Find the greatest common divisor of 100 and 254, using • prime factorization- • euclidean algorithm-

You can calculate the scale factor by dividing the coordinates of the image by the corresponding coordinates of the pre-image.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Assume that the initial coordinates are (x, y) and that the dilated coordinates are (x', y').

The dilation is therefore:

(x, y) → (x', y')

Now, let's assume that the dilation factor is k.

Therefore:

x' = kx

y' = ky

To get the initial coordinates and the final ones and then substitute in any of the above two equations to get the value of k, which is the scale factor,

For example =

Assume an original point at (2,4) is dilated to coordinates (4,8) we need to find the dilation factor.

Assume the dilation coefficient is k.

(x, y) are (2,4) and (x', y') are (4,8)

Therefore:

x' = kx → 4 = k×2 → k = 2

or:

y' = ky → 8 = k×4  → k = 2

Based on the above, the dilation coefficient would be 2.

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Slope-intercept form is y = mx +b, where the variable m represents the slope of the line and the variable b represents the y-intercept of the line. Since we weren't given the y-intercept, one way to solve this problem is substitute the slope for the variable m and then the x and y values from the ordered pair to solve for b.

y = mx + b

y = 3x + b

-4 = 3(9) + b

Now, we can simplify by computing the multiplication on the right side of the equation.

-4 = 27 + b

Finally, we can find the value for b by subtracting 27 from both sides of the equation to get:

-31 = b

Now, we should substitute this value for b back into our equation with the slope.

y = 3x - 31

Therefore, your answer is y = 3x - 31.

Hope this helps!

Answer:

The correct answer would be y = 3x - 31

Step-by-step explanation:

In order to find the answer to this question, we must use point-slope from, which is listed below.

y - y1 = m(x - x1)

Now we input the ordered pair in for x1 and y1 and the slope in for m.

y - -4 = 3(x - 9)

Then we solve for y.

y + 4 = 3x - 27

y = 3x - 31

Answer:

B. Time

Step-by-step explanation:

In general, x-axis is the variable (cause) and the y-axis is the response (effect)

So, according to the given information, TIME would be represented by the x-axis.

Answer:

Stan would need 960 sprinkles to make 60 cookies.

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

Since we are given 3 values, which are the amount of sprinkles to make 24 cookies, 60 cookies, and give us one variable. We can use the Rule of Three technique to find the amount of sprinkles needed for 60 cookies. This technique is shown in the picture that is attached below.

24 cookies   ⇒   384 sprinkles

60 cookies   ⇒   x

[tex]\frac{60*384}{24} = x[/tex]

[tex]960 sprinkles = x[/tex]

Therefore, we can see that Stan would need 960 sprinkles to make 60 cookies.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Final answer:

The equation according to Dolbear's law is T = 0.25x + 40. For 100 chirps, the temperature is 65°F. For a temperature of 96°F, the cricket would make 224 chirps.

Explanation:

According to Dolbear's law, the relationship between the temperature and the number of chirps made by a snowy tree cricket can be used to predict the temperature. We are given that at 50°F, a cricket chirps 40 times in one minute, and for each increase of 0.25°F, there is one additional chirp per minute. To write an equation in slope-intercept form (T = mx + b), where m is the slope and b is the y-intercept, we must find these values. Since we know that 40 chirps correspond to 50°F, we can use this as our starting point (b). Also, because each additional chirp represents a 0.25°F increase in temperature, the slope (m) is 0.25. Therefore, the equation is:

T = 0.25x + 40

If you count 100 chirps in one minute, to find the temperature, simply plug in the value for x in the equation:

T = 0.25(100) + 40

T = 25 + 40

T = 65°

The temperature is 65°F.

If the temperature is 96°F, to find the number of chirps (x), we rearrange the equation to solve for x:

96 = 0.25x + 40

x = (96 - 40) / 0.25

x = 224 chirps

You would expect the cricket to make 224 chirps.

Final answer:

There are 999,999,999 possible Social Security number combinations, subtracting one from the 10^9 available combinations to account for the restriction against the number 000-00-0000.

Explanation:

A Social Security number (SSN) consists of nine digits, traditionally written in the format XXX-XX-XXXX, where each X represents one digit from 0 to 9. When calculating the number of possible SSN combinations, one would consider that each digit position in the SSN can take on any value between 0 and 9, making for 10 possibilities per position. However, we also know that a SSN cannot be 000-00-0000. Hence, the total number of SSN combinations would be:

Total Combinations = 109 (number of combinations for nine digits) - 1 (excluding the number 000-00-0000).

109 equals 1,000,000,000, so removing one for the restricted number results in a total of 999,999,999 possible SSN combinations.

The points that satisfy both inequalities are:

B) (0.5, 2)

D) (−2, 4)

To identify which points are solutions to the system of inequalities:

2x + 3y > 6

3x + 2y < 6

We need to check each point to see if it satisfies both inequalities.

2(1.5) + 3(1) = 3 + 3 = 6 - Not a solution

3(1.5) + 2(1) = 4.5 + 2 = 6.5 Not a solution

2(0.5) + 3(2) = 1 + 6 = 7 This a solution

3(0.5) + 2(2) = 1.5 + 4 = 5.5 -  This a solution

2(-1) + 3(2.5) = -2 + 7.5 = 5.5 - Not a solution

3(-1) + 2(2.5) = -3 + 5 = 2 - Not a solution

2(-2) + 3(4) = -4 + 12 = 8 -  This a solution

3(-2) + 2(4) = -6 + 8 = 2-  This a solution

Complete question

Identify any solutions to the system shown here.

2x+3y>6

3x+2y<6

A) (1.5,1)

B) (0.5,2)

C) (−1,2.5)

D) (−2,4)

To calculate the volume of a cylinder with a diameter of 28 units and a height of 28 units, use the formula V = πr²h. The calculated volume is approximately 17240.896 cubic units.

To find the volume of a cylinder, we use the formula:

V = πr²h

Here, the diameter of the cylinder is 28 units. To find the radius, we divide the diameter by 2:

r = 28 / 2 = 14 units

The height of the cylinder is given as 28 units. Substituting the values into the formula, we get:

V = π × (14)² × 28

V = π × 196 × 28

V = 5488π

Using the approximation π ≈ 3.142,

V ≈ 5488 × 3.142 ≈ 17240.896 cubic units

Therefore, the volume of the cylinder is approximately 17240.896 cubic units.

To determine the amount of hardener needed for 14 containers of resin, multiply the amount of hardener needed for one container (55mL) by the number of containers (14), resulting in 770mL of hardener.

To determine the amount of hardener needed for 14 containers of resin, we can use the given formula of adding 55mL of hardener to each container. We can multiply the amount of hardener needed for one container (55mL) by the number of containers (14).

Calculation:

Therefore, 770mL of hardener should be added to 14 containers of resin.

To calculate the total amount of hardener needed for 14 containers of resin, multiply the 55 mL required per container by 14, resulting in 770 mL of hardener needed.

You are asked to determine how much hardener should be added to 14 containers of resin if it is known that 55 mL of hardener is required for each container. To find the total amount of hardener needed for 14 containers, you would use multiplication:

Total hardener needed = Hardener per container × Number of containers

So, Total hardener needed = 55 mL/container × 14 containers

Now by multiplying 55 by 14, we get:

Total hardener needed = 770 mL

Therefore, 770 mL of hardener is needed for 14 containers of resin.

Answer(s):

[tex]\displaystyle y = 4cos\:(4\theta \pm \pi) \\ y = -4cos\:4\theta[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Acos(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\pm\frac{\pi}{4}} \hookrightarrow \frac{\pm\pi}{4} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4[/tex]

OR

[tex]\displaystyle y = -Acos(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that this cosine graph will have TWO equations because the curvature begins upward from [tex]\displaystyle [0, -4][/tex] instead of downward from [tex]\displaystyle [0, 4],[/tex] telling you that one equation will have a “negative” symbol inserted in the beginning of the equation. Before we go any further though, we must figure the period of the graph out. So, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, -4],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{2}, -4],[/tex] they are obviously [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{2}.[/tex] Now, as you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4cos\:4\theta.[/tex] Now, if you look hard enough, you will see that both graphs are “mirror reflections” of one another, meaning you can figure the rest of the terms out one of two ways. The first way is to figure the appropriate C-term out that will make the graph horisontally shift and map onto the original cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also, keep in mind that −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the rightward graph is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex] on both sides of the y-axis, which means that in order to match the original graph, we need to shift the graph back, which means the C-term will be both negative and positive; and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\pm\frac{\pi}{4}} = \frac{\pm\pi}{4}.[/tex]So, one equation of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4cos\:(4\theta \pm \pi).[/tex] Now that we got this out the way, we can focuss on finding the second equation. Another way is to write an equation with a “negative” symbol inserted in the beginning [like I mentioned earlier]. Now, sinse we are writing an equation with the negative, the graph will not have a horisontal shift; so, C will be zero. With this said, the second equation is [tex]\displaystyle y = -4cos\:4\theta.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex] in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Complete the chart:

Dimension What Can Be Measured Example Object

Zero Nothing Point

One Length Line

Two Length, Width Polygon

Three Length, Width, Height Solid

Zero Dimensions:

What Can Be Measured: Nothing. Zero dimensions imply a mathematical point without any length, width, or height.

Example Object: Point. A point in geometry is a location represented by a dot and has no size or dimensions.

One Dimension:

What Can Be Measured: Length. In one dimension, objects have only length and can be measured in a straight line.

Example Object: Line. A line is a straight path that extends infinitely in both directions. It is characterized by its length.

Two Dimensions:

What Can Be Measured: Length, Width. Two-dimensional objects have both length and width. They are flat and can be measured in both directions.

Example Object: Polygon (e.g., Square). A polygon is a closed two-dimensional shape with straight sides, and a square is an example with equal length and width.

Three Dimensions:

What Can Be Measured: Length, Width, Height. Three-dimensional objects have length, width, and height. They are solids and occupy space.

Example Object: Solid (e.g., Cube). A cube is a three-dimensional shape with equal length, width, and height. It represents a solid object.

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Answer:

D

Step-by-step explanation:

Answer:

Graph B

Step-by-step explanation:

The pink line going downward to the right.

Answer:

Graph B

Step-by-step explanation:

The pink line going downward to the right.

Answer:

Step-by-step explanation:

You take the amount of 2-digit numbers there are (90) and subtract it from the  amount of two digit numbers that are multiples of 5 and 7 (29). You should get 61.

Answer:  The number 2-digit numbers are multiples of neither 5 nor 7 is 61.

Step-by-step explanation:  We are given to find the number of 2-digit numbers that are multiples of neither 5 nor 7.

Let A denote the set of 2-digit numbers that are multiples of 5 and B denote the set of 2-digit numbers that are multiples of 7.

Then,

A = {10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95}

and

B = {14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98}

That is, n(A) = 18  and  n(B) = 13.

Now, the set of 2-digit numbers that are multiples of both 5 and 7 is given by

[tex]A\cap B=\{35, 70\}~~~~~~\Rightarrow n(A\cap B)=2.[/tex]

Therefore, the number of 2-digit numbers that are multiples of either 5 or 7 is given by

[tex]n(A\cup B)=n(A)+n(B)-n(A\cup B)=18+13-2=29.[/tex]

Now, there are 90 2 -digit numbers.

Thus, the number 2-digit numbers are multiples of neither 5 nor 7 is

90 - 29 = 61.

Hence, the total number of numbers is 61.

Answer:

Chiara has 2 penny coins and 24 nickel coins

Step-by-step explanation:

Let

p ----> the number of penny coins

n ---> the number of nickel coins

Remember that

[tex]1\ penny=\$0.01[/tex]

[tex]1\ nickel=\$0.05[/tex]

Chiara has 26 coins that equal 34 cents

so

[tex]p+n=26[/tex]

isolate the variable x

[tex]p=26-n[/tex] ----> equation A

34 cents=$0.34

[tex]0.01p+0.05n=0.34[/tex]

Multiply by 100 both sides

[tex]p+5n=34[/tex]

isolate the variable x

[tex]p=34-5n[/tex] -----> equation B

Create a table  to guess

assume  different values of n and determine the value of p in equation A and equation B

The solution is when the value of p in the equation A must be equal to the value of p in equation B

1) For n=1

equation A

[tex]p=26-1=25[/tex]

equation B

[tex]p=34-5(1)=29[/tex]

[tex]29\neq 25[/tex]

2) For n=2

equation A

[tex]p=26-2=24[/tex]

equation B

[tex]p=34-5(2)=24\\24=24[/tex]

therefore

The solution is (2,24)

Chiara has 2 penny coins and 24 nickel coins

Answer:

Step-by-step explanation:

Sorry I'm late but the other person is wrong this is the answer