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2 years ago

If t(n) = 15 - 2.5n, how do I find t1,t2,t3,and tn+1? I also have to express tn+1-tn in its simplest form.

Mathematics

1 answer:

Anvisha [2.4K]2 years ago

8 0

Answer:

Just substitute, and the simplified form is 1

Step-by-step explanation:

Substitute the values needed into the original equation. For example, if n=1

t(1)=15-2.5(1)=15-2.5=12.5. Or, if tn+1 substitute f(tn+1)=15-2.5(tn+1) and simplify.

tn+1-tn in its simplest form is just 1, as tn and -tn cancel out to leave 1.

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3 years ago

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2 years ago

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3 years ago

Write an equation in slope-intercept form of the line that passes through (-1, 4) and (0, 2).

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Answer:

$y=-2x+2$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

<u>1) Determine the slope</u>

$m=\frac{y_2-y_1}{x_2-x_1}$ where the two given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (-1, 4) and (0, 2)

$=\frac{2-4}{0-(-1)}\\=\frac{-2}{0+1}\\=\frac{-2}{1}\\= -2$

Therefore, the slope of the line is -2. Plug this into $y=mx+b$ :

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<u>2) Determine the y-intercept</u>

$y=-2x+b$

Recall that the y-intercept is the value of y when the line crosses the y-axis, meaning that the y-intercept occurs when x is equal to 0.

One of the given points is (0,2). Notice how y=2 when x=0. Therefore, the y-intercept of the line is 2.

Plug this back into the equation:

$y=-2x+2$

I hope this helps!

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3 years ago