Solve for brainliest

She travels a total distance of 72 feet before the swing stops

This is an infinite geometric series problem. Theoretically, it is assumed the swing never stops, but we know it does.  

But we will calculate mathematically as if it the swing never stops, but swings through a negligibly small distance.

The formula for an infinite geometric series is given by:

S∞ = a₁/(1 - r)

where a₁ = 12 feet and r = 5/6

S∞ = 12/(1 - 5/6)

S∞ = 12/(1/6)

S∞ = 72 feet

Thus, travels a distance of 72 feet

Learn more about infinite geometric series on:

brainly.com/question/16646281

#SPJ1

[tex]f^-1(x) = (5x-15)/2[/tex]

To find the inverse of a function, you need to switch the roles of the input and output.

So, if we let y = f(x), then the inverse function, denoted as f^(-1)(x), would be x = [tex]f^-1(y)[/tex].

In this case, we can start by setting y = (2x+15)/5.

Then, we can solve for x to find the inverse function:

y = (2x+15)/5

5y = 2x + 15

2x = 5y - 15

x = (5y-15)/2

Therefore, the inverse of f(x) = (2x+15)/5 is [tex]f^-1(x) = (5x-15)/2[/tex].

Learn more about the Inverse of a function here:

https://brainly.com/question/3831584

The equation that represents the function g(x) is g(x) = 9cos(x - π/3) + 7

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

f(x) = 9cos(x-pi/2)+3

Express the terms of the equation properly

So, we have the following representation

f(x) = 9cos(x - π/2) + 3

The transformation is given as translating π/6 units left and 4 units up

Mathematically, this can be expressed as

g(x) = f(x + π/6) + 4

So, we have

g(x) = 9cos(x - π/2 + π/6) + 3 + 4

Evaluate the like terms

g(x) = 9cos(x - π/3) + 7

Hence, the equation is g(x) = 9cos(x - π/3) + 7

Read more about transformation at

https://brainly.com/question/1548871

#SPJ1

On solving the provided question, we can say that - here in inequality equation  value of p for the inequality [tex]4p - 5 \leq 25[/tex] is [tex]7.5[/tex]

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.

here,

4p - 5 ≤ 25

[tex]4p - 5 \leq 25\\4p \leq 25 + 5\\4p \leq 30\\p \leq 30/4\\p \leq 7.5[/tex]

value of p for the inequality [tex]4p - 5 \leq 25[/tex] is [tex]7.5[/tex]

To know more about inequality visit:

https://brainly.com/question/29914203

#SPJ1

The expression 2√2 is equivalent to 2.83.

A radical, or root, is the mathematical opposite of an exponent, in the same sense that addition is the opposite of subtraction. Mathematically -

[tex]$\underbrace{\sqrt[n]{x} \times \sqrt[n]{x} \times \dots}_{n \text{ times}} = x[/tex]

Given is the expression as -

2√2

We can write -

2√2 = 2[tex]$(2)^{\frac{1}{2}}[/tex]

2√2 = 2 x 1.414

2√2 = 2.83

Therefore, the expression 2√2 is equivalent to 2.83.

To solve more questions on radicals, visit the link below -

https://brainly.com/question/2289044

#SPJ1

Answer:

|BC| = 24.5

Step-by-step explanation:

It is stared that the triangles are similar triangles.

Since they are similar triangles, we can find the length of the missing side using the ratio of similar sides.

DE/AB = EC/BC

[tex] \frac{6}{21} = \frac{2x + 3}{13x - 1.5} [/tex]

78x - 9 = 42x + 63

78x - 42x = 63 + 9

37x = 72

x = 2

now, replace x with 2 in the given expression for the length of BC:

13x - 1.5 = 13×2 - 1.5

|BC| = 24.5

The mean, median, and mode 0, 4, 6, 11, 9, 8, 9, 1, 5, 9, 7 are 6.2, 7, and 9.

A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.

From the data set:

0, 4, 6, 11, 9, 8, 9, 1, 5, 9, 7

Mean = ( 0+ 4+ 6+11+ 9+ 8+ 9+ 1+ 5+ 9+7)/11 = 6.2

The mean is the middle number(s) in a data set. Hence

Median = 7

The mode is the most occurring number in a data set

Hence,

Mode = 9

Thus, the mean, median, and mode 0, 4, 6, 11, 9, 8, 9, 1, 5, 9, 7 are 6.2, 7, and 9.

Learn more about  measurements of central tendency  at:https://brainly.com/question/28101345

#SPJ1

Answer:

Step-by-step explanation:

The area of a rectangle is length times the width. So it will be 4 7/10 times 6 2/3=31 1/3.

Perimeter will be length plus the width=11 11/30.

Answer:

1440.63

Step-by-step explanation:

August 23 - October 1 = 39 days

5.5%/365 in days a year

=5.5/365%

for the amount in savings is:

= Amount x ( 1 + rate) ^ number of periods

= 1,432.19 x ( 1 + 5.5/365%)^39

= $1,440.63

Answer: 0

Step-by-step explanation:

To find the y-coordinate of point Q, we first need to find the coordinates of point Q. Since points P, Q, and R are collinear and the ratio of PQ to PR is 3/4, we know that the ratio of their x-coordinates and y-coordinates must also be 3/4.

Let's call the coordinates of point Q (x, y). We know that the x-coordinate of point Q is 3/4 of the way between the x-coordinates of points P and R. This means that the x-coordinate of point Q is (3/4) * (-4 - 3) + 3 = -1.

Similarly, the y-coordinate of point Q is (3/4) of the way between the y-coordinates of points P and R. This means that the y-coordinate of point Q is (3/4) * (5 - (-5)) - 5 = 0.

Therefore, the coordinates of point Q are (-1, 0). The y-coordinate of point Q is 0.

The coordinates of point Q are (3, -5), and the y-coordinate of point Q is -5.

Collinear points are points that lie on the same straight line. In other words, if you can draw a straight line through two or more points, then those points are said to be collinear.

Given that the ratio of PQ to PR is 3/4.

Let's assume the coordinates of point Q are (x, y).

Using the midpoint formula, we can find the coordinates of the midpoint M of line segment PR:

M = ((x1 + x2)/2, (y1 + y2)/2)

Substituting the coordinates of points P (3, -5) and R (-4, 5), we have:

M = ((3 - 4)/2, (-5 + 5)/2) = (-1/2, 0)

and, M = ((x + (-4))/2, (y + 5)/2)

Equating the x-coordinates and y-coordinates, we get:

-1/2 = (x - 4)/2 => x - 4 = -1 => x = 3

0 = (y + 5)/2 => y + 5 = 0 => y = -5

Therefore, the coordinates of point Q are (3, -5), and the y-coordinate of point Q is -5.

Learn more about Collinear points here:

https://brainly.com/question/5191807

#SPJ2

Answer:

x=10922

Step-by-step explanation:

Answer: (2n + 2 + n) x 2 and (2n + 2) x 2 + n x 2

Step-by-step explanation:

width = n

length = 2n + 2

perimeter = (2n + 2 + n) x 2

perimeter = (2n + 2) x 2 + n x 2

Answer:

a + B = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

the sum of the roots a + B = - [tex]\frac{b}{a}[/tex]

where a and b are the coefficients in the standard quadratic equation

ax² + bx + c = 0 ( a ≠ 0 )

3x² - x - 5 = 0 ← is in standard form

with a = 3 and b = - 1 , then

a + B = - [tex]\frac{-1}{3}[/tex] = [tex]\frac{1}{3}[/tex]

Answer:

x=1

Step-by-step explanation:

.................................

Laila should create a "box plot" to display the data would display the median, minimum, and maximum clearly.

A box and whisker plot (also known as a box plot) depicts a five-number summary of a set of data: lowest, lower quartile, median, upper quartile, and maximum.

To present the data, Laila should make a box plot.

This is because a box plot would clearly display the median, minimum, and maximum salary, which is what Laila wants to show.

A histogram cannot be used to determine the median, and a dot plot would not work well because there are too many different values in the data set.

To learn more about the box and whisker plot click here:

https://brainly.com/question/11859288

#SPJ1

Answer:

[tex]y = 5( {3}^{x} )[/tex]

The position at which the wire must be connected to the ground so it uses the least amount of wire is given as follows:

51.4 meters to the right of the pole with height 80 meters.

Similar triangles are triangles that share these two features given as follows:

There are two similar triangles in this problem, with side lengths given as follows:

Hence the proportional relationship to find the value of x is given as follows:

80/60 = x/(90 - x).

Symplifying by 20, we have that:

4/3 = x/(90 - x).

Applying cross multiplication, the value of x is obtained as follows:

360 - 4x = 3x

7x = 360

x = 360/7

x = 51.4 meters.

More can be learned about similar triangles at brainly.com/question/14285697

#SPJ1

The equation of the line that passes through the points (7, 8) and (9, -9) in fully reduced point-slope form is y = -17x/2 + 135/2.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line and passes through the points (7, 8) and (9, -9) by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 8 = (-9 - 8)/(9 - 7)(x - 7)

y - 8 = -17/2(x - 7)

y - 8 = -17x/2 + 119/2

y = -17x/2 + 119/2 + 8

y = -17x/2 + 135/2

Read more on slope here: brainly.com/question/23086745

#SPJ1

The number of ways for which the square can be painted is given as follows:

16 ways.

The square is composed by four regions, and for each region the painting is independent of other regions, meaning that the Fundamental Counting Theorem is used to solve this problem.

The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem, the square is composed by four regions, each with two possible options for the paint color, hence the number of ways in which the square can be painted is given as follows:

N = 2 x 2 x 2 x 2 = 2^4 = 16 ways.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/15878751

#SPJ1

Answer:

D. A princess must choose the fate of her lover; lady or tiger.

Answer:

-7 is the further number from 0

Step-by-step explanation:

So lets say you start at 0

count 4 spaces to the right because it is a positive 4

and count 7 spaces to the left because it is a negative 7

7 is greater than 4 which means -7 is farther from 0 than 4 on a number line

Answer:

  x = -5

Step-by-step explanation:

You want the solution to 8-(x+12)=1.

Eliminate parentheses using the distributive property:

  8 -x -12 = 1

Combine like terms.

  -4 -x = 1

We like to have the x-coefficient be positive, so we're going to add x to both sides:

  -4 = 1 +x

Subtract 1 to get x by itself.

  -5 = x

The value of x is -5.

__

Additional comment

We could have solved this by adding 4 to both sides in the third step:

  -x = 5

Now, we need to multiply (or divide) by -1:

  x = -5

Any operation (add, subtract, multiply, divide, root, log, or any other function) is done to both sides of the equation, according to the properties of equality.

According to the solving he painting crew will need 58 more hours to repaint the road.

Mathematical operations come in various types, with division being one. In this procedure, the phrases or numbers are divided into the exact number of components.

Each state is in charge of its own Department of Transportation, which is in charge of maintaining and repairing its roadways.

The task of repainting faded or worn-out road lines is crucial.

A 24-mile length of road is now being painted by painters.

A total of 9.5 miles of the road have already been finished.

24 miles less 9.5 miles equals 14.5 miles of road remain.

The team is still painting at the same 0.25 mile per hour rate as they have been.

The remaining distance travelled in 58 hours (14.5 / 0.25).

Thus, the crew still needs 58 more hours.

To learn more about the division visit:

https://brainly.com/question/21416852

#SPJ1

By using the vertical line test, the relation graphed above is a function. Therefore, the correct answer choice is: A. yes.

In Mathematics, a vertical line test can be defined as a technique which is typically used to determine whether or not a given relation is a function.

According to the vertical line test, a vertical line must cut through the x-coordinate (x-axis) on the graph of a function at only one (1) point, in order for it to represent a function. Else, the relation does not represent a function because it can only have one output value (y) for a unique input value (x).

In conclusion, we can reasonably infer and logically deduce that relation graphed above represents a function because it passed the vertical line test as shown in the graph attached below.

Read more on function here: brainly.com/question/9795474

#SPJ1

Answer: function

Step-by-step explanation:

The addition of 2/3 with the addition of 4/9 and 7/9 is 1 8/9

The addition of fractions teaches us to add two or more fractions with the same or different denominators. The addition of fraction depends on two major conditions: Same denominators. Different denominators.

When adding fractions of same denominator, it easier, for example 2/5+1/5 =( 2+1)/5 = 3/5

But, the addition of fractions with different denominators, we have to find the LCM of the two denominator. for example 1/2+1/3, the LCM of 2 and 3 is 6, Therefore; = (3+2)/6 = 5/6

Similarly, 2/3+( 4/9+7/9)

2/3 + 11/9 =( 6+11)/9

= 17/9 = 1 8/9

learn more about addition of fractions from

https://brainly.com/question/25412

#SPJ1

The triangle in the figure given is a scalene triangle

There are three main types of triangles: right triangles, acute triangles, and obtuse triangles. Right triangles have one angle that is 90 degrees, while acute triangles have all angles less than 90 degrees, and obtuse triangles have one angle that is greater than 90 degrees.

1. Equilateral Triangle: All sides and angles are equal in an equilateral triangle.

2. Isosceles Triangle: Two sides and two angles are equal in an isosceles triangle.

3. Scalene Triangle: No sides or angles are equal in a scalene triangle.

4. Right Triangle: A right triangle has one angle that is 90 degrees.

5. Acute Triangle: All angles in an acute triangle are less than 90 degrees.

6. Obtuse Triangle: One angle in an obtuse triangle is greater than 90 degrees.

The angles given in this triangle have all their values less than 90 degrees. This makes them a scalene triangle.

Learn more on types of triangle here;

https://brainly.com/question/14285697

#SPJ1

The value of the function f(g(1)) = 1

A function is a mathematical expression that shows the relationship between two variables.

Consider functions f and g.

f(x) = 3 √x + 1, to determine the value of f(g(1)), we substitute g(x) into the equation for f(x).

So, f(x) = 3 √x + 1

f(g(x)) = 3√x + 1

f(g(x)) = 3√g(x) + 1

So, substititng x = 1, we have that

f(g(1)) = 3√g(1) + 1

We see that from the table g(1) = 0.

So, susbtituting the values of the variables into the equation, we have that

f(g(1)) = 3√g(1) + 1

f(g(1)) = 3√0 + 1

= 3(0) + 1

= 0 + 1

= 1

So, f(g(1)) = 1

Learn more about functions here:

https://brainly.com/question/10439235

#SPJ1

Step-by-step explanation:

A triangle will ALWAYS be 180 degrees

4. 34 + 21 = 55

180 - 55 = 125

x = 125

5. 100 + 51 = 151

180 - 151 = 29

2x + 3 = 29

2x = 26

x = 13

6. 94 + 60 = 154

180 - 154 = 26

2x = 26

x = 13