Which are vertical angles?
O AFE and BFD
O BFC and DFE
O AFE and CFD
O BFC and EFA

6i(7-6i)

42i-36i^2

hope it helps

Answer:

36+42i

Step-by-step explanation:

6i(7-6i)

=42i-[tex]36i^2[/tex]

=42i-(36x -1)

=42i+36

=36+42i

Answer:

The equation is:

(1/a)x + (1/b)y + (1/c)z = 1

Step-by-step explanation:

The direction vector between the points (a, 0, 0) and (0, b, 0) is given as:

<0 - a, b - 0, 0 - 0>

<-a, b, 0> .....................(1)

The direction vector between (0, 0, c) and (0, b, 0) is given as:

<0 - 0, b - 0, 0 - c>

= <0, b, -c> .....................(2)

To obtain the direction vector that is normal to the surface of the plane, we take the cross product of (1) and (2).

Doing this, we have:

<-a, b, 0> × <0, b, -c> = <-bc, -ac, -ab>

To find the scalar equation of the plane we can use any of the points that we know. Using (0, b, 0), we have:

(-bc)x + (-ac)y + (-ab)z = (-bc)0 + (-ac)b + (-ab)0

(bc)x + (ac)y + (ab)z = (ac)b

Dividing both sides by abc, we have:

(1/a)x + (1/b)y + (1/c)z = 1

We will call π,  the plane with points P, Q, R  ( the intercepts )

The solution is:

π :  -bc×x + ac×y -ab×z - bac = 0

c) d =   | bac|/√ ( -bc)² + (-ac)² + ( -ab)²

The intercepts  P Q R are three points of the plane, according to that

P ( 0, b, 0 ) intercept with y-axis

Q ( a, 0, 0 ) intercept with x-axis

R ( 0, 0, c ) intercept with  z-axis

We will find the vectors PQ  and  PR both are on the plane

PQ  = [ a, 0, 0 ] - [ 0, b, 0 ]         ⇒     PQ = ( a , -b, 0 )

PR  =  [ 0, 0, c ] - [ 0, b, 0 ]          ⇒     PR = ( 0, -b  c )

The vectorial product of these two vector will give us, one normal vector to the plane.

                        i        j         k

PQ * PR  =     a      -b        0    =   i (-bc)  - j ( ac - 0 ) + k ( -ab - 0)

                       0      -b        c

PQ * PR  = [ -bc,  -ac,  -ab ]

we call this vector n =  [ -bc, -ac, -ab ]

Let´s now find a vector between P,  and a general point T ( x , y , z ) on the plane.

PT = [ x, y, z ] - [ 0, b, 0 ]    ⇒  PT = [ x-0 , y - b , z - 0 ]

PT = [ x, y-b, z ]

Vector PT is perpendicular to vector n, then their dot product must be 0

Then:

PT × n = 0

[ x, y-b, z ] ×   [ -bc, -ac, -ab ] = 0

x × (-bc) + ( y - b )× (ac) + z × (- ab) = 0

-bc×x + ac×y -bac - ab×z = 0

-bc×x + ac×y -ab×z = bac         (1)

Finally,  we got the implicit equation for plane π as:

π :  -bc×x + ac×y -ab×z - bac

c) The distance (d) between the plane and the origin is:

d = | D | / | n |

| n | = √ ( -bc)² + (-ac)² + ( -ab)²

|D| = | bac|     the right side of the equation (1)

Then

d =   | bac|/√ ( -bc)² + (-ac)² + ( -ab)²

Related Link :https://brainly.com/question/3914382

Answer:

Step-by-step explanation:

[tex] \sf{ \frac{1}{2} (x - 3) = 9}[/tex]

Distribute 1/2 through the parentheses

⇒[tex] \sf{ \frac{1}{2} x - \frac{1}{2} \times 3 = 9}[/tex]

Multiply the fractions

⇒[tex] \sf{ \frac{1}{2} x - \frac{1 \times 3}{2 \times 1} = 9}[/tex]

⇒[tex] \sf{ \frac{1}{2} x - \frac{3}{2} = 9}[/tex]

While performing the addition or subtraction of like fractions, you just have to add or subtract the numerator respectively in which the denominator is retained same.

⇒[tex] \sf{ \frac{x - 3}{2} = 9}[/tex]

Apply cross product property

⇒[tex] \sf{x - 3 = 9 \times 2}[/tex]

Multiply the numbers

⇒[tex] \sf{x - 3 = 18}[/tex]

Move 3 to right hand side and change it's sign

⇒[tex] \sf{x = 18 + 3}[/tex]

Add the numbers

⇒[tex] \sf{x = 21}[/tex]

Hope I helped!

Best regards!!

Answer:

Population and Sample

Step-by-step explanation:

The state of Mississippi is the population

The randomly selected resident is the sample

Population Belt Use: 60%

Population No-belt Use: 40%

Sample (selected resident's) Seat-belt Use = Y

Note: the question doesn't state or ask whether Y is positive (use of seat belt) or negative (no use of seat belt).

How does the standard deviation of X compare with the standard deviation of Y?

X is the population standard deviation of seat belt use from the mean value of seat belt use WHILE Y is the sample standard deviation of seat belt use from the mean value (of all persons in the sample) of seat belt use.

Answer:

The student got 90% correct and 10% incorrect.

Step-by-step explanation:

Answer:

Step-by-step explanation:

a)  Since the x's of the original equation are equal to the y's of the inverse equation, and vice versa, you can simply put the x-values of the table for the inverse equation into the y-values of the original equation.  The same principle applies to the inverse equation.  The table should look like the tables attached.

b)  The x's and y's in the points of the inverse are switched.  The points will be

(10, 27)  -->  (27, 10)

(3.5, 14)  -->  (14, 3.5)

(a, b)  -->  (b, a)

(x, y)  -->  (y, x)

 A. Draw a second line using a straightedge so that it intersects the first.

Step-by-step explanation:

trust me i took the test and got it right

Answer:

Draw a second line using a straightedge so that it intersects the first.

Answer above is correct, just took the test.

Step-by-step explanation:

Answer:

a) the probability that the minimum of the three is between 75 and 90 is 0.00072

b) the probability that the second smallest of the three is between 75 and 90 is 0.396

Step-by-step explanation:

Given that;

fx(x) = { 1/5 ; 50 < x < 100

              0, otherwise}

Fx(x) = { x-50 / 50 ; 50 < x < 100

                          1 ;   x > 100

a)

n = 3

F(1) (x) = nf(x) ( 1-F(x)^n-1

= 3 × 1/50 ( 1 - ((x-50)/50)²

= 3/50 (( 100 - x)/50)²

=3/50³ ( 100 - x)²

Therefore P ( 75 < (x) < 90) =  ⁹⁰∫₇₅ 3/50³ ( 100 - x)² dx

= 3/50³ [ -2 (100 - x ]₇₅⁹⁰

= (3 ( -20 + 50)) / 50₃

= 9 / 12500 = 0.00072

b)

f(k) (x) = nf(x)  ( ⁿ⁻¹_k₋ ₁) ( F(x) )^k-1 ; ( 1 - F(x) )^n-k

Now for n = 3, k = 2

f(2) (x) = 3f(x) × 2 × (x-50 / 50) ( 1 - (x-50 / 50))

= 6 × 1/50 × ( x-50 / 50) ( 100-x / 50)

= 6/50³ ( 150x - x² - 5000 )

therefore

P( 75 < x2 < 90 ) = 6/50³ ⁹⁰∫₇₅ ( 150x - x² - 5000 ) dx

= 99 / 250 = 0.396

Answer:

x=60

Step-by-step explanation:

1/6x=10

multiply both sides by 6 to get x

x=60

Answer:

x=60

Step-by-step explanation:

In order to solve for x, we must isolate x on one side of the equation.

The equation given is:

[tex]\frac{1}{6}x=10[/tex]

1/6 and x are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 1/6

[tex]\frac{1}{6}x/\frac{1}{6}=10/\frac{1}{6}[/tex]

When dividing by a fraction, you can multiply by the reciprocal of the fraction instead.

To find the reciprocal, flip the numerator and denominator.

1/6 ⇒ flip top number and bottom number ⇒ 6/1=6

Replace the division by 1/6 with multiplication by 6.

[tex]\frac{1}{6}x * 6=10*6[/tex]

[tex]x= 10 *6[/tex]

[tex]x=60[/tex]

The solution to this equation is x=60

Greetings from Brasil...

The point (-2; -4) is in the blue area, so it is the solution to the equation;

The point (-1; -5) is in the blue area, so it is the solution to the equation;

The point (0; -3) is in the blue area, so it is the solution to the equation;

The point (2; -1) is exactly on the function line. As this line is dashed, it does not include its values, so this point is not a solution (no point on the dashed line is a solution)

Answer:

Wii 467847585848584585869t8569

Answer:

Average Rate of Change : 3

Step-by-step explanation:

" Remember that the average rate of change of function f say, on interval [a,b] would be f(b) - f(a) / b - a. Similarly we can solve for the average rate of this function. "

f(5) = x² - 2x - 15 = 5² - 2(5) - 15 = 25 - 10 - 15 = 0,

f(0) = 0² - 2(0) - 15 = 0 - 0 - 15 = - 15

And the average rate of change will be,

f(5) - f(0) / 5 - 0 = 0 - ( - 15 ) / 5 - 0

= 0 + 15 / 5 = 15 / 5 = 3

The average rate of change over the interval [0, 5] is hence 3.

Answer:

Brainleist!

Step-by-step explanation:

7 dollars

6+3 = 9 dollars spent

he will have -2 dollars

this is not possible but this is a fake made up problem so it is -2

Answer:

He'd have nothing because he can't afford it. So if he wants to eat at all he can have a sandwich, which will bring him down to a dollar

Step-by-step explanation:

==========================================================

Work Shown:

x = number of plates Bull 1 broke

y = number of plates Bull 2 broke

z = number of plates Bull 3 broke

y = x+6 because the second bull broke 6 more plates compared to the first

z = y+4 since the third bull broke 4 more plates compared to the second

They all broke a combined 58 plates, meaning,

x+y+z = 58

Replace z with y+4 to get

x+y+z = 58

x+y+y+4 = 58

x+2y+4 = 58

Then replace y with x+6

x+2y+4 = 58

x+2(x+6)+4 = 58

From here solve for x

x+2(x+6)+4 = 58

x+2x+12+4 = 58

3x+16 = 58

3x = 58-16

3x = 42

x = 42/3

x = 14

Bull 1 broke 14 plates

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

If you want to find out how many plates the other bulls broke, then use that x value to find y and z

y = x+6 = 14+6 = 20

Bull 2 broke 20 plates

z = y+4 = 20+4 = 24

Bull 3 broke 24 plates

Overall, they broke 14+20+24 = 58 plates in total, which matches the total given in the instructions. The answer has been confirmed.

Answer:

B1 = 14 plates broken

Step-by-step explanation:

Method 1

We start with (58 - 6- 4) = (58 - 10) = 48

= 48                 : We prove 6+4 = 10

To find who has the fewest plates we can now try again

with 48-6 = 42   or 48-4 = 44

42/3 = 14

We add 6  = 20

We add 4 = 24

We get 14+ 20 +24 = 58 broken plates.

So we know starting with -6 gets us our answer and our order correct.

Method 2 ; We deduct the difference from the total to find B1 distribution

B1 = 14 so 58-6  is 52 (-10)

We divide 42/3

To get 14

Conclusion;

We find method 1 shows us  

B1 = 48  B2 = 48 (+6) =54  B3 = 54(+4) = 58

And try now for (14 + 14 + 6 ) + ( 22 + 4)

= 14  + 20 + 24 = 58 broken plates.

Subtract starting population from current one:

6.34 - 1.9 = 4.44

The population increased by 4.44 million.

Answer: [tex](-\infty, \infty)[/tex]

=================================================

Explanation:

Draw out a number line. Plot 0 and -4 on the number line.

Shade to the left of x = 0, and have a filled in circle at the endpoint. This is the graph of [tex]x \le 0[/tex]

Then graph [tex]x \ge -4[/tex] by plotting a filled in circle at -4, and shading to the right.

Note how the two graphs overlap to cover the entire real number line

So if we have [tex]x \le 0 \ \text{ or } \ x \ge -4[/tex] then we're basically saying x is any real number. To write this in interval notation, we write [tex](-\infty, \infty)[/tex]

This is the interval from negative infinity to positive infinity (or just infinity). We exclude each endpoint because we can't actually reach infinity itself. Infinity is not a number. Infinity is a concept.

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

Side note: if you change the "or" to "and", then the solution to [tex]x \le 0 \ \text{ and } \ x \ge -4[/tex] would be [tex][-4, 0][/tex] to indicate the interval from x = -4 to x = 0, including both endpoints. This is the region where the two graphs overlap.

Answer:

[tex]\Huge \boxed{x=-2}[/tex]

Step-by-step explanation:

[tex]-136=8(6x-5)[/tex]

Dividing both sides by 8.

[tex]-17=6x-5[/tex]

Adding 5 to both sides.

[tex]-12=6x[/tex]

Dividing both sides by 6.

[tex]-2=x[/tex]

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 2}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ - 136 = 8(6x - 5)}[/tex]

Distribute 8 through the parentheses

⇒[tex] \sf{ - 136 = 48x - 40}[/tex]

Swap the sides of the equation

⇒[tex] \sf{48x - 40 = - 136}[/tex]

Move 40 to right hand side and change it's sign

⇒[tex] \sf{48x = - 136 + 40}[/tex]

Calculate

⇒[tex] \sf{48x = - 96}[/tex]

Divide both sides of the equation by 48

⇒[tex] \sf{ \frac{48x}{48} = \frac{ - 96}{48} }[/tex]

⇒Calculate

[tex] \sf{x = - 2}[/tex]

Hope I helped!

Best regards!!

Answer:

36 cans for $3.32

Step-by-step explanation:

36 cans = $3.32

1 can =$ 0.092

9 cans = $0.91

1 can = $0.01

0.09 and 0.1 the cheaper is 0.09 dollars so 36 cans for $3.32 is better

Answer:

y = 3 4 x − 25 4

Explanation:

We could use calculus but first as with all Mathematical problems one should step back and think about what the question is asking you, and in this case we can easily answer the question using knowledge of the equation, in this case:

x 2 + y 2 = 25

represents a circle of centre ( a , b ) = ( 0 , 0 ) and radius r = 5

First verify that ( 3 , − 4 ) actually lies on the circle;

Subs x = 3 oito the circle equation:

⇒ 3 2 + y 2 = 25 = y 2 = 16 ⇒ y = ± 4 So ( 3 , − 4 )

So does indeed lie on the circle. A straight line passing between that point and the centre of the circle ( 0 , 0 ) will be perpendicular to the tangent. So the gradient of the normal is given by:

m N = Δ y Δ x = − 4 − 0 3 − 0 = − 4 3 Then as the normal is perpendicular to the tangent the product of their gradients is − 1 , so then: m T = 3/4

So using the point/slope form y − y 1 = m ( x − x 1 ) the equation we seek is;

y − ( − 4 ) = 3/4 ( x − 3 )

∴ y + 4 = 3/4 x − 9/4

∴ y = 3/4 x − 25/4

We can confirm this solution is correct graphically:

If x 2 + y 2 = 25 then differentiating wrt x implicitly gives us:

2 x + 2 y d y d x = 0

∴ d y d x = − x/y

When x = 3 and y = − 4 ⇒ d y d x = − 3 − 4 = 3 4 , which is what we obtained.

Hoped I helped

Please give me a brainliest

Answer:

500 ft

Step-by-step explanation:

Perimeter: The total border of the outside of a given shape

Step 1: Find missing length

100 - 80 = 20 ft

Step 2: Add all together

100 + 150 + 80 + 85 + 65 + 20 = 500 ft

So we would need 500 ft of fence to border her yard completely.

Step-by-step explanation:

5³ = 5×5×5 =125

10²/2 =100/2 =50

(3+2) ×5 = 5×5 = 25

Answer:

OD. 13/12 or 1 1/12

Step-by-step explanation:

[tex] \frac{1}{6} + \frac{2}{3} + \frac{1}{4} \\ lcm = 12 \\ = \frac{2 + 8 + 3}{12} \\ [/tex]

[tex] = \frac{13}{12 } \\ 13 \div 12 = 1r1 \\ = 1 \frac{1}{12} [/tex]

Answer:

Step-by-step explanation:

price of 1 pen= $ 2

price of 1 pencil= $1

total money spent= $12

Let the number of pen be a and number of pencil be b.

 2 a + b = 12   ----------------Equation 1

We have, she bought 3 more pens than pencils

  a - b = 3   ------------------  Equation 2

 Equation 1 +Equation 2,  

   2 a + b +  a - b = 12 + 3

                     3a = 15

                     a = 5

 Substituting in  equation

           5 - b = 3

               b = 2

 Number pencils Ava bought = 2

Answer:

f(n)= (n-50)²

Step-by-step explanation:

The difference between a number n and fifty:

Square of this difference:

It would look like this as variable expression:

Answer:

78 games

Step-by-step explanation:

Think of it this way. Let's name the teams Team 1 through Team 13. Team 1 needs to have 12 games to play each other team. Once those are scheduled, Team 2 needs to have 11 games scheduled to play all the other teams (remember their game against Team 1 was already scheduled). Team 3 needs to have 10 games scheduled to play all the other teams (remember their games against Team 1 and Team 2 have already been scheduled). This patten continues until you schedule a single game between Team 12 and Team 13. So the total number of games that need to be scheduled are:

12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 =  78

I don't know if the concept of triangular numbers has been touched on in your class, but if so, there is a much simpler way to calculate this using the triangular number formula with n = 12. The formula is:

T = (n * (n + 1)) / 2

So in this case:

(12 * (12 + 1)) / 2 = (12 * 13) / 2 = 6 * 13 = 78

Answer:

  real, rational

Step-by-step explanation:

Without knowing what the average number of students is, we know the number must be a real number, and must be rational. (An average of integers is always the ratio of two integers.) It may or may not be a natural number, whole number, or integer.

Answer:

B and D

Step-by-step explanation:

A convex mirror ALWAYS produces a virtual and upright image.

The true statements are:

A spherical mirror is a mirror with curved surface; it can either be convex or concave.

Convex mirrors

The image of a convex mirror is a virtual and an upright/erect image

Concave mirrors

The image of a concave mirror can be real or virtual, but the image is always inverted.

The above highlights mean that options (b), (d) and (f) are correct.

Read more about spherical mirrors at:

https://brainly.com/question/13068249

Answer:

y=1/3x+4

Step-by-step explanation:

It should be correct as the gradient = 1/3

and the y-intercept = C

= +4

Answer: ∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ 5dA =  5/3

Step-by-step explanation:

Given that;

∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy)

Green's Theorem is given as;

∫c (P(x,y)dx + Q(x,y)dy) = ∫∫ₐ { (-β/βy) P(x,y) + (β/βy) Q(x,y) } dA

Now our P(x,y) = 3y + 7e^(√x) and our Q(x,y) = 8x + 5 cos (y²)

Since we know this, therefore; we substitute

∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ { (-β/βy) (3y + 7e^(√x))  + (β/βy) (8x + 5 cos (y²)) } dA

∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ ( 8-3) dA

∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy)  = ∫∫ₐ 5dA

from the question, our region is defined by a lower bound: y = x² and an upper bound of y = √x

going from x = 0 to x = 1

Now calculating ∫∫ₐ 5dA  by means of the description of the region, we say;

∫∫ₐ 5dA  = 5¹∫₀   ₓ²∫^(√x) dydx

∫∫ₐ 5dA =  5¹∫₀ (y)∧(y-√x) ∨(y-x²)  dx

∫∫ₐ 5dA = 5¹∫₀ (√x-x²) dx

∫∫ₐ 5dA = 5 [ ((x^(3/2))/(3/2)) - x³/3]¹₀     NOW since ∫[f(x)]ⁿ dx = ([f(x)]ⁿ⁺¹ / n+1) + C

then

∫∫ₐ 5dA = 5 [ ((1^(3/2))/(3/2)) - 1³ / 3) - ((0^(3/2))/(3/2)) - 0³ / 3) ]

∫∫ₐ 5dA = 5 [ ((1^(3/2))/(3/2)) - 1³ / 3)

∫∫ₐ 5dA = 5/3

Therefore ∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ 5dA =  5/3

In this exercise we have to use green's theorem to calculate the values ​​of the curve through the integers, so we will find that:

[tex]\int\limits \int\limits_a{5} \, dA = 5/3[/tex]

First, the integral given in this exercise corresponds to:  

[tex]\int\limits_C {((3y+7e{\sqrt{x}} dx) + (8x+5cos(y^2)) } \, dy[/tex]

Green's Theorem is given as;

[tex]\int\limits_C {(P(x,y)dx + Q(x,y)dy)} \, = \int\limits \int\limits_a { (-\beta/ \beta_y) P(x,y) + (\beta/ \beta_y) Q(x,y) } dA \,[/tex]

Now our:

[tex]P(x,y) = 3y + 7e^{(\sqrt{x} )} \\ Q(x,y) = 8x + 5 cos (y^2)[/tex]

Since we know this, therefore; we substitute:

[tex]\int\limits_C {((3y + 7e^{(\sqrt{x} )} dx + (8x + 5 cos (y^2)) dy)} = \int\limits \int\limits_a {(-\beta / \beta_y) (3y + 7e^{(\sqrt{x} )} + (\beta / \beta_y) (8x + 5 cos (y^2))} \, dA\\\int\limits_C {((3y + 7e^{(\sqrt{x} )}dx + (8x + 5 cos (y^2)) dy} = \int\limits \int\limits_a {( 8-3) dA}\\\int\limits_C {((3y + 7e^{(\sqrt{x} )}dx + (8x + 5 cos (y^2)) dy} = \int\limits \int\limits_a {5 dA}\\[/tex]

From the question, our region is defined by:

Now calculating  by means of the description of the region, we say;

[tex]\int\limits \int\limits_a {5} \, dA = 5 \int\limits^1_0 \int\limits^{\sqrt{x} }_{x^2} {x^2} \, dydx\\\int\limits \int\limits_a {5} \, dA = 5 \int\limits^1_0 {y^{\sqrt{x} } \, dx \\\int\limits \int\limits_a {5} \, dA = 5 \int\limits^1_0 {{\sqrt{x} -x^2} \, dx\\\int\limits \int\limits_a {5} \, dA = 5 [ ((x^{3/2})/(3/2)) - x^3/3][/tex]  

Knowing the formula:

[tex]\int\limits {[f(x)]^n} \, dx = ([f(x)]^{n+1} / n+1) + C[/tex]

Applying the values ​​in the presented formula we find that:

[tex]\int\limits \int\limits_a{5} \, dA = 5/3[/tex]

See more about Green's Theorem at brainly.com/question/15062695