Find the focus and directrix of the parabola y= 1/2 (x+2)^2 - 3 A. The focus is at (–2,–2) and the directrix is at y = –4. B. The focus is at (–2,–3) and the directrix is at y = –5. C.The focus is at (–2,–2 1/2) and the directrix is at y = –3 1/2. D. The focus is at (–2,–1 1/2) and the directrix is at y = –2 1/2.

Given :

Two points [tex]P_1(-2,3,2)\ and\ P_2(1,2,0)[/tex] .

To Find :

The direction of [tex]P_1P_2[/tex] and midpoint of line segment [tex]P_1P_2[/tex] .  

Solution :

Direction of [tex]P_1[/tex] and [tex]P_2[/tex] is given by :

[tex]\vec{D}=\dfrac{P_2-P_1}{|P_2-P_1|}\\\\\vec{D}=\dfrac{(-2i+3j+2k)-(i+2j+0)}{P_2-P_1}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{3^2+1^2+2^2}}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{14}}[/tex]

Now , mid point is given by :

[tex]M(\dfrac{-2+1}{2},\dfrac{3+2}{2},\dfrac{2+0}{2})\\\\M(\dfrac{-1}{2},\dfrac{5}{2},1)[/tex]

Hence , this is the required solution .

Answer:

1. RATIO SCALE

2. INTERVAL SCALE

3. NOMINAL SCALE

4. ORDINAL SCALE

Step-by-step explanation:

The scales are:

- Nominal Scale

- Ordinal Scale

- Interval Scale

- Ratio Scale

Rule: Each scale will be used exactly once.

For number 1, the description is that of a Ratio Scale because size comparisons can be made between values on the scale, such as the example given - that one value is twice as big as another value.

For number 2, the description is that of an Interval Scale because the values of data measured on the scale can be ranked e.g. Yes ranks as 1, No ranks as 2, Indifferent ranks as 3 and there is meaningful difference (not numerical difference) between scale points.

For number 3, the description is that of a Nominal Scale, because it says obviously that the values of data measured on this scale can be in form of names (watch out for keywords like this when reading through) and cannot be rank ordered! A good example is the following data set:

- Yellow, Brown, Purple, Cream, Fustian Pink

For number 4, the description is that of an Ordinal Scale. A keyword "rank" is to be given attention here, even as the statement is straightforward and gives just a simple information.

Question:

Express each vector as a product of its length and direction.

[tex]\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]

Answer:

[tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Step-by-step explanation:

A vector v can be expressed as a product of its length and direction as follows;

v = |v| u

Where;

|v| = length/magnitude of v

u = unit vector in the direction of v

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

Let the given vector be v, i.e

[tex]v = \frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]

(i) The length/magnitude |v| of vector v is therefore,

|v| = [tex]\sqrt{(\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2[/tex]

|v| = [tex]\sqrt{(\frac{1}{6}) + (\frac{1}{6}) + (\frac{1}{6})[/tex]

|v| = [tex]\sqrt{(\frac{3}{6})[/tex]

|v| = [tex]\sqrt{(\frac{1}{2})[/tex]

|v| = [tex]\frac{1}{\sqrt{2}}[/tex]

(ii) The unit vector u in the direction of vector v, is therefore,

u = [tex]\frac{v}{|v|}[/tex]

[tex]u = \frac{\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k}{\frac{1}{\sqrt{2}}}[/tex]

[tex]u = \sqrt{2}(\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k)[/tex]

[tex]u = (\frac{\sqrt{2}}{\sqrt{6}}i - \frac{\sqrt{2}}{\sqrt{6}}j - \frac{\sqrt{2}}{\sqrt{6}}k)[/tex]

[tex]u = (\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Therefore, the vector can be expressed as a product of its length and direction as:

|v| u = [tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Answer:

10 x 10 x 10 x 10.

Step-by-step explanation:

2(5)^4

10^4

Expanded form; 10*10*10*10.

Answer:

10 x 10 x 10 x 10

Step-by-step explanation:

the first two professors did not know if everyone wanted coffee because the third professor had to choose yes or no if he wanted coffee. the first two professors were waiting for the third to say something, and when he said no, they knew he did not want coffee. if one of the first two professors said no, the answer would be no.

Answer:

modulus of  |9+40i|  is 41

Step-by-step explanation:

Let z = 9+40i

then

|z| = [tex]\sqrt{9^{2}+40^{2} }[/tex]

   = [tex]\sqrt{81+1600}[/tex]

   = [tex]\sqrt{1681}[/tex]

   = 41

|z| = 41

Answer:

Step-by-step explanation:

1. |9+40i| = 41

2. |-10+24i| = 26

Step-by-step explanation:

r+4r=24+1

5r=25

r=25/5

r=5

Answer:

r = 5

Step-by-step explanation:

r + 4r - 1 = 24

r + 4r = 25

5r = 25

r = 5

Answer:

-17 × 0 = 0

every number multiplied by 0 is equal to 0

Answer:

rational numbers and irrational numbers

Step-by-step explanation:

Answer:

28 (0,2,4,14,28)

34 (0,2,17,34)

42 (0,2,6,7,21,42)

the greatest common factor is 2 because it's the greatest number that can be divided by 28, 34 and 42

We can use the points (-4, 0) and (0, 2) to solve.

Slope formula: y2-y1/x2-x1

2-0/0-(-4)

2/4

1/2

Best of Luck!

Here are the expressions on the left matched with the simplifed form on the right:

Here are some mathematical rules:

Also, this sign | | indicates that the number is postive.

To learn more about addition, please check: https://brainly.com/question/349488

#SPJ2

Answer:

i think is the second one

Step-by-step explanation:

Answer:

up is equal to 5/ 6

left side is equal to 3/4

Step-by-step explanation:

1/6 + 1/6+ 1/6+ 1/6+ 1/6= 5/6

1/4 + 1/4 + 1/4= 3/4

Answer:

C

Step-by-step explanation:

2/3=66 therefore it also equals 2/3%

Answer: C

Step-by-step explanation:

First find the decimal of 2/3  

Divide it  2/3 = 0.6666666

Now multiply it by 100 to convert it to a percent  

You get 66.66..%  which is the same as 66 2/3%

Answer:

The value of m + k = [tex]5+\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex].

Step-by-step explanation:

We are given that C is the midpoint of segment AB where A(-3,m) , B (4, -1) , and C (k, 2).

As we know that the mid-point formula states that;

Mid-point = [tex]\frac{a+b}{2}[/tex]

This means that;

Mid-point of AB = [tex]\frac{A+B}{2}[/tex]

C(k, 2) = [tex](\frac{-3+4}{2}, \frac{m+(-1)}{2} )[/tex]

C(k, 2) = [tex](\frac{1}{2}, \frac{m-1}{2} )[/tex]

This means that;

[tex]k = \frac{1}{2}[/tex]  and  [tex]2=\frac{m-1}{2}[/tex]

[tex]k = \frac{1}{2}[/tex]  and  [tex]m-1=4[/tex]

[tex]k = \frac{1}{2}[/tex]  and  [tex]m = 4+1 = 5[/tex]

So, the value of m + k = [tex]5+\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex].

Answer:

x = -8

Step-by-step explanation:

[tex]6(x - 1) = 9(x + 2)[/tex]

Expand :

[tex]6(x - 1) = 6x - 6 \\ 9(x + 2) = 9x + 18[/tex]

[tex]6x - 6 = 9x + 18[/tex]

Collect like terms and simplify

[tex]6x - 9x = 18 + 6 \\ - 3x = 24[/tex]

Divide both sides of the equation by -3

[tex] \frac{ - 3x}{ - 3} = \frac{24}{ - 3} \\ x = - 8[/tex]

Answer:

Step-by-step explanation:

6x - 6 = 9x + 18

-3x - 6 = 18

-3x = 24

x = -8 is the solution

Answer:

x>18

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

Coordinate A ins not intercepting any axis.

Step-by-step explanation:

For a coordinate to intercept an axis, it will be in the form [tex](a, b)\ such\ that:\ a=0, b \in \mathbb{R},\ or:a\in \mathbb{R}, b=0.[/tex]

Since in (3, 6), none of the components are 0, it is not intercepting any axes.

l=3w

3w(4)=48

12w=48

w=4

l=12

hope it helps

comment if u have any questions

Answer:

Length is 18; width is 6.

Step-by-step explanation:

The formula for the perimeter of a rectangle is:

[tex]P=2l+2w[/tex]

We are given that the perimeter is 48 feet. We are also told that the length is 3 times the width. In other words:

[tex]l=3w[/tex]

So, substitute this for l and 48 for P. Thus:

[tex]48=2(3w)+2w[/tex]

Distribute:

[tex]48=6w+2w[/tex]

Combine like terms:

[tex]48=8w[/tex]

Divide both sides by 8:

[tex]w=6[/tex]

So, the width is 6.

The length as we know is 3 times the width, so the length is 3(6) is 18.

And we are done!

Answer:

-15

Step-by-step explanation:

-10+-9=-19+4=-15

Answer:

$818,3

Step-by-step explanation:

16.7% in decimal is 0.167

= 0.167 x $4900

= $818,3

Answer:

7

Step-by-step explanation:

Answer:

1.618

The Fibonacci sequence is significant because of the so-called golden ratio of 1.618, or its inverse 0.618. In the Fibonacci sequence, any given number is approximately 1.618 times the preceding number, ignoring the first few numbers.

Step-by-step explanation:

Plz Mark me as brainliest

[tex]\Large \boxed{\sf golden \ ratio}[/tex]

A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.

Answer:

The equation of the sphere with center (-3, 2 , 5) and radius 4 is [tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]

The intersection of the sphere with the yz- plane gave the equation [tex](y-2)^{2} + (z-5)^{2} = 7[/tex] which is a 2D- circle with center (0,2,5) and radius [tex]\sqrt{7}[/tex].

Step-by-step explanation:

The equation of a sphere of radius r, with center (a,b,c) is given by

[tex](x-a)^{2} +(y-b)^{2} + (z-c)^{2} = r^{2}[/tex]

where, [tex]x,[/tex] [tex]y,[/tex] and [tex]z[/tex] are the coordinates of the points on the surface of the sphere.

Hence, the equation of the sphere with center,  (-3, 2 , 5) and radius 4 becomes

[tex](x-a)^{2} +(y-b)^{2} + (z-c)^{2} = r^{2}[/tex]

[tex](x-(-3))^{2} +(y-(2))^{2} + (z-(5))^{2} = 4^{2}[/tex]

Then,

[tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]

This is the equation of the sphere with center (-3, 2 , 5) and radius 4,

Now, for the intersection of this sphere with the yz- plane,

The [tex]yz -[/tex]plane is where [tex]x = 0[/tex], then we set [tex]x = 0[/tex]

Them the equation [tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex] becomes

[tex](0+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]

[tex](3)^{2} +(y-2)^{2} + (z-5)^{2} = 16\\9 +(y-2)^{2} + (z-5)^{2} = 16\\(y-2)^{2} + (z-5)^{2} = 16 - 9\\(y-2)^{2} + (z-5)^{2} = 7[/tex]

This equation is the equation of a 2D- circle with center (0,2,5) and radius [tex]\sqrt{7}[/tex]

This is the part of the sphere that intersects with the yz-plane.

Answer:

Step-by-step explanation:

Product—Multiplication

Sum— Addition

Difference—Subtraction

Quotient—Division

Quantity— Parenthesis