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cestrela7 [59]
3 years ago
8

Write the equation of the line that passes through the points (1,9) and (-1,1). Put

Mathematics
1 answer:
SpyIntel [72]3 years ago
7 0

Answer:

Point slope form

                 y - 9 = 4(x-1)

Equation of the straight line passing through the point (1,9) and slope 'm' = 4 is    4 x - y +5=0

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that the points are (1,9) and (-1,1)

slope of the line

                m = \frac{y_{2}-y_{1}  }{x_{2} - x_{1} }

               m = \frac{1-9}{-1-1}

             m = 4

<u><em>step(ii):-</em></u>

Equation of the straight line passing through the point (1,9) and slope 'm' = 4

                     y-y₁ = m( x-x₁)

                   y - 9 = 4(x-1)

                  y -9 = 4x-4

           4 x - y -4+9 =0

          4 x - y +5=0

Equation of the straight line passing through the point (1,9) and slope 'm' = 4 is    4 x - y +5=0

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Find a101of the sequence 5, 8, 11
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Answer:

305

Step-by-step explanation:

find a101of the sequence 5, 8, 11

You want the 101th term of this sequence: 5, 8, 11

a_1 = 5

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a_101 = (101 - 1)*3 + 5

a_101 = 100*3 + 5

a_101 = 300 + 5 = 305

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3 years ago
V5. Suppose you invest $5,000 at 9% interest, compounded annually, for 10 years. Determine the future value of your investment,
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Answer: $11836.8

Step-by-step explanation:

Given. That :

Amount invested = $5000

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Period = 10 years, compounded annually

Using the compound interest formula :

A = p(1 + r/n)^nt

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t = period

A = 5000(1 + 0.09/1)^(1*10)

A = 5000(1.09)^10

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3 years ago
(2,2) (2,-4) (-5,-4)(-5,2)
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3 years ago
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Which choices listed below indicate that a linear model is not the best fit for a dataset? Choose all that apply.
Lera25 [3.4K]
<span>The following indicate that a linear model is not the best fit for a dataset:
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• Scatterplot shows a curve pattern. 
• Residual plot shows no pattern. 
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6 0
3 years ago
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Advocard [28]
1)

An irrational number is a number that a) can't be written as a fraction of two whole numbers AND b) is an infinite decimal without any sort of pattern.

For the first answer choice, clearly \frac{1}{3} does not pass the first criterion so we look at the second choice.

Let's come back to \sqrt{2} and \pi.

\frac{2}{9} doesn't meet our first criterion, and let's skip \sqrt{3} for now.

It is often easier to disprove an irrational number than to prove one. There are a few famous irrationals to know (although there is an infinite number of irrationals). The most common are \sqrt{2},  \pi, e,  \sqrt{3}. For now, it's just helpful to know these and recognize them.

So we can check off \sqrt{2},  \pi and \sqrt{3}.

2) 

For this next question, we know that \sqrt{64} = 8. Clearly this isn't irrational. Likewise, \frac{1}{2} isn't irrational. \frac{16}{4} =  \frac{4}{4} = 1, which is rational, leaving only \frac{ \sqrt{20}}{5} =  \frac{2 \sqrt{5} }{5}. By process of elimination, this is the correct answer. Indeed, \sqrt{5} is an irrational number.

3) This notation means that we have 0.3636363636... and so on, to an infinite number of digits. It is called a repeating decimal.

But it can be written as a fraction because its pattern repeats, unlike for an irrational number.

Let's say x=0.36363636.... Would you agree that 100x=36.36363636...? (We choose to multiply by 100 because there are two decimals that repeat. For 1, choose 10, for 3 choose 1,000, and so on.)

Now, let's subtract x from 100x and solve.

100x=36.36363636\\-x \ \ \ \ \ \ \ -0.36363636\\99x=36\\\\x= \dfrac{36}{99}= \dfrac{4}{11}

Voila!
4 0
3 years ago
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