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DanielleElmas [232]
4 years ago
14

There question is down below, plz help

Mathematics
1 answer:
Anvisha [2.4K]4 years ago
6 0

Adding 7 to the X, would move the original image 7 units to the right, then adding 1 to the Y moves that image up 1 unite.

The image is then reflected across the X axis ( horizontal axis).


The answer is A.

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Evaluate the integral, show all steps please!
zalisa [80]

Answer:

\dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}

Step-by-step explanation:

<u>Fundamental Theorem of Calculus</u>

\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x

Take <u>partial fractions</u> of the given fraction by writing out the fraction as an <u>identity</u>:

\begin{aligned}\dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A}{x-4}+\dfrac{B}{x+2}\\\\\implies \dfrac{x+5}{(x-4)(x+2)} & \equiv \dfrac{A(x+2)}{(x-4)(x+2)}+\dfrac{B(x-4)}{(x-4)(x+2)}\\\\\implies x+5 & \equiv A(x+2)+B(x-4)\end{aligned}

Calculate the values of A and B using substitution:

\textsf{when }x=4 \implies 9 = A(6)+B(0) \implies A=\dfrac{3}{2}

\textsf{when }x=-2 \implies 3 = A(0)+B(-6) \implies B=-\dfrac{1}{2}

Substitute the found values of A and B:

\displaystyle \int \dfrac{x+5}{(x-4)(x+2)}\:\:\text{d}x = \int \dfrac{3}{2(x-4)}-\dfrac{1}{2(x+2)}\:\:\text{d}x

\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ax^n\:\text{d}x=a \int x^n \:\text{d}x$\end{minipage}}

If the terms are multiplied by constants, take them outside the integral:

\implies \displaystyle \dfrac{3}{2} \int \dfrac{1}{x-4}- \dfrac{1}{2} \int \dfrac{1}{x+2}\:\:\text{d}x

\boxed{\begin{minipage}{5 cm}\underline{Integrating}\\\\$\displaystyle \int \dfrac{f'(x)}{f(x)}\:\text{d}x=\ln |f(x)| \:\:(+\text{C})$\end{minipage}}

\implies \dfrac{3}{2} \ln |x-4| - \dfrac{1}{2} \ln |x+2| + \text{C}

Learn more about integration here:

brainly.com/question/27805589

brainly.com/question/28155016

4 0
2 years ago
Estimate the square root of - 27 to the nearest tenth.
Aleonysh [2.5K]

Answer:

C (5.2)

Step-by-step explanation:

5 0
3 years ago
Brenda is planning her birthday party. She wants to have 10.82 liters of punch, 6.5 gallons of ice cream 3.9 pounds of fudge and
faltersainse [42]

The answer is 0.4328 liters hope this helped!


6 0
3 years ago
2.2,<br> Write the ratio 1 2/3: 2 2/3 in the simplest form.<br> ,
gulaghasi [49]

Answer:

1:2

Step-by-step explanation:

this would be the answer as 1 2/3: 2 2/3 are the same as 1:2 if you cancel out the 2/3 from both sides.

6 0
3 years ago
Read 2 more answers
How do you solve:(x-4)(x+2)=0
riadik2000 [5.3K]

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x2−2x−8=0

Step 2: Factor left side of equation.

(x+2)(x−4)=0

Step 3: Set factors equal to 0.

x+2=0 or x−4=0

x=−2 or x=4

5 0
3 years ago
Read 2 more answers
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