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3 years ago

What is the solution of the system? Use elimination. 3x - 4y = 9 -3x + 2y = 9

2 answers:

6 0

You add two equations together to eliminate a variable. This particular problem is nice, because it's already setup to eliminate X.

3x - 4y = 9
-3x + 2y = 9

When we add these two together, 3x - 3x cancels each other out, leaving us with 0x, or nothing.

We continue with -4y + 2y (leaves us with -2y) and 9+9 (18).

-2y = 18

18/-2 = -9.

Now we have y = -9, and we can go back into the problems to solve for x.

3x - 4(-9) = 9

3x + 36 = 9.

3x = -27

x = -9.

Confirm with the final equation:

-3(-9) + 2(-9) = 9
27 - 18 = 9
9 = 9 --- Confirmed.

ale4655 [162]3 years ago

4 0

Answer:

[-9, -9]

Step-by-step explanation:

Here is how the Eliminasyon Metòd is done:

{3x - 4y = 9

{-3x + 2y = 9

--------------

-2y = 18; -9 = y [plug this back into both equations for y to get -9 = x]

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my You-Tube channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

**I do have videos that talk about how to solve systems of equations in two to three variables using the Elimination and Substitution methods. I encourage you to check them out!

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The coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

daser333 [38]

Answer: The correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

Explanation:

It is given that coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

The distance formula for two points is given below,

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$DE=\sqrt{(2+2)^2+(4-5)^2}=\sqrt{17}$

$EF=\sqrt{(0-2)^2+(0-4)^2}=\sqrt{20}$

$FG=\sqrt{(-4-0)^2+(1-0)^2}=\sqrt{17}$

$DG=\sqrt{(-4+2)^2+(1-5)^2}=\sqrt{20}$

Slope formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of DE,

$m_1=\frac{4-5}{2+2}= \frac{-1}{4}$

Slope of EF,

$m_2=\frac{0-4}{0-2}= 2$

Slope of FG,

$m_3=\frac{1-0}{-4-0}= \frac{-1}{4}$

Slope of DG,

$m_4=\frac{1-5}{-4+2}= 2$

The slope of opposite sides are equal, it means the opposite sides are parallel.

All four sides do not have the same length. It means it is not a rhombus.

From the figure it is noticed that the opposite sides are parallel.

Therefore, the correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

3 0

3 years ago

Read 2 more answers

I really need help with this one please help me thank you

sveta [45]

Answer:

Step-by-step explanation:

3 0

3 years ago

PLEASE HELP I WILL MARK YOU BRAINLIEST. Ms. Simmons is using sticky notes to write reminders to herself. Each sticky note is 5/6

Masja [62]

Answer:

5 square inches

Step-by-step explanation:

First, we need to find the area of one sticky note:

The formula is Lenth*Width

Area of one sticky note:

5/6*2/3=10/18

=5/9 square inches

Now, we find the area of 9 sticky notes:

5/9*9=5

5 square inches

Hope this helps! Have an amazing day!

7 0

3 years ago

If P(A) = 0.2, P(B) = 0.2, and P(A ∪ B) = 0.4, then P(A ∩ B) = _______.

Pavlova-9 [17]

Answer:

P(A ∩ B) = 0.

a) NO

b) YES

Step-by-step explanation:

Thinking about this through Venn diagrams we can sort of understand that:

if P(A) = 0.2 and P(B) = 0.2, and P(A∪B) = 0.4.

there's no overlapping between P(A) and P(B).

(If there was overlapping then P(A∪B) < 0.4, since you'd be excluding the overlapped part from getting counted twice.

Think of it in terms of calculating areas circles A and B, if the circles were disjoint, then the sum of the areas A and B would be 0.2+0.2. But if the circles were overlapping then the sum of the areas would be 0.2+0.2-P(A ∩ B), where P(A ∩ B) is the overlapping part)

since there's no overlapping P(A ∩ B) = 0.

a) NO

events A and B are only independent when P(A ∩ B) > 0 (or overlapping)

b) YES

events A and B are mutually exclusive when P(A ∩ B) = 0 (or disjoint)

8 0

3 years ago

How many cubes that measure 2 inches by 2 inches by 2 inches would fit inside a cube that measures 10 inches by 10 inches by 10

11111nata11111 [884]

25, because a cube that is 10x10 would have an area of 100. and the cubes that are 2x2 would have an area of 4. so you take 100 and divide it by 4. answer is 25.

5 0

2 years ago