Answer:the third option is the correct answer
Step-by-step explanation:
The given system of linear equations is expressed as
y – 3x = –2 - - - - - - - - - - - -1
y = 4 - - - - - - - - - - - - - 2
The first step is to substitute equation 1 into equation 2. It becomes
4 – 3x = –2
Subtracting 4 from the left hand side and the right hand side of the equation, it becomes
4 - 4 - 3x = –2 - 4
- 3x = - 6
Dividing the left hand side and the right hand side of the equation by - 3, it becomes
- 3x/ - 3 = - 6/ - 3
x = 2
(2, 4)
Answer: 6.125 hour
Explanation:
Train 1 ===> 1 hour = 90 miles
Train 2 ===> 1 hour = 120 miles
1 hour = 90 + 120 = 210 miles apart
210 miles = 1 hour
735 miles = 735 ÷ 210 = 6.125 hours
Great question. The answer is N-1.
Think about doing long division. We append a 0, get another digit in the quotient, multiply and subtract to get a remainder. We can assume that remainder is not zero because then we wouldn't have a repeating decimal. At each step the remainder has to be less than N, because we're dividing by N.
So there are N-1 possibilities for the remainder. On the off chance we generate N-1 digits and N-1 remainders and none repeat, we know the next one will repeat, because we've already generated all the possible remainders.
So the largest size of the repeating portion is N-1. This maximum happens first for 1/7.
Answer:
fourth option
Step-by-step explanation:
let t be tennis balls and g be golf balls, then
5t + 3g = 70 → (1)
2t + 5g = 85 → (2)
Multiplying (1) by 5 and (2) by - 3 will eliminate g
25t + 15g = 350 → (3)
- 6t - 15g = - 255 → (4)
Add (3) and (4) term by term to eliminate g
19t = 95 ( divide both sides by 19 )
t = 5
Substitute t = 5 into either of the 2 equations and solve for g
Substituting into (1)
5(5) + 3g = 70
25 + 3g = 70 ( subtract 25 from both sides )
3g = 45 ( divide both sides by 3 )
g = 15
Thus
$5 for tennis balls and $15 for golf balls
Answer:y = -3x + 10
Step-by-step explanation:
To find an equation of a line that passes through two points, we have to first find the slope between the two equation. We can do this by using the slope formula:
where (x₁, y₁) and (x₂, y₂) are the two points that we are finding the slope between.
Lets make (x₁, y₁) equal to (0, 10) and (x₂, y₂) equal to (3, 1). Now we plug them into the slope formula:
So the slope between the two points is -3.
From here, I would normally take one of the points given to us and plug in the point and slope into the point-slope form of a line and then simplify until we get it in slope-intercept form. But if you look carefully, the y-intercept is given to us as the point (0, 10). So we now know that the y-intercept of the line is 10. We can now take the y-intercept and the slope and plug it into the slope-intercept form of a line to get out equation:
y = mx + b
plug in -3 for m (the slope) and 10 for b (the y-intercept)
y = -3x + 10
So now we have our equation.
I hope you find my answer and explanation helpful. Happy studying. :)
