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3 years ago

(4x – 3) + (–x + 5) =

Mathematics

2 answers:

tekilochka [14]3 years ago

7 0

Answer:

3x+2

Step-by-step explanation:

Volgvan3 years ago

5 0

Answer:

x=-0.4

Step-by-step explanation:

(4x-3)+(-x+5)=0

Distribute the positive

4x-3+x+5=0

Combine like terms

5x+2=0

5x=-2

x=-0.4

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-74 + 36.2=<br> Step by step

My name is Ann [436]

Step-by-step explanation:

-74+36.2=-37.8

I hope it will help you

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3 years ago

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a triangular pyramid has a volume 150 cubic centimeters. which of the following represents the volume of a triangular prism with

soldi70 [24.7K]

Wouldn't it be 150 cubic centimeters? Since it has the same area of base and height, it would be the same prism.

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3 years ago

WILL GIVE BRAINLIEST. If x+y=3 and 3x+5y=13, then x-y is equal to?

Alex17521 [72]

Answer:

(1,2)

y=2

x=1

Step-by-step explanation:

x+y=3

3x+5y=13

solve the equation

x=3-y

3x+5y=13

substitute the value of x into an equation

3(3-y)+5y=13

distribute

9-3y+5y=13

add -3y to 5y

9+2y=13

subtract 9 from both sides

2y=4

divide both sides by 2

y=2

substitute the value of y into an equation

x=3-2

subtract 3 to 2

x=1

--------

(1,2)

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6 0

2 years ago

Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficie

Dvinal [7]

For part (a), you have

$\dfrac x{x^2+x-6}=\dfrac x{(x+3)(x-2)}=\dfrac a{x+3}+\dfrac b{x-2}$
$x=a(x-2)+b(x+3)$

If $x=2$ , then $2=b(2-3)\implies b=-2$ .

If $x=-3$ , then $-3=a(-3-2)\implies a=\dfrac35$ .

So,

$\dfrac x{x^2+x-6}=\dfrac 3{5(x+3)}-\dfrac 2{x-2}$

For part (b), since the degrees of the numerator and denominator are the same, you first need to find the quotient and remainder upon division.

$\dfrac{x^2}{x^2+x+2}=\dfrac{x^2+x+2-x-2}{x^2+x+2}=1-\dfrac{x+2}{x^2+x+2}$

In the remainder term, the denominator $x^2+x+2$ can't be factorized into linear components with real coefficients, since the discriminant is negative $(1-4\times1\times2=-7)$ . However, you can still factorized over the complex numbers, so a partial fraction decomposition in terms of complexes does exist.

$x^2+x+2=0\implies x=-\dfrac12\pm\dfrac{\sqrt7}2i$
$\implies x^2+x+2=\left(x-\left(-\dfrac12+\dfrac{\sqrt7}2i\right)\right)\left(x-\left(-\dfrac12-\dfrac{\sqrt7}2i\right)\right)$
$\implies x^2+x+2=\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)$

Then you have

$\dfrac{x+2}{x^2+x+2}=\dfrac a{x+\dfrac12-\dfrac{\sqrt7}2i}+\dfrac b{x+\dfrac12+\dfrac{\sqrt7}2i}$
$x+2=a\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)+b\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)$

When $x=-\dfrac12-\dfrac{\sqrt7}2i$ , you have

$-\dfrac12-\dfrac{\sqrt7}2i+2=b\left(-\dfrac12-\dfrac{\sqrt7}2i+\dfrac12-\dfrac{\sqrt7}2i\right)$
$\dfrac32-\dfrac{\sqrt7}2i=-\sqrt7ib$
$b=\dfrac12+\dfrac3{2\sqrt7}i=\dfrac1{14}(7+3\sqrt7i)$

When $x=-\dfrac12+\dfrac{\sqrt7}2i$ , you have

$-\dfrac12+\dfrac{\sqrt7}2i+2=a\left(-\dfrac12+\dfrac{\sqrt7}2i+\dfrac12+\dfrac{\sqrt7}2i\right)$
$\dfrac32+\dfrac{\sqrt7}2i=\sqrt7ia$
$a=\dfrac12-\dfrac3{2\sqrt7}i=\dfrac1{14}(7-3\sqrt7i)$

So, you could write

$\dfrac{x^2}{x^2+x+2}=1-\dfrac{x+2}{x^2+x+2}=1-\dfrac {7-3\sqrt7i}{14\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)}-\dfrac {7+3\sqrt7i}{14\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)}$

but that may or may not be considered acceptable by that webpage.

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3 years ago

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What is 27 times 30 to the power of 2?(“real” question)

tankabanditka [31]

Answer:

24300

Step-by-step explanation:

first find the square for 30 * 30

then multiply!

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2 years ago