The figure below is reflected over the y-axis. What are the coordinates of the image of point R after this transformation?

Answer:

A

Step-by-step explanation:

I did the math and i have no doubt

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

The division expression is (5x³ - 22x² - 17x + 11)/(x - 5) = 5x² + 3x -  2 + (2/(x - 5))

From the question, we have the following parameters that can be used in our computation:

(5x³ - 22x² - 17x + 11)/(x - 5)

Using a synthetic setup, we have

x - 5 = 0

This gives

x = 5

So, the set up becomes

5 | 5   -22   -17   11

The synthetic division is then carried out as follows

5 | 5   -22   -17   11

           25   15   -10

     5     3     -2   1

So, we have

Quotient = 5   3   -2

Remainder = 1

Introduce the variable

Quotient = 5x² + 3x -  2

Remainder = 2

Hence, the quotient is 5x² + 3x -  2 and the remainder is 2

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Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.

To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).

The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.

We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.

Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.

To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)

Density = 600g / 600 cubic feet = 1g/cubic foot

Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.

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Check the picture below.

so let's recall that the area of a circle is just πr² where r = radius, so since the sizes of each pizza are 10, 14, 18 and 22, that's simply their diameter, so that means they each have a radius half of that, or namely 5, 7, 9 and 11, as you see in the picture, so, hmmm which radius gives us the most area per the fraction provided, namely per slices provided?

\(\cfrac{4}{8}\pi 5^2\implies \cfrac{25\pi }{2} ~~ \approx ~~ 39.26~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3}{8}\pi 7^2\implies \cfrac{147\pi }{8} ~~ \approx ~~ 57.73~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{2}{8}\pi 9^2\implies \cfrac{81\pi }{4}~~ \approx ~~ 63.62~in^2 ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{8}\pi 11^2\implies \cfrac{121\pi }{8}~~ \approx ~~ 47.52~in^2\)

Answer: Large

Step-by-step explanation:  Hope it helps Good luck!!!

Answer:

E. -1/2

Step-by-step explanation:

When two lines are said to be perpendicular to each other, the slope of one is the negative reciprocal of the other.

Therefore, given that \( \frac{x - 1}{4} \) is the slope of \( \overline{QR} \), and ⁸/3 is the slope of \( \overline{ST} \), if both lines are perpendicular, it means that the slope of \( \overline{ST} \) would be the negative reciprocal of the slope of \( \overline{QR} \).

Therefore:

\( \frac{x - 1}{4} = -\frac{3}{8} \)

Cross multiply

\( (x - 1)(8) = (-3)(4) \)

\( 8x - 8 = -12 \)

Add 8 to both sides

\( 8x = -12 + 8 \)

\( 8x = -4 \)

Divide both sides by 8

\( x = \frac{-4}{8} \)

\( x = \frac{-1}{2} \)

Answer:

y = 120

x = 90

z = 150

Step-by-step explanation:

i hope this helps :D

Answer:

7/10 = .70

3/5 = .60

9/11 = .81

1/2 = .50

9/11 is the most

Answer:

423

Step-by-step explanation:

2313

The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

y = 5/4x - 8

Step-by-step explanation:

first you convert the equation to y = mx + b

then you add the the -8 into the x and the 2 into the y and solve for b

b = -8 and since it is parallel same slope.

hope this helps :)

Answer:

Half of perimeter (or L+ W) is:

98/2= 49 (cm)

L- W= 15

L+ W= 49

L= (49+ 15)/2= 32

W= (49-15)/2= 17

The length is 32 cm and the width is 17 cm~

Step-by-step explanation:

Answer:

980

i hope this helps.

Answer:

The answer is explained below

Step-by-step explanation:

We have a system that would be a cylindrical shell with a certain length. I will attach an allusive image, they ask us to determine which would be the most suitable system of coordinates:

Most suitable surface is cylindrical annular for this annular 30 disk most suitable coordinate system would be Cylindrical Coordinate System as one at coordinate "z" remains constant and that would be advantageous

Answer:

5/37 as a decimal is 0.13513513513514.

5/37 as a percentage is 13.5135%.

Step-by-step explanation:

Answer:

5/37 = 0.135 (3 dp) = 13.513% (3 dp)

Step-by-step explanation:

5/37 = 0.135 (3 dp) = 13.513% (3 dp)

To convert a fraction to a decimal, use long division

To convert to a percent, multiply the decimal by 100.

Answer:

52630

Step-by-step explanation:

Simplify all the words into numbers.

30 + 2000 + 40000 + 600 + 10000

Add.

52630

Answer: B.A point is a location, and a line has many points located on it.

Step-by-step explanation:

The equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.

Given points:

Point 1: (1, 0)

Point 2: (3, 6)

Step 1: Calculate the slope (m) using the formula:

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

Substituting the coordinates:

m = (6 - 0) / (3 - 1)

m = 6 / 2

m = 3

Step 2: Substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).

Using Point 1 (1, 0):

0 = 3(1) + b

0 = 3 + b

b = -3

Step 3: Write the equation of the line using the slope (m) and the y-intercept (b):

y = 3x - 3

Therefore, the equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

This equation represents a line with a slope of 3, indicating that for every increase of 1 unit in the x-coordinate, the y-coordinate increases by 3 units. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). By substituting any x-value into the equation, we can determine the corresponding y-value on the line.

Hence, the equation of the line passing through (1, 0) and (3, 6) is y = 3x - 3.

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Answer:

fraction answer: 3/4

decimal answer: 0.75

Answer:

\(y = 8,50x\)

Step-by-step explanation:

Given

Let

\(y\to\)earnings

\(x \to\) hours

Solving (a): The proportion

x and y can be expressed as:

\(y\ \alpha\ x\) --- direct variation

Write as an equation

\(y = kx\)

Where

\(k = 8.50\) --- the hourly rate

So, we have:

\(y = 8,50x\)

Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.

In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.

For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.

To find the image of point E under this translation, you can apply the same translation to point E:

Point E is located at (5, 5).

The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).

You can follow the same process to find the images of the other points under the translation.

Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.

In this case, the translation vector is given by the displacement from point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).

To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:

Point E is located at (5, 5).

The translation vector is (-8, -7).

The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).

You can follow the same process to find the images of the other points under the translation.

Step-by-step explanation:

The point (2,-4) satisfies y < 3x - 6

Simply count the number of red marbles in each sample and divide by the total number of marbles in the sample (16). Then, take the average of those proportions to estimate the proportion of red marbles in the jar as a whole

Based on the information provided, the best conclusion we can make is an estimate of the proportion of red marbles in the jar. We can use the four random samples of 16 marbles to calculate the proportion of red marbles in each sample, and then take the average of those proportions to estimate the overall proportion of red marbles in the jar.

It's important to note that this estimate may not be perfectly accurate, since the samples are small and may not perfectly represent the entire jar. However, it's a useful way to get an idea of how many red marbles are in the jar without having to count all of them.

To calculate the proportion of red marbles in each sample

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Answer:

C.

Step-by-step explanation:

because f(x) is directly proportional to the numerator which greater than the denominator ( 5>1 ).

While in other cases, f(x) is inversely proportional to the greatest value which is the denominator

Answer:

m < -12

Step-by-step explanation:

2m + 8 < -16

(-8)

2m < -24

(divide both sides by 2) (2m÷2) (-24÷2)

m < -12

Apply the fraction rule:

\(\text{a}\times\dfrac{\text{b}}{\text{c}} =\dfrac{\text{a}\times\text{b}}{\text{c}}\)

Answer:

\(\longrightarrow\boxed{\bold{\frac{\text{fx}}{\text{g}}}}\)