If the slope(m) and a point (x1,y1) of a line are known, the equation of line is given by

A. x - x1 = m(y - y1)
B. y - y1 = m (x - x1)
C. y + y1 = m (x - x1)
D. y - y1 = m (x + x1)

Answer:

-0.25 ; 120 seconds 72 seconds

Step-by-step explanation:

Dive rate is constant :

Change in elevation after 8 seconds :

18 feets to 20 feets below

Rate of change = distance / time

(18 - 20) feets / 8 seconds

(-2 / 8) = - 0.25 feets per second

To reach 50.feets :

She needs to cover (50 - 20) = 30 feets

Time = distance / speed ; 30 feets / 0.25 = 120 seconds

C.) At the time update was requested, elevation = 18 feets below sea level

Surfave of water = 0 feets

Since rate is - 0.25 feets per second

Time = (0 - 18) / - 0.25

Time = - 18 / - 0.25

Time = 72 seconds

72 seconds update was requested, deliver was at the surface

In this exercise we have to use the knowledge of distance to calculate the time needed to reach this space, so:

A)-0.25

B)120 seconds

C) 72 seconds

A)So from the rate of change formula we can calculate with the already known values:

\(Rate\ of \ change = distance / time\\(18 - 20) feets / 8 seconds\\(-2 / 8) = - 0.25 feets\ per \ second\)

B) To reach 50.feets, we will use the time formula to calculate the total time used, so:

\((50 - 20) = 30 feets\\Time = distance / speed\\30 feets / 0.25 = 120 seconds\)

C)Now, using the time formula given earlier, we find that:

\(Time = (0 - 18) / - 0.25\\Time = - 18 / - 0.25\\Time = 72 seconds\)

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A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time. The speed of the car is 50 km/h. The speed of truck is 70 km/h.

You can determine an object's speed if you know how far it moves in a given amount of time. For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in an hour (miles per hour).

Given,

A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time.

Let s represent the truck's speed and (s+20) represent the car's speed.

to determine each vehicle's time

Time = Speed / Distance

truck time = 350/s

Time in an automobile is 350/(s+20)

Truck time - car time = 2 hours

So,

(350/s) - [350/(s+20)] = 2

LCM is s(s+20)

[350(s+20) - 350s]/s(s+20) = 2

Cross multiplying,

350(s+20) - 350s = 2s(s+20)

Simplifying the equation,

350s + 7000 - 350s = 2s² + 40s

Now, we have quadratic equation to simplify,

2s² + 40s - 7000 = 0

Dividing the equation by 2

s² + 20s - 3500 = 0

Factorizing,

s= 50

s= -70 (impossible because of the sign)

Hence the truck's speed is s = 50 km/h.

The speed of the car is s + 20 = 70 km/h.

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Answer: 8

Step-by-step explanation:

let x = the number

(x + 2)*10 = 8x + 36

10x + 20 = 8x + 36

2x = 16

x = 8

22.4 calories would be present in 8 chips.

The provided information is useful.

According to the serving size, 50 chips have 140 calories.

50 chips provide 8 servings.

To calculate the number of calories in 8 chips, we can set up a proportion:

(50 chips) / (140 calories) = (8 chips) / (x calories)

Cross-multiplying, we get:

50 chips * x calories = 140 calories * 8 chips

50x = 1120

Dividing both sides by 50, we find:

x = 22.4 calories

Therefore, 22.4 calories would be present in 8 chips.

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The statement "if a > √n and b > √n, then n ≠ ab" is saying that if two positive integers, a and b, are both greater than the square root of another positive integer n, then the product of a and b is not equal to n. This statement can be proven by contradiction.

Suppose the opposite is true, and that n = ab, where a and b are positive integers such that a > √n and b > √n. Then, because n = ab, we have n/a = b and n/b = a. But because both a and b are greater than the square root of n, we have √n < a and √n < b. This leads to a contradiction, because it means that n/a = b > √n, but √n is the largest possible value of b such that b < n/a.

Thus, we have proven that if a > √n and b > √n, then n cannot equal ab, and our original statement is true.

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Explanation:

The y-intercept is the point where the line crosses the y-axis. This always happens when x = 0.

In this case x = 0 represents 0 days. The y-intercept is 400 pages remaining

Answer:

The answer is option a. At 0 days there are 400 pages remaining

The relationship between the balance in the phone and the number of  

minutes of talking is a linear relationship.

Reasons:

First question

Initial balance in Julie's phone = $40

The balance after talking for 5 minutes = $39.25

Her balance after talking for 30 minutes = $34.75

Required:

Her balance after she has talked for 75 minutes

Solution:

\(The \ rate \ of \ change \ of \ her \ balance =\dfrac{34.75 - 39.25}{35 - 5 } = -0.15\)

Therefore, the rate of change of her balance with time = -0.15 Dollars/minute

The equation for her balance is; y - 39.25 = -0.15 × (x - 5)

y = -0.15·x + 0.75 + 39.25 = -0.15·x + 40

y = 40 - 0.15·x

When x = 75, y = 40 - 0.15×75 = 28.75

Second question:

The amount charged for paint = $90

Number of hours to paint the bedroom = 1 hour

Cost to paint the bedroom = $125

Number of hours to paint the kitchen = 4 hour

Cost to paint the kitchen  = $230

The cost to paint per hour is therefore;

\(Cost \ per \ hour =\dfrac{230- 125}{4 - 1 } = 35\)

The cost to paint per hour = $35 /hour

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Steps to solve:

185 = -5(10r + 3)

~Distribute right side

185 = -50r - 15

~Add 15 to both sides

200 = -50r

~Divide -50 to both sides

-4 = r

Best of Luck!

Answer:

r=-4

Step-by-step explanation:

185= - 5 10 r + 3

37= 10 r + 3

10r = - 3 - 37

10 r = - 40

The length of each side of the octagon is 6 cm

It is a polygon with eight sides and eight angles. There are a total of 20 diagonals in it. All its interior angles sum up to 1080°.

Given that, a regular octagon has an area of 288 square centimeters and an apothem of 12 cm.

We need to find the side of the octagon,

We know that area of the octagon = 8/2 × side × apothem

Therefore,

288 = 8/2 × side × 12

side = 288 / 48

side = 6

Hence, the length of each side of the octagon is 6 cm

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Answer:

you would see which bank has a good business and have loyal customers and which one is giving you a better offer

Step-by-step explanation:

HOPE THIS HELPED!

Answer:

e.

Step-by-step explanation:

Answer:

Step-by-step explanation:

357x

The probability that it will rain on exactly one of the seven days the Hiking Club is camping in the state park is approximately 0.293, rounded to the nearest thousandth.

The probability of rain on any given day is 0.66.

To find the probability that it will rain on exactly one of the seven days the Hiking Club is there, we can use the binomial probability formula.

The binomial probability formula is

\(P(x) = C(n, x) * p^x * (1-p)^{(n-x)}\),

where:

P(x) is the probability of exactly x successes,

C(n, x) is the combination formula, which calculates the number of ways to choose x successes from n trials,

p is the probability of success on a single trial, and

n is the total number of trials.

In this case, we want to find the probability of rain on exactly one day out of the seven days.

So, x = 1,

n = 7, and

p = 0.66.

Using the combination formula,

C(n, x) = n! / (x! * (n-x)!),

we can calculate

C(7, 1) = 7! / (1! * (7-1)!)

C(7, 1) = 7.

Plugging the values into the binomial probability formula, we get:

\(P(1) = C(7, 1) * 0.66^1 * (1-0.66)^{(7-1)}\)

\(= 7 * 0.66^1 * 0.34^6\)

Calculating this expression, we find that P(1) is approximately 0.293.

Therefore, the probability that it will rain on exactly one of the seven days the Hiking Club is camping in the state park is approximately 0.293, rounded to the nearest thousandth.

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Answer:

A single number that estimates the value of an unknown parameter is called a point estimate.

Step-by-step explanation:

Don't see the point (haha) of elaborating

Answer: 50 mph

Step-by-step explanation:

Exponential smoothing is a popular forecasting technique used to predict future trends in time-series data. It works by assigning weights to historical data points, with more recent data points receiving higher weights. The level of smoothing is controlled by a smoothing parameter called alpha, which ranges between 0 and 1. As alpha increases, the influence of older data points decreases, and the model becomes more reactive to recent changes in the data.

When alpha is high, the exponential smoothing model group of answer choices tends to produce sluggish forecasts. This is because the model gives more weight to recent data points, which can cause it to overreact to short-term fluctuations in the data. As a result, the model may miss important trends or patterns in the data that would have been captured by a more balanced weighting scheme.

On the other hand, when alpha is low, the model tends to be more stable and less reactive to short-term changes in the data. This can be useful for predicting long-term trends or for smoothing out noisy data sets.

In summary, the choice of alpha in an exponential smoothing model depends on the characteristics of the data and the goals of the forecast. A high alpha value may be appropriate for short-term forecasting or for data sets with high volatility, while a low alpha value may be more suitable for long-term forecasting or for data sets with low volatility.

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Step-by-step explanation:

here's the answer to your question

The total area of the given shape is 71cm².

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. A shape's area can be calculated by contrasting it with squares of a known dimension. The square meter (abbreviated as m²), which is the area of a square whose sides are one metre long, is the common measure of area in the International System of Units (SI). Three such squares would be the same size as a shape with a three square metre surface.

The following figure can be divided into a rectangle 7cm x 8cm and a triangle of height and base 6 cm and 5 cm respectively.

Area of rectangle= 7*8= 56 cm²

Area of triangle= 1/2* base*height= 1/2*6*5 = 15 cm²

Total area of shape = 56+15= 71 cm²

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Answer: x = 6

Step-by-Step Explanation:

=> -9x + 2x + 32 = -10

= -7x + 32 = -10

= -7x = -10 - 32 = -42

=> x = -42/-7 = 42/7 = 6

Therefore, x = 6

\(\rule{300}{1}\)

\(\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}\)

-9x+2x+32=-10. what is x?

\(\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer \& How to solve:-}}}\)

   When solving an equation, we need to make sure all variables are on the

    left-hand side, and all numbers are on the right-hand side.

    There are numbers on both sides, so we need to move all of them to the right.

  \(\bold{-9x+2x=-10-32}\)

\(\bigstar\) On simplification,

        \(\bold{-9x+2x=-42}\)          Next, combine like terms (-9x+2x).

\(\bigstar\) On further simplification,

   \(\bold{-7x=-42}\)                Next, divide by -7 on both sides.

\(\bigstar\) Which results in

\(\bold{x=6}\)

It's always a good idea to make sure the solution is correct.

We can check that by substituting the value of x (x=6) in lieu of x (into the original equation) and seeing whether or not we have a true statement:-

\(\bold{-9(6)+2(6)+32=-10}\)

\(\dagger\) On simplification,

\(\bold{-54+12+32=-10}\)

\(\dagger\) On further simplification,

\(\bold{-42+32=-10}\)

\(\dagger\) Which results in

\(\bold{-10=-10}\)

LHS=RHS, so our solution is indeed correct.

So we conclude that \(\boxed{\bold{x=6}}\).

\(\rule{300}{2}\)

Answer:

32

Step-by-step explanation:

f(x)= 3(x-2)² + 5

Let x = -1

f(-1)= 3(-1-2)² + 5

Parentheses first

f(-1) = 3(-3)^2 +5

Exponents

f(-1)= 3*9 + 5

Multiply

f(-1) = 27+5

Add

f(-1) = 32

The x-intercept is 12 and the y-intercept is 48 for the equation y = 48 - 4x.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that four-inch pieces are repeatedly cut from a 48-inch string. The length of the string after x cuts is given by y=48 - 4x.

The x-intercept will be calculated as,

y = 48 - 4x

0 = 48 - 4x

4x = 48

x = 12

The y-intercept will be calculated as,

y = 48 - 4x

y = 48 - 0

y = 48

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Answer:

the difference is the + and the -

sorry if it's wrong

Given that f(x) is an exponential function with f(3.5) = 21 and f(6.5) = 69, we need to find the value of f(9) to the nearest hundredth.

To find the value of f(9), we can use the information given to determine the equation for the exponential function. The general form of an exponential function is f(x) = a * b^x, where 'a' is the initial value or y-intercept, and 'b' is the base of the exponential function.

Using the given data points, we can set up two equations:

21 = a * b^(3.5) -- Equation 1

69 = a * b^(6.5) -- Equation 2

We have two equations with two variables (a and b). By solving these equations simultaneously, we can find the values of 'a' and 'b'. Once we have those values, we can substitute x = 9 into the equation f(x) = a * b^x to find the value of f(9) to the nearest hundredth.

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Answer:

equivalent  i think

Step-by-step explanation:

Answer:

Alexis: 2.5x

Gary: x

James: x + 18

Total: (2.5x) + (x) + (x + 18)

              = 4.5x + 18

Bonus:

4.5x + 18 = 1206

4.5x = 1188

    x = 264

Alexis: 2.5(264) = 660

Gary: 264

James: 264 + 18 = 282

The solution to the equation f/3 + 22 = 17 is f = -15.

Solve the equation f/3 + 22 = 17, we need to isolate the variable f on one side of the equation. Here's a step-by-step solution:

Let's start by subtracting 22 from both sides of the equation to move the constant term to the right side:

f/3 + 22 - 22 = 17 - 22

f/3 = -5

Now, to eliminate the fraction, we can multiply both sides of the equation by 3. This will cancel out the denominator on the left side:

(f/3) × 3 = -5 × 3

f = -15

Therefore, the solution to the equation f/3 + 22 = 17 is f = -15.

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As per the quadrilateral ABCD, the value of x will be equal to 36°.

A polygon is described in geometry as a compact, two-dimensional shape having three or more straight lines. Poly, which means "many," and gon, which means "angle," make up the Greek word "Polygon." Polygons of several kinds can be seen all around us.

As per the given diagram in the question,

The given angles are:

∠ A = 72°

∠ C = 3x

For a cyclic quadrilateral,

∠ A + ∠ C = 180°

72 + 3x = 180

3x = 180 - 72

3x = 108

x = 108/3

x = 36°

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Answer:

2 ± i

Step-by-step explanation:

by 5, I assume you mean +5

x² - 4x + 5 = 0

x = (-b±(√(b²-4ac)) / 2a

x = (4 ± (√(16 - 20)) / 2

x = (4 ± (√(-4)) / 2

√-4 = √4√-1 which is 2i

x = (4 ± 2i) / 2

x = 2 ± i

The energy of a photon of light differs from that of a mechanical wave (such as a wave on a rope) in that it depends upon frequency.

The energy of a photon of light differs from that of a mechanical wave (such as a wave on a rope) in that it depends upon frequency. The energy of a photon is related to its frequency and is calculated using the Planck constant, while the energy of a mechanical wave (such as a wave on a rope) is related to its amplitude, which is a measure of how much the medium is disturbed from its equilibrium position. The frequency of a photon of light determines its energy. The higher the frequency, the higher the energy, and vice versa. The energy of a photon is given by the equation E = hf, where E is energy, h is Planck's constant (6.626 x 10^-34 J s), and f is frequency.

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The congruent statement DG = EF has been proved

The given parameters are

DG = 11

GF = 11

GF = EF

To prove that

DG = EF

So, we start the proof as follows:

1. DG = 11, GF = 11, GF = EF ------ Given

By the substitution property of an equation, we have

2. DG = GF ----- substitution property of an equation

For step (2) above, we simply substitute DG = 11 in GF = 11

By the substitution property of an equation, we have

3. DG = EF ----- substitution property of an equation

For step (3) above, we simply substitute GF = EF in DG = GF

Hence, the congruent statement DG = EF has been proved

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