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Marianna [84]
3 years ago
5

6x^2 -14x = 0 , Using factoring method.

Mathematics
1 answer:
lana66690 [7]3 years ago
8 0
Take out the highest common factor.

The highest common factor between 6 (which 2*3) and 14 (which 2*7) is 2

The highest common factor between x^2 (which is x * x) and x(which is x) is x.

2x(3x - 7) = 0

Now either 2x = 0 in which case x = 0
or
3x - 7 = 0
3x = 7
x = 7/3 

The graph below shows you the answers to where 6x^2 - 14x cuts the x axis is below.

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Find the real numbers x and y if -3+ix^2y and x^2+y+4i are conjugate of each other. Pls solve with the steps
Firdavs [7]
ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work

EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same

For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y

For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4

Therefore, for the two expressions to be conjugates, we must satisfy the two conditions. 

Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the 

   x²y = -4 ... (I)

Condition 2: Real parts are the same

   x² + y = -3 ... (II)

We have a system of equations since both conditions must be satisfied

   x²y = -4 ... (I)
   x² + y = -3 ... (II)

We can rearrange equation (II) so that we have

   y = -3 - x² ... (II)

Substituting into equation (I)

   x²y = -4 ... (I)
   x²(-3 - x²) = -4
   -3x² - x⁴ = -4
   x⁴ + 3x² - 4 = 0
   (x² + 4)(x² - 1) = 0
   (x² + 4)(x-1)(x+1) = 0

Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.

Solve for y:

   y = -3 - x² ... (II)
   y = -3 - (±1)²
   y = -3 - 1
   y = -4

So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:

   -3 + ix²y 
   = -3 + i(±1)²(-4)
   = -3 - 4i

   x² + y + 4i
   = (±1)² - 4 + 4i
   = 1 - 4 + 4i
   = -3 + 4i

They result in conjugates
4 0
3 years ago
Read 2 more answers
I will give brainliest, Please help on this... Show ur work please and thank you
Elanso [62]

Answer:

n=9

Step-by-step explanation:

-5-4n=-41

+5        +5

---------------

-4n=-36

---------------

-4n/4=-36/-4

---------------

n=9

5 0
3 years ago
Give ur answer in standard form. <br>3 x 10^4 ÷6 x 10^-4<br>​
Anni [7]

Answer:

5.0×10⁷

Step-by-step explanation:

(3÷6)×(10⁴÷10^-4)

(0.5)×(10⁸)

5.0×10^-1×10⁸

5.0×10⁷

7 0
2 years ago
Read 2 more answers
Factor the polynomial 16b^4+30b^3-12b^2
Lelu [443]

Answer:

2b²(8b²+15b-6)

Step-by-step explanation:

16b^{4}+30b³-12b²

2b²(8b²+15b-6)

This is not further factorable. If you want to find the roots, you'd have to use the quadratic formula for the polynomial in the parentheses. Therefore that is our final answer.

4 0
3 years ago
Simplify 5 cube root of 72
goldenfox [79]
The answer is 2.35215804
4 0
3 years ago
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