The slope of the line passing through the points (0,0) and (2,3) is

Final answer:

There can be a total of 11,175 two-person conversations at the party.

Explanation:

In a party with 150 people, the number of two-person conversations that can occur can be calculated using the formula for combinations. Since each conversation involves two people, we need to choose 2 people from the total of 150. The formula for combinations is:

C(n, r) = n! / (r!(n-r)!)

Where n is the total number of people and r is the number of people we need to choose. Plugging in the values, we have:

C(150, 2) = 150! / (2!(150-2)!)

C(150, 2) = (150 ×149) / (2 ×1)

C(150, 2) = 11175

Therefore, there can be a total of 11,175 two-person conversations at the party.

Final answer:

At a party with 150 people, there can be 11175 unique two-person conversations, calculated using the combination formula 150C2.

Explanation:

The question is asking how many two-person conversations can occur at a party with 150 people. This is a classic combination problem where we need to calculate the number of unique pairs that can be made from 150 people. Since the order in which the pair is chosen does not matter, we use the combination formula nCr = n! / (r!(n-r)!), where 'n' is the total number of people and 'r' is the group size (in this case, 2 for a two-person conversation).

For 150 people, the calculation is:

150C2 = 150! / (2!(150-2)!) = 150! / (2! x 148!) = (150 x 149) / (2 x 1) = 11175.

Therefore, there can be 11175 unique two-person conversations at a party with 150 people.

The equation that models the data in the table is:

                        [tex]c=22d[/tex]

The table that represent the days and cost is given by:

       Days Cost

           2          44

           3          66

           5           110

           6          132

We see that the cost is a constant multiple of  the number of days.

i.e. the equation is given by:

             c=22d

i.e. the relationship is linear.

( Since, when d=2

we have: c=22×2=44

when d=3 we have:

c=22×3=66

and so on )

Answer:

$16.98

hope this helps you! good luck ;)

Answer:

[tex]m=\frac{s-c}{c}[/tex]

Step-by-step explanation:

The given expression is

[tex]s=c+mc[/tex]

Now, to find the expression for [tex]m[/tex], we just have to isolate it. First, we have to move the term [tex]c[/tex] to the other side of the equation, and then to move the coefficient [tex]c[/tex], which is gonna pass to the other side dividing.

[tex]s=c+mc\\s-c=mc\\\frac{s-c}{c}=m\\m=\frac{s-c}{c}[/tex]

Therefore, the percent markup is defined as the difference between the selling price and cost, divided by that cost.

To find the side of a square with a given diagonal length, apply the Pythagorean theorem. With a diagonal of 8 miles, the side length is calculated to be 4√2 miles.

To find the side of a square whose diagonal is given, we can use the Pythagorean theorem. In a square, the diagonal creates two right-angled triangles, each with the square's sides as the legs.

Let the side of the square be s, and the given diagonal is 8 miles. According to the Pythagorean theorem, the diagonal (d) is calculated as d = √(s² + s²). Simplifying, this becomes d = √(2 * s²) or s = d / √2. Substituting the value of the diagonal, we get s = 8 / √2. To get rid of the radical in the denominator, we can multiply both the numerator and denominator by √2, giving us s = (8√2) / 2, which simplifies to s = 4√2 miles. Therefore, the side of the square is 4√2 miles.

The missing part of the unit rate in the given situation is 8 students per group. This is obtained from dividing the total number of students (40) by the total number of groups (5).

To find the missing part of the unit rate, we'll need to divide the total number of students (40) by the total number of groups (5). This is because a unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

So in this case, the unit rate would be 40 ÷ 5 = 8. Therefore, the missing part of the unit rate is 8 students per group.

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Final answer:

Each friend would receive $88 from the total earnings of $264 over three days, after splitting the amount equally.

Explanation:

The question asks how much money each person would get from a total earning of $75 on the first day, $84 on the second day, and $105 on the third day after splitting it equally among three friends. To find this out, first, we need to calculate the total earnings by adding the amounts from all three days, and then we divide the total by three, since there are three friends.

The total earnings over the three days are $75 + $84 + $105 = $264. To find out how much each person gets, we divide this amount by 3:

$264 ÷ 3 = $88

So, each friend would get $88 for their work over those three days.

The translation of a phrase into a variable expression is given by:

                            b+7

The letter ' b ' is used to name the variable.

The total number of slices of bread used for the sandwiches and the 7 still left in the loaf.

Let b be the total number of slices that were used for the sandwiches.

and also 7 are still left in the loaf

The total number of slices of bread= Number of slices used fro sandwich+Left over

                    Hence, the expression is:

                                 b+7

The equation of the parabola that models the movement of the football is y = -2x² + 5x + 12. The time at which the ball hits the ground is x = 4 seconds.

The quadratic equation is defined as a function containing the highest power of a variable is two.

a. We know that the general form of the quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

We are given three points that the football passes through: (1, 15), (2, 14), and (3, 9).

We can substitute these points into the quadratic equation and solve for a, b, and c.

For the first point, we have: 15 = a(1)² + b(1) + c

For the second point, we have: 14 = a(2)² + b(2) + c

For the third point, we have: 9 = a(3)² + b(3) + c

Solving this system of equations using elimination gives us:

a = -2

b = 5

c = 12

Therefore, the equation of the parabola that models the movement of the football is y = -2x² + 5x + 12.

b. To find the time at which the ball hits the ground, we can set the value of y equal to 0 and solve for x.

y = -2x² + 5x + 12

0 = -2x² + 5x + 12

-12 = -2x² + 5x

-2x² + 5x - 12 = 0

We can use the quadratic formula to solve for x:

x = (-5 +/- √(5² - 4(-2)(-12)))/(2(-2))

x = (-5 +/- √(25 + 96))/(-4)

x = (-5 +/- √(121))/(-4)

x = (-5 +/- 11)/(-4)

Therefore, x = 4 or x = -3/2.

The time at which the ball hits the ground is x = 4 seconds.

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Final answer:

The value of r that makes the line through (5, 2) and (7, r) have a slope of -1/2 is 1.

Explanation:

To determine the value of r so that the line through the points (5, 2) and (7, r) has a slope of m= -1/2, we use the slope formula m = (y2 - y1) / (x2 - x1). Here, (x1, y1) is (5, 2) and (x2, y2) is (7, r).

Slope calculation:
-1/2 = (r - 2) / (7 - 5)
-1/2 = (r - 2) / 2

Multiplying both sides by 2 to isolate the variable r:
-1 = r - 2
r = 2 - 1
r = 1

Therefore, the value of r that makes the slope -1/2 is 1.

The Panthers are expected to win approximately 73 games out of 110 based on their current win rate.

To find out how many games the Panthers will win in a normal 110-game season based on their current winning rate from the beginning of the season, we use a simple proportion. Initially, they won 40 games out of 60, which gives us a winning ratio.

The ratio can be written as:

40 wins / 60 games = number of wins / 110 games

To find the number of wins, we cross-multiply and solve for the unknown:

(40 wins / 60 games) * 110 games = number of wins

After the calculation:

40 * 110 / 60 ≈ 73.33

As we need to round to the nearest game, it gives us approximately 73 games out of 110.

n + q = 35

n = 35-q

0.05n + 0.25q = 8.15

0.05(35-q) +0.25q = 8.15

1.75 -0.05q + 0.25q =8.15

1.75 + 0.20q = 8.15

0.20q = 6.40

q = 6.40 / 0.20 = 32

32 quarters and 3 nickels

this cannot be factored.

 there are no 2 numbers that when added will equal - 12 and when multiplied together would equal -36

The truck's displacements in the North-South and East-West directions are calculated separately. The final displacement is 5 blocks South and 12 blocks East.

To solve this problem, we need to consider the truck's displacement in the North-South direction and the East-West direction separately.

Starting with the North-South direction, the truck moves 21 blocks North and then 26 blocks South. Thus, its total displacement in the North-South direction is 21 - 26 = -5 blocks. The negative sign indicates that the truck is 5 blocks South from its starting point.

Considering the East-West direction, the truck moves 12 blocks East. Therefore, its total displacement in the East-West direction is +12 blocks.

Overall, the displacement of the truck from the origin is 5 blocks South and 12 blocks East.

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Answer:

In forensic science trigonometry can be used to calculate a projectile’s trajectory, to estimate what might have caused a collision in a car accident or how did an object fall down from somewhere, or in which angle was a bullet shot etc.

Electrical engineers also use trigonometry. Modern power companies use alternating current to send electricity over long-distance wires. In an alternating current, the electrical charge regularly reverses direction to deliver power safely and reliably to homes and businesses.

Electrical engineers use trigonometry to model this flow and the change of direction, with the sine function used to model voltage. Every time you flip on a light switch or turn on the television, you’re benefiting from one of trigonometry's many uses.

Answer:

The slope of ZW is [tex]\frac{2}{5}[/tex]

The lenght of ZY is [tex]\sqrt{29}[/tex]

Quadrilateral WXYZ is a square

Step-by-step explanation:

Statements

case A) The slope of ZW is [tex]\frac{2}{5}[/tex]

The statement is True

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex]Z(-3,1),W(2,3)[/tex]

substitute

[tex]m=\frac{3-1}{2+3}[/tex]

[tex]m=\frac{2}{5}[/tex]

case B) The slope of YX is [tex]-\frac{5}{2}[/tex]

The statement is False

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex]Y(-1,-4),X(4,-2)[/tex]

substitute

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

[tex]m=\frac{2}{5}[/tex]

case C) The lenght of ZY is [tex]\sqrt{29}[/tex]

The statement is True

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]Z(-3,1),Y(-1,-4)[/tex]

substitute

[tex]d=\sqrt{(-4-1)^{2}+(-1+3)^{2}}[/tex]

[tex]d=\sqrt{(-5)^{2}+(2)^{2}}[/tex]

[tex]d=\sqrt{29}\ units[/tex]

case D) The lenght of WX is [tex]5[/tex]

The statement is False

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]W(2,3),X(4,-2)[/tex]

substitute

[tex]d=\sqrt{(-2-3)^{2}+(4-2)^{2}}[/tex]

[tex]d=\sqrt{(-5)^{2}+(2)^{2}}[/tex]

[tex]d=\sqrt{29}\ units[/tex]

case E) Quadrilateral WXYZ is a square

The statement is True

Because  sides ZW and YX are parallel sides (has the same slope)

Slope ZY

we have

[tex]Z(-3,1),Y(-1,-4)[/tex]

[tex]m=\frac{-4-1}{-1+3}[/tex]

[tex]m=-\frac{5}{2}[/tex]

so

ZW and ZY are perpendicular sides (the product of their slopes is equal to minus one)

[tex]-\frac{5}{2}*\frac{2}{5}=-1[/tex]

Slope WX

we have

[tex]W(2,3),X(4,-2)[/tex]

[tex]m=\frac{-2-3}{4-2}[/tex]

[tex]m=-\frac{5}{2}[/tex]

ZY and WX are parallel sides (has the same slope)

distance ZW

we have

[tex]Z(-3,1),W(2,3)[/tex]

[tex]d=\sqrt{(3-1)^{2}+(2+3)^{2}}[/tex]

[tex]d=\sqrt{(2)^{2}+(5)^{2}}[/tex]

[tex]d=\sqrt{29}\ units[/tex]

distance YX

we have

[tex]Y(-1,-4),X(4,-2)[/tex]

[tex]d=\sqrt{(-2+4)^{2}+(4+1)^{2}}[/tex]

[tex]d=\sqrt{(2)^{2}+(5)^{2}}[/tex]

[tex]d=\sqrt{29}\ units[/tex]

The four sides are congruent

case F) [tex]YZ=\sqrt{(-3-(-1))^{2}+(1-4)^{2}}[/tex]

The statement is False

[tex]YZ=\sqrt{(-2)^{2}+(-3)^{2}}[/tex]

[tex]YZ=\sqrt{13}[/tex]  ----> is not correct

the value of YZ is  [tex]\sqrt{29}[/tex]  

Distance between the points A (-4, 2) and B (15, 6) is 19.41.

Here,

The points are A (-4, 2) and B (15, 6).

We have to find the distance between the points A (-4, 2) and B (15, 6).

What is Distance between two points?

Distance between two points A (x₁, y₁) and B (x₂, y₂) is given by:

[tex]D_{AB} = \sqrt{(x_{2}-x_{1} )^2+(y_{2} -y_{1} )^2}[/tex]

Now,

Distance between the points A (-4, 2) and B (15, 6) is;

[tex]D_{AB} = \sqrt{(15-(-4))^2+(6-2)^2}[/tex]

       [tex]= \sqrt{19^2+4^2}[/tex]

       [tex]= \sqrt{361+16}[/tex]

       [tex]= \sqrt{377}[/tex]

       [tex]= 19.41[/tex]

Hence, Distance between the points A (-4, 2) and B (15, 6) is 19.41.

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