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The following cases for the solutions of a system of linear equations are listed below:

In this problem we find the case of a system of linear equations with two variables, of which we must determine the nature of its dependent constants for the following three cases:

The implicit form of this system is shown below:

a · x - y = - b                (1)

c · x - y = - d                (2)

According to the linear algebra, a system of linear equations has no solutions if the determinant of the matrix of dependent coefficients is equal to zero. Then, by Cramer's law we find that:

a - c = 0

a = c

Therefore, the system of linear equations has no solutions for a = c.

Also by linear algebra, we know that the two linear equations have infinite solutions if and only if both equations are multiples of each other, then:

a · x - y + b = k · (c · x - y + d)

a · x - y + b = (k · c) · x - k · y + (k · d)

The system has infinite solutions when a = k · c and b = k · d.

Then, the system has only one solution if and only if a ≠ k · c and b ≠ k · d.

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Answer:

d brainest plz

Step-by-step explanation:

Answer:

A. A variable

Step-by-step explanation:

Answer:

We get the value of x: x = 3

Step-by-step explanation:

Point G lies between points F and H on Line segment F H.

Space between F and G = 4x

Space between G and H = 2x

Length of FH = 18

We need to find value of x.

As point G lies between point F and H, sum of FG and GH will give FH, we can write

[tex]FG + GH = FH[/tex]

Putting values to make equation

[tex]4x + 2x = 18[/tex]

Now, solving the equation we can find value of x

[tex]4x + 2x = 18 \\6x=18\\x=\frac{18}{6}\\x=3[/tex]

So, we get the value of x: x = 3

Answer:

dlfkv

Step-by-step explanation:

Answer:

-44

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The rotation of the point is (-5, 6)

The point is given as:

Point = (6,5)

The rule of 90 degrees counterclockwise rotation around the origin is

(x, y) = (-y, x)

So, we have

Image = (-5, 6)

Hence, the rotation of the point is (-5, 6)

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Answer:

ur x intership is (4) and ur y intership is (1)

Step-by-step explanation: its where the dots are or are u doing an equation?

The answer is: 8m=152

-12 * 4= 48 and -12+4= -8

Answer:

Keep the ladder at a 66 degree angle of elevation at most.

Step-by-step explanation:

Hypotenuse is 20 feet

Adjacent side is 8 feet

We use inverse cosine to find the angle

arccos(8/20) = 66.4 deg

Answer:

words are big and if words are big am I small

Answer:

37.8

Step-by-step explanation:

Answer:

14 degrees.

Step-by-step explanation:

I am assuming that the 56 degree angle is at the centre of the circle.

The angle at the top in the circle = 1/2 * 56 = 28 degrees.

The reflex angle = 360 - 56 = 304 degrees.

If we draw a line from the vertex of the 56 degrees angle to the vertex of 28 degree angle we bisect the reflex angle and the 28  degree angle. Also the 2  triangles formed are congruent ( by SSS).

So x = 180 - 1/2 * 28 - 1/2 * 304

= 180 - 14 - 152

= 180 - 166

= 14 degrees.

Answer:

[tex]y - (-2) = (-5/3)\, (x - 6)[/tex].

.Step-by-step explanation:

The [tex]x[/tex]-coordinates of the two given points are different. Therefore, the line that goes through these points would not be vertical. Likewise, this line would not be horizontal since the [tex]y[/tex]-coordinates of the given points are different.

If a line in a plane is of slope [tex]m[/tex] and goes through point [tex](x_{0},\, y_{0})[/tex], the point-slope equation of this line would be [tex]y - y_{0} = m\, (x - x_{0})[/tex].

If a line in a plane goes through the points [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex] (where [tex]x_{0} \ne x_{1}[/tex],) the slope of this line would be [tex]m = (y_{1} - y_{0}) / (x_{1} - x_{0})[/tex].

Since the line in this question goes through points [tex](6,\, -2)[/tex] and [tex](0,\, 8)[/tex], the slope of this line would be:

[tex]\begin{aligned} m &= \frac{8 - (-2)}{0 - 6} \\ &= \frac{10}{(-6)} \\ &= -\frac{5}{3}\end{aligned}[/tex].

Let [tex](6,\, -2)[/tex] be the point [tex](x_{0},\, y_{0})[/tex]. The point-slope equation of this line would be:

[tex]y - (-2) = (-5 / 3)\, (x - 6)[/tex].

Answer:

3

Step-by-step explanation:

I think ttttttttttttttttttttt

Answer: is 10

Step-by-step explanation:input :

Changes made to your input should not affect the solution:

(1): "3.4" was replaced by "(34/10)". 4 more similar replacement(s)

STEP

1

:

17

Simplify ——

5

Equation at the end of step

1

:

89 14 65 17

((——-(——•x))+(——•x))+——

10 10 10 5

STEP

2

:

13

Simplify ——

2

Equation at the end of step

2

:

89 14 13 17

((——-(——•x))+(——•x))+——

10 10 2 5

STEP

3

:

7

Simplify —

5

Answer:

x = - 1, y = 1

Step-by-step explanation:

Given the 2 equations

2y + 7x = - 5 → (1)

5y - 7x = 12 → (2)

Adding the2 equations term by term will eliminate the term in x, that is

7y = 7 ( divide both sides by 7 )

y = 1

Substitute y = 1 into either of the 2 equationsand solve for x

Substituting into (1)

2(1) + 7x = - 5

2 + 7x = - 5 ( subtract 2 from both sides )

7x = - 7 ( divide both sides by 7 )

x = - 1

solution is x = - 1, y = 1

Answer: 6 bags

Step-by-step explanation:

     We will divide the total amount [3/4 pounds] by the amount per bag [1/8 pound] to find how many bags he can make.

    After writing the problem, we will use "Keep, change, flip" (Keep the first fraction, change to multiplication, flip the second fraction).

[tex]\displaystyle \frac{3}{4}\ \text{pounds} \div \frac{1}{8} \ \text{pounds}[/tex]

[tex]\displaystyle \frac{3}{4}\ \text{pounds} * \frac{8}{1} \ \text{pounds}[/tex]

[tex]\displaystyle \frac{3*8\ \text{pounds}}{4*1\ \text{pounds}}\[/tex]

[tex]\displaystyle \frac{24}{4}\[/tex]

6 bags

Answer:

Step-by-step explanation:

[tex]2 {a}^{2} b + 6a {b}^{2} [/tex]

Factor out common term : 2ab

[tex] 2 {a}^{2}b \div 2a = a \\ 6a {b}^{2} \div 2ab = 3b \\ 2ab(a + 3b)[/tex]

[tex]2a^2b+6ab^2[/tex]

Perhaps, you mean 6ab² (If not please remind me.)

Factoring the polynomials can be done by pulling out the terms that can be divided by that terms.

For example, [tex]2x^2+4[/tex]    We can divide the whole polynomial by 2. Thus, we factor 2 out of the polynomial as we get [tex]2(x^2+2)[/tex] -- Factoring is like dividing, but instead - we pull them out.

Now let's get back to the question.

Notice that the polynomial can be divided by 2, a and b.

So we pull 2, a and b out of the polynomial and divide them.

[tex]\frac{2a^2b+6ab^2}{2ab}\\a+3b[/tex]

When dividing, we should get a + 3b.

Then we pull out 2ab outside the bracket.

[tex]2ab(a+3b)[/tex]

Thus, the answer is 2ab(a+3b)

Answer:

3/2

Step-by-step explanation:

move the 3x to the other side and divide it by 2

Answer:

umm i am pretty sure it is 20 to 22

Step-by-step explanation:

Answer:

y = -3x + 30

Step-by-step explanation:

First, find the slope using the slope formula:

m = (y2 - y1) / (x2 - x1)

m = (9 - (-3)) / (7 - 11)

m = -12/4

m = -3

Next, find the y-intercept by substituding one of the two points into what the equation is so far:

y = -3x + b

(7, 9)

9 = -3(7) + b

9 = -21 + b

30 = b

Now you have the full equation:

y = -3x + 30

Answer:

d

Step-by-step explanation:

5 =5v^+^

Answer:

b=20 or b=-20

Step-by-step explanation:

Keep in mind the meanings of the values of the discriminant:

If b^2-4ac=0, then the quadratic will have only 1 solution (double root)

If b^2-4ac<0, then the quadratic will have no real solutions

If b^2-4ac>0, then the quadratic will have 2 unique solutions

In this case, to get one real solution, the discriminant must be set up as b^2-4ac=0. Setting up the equation we get:

b^2-4(4)(25)=0

b^2-400=0

b^2=400

b=20 or b=-20

So the values of b would have to be either 20 or -20

The values of b will cause 4x^2+bx+25=0 to have one real solution is -20 and 20

Given the quadratic equation [tex]4x^2+bx+25= 0[/tex], for this expression to have a real solution, the discriminant must be greater than zero

D > 0

b^2 - 4ac > 0

Given that a = 4, b = b, c = 25

b^2 - 4(4)(25) > 0

b^2 - 400 > 0

b^2 > 400

b > ±20

Hence the values of b will cause 4x^2+bx+25=0 to have one real solution is -20 and 20

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Answer:

20

Step-by-step explanation: