Triangle FGH is translated using the rule (x,y) > (x+3,y-1). What are the coordinates of H ?

The exact circumference of the circle is [tex]7 \frac{49}{150} k m[/tex]

The approximate circumference of the circle is [tex]7.33 k m[/tex]

Explanation:

The diameter of the circle is [tex]2 \frac{1}{3} \mathrm{km}[/tex]

Now, we shall find the circumference of the circle.

The formula to determine the circumference of the circle is given by

[tex]C=\pi d[/tex]

Where C is the circumference , [tex]\pi[/tex] is 3.14 and [tex]d=2 \frac{1}{3} \mathrm[/tex] is the diameter of the circle.

The exact circumference of the circle is given by

[tex]\begin{aligned}C &=\pi d \\&=(3.14)\left(2 \frac{1}{3}\right) \\&=(3.14)\left(\frac{7}{3}\right) \\&=\frac{21.98}{3}\end{aligned}[/tex]

Multiply both numerator and denominator by 100, we get,

[tex]C=\frac{2198}{300} \\C=\frac{1099}{150}[/tex]

Converting [tex]\frac{1099}{150}[/tex] into mixed fraction, we get,

[tex]C=7 \frac{49}{150}[/tex]

Thus, the exact circumference of the circle is [tex]7 \frac{49}{150} k m[/tex]

The approximate value of the circumference can be determined by dividing the value [tex]\frac{1099}{150}[/tex]

[tex]C=\frac{1099}{150}=7.327[/tex]

[tex]C=7.33km[/tex]

Thus, the approximate circumference of the circle is [tex]7.33 k m[/tex]

(3x³ - 17x² + 15x - 25)/(x - 5) =

= (3x³ - 15x² - 2x² + 0x + 5x - 25)/(x - 5)

= [3x²(x - 5) - 2x(x - 5) + 5(x - 5)]/(x - 5)

= (3x² - 2x + 5)(x - 5)/(x - 5)

= 3x² - 2x + 5

(5x³ + 18x² + 7x - 6)/(x + 3) =

= (5x³ + 5x² + 13x² + 13x - 6x - 6³)/(x + 3)

= [5x²(x + 1) + 13x(x + 1) - 6(x + 1)]/(x + 3)

= (x + 1)(5x² + 13x - 6)/(x + 3)

= (x + 1)(5x² + 15x - 2x - 6)/(x + 3)

= (x + 1)[5x(x + 3) - 2(x + 3)]/(x + 3)

= (x + 1)(5x - 2)(x + 3)/(x + 3)

= (x + 1)(5x - 2)

(4x³ + 8x² - 9x - 18)/(x + 2) =

= [4x²(x + 2) - 9(x + 2)]/(x + 2)

= (4x² - 9)(x + 2)/(x + 2)

= (4x² - 9)

= (2x - 3)(2x + 3)

(9x³ - 16x - 18x² + 32)/(x - 2) =

= [x(9x² - 16) - 2(9x² - 16)]/(x - 2)

= (9x² - 16)(x - 2)/(x - 2)

= 9x² - 16

= (3x - 4)(3x + 4)

(- x³ + 75x - 250)/(x + 10) =

= ( - x³ + 5x² - 5x² + 25x + 50x - 250)/(x + 10)

= [ - x²(x -5) - 5x(x - 5) + 50(x - 5)]/(x + 10)

= - (x - 5)(x² + 10x - 5x - 50)/(x + 10)

= - (x - 5)[x(x + 10) - 5(x + 10)]/(x + 10)

= - (x - 5)(x - 5)(x + 10)/(x + 10)

= - (x - 5)²

(3x³ - 16x² - 72)/(x - 6) =

= (3x³ - 18x² + 2x² - 72)/(x - 6)

= [3x²(x - 6) + 2(x² - 36)]/(x - 6)

= [3x²(x - 6) + 2(x - 6)(x + 6)]/(x - 6)

= [3x² + 2(x + 6)](x - 6)/(x - 6)

= 3x² + 2x + 12

Answer:

a negative correlation between the temperature and the amount of snow still on the ground

a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left

Explanation:

When it comes to "correlations," a negative one refers to an "inverse" relationship between two variables. So, this means that as one variable increases, the other decreases and vice-versa.

The question is asking for two options that are "casual" (common) when it comes to "negative correlation." So, the answers are:

a negative correlation between the temperature and the amount of snow still on the ground

a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left

Answer:

Step-by-step explanation:

These are the two relationships that are most likely to be causal. Causal relationships are those in which one aspect is the cause of the second one being described. Moreover, a negative correlation is one in which one aspect of the relationship increases while the other one decreases. In the first example, as the temperature goes up, this causes the amount of snow on the ground to go down. In the second example, as you upload more pictures to a website, there is less storage space.

Answer:

The answer to your question is letter B or C they have the same response.

Step-by-step explanation:

From the graph we get the center and the radius

- The center is the point shown in the graph and its coordinates are (1, -4).

- The length of the radius is 3 units, from the center we count horizontally the number of squares (3)

Substitution

                    (x - 1)² + (y + 4)² = 3²

or                 (x - 1)² + (y + 4)² = 9

Answer:

In a study to determine whether how long a student sleeps affects test scores, the independent variable is the length of time spent sleeping while the dependent variable is the test score. You want to compare brands of paper towels, to see which holds the most liquid.

hopes it helps

Answer:

c

Step-by-step explanation:

in the question there is a confusion about " schedule shown" , either it is missing or by schedule shown it mean looking to the choices given

so if it is missing then sorry, but if it mean choices then the only possible answer is option C i.e. 12 hours because she works daily and missing only one day thus possible answer is 12 i.e. 6*2=12

hope it may help you

Answer:D

Step-by-step explanation:

Hope this helps

Answer:

Segment [tex]EB[/tex] is parallel to segment [tex]FC[/tex].

Segment  [tex]CD[/tex] is skew to segment  [tex]AB[/tex].

Step-by-step explanation:

For this exercise it is necessary to know the following definitions:

1. Coplanar lines are defined as those lines that lie in the same plane.

2. Non-Coplanar lines  are defined as those lines that does not lie in the same plane.

3. Parallel lines  are defined as Coplanar lines that never intersect each other.

4. Skew lines are defined as Non-Coplanar lines that never intersect each other.

Knowing those definitions, you can solve the exercise.

You need to analize the figure given in the exercise.

Based on the explanation given above,  you can conclude that the segment [tex]EB[/tex] is parallel to the segment [tex]FC[/tex], because they are in the same plane and they never intersect each other.

You can also identify in the figure that the segment [tex]AB[/tex] and the segment [tex]CD[/tex] are not in the same plane and they never intersect each other.

Therefore, you can determine that the segment  [tex]CD[/tex] is skew to the segment  [tex]AB[/tex].

Answer:

The approximate length of the actual car is 43 feet.

Step-by-step explanation:

Given:

The scale on a model railroad train set is 3.5 millimeters to 1 foot. If the length of a model car in the set is 150 millimeters.

Now, to find the approximate length of the actual car.

Let the actual length of the car is [tex]x.[/tex]

The length of a model car in the set is 150 millimeters.

As, given the scale on a model railroad train set is 3.5 millimeters to 1 foot.

So, 3.5 millimeters equivalent to 1 foot.

Thus, 150 millimeters to [tex]x[/tex].

Now, to get the actual length of the car by using cross multiplication method:

[tex]\frac{3.5}{1} =\frac{150}{x}[/tex]

By using cross multiplying we get:

[tex]3.5x=150[/tex]

Dividing both sides by 3.5 we get:

[tex]x=42.85\ feet.[/tex]

The approximate length of the actual car = 43 feet.

Therefore, the approximate length of the actual car is 43 feet.

Answer:

43ft

Step-by-step explanation:

The answer is B.

Here's another way to solve this problem.

1. Write the scale ratio

3.5 mm

1 ft

2.  Choose a variable, such as r, to represent the approximate length of the actual railroad car

3. Write the ratio of the length of the model car to the length of the actual car:

150 mm

r ft

4. Write a proportion

3.5=150

1= r

5. Cross multiply

3.5

r=150

   3.5

r=42.9, which rounds to 43.

so the, approximate length of the actual car is 43 feet

Answer:

3hrs 12 mins

Step-by-step explanation:

For every 10% charge she gets 1hr 20mins (or 80 mins)

Charge drop = (81% - 57%) = 24%

Since 10% gives 80 mins;

          24% gives (24/10) x 80 mins = 192 mins

since 1hr = 60 mins

192 mins = 192/60 = 3hrs 12 mins

Final answer:

Mandi played the game on her phone for 3 hours and 12 minutes, as she experienced a 24% drop in battery charge, with each 10% equating to 1 hour and 20 minutes of playtime.

Explanation:

The student's question involves calculating the duration of time Mandi played a game on her phone based on the percentage drop in battery charge. Mandi’s phone loses 10% charge for every 1 hour and 20 minutes of use. The charge dropped from 81% to 57%, which is a 24% drop. To find out how long she played the game, we calculate the number of 10% intervals in 24% and then multiply by the duration of one interval.

First, we determine how many 10% intervals are in 24%, which is calculated as 24% ÷ 10% = 2.4 intervals. Each interval equates to 1 hour and 20 minutes (which is the same as 80 minutes). Therefore, Mandi played for 2.4 intervals × 80 minutes per interval:

2.4 intervals × 80 minutes/interval = 192 minutes.

To convert minutes into hours and minutes, we divide by 60:

192 minutes ÷ 60 minutes/hour = 3 hours and 12 minutes.

So, Mandi played the game for 3 hours and 12 minutes.

Answer: she can only make 6 completed barrettes

Step-by-step explanation:

Samantha makes hair barrettes from ribbon. The total length of ribbon that she has is 3 1/4 feet. Converting 3 1/4 feet to improper fraction, it becomes 13/4 feet.

She uses 1/2 feet of ribbon to make each barrette. This means that the number of completed barrettes that Samantha can make with the ribbon she has would be

(13/4)/(1/2) = 13/4 × 2/1

= 6 1/2 barrettes

The complete barrette must be whole number.

Therefore, she can only make 6 completed barrettes

Answer:

6

Step-by-step explanation:

Answer:

55.96 miles

Step-by-step explanation:

Distance = Speed X time

Car first moved east for 1 hr , distance = 40 x 1 = 40 miles

Car then moved north-east for 30 min, distance = 40 x 0.5 = 20 miles

From trigonometry,

sin 45 = [tex]\frac{y}{20}[/tex] ; y = 20 sin 45 ; y= 14.14 miles

cos 45 = [tex]\frac{x}{20}[/tex] ; x = 20 cos 45 ; x = 14.14 miles

using Pythagoras theorem;

[tex]z^{2}[/tex] = [tex]y^{2}[/tex] + [tex](40+x)^{2}[/tex]

    = [tex]14.14^{2}[/tex] + [tex](40+14.14)^{2}[/tex]

     = 3131.08

[tex]z^{2}[/tex] = [tex]\sqrt{3131.08}[/tex]

z = 55.96 miles

Answer:

a=128 feet   b=256 feet

Step-by-step explanation:

hope i got it

Answer:

A.) 128FT

B.) A=256

Step-by-step explanation:

A.)

16 x 4 = 64FT

62 x 2 = 128FT

So, 2 Laps Would Equal Up To 128FT.

B.)

Find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.

Answer:

47 ducks and 7 cows

Step-by-step explanation:

Ducks have 2 legs and cows have 4 legs.

If all the animals are ducks,

number of legs= 54(2)= 108

Difference in number of legs= 122 -108= 14

Difference in no. of legs per animal= 4 -2 = 2

Number of cows=14 ÷2 = 7

Number of ducks= 54-7= 47

Thus, he have 47 ducks and 7 cows.

Let's check:

Total number of feet= 7(4)+ 47(2) = 122 ✓

You could also first assume that all the animals are cows. The answer would be the same.

Answer:

t = 460.52 min

Step-by-step explanation:

Here is the complete question

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.

Solution

Let Q(t) represent the amount of dye at any time t. Q' represent the net rate of change of amount of dye in the tank. Q' = inflow - outflow.

inflow = 0 (since the incoming water contains no dye)

outflow = concentration × rate of water inflow

Concentration = Quantity/volume = Q/200

outflow = concentration × rate of water inflow = Q/200 g/liter × 2 liters/min = Q/100 g/min.

So, Q' = inflow - outflow = 0 - Q/100

Q' = -Q/100 This is our differential equation. We solve it as follows

Q'/Q = -1/100

∫Q'/Q = ∫-1/100

㏑Q  = -t/100 + c

[tex]Q(t) = e^{(-t/100 + c)} = e^{(-t/100)}e^{c} = Ae^{(-t/100)}\\Q(t) = Ae^{(-t/100)}[/tex]

when t = 0, Q = 200 L × 1 g/L = 200 g

[tex]Q(0) = 200 = Ae^{(-0/100)} = Ae^{(0)} = A\\A = 200.\\So, Q(t) = 200e^{(-t/100)}[/tex]

We are to find t when Q = 1% of its original value. 1% of 200 g = 0.01 × 200 = 2

[tex]2 = 200e^{(-t/100)}\\\frac{2}{200} = e^{(-t/100)}[/tex]

㏑0.01 = -t/100

t = -100㏑0.01

t = 460.52 min

Answer: The salesperson would take home $1088.01 for the day

Step-by-step explanation:

Let x represent the salesperson's total sales per day.

A salesperson earns $99 per day, plus a 9% sales commission. This means that in a day in which the salesperson makes a total sales of x dollars, the total amount that he would earn is

99 + 0.09x

Therefore, the function that expresses her earnings as a function of sales is

99 + 0.09x

if the total sales were $999, then the amount that the salesperson would take home for the day is

99 + 0.99 × 999

= $1088.01

Multiply the price of popcorn by the number of bags so 6b.

Multiply the price of candy by the number bought, so 3.25c

Add those together to get total :

6b + 3.25c

Now the most she can spend is 50 so set the equation to less than it equal to what she can spend:

6b + 3.25c <= 50

Final answer:

The inequality representing Samantha's budget for purchasing popcorn and candies is 6b + 3.25c ≤ 50.

Explanation:

To formulate the inequality representing the possible values for the number of bags of popcorn (b) and the number of candies (c) Samantha can purchase without exceeding her $50 budget, we can set up an expression based on the given prices for each item.

The cost of the popcorn bags is $6, and the cost of each candy is $3.25.

The inequality that represents this scenario would be:

6b + 3.25c ≤ 50

This inequality denotes that the total cost of b popcorn bags and c candies, which is the sum of $6 times the number of popcorn bags plus $3.25 times the number of candies, should be less than or equal to $50.

Samantha must choose combinations of b and c that satisfy this inequality to stay within her budget.

Answer: the number of adult and student tickets sold are (45, 29)

Step-by-step explanation:

Let x represent the number of adult tickets that were sold.

Let y represent the number of student tickets that were sold.

On Wednesday, a total of 74 tickets were sold. This means that

x + y = 74

x = 74 - y- - - - - - - - - - - - - - 1

If adult tickets are sold for $15 and student tickets are sold for $11 and the money collected was $994, it means that

15x + 11y = 994- - - - - - - - - - - - - - 2

Substituting equation 1 into equation 2, it becomes

15(74 - y) + 11y = 994

1110 - 15y + 11y = 994

- 15y + 11y = 994 - 1110

- 4y = - 116

y = - 116/ - 4

y = 29

Substituting y = 29 into equation 1, it becomes

x = 74 - 29 = 45

The number of adult tickets and student tickets sold is (x, y) = (45, 29)

To determine the number of adult tickets x and student tickets y sold, we need to solve the system of equations given by the following conditions:

1. The total number of tickets sold is 74:

x + y = 74

2. The total revenue from the tickets is $994, with adult tickets sold for $15 each and student tickets sold for $11 each:

15x + 11y = 994

We can solve this system of equations using the substitution or elimination method. Here, we will use the elimination method.

First, let's write the two equations clearly:

x + y = 74

15x + 11y = 994

To eliminate one of the variables, we can multiply the first equation by 11, so the coefficients of  y in both equations will be the same:

[tex]\[ 11(x + y) = 11 \cdot 74 \][/tex]

11x + 11y = 814

Now we have:

11x + 11y = 814

15x + 11y = 994

Next, we subtract the first modified equation from the second equation to eliminate y

(15x + 11y) - (11x + 11y) = 994 - 814

15x + 11y - 11x - 11y = 180

4x = 180

x = 45

Now, substitute x = 45 back into the first original equation to find y

x + y = 74

45 + y = 74

y = 29

Therefore, the number of adult tickets and student tickets sold is:

(x, y) = (45, 29)

x = 37.5 (or) [tex]\frac{75}{2}[/tex]

Solution:

Given [tex]\triangle A B C \sim \triangle D B E[/tex].

Let us take BE = x and BC = 25 + x.

To determine the value of x:

If two triangles are similar then the corresponding angles are congruent and the corresponding sides are in proportion.

[tex]$\frac{AC}{DE}=\frac{B C}{B E}[/tex]

[tex]$\frac{50}{30} =\frac{25+x}{x}[/tex]

Do cross multiplication, we get

[tex]50x=30(25+x)[/tex]

[tex]50x=750+30x[/tex]

Subtract 30x from both sides of the equation.

[tex]20 x=750[/tex]

Divide by 20 on both sides of the equation, we get

x = 37.5 (or) [tex]\frac{75}{2}[/tex]

Hence the value of x is 37.5 or [tex]\frac{75}{2}[/tex].

Answer:

ARITHMETIC SENTENCE

Step-by-step explanation:

Final answer:

Naledi's altitude sequence is an arithmetic sequence because it increases by a constant amount each hour.

Explanation:

Naledi's altitude at the beginning of the nth hour of her climb can be described by the function g(n), where g(n) is the altitude at that hour. Since she starts at 40 meters above sea level and increases her altitude by 10 meters every hour, the sequence representing her altitude over time is an arithmetic sequence. This is because each term in the sequence increases by a constant value, which is the definition of an arithmetic sequence.

The general formula for the nth term of an arithmetic sequence is aₙ = a₁ + (n - 1)d, where a₁ is the first term and d is the common difference between terms. In Naledi's case, a₁ is 40 meters (her initial altitude), and d is 10 meters (the constant increase each hour).

Yo sup??

This question can be solved by applying trigonometric ratios

let angle U be x, then

tanx=4/7

x=29.7

Hope this helps

Answer:

Option A:        [tex]$ \sum_{n = 1}^{15} {\textbf{- 9 + 6 n}} $[/tex]

Step-by-step explanation:

We are given with the series - 9  - 3  + 3   +  9 +  . . . .  +  81.

Note that the second term is obtained by adding 6 to the first term.

Each consecutive term is obtained by adding 6 to its previous term.

Therefore, we should be adding six two times to get the third term from the first term.

Putting it Mathematically, we get: - 9 + 6n

This gives all the terms of the sequence. Since, we have to add all the terms we take the summation.

Also, note that 81 is the 15 th term.

Therefore, - 9  - 3  + 3   +  9 +  . . . .  +  81 =    [tex]$ \sum_{n = 1}^{15} {- 9 + 6 n} $[/tex]

Hence, the answer.

Final answer:

The sequence -9, -3, 3, 9, ..., 81 increases by 6 each time and follows the arithmetic sequence formula -9 + 6(n-1), which simplifies to -15 + 6n. The summation notation that represents this sequence is the sum of -15 + 6n from n = 0 to 15.

Explanation:

The given sequence is -9, -3, 3, 9, ..., 81, and we can see that it is increasing by 6 each time (an arithmetic sequence). The nth term of an arithmetic sequence can be written as a + (n-1)d, where a is the first term and d is the common difference. Here, the first term a is -9 and the common difference d is 6. Plugging these values into the formula gives us the nth term as -9 + 6(n-1). We can simplify this to -9 + 6n - 6, which further simplifies to -15 + 6n.

To find the last term which is 81, we can set the nth term equal to 81: -15 + 6n = 81. Solving for n gives us n = 16, meaning there are 15 terms before it (since we start counting from n = 0).

The summation notation for the given sequence is then the sum of the terms from n = 0 to n = 15 of the general term -15 + 6n.

Duku is 9 meters below the surface of the water, calculated by adding Duku's 5 meters above Kojo's position to Kojo's 14 meters below the surface.

The question asks about Duku's position relative to the surface of the water given Kojo is 14 meters below the surface and Duku is 5 meters above Kojo. To find Duku's position, subtract 5 meters (Duku's position above Kojo) from -14 meters (Kojo's position below the surface). Therefore, Duku's position relative to the surface of the water is -14 meters + 5 meters = -9 meters. This means Duku is 9 meters below the surface of the water.

(1) Vertical asymptote: [tex]x=-4[/tex]

(2) Domain: [tex]x>-4[/tex]

(3) X intercept: [tex](-2,0)[/tex] and Y intercept : [tex](0,1)[/tex]

(4) The function g(x) is shifted 4 units to the left and shifted 1 unit down.

Explanation:

The parent function is [tex]f(x)=\log _{2} x[/tex]

The transformed function is [tex]g(x)=\log _{2}(x+4)-1[/tex]

(1) Vertical asymptote:

The vertical asymptote of a function can be determined by equating

[tex]x+4=0[/tex]

Thus, [tex]x=-4[/tex]

The vertical asymptote is [tex]x=-4[/tex]

(2) Domain:

The domain of a function is the set of all independent x-values.

[tex]x+4>0[/tex]

Thus, [tex]x>-4[/tex]

The domain of a function is [tex]x>-4[/tex]

(3) X and Y intercepts:

To determine the x intercept, let us substitute y=0 in [tex]g(x)=\log _{2}(x+4)-1[/tex]

[tex]\begin{equation}\begin{aligned}\log _{2}(x+4)-1 &=0 \\\log _{2}(x+4) &=1 \\x+4 &=2^{1} \\x &=-2\end{aligned}[/tex]

Thus, the x intercept is [tex](-2,0)[/tex]

To determine the y intercept, let us substitute x=0 in [tex]g(x)=\log _{2}(x+4)-1[/tex]

[tex]\begin{equation}\begin{aligned}y &=\log _{2}(0+4)-1 \\&=\log _{2} 4-1 \\&=2-1 \\&=1\end{aligned}[/tex]

Thus, the y intercept is [tex](0,1)[/tex]

(4) To determine the transformation:

The transformed function [tex]g(x)=\log _{2}(x+4)-1[/tex] is shifted 4 units to the left and shifted 1 unit downwards.

Answer:

Therefore [tex](\frac{46}{59},-\frac{62}{59} )[/tex] is a solution of given liner equations.

Step-by-step explanation:

Given system of equation are

7x+9y=-4..............(1)

5x-2y=6...............(2)

Equation (1)×5 - equation (2)×7

35x +45y-(35x-14y)= -20-42

⇔ 35x+45y-35x+14y = -62

⇔59 y = -62

[tex]\Leftrightarrow y =-\frac{62}{59}[/tex]

Putting the value of y in equation (1)

[tex]7x +9.(-\frac{62}{59} )= -4[/tex]

[tex]\Leftrightarrow 7x += -4+\frac{558}{59}[/tex]

[tex]\Leftrightarrow 7x = \frac{322}{59}[/tex]

[tex]\Leftrightarrow x =\frac{322}{59\times 7}[/tex]

[tex]\Leftrightarrow x =\frac{46}{59}[/tex]

Therefore  [tex]x =\frac{46}{59}[/tex] and  [tex]y =-\frac{62}{59}[/tex]

Therefore [tex](\frac{46}{59},-\frac{62}{59} )[/tex] is a solution of given liner equations.

Answer:

D.)He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.

Step-by-step explanation:

I just got this right for the exam review on edge

Answer:

The work done is 5.084 J

Step-by-step explanation:

From Hooke's law of elasticity,

F = ke

F/e = k

F1/e1 = F2/e2

F2 = F1e2/e1

F1 = 10 lbf, e2 = 6 in, e1 = 4 in

F2 = 10×6/4 = 15 lbf

Work done (W) = 1/2F2e2

F2 = 15 lbf = 15×4.4482 = 66.723 N

e2 = 6 in = 6×0.0254 = 0.1524 m

W = 1/2×66.723×0.1524 = 5.084 J

Answer:

The slope is = -1/4

Step-by-step explanation:

We are looking for the slope of the line CD. You are given the coordinates for each point as follows:

A(0,-1)     B(5,3)    C(2,3)   D(6,2)

To find the slope of a straight line, you use the formula:

slope (m) = (y2 - y1)/(x2 - x1)

In other words the slope is the "rise over run":

Remember: the coordinates of a point are (x;y). Choose one of the points to be point 1 and the other to be point 2. I would suggest that you follow the order they have given you ie. CD:

So if our points are C (2; 3) and D (6, 2) we can say point C is point 1 and point D is point 2. Plug into the formula:  

slope (m) = (y2-y1)/(x2-x1)

y1  = 3

y2 = 2

x1  = 2

x2 = 6

∴ m = (2-3)/(6-2)

      = -1/4

Answer:

Step-by-step explanation:

Answer:

(f+g)(3) = 347 calories

Step-by-step explanation:

f(x) = 2x + 210

g(x) = 2x + 125

(f+g)(x) is the sum of the functions

(f+g)(x) = 2x+210 + 2x+125

Combining like terms

           =4x+335

Now let x = 3

(f+g)(3) = 4*3 +335

            = 12 +335

            = 347

(f+g)(3) = 347 calories

Answer:

347

Step-by-step explanation:

f(x) = 2x + 210

g(x) = 2x + 125

we know that (f+g)(x)=f(x)+g(x)

so (f+g)(x)= 2x + 210 + 2x + 125 = 4x + 335

(f+g)(3) simply means that x=3

therefore

(f+g)(3) = 12 + 335 = 347

Answer:

0.40

Step-by-step explanation:

to find out the probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 8

Let A = sum of dice is 8

B = one lands in 5

P(B/A) = P(AB)/P(A) by conditional probability

P(AB) = sum is 8 and one is 5

So (5,3) or (3,5)

P(A) = sum  is 8.

i.e. (2,6) (2,6) (3,5) (5,3) (4,4)

Required probability

= n(AB)/n(A)

=[tex]\frac{2}{5} =0.40[/tex]