Answer:
Option 2: (1, 0) and (0, -5)
Step-by-step explanation:
Let's solve this system of equations using the elimination method.
Start by labelling the two equations.
5x -y= 5 -----(1)
5x² -y= 5 -----(2)
(2) -(1):
5x² -y -(5x -y)= 5 -5
Expand:
5x² -y -5x +y= 0
5x² -5x= 0
Factorise:
5x(x -1)= 0
5x= 0 or x -1= 0
x= 0 or x= 1
Now that we have found the x values, we can substitute them into either equations to solve for y.
Substitute into (1):
5(0) -y= 5 or 5(1) -y= 5
0 -y= 5 or -y= 5 -5
y= -5 or -y= 0
y= 0
Thus, the solutions are (0, -5) and (1, 0).
Answer:
Step-by-step explanation:
The total number of sums (not distinct) is 
, because we're removing without replacement.
Count the sums that fit the stipulation (sum 
5):
There are 8 sums that work. Therefore, the desired answer is 
Answer:
Last choice.
Step-by-step explanation:
To find the option that is equivalent to this equation, we can begin by narrowing down our options. The slope contains a negative number, meaning the second point must have a lower y value than the first.
Using this criteria, we can eliminate the first and the third answer. Now, we can test the second and fourth answer.
We can test using the slope formula and plugging in values. When the slope formula: 
We get a slope of -5 for both of these equations. Let's plug in the point values to check whether they work:
Choice 2:
-24 = -5(4) + 4
-24 = -20 + 4
-24 ≠ -16
Choice 4:
-16 = -5(4) + 4
-16 = -20 + 4
-16 = -16
Therefore, choice 4 is correct!
Answer: it will take 9 days
Step-by-step explanation:
The water level was initially at 34feet it was receding at the rate of a foot per day. The rate at which it was receding is linear, thus, it is in an arithmetic progression. The formula for the nth term of an arithmetic progression is expressed as
Tn = a+(n-1)d
Where
a is the first term if the sequence
d is the common difference
n is the number of terms.
From the information given,
a = 34 feet because it is the initial height
n is the number of days it will take to get to 26 ft
d = -1 because it is decreasing by 1 foot per day.
Tn = T26 = 26 feet. Therefore, the equation will be
Tn = 34 -1(n-1)
To find for T26,
26= 34 + (n - 1)-1
26 - 34 = -n + 1
n - 1 = 8
n = 8 + 1 = 9
