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3 years ago

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]

Answer: try going to question cove to get answer

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
So the fraction of white marbles to total would be 15/20

Because the answer is wanted as a decimal divide 15 by 20
15/20=.75

There is a .75 chance that she will not draw a black marble

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

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

____________

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

-2 | 1 -3 -7

-2

___________

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