordinate Q is (0.8, 0.7)
Step-by-step explanation:
We are told that the coordinates of point Pare (0.6,0.1).
This means that along the x-axis, x = 0.6 and along the y-axis, y = 0.1.
Now, by inspection of the graph, we can see that when we count boxes from the origin to the point P, we have 6 boxes. Thus, each box corresponds to 0.1. So, for point Q, from the origin to that point, on the x-axis, we have 8 boxes. Since one box = 0.1, then the x - value of Coordinate Q is 0.8.
On the y - axis, we see that we have one box from the origin up for the corresponding y-value of coordinate P.
This means that one box is 0.1.
For coordinate Q, we will count 7 boxes. Thus, y-value of coordinate Q is 0.7.
Thus,coordinate Q is (0.8, 0.7)
Answers:
(a) p + m = 5
0.8m = 2
(b) 2.5 lb peanuts and 2.5 lb mixture
Explanations:
(a) Note that we just need to mix the following to get the desired mixture:
- peanut (p) - peanuts whose amount is p
- mixture (m) - mixture (80% almonds and 20% peanuts) that has an amount of m; we denote this as
By mixing the peanuts (p) and the mixture (m), we combine their weights and equate it 5 since the mixture has a total of 5 lb.
Hence,
p + m = 5
Note that the desired 5-lb mixture has 40% almonds. Thus, the amount of almonds in the desired mixture is 2 lb (40% of 5 lb, which is 0.4 multiplied by 5).
Moreover, since the mixture (m) has 80% almonds, the weight of almonds that mixture is 0.8m.
Since we mix mixture (m) with the pure peanut to get the desired mixture, the almonds in the desired mixture are also the almonds in the mixture (m).
So, we can equate the amount of almonds in mixture (m) to the amount of almonds in the desired measure.
In terms mathematical equation,
0.8m = 2
Hence, the system of equations that models the situation is
p + m = 5
0.8m = 2
(b) To solve the system obtained in (a), we first label the equations for easy reference,
(1) p + m = 5
(2) 0.8m = 2
Note that using equation (2), we can solve the value of m by dividing both sides of (2) by 0.8. By doing this, we have
m = 2.5
Then, we substitute the value of m to equation (1) to solve for p:
p + m = 5
p + 2.5 = 5 (3)
To solve for p, we subtract both sides of equation (3) by 2.5. Thus,
p = 2.5
Hence,
m = 2.5, p = 2.5
Therefore, the solution to the system is 2.5 lb peanuts and 2.5 lb mixture.
