Transformation of functions

Answer and Step-by-step explanation:

0 to the power of 4 is 0.

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Answer:

x = 16

Step-by-step explanation:

71 - 15 = 56

56 ÷ 14 = 4

\(\sqrt{16}\) = 4

Check work:

\(\sqrt{16}\) = 4

14 x 4 = 56

56 + 15 = 71

The area of the square lies between 419.4304 cm² and 488.7744 cm², considering the uncertainties.

To determine the area of the square, we need to square the length of its side. Given that the side length is S = 21.3 ± 0.82 cm, we can calculate the area as follows:

Lower bound of side length: \(S_{lower}\) = S - δS = 21.3 cm - 0.82 cm = 20.48 cm

Upper bound of side length: \(S_{upper}\) = S + δS = 21.3 cm + 0.82 cm = 22.12 cm

Lower bound of area: \(A_{lower}\) = (\(S_{lower}\))² = (20.48 cm)² = 419.4304 cm²

Upper bound of area: \(A_{upper}\) = (\(S_{upper}\))² = (22.12 cm)² = 488.7744 cm²

Therefore, the area of the square lies between 419.4304 cm² and 488.7744 cm², considering the uncertainties.

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Answer:

AD = 10

Step-by-step explanation:

It's given that ABCE is a rectangle.

Therefore, measure of opposite sides of the rectangle will be equal.

AB = EC

AB = ED + DC

12 = ED + 4

ED = 8

Measure of side AE = 6

Since, measure of interior angles of a rectangle = 90°

Therefore, ΔEAD will be a right triangle.

By Pythagoras theorem,

AD² = AE² + ED²

      = 6² + 8²

AD = \(\sqrt{36+64}\)

      = \(\sqrt{100}\)

      = 10

Therefore, measure of side AD = 10 units

Answer:

happy/ opens up

Step-by-step explanation:

since it is a positive equation it will open up

Answer: (1,500 = 30) (90 = 1.80)

Step-by-step explanation:

(1,500 = 30) (90 = 1.80) - This I'm pretty sure is the answer.

Answer:

70 degrees

Step-by-step explanation:

Since the angles of a triangle have to add up to 180 degrees, you know that the third angle of the triangle on the left would be 180 - 60 - 65 = 55 degrees. Then, since the angles on a straight line have to add up to 180 degrees you could find one of the two missing angles of the second triangle by doing

180 - 55 - 50 = 75.

Then, you have 2 out of the 3 angles of the triangle on the right and you can find the third, the ?, by doing 180 - 75 - 35 = 70 degrees

Solution:

Probability of the second outcome occurring is 1-p

Explanation:

In an experiment with only two outcomes, the probabilities of both outcomes must add up to 1.

This means that if the first outcome has a probability of p, the second outcome must have a probability of 1-p.

Therefore, the equation for this situation would be: p + (1-p) = 1Solving for p, we get: p = 1 - (1-p) = 1 - 1 + p = p.

Therefore, the probability of the first outcome occurring is simply p, as given in the question.

The probability of the second outcome occurring is 1-p.

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The probability of the first outcome, p, is equal to the total probability of all outcomes, minus the probability of the second outcome, p2. So, p = 1 - p2.

In an experiment with only two outcomes, the sum of the probabilities of the two outcomes must equal 1. This means that if the first outcome has a probability of p, the second outcome must have a probability of 1-p.

Therefore, the probability of the first outcome, p, can be found by subtracting the probability of the second outcome, p2, from 1:
p = 1 - p2

So, if you know the probability of the second outcome, you can find the probability of the first outcome by subtracting it from 1.

For example, if the probability of the second outcome is 0.3, the probability of the first outcome would be:
p = 1 - 0.3 = 0.7

So the probability of the first outcome is 0.7.

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Answer:

-4/5,-1/2,-0.2,0.25

Step-by-step explanation:

To order these, it would be best to convert them into decimals.

-4/5 is equal to -0.8

-1/2 is equal to -0.5

-0.8 is the least, because the further left on a number line, the less the number is.

-0.5 is next and then -0.2

Finally, 0.2 is the greatest

-4/5,-1/2,-0.2,0.25

Hope this helps :-)

Answer:

35°

Step-by-step explanation:

Total: 360°

{[360-(110*2)]/2}2

Answer:

The one on the top left

Step-by-step explanation:

What makes a function, a function is that the x coordinate (x,y), cannot be repeated in the tables. The y coordinate can though.

The number of kilometers till the tank is empty, given the graph on petrol and distance travelled is 240 kilometers .

Assuming the interval is 10, the slope - intercept form would be:

Petrol = Slope x Kilometers + y - intercept

The slope can be found because we have the y - intercept as 60 liters. We can then pick a point on the graph to slope for the slope. We'll pick ( 80, 40 ).

40 = 80 x slope + 60

Slope = ( 40 - 60 ) / 80

Slope = - 1 / 4

The formula is:

petrol = - 1 / 4 ( distance ) + 60

Assuming the petrol is 0 for when the tank is empty, the distance is:

0 = - 1 / 4 x distance + 60

- 1 / 4 x distance = - 60

distance = - 60 / - 1 / 4

distance = 240 kilometers

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Answer:

given us,

n=4

here

3^-n+1-3^-n+2

3^-4+1-3^-4+2

-4+1-4+2

-5

Step-by-step explanation:

we can put value in n .we can power add and subtract then we can cut 3 then power we can add or subtract

9514 1404 393

Answer:

  d.  (10, 5)

Step-by-step explanation:

Add the two equations, and you get ...

  2e = 10

  e = 5

Solve the first one for d and you have ...

  d = 15 -e

  d = 15 -5 = 10

So, the solution is ...

  (d, e) = (10, 5) . . . . . matches the last choice

_____

Check

  d + e = 10 + 5 = 15

  -d + e = -10 +5 = -5

The equation of the line r is y = ₋(10/9)x ₊ 7.

Given, parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope intercept form

equation of line q is y = ₋10/9x ₊ 2

it's already in slope intercept form.

hence slope is:

m = (₋10/9) from the above the equation.

we know that the second line will also have a slope of ₋10/9 and we are given the point (9 , ₋3). We can setup an equation in slope intercept form and use these values to solve for the y inetrcept.

y = mx ₊ b

₋3 = ₋10/9 (9) ₊ b

₋3 = ₋10 ₊ b

b = 7

plug the y intercept back into the equation to get our final answer.

y = ₋(10/9)x ₊ 7

hence  we get the equation of the line r as y = ₋(10/9)x ₊ 7.

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The correct statement is: A. P(E) = 0.3. The probability of event E, denoted as P(E), is equal to 0.3.

To determine the correct answer, let's analyze the given information.

We know that events D and E are independent, which means that the occurrence of one event does not affect the probability of the other event happening.

Given:

P(D) = 0.6

P(D and E) = 0.18

Since events D and E are independent, the probability of both events occurring (P(D and E)) can be calculated as the product of their individual probabilities:

P(D and E) = P(D) * P(E)

Substituting the given values:

0.18 = 0.6 * P(E)

To find the value of P(E), we can rearrange the equation:

P(E) = 0.18 / 0.6

P(E) = 0.3

Therefore, the correct answer is A. P(E) = 0.3.

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Answer:

Step-by-step explanation:

(CAB) = (ZXY)

(ABC) = (ZYX)

=>  ∆ABC ~ ∆XYZ

Answer:

36/11

Step-by-step explanation:

3/11 (12)

36/11

Step-by-step explanation:

Figure ABCD is similar to figure A'B'C'D'. is the correct awnser.

Figure ABCD is similar to figure A'B'C'D'. is the correct awnser.this is became ABCD is reflected over the y-axis so it is simular too A'B'C'D.

A is incorrect because the size of the shape doesn't change when getting reflected.

B and D is incorrect because just by looking at the shape D is not equal to A' or B'

Hope this helps!!

The estimated sum of  \(10\frac{17}{20}\)+\(8\frac{6}{29}\) is 19.

Addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers.

The given expression is \(10\frac{17}{20}\)+\(8\frac{6}{29}\)

These are in the form of mixed fractions.

We have to convert them to improper fraction

\(10\frac{17}{20}\) =217/20

\(8\frac{6}{29}\)=238/29

So 217/20+238/29

6293+4760/580

11053/580

19.056

It is approximately 19.

Hence  the estimated sum of  \(10\frac{17}{20}\)+\(8\frac{6}{29}\) is 19.

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Answer:

divident

Step-by-step explanation:

The magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.

The value of the net electrostatic force on the 5.0-nC

charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0),

charge Q2 = −1.0 nC is at (0, 0.10 m), and

charge Q3 = 5.0 nC is at (0, 0) can be calculated as follows:

Given data,Charge Q1 = 6.0 nC is at (0.30 m, 0),

Charge Q2 = -1.0 nC is at (0, 0.10 m),

Charge Q3 = 5.0 nC is at (0, 0)

The formula to find out the force on the third charge Q3 is:

                      F = k * |Q1 * Q3| / r1^2 + k * |Q2 * Q3| / r2^2

Here, k = 8.99 × 10^9 N·m^2/C^2, Q1 = 6.0 nC, Q2 = -1.0 nC, Q3 = 5.0 nC

For the third charge Q3, the distance from Q1 is:

                                r1 = √(0.3^2 + 0^2) = 0.3 m

And the distance from Q2 is: r2 = √(0^2 + 0.1^2) = 0.1 m

Substituting all the given values in the formula:

                               F = 8.99 × 10^9 * [ (6.0 × 10^-9 * 5.0 × 10^-9) / 0.3^2 ] + 8.99 × 10^9 * [ (-1.0 × 10^-9 * 5.0 × 10^-9) / 0.1^2 ]F = 6.21 N

Therefore, the magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.

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The approximate cost of producing the 11th roll of film can be calculated using the given marginal cost function and  total cost of producing one roll ($1,000) to obtain the approximate cost of the 11th roll of film.

The marginal cost function provided is 5 + 2a(1/x), where 'x' represents the roll number. The total cost to produce one roll is given as $1,000. To find the approximate cost of producing the 11th roll, we can substitute 'x' with 11 in the marginal cost function.

For the 11th roll, the marginal cost becomes 5 + 2a(1/11). Since the value of 'a' is not provided, we cannot determine the exact cost. However, we can still evaluate the expression by considering 'a' as a constant.

By substituting the value of 'a' as a constant in the expression, we can find the approximate cost of producing the 11th roll. The calculation of the expression would yield a numerical value that can be added to the total cost of producing one roll ($1,000) to obtain the approximate cost of the 11th roll of film.

Please note that without the value of 'a', we can only provide an approximate cost for the 11th roll of film.

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Answer:

A (x = 18)

Step-by-step explanation:

180 - (140 + 22) = 18

           162

Answer:

36

Step-by-step explanation:

Let Brandon's age be b. We can write 4b = b + 27 which gives us b = 9. Because Michael is 4 times as old as Brandon, he is 9 * 4 = 36 years old.

Answer:

36

Step-by-step explanation:

Micheal is 4 times as old as Brandon.

y = 4x

Micheal is also 27 years older than Brandon.

y = x +27

Y represents Micheal's age, and x represents Brandon's age.

Since both equations above are equal to the same value, y, you can set the two equations equal to each other.  Solve for x.

4x = x + 27

3x = 27

x = 9

Brandon is 9 years old.  

Plug Brandon's age into one of the equation to solve for Micheal's age.

y = x + 27

y = 9 + 27

y = 36

Micheal is 36 years old.

Answer:

Approximately 17%

Step-by-step explanation:

To find what percent 9 is of 51.89, you have to divide 9 by 51.89.

9/51.89 is 0.17344...

Since they said approximately, you can round 0.17344 to 0.17, which is equal to 17%.

Answer:

I know that A is one of the answers.

The volume of the object is 285 cubic feet based on the individual volume of cylinder and rectangular prism.

We will calculate the volume of each shape individually followed by their addition.

To calculate the volume of cylinder, we will find radius.

Radius = diameter/2

Radius = 4/2

Radius = 2 ft

Volume of cylinder = πr²h, where r is radius and h is height. Keep the values in formula -

Volume of cylinder = 3 × 2² × 5

Take square and multiply the digits

Volume of cylinder = 60 cubic feet

Volume of rectangular prism = l × w × h, where l is length, w is width and h is height

Volume of rectangular prism = 5 × 5 × 9

Volume = 225 cubic feet

Total volume = 60 + 225

Total volume = 285 cubic feet

Hence, the volume of object is 285 feet.

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