The linear equation that represents the line that passes through the points (4,5) and (0,-3) is given by:
B. y = 2x - 3
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The line passes through (0,-3), that is, when x = 0, y = -3, hence the y-intercept is of b = -3.
The slope is given by the <u>change in y divided by the change in x</u>, hence:
m = (5 - (-3))/(4 - 0) = 2
Hence the equation is:
y = 2x - 3.
Which means that option B is correct.
More can be learned about linear equations at brainly.com/question/24808124
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There are 85 candy bars in each box, and he will have 340 candy bars left after he gives three boxes to a friend.
Answer:
isn't it i96
Step-by-step explanation:
because you have 97 I's and you are taking one away... So, yeah, i96... Unless I am wrong. Then, I am sorry hehe
Unless you mean i^97. Then, it is 0 because i^97 is just i and i - i =0
For (2), start with the base case. When n = 2, we have
(n + 1)! = (2 + 1)! = 3! = 6
2ⁿ = 2² = 4
6 > 4, so the case of n = 2 is true.
Now assume the inequality holds for n = k, so that
(k + 1)! > 2ᵏ
Under this hypothesis, we want to show the inequality holds for n = k + 1. By definition of factorial, we have
((k + 1) + 1)! = (k + 2)! = (k + 2) (k + 1)!
Then by our hypothesis,
(k + 2) (k + 1)! > (k + 2) 2ᵏ = k•2ᵏ + 2ᵏ⁺¹
and k•2ᵏ ≥ 2•2² = 8, so
k•2ᵏ + 2ᵏ⁺¹ ≥ 8 + 2ᵏ⁺¹ > 2ᵏ⁺¹
which proves the claim.
Unfortunately, I can't help you with (3). Sorry!
Answer:
-44
Step-by-step explanation:
(-4+1)+(10-51)
-4+1+10-51
-3-41
-44
