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3 years ago

What is the equation of the graph shown?

Mathematics

1 answer:

Vikki [24]3 years ago

6 0

Answer:

2y+3x-2=0

Step-by-step explanation:

The slope of the line is 3/2 and the equation of line is y=-1.5x+1

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Maggie has a ribbon 27 feet long. what is the length of the ribbon in yards? equation : answer :

nadezda [96]

3 feet in a yard so you would divide 27 by 3 that gives an answer of 9

3 0

3 years ago

In the image below, 10 is the long leg of the 30-60-90 triangle. True or false?

never [62]

The measure of the angle between the hypotenuse and the short leg is 60° and we can conclude that the side with length 10 is not the long leg of the 30 - 60 - 90 right triangle. (Right choice: False)

<h3>Is the length of a known arm in a 30 - 60 - 90 right triangle the long arm?</h3>

In accordance with geometry, the length of the long arm of a 30 - 60 - 90 right triangle is √3 / 2 times the length of the hypotenuse, the length of the short arm is 1 / 2 times the length of the hypotenuse and the length of the long arm is √3 times the length of the arm.

Thus, the measure of the angle between the hypotenuse and the short leg is 60° and we can conclude that the side with length 10 is not the long leg of the 30 - 60 - 90 right triangle. (Right choice: False)

To learn more on right triangles: brainly.com/question/6322314

#SPJ1

3 0

1 year ago

Explain how to use the combine place values strategy to find 223 - 119

ololo11 [35]

the anwser is 104 because u subrtacted

8 0

3 years ago

Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

$(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14$ .

(Expand to obtain an equivalent expression for the sphere: $x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between $\left(x_1, \, y_1, \, z_1\right)$ and $\left(x_2, \, y_2, \, z_2\right)$ would be:

$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .

The equation for a sphere of radius $r$ and center $\left(x_0,\, y_0,\, z_0\right)$ would be:

$\left(x - x_0\right)^2 + \left(y - y_0\right)^2 + \left(z - z_0\right)^2 = r^2$ .

In this case, the equation would be:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z - (-6)\right)^2 = \left(\sqrt{56}\right)^2$ .

Simplify to obtain:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z + 6\right)^2 = 56$ .

Expand the squares and simplify to obtain:

$x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ .

8 0

3 years ago

The mean of six numbers is 41. If one number is removed, the mean of the five numbers is 46. Find the unknown number.

klasskru [66]

Let n be the sum of all 6 numbers:

In the 1st case n/6 = 41 ==> n =246

in the 2nd case n'/5 = 46===> n' =230, the unknown number is n-n' =246-230

= 16

5 0

3 years ago