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stellarik [79]
3 years ago
5

Can someone pls help me answer this :/​

Mathematics
1 answer:
eimsori [14]3 years ago
5 0

Answer:

y = - \frac{3}{2} x + 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

Calculate m using the slope formula

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

with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = \frac{0-6}{4-0} = \frac{-6}{4} = - \frac{3}{2}

Since the line crosses the y- axis at (0, 6) ⇒ b = 6

y = - \frac{3}{2} x + 6 ← equation of line

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Integral of x"2+4/x"2+4x+3
dolphi86 [110]

I'm guessing you mean

\displaystyle \int\frac{x^2+4}{x^2+4x+3}\,\mathrm dx

First, compute the quotient:

\displaystyle \frac{x^2+4}{x^2+4x+3} = 1 + \frac{4x-1}{x^2+4x+3}

Split up the remainder term into partial fractions. Notice that

<em>x</em> ² + 4<em>x</em> + 3 = (<em>x</em> + 3) (<em>x</em> + 1)

Then

\displaystyle \frac{4x-1}{x^2+4x+3} = \frac a{x+3} + \frac b{x+1} \\\\ \implies 4x - 1 = a(x+1) + b(x+3) = (a+b)x + a+3b \\\\ \implies a+b=4 \text{ and }a+3b = -1 \\\\ \implies a=\frac{13}2\text{ and }b=-\frac52

So the integral becomes

\displaystyle \int \left(1 + \frac{13}{2(x+3)} - \frac{5}{2(x+1)}\right) \,\mathrm dx = \boxed{x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C}

We can simplify the result somewhat:

\displaystyle x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C \\\\ = x + \frac12 \left(13\ln|x+3| - 5\ln|x+1|\right) + C \\\\ = x + \frac12 \left(\ln\left|(x+3)^{13}\right| - \ln\left|(x+1)^5\right|\right) + C \\\\ = x + \frac12 \ln\left|\frac{(x+3)^{13}}{(x+1)^5}\right| + C \\\\ = \boxed{x + \ln\sqrt{\left|\frac{(x+3)^{13}}{(x+1)^5}\right|} + C}

3 0
3 years ago
Determine the range of the following graph:
Gnoma [55]

Answer:(-infinity, infinity)

Step-by-step explanation: the end behavior shows that it forever goes up or down.

4 0
2 years ago
Identify the variables in this Algebraic Expression<br> X+ 4y - 9
Lesechka [4]

Answer:

The expression x + 4y - 9 has two variables x and y.

Step-by-step explanation:

<u>What is a variable?</u>

A variable is a letter, for instance x or y, that represents an unknown number.

Given the expression

x + 4y - 9

The given expression has three terms which are x, 4y, and -9.

Here:

  • The term 'x' is the unknown variable x.
  • The term '4y' has a coefficient (the number next to a variable y) of 4.
  • The term '-6' is a constant.

As we already know that a variable is a letter, for instance x or y, that represents an unknown number. In other words, the values of x, or y are unknown to us.

Thus, the expression x + 4y - 9 has two variables x and y.

5 0
3 years ago
The function for the cost of materials to make a muffin is f(x)=3/4x+3, where x is the number of muffins. The function for the s
scoray [572]
<span>the first one is from walmart which is 5.99$ the other store sells it for 3.49 which one is better to buy

</span>
8 0
3 years ago
Help asap
ZanzabumX [31]

Your fruit punch recipe can be composed of 4 juice containers of lemonade, 2 juice containers of orange juice, 2 juice containers of grape juice, 2 juice containers of apple juice, 2 juice containers of cranberry juice, and 2 juice containers of pineapple juice.

<h3>Unit conversion</h3>

Unit conversion is a tool very useful to solve some questions. For this exercise, you should know that  1 liter (l) = 1000 milliliters (ml).

The question asks you a design your own fruit punch recipe with exactly 5 liters of punch and includes at least three of the juice.

You have several options, an alternative is to use all juices.

  • Step 1 - Convert the units for each given juice containers

         250 milliliters of lemonade = 0.250 l of lemonade juice

         500 milliliters of orange juice = 0.500 l of orange juice

         250 milliliters of grape juice = 0.250 l of grape juice

         250 milliliters of apple juice= 0.250 l  of apple juice

         500 milliliters of cranberry juice =  0.500 l of cranberry juice

         500 milliliter’s of pineapple juice = 0.500 l of pineapple juice

  • Step 2 -Design your own fruit punch recipe with  exactly 5 liters

 4 juice containers of lemonade = 4* 0.250 l = 1 l of lemonade

 2 juice containers of orange juice= 2* 0.500 l = 1 l of orange juice

2 juice containers of grape juice= 2* 0.250 l = 0.500 l of grape juice

2 juice containers of apple juice= 2* 0.250 l = 0.500 l of apple juice

 2 juice containers of cranberry juice= 2* 0.500 l = 1 l of cranberry juice

 2 juice containers of  pineapple juice= 2* 0.500 l = 1 l pineapple juice

Thus, your own fruit punch recipe is composed of: 4 juice containers of lemonade, 2 juice containers of orange juice, 2 juice containers of grape juice, 2 juice containers of apple juice, 2 juice containers of cranberry juice, and 2 juice containers of pineapple juice.

Read more about the unit conversion for capacity here:

brainly.com/question/14965845

4 0
2 years ago
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