Sara took skydiving lessons. The Skydiving Shack charges $30 per hour for lessons. Sara also gave her
Skydiving Instructor a tip of $15.
(a) Define the unknown in the scenario and assign it a letter or symbol.

Step 1

Redraw the diagram and use the Pythagoras theorem to find the value of c\x.

Step 2:

Find the value of y from the right-angle triangle of sides: 10, 25 and y using the Pythagoras theorem

Opposite = y

Adjacent = 10

Hypotenuse = 25

Step 3

Next, use the Pythagoras theorem to find x from the triangle with sides

28, x and y

Hypotenuse = 28

Opposite = x

Adjacent = y

Final answer

x = 16.1

Answer:

y = 5^(x+1)

Step-by-step explanation:

y = 5^(x+1)

x = 1 for the initial step

Answer:

32/5 is the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

Triangle PQR is in a coordinate plane. The triangle is reflected across the y–axis and

then translated 11 units left to form Triangle P'Q'R'. Determine which of the following statements must be true regarding this transformation. Select True or False for each statement.

Angle P has the same measure as angle P'. T or F

Angle Q has the same measure as angle R'. T or F

Angle R has the same measure as angle R'. T or F

Answer:

A) The point( -1 , 5)  is satisfies the  given graph  \(g(x) = (\frac{1}{5} )^{x}\)

B) The point( 3 , 1/125)  is satisfies the  given graph  \(g(x) = (\frac{1}{5} )^{x}\)

Step-by-step explanation:

Explanation:-

Given graph  

               y =      \(g(x) = (\frac{1}{5} )^{x}\)

Put the point ( -1 , 5)

Put y =5 and x =-1

            \(5 = (\frac{1}{5} )^{-1} = 5\)

The point( -1 , 5)  is satisfies the  given graph

ii)

Given graph  

               y =      \(g(x) = (\frac{1}{5} )^{x}\)

             \(\frac{1}{125} = (\frac{1}{5} )^{3} = \frac{1}{125}\)

The point( 3 , 1/125)  is satisfies the  given graph  \(g(x) = (\frac{1}{5} )^{x}\)

Answer:

Step-by-step explanation:

number of committees=9C4×30C2

=(9×8×7×6)/(4×3×2×1)×(30×29)/(2×1)

=63×30×29

=54810

Answer:

\(\frac{43}{16}\)

Step-by-step explanation:

\((\frac{1}{4})^{3}+(\frac{3}{4})^{3}+3(\frac{1}{4})(\frac{3}{4})(\frac{1}{4}+\frac{3}{4}) = \\\\\frac{1}{64}+\frac{27}{64}+3(\frac{3}{4})(\frac{4}{4}) = \\\\\frac{28}{64}+3(\frac{3}{4}) = \\\\\frac{28}{64}+\frac{9}{4} =\\\\\frac{28}{64}+\frac{144}{64} = \frac{172}{64} = \frac{43}{16}\)

\( \sf{\blue{«} \: \pink{ \large{ \underline{A\orange{N} \red{S} \green{W} \purple{E} \pink{{R}}}}}}\)

Expression: \(\displaystyle\sf (6-2x) +(15-3x)\)

Substituting \(\displaystyle\sf x=0.2\):

\(\displaystyle\sf (6-2(0.2)) +(15-3(0.2))\)

Simplifying the expression inside the parentheses:

\(\displaystyle\sf (6-0.4) +(15-0.6)\)

\(\displaystyle\sf 5.6 +14.4\)

Calculating the sum:

\(\displaystyle\sf 20\)

Therefore, \(\displaystyle\sf (6-2x) +(15-3x)\) evaluated at \(\displaystyle\sf x=0.2\) is equal to \(\displaystyle\sf 20\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

She will have 7 extra bags.

Step-by-step explanation:

[13(7+6)]/9

(13 * 13)/9

169/9

18.8

9 * 18 = 162

169 - 162 = 7

She will have 7 extra bags.

The point (\(-3\frac{1}{2}\), \(-1\frac{1}{4}\) ) on the coordinate plane is shown in the figure .

The Coordinate plane can be defined as a 2 D plane formed by the intersection of two line ,

where the horizontal line is called x axis and

the vertical line is called y axis .

In the question ,

the point is given

the point is  (\(-3\frac{1}{2}\) , \(-1\frac{1}{4}\) )

writing the mixed fraction  in decimal form , we get

x coordinate = \(-3\frac{1}{2}\) ⇒ -(3*2+1)/2 = -7/2 = -3.5

y coordinate = \(-1\frac{1}{4}\) ⇒ -(1*4+1)/4 = -5/4 = -1.25

So, the point to be plotted on the coordinate plane becomes (-3.5,-1.25)

the points plotted are shown in the figure below .

Therefore , the point ( \(-3\frac{1}{2}\), \(-1\frac{1}{4}\) ) on the coordinate plane is shown in the figure .

The given question is incomplete , the complete question is

Where is (\(-3\frac{1}{2}\) , \(-1\frac{1}{4}\)  ) on the coordinate plane?

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Step-by-step explanation:

Given the following systems of linear equations, 2x + y = 5, and 3y = 9 − 6x

The slope-intercept form is: y = mx + b, where m = slope, and b = y-intercept.

Subtract 2x from both sides:

2x - 2x + y = - 2x + 5

y = -2x + 5 ⇒ This is the slope-intercept form, where the slope, m = -2, and the y-intercept, b = 5.

Divide both sides by 3 to isolate y:

3y = − 6x + 3

\(\frac{3y}{3} = \frac{-6x + 9}{3}\)

y = -2x + 3 ⇒ This is the slope-intercept form, where the slope, m = -2, and the y-intercept, b = 3.

y = -2x + 5

y = -2x + 3

These equations have the same slope, m = -2.

They have different y-intercepts.

y = -2x + 5  ⇒ The y-intercept is (0, 5), where b = 5.

y = -2x + 3  ⇒ The y-intercept is (0, 3), where b = 3.

The equations have the same slope but different y-intercepts, meaning they are parallel lines that run parallel to each other and are spaced vertically apart by a difference of 2 units.

Step 1: Write each equation in slope-intercept form.

Given system of equations:

1. 2x + y = 5

2. 3y = 9 - 6x

Slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.

Let's rewrite the equations in slope-intercept form:

1. 2x + y = 5

  Subtract 2x from both sides: y = -2x + 5

2. 3y = 9 - 6x

  Divide both sides by 3: y = -2x + 3

Step 2: The equations have the same slope (-2) but different y-intercepts 5 and 3.

The common slope (-2) indicates that the lines represented by these equations have the same steepness or inclination.

The difference in y-intercepts means that the lines are parallel and run parallel to each other.

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Answer:

6 red and 1 yellow

Step-by-step explanation:

Multiply 2 and 1/3 by the same value

* 2

4 Red and 2/3 Yellow

*3

6 red and 1 yellow

Etc.

Answer:

18 cm

Step-by-step:

The formula for the volume of a triangular prism is given by:

V_triangular_prism = (1/2) * base * height * length

where the base is the area of the base triangle, height is the perpendicular distance between the two parallel base planes, and length is the distance between the two triangular faces.

We are given that the base area of the triangular prism is 36 cm² and the volume is 432 cm³. Using these values, we can solve for the height:

432 = (1/2) * 36 * height * length

height * length = 24

Since we want to find the base side length of a rectangular prism that has the same volume, we can use the formula for the volume of a rectangular prism:

V_rectangular_prism = length * width * height

We know that the volume of the rectangular prism is also 432 cm³, so we can substitute this value and the value we found for the height * length product:

432 = length * width * height

432 = length * width * (24/length)

432 = 24 * width

width = 18

Therefore, the base side length of the rectangular prism needs to be 18 cm.

Hope this helps!

Answer:

x >-72

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Domain is the x-values range is y-values

Answer:

The intersection of sets are the common elements. In this case it is {2, 4}.

Answer:

{2,4}

Step-by-step explanation:

The intersection is what the two sets have in common

{1, 2, 3, 4, 5}∩ {2, 4, 6, 8, 10}

= {2,4}

Step-by-step explanation:

To determine whether a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's denote the three sides of the given triangle as a = 23, b = 30, and c = 19. We can check if these side lengths satisfy the Pythagorean theorem as follows:

c^2 = a^2 + b^2

19^2 = 23^2 + 30^2

361 = 529 + 900

Since 361 is not equal to 529 + 900, we can see that the given triangle is not a right triangle.

Considering the given image, we can easily spot that (B) line 2 is the line of symmetry.

A form or item is divided into two equal and symmetrical portions by a line of symmetry.

Because it divides the figure symmetrically and the separated portions resemble mirror images of one another, we also refer to this line as the axis of symmetry or the mirror line.

Rotational symmetry, reflection symmetry, translation symmetry, and glide reflection symmetry are some examples of symmetries.

Planar symmetry, which refers to various types of symmetry on a flat surface, is illustrated by these four different types of symmetry.

So, according to the given image:

LIne 1 and 3 are not making the 2 identical halves of the figure.

Line 2 is making the exact identical half of the figure.

Therefore, considering the given image, we can easily spot that (B) line 2 is the line of symmetry.

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Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

Answer:

^algebra^

#1). a - b=4

a=4 + b .....(equation 1)

#2) a + b=12

(4 + b) + b= 12

4 + b + b=12

4 + 2b=12

2b= 12 - 4

2b =8

b= 8:2

b=4

subtituted b in equation 1

a= 4 + b

a= 4 + 4

a=8

so, the number is 8 and 4

The sum of the measures of the interior angles of a nonagon is 1260 degrees

The measure of each interior angle of a regular octagon is 135 degrees

A nonagon is a polygon with nine sides, and the formula to calculate the sum of the measures of the interior angles of a polygon with n sides is:

Sum of interior angles = (n-2) x 180 degrees

Therefore, the sum of the measures of the interior angles of a nonagon is:

Sum of interior angles = (9-2) x 180 degrees = 1260 degrees

An octagon is a polygon with eight sides, and the formula to calculate the measure of each interior angle of a regular polygon with n sides is:

Measure of each interior angle = (n-2) x 180 degrees / n

Therefore, the measure of each interior angle of a regular octagon is:

Measure of each interior angle = (8-2) x 180 degrees / 8 = 135 degrees

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Answer:

7w

Step-by-step explanation:

Simplify the parenthesis first

(13-6)=7

Then multiply by the w

7*w=7w

(13-6)*w=7w

* Can be rewritten as (13-6)w or w(13-6) or w*(13-6).

It is difficult to make a general statement about whether tennis coaches generally get paid more than football coaches in Jacksonville or elsewhere, as the salaries of coaches are influenced by a Wide range of factors

As an AI language model, I do not have access to up-to-date information about salaries of coaches in Jacksonville. However, in general, the salaries of coaches vary widely depending on a number of factors, such as the type of sport, the level of competition, the location, the success of the team, and the budget of the institution.

In terms of tennis and football, football is generally considered to be a more popular and high-profile sport than tennis in the United States, which could result in higher salaries for football coaches at the collegiate level. Football also typically generates more revenue and has larger budgets for athletic programs, which could also influence the salaries of coaches.

However, there are also factors that could affect the salaries of tennis coaches. For example, if a tennis program has a particularly successful season or has produced successful players, the coach may negotiate a higher salary. Additionally, some colleges may place a greater emphasis on tennis or have larger budgets for tennis programs, which could also impact the salaries of coaches.

Overall, it is difficult to make a general statement about whether tennis coaches generally get paid more than football coaches in Jacksonville or elsewhere, as the salaries of coaches are influenced by a wide range of factors. It is also important to note that salaries can vary widely between individual institutions, even within the same sport, and that negotiations between coaches and their institutions can play a significant role in determining salaries.

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The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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The experimental probability farthest from the theoretical probability is P(greater than 8). The theoretical probability of rolling a 9 is 1/12 because there is one 9 out of twelve total possible outcomes.

Experimental probability refers to the probability of an event based on data acquired from repeated trials or experiments.

Theoretical probability is the probability of an event occurring based on logical reasoning or prior knowledge. In Todd’s case, he rolled a 12-sided die marked with the numbers 1 to 12.

The probabilities are as follows:P(odd number) = 18/48P(greater than 8) = 16/48P(9) = 12/48To answer the questions:1. Which experimental probability matches the theoretical probability exactly?The theoretical probability of rolling an odd number is 6/12 or 1/2 because there are six odd numbers out of the twelve total possible outcomes.

The experimental probability Todd obtained was 18/48. Simplifying 18/48 to lowest terms gives 3/8, which is equal to 1/2, the theoretical probability.

Therefore, the experimental probability that matches the theoretical probability exactly is P(odd number).2. Which experimental probability is farthest from the theoretical probability? The theoretical probability of rolling a number greater than 8 is 3/12 or 1/4 because there are three numbers greater than 8 out of twelve total possible outcomes.

The experimental probability Todd obtained was 16/48. Simplifying 16/48 to lowest terms gives 1/3, which is not equal to 1/4, the theoretical probability.

The experimental probability Todd obtained was 12/48. Simplifying 12/48 to lowest terms gives 1/4, which is not equal to 1/12, the theoretical probability.

However, the difference between the experimental probability and the theoretical probability for P(9) is smaller than that of P(greater than 8). Therefore, P(greater than 8) is the experimental probability that is farthest from the theoretical probability.

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B is the correct answer ,,,

Answer: B

Step-by-step explanation:

The inverse of the function f(x) = x + 4 is given as f⁻¹(x) = x - 4

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1.

In this problem, the function given is f(x) = x + 4;

We can find the inverse of the function as;

y = x + 4;

Let's switch the variables by replacing x as y and y as x;

x = y + 4

Solving for y;

y = x - 4

f⁻¹(x) = x - 4

The graph of the function is attached below

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Answer:

-7.225 according to a calculator.