Which relation is a function? A. {(–4, –6), (–3, –2), (1, –2), (1, 0)} B. {(–2, –12), (–2, 0), (–2, 4), (–2, 11)} C. {(0, 1), (0, 2), (1, 2), (1, 3)} D. {(8, 1), (4, 1), (0, 1), (–15, 1)}

Answer:

  B.  10.71 cents

Step-by-step explanation:

Benito's other expenses total ...

  $809 +170 +57 = $1036

so his gas expense is ...

  $1822 -1036 = $786

Then the per-mile cost is ...

  $786/(7340 mi) ≈ $0.10708/mi

Benito's gas cost averaged 10.71¢ per mile.

Answer is B) 10.71 cents.

You just add Benito's operating expenses togther, like so:

809 + 170 + 57 = $1036 so far.

Next, subtract the total amount he spent this last year (1822), with how much he spent so far (1036).

1822 - 1036 = $786

Finally, divide the final total with the 7340 miles he plans to drive.

786 ÷ 7340 = 0.10708

Answer is B) 10.71 cents.

☺☺☺☺

Final answer:

The elephant is likely measured in pounds, as it fits the known weight range for adult elephants. The mouse is measured in a smaller unit such as grams due to its size. The puppy is best measured in pounds, a common unit for pet animals.

Explanation:

In mathematics, specifically in the context of measurement, it is important to choose the most appropriate unit of measurement depending on the size of the object or substance being measured. When we look at the example scenarios, we can determine the best units as follows:

Answer:

D: (-1,2)

Step-by-step explanation:

The X coordinate is between 2 and -4. There is a difference of 6, so you should do -4 + (6/2) = -1.

so the X coordinate is -1

The y coordinate is between 0 and 4. There is a difference of 4, so you should do 0 + (4/2) = 2.

so the y coordinate is 2

This results in the centre being (-1,2)

The coordinates of the center of the equation is (- 1, 2).

We have a ellipse in the figure.

We have to find out the coordinates of the center of ellipse (x, y).

The general equation of an ellipse in the rectangular coordinate system is -

[tex]\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } = 1[/tex]

In the figure given to us, the center of the ellipse at the point of intersection of the lines of equation -

x + 1 = 0

and

y - 2 = 0

The coordinates of the center -

x = - 1    and   y =  2.

Hence, the coordinates of the center of the ellipse is (- 1, 2).

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Steps:

---> Re arrange equation to get the format: y = mx + c

---> Work out the perpendicular gradient from the first equation

----> Substitute the x and y coordinates of point (-1, 0) and the perpendicular      gradient into y = mx + c   and work out c

---> Finally, substitute the perpendicular gradient and the value for c into y =mx + c  to get the gradient of the perpendicular line:

__________________________________________

Rearranging equation into the format: y = mx + c:

[tex]5y = x - 5[/tex]                  (Just divide both sides by y)

[tex]y = \frac{1}{5}x -1[/tex]

___________________________________________

Working out the perpendicular gradient:

To work out the perpendicular gradient, we just take the negative reciprocal of the gradient of [tex]y = \frac{1}{5}x -1[/tex]

Note: negative reciprocal means we just flip the fraction and put a minus sign.

The regular gradient is: [tex]\frac{1}{5}[/tex]

So the perpendicular gradient is the negative reciprocal of [tex]\frac{1}{5}[/tex]

which is -5       (note: [tex]\frac{-5}{1}[/tex] is just 5-)

___________________________________________

Now lets substitute in the values for the gradient (m), the y coord (0) and x coord (-1) of the point (-1, 0)   into y = mx + c, and solve for c:

y = mx + c     (substitute in all known values)

0 = -5(-1) + c   (the -1 times -5 will make + 5)

0 = 5 + c        (subtract 5 from both sides to cancel out the + 5)

-5 = c

so c = -5

____________________________________________

Finally, just substitute in the perpendicular gradient and the value for c into y = mx + c   to get the equation of the perpendicular line:

y = mx + c        (substitute in the perp. gradient and c)

y = -5x - 5

____________________________________________________

The equation to the line perpendicular to 5y = x - 5 through point (-1, 0) is :

C. y = -5x - 5

_______________________________________________

A quicker way to get equation of the perpendicular line once you know the perp. gradient is to use the equation:

y - y1 = m (x - x1)

y1 is the y coordinate of (-1, 0)

x1 is the x coordinate of (-1, 0)

m is the perpendicular gradient.

y - y1 = m (x - x1)       (Substitute in values)

y - 0 = -5 ( x - - 1)       (simplify)

y = -5 (x + 1)              (expand the brackets)

y = -5x - 5

Answer:

False

Step-by-step explanation:

Correct me if I'm wrong but this suppose to be a true or false question.

The measure of angle of B is going to be half the arc measure of AC so they don't have the same measurement. If they don't have the same measurement, then they can't be congruent.

Answer:

Step-by-step explanation:

Both x and y are inscribed angles.  The value of an inscribed angle is half the measure of its intercepted arc.  This means that x has a value of 33°, and y has a value of 48°.  That means that, according to the triangle angle sum theorem, the third angle has to equal 180 - 33 - 48 = 99°.

This angle is vertical with angle z, so angle z also equals 99°

Answer:

The function that represents the total cups of coffee they made today is [tex]h(x)=9x-7[/tex].

Step-by-step explanation:

The given function are

[tex]f(x)=6x-8[/tex]

[tex]g(x)=3x+1[/tex]

Where, Kate's total cups of coffee made is represented by f(x) and Stella's total cups of coffee made is represented by g(x).

The total cups of coffee they made today is represented by the function

[tex]h(x)=f(x)+g(x)[/tex]

Substitute the value of functions.

[tex]h(x)=6x-8+3x+1[/tex]

Combine like terms.

[tex]h(x)=(6x+3x)+(-8+1)[/tex]

[tex]h(x)=9x-7[/tex]

Therefore the function that represents the total cups of coffee they made today is h(x)=9x-7.

Answer:

its 9x-7

Step-by-step explanation:

Answer:

  c.  1 ≤ y ≤ 3; y ≥ -2x +2

Step-by-step explanation:

The shading between the solid lines y=1 and y=3 tells you that one of the inequalities is 1 ≤ y ≤ 3 (including the "or equal to" case). The shading above the solid diagonal line tells you that inequality will be y ≥ (something).

Choice C matches these observations.

The number of ways to distribute five identical fruits into three bowls is solved using the stars and bars technique in combinatorics, resulting in 21 different ways.

The student is asking about the number of ways to distribute five identical fruits into three bowls, where bowls can be left empty.

This problem is a classic example of a combinatorial problem in mathematics, often approached using the stars and bars method.

The stars and bars technique is a way to solve problems related to distributing indistinguishable items into distinguishable groups.

To solve this, think of the five identical fruits as stars (*) and the separations between bowls as bars (|).

We need to place two bars to create three sections (bowls) among the five stars.

The question then becomes: In how many ways can we arrange five stars and two bars?

This is equivalent to choosing two places for bars out of seven possible positions (five stars plus two bars).

The number of ways we can choose two positions out of seven for the bars is given by the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of items and k is the number of items to choose.

In this case, C(7, 2) = 7! / (2!5!) = 21 ways.

Therefore, there are 21 different ways to distribute five identical fruits into three bowls.

Answer:

  a)  t = 2 seconds

  b)  6.05 meters

Step-by-step explanation:

I prefer a graph for questions like this, but I have attached a table, too. Here, the table is created using a graphing calculator to evaluate the function. A spreadsheet can do this nicely, too.

The maximum height occurs at t=0.9 seconds, and the ball hits the ground at a time that is slightly more than double that, 2.0 seconds.

The maximum height is 6.05 meters.

Answer:

C. is your answer

Step-by-step explanation:

In order to determine the line of symmetry, it would help to put this standard form parabola into vertex form, which is

[tex]y=a(x-h)^2+k[/tex],

where x = h is the equation of the line of symmetry.

To get this into vertex form we will complete the square.  The first couple of steps I will combine into 1.  We will set the quadratic equal to zero, then move the constant over to the other side:

[tex]88x^2-264x=-300[/tex]

The next rule is that the leading coefficient HAS to be a positive 1.  Ours is a positive 88, so we have to factor it out:

[tex]88(x^2-3x)=300[/tex]

Now we can perform the process of completing the square.  The rule is to take half the linear term, square it, and add it to both sides.  Our linear term is 3.  Half of 3 is 3/2, and 3/2 squared is 9/2.  We will add 9/2 inside the parenthesis on the left, but don't forget about that 88 sitting out front which refuses to be ignored.  It serves as a multiplier into the parenthesis.  What we actually added in, then, was 88(9/2) which is 198:

[tex]88(x^2-3x+\frac{9}{4})=-300+198[/tex]

The purpose of completing the square is to give us a perfect square binomial which serves as the axis of symmetry of the parabola and also gives us the h coordinate of the vertex.  We will state that binomial and at the same time do the addition on the right:

[tex]88(x-\frac{3}{2})^2=-102[/tex]

Now we can move the constant back over and set it back equal to y:

[tex]y=88(x-\frac{3}{2})^2+102[/tex]

From that form you can see that the equation of the line of symmetry is x = 1.5.  The coordinates of the vertex are (1.5, 102).  If we move 1 unit to the left of the vertex, or 1 unit to the right of the vertex, we will be at the same height.

C then is your answer.

The solution is : C. is the answer.

C. The trajectory of the airplane is symmetric about the line x = 1.5 km, which indicates that the height of the airplane when it moves a horizontal distance of 0.5 km is the same as the height of the airplane when it moves a horizontal distance of 2.5 km.

The parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. It fits several superficial different mathematical descriptions.

here, we have,

In order to determine the line of symmetry, it would help to put this standard form parabola into vertex form, which is

y = a (x-h)^2 + k

,where x = h is the equation of the line of symmetry.

To get this into vertex form we will complete the square.  The first couple of steps I will combine into 1.  We will set the quadratic equal to zero, then move the constant over to the other side:

88x^2 - 264x = -300

The next rule is that the leading coefficient HAS to be a positive 1.  Ours is a positive 88, so we have to factor it out:

88( x^2 - 3x) = 300

Now we can perform the process of completing the square.  The rule is to take half the linear term, square it, and add it to both sides.  Our linear term is 3.  Half of 3 is 3/2, and 3/2 squared is 9/2.  We will add 9/2 inside the parenthesis on the left, but don't forget about that 88 sitting out front which refuses to be ignored.  It serves as a multiplier into the parenthesis.  What we actually added in, then, was 88(9/2) which is 198:

88( x^2 - 3x + 9/4 ) = -300 + 198

The purpose of completing the square is to give us a perfect square binomial which serves as the axis of symmetry of the parabola and also gives us the h coordinate of the vertex.  We will state that binomial and at the same time do the addition on the right:

88( x - 3/2)^2 = -102

Now we can move the constant back over and set it back equal to y:

y = 88( x - 3/2)^2 + 102

From that form you can see that the equation of the line of symmetry is x = 1.5.  The coordinates of the vertex are (1.5, 102).  If we move 1 unit to the left of the vertex, or 1 unit to the right of the vertex, we will be at the same height.

C then is the answer.

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Answer:

A  f(x) = 1/3x^3

Step-by-step explanation:

g(x) = x^3

We want f(x) to be vertically compressed

f(x) = ag(x )    

a is vertical stretch/compression

|a| > 1 stretches  

|a| < 1 compresses

so we need to multiply by a number less than between 0 and 1

If a is negative it is a reflection, which was not asked for

f(x) = 1/3 x^3

Answer:

A  f(x) = 1/3x^3

Step-by-step explanation:

g(x) = x^3

We want f(x) to be vertically compressed

f(x) = ag(x )    

a is vertical stretch/compression

|a| > 1 stretches  

|a| < 1 compresses

so we need to multiply by a number less than between 0 and 1

If a is negative it is a reflection, which was not asked for

f(x) = 1/3 x^3

Let Tony's age = x

He is 4 years younger than his brother Josh, so Josh's age would be x + 4

He is 2 years older than his sister, so her age would be x - 2

He has a twin, which would be the same age, so the twins age is also x

They all add together to equal 66, so you get:

x  + x + x+4 + x-2 = 66

Simplify:

4x +2 = 66

Subtract 2 from both sides:

4x = 64

Divide both sides by 4:

x = 64/4 = 16

Tony is 16 years old.

Final answer:

By setting up an equation with Tony's age as T, and considering the ages of his siblings, we find that Tony is 16 years old.

Explanation:

Tony is 4 years younger than his brother Josh and two years older than his sister Cindy. Additionally, Tony has a twin brother, Evan. If we add the ages of Tony, Josh, Evan, and Cindy, the total is 66 years. To solve for Tony's age, we need to set up an equation. Let's assume Tony's age is T years.

Since Tony is 4 years younger than Josh, Josh is T + 4 years old. As Tony has a twin brother, Evan, Evan is also T years old. Cindy, being two years younger than Tony, is T - 2 years old. So, the sum of all their ages is:

T + (T + 4) + T + (T - 2) = 66

Combining like terms, we get:

4T + 2 = 66

Subtracting 2 from both sides gives us:

4T = 64

Dividing both sides by 4 results in:

T = 16

Therefore, Tony is 16 years old.

[tex](x-(-2))(x-(-3))(x-(3-6i)(x-(3+6i))=\\(x+2)(x+3)(x-3+6i)(x-3-6i)=\\(x^2+3x+2x+6)((x-3)^2+36)=\\(x^2+5x+6)(x^2-6x+9+36)=\\(x^2+5x+6)(x^2-6x+45)=\\x^4-6x^3+45x^2+5x^3-30x^2+225x+6x^2-36x+270=\\x^4-x^3+21x^2+189x+270[/tex]

Answer:

A.  70 miles per hour B.  620 miles from home

Step-by-step explanation:

This function is a linear equation, following the slope-intercept form of a line.  This standard form is y = mx + b, where m is the slope and b is the y-intercept.  The slope of a line is the rate at which the steepness of the line is changing.  The y-intercept is where the function is "starting".

In our case, the number in the rate of change position is 70.  It is being multiplied by t.  If t = 1, that means that after 1 hour, we have gone 70 miles.  If t = 2, that means after 2 hours we have gone 140 miles.  If t = 3, that means that after 3 hours, we have gone 210 miles; etc.  That number in the slope position represents the rate at which you are traveling PER HOUR; the slope.

The "starting" position of day 2 is found in the y-intercept.  Replacing x with 0, meaning NO time has gone by at all, at the beginning of the second day, we are starting 620 miles from home.

The family's car is traveling at an average speed of 70 miles per hour. The distance between the family's house and the starting point on the second day is 620 miles.

The given function d(t) = 70t + 620 models the distance in miles from the family's house t hours after starting to drive on the second day of their road trip.

A) At what average speed is the family's car traveling?

The coefficient of t in the distance function, which is 70, represents the family's car average speed. Therefore, the car is traveling at an average speed of 70 miles per hour.

B) What is the distance between the family's house and the point where they started driving on the second day?

The constant term in the distance function, which is 620, signifies the distance in miles from the family's house at t = 0 or the starting point. Thus, the distance between the family's house and the starting point on the second day is 620 miles.

Answer:

[tex]\large\boxed{Q5.\ x=45\sqrt2}\\\boxed{Q6.\ x=8\sqrt2,\ y=4\sqrt6}[/tex]

Step-by-step explanation:

Q5.

x it's a diagonal of a square.

The formula of a length of diagonal of a square:

[tex]d=a\sqrt2[/tex]

a - side of a square

We have a = 45.

Substitute:

[tex]x=45\sqrt2[/tex]

Q6.

Look at the first picture.

In a triangle 45° - 45° - 90°, all sides are in ratio 1 : 1 : √2.

In a triangle 30° - 60° - 90°, all sidea are in ratio 1 : √3 : 2.

Look at the second picture.

from the triangle 45° - 45° - 90°

[tex]a\sqrt2=8[/tex]        multiply both sides by √√2  (use √a · √a = a)

[tex]2a=8\sqrt2[/tex]      divide both sides by 2

[tex]a=4\sqrt2[/tex]

from the triangle 30° - 60° - 90°

[tex]x=2a\to x=2(4\sqrt2)=8\sqrt2[/tex]

[tex]y=a\sqrt3\to y=(4\sqrt2)(\sqrt3)=4\sqrt6[/tex]

Answer:

6. [tex]\displaystyle 4\sqrt{6} = y \\ 4\sqrt{2} = x[/tex]

5. [tex]\displaystyle 45\sqrt{2} = x[/tex]

Step-by-step explanation:

30°-60°-90° Triangles

Hypotenuse → 2x

Short Leg → x

Long Leg → x√3

45°-45°-90° Triangles

Hypotenuse → x√2

Two identical legs → x

6. You solve the shorter triangle first:

[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ \\ x^2 + x^2 = 8^2 \\ \\ \frac{2x^2}{2} = \frac{64}{2} → \sqrt{x^2} = \sqrt{32} \\ \\ 4\sqrt{2} = x[/tex]

Now that we know our x-value, we can solve the larger triangle:

[tex]\displaystyle 4\sqrt{6} = 4\sqrt{2}\sqrt{3} \\ \\ 4\sqrt{6} = y[/tex]

5. This exercise is EXTREMELY SIMPLE since two congruent isosceles right triangles form that square, so all you have to do, according to the rules for 45°-45°-90° triangles, is attach [tex]\displaystyle \sqrt{2}[/tex]to 45, giving you [tex]\displaystyle 45\sqrt{2}.[/tex]

I am joyous to assist you anytime.

Answer:

The answer would be C. 1,926.97 :)

Answer:

Option C

Step-by-step explanation:

Principal,P = $8180

Time = 10 years

Rate,R = 5.3% compounded monthly

Formula: [tex]P(1+\frac{R}{n} )^{nt}[/tex], where n is the number of times interest is compounded that is monthly, quarterly, yearly.

Now, we have to calculate the interest by the time Sebastian has graduated that is the time now is 4 years, t = 4 and n = 12, because the interest is compounded monthly.

Puttin all the values in the formula

Amount = [tex]8180(1+ \frac{5.3}{1200} )^{48}[/tex] = 10106.9707$

Also, Interset = Amount - Principal

Interest = 10106.9707$ - 8180$ = 1926.97074$

Option C

Answer:

C is correct as well as D.

Step-by-step explanation:

The rhombus also shares the common traits that the picture shows

Answer:

so  equation for the temperature in terms of t is D = 5 sin [tex]\pi[/tex] / 12 (t) + 45

Step-by-step explanation:

Given data

temperature = 45 degrees

high temperature = 50 degrees

low temperature = 40 degrees

to find out

an equation for the temperature in terms of t

solution

first we find the amplitude i.e.

Amplitude (A) = ( high temperature - low temperature )  / 2

Amplitude (A) = (50 - 40)  / 2

Amplitude (A)  = 5

here we know in a day 24 hours so

2[tex]\pi[/tex] /K = 24

K = [tex]\pi[/tex] / 12

so we have temperature equation is

temperature D = amplitude sinK (t) + avg temperature midnight

D = 5 sin [tex]\pi[/tex] / 12 (t) + 45

so  equation for the temperature in terms of t is D = 5 sin [tex]\pi[/tex] / 12 (t) + 45

The temperature over a day can be modeled as a sinusoidal function. The equation for the temperature, D, in terms of t is: D = 5cos((pi/12)t) + 45.

The temperature over a day can be modeled as a sinusoidal (sine or cosine) function. To find an equation for the temperature, we can use the cosine function because it starts at its maximum value at t = 0, which corresponds to midnight. The equation for the temperature, D, in terms of t is:

D = 5cos((pi/12)t) + 45

Here, t represents the number of hours since midnight, and D represents the temperature in degrees. The amplitude of the sinusoidal function is 5, which represents the difference between the high and low temperatures. The cosine function is scaled and shifted to match the given data: it is multiplied by 5 to match the amplitude, and 45 is added to shift the function vertically so that it starts at 45 degrees at t = 0.

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Answer:

Option C is correct.

Step-by-step explanation:

Homework is assigned: 3 times a week

Each assignment consists problems = 12

Total questions in 1 week = 12*3 = 36

Total no of students = 25

So, Problems Darren must correct each week = Total no of students * Total questions in 1 week

Problems Darren must correct each week = 25*36

Problems Darren must correct each week = 900

So, Option C is correct.

For this case we have that each week assign 3 tasks, each of 12 problems, then multiply:

[tex]3 * 12 = 36[/tex]

Thus, assign 36 weekly problems to each student. Darren has 25 students, so, multiplying, we have:

[tex]36 * 25 = 900[/tex]

Thus, Darren must correct 900 weekly problems.

Answer:

Option C

Answer:

They are both the same at 3/4 of an hour

Step-by-step explanation:

We have a system of equations here.  The first one is for Friday:

3A + 5B = 6, which says that 3 people at the number of hours for plan A plus 5 people at the number of hours for plan B equals 6 hours total.

The second equation is for Saturday:

9A + 7B = 12, which says that 9 people at the number of hours for plan A plus 7 people at th number of hours for plan B equals 12 hours total.

We can solve this easily using the addition/elimination method.  Begin by multipying the first equation through by a -3 to eliminate the A's.  That gives you a new first equation of:

  -9A  -  15B  =  -18

  9A  +    7B  =  12

You can see that the A's are eliminated, and adding what remains leaves us with

-8B = -6 so

B = 3/4 hour

Now we can sub that back in for B in either one of our original equations to solve for A.  I changed the 3/4 to .75 for ease of multiplying:

9A + 7(.75) = 12 and

9A + 5.25 = 12 and

9A = 6.75 so

A = .75 which is also 3/4 of an hour

Answer:

[tex]\large\boxed{A).\,x^2+3x+5}[/tex]

Step-by-step explanation:

In this question, we're trying to figure out what f(x) + g(x)  equals to.

We are going to be plugging in the equations they gave to us and solve.

Equations we're going to use:

Now, lets get to solving.

We would plug the equations in the appropriate spot. In other words, we're pretty much plugging them in to the right variable.

Your expression should look like this:

[tex]3x+5+x^2[/tex]

Now we solve.

[tex]3x+5+x^2\\\\x^2\,\text{can't combine with 3x because of the exponent, so we will eave it as is}\\\\\text{There is nothing else we can combine, so it would stay as:}\\\\x^2+3x+5[/tex]

You should end up with x²+3x+5.

This means that your final answer would be A) x^2 +3x+5

Answer:

1st line

Step-by-step explanation:

Should be z=11-3x-2y, then solve from there.

Answer: [tex](11.44,\ 17.4)[/tex]

Step-by-step explanation:

The confidence interval for population mean is given by :-

[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]

Given : Sample size : [tex]n=36[/tex]

Sample mean : [tex]\ovreline{x}=14.42[/tex]

Standard deviation : [tex]\sigma=6.95[/tex]

Significance level : [tex]\alpha=1-0.99=0.01[/tex]

Critical value : [tex]z_{\alpha/2}=z_{0.005}=2.576[/tex]

Now, the 99% confidence interval for the mean percent body fat in all men aged 20 to 29 will be :-

[tex]14.42\pm (2.576)\dfrac{6.95}{\sqrt{36}}\\\\\approx14.42\pm2.98\\\\=(14.42-2.98,\ 14.42+2.98)=(11.44,\ 17.4)[/tex]

Answer:

The answer is 0.067.

Step-by-step explanation:

Let the entire sample size be = s

Now there are 2 laptops in sample size, hence these can be chosen in one way only.

The required probability that both selected setups are for laptop computers can be found as:

[tex]p(two laptops)=\frac{s(two laptops)}{s}[/tex]

= [tex]\frac{1}{15}[/tex] or 0.067.

So, the probability is 0.067.

The probability of both selected setups being for laptop computers is 2/15.

The probability of both selected setups being for laptop computers can be calculated as the ratio of favorable outcomes to total outcomes. Out of the six computers, two have been selected to be laptops. The first laptop can be any of the two laptops, and the second laptop can be any of the remaining one laptop. Therefore, the probability of both selected setups being for laptop computers is 2/15.

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Answer:

$352

Step-by-step explanation:

Simple interest (I) is calculated as

I = [tex]\frac{PRT}{100}[/tex]

where P is the principal ( investment), R is the rate of interest and T is time in years, thus

I = [tex]\frac{275(8)(16)}{100}[/tex] = $352

Answer:

$352

Step-by-step explanation:

Explanation:

Polygons are classified by ...

The number of coordinate pairs will define the number of vertices.

The differences between "adjacent" coordinate pairs can be used to find side lengths and relationships (angles, parallel, perpendicular).

_____

If the differences between adjacent coordinate pairs are ...

  (∆x, ∆y) = (x2 -x1, y2 -y1)

then the slope of the line joining those coordinates is ∆y/∆x. (This may be "undefined" if ∆x = 0.) Two line segments with the same slope are parallel. Two line segments with slopes that have a product of -1 are perpendicular. (Two segments with slopes of 0 and "undefined" are also perpendicular.)

It can be useful on occasion to know that the angle (α) a line segment makes with the x-axis can be found from ...

  α = arctan(slope)

The length of a line segment (d) can be found from the Pythagorean theorem:

  d = √((∆x)² +(∆y)²)

Answer:

1/2 units (I'm not sure what units the scale is using).

Step-by-step explanation:

We could setup a proportion. The trick to doing this is lining up corresponding parts.

The scale of a plan is 1 to 200.

We want to know the scale distance that represents the distance 100 m.

So we have:

1 to 200

x to 100

Setting up a proportion:

[tex]\frac{1}{x}=\frac{200}{100}[/tex]

Cross multiply:

[tex]100(1)=200(x)[/tex]

Divide both sides by 200:

[tex]\frac{100(1)}{200}=x[/tex]

[tex]\frac{100}{200}=x[/tex]

[tex]\frac{1}{2}=x[/tex]

[tex]x=\frac{1}{2}[/tex]

So a 1/2 units in length on the scale represents 100 m.

Answer:

Step-by-step explanation:

if you can pick the same card 3 times the probability of winning is

[tex](\frac{5}{10})^{3} = \frac{1}{8}[/tex]

but if you remove each card after you've picked them it's :

[tex]\frac{5}{10}.\frac{4}{9}.\frac{3}{8}= \frac{60}{720}[/tex]

notice if you remove an odd card every time you pick one of them you are also removing one of the overall cards

and if you subtract these two you get : [tex]\frac{1}{8} - \frac{60}{720} =0.0417[/tex]

which is like 4 percent

Answer:

[tex]\theta=\frac{\pi}{2},\frac{3\pi}{2}\frac{2\pi}{3}\frac{4\pi}{3}[/tex]

Step-by-step explanation:

You need 2 things in order to solve this equation:  a trig identity sheet and a unit circle.

You will find when you look on your trig identity sheet that

[tex]cos(2\theta)=1-2sin^2(\theta)[/tex]

so we will make that replacement, getting everything in terms of sin:

[tex]sin(\theta)+1=1-2sin^2(\theta)[/tex]

Now we will get everything on one side of the equals sign, set it equal to 0, and solve it:

[tex]2sin^2(\theta)+sin(\theta)=0[/tex]

We can factor out the sin(theta), since it's common in both terms:

[tex]sin(\theta)(2sin(\theta)+1)=0[/tex]

Because of the Zero Product Property, either

[tex]sin(\theta)=0[/tex] or

[tex]2sin(\theta)+1=0[/tex]

Look at the unit circle and find which values of theta have a sin ratio of 0 in the interval from 0 to 2pi.  They are:

[tex]\theta=\frac{\pi}{2},\frac{3\pi}{2}[/tex]

The next equation needs to first be solved for sin(theta):

[tex]2sin(\theta)+1=0[/tex] so

[tex]2sin(\theta)=-1[/tex] and

[tex]sin(\theta)=-\frac{1}{2}[/tex]

Go back to your unit circle and find the values of theta where the sin is -1/2 in the interval.  They are:

[tex]\theta=\frac{2\pi}{3},\frac{4\pi}{3}[/tex]