Tim had 4 paper fraction pieces, each of thirds, fourths, sixths, and twelfths. He did not have enough pieces to show both 2/4 and 1/3 as equivalent fractions with the same denominator. How could he form enough pieces by making 1 cut with a scissors
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1/3 + 1/6=4/12 + 2/12=6/12=2/4
1/4 + 1/12=3/12 + 1/12= 4/12= 1/3or 1/4
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The real-world problem that could be modeled by a linear function will be y = 60 - 12x.
What is a linear equation?
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
The linear function whose x-intercept is 5 and y-intercept is 60. Then the equation is given as,
x/5 + y/60 = 1
Convert the equation into a slope-intercept form. Then we have
x/5 + y/60 = 1
12x + y = 60
y = 60 - 12x
The real-world problem that could be modeled by a linear function will be y = 60 - 12x.
More about the linear equation link is given below.
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If it is me, my first step would be either doubling the first equation so the coefficients of x in both equations equal to each other, or tripling the second equation so the coefficient of y in both equations is set equal.
2x-9y=6
4x-3y=-7
3(second euation) =12x-9y=-7
second equation subtract the first equation
10x=-13
x=-13/10
Then we can plug x in any of the two original equations and solve for y which i got to be -19/15
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Because a prime number only has factors that are 1 and 0
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Answer:
Based on the data provided, Sergei can make the following predictions and set a benchmark for his performance:
Prediction 1: With consistent training and improvement over the summer, Sergei can predict that he will run the mile faster than 8:45 in his upcoming tryouts. This is based on the pattern of improvement he has shown from 9:30 (eighth grade) to 8:45 (freshman year) and his continued training.
Prediction 2: Sergei can aim to break the 8-minute mark for the mile based on the trend of his improvements. This is a reasonable goal given his past progress, and it aligns with his objective of making the varsity team where all runners need to run under 6:15.
Benchmark: The benchmark against which Sergei is measuring his performance is the time required to run a mile. He's tracking his progress in terms of how long it takes him to complete a mile, aiming to continuously improve and meet the varsity team's standard of running under 6:15 for the mile.