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3 years ago

Y = -x + 3 and y = 2x - 6

Mathematics

2 answers:

aleksandrvk [35]3 years ago

7 0

Answer: x = 3 and y = 0

Step-by-step explanation:

These two are linear equations. It means that they are straight lines.

When we are solving these two equations, we are finding the point where these two lines meet each other and that point will be common to both these equations.

Now,

y = -x + 3 (equation 1)

y = 2x - 6 (equation 2)

We know that point will be the same for these two equations, so put the value of y of equation 1 in equation 2.

-x + 3 = 2x - 6

-3x = -9

x = -9/-3

x = 3

Now, find value of y.

y = -x + 3

y = -3 + 3

y = 0

(3, 0) is where these equations meet each other.

vredina [299]3 years ago

3 0

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Hello Guys, I really need help with these questions. Here they are.

Slav-nsk [51]

Answer:

See below.

Step-by-step explanation:

It can really help to think when you see |expression| that it means the distance from expression to zero.

(a) |x| < 7 means the distance from x to 0 is less than 7. That puts x between -7 and 7. The solution set is -7 < x < 7.

(b) |x + 3| < 9 means that the distance from x + 3 to 0 is less than 9. That puts x + 3 between -9 and 9:

-9 < x + 3 < 9 Now subtract 3 from all three parts.

-12 < x < 6

(c) |y - 8| > 11 means that the distance from y - 8 to 0 is more than 11 units. That puts y - 8 in one of two places: left of -11 or right of 11.

$y-8 < -11 \text{ or } y-8 > 11\\\\y < -3 \text{ or } y > 19$

(g) $|3x-1| \ge 18$ means that the distance from 3x - 1 to 0 is more than (or equal to) 18. Another way to say it is, 3x - 1 is farther from 0 than 18 units. That puts 3x - 1 in one of two places: to the left of -18 or to the right of 18.

$3x-1 \le -18 \text{ or } 3x-1 \ge 18\\\\3x \le -17 \text{ or } 3x \ge 19\\\\x \le -\frac{17}{3} \text{ or } x \ge \frac{19}{3}$

$|4y+3| \le 13$ means that 4y + 3 is closer to 0 than 13; it is between -13 and 13.

$-13 \le 4y+3 \le 13\\\\-16 \le 4y \le 10\\\\-4 \le y \le \frac{5}{2}$

(That last fraction is 10/4 simplified.)

3 0

3 years ago

Read 2 more answers

A garden has an area of 286ft. It’s length is 9ft more than it’s width. What are the dimensions of the garden?

Gelneren [198K]

Answer:

Step-by-step explanation:

x × (x + 9) = x² + 9x = 286
x² + 9x - 286 = 0
(x - 13)(x + 22)
x = 13 or -22
Since you cannot have negative length, it’s 13

3 0

3 years ago

Solve (x + 3)2 + (x + 3) – 2 = 0. Let u = Rewrite the equation in terms of u. (u2 + 3) + u – 2 = 0 u2 + u – 2 = 0 (u2 + 9) + u –

Verdich [7]

Answer:

The solutions of the original equation are x=-5 and x=-2

Step-by-step explanation:

we have

$(x+3)^2+(x+3)-2=0$

Let

$u=(x+3)$

Rewrite the equation

$(u)^2+(u)-2=0$

Complete the square

$u^2+u=2$

$u^2+u+1/4=2+1/4$

$u^2+u+1/4=9/4$

rewrite as perfect squares

$(u+1/2)^2=9/4$

square root both sides

$(u+1/2)=\pm\frac{3}{2}$

$u=(-1/2)\pm\frac{3}{2}$

$u=(-1/2)+\frac{3}{2}=1$

$u=(-1/2)-\frac{3}{2}=-2$

the solutions are

u=-2,u=1

Alternative Method

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$(u)^2+(u)-2=0$

$a=1\\b=1\\c=-2$

substitute in the formula

$u=\frac{-1\pm\sqrt{1^{2}-4(1)(-2)}} {2(1)}$

$u=\frac{-1\pm\sqrt{9}} {2}$

$u=\frac{-1\pm3} {2}$

$u=\frac{-1+3} {2}=1$

$u=\frac{-1-3} {2}=-2$

the solutions are

u=-2,u=1

Find the solutions of the original equation

For u=-2

$-2=(x+3)$ ----> $x=-2-3=-5$

For u=1

$1=(x+3)$ ----> $x=1-3=-2$

therefore

The solutions of the original equation are

x=-5 and x=-2

4 0

3 years ago

Read 2 more answers

Please help me no one would help me i really need help due tomorrow.

irina [24]

Option B is correct.

Step-by-step explanation:

A triangle has vertices A(-3,-1), B(-6,-5), C(-1,-4). We need to find the transformation that will produce the triangle with vertices: A(3,-1), B(6,-5), C(1,-4)

Seeing the vertices of transformed triangle, we observe that the x-coordinate of vertices has been opposite of that in the original vertices, while y-coordinate remains same.

This shows it is reflection over y-axis. In which x-coordinate becomes the negative (opposite) of original coordinate while y-coordinate remains the same.

So, Option B is correct.

Keywords: Transformation of Triangles

Learn more about Transformation of Triangles at:

#learnwithBrainly

7 0

3 years ago

Explain why the absolute value of a number is never a negative number ?

omeli [17]

The absolute value of a number is never a negative number because absolute value describes the distance of a number on the number line from 0 without considering which direction from zero the number lies. The absolute value of a number is never negative.

4 0

3 years ago

Read 2 more answers

Y = -x + 3 and y = 2x - 6​

Y = -x + 3 and y = 2x - 6