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Anarel [89]
3 years ago
9

Pleaseeee i will mark brainlesttttt solve this system of equations 12x−15y=14 8x−15y=6

Mathematics
1 answer:
Sphinxa [80]3 years ago
3 0

Answer:

x = 2 and  y = \frac{2}{3}

Step-by-step explanation:

To solve this system of equation, we will follow the steps below;

We will use both elimination and substitution method to solve this system of equations

12x−15y=14 ------------------------------------------------------------------------(1)

8x−15y=6 --------------------------------------------------------------------------(2)

subtract equation (2) from equation (1)

(By doing that the y  variable will be eliminated)

4x = 8

Divide both-side of the equation by 4

4x/4 = 8/4

x = 2

Substitute x =2 into equation (2) and then solve for y

8x−15y=6

8(2)−15y=6

16 - 15y = 6

subtract 16 from both-side of the equation

16 - 16- 15y = 6-16

-15y = -10

Divide both-side of the equation by -15

-15y/-15  = -10/-15

y = \frac{2}{3}

x = 2 and  y = \frac{2}{3}

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The sides of a triangle are 1, x, and x2. what are possible values of x?
Whitepunk [10]
The sides of the triangle are given as 1, x, and x².

The principle of triangle inequality requires that the sum of the lengths of any two sides should be equal to, or greater than the third side.

Consider 3 cases
Case (a):  x < 1,
      Then in decreasing size, the lengths are 1, x, and x².
      We require that x² + x ≥ 1
      Solve x² + x - 1 = 
      x = 0.5[-1 +/- √(1+4)] = 0.618 or -1.618.
      Reject the negative length.
     Therefore, the lengths are 0.382, 0.618 and 1.

Case (b): x = 1
   This creates an equilateral triangle with equal sides
    The sides are 1, 1 and 1.

Case (c): x>1
  In increasing order, the lengths are 1, x, and x².
  We require that x + 1 ≥ x²
  Solve x² - x - 1 = 0
  x = 0.5[1 +/- √(1+4)] = 1.6118 or -0.618
  Reject the negative answr.
 The lengths are 1, 1.618 and 2.618.

Answer:
The possible lengths of the sides are
(a) 0.382, 0.618 and 1
(b) 1, 1 and 1.
(c) 2.618, 1.618 and 1.

7 0
3 years ago
Elijah drove 45 miles to his job in an hour and ten minutes in the morning. On the way home: however, traffic was much heavier a
olchik [2.2K]

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8 0
3 years ago
Got it wrong plss help and explain
Karolina [17]
Because it says "not black" we would do white marbles
There are 15 white marbles and a total of 20
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Because the answer is wanted as a decimal divide 15 by 20
15/20=.75

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8 0
3 years ago
21 POINTS!! Thank you so much!! There’s also things on my page worth lots points points as well! So if you could help with those
Art [367]

Answer:

Second one

third one

fifth one

last one

Step-by-step explanation:

Based on the x intercepts we can write

a(x+1)(x-5)

where a is some constant

solve for a by plugging in some coordinates

let's plug in (1,-8)

-8=a(1+1)(1-5)

-8= -8a

a=1

therefore the quadratic is (x+1)(x-5)

expand this

x²-4x-5

To find out where something is decreasing/increasing it's easiest to take the first derivative

x²-4x-5= 2x-4

set this equal to 0

2x-4=0

2x=4

x=2

Which means that our two intervals are

(-∞,2)U(2,∞)

plug in any values in the intervals to see whether or not the function is increasing/decreation

Let's plug in 0 for (-∞,2)

2(0)-4

-4

It's negative so it's decreasing on this interval

DO the same thing with the other one

let's plug in x=3

2(3)-4

2

this is positive so it's increasing on this interval

Go back to the critical value of x=2 and plug this into the equation to find the max/min

(2+1)(x-5)= -9

This is a minimum because the cofeccient for the degree is positive

For the limit one notice that we have a positive, even degree which means the end behavior is positive, positive

what this means is as x approaches negative infinity it's infinity

and as x approaches infinity it's infinity

6 0
2 years ago
X² – 3x-7<br> x+2<br> Divide the following using synthetic division
Ksenya-84 [330]

Answer:

x-5+ \frac{3}{x+2}

Step-by-step explanation:

If x+2 is a factor, -2 is a zero. So we can put -2 in the left-hand corner of your synthetic division, bring the coefficients down so you'll have a set up like this:

-2 |   1    -3    -7

____________

1. bring down the 1:

-2 |   1    -3    -7

____________

       1

2. multiply that by -2 and enter the result underneath 3:

-2 |   1    -3    -7

             -2

___________

       1

a. then, add through:

-2 |   1    -3    -7

             -2

___________

       1     -5

3. Do the same for -5 (multiply by the zero -2), enter that underneath -7 and add through:

-2 |   1    -3    -7

             -2    10

___________

       1     -5    3

Now, reassign the coefficients to their x. Because we already factored out an x with the zero, the 1 is assigned to 'x' rather than back to 'x^{2}'. The '-5' will not have an x attached. '3' is your remainder and cannot be divided out any further, so it will be written as \frac{3}{x+2}. Finally, just put them back together to get x-5+\frac{3}{x+2}.

Hope this helped!

4 0
3 years ago
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