Kapil's robot starts 70cm from its charging base. It faces the base, then turns 60 degrees clockwise, as shown. Finally, the robot moves 50cm. After moving, how far is the robot from the charging base? Do not round during your calculations. Round your final answer to the nearest centimeter.

Based on the tables given and the functions represented, the two functions that are inverses of each other are Tables 3 and 4.

When two functions are said to be inverses of each other, it means that the value of x is one is the corresponding value of y in the other function.

For instance, when the point is (5, 16) in one function, the other function's point would be (16,5).

The functions that are inverses are therefore Tables 3 and 4 as shown attached.

Find out more on inverse functions at https://brainly.com/question/1144043.

#SPJ1

Answer:

13/20

Step-by-step explanation:

2/5*4=8/20

1/4*5=5/20

8+5=13

13/20

Answer:

The circumference of Pool B is greater than the circumference of Pool A by about 0.56 meters

Step-by-step explanation:

Identify the diameter of Pool A.

d = 2r

d = 2(18) Substitute 18 for r.

d = 36 ft

Convert from feet to meters. Use the ratio of 1 foot to 0.305 meters.

36 × 0.305 = 10.98

The diameter of Pool A is about 10.98 meters.

Use the formula to find the circumference of Pool A.

C = πd

C = π(10.98) Substitute 10.98 for d.

C ≈ 3.14(10.98) Substitute 3.14 for π.

C ≈ 34.48 Multiply. Round to the nearest hundredth.

The circumference of Pool A is about 34.48 meters.

Identify the diameter of Pool B.

d = 11.16 m

The diameter of Pool B is 11.16 meters.

Use the formula to find the circumference of Pool B.

C = πd

C = π(11.16) Substitute 11.16 for d.

C ≈ 3.14(11.16) Substitute 3.14 for π.

C ≈ 35.04 Multiply. Round to the nearest hundredth.

The circumference of Pool B is about 35.04 meters.

The circumference of Pool B is greater than the circumference of Pool A.

Find how much greater the circumference of Pool B is compared to the circumference of Pool A.

35.04 − 34.48 = 0.56

The circumference of Pool B is greater than the circumference of Pool A by about 0.56 meters.

The right method to use in order to represent the numerical data on the vertical axis of a Bar Chart is  0 to 40.

In setting the  vertical axis of a Bar Chart, note that it is vital for the categories to be natural as possible.

That is, the vertical axis should always begin with the number zero (0) and the scale values for the x axis must range from the lowest value on the left hand side to highest on the right hand side.

Therefore, due to the explanation given, the right method to use in order to represent the numerical data on the vertical axis of a Bar Chart is  0 to 40 as it range from 0 to the highest value.

Learn more about Bar Chart from

https://brainly.com/question/24741444

#SPJ1

Answer:

A

Step-by-step explanation:

i think i can be wrong

A function assigns the values. The function will be 8cos(2x-π)+4.

A function assigns the value of each element of one set to the other specific element of another set.

Given the maximum value is 12, while the minimum value is -4, therefore,

A = (Max-Min)/2 = 12-(-4)/2 = 8

D = (Max+Min)/2 = (12-4)/2 = 4

Period=π, but since x =-4 at 0 or π, therefore,

(2π/B) = π

B = 2π/π = 2

C/B = π/2, {∴At π/2 maximum}

C=π

Hence, the function will be 8cos(2x-π)+4.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ4

The base area of the prism is 36 square centimeters and the volume of the prism is 288 cubic centimeters

The base area is calculated as:

Base area =Length * Width

From the complete question (see attachment), we have:

Length = 12

Width = 3

So, we have:

Base area = 12 * 3

Base area = 36

The volume is calculated as:

Volume = Base area * Height

So, we have:

Volume = 36 * 8

Evaluate

Volume = 288

Hence, the volume of the prism is 288 cubic centimeters

Read more about volume at:

https://brainly.com/question/1972490

#SPJ4

From the above function, it is clear that the value of f is never 0. Hence the statement that is true is (Option E), See explanation of same below.

Note that the function is related to Euler's number which is depicted as:
e ≈ 2.7182. The function is given as:

f(x) = 100 * [tex]e^{-x}[/tex]

Assuming x = -2, we'd have:

100 * 2.7182[tex]^{-2}[/tex]

= 271.82[tex]^{-2}[/tex]

= 0.00001353354

Hence, even when x tends < 0 the function f(x) thus, is never 0. See the attached graph for confirmation.

Learn more about functions at:

https://brainly.com/question/25638609

#SPJ1

The value of ABC when AC is given as 152 will be 76°.

It should be noted that the angles that are opposite to equal sides are equal and that the angle sum property of triangle is 180°.

In this case, (2 × ABC) = 152°

2ABC = 152°

ABC = 152°/2

ABC = 76°

In conclusion, the correct option is C.

Learn more about angles on:

brainly.com/question/3652233

#SPJ1

Answer:

Step-by-step explanation:

The order of the transformations affects the values used for translation. Here, the translation is described before the reflection and compression.

__

The grayed-out graph of the square root function opens to the right. The darker graph of the transformed function opens to the left, so the reflection is across the y-axis.

__

The square root function goes through the point (1, 1), that is, 1 unit right of the vertex, and 1 unit up. The transformed function goes through the point (1, -1/2), that is, 1 unit left of the vertex and 1/2 unit up. The vertical height of 1 unit on the original graph is compressed to a height of 1/2 unit on the transformed graph. Vertical compression is by a factor of 1/2.

__

The description of the transformation gives the translation before the reflection and compression. So, to find where the uncompressed and unreflected vertex is, we need to reverse those transformations.

Expanding the transformed square root graph by a factor of 2 will undo its compression by a factor of 1/2. That will move the vertex from (2, -1) to (2, 2×(-1)) = (2, -2).

Reflecting this expanded function back across the y-axis will undo the original reflection. That moves the vertex from (2, -2) to (-2, -2). This is where the original translation left the function's vertex before the reflection and compression moved it to the location shown.

The translation is right -2 and down 2.

_____

Additional comment

It is possible that you will get pushback on these answers. If so, you should have your teacher demonstrate the transformations in the order described.

__

In the order described, we have ...

  [tex]f(x)=\sqrt{x}\\\\f_1(x)=\sqrt{x-(-2)}=\sqrt{x+2}\qquad\text{translation right -2}\\\\f_2(x)=\sqrt{x+2}-2\qquad\text{translation down 2}\\\\f_3(x)=\sqrt{-x+2}-2\qquad\text{reflection in the y-axis}\\\\g(x)=\dfrac{1}{2}(\sqrt{-x+2}-2)\qquad\text{compression vertically by $\dfrac{1}{2}$}[/tex]

The attached graph shows the result of this sequence of transformations.

__

If the reflection and compression were done before the translation, then the translation would be 2 right and 1 down.

Answer:

[tex]y = 2x - 5[/tex]

Step-by-step explanation:

slope-intercept form is [tex]y = mx + b[/tex] with [tex]m[/tex] being the slope of the line and [tex]b[/tex] being the y-intercept (where the line touches the y-axis)

First we can find [tex]m[/tex] using the formula for slope, [tex]\frac{rise}{run}[/tex] (or [tex]\frac{y_1 - y_2}{x_1 - x_2}[/tex]), which is the change in y over the change in x.

We can use any points on the line, but I am going to use [tex](4, 3)[/tex] and [tex](3, 1)[/tex] for this example. We can now find the slope.

[tex]\frac{3-1}{4-3} = \frac{2}{1}[/tex]

This means your slope is 2, which means [tex]m[/tex] is 2.

Finding the y-intercept is easy. This line crosses the y-axis at -5, and so [tex]b[/tex] is -5.

Now we can plug in the values into our original equation to get the equation of the line.

[tex]y = 2x - 5[/tex]

That is the answer

- Kan Academy Advance

Answer:

It would be 30.

Step-by-step explanation:

If we make a list of all the sums that we can get, we have:

1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6

These 15 sums can be chosen in two ways, since order matters, and we could do 2+1 instead of 1+2.

That gets us to 15x2 which is 30.

The number of ways that we can choose the marbles such that the sum of the numbers on my marbles equals the number on his would be 30.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

I have a bag with 6 marbles numbered from 1 to 6.

Mathew has a bag with 12 marbles numbered from 1 to 12.

1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6

These 15 sums can be chosen in two ways,

Since order matters, and we could do 2+1 instead of 1+2.

15 x 2 which is 30.

Learn more about the unitary method;

https://brainly.com/question/23423168

#SPJ1

Answer:

81920

Step-by-step explanation:

Finding the common ratio (r) :

Finding the 14th term :

Answer:

the 14th term in the sequence would be 81920.

Step-by-step explanation:

because you are multiplying by 2 each time to find the next multiply 80 by 2 giving you 160 again giving you 320 again giving you 640 than 1280 , 2560 ,5120 ,10240 ,20480 ,40960 ,finally the 14th number in the sequence multiplying 40960 by 2 would give you your answer of 81920.

Answer:

284.3

Step-by-step explanation:

Trapezoid Formula:

A=a+b/2*h

plug in the numbers

Step-by-step explanation:

Answer:Mxy= [(Xa+Xb/2);(Ya+Yb/2)]

=(2+8/2);(3+9/2)

Midpoint= (5, 6)

Step-by-step explanation:

Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:

The identity that relates the sine squared and the cosine squared of the angle, as follows:

[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]

In this problem, we have that the sine is given by:

[tex]\sin{\theta} = \frac{1}{3}[/tex]

Hence, applying the identity, the cosine is given as follows:

[tex]\cos^2{\theta} = 1 - \sin^2{\theta}[/tex]

[tex]\cos^2{\theta} = 1 - \left(\frac{1}{3}\right)^2[/tex]

[tex]\cos^2{\theta} = 1 - \frac{1}{9}[/tex]

[tex]\cos^2{\theta} = \frac{8}{9}[/tex]

[tex]\cos{\theta} = \pm \sqrt{\frac{8}{9}}[/tex]

[tex]\cos{\theta} = \pm \frac{2\sqrt{2}}{3}[/tex]

The tangent is given by the sine divided by the cosine, hence:

[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]

[tex]\tan{\theta} = \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}[/tex]

[tex]\tan{\theta} = \pm \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}[/tex]

[tex]\tan{\theta} = \pm \frac{\sqrt{2}}{4}[/tex]

More can be learned about trigonometric identities at https://brainly.com/question/24496175

#SPJ1

Answer:

yes there is a correlation

Step-by-step explanation:

here's how I found this by looking up all key words.

Answer:

radius = √35 mm or 5.916 mm

Explanation:

Here:

Solve for radius:

[tex]\rightarrow \sf \pi r^2 = 110[/tex]

[tex]\rightarrow \sf \dfrac{22}{7} r^2 = 110[/tex]

[tex]\rightarrow \sf r^2 = \dfrac{110(7)}{22} =35[/tex]

[tex]\rightarrow \sf r = \sqrt{35}[/tex]

Let's see

Answer: B

Step-by-step explanation:

    We will test the options and see if they apply to the given values.

[A]  ✗

1 * 6 = 6 ✓

4 * 6 ≠ 15✗

[B] ✓

1 * 3 = 3, 3 + 3 = 6 ✓

4 * 3 = 12, 12 + 3 = 15 ✓

6 * 3 = 18, 18 + 3 = 21 ✓

[C] ✗

1 * 8 = 8, 8 - 2 = 6 ✓

4 * 8 = 32, 32 - 2 = 30, 30 ≠ 15 ✗

Using proportions, it is found that the ordered pair that represents the location of the layover is given by: (2.75, 1.5).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the flight distance is partitioned in a ratio of 3:1, hence:

L - Nv = 3/4(Ny - Nv).

This ratio is applied for both coordinates, hence, for the x-coordinate:

[tex]x + 4 = \frac{3}/{4}(5 + 4)[/tex]

[tex]x = \frac{27}{4} - \frac{16}{4}[/tex]

[tex]x = \frac{11}{4}[/tex]

x = 2.75.

For the y-coordinate:

[tex]y = \frac{3}/{4}(2 - 0)[/tex]

[tex]y = \frac{6}{4}[/tex]

x = 1.5.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

See below

Step-by-step explanation:

Fill the 5   and pour into the 3    ....this will leave 2 gal in the 5 bucket

  empty the 3 bucket and put that 2 gallon in to it.....

      then fill the 5 bucket again......pour 1 gallon into the 3 gallon bucket to fill it....then there will be 4 gallons left in the 5 bucket

Answer:

8x+19=9x+9

Step-by-step explanation:

Simplifying

(8x + 19) = (9x + 9)

Reorder the terms:

(19 + 8x) = (9x + 9)

Remove parenthesis around (19 + 8x)

19 + 8x = (9x + 9)

Reorder the terms:

19 + 8x = (9 + 9x)

Remove parenthesis around (9 + 9x)

19 + 8x = 9 + 9x

Solving

19 + 8x = 9 + 9x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-9x' to each side of the equation.

19 + 8x + -9x = 9 + 9x + -9x

Combine like terms: 8x + -9x = -1x

19 + -1x = 9 + 9x + -9x

Combine like terms: 9x + -9x = 0

19 + -1x = 9 + 0

19 + -1x = 9

Add '-19' to each side of the equation.

19 + -19 + -1x = 9 + -19

Combine like terms: 19 + -19 = 0

0 + -1x = 9 + -19

-1x = 9 + -19

Combine like terms: 9 + -19 = -10

-1x = -10

Divide each side by '-1'.

x = 10

Simplifying

x = 10

Answer:

Step-by-step explanation:

8x + 19 = 9x +9

19 - 9 = 9x - 8x

10 = 1x

x = 10

check

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

8 * 10 + 19 = 9 * 10 + 9

80 + 19 = 90 + 9

99 = 99

the answer is good

Both lines are parallel because: A. both lines have a slope of 4/3.

The slope of a line = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

The slope of parallel lines are the same, while the slope of perpendicular lines are negative reciprocals.

Slope of AB = 4 units/3 units = 4/3

Slope of CD = 4 units/3 units = 4/3

Both lines have the same slope, therefore, they are parallel to each other.

Learn more about slope on:

https://brainly.com/question/1542999

#SPJ1

Answer:

Answer:

Graph C shows the solution for the inequality

Step-by-step explanation:

y - 4 > 2(x + 2)

y > 2x + 4 + 4

y > 2x + 8

Let y = 2x + 8, Then

X-intercept (0, 8)

Y-intercept (-4, 0)

Since the inequality sign is > we use broken line.

Put,  (0, 0)

y > 2x + 8

0 > 0+ 8

0 > 8 Which is false

so, the answer will be above the broken line

Hence , Graph C shows inequality

#SPJ1

Answer:

  (c)  Yes, +4 more

Step-by-step explanation:

The problem statement is telling you the available quantity in pounds. The answer choices are expressing the difference in terms of packets. A conversion of units of measure is needed.

__

Patel has 8 pounds of seed, and he puts it into 1/2-pound packets. Each pound will fill two (2) half-pound packets, so he has enough for ...

  (8 lb) × (2 packets/lb) = 16 packets

Patel has 12 people planting seed, so needs 12 of the 16 packets in order to give each team member one packet.

He has enough seed for this need, and enough for 16 -12 = 4 more packets than he needs.

Randy sells, in average, 460 vacuum cleaners per month.

First, we know that Janice sells 690 units per year.

There are 12 months in a year, so the amount that she sells, in average, per month is:

J = 690/12 = 57.5

This means that Janice sells, in average, 57.5 units per month. And Randy sells 8 times as many, then we can solve the product:

R = 8*57.5 = 460

This means that Randy sells 460 units per month.

If you want to learn more about products:

https://brainly.com/question/10873737

#SPJ2

Answer:

B.) No, because it fails the vertical line test.

Step-by-step explanation:

You can determine whether or not graphs represent functions by performing the vertical line test. This test states that to be a function, there must only be one output for every input. In other words, there must be only one "y" value per "x" value. As you can see, for some "x" values there is more than one "y" value.

The easiest way to perform this test is by placing your finger at the top of the graph and moving it downwards. If you cross the line twice, then it must not be a function.

Answer:

What is the context, at least give a figure

Step-by-step explanation:

mean value is always the sum of all data divided by the number of data points.

we can see just by looking at the numbers that team B is way below team A.

mean team A : 1529/8 = 191.125

mean team B : 1141/8 = 142.625

so, clearly, team B had to make dinner.

the median is the value of all the data points, where half of the others are smaller, and the other half are bigger.

in case of an even number of data points (like here with 8), we find the 2 middle values and calculate the mean value of these 2 :

median team A : (180+189)/2 = 184.5

median team B : (143+134)/2 = 138.5

the mode is the number in the set of data that occurred must often. if they are all unique, then they ALL are the mode. it is NOT 0 or empty. it is then really all the data points.

mode team A : 212

mode team B : 99, 102, 105, 134, 143, 145, 202, 211