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Nikolay [14]
3 years ago
12

Write the standard form of the line that contains a slope of 2/3 and passes through the point (1, 1). Include your work in your

final answer. Type your answer in the box provided or use the upload option to submit your solution. Please explain how you got the answer.
Mathematics
1 answer:
Aneli [31]3 years ago
5 0
In this item, we are given with the slope, m = 2/3 and intercept of (1,1). The equation of the line that contains these properties is,

    y - y₁ = m(x - x₁)

Substituting the known values,

   y - 1 = (2/3)(x - 1)

Simplifying,

    3y - 3 = 2x - 2

Further simplifying,

<em>  2x - 3y = -1</em>
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∫<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bxdx%7D%7B%28x%5E%7B2%7D%2B4%29%5E%7B3%7D%20%7D" id="TexFormula1" title="\frac{xdx}{
photoshop1234 [79]

Substitute u=x^2+4 and du=2x\,dx. Then the integral transforms to

\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \int \frac{du}{u^3}

Apply the power rule.

\displaystyle \int \frac{du}{u^3} = -\dfrac1{2u^2} + C

Now put the result back in terms of x.

\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \left(-\dfrac1{2u^2} + C\right) = -\dfrac1{4u^2} + C = \boxed{-\dfrac1{4(x^2+4)^2} + C}

3 0
2 years ago
Banks provide a number of services including all of the following except __________.
olchik [2.2K]

Answer:

A. Payday Lending

Explanation:

Payday Lending is common for <em>small lending companies</em> and <u>not banks</u>. They assist clients who have a <em>minimal amount of salary</em> to borrow <u>a small amount of money with a high interest.</u> The amount of money he can borrow will depend on the amount of salary he receives per month. <em>The client will not be required to give any form of collateral</em> for the borrowed money, thus, the client is said to be <em>high-risk</em>. However, he will have to return the money over a<em> short period of time</em> with an interest rate that is high. Though it is easy to get a loan with this kind of service, you have to make sure that you are employed.

<em>Banks prefer to offer loans to people who have a steady income and a certain amount of salary.  </em>

7 0
3 years ago
If it takes 5 years for an animal population to double, how many years will it take until the population
muminat

9514 1404 393

Answer:

  7.92 years

Step-by-step explanation:

We want to find t such that ...

  3 = 2^(t/5)

where 2^(t/5) is the annual multiplier when doubling time is 5 years.

Taking logs, we have ...

  log(3) = (t/5)log(2)

  t = 5·log(3)/log(2) ≈ 7.92 . . . years

It will take about 7.92 years for the population to triple.

6 0
2 years ago
Note: Figure is not drawn to scale. If m1 + m2 = 134°, what is m3? A. 138° B. 49° C. 46° D. 136°
NemiM [27]

Answer:

Measure of angle 3: C (46 degrees)

Step-by-step explanation:

As there is no attachment, I will assume the question is in reference to a triangle. Knowing that a triangle contains 3 angles the answer can be retrieved through simple steps:

m∠1 + m∠2 + m∠3 = 180 degrees, by Sum of Angles in Triangle Theorem, <em>thus;</em>

Through substitution + algebra:

134 + m∠3 = 180,

m∠3 = 46 degrees

8 0
3 years ago
Point P' is the image of P(3,5) under a reflection across the y-axis.
Kryger [21]

Answer:

(-3,5)

Step-by-step explanation:

In reflections the x axis is the opposite only

8 0
3 years ago
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