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3 years ago

Write the equation of a line that has a slope of -2 and goes through point (1, 2).

Mathematics

1 answer:

Roman55 [17]3 years ago

7 0

Answer:

y = -2x + 4

Step-by-step explanation:

Equation in point slope form:

y - 2 = -2(x - 1)

y - 2 = -2x + 2

y = -2x + 4 ..............<------------------------------- slope intercept form

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A sample is taken from all college freshman . Right-handed students are excluded.what is this an example of?

Anarel [89]

Answer:

All college freshman is called Population and Right handed students are excluded is called sample from Population

Step-by-step explanation:

Explanation:-

Population:- The total of the observations which we are concerned

given data all college freshman is called Population

Sample :-

A sample is a subset of a Population

Given data all college freshman is called Population and Right handed students are excluded is called sample from Population

4 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

In the diagram of circle R, m∠FGH is 50°. What is m? 130° 230° 260° 310°

omeli [17]

we know that

The measurement of the exterior angle is the semi-difference of the arcs which comprises

In this problem

∠FGH is the exterior angle

∠FGH= $50\°$

∠FGH= $\frac{1}{2}(arc\ FEH-arc\ FH)$

$50\°=\frac{1}{2}(arc\ FEH-arc\ FH)$

$100\°=(arc\ FEH-arc\ FH)$ -----> equation A

$arc\ FEH+arc\ FH=360\°$

$arc\ FH=360\°-arc\ FEH$ --------> equation B

Substitute equation B in equation A

$100\°=(arc\ FEH-[360\°-arc\ FEH])$

$100\°=2arc\ FEH-360\°$

$2arc\ FEH=360\°+100\°$

$arc\ FEH=230\°$

therefore

The answer is

The measure of arc FEH is equal to $230\°$

6 0

4 years ago

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¿Cómo influye el fenómeno de capilaridad en la vida de las plantas?

Arlecino [84]

Answer:

Plants use capillary action to bring water up the roots and stems to the rest of the plant. Therefore, if the plant could not do this the plant would die.

Step-by-step explanation:

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3 years ago

Oliver made 8 pints of jam last year. How many pints does he make this year?

Gekata [30.6K]

Answer:

23 pints

Step-by-step explanation:

5 0

3 years ago

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