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Leya [2.2K]
3 years ago
15

Use the system of two linear equations to answer the question. 2x+5y=4 y=2x+8 Which of the following statements is correct about

the solution of the system? A The x-coordinate is 2. B The x-coordinate is -3. C The y-coordinate is -3. D The y-coordinate is 5.
Mathematics
1 answer:
Blababa [14]3 years ago
5 0
2x + 5(2x+8) = 4
2x + 10x + 40 = 4
12x = -36
x= -3
So it’s B
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Complete the square for 3x^2-12x=9
larisa [96]

Answer:

The solutions are -0.65 and 4.65.

Step-by-step explanation:

3x^2 - 12x = 9

Divide both sides by 3

x^2 - 4x = 3

To make a square with "x^2 - 4x", you need to have a "+ 4" after it so it can be simplified as (x-2)^2.  So add 4 to both sides.

x^2 - 4x + 4 = 7

(x-2)^2 = 7

x - 2 = (square root) of 7

x = 2 (+/-) (square root) of 7.

x = {-0.65, 4.65}

The solutions are -0.65 and 4.65.

hope this helps:)sorry if it doesnt

8 0
3 years ago
Read 2 more answers
If a current of 12 amps produces 480 volts across a resistor then how many volts does a 15 amp produce?​
LekaFEV [45]

Answer:

600 volts

Step-by-step explanation:

Given =

A = 12 ampere

V = 480 volts

A2 = 15 ampere

Solution =

R = V/I

= 480 / 12

= 40 ohms

R = V / I

V = R x I

= 40 x 15

= 600 volts

7 0
3 years ago
1. (i) Express 2704 as a product of its prime factors.
lidiya [134]

Answer:

all answers below

Step-by-step explanation:

(i) 2704 = 2^4 x 13^2

(ii) as both indices (the powers) are divisible by 2, it is a perfect square.

(iii) as both indices are not divisible by 3, it is not a perfect square.

8 0
3 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.
5 0
3 years ago
Read 2 more answers
I Hope yall have an Amazing day!!
DIA [1.3K]
Yu too man :) :):) :)
6 0
3 years ago
Read 2 more answers
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