Write a coordinate rule for the translation of f(x) to g(x).




(x, y) → (x + 4, y – 5)


(x, y) → (x + 5, y – 4)


(x, y) → (x – 4, y + 5)


(x, y) → (x – 5, y + 4)

Answer:

38.4

Step-by-step explanation:

48*20%=9.6 48-9.6=38.4

Answer:

The cannonball will hit the ground after about 5.926 seconds.

Step-by-step explanation:

h(t) = -4.9t² + 27.5t + 9.1

If you graphed the function on a graph, the cannonball would be hitting the ground when the function crossed the x-axis at 0. So, to solve this arithmetically, you just need to set h(t) equal to 0.

-4.9t² + 27.5t + 9.1 = 0   Plug this into a calculator if you have one, if not solve with the quadratic formula.

[tex]\frac{-27.5 \pm \sqrt{(27.5^2) - 4(-4.9)(9.1)} }{2(-4.9)}[/tex]

t = -.0313

t = 5.9256

Since time can't be negative, you know your answer will be 5.926 seconds.

Answer:

t =5.93 seconds

Step-by-step explanation:

h(t) represents the height of the cannon ball.  Zero is when the ball will hit the ground.    Substitute zero for h(t).

0 = -4.9t² + 27.5t + 9.1

This is a complicated quadratics, so we will need to use the quadratic formula to solve

-b ± sqrt(b^2 -4ac)

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

  2a

where a = -4.9   b = 27.5   and c = 9.1

-27.5  ± sqrt(27.5 ^2 -4 (-4.9) 9.1)

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

  2(-4.9)

-27.5  ± sqrt(756.25 +178.36)

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

  -9.8

-27.5  ± sqrt(943.61)

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

  -9.8

-27.5  ± 30.57139186

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

  -9.8

3.071391856/-9.8   or  -58.07139186/-9.8

-.313407332  or  5.925652231

But time cannot be negative,  the ball cannot land before it takes off,

so t= 5.925652231 seconds

Rounding to the nearest hundredth

t =5.93 seconds

Answer:835.893

Step-by-step explanation:

do the interest rate thing you learned in class

if you didn't learn it im adding a picture on the bottom for help

Answer:

The ratio of girls to boys is 16:15

Step-by-step explanation:

To find this, we simply start by using the words.

Girls:Boys

Now we plug in the values.

16:15

Answer:

We have to find the equation of least squares regression line in order to find the number of ice cream cones that the shopkeeper to sell if the temperature is 106 degrees. We can use excel regression data analysis tool to find the equation of the regression line. The excel output is attached here.

The equation of the least squares regression line is:

[tex]\hat{y}=46.587+5.080x[/tex]

Now, if the temperature is 106 degrees, then the number of cones expected to be sold is given below:

[tex]\hat{y}=46.587+5.080 \times 106[/tex]

         [tex]=585.1 \approx 585[/tex]

Therefore, the number of ice cream cones that the shopkeeper would expect to sell if the temperature is 106 degrees is 585.

Answer: I think it 3/1

Step-by-step explanation: Because 2 to get to 5 is 3 and 5 to get to 6 is 3. Hope I am correct

Answer:

D) n=25

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

I didi the quiz

Nicolas sells 5.125 pounds of shrimp per hour.

Therefore, he can sell 46.125 pounds of shrimp in 9 hours.

To determine how many pounds of shrimp Nicolas sold in one hour, we need to divide the total pounds of shrimp by the total number of hours.

Nicolas sold 20 1/2 pounds of shrimp in 4 hours.

Therefore, we divide 20.5 (which is the decimal equivalent of 20 1/2) by 4 to find the rate per hour:

20.5 ÷ 4 = 5.125

Nicolas sold 5.125 pounds of shrimp per hour.

To find out how many pounds he can sell in 9 hours, we multiply the rate per hour by 9:

5.125 × 9 = 46.125

Nicolas can sell 46.125 pounds of shrimp in 9 hours.

Answer:

600kW

Step-by-step explanation:

Referring to the fact that 10m/s of wind is 500kW so divide 500 by 10.

500/10=50

So there is 50 kW is 1m/s of wind. Now multiply 12 by 50

12x50=600

So for 12m/s of wind there is 600kW

At 12 m/s, the turbine generates 864 kW.

We can express the given relationship as P = k * v^3, where k is a constant of proportionality.

Given that a turbine generates 500 kW at a wind speed of 10 m/s, we can find k using the equation:

500 = k * 10^3

k = 500 / 1000

k = 0.5.

Now, to find out how much power the turbine would generate at 12 m/s. The calculation is :

P = 0.5 * 12^3

P = 0.5 * 1728

P = 864 kW.

The wind turbine generates 864 kW in a 12 m/s wind.

Answer:

i think the answer would be C

Step-by-step explanation:

since it seemed you had to divide the numbers a hundred would turn into ten and ninety would turn into nine and because you have one negative and one positive that means it would have to be a negative so it would be

10 - 9i

Answer: B

Step-by-step explanation:

[tex]\sqrt{100} + \sqrt{-81}[/tex]

  [tex]\sqrt{100} + \sqrt{-81}[/tex]

=    10    +    9i

The choice that describes whether x = 19 is the solution of the equation 42 = 3x - 15 is that x = 19 is the solution because 3 * 19 - 15 = 57 - 15 = 42.

The choice that describes whether x = 19 is the solution of the equation 42 = 3x - 15 is the option: x = 19 is not the solution because 3 * 19 - 15 = 3 * 4 = 12, not 42.

To check if a value is the solution to an equation, we substitute the value into the equation and perform the necessary calculations. In this case, substituting x = 19 into the equation 42 = 3x - 15 gives us 42 = 3 * 19 - 15 = 57 - 15 = 42. Since both sides of the equation are equal, x = 19 is indeed the solution.

The question is asking to determine if x = 19 is the solution for the equation 42 = 3x – 15. To verify this, we need to substitute x = 19 into the equation. So, we have 42 = 3(19) - 15 which simplifies to 42 = 57 - 15. After subtraction on the right side, we get 42 = 42, which is a true statement. Hence, x = 19 is indeed the solution to the equation 42 = 3x – 15.

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Answer:

Step-by-step explanation:

The edge length (s) of an equilateral triangle is (2/3)√3 times the height. This means the edge length of your triangle is ...

... s = (2/3)√3 × 12√2 = 8√6

The perimeter is 3 times the side length:

... p = 3s = 3×8√6 = 24√6 . . . cm

The area is half the product of edge length and height:

... a = (1/2)sh = (1/2)(8√6)(12√2) = 48√12 = 96√3 . . . cm²

The perimeter of the equilateral triangle is 24√6 cm, and its area is 96√3 cm².

To find the perimeter and area of an equilateral triangle with a given height, we can follow these steps:

First, let's denote the side length of the equilateral triangle as a. In an equilateral triangle, the height (h) can be found using the formula:

h = (a√3)/2

We know the height is 12√2 cm. Therefore,12√2 = (a√3)/2

To find the side length a, we can rearrange the equation: a = 2 * 12√2 / √3

Simplify the expression: a = 24√2 / √3

Multiplying numerator and denominator by √3 to rationalize the denominator: a = 24√6 / 3

a = 8√6

Now, the perimeter (P) of the equilateral triangle is given by: P = 3a

Substitute the value of a: P = 3 * 8√6

P = 24√6 cm

Next, we calculate the area (A) using the formula: A = (base * height) / 2

In an equilateral triangle, the base is equal to the side length a, and the height is given as 12√2 cm:

A = (8√6 * 12√2) / 2

Multiplying the bases and simplifying: A = (96√12) / 2

Since √12 can be simplified to 2√3: A = (96 * 2√3) / 2

A = 96√3 cm²

The perimeter of the equilateral triangle is 24√6 cm, and its area is 96√3 cm².

Answer:

65,1,5.5

Step-by-step explanation:

Replace with 1 and simplify.

Answer:

y = 2x+4

Step-by-step explanation:

We need to find the slope

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

 = (8--6)/(2--5)

  = (8+6)/(2+5)

  = 14/7

  =2

Now we can use the point slope form of a line

y-y1 = m(x-x1)

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

y+6 = 2(x+5)

If we want it in slope intercept form

Distribute the 2

y+6 = 2x+10

Now subtract the 6 from both side

y+6-6=2x+10-6

y = 2x+4

Answer:

y = 2x - 1

Step-by-step explanation:

The line passes through points A(1, 1) and B(2, 3).

The slope-intercept form of the equation of a line is

y = mx + b,

where m = slope, and b = y-intercept.

We see from the graph that the y-intercept is -1, so b = -1, and we have

y = mx - 1

Going from point A to point B, we go up two units and right 1 unit. Slope = m = difference in y over difference in x, so

m = 2/1 = 2

The equation is

y = 2x - 1

Answer: 2x + -1

Step-by-step explanation: In this problem, we're asked to write the equation of the given line in slope-intercept form.

Slope-intercept form is the same thing as y = mx + b form where m represents the slope of the line and b represents the y-intercept. So our first step is to find the slope and the y-intercept of the given line.

To find the slope, we use the ratio rise over run between any two points on the line. To get from point A to point B along this line, we rise 2 units and run 1 unit. So our slope or rise over run is 2/1 or just 2.

Next, to find the y-intercept, it's important  to understand that the y-intercept is the point where the line crosses the y-axis. Notice that this line crosses the y-axis at the point (0,-1) which means that the y-intercept is -1.

Therefore, m = 1/2 and b = -1 and we substitute these values into our formula for m and b to get y = 2x + -1.

So the equation of the given line in slope-intercept form is y = 2x + -1.

Answer:

6

Step-by-step explanation:

f(x) = 3x - 1

f(2) means evaluate  f(x) when x=2

f(2) = 3(2) -1

f(2) = 6-1=5

g(5) means evaluate g(x) when x=5

g(5) = -5+6

g(5) =1

f(-2) + g(5)

5+1

6

Answer:

6

Step-by-step explanation:

Answer:25

Step-by-step explanation:cause it is

To calculate the number of trucks Team Three expects to load based on the information provided.

To calculate the number of trucks Team Three expects to load:

Calculate 3.5 times the number of trucks loaded by team one: 5.5 trucks x 3.5 = 17.5 trucks.

Therefore, team three expects to load 17.5 trucks.

Answer: 2x^3 - 7x^2 + 6x - 9 which is choice D

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

Work Shown:

One way is to use the distribution rule two times

(x-3)(2x^2-x+3) = y(2x^2-x+3) ........... replace (x-3) with y

(x-3)(2x^2-x+3) = y(2x^2)+y(-x)+y(3) .... distribution rule

(x-3)(2x^2-x+3) = 2x^2*(y) - x(y) + 3(y)

(x-3)(2x^2-x+3) = 2x^2*(x-3) - x(x-3) + 3(x-3) .... replace y with x-3

(x-3)(2x^2-x+3) = 2x^3-6x^2 - x^2 + 3x + 3x - 9 ... distribution rule

(x-3)(2x^2-x+3) = 2x^3 - 7x^2 + 6x - 9

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

Or we can use the box method (see the attached image below). This is a visual way to organize the terms. You'll probably notice that the box method is basically the distribution rule. Each row is one distribution being applied. In row 1, we have x distributed to (2x^2-x+3). In row 2, we have -3 distributed to (2x^2-x+3). I color coded the table cells to highlight the like terms. Those like terms combine to -6x^2-x^2 = -7x^2 and 3x+3x = 6x as shown in the steps for the distribution above.

Each interior cell in the box is found by multiplying the corresponding outer terms. For example, in the first row, first column we have x^3 which is the result of multiplying the outer x and x^2 terms.

The correct choice is D) [tex]\(2x^3 - 7x^2 + 6x - 9\)[/tex].

To find the product[tex]\((x - 3)(2x^2 - x + 3)\)[/tex], we can use the distributive property:

[tex]\((x - 3)(2x^2 - x + 3) = x(2x^2 - x + 3) - 3(2x^2 - x + 3)\)[/tex]

Now, distribute the terms:

[tex]\[= x \cdot 2x^2 - x^2 + 3x - 3 \cdot 2x^2 + 3x - 9\][/tex]

Combine like terms:

[tex]\[= 2x^3 - x^2 + 6x - 6x^2 + 6x - 9\][/tex]

Combine the x terms:

[tex]\[= 2x^3 - 7x^2 + 6x - 9\][/tex]

Therefore, the expression [tex]\((x - 3)(2x^2 - x + 3)\)[/tex]  is equal to \[tex](2x^3 - 7x^2 + 6x - 9\)[/tex].

So, the correct choice is D) [tex]\(2x^3 - 7x^2 + 6x - 9\)[/tex].

For a general quadratic equation with rational coefficients

[tex]ax^2+bx+c=0,\,\,\,\,a,b,c \in Q[/tex]

the two solutions are:

[tex]x_{1,2} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-b\pm\sqrt{D}}{2a}[/tex]

where D is the determinant.

Clearly, a solution will a rational number as long as [tex]\sqrt{D}[/tex] is rational. However, it can be shown that a square root of an integer is only rational if its value is an integer. In other words, [tex]\sqrt{D}[/tex] is rational if and only if the determinant is a perfect square, [tex]D=n^2, \,\,\,n\in N[/tex], otherwise the square root is irrational. Therefore the coefficients of quadratic equations that are to have rational solutions must satisfy the following condition:

[tex]b^2-4ac=n^2\,\,\,n\in N[/tex]

The question requires us to use the exponential distribution to calculate the probability of waiting more than 15 minutes between two successive calls given a Poisson process with β parameter 1/6. We achieve this by using the cumulative distribution function. The probability is approximately 96.4%.

This question is essentially asking us to use the exponential distribution to calculate the probability of waiting for more than 15 minutes (which is 0.25 hour because we are dealing with hours as units of time) between two successive calls when the parameter β =1/6 is given. The exponential distribution is used to model the time between events in a Poisson process, and the probability density function is given by f(x) = βe^(-βx) for x ≥ 0.

The cumulative distribution function is F(x) = 1 - e^(-βx), so to compute the probability of waiting time that is more than 0.25 hour, we subtract the cumulative distribution function from 1.

So, P(X > 0.25) = 1 - P(X ≤ 0.25) = 1 - [1 - e^(-β * 0.25)] = e^(-β * 0.25) = e^(-(1/6) * 0.25) ≈ 0.964, or 96.4% as the answer.

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Answers:

Mean = 13.55

Median = 13

Mode = 13

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

Explanations

Mean:

To get the mean, multiply the ages with their corresponding frequencies. Then add up the results. I show this in the attached image below. The highlighted yellow cell is the sum of the x*y column (x = age, y = frequency). This value is 718.

Once you get to 718, you divide this over the total frequency which is 7+9+11+10+9+4+3 = 53 (so there is 53 people).

The mean is therefore 718/53 = 13.5471698113208 which rounds to 13.55

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

Median:

The median is the middle most value. There are 53 values here (add up the frequencies), so the midpoint is at slot 53/2 = 26.5 = 27. The first 26 values are below the median, and the last 26 values are above the median leaving 53-26-26 = 53 - 52 = 1 value in the very exact center.

Add up the frequencies starting from 7 then to 9, etc until you get to 27. So we have

7+9 = 16 which isn't 27

7+9+11 = 16+11 = 27 perfect, we landed on 27

This means that the last copy of 13 is in slot 27. This is because the last frequency added (11) corresponds to the age 13.

That is why the median is 13

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

Mode:

The mode is the most frequent value. Simply record the age that has the highest frequency. In this case, the highest frequency is 11 which corresponds to age 13, pointing to the mode being 13.

Answer:

3/40

Step-by-step explanation:

After you multiply across, you get 3/40. Since these two numbers don't have common multiples, it just stays as 3/40

Answer:

the third option

Step-by-step explanation:

1*3= 3

10*4= 40

3/40

Answer:

C = 81.6 degrees

Step-by-step explanation:

The formula for law of sines

sin A       sin B          sin C

--------  = -----------  = -------------

a                  b               c

Looking at the diagram,  we know A = 54, b = 7.4 and c = 15.8

not enough to use the law of sines

We will need to use the law of cosines

a^2 = b^2 + c^2 - 2ac cos A

Using the law of cosines, we can calculate the length of a

a^2 = 7.4^2 + 15.8^ -2*7.4*15.8 cos 54

a^2 = 54.6+249.64-233.84cos54

a^2 =166.7922966

a = 12.921

Now we can use the law of sines to find C

sin 54      sin C

--------  =  -------------

12.921           15.8

Using cross products

15.8 * sin 54 = 12.921 * sin C

Divide each side by 12.921

15.8 /12.921 * sin 54  = sin C

Take the arcsin of each side

arcsin (15.8 /12.921 * sin 54)  = arcsin (sin C)

arcsin (15.8 /12.921 * sin 54)  = C

C = 81.6 degrees

Answer: (1,3)

All you're doing is looking for where the two lines cross, or the point of intersection. What you can do is draw a vertical line through this intersection point to see that the vertical line lands on x = 1 on the x axis. At the same time, draw a horizontal line to the y axis and it will get to y = 3.

So together x = 1 and y = 3 pair up to get (x,y) = (1,3)

Final answer:

To find out how much longer we have before we finish the movie, subtract the time already watched from the total duration of the movie.

Explanation:

To find out how much longer we have before we finish the movie, we need to subtract the time we have already watched from the total duration of the movie.

Given that the movie is 28 minutes and 58 seconds long, and we have already watched 13 minutes and 44 seconds, we subtract the time already watched from the total duration:

28 minutes 58 seconds - 13 minutes 44 seconds = 15 minutes 14 seconds.

Therefore, we have 15 minutes and 14 seconds left before we finish the movie.

Answer:

D.525 M

Step-by-step explanation:

We know the equation

d = st

where d is the distance, s is the speed and t is the time

The problem gives us the speed of 35 m/s and the time of 15 seconds

s = 35 m/s and t =15 s, we can substitute them in

d =st

d = 35 * 15

d = 525 m

Answer:

525 m

Step-by-step explanation:

Answer:

10 ways, 6th row

Step-by-step explanation:

You will flip a coin five times and get three heads and two tails. You can get it in

[tex]C_5^3=\dfrac{5!}{3!(5-3)!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot1\cdot 2}=10[/tex]

different ways.

6th row tells her the number of favorable outcomes for this event.

Answer:

Let B represents the number of basil plants and F represents the number of fennel plants,

As per the given condition: Michelle has a maximum of 4500 milliliters  of water for her plants today. Each basil plant requires 350 of water, and each fennel plant requires 525  of water.

Each basil plant require 350 of water

⇒ total number of basil plant require water = 350B

Each Fennel plant require 525 of water.

⇒ total number of fennel plant require water = 525F

Since, Michelle has a maximum of 4500 milliliters of water;

then;

[tex]350B+525F \leq 4500[/tex]

Therefore, an inequality that represents the number of basil plants(B) and fennel plants can water today is; [tex]350B+525F \leq 4500[/tex]

Final answer:

78,045 rounded to the nearest thousand is 78,000. You round down because the hundreds digit (0) is less than 5. This approach to rounding applies in various arithmetic contexts.

Explanation:

To round 78,045 to the nearest thousand, we need to consider the hundreds digit, which is 0. In rounding, if the hundreds digit is 5 or greater, we would round up. However, because it is 0, we keep the thousands digit the same and replace all subsequent digits with zeros. Thus, 78,045 rounded to the nearest thousand is 78,000.

When dealing with whole numbers and rounding to a certain place value, it is crucial to look at the number to the immediate right of the place value you are rounding to. If this number is 5 or higher, you round up. Otherwise, you round down. This principle is true regardless of whether you are serving a subtraction operation, like 78,500 m - 362 m which rounds to 78,100 m, or if you're dealing with large numbers in scientific notation, such as 79,345 which can be represented as 7.9345 × 104.

Answer:6: 8.64

7: 584

Step-by-step explanation:

48×.18=8.64

800×.73=584

Hope this helps

Answer:

Answer for question number 7 is 58.4

Step-by-step explanation: