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3 years ago

If CE= 7x+4 x+3 + 8x-9 = 7x+4

1 answer:

4 0

The answer is 39.

Explanation:
To find the x, you need to start by adding your “like” terms on each side of the equal sign. This means the parts that you can add together. So, on the left side, you would add 3 and -9 together, which will make -6. Then, you would add x and 8x together, which would make 9x. So your left side will look like “9x-6”. There is nothing you can add together on the right side, so now you move on to the second step: combining the terms on both sides. You can do this by knowing that the opposite of subtraction is addition, and it’s the same the other way. Let’s look at our equation now:
9x-6=7x+4

9x and 7x are “like terms” so we can subtract. So now we have:
2x-6=4

We still need to make x be by itself, so now we can move the -6 over to the 4. We add because the opposite of subtraction is addition. So now we have:
2x=10

When a number is next to a missing number, that means they are being multiplied, and the opposite of multiplication is division. So we can divide 10 by 2, which equals five. So, x=5 and we can add that to our other missing number, CE. Replace “x” with “5” and you will see that CE=39.

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Use the definition of a Taylor series to find the first three non zero terms of the Taylor series for the given function centere

Ket [755]

Answer:

$e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...$

$\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n$

Step-by-step explanation:

<u>Taylor series</u> expansions of f(x) at the point x = a

$\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...$

This expansion is valid only if $\text{f}\:^{(n)}(a)$ exists and is finite for all $n \in \mathbb{N}$ , and for values of x for which the infinite series converges.

$\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1$

$\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...$

$\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}$

$\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4$

$\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4$

$\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4$

Substituting the values in the series expansion gives:

$e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...$

Factoring out e⁴:

$e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right]$

<u>Taylor Series summation notation</u>:

$\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n$

Therefore:

$\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n$

7 0

1 year ago

Choose the solutions to the quadratic equation x2 – 8x – 9 = 0. –21 –1 9 29

8090 [49]

Answer:

-1 and 9

Step-by-step explanation:

To solve the quadratic, factor and set its factors equal to 0. Factoring is the action of breaking up a polynomial into pieces which multiply to make it. The factors are found by multiplying numbers to make C and add to B of $ax^2+bx+c$ .

Here c = -9 and b = -8. The numbers -9 and 1 multiply to -9 and add to -8. These are the factors (x-9)(x+1).

Set each equal to 0 and solve for x.

x-9 = 0

x = 9

x+1 =0

x = -1

6 0

3 years ago

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quester [9]

Answer:

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4 0

2 years ago

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Find all missing variables and measures of each angle

iVinArrow [24]

Answer:

x= 18

10x=180

x=180/10

x=18

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3 years ago

The Lisbon’s new heat pump cost $4,500.

Alex73 [517]

Answer:

4.1 years.

Step-by-step explanation:

We have been given that The Lisbon’s new heat pump cost $4,500. They bought it to replace their old furnace and air conditioner which cost about $2,800 a year to run. The heat pump will save them approximately 39% a year.

Yearly cost was 2800 at first and the pump will save 39% of 2800. So annual saving with new heat pump will be:

$\frac{39}{100}*2800=0.39*2800$