How to graph the linear inequality

23÷10=<br> how to work it out

zaharov [31]

The answer is 2.3 :)

7 0

4 years ago

Read 2 more answers

Given B(17,5), C(11, -3), D-1, 2), and<br> E(x, -6), find the value of x so that BC || DE.

son4ous [18]

Answer:

$x=-7$

Step-by-step explanation:

Remember that:

Two lines are parallel if their slopes are the same.
Two lines are perpendicular if their slopes are negative reciprocals.
And two lines are neither (a.k.a intersecting) if they are neither parallel nor perpendicular.

We want to find the value of x such that $\overline{BC}\parallel\overline{DE}$ .

Therefore, the slopes of BC and DE must be equivalent.

So, let's find the slope of BC first.

BC)

We can use the slope formula:

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

Let B(17, 5) be (x₁, y₁) and let C(11, -3) be (x₂, y₂). Substitute:

$m=\frac{-3-5}{11-17}$

Subtract:

$m=-8/-6=4/3$

So, the slope of BC is 4/3.

DE)

Let D(-1, 2) be (x₁, y₁) and let E(x, -6) be (x, y₂). Substitute:

$m=\frac{-6-2}{x-(-1)}$

We know that the two slopes must be equal. So, the slope of DE must also be 4/3. Substitute 4/3 for m:

$\frac{4}{3}=\frac{-6-2}{x-(-1)}$

Solve for x. Simplify the right:

$\frac{4}{3}=\frac{-8}{x+1}$

Cross multiply:

$4(x+1)=-8(3)$

Multiply on the right:

$4(x+1)=-24$

Divide both sides by 4:

$x+1=-6$

Subtract 1 from both sides:

$x=-7$

So, the value of x is -7.

And we're done!

6 0

3 years ago

Identify the graph of the equation. What is the angle of rotation for the equation? (Picture provided)

Ronch [10]

Answer:

The equation is that of ellipse withe angle of rotation 30° ⇒ answer (d)

Step-by-step explanation:

* Lets talk about the general form of the conic equations

- Ax² + Bxy + Cy² +D = 0 (center is the origin)

- A is the coefficient of x² , B is the coefficient of xy

C is the coefficient of y² , D is the numerical term

* Now we will study how to know the type of the graph of this equation

- If A and C have different signs (different values)

∴ The equation is that of an ellipse

- If A and C have different signs (different values)

∴ The equation is on a hyperbola

* Now look at the equation:

13x² + 6√3 xy + 7y² - 16 = 0

∵ A = 13 , B = 6√3 , C = 7 , D = -16

∵ A and C have same sign

∴ The equation is that of an ellipse

* Now lets find the angle of rotation by using the Rule:

- tan(2Ф) = B/(A - C) ⇒ Ф is the angle of rotation

- By using the value of A , B and C

∴ tan(2Ф) = 6√3/(13 - 7) = 6√3/6 = √3

∴ 2Ф = $tan^{-1}\sqrt{3}=60$

∴ 2Ф = 60° ⇒ divide both sides by 2

∴ Ф = 30°

∴ The angle of rotation is 30°

∴ The equation is that of ellipse withe angle of rotation 30°

* The graph represent the ellipse

- The purple line represents the angle of rotation

8 0

3 years ago

What is the first step when multiplying mixed numbers.

jasenka [17]

Answer:

To multiply mixed numbers, first change any mixed number to an improper fraction. Then multiply the numerators together and the denominators together, as shown in Example .

Step-by-step explanation:

6 0

3 years ago

The area of a circle is 9pi cm². Find its radius. <br>Please do this question with full solution:)

kirill115 [55]

Answer:

3 cm

Step-by-step explanation:

The formula for the area of a circle is:

$A = \pi r^2$