Surface Area of a Triangular Prism
If the net is assembled, which of the following
polyhedra would it make?
А
B
A
10
10
10
8
10
С
D
C С
D
5
10
10
10
10
10
8

Answer:

First, let's explain the transformations in a general way:

Vertical shift.

If we have a function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

This will move the graph of f(x) up or down a distance of N units.

if N is positive, then the shift is upwards

if N is negative, then the shift is downwards.

Horizontal shift.

If we have a function f(x), a horizontal shift of N units is written as:

g(x) = f(x + N)

This will move the graph of f(x) to the right or left a distance of N units.

if N is positive, then the shift is to the left

if N is negative, then the shift is to the right.

Horizontal dilation/contraction.

For a function f(x), an horizontal contraction dilation is written as:

g(x) = f(k*x)

where:

k is called the "scale factor"

If k < 1, then the graph "dilates" horizontally.

if k > 1, then the graph "contracts" horizontally.

Now, in this problem we have:

f(x) = log(x)

And the transformed function is:

g(x) = f(0.25*(x - 5)) + 3

Then, the transformations that take place here are, in order:

Vertical shift of 3 units up:

g(x) = f(x) + 3.

Horizontal shift of 5 units to the right:

g(x) = f(x - 5) + 3

Horizontal dilation of scale factor 0.25

g(x) = f( 0.25*(x - 5)) + 3

replacing f(x) by log(x) we have

g(x) = log(0.25*(x - 5)) + 3.

Answer:

number 3 maybe . sorry if wrong

Answer:

Slope is 20 and y-intercept is 40.

Step-by-step explanation:

First, let's find slope. I'll be using the points (1,60) and (3,100).

\(m=\frac{y2-y1}{x2-x1}=\frac{100-60}{3-1}=\frac{40}{2}=20\)

So the slope is \(m=20\). Now we need to find y-intercept. We can do this by using our slope and a point in the point-slope equation, \(y=mx+b\). I'll use the point (1,60).

\(y=mx+b\\60=20(1)+b\\60=20+b\\b=40\)

I hope this helps!

Answer: Answer: CB = 7.    AC = 5.

Step-by-step explanation:

Well we know that A-B is 7. And this is a right triangle, so the CB will be the same length. So CB = 7.

Now AC.

You divide 45 degrees by 7. And you get five.

So AC = 5 and CB = 7.

Answer:

what is your question

Step-by-step explanation:

Answer:

Step-by-step explanation:

there is no picture....

Using the same guideline, for a four-credit class, you would ideally spend:

4 credits * 2-3 hours/credit = 8-12 hours per week.

it is suggested that students allocate around 2-3 hours of study time per credit hour per week for a college-level course. However, the actual study time required may vary based on individual learning styles, prior knowledge, and the specific requirements set by professors or institutions.

Let's apply this general guideline to your scenario:

One three-credit class that is less demanding:

Assuming 2-3 hours of study per credit hour, for a three-credit class, you would ideally spend:

3 credits * 2-3 hours/credit = 6-9 hours per week.

Two three-credit classes that are typically demanding:

Similarly, for each of the two three-credit classes, you would spend:

3 credits * 2-3 hours/credit = 6-9 hours per week.

Since you have two such classes, the total time would be:

2 * (6-9) hours = 12-18 hours per week.

One four-credit class that is very challenging:

Using the same guideline, for a four-credit class, you would ideally spend:

4 credits * 2-3 hours/credit = 8-12 hours per week.

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The equation that can be used to model the total number of yards of fabric, y. needed to make x curtain panels is y = (10 2/4 ÷ 4) × x

It should be noted that Mary used 10 2/3 yards of fabric to make 4 identical curtain panels.

Therefore, the equation that can be used to model the total number of yards of fabric, y. needed to make x curtain panels will be:

y = (10 2/4 ÷ 4) × x

where

y = number of yards

x = number of panels

Therefore, the equation is y = (10 2/4 ÷ 4) × x

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Answer:

14

Step-by-step explanation:

31 - 7 = 14. We subract to find the overlap.

Answer:

no solutions

Step-by-step explanation:

6n - 6n - 12 = 14 - 2 = 12 ( add 12 to both sides )

0 = 24 ← not possible

this indicates the equation has no solution

Answer: 500 milligrams

Step-by-step explanation:

edge 2021

Answer:

500 milligrams

Step-by-step explanation:

Using the formula they gave us:

Cost of shipping = 2.79 + 0.38(8)

Cost of shipping = 2.79 + 3.04

Cost of shipping = 5.83(currency unit)

The probability that a box of 40 light bulbs will last for 5 years is very low, due to the short mean lifetime of 2 months and the relatively high standard deviation of 0.25 months.

The mean lifetime of a particular type of light bulb is given as 2 months, and the standard deviation is given as 0.25 months. The mean lifetime represents the average time that the light bulbs will last, while the standard deviation represents how much the lifetimes of the bulbs vary from the mean.

To determine the probability that a box of 40 light bulbs will last for 5 years, we need to convert the given information into a format that we can work with. 5 years is equal to 60 months, and since we have 40 light bulbs, we can assume that the lifetimes of the bulbs are independent and identically distributed. This means that the probability of one bulb lasting for 60 months is the same as the probability of any other bulb lasting for 60 months.

Next, we need to calculate the standard deviation of the sample mean. The standard deviation of the sample mean represents how much the means of different samples of size 40 would vary from the population mean. The formula for the standard deviation of the sample mean is given by the following equation:

standard deviation of the sample mean = standard deviation of the population / square root of the sample size

In this case, the standard deviation of the population is given as 0.25 months, and the sample size is 40. Therefore, the standard deviation of the sample mean is:

0.25 / sqrt(40) = 0.0395

Now that we have the mean lifetime and the standard deviation of the sample mean, we can use the normal distribution to determine the probability that a box of 40 light bulbs will last for 5 years. We can assume that the lifetimes of the bulbs follow a normal distribution with a mean of 2 months and a standard deviation of 0.0395 months (which is the standard deviation of the sample mean).

To find the probability that a bulb will last for 60 months, we can use the following equation:

z = (x - μ) / σ

where z is the standard score, x is the value we want to find the probability for (60 months in this case), μ is the mean, and σ is the standard deviation.

Plugging in the values, we get:

z = (60 - 2) / 0.0395 = 1509.49

To find the probability corresponding to this standard score, we can use a standard normal distribution table or a calculator. The probability is extremely small (close to zero), which means that it is highly unlikely that all 40 light bulbs will last for 5 years.

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Answer:

x>24

Step-by-step explanation:

−2x+7< −41

−2x+7−7< −41−7

−2x< −48

−2x /−2  <  −48 /−2

x>24

it should be flipped over the x-axis and translated to the right by 2

There are 560 ways to fill the 5 positions on the shelf, with the first 2 positions occupied by math books and the last 3 positions occupied by computer science books.

To determine the number of ways to fill the positions on the shelf, we need to consider the different combinations of books for each position.

First, let's select the math books for the first two positions. Since Mike has 8 different math books, we can choose 2 books from these 8:

Number of ways to choose 2 math books = C(8, 2) = 8! / (2! * (8-2)!) = 28 ways

Next, we need to select the computer science books for the last three positions. Since Mike has 6 different computer science books, we can choose 3 books from these 6:

Number of ways to choose 3 computer science books = C(6, 3) = 6! / (3! * (6-3)!) = 20 ways

To find the total number of ways to fill the positions on the shelf, we multiply the number of ways for each step:

Total number of ways = Number of ways to choose math books * Number of ways to choose computer science books

= 28 * 20

= 560 ways

Therefore, there are 560 ways to fill the 5 positions on the shelf, with the first 2 positions occupied by math books and the last 3 positions occupied by computer science books.

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Answer:

y= 4x +5

Step-by-step explanation:

Let's rewrite the equation so that it is in the form of y=mx+c, where m is the gradient and c is the y-intercept.

4x-y=1

y= 4x -1

parallel lines have the same gradients. Thus the gradient of the line is 4.

y=4x+c

To find c, substitute a pair of coordinate.

When x=-2, y= -3,

-3= 4(-2) +c

-3= -8 +c

c= 8 -3

c= 5

Thus, the equation of the line is y= 4x +5.

The partial derivatives of the function with respect to x and y are both zero at the critical point (0,0), which is a saddle point.  

The local maxima, local minima, and saddle points of the function f(x,y) = \(x^3 - 18xy y^3\), we need to take the partial derivatives of the function with respect to x and y and set them equal to zero.

First, we can find the critical points of the function by setting the partial derivatives equal to zero:

\(x^3 - 18xy y^3 = 0\)

Taking the partial derivative of \(x^3\) with respect to x, we get:

\(3x^2 = 18xy\)

Taking the partial derivative of \(y^3\) with respect to y, we get:

\(3y^2 = -18x\)

Now, we can set these equal to zero and solve for x and y:

\(3x^2 = 18xy\\x^2 = 6y\\3y^2 = -18x\\y^2 = -6x\)

Substituting these expressions for x and y into the previous equation, we get:

6y = 6y

y = 0

\(x^2 = 6(0)\\x^2 = 0\)

Therefore, the critical points of the function are (0,0), which correspond to a saddle point.

To check that this is a saddle point, we can calculate the Jacobian matrix of the function at this point:

J(0,0) = [3, 6]

The determinant of the Jacobian matrix is 3, which is positive. Therefore, the critical point (0,0) is a local minimum.

Since the critical point (0,0) is a saddle point, it is also a local maximum.

Next, we can find the partial derivatives of the function with respect to x and y at the critical point:

\(x^3 - 18xy y^3 = 0\)

\(3x^2 = 18xy\\3y^2 = -18x\)

At the critical point (0,0), we have:

x = 0

y = 0

The partial derivatives, we get:

0 = 18(0)y

y = 0

Substituting this value of y into the partial derivative of \(x^3\) with respect to x, we get:

0 = 0

Therefore, the partial derivatives of the function with respect to x and y are both zero at the critical point (0,0), which is a saddle point.  

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The thing that will be always true about quadrilateral ABCD is C. m∠A+m∠B=180°

The coordinates of the center of the circle is B. (6, 4)

Based on the fact that opposite angles in an inscribed quadrilateral are always equal, then m∠A+m∠B=180°. As a result, ∠A + ∠C = 180 degrees and likewise for ∠B + ∠D = 180 degrees.

The intersection of the two lines, namely, the perpendicular bisector of AB (passing through midpoint (6, 3.5) with a slope -12/7) and the vertical line whose undefined own slope penetrates the midpoint (6, 0) of AC, is exactly the center of circle, which has its coordinates as (6, 4).

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20 ft/sec must she let out the string when the kite is 500 ft away from her.

What is rate?

A rate is a unique ratio where the two words are expressed in several units.

For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. Cents and ounces are the two dissimilar units in this ratio.

Let x = distance of girl from the point on the ground directly below the     kite at time t

y = length of string at time t

At time t, we have a right triangle with horizontal leg of length x, vertical leg of length 300, and hypotenuse of length y.

Given:  dx/dt = 25

Find:  dy/dt when y = 500

By the Pythagorean Theorem, \(x^2 +300^2 = y^2\)

Differentiating both sides, with respect to t,

\((2x)\frac{dx}{dt} = 2y\frac{dy}{dt}\)           ...(1)

Since, \(x^2 +300^2 = y^2\),  y = 500,

So, x = 400

Plug these values in equation (1).

\(2(400)(25) = 2(500)\frac{dy}{dt}\)

After solving,

\(\frac{dy}{dt} = 20 ft/sec\)

Therefore, 20 ft/sec must she let out the string when the kite is 500 ft away from her.

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Equation that will help determine how many days it will take for the average charge per day for company a to be the same as the average charge per day for company b is \(\frac{80+22d}{d} = 32d\)

For finding the equation we will first form separate equations of both company a and company b and then we will equate the formed equation to find the number of days.

Let the number of days be d.

For company a, we will first add the service charges and per day charge multiplied with number of days, and then divide the sum with number of days.

= \(\frac{80+22d}{d}\)

For company b, we will multiply the per day charges with the number of days.

= \(32d\)

Now, we will equate both the formed equation

\(\frac{80+22d}{d} = 32d\)

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Answer:

C) -0.5

Step-by-step explanation:

Since the y₁ is decreasing, that automatically makes it a negative slope, and its decreasing by 0.5, so it's C!

Answer:

3a² + ab + 4b²

Step-by-step explanation:

P - Q

= - 4a² - 2ab + 9b² - (- 7a² - 3ab + 5b² ) ← distribute parenthesis by - 1

= - 4a² - 2ab + 9b² + 7a² + 3ab - 5b² ← collect like terms

= 3a² + ab + 4b²

Answer:

3a² + ab + 4b²

Step-by-step explanation:

Combine like terms. Like terms have same variable with same power.

P - Q = -4a² - 2ab + 9b² - (-7a² - 3ab + 5b²)

To open the brackets, multiply each term of Q by (-1)

          = -4a² - 2ab + 9b² + 7a²+ 3ab - 5b²

-4a² and 7a² are like terms.

(-2ab) and  3ab  are like terms.

9b² and (-5b²) are like terms.

          = -4a² + 7a² -2ab + 3ab + 9b²- 5b²

          = 3a² + ab + 4b²

Answer:

total weight = 5.62 X 3 = 16.86 grams

Answer:

so first we have to find km per hour

so lets divide 452/17=26.5882352941

so it travels 26.6 km per hour so lets mulitply for the 9 hours

26.6*9=239.4

it can travel 239.4 km in 9 hours

Hope This Helps!!!

Answer:

y= 2x-2

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Find two lattice points

I chose (-2, 0) and (0, -2)

Since you are using a graph, you don't need an equation.

Starting from (-2, 0), you go down -2 points and 2 across to get to the second point.

-2/2 = -1

The mean number of miles the hiker walked for the 6 days was 6.5 miles.

To calculate the mean or average of a set of numbers, we add up all the numbers and then divide the sum by the number of items in the set. In this case, we have the number of miles the hiker walked on each of the six days. To find the total number of miles the hiker walked, we simply add up all the numbers

8 + 5 + 7 + 2 + 9 + 8 = 39

Next, we divide the total number of miles by the number of days (which is 6) to get the average or mean number of miles the hiker walked per day:

Mean number of miles = Total number of miles / Number of days

= 39 / 6

= 6.5

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The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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Answer:

Step-by-step explanation:

(9). Reflection across the x-axis keeps the same x-coordinate and y-coordinate is the opposite to original ( x , y ) ------> ( x , - y )

(10).  Reflection across the y-axis keeps the same y-coordinate and x-coordinate is the opposite to original ( x , y ) ------> ( - x , y )

(11). Translation along the vector < 0, 2 >  means that each point of triangle moves 2 units UP  ( x , y ) ------> ( x , y + 2 )

(12). Translation along the vector < 3, - 4 >  means, that each point of triangle moves 3 units to the RIGHT and 4 units DOWN  ( x , y ) ------> ( x + 3 , y - 4 )

(13). ( x , y ) ------> ( - x , - y )

(14). ( x , y ) ------> ( - y , x )  

The difference quotient for the given function is 9 -2/h.

The difference quotient for the given function can be calculated as:

[f(x+h) - f(x)]/h

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

= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h

= (6xh + 3h² - 2h)/h

= (6x + 3h -2)/h

Simplifying the expression further, we get:

(6x + 3h -2)/h = 6 + 3h/h -2/h

= 6 + 3 -2/h

= 9-2/h

Therefore, the difference quotient for the given function is 9 -2/h.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.

f(x)=3x² -2x+5. Simplify your answer as much as possible.

Answer:

see explanation

Step-by-step explanation:

a

the error she has made is in cancelling the values in the denominators.

When cancelling fractions, this is performed between values on the numerator with values on the denominator.

correct result is

\(\frac{1}{15}\) × \(\frac{3}{5}\) ( cancel the 3 and 15 by 3 )

= \(\frac{1}{5}\) × \(\frac{1}{5}\)

= \(\frac{1}{25}\)

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

b

as an estimate, multiply the numerators and denominators, that is

\(\frac{1(3)}{15(5)}\) = \(\frac{3}{75}\) = \(\frac{1}{25}\)

Answer:

No, it's just maximum of two tables that lost balloon so there is no way it affected each table.

Step-by-step explanation:

Number of balloons purchased= x

Number of tables = 8.

Each table has = x/8 balloons

If 2 balloons pop.

Let's assume it's just from a table

That table has( x/8 -2)

If it's from 2 table

The two table has

(X/8-1) for both tables

But the total balloon remaining = x-2

There is no particular equation that can describe the gallon on each table because it's only two balloons that popped.

Answer:

That expression is not true. To evenly distribute the balloons you use x/8. Then you subtract 2 balloons from that total amount. The subtraction must be done after the division. There will not be the same number of balloons at each table.

Step-by-step explanation:

It was the sample answer.