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3 years ago

What is the solution to the system of equation? -3x-4y-32= -7 2x-6y+2=3 5x-2y+5z=9

2 answers:

5 0

Simplifying 8x + 336 = 336 + -3x Reorder the terms: 336 + 8x = 336 + -3x Add '-336' to each side of the equation. 336 + -336 + 8x = 336 + -336 + -3x Combine like terms: 336 + -336 = 0 0 + 8x = 336 + -336 + -3x 8x = 336 + -336 + -3x Combine like terms: 336 + -336 = 0 8x = 0 + -3x 8x = -3x Solving 8x = -3x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3x' to each side of the equation. 8x + 3x = -3x + 3x Combine like terms: 8x + 3x = 11x 11x = -3x + 3x Combine like terms: -3x + 3x = 0 11x = 0 Divide each side by '11'. x = 0 Simplifying x = 0

kozerog [31]3 years ago

4 0

Answer:

$x=\dfrac{38}{13},y=\dfrac{4}{13}\text{ and }z=-1$

Step-by-step explanation:

we are given three equation of variable x, y and z.

-3x-4y-3z= -7 ------------- (1)

2x-6y+z=3 ------------- (2)

5x-2y+5z=9 ------------- (3)

Using elimination method to eliminate z from equation (1) and (2)

Make the coefficient of z same in both equation.

Multiply equation (2) by 3

-3x - 4y - 3z = -7

6x - 18y + 3z = 9

Add above equation to eliminate z

3x - 22y = 2 ---------------(4)

Using elimination method to eliminate z from equation (2) and (3)

Make the coefficient of z same in both equation.

Multiply equation (2) by -5

-10x + 30y - 5z = -15

5x - 2y + 5z = 9

Add above equation to eliminate z

-5x + 28y = -6 ---------------(5)

Using elimination method to eliminate x from equation (4) and (5)

Make the coefficient of x same in both equation.

Multiply equation (4) by 5 and equation (5) by 3

15x - 110y = 10

-15x + 84y = -18

Add above equation to eliminate x

-26y = -8

$y=\dfrac{4}{13}$

Substitute y into equation (5) to get x

So, $-5x+28(\frac{4}{13})=-6$

$x=\dfrac{38}{13}$

Substitute x and y into equation (1)

$-3\cdot \frac{38}{13}-4\cdot \frac{4}{13}-3z=-7$

$z=-1$

Solution:

$x=\dfrac{38}{13},y=\dfrac{4}{13}\text{ and }z=-1$

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Let ABC be a triangle such that AB=13 BC=14 and CA=15. D is a point on BC such that AD Bisects

Yuri [45]

Answer:

Area of triangle ADC is 54 square unit

Step-by-step explanation:

Here is the complete question:

Let ABC be a triangle such that AB=13, BC=14, and CA=15. D is a point on BC such that AD bisects angle A. Find the area of triangle ADC .

Step-by-step explanation:

Please see the attachment below for an illustrative diagram

Considering the diagram,

BC = BD + DC = 14

Let BD be $x$ ; hence, DC will be $14-x$

and AD be $y$

To, find the area of triangle ADC

Area of triangle ADC = $\frac{1}{2} (DC)(AD)$

= $\frac{1}{2}(14-x)(y)$

We will have to determine $x$ and $y$

First we will find the area of triangle ABC

The area of triangle ABC can be determined using the Heron's formula.

Given a triangle with a,b, and c

$Area =\sqrt{s(s-a)(s-b)(s-c)}$

Where $s = \frac{a+b+c}{2}$

For the given triangle ABC

Let $a$ = AB, $b$ = BC, and $c$ = CA

Hence, $a = 13, b= 14,$ and $c = 15$

∴ $s = \frac{13+14+15}{2} \\s= \frac{42}{2}\\s = 21$

Then,

Area of triangle ABC = $\sqrt{(21)(21-13)(21-14)(21-15)}$

Area of triangle ABC = $\sqrt{(21)(8)(7)(6)}$ = $\sqrt{7056}$

Area of triangle ABC = 84 square unit

Now, considering the diagram

Area of triangle ABC = Area of triangle ADB + Area of triangle ADC

Area of triangle ADB = $\frac{1}{2} (BD)(AD)$

Area of triangle ADB = $\frac{1}{2}(x)(y)$

Hence,

Area of triangle ABC = $\frac{1}{2}(x)(y)$ + $\frac{1}{2}(14-x)(y)$

84 = $\frac{1}{2}(x)(y)$ + $\frac{1}{2}(14-x)(y)$

∴ $84 = \frac{1}{2}(xy) + 7y - \frac{1}{2}(xy)$

$84 = 7y\\y = \frac{84}{7}$

∴ $y = 12$

Hence, $y =$ AD = 12

Now, we can find BD

Considering triangle ADB,

From Pythagorean theorem,

/AB/² = /AD/² + /BD/²

∴13² = 12² + /BD/²

/BD/² = 169 - 144

/BD/ = $\sqrt{25}$

/BD/ = 5

But, BD + DC = 14

Then, DC = 14 - BD = 14 - 5

BD = 9

Now, we can find the area of triangle ADC

Area of triangle ADC = $\frac{1}{2} (DC)(AD)$

Area of triangle ADC = $\frac{1}{2} (9)(12)$

Area of triangle ADC = 9 × 6

Area of triangle ADC = 54 square unit

Hence, Area of triangle ADC is 54 square unit.

5 0

3 years ago

A number cube is rolled three times. What is the probability of rolling a number less than 3 each time?

sergeinik [125]

Answer:

1/27

Step-by-step explanation:

The outcomes when rolling a die are 1,2,3,4,5,6

getting less than 3 = 1,2

P( less than 3) = outcomes of less than 3 / total

= 2/6 = 1/3

Since the events are independent we can multiply the probabilities

P( less than 3, less than 3, less than 3) = 1/3 * 1/3*1/3 = 1/27

6 0

3 years ago

Which polynomial function could be represented by the graph below?

Zinaida [17]

Answer:

third answer

Step-by-step explanation:

The end behavior of the function indicates that the leading coefficient of x is negative (as x approaches infinity, f(x) approaches negative infinity for cubic functions with negative leading coefficients). This eliminates the first 2 answers. Next, factor out the common factor from the 3rd answer and set it to 0 to see if the roots of the polynomial shown on the graph (x=-3, x=2) match that of the answer.

factor out -2x since each term in the 3rd answer is divisible by -2x => -2x(x^2+x-6)

set the factored polynomial equal to 0 => -2x(x^2+x-6)
divide both sides by -2x => 0 = x^2+x-6
factor => (x+3)(x-2) = 0
find zeros by setting both factors equal to 0 => x=-3, x=2

This means that the 3rd answer is correct. The last answer, while having the correct leading coefficient, will produce roots of 3 and -2 instead of -3 and 2, which is shown on the graph.

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3 years ago

Factor completely: 64x^3+1

pantera1 [17]

Answer:

Step-by-step explanation:

Sum of cubes is a^3+b^3=(a+b)(a^2-ab+b^2)

64x^3+1

(4x+1)(16x^2-4x+1)

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