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We can write equations by rewriting the important phrases of information using variables. These variables make the equation look neater and it is faster to write a letter instead of constantly repeating 'cost of student tickets', for example.

The important pieces of information lies in the second last sentence of this question.

Now, let's rewrite them into equations.

Given

x= cost of adult tickets

y= cost of student tickets

Assuming that your friend and her little sister are students, the two equations are:

To convert these equations into slope-intercept form, move all the terms that are not y to the right-hand side of the equation before dividing both sides by the coefficient of y. This is to ensure that the coefficient of y is 1 and that your equation is in y= mx +c, where m is the slope and c is the y-intercept.

From equation (1):

x +2y= 23

2y= -x +23

Divide both sides by 2:

[tex]\bf{y = - \frac{1}{2} x + \frac{23}{2} }[/tex]

From equation (2):

2x +3y= 39

3y= -2x +39

Divide both sides by 3:

[tex]\bf{y= - \frac{2}{3} x + 13}[/tex]

The solution to the system of equations is the point at which the two lines intercept on the graph. I have attached the graph as an image.

The solution is (9, 7).

The x coordinate is the cost of an adult ticket, while the y coordinate is the cost of a student ticket. This means that adult tickets cost $9 and student/ child tickets cost $7.

Problem 1

The error happens on the third step. The result should be 47 degrees (approximately). Refer to the steps below to see how I got that value.

[tex]\frac{\sin x}{7} = \frac{\sin 110^{\circ}}{9}\\\\\sin x = \frac{7*\sin 110^{\circ}}{9}\\\\\sin x \approx 0.73087203838903\\\\x \approx \sin^{-1}(0.73087203838903)\\\\x \approx 46.9595500055922^{\circ}\\\\x \approx 47^{\circ}\\\\[/tex]

Make sure your calculator is in degree mode.

If I had to guess where the [tex]m\angle \text{x} = 73^{\circ}[/tex] mistakenly came from, it's probably from the 0.73 shown on step 3, but the student somehow lost the decimal point out front.

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Problem 2

The error happens on step 1. The sin(120) should be over top the 35 because the 120 degree angle is opposite the side length of 35.

Similarly, the sin(50) should be over the x

Each fraction involves the angle with its paired opposite side, and vice versa.

Here's one way to write the correct steps to find x.

[tex]\frac{\sin(120)}{35} = \frac{\sin(50)}{x}\\\\x\sin(120) = 35\sin(50)\\\\x = \frac{35\sin(50)}{\sin(120)}\\\\x \approx 30.9593175812171\\\\x \approx 30.96\\\\[/tex]

The summation notation for the geometric series will be expressed as [tex]\sum5(-2)^{n-1}\\[/tex]

Series are sum of sequences

Given the following alternating series as shown:
5 - 10 + 20 - 40 + 80

The series is geometrc series with the following parameters

First term "a" =5

ratio= -10/5 = 20/-10 = -2

Since the nth term of geometric sequence is expressed as:

Tn = ar^n-1
Tn =5(-2)^n-1

Hence the  summation notation for the geometric series will be expressed as [tex]\sum5(-2)^{n-1}\\[/tex]

Learn more on geometric series here: https://brainly.com/question/24643676

Answer:

A

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

Answer: 1/2 or 0.5

Step-by-step explanation:

attached the solution below for better understanding...

Hope that helps...

Answer:

D

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ BCD is an exterior angle of the triangle , then

∠ BCD = 35° + 67° = 102°

Answer:

P, R

Step-by-step explanation:

If you dilate P, you can find out that P can be the same as R.

Answer:

2x+y²

Step-by-step explanation:

add the similar terms. since x and x is similar so it'd be

2x + y * y

notice that y and y is also similar so y times y would become

2x+y^2 will be the final answer

Answer:

Vendor 1 had a higher unit rate.

Step-by-step explanation:

The factored expression ofx^3 - 7x^2 -5x +35 is (x^2 - 5)(x - 7)

An expression is an algebraic term used for a mathematical statement that includes addition subtraction multiplication and division

x^3 – 7x^2 – 5x + 35

factor the given equation

x^2(x – 7) – 5(x - 7)

Factor out x - 7

(x^2 - 5)(x - 7)

Therefore, the factored expression is (x^2 - 5)(x - 7)

To learn more about the factored expression visit:

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Answer:

c. (x^2 - 5)(x - 7)

Step-by-step explanation:

c. (x^2 - 5)(x - 7)

D. 6.

We have been given graph of a function. We are asked to find the average rate of change of our given function for the interval from [tex]x=-4[/tex] to [tex]x=-2[/tex].

We will use formula [tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{f(b)-f(a)}{b-a}[/tex] to solve our given problem.

[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{f(-2)-f(-4)}{-2--4}[/tex]

[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{6--6}{-2+4}[/tex]

[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{6+6}{2}[/tex]

[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=\frac{12}{2}[/tex]

[tex]Average[/tex] [tex]rate[/tex] [tex]of[/tex] [tex]change[/tex] [tex]=6[/tex]

Therefore, the average rate of change for our given function on given interval would be 6 and option B is the correct choice.

Answer:

6

Step-by-step explanation:

because i am in credit recovery and i had a test on it

Answer:

y= -0.5x² + 1x + 7.5

Step-by-step explanation:

I graphed the points in Desmos and saw they looked liked a parabola the point (1,8) is in between -3 and 5 for the x-coordinate.

I put the values in a table. and had desmos do a regression

Answer:

f(x) = (-1/2)(x^2 + 8x - 15)

Step-by-step explanation:

Hope this helps

There are 9 men and 10 women, including Julia, who are trying out for a team. so there are 31,752 possible teams that would include Julia.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

Each of the teams in a mixed volleyball league consists of 5 men and 5 women.

There are 9 men and 10 women, including Julia, who are trying out for a team.

The number of combinations for men

= (9 × 8 × 7 × 6 × 5)/(1 × 2 × 3 × 4 × 5)

=126.  

The number of combinations for women

= (10 × 9 × 8 × 7 × 6)/(1 × 2 × 3 × 4 × 5)

=252.

The number of the possible team would include Julia

(126 × 252) = 31,752.

Learn more about combinations;

https://brainly.com/question/19692242

Step-by-step explanation:

how is water used in this place write a brief explanation of the answer sheet

Answer:

1: x = 93, verticle, congruent

2: x=135 or 85, same side exterior

3: x=103, alternate interior

4: x=108

5: m<1=m<5, m<3=m<7, m<4=m<12, m<11=m<15, m<7, m<16=m<12

Answer:0.20 pounds remain .0.21 minus 0.01 = 0.20

Answer:

0.20

Step-by-step explanation:

Using the concepts of domain and range, it is found that for the function given in the graph:

The graph in this problem gives the height of a projectile after t seconds, hence:

More can be learned about the domain and range of a function at https://brainly.com/question/10891721

Answer:

Hope that the payment picture will help you.Please mark me brilliant

Answer:

Its B

Step-by-step explanation: on edg 2022

Answer:

The answer is A. I have comfirmed it by having to maximize my screen and look at each dot carefully.

Answer:

D

Step-by-step explanation:

The rate of chnage is the same as the slope.

Slope is x/y. How many y increases/decreases per increase of 1 x

slope for A is

2/500 every 2 x increase, y goes up by 500.

slope for B is

2/500 every 2 x increase, y goes up by 600-100 = 500

slope for C is

1/250

slope for D is

756/3

The greatest one out of these options is D, 756/3

A) = 23.0 miles

B) 14.4 Miles

   [tex]sin60\textdegree\ =\frac{opp}{hyp}=\frac{z}{10}[/tex]

           [tex]z=10\times sin60\textdegree =10\times 0.8660=8.66\ miles[/tex]

                  [tex]use\ pythagores\ theorem\ to\ get\ the\ value\ of\ y.\ l,e[/tex]

                    [tex]y=\sqrt{{20}^2-z^2}=\sqrt{{20}^2-{8.66}^2}=\sqrt{325.0044}[/tex]

                                                                       [tex]=18.03\ miles[/tex]

    [tex]\therefore\ distance\ AD=5+18.03[/tex]

                               [tex]=23.03\\ 23.0\ miles[/tex]

[tex]< ABN=\varphi=30\textdegree\ \{Beary\ 4A\ from\ B=360\textdegree\ -60\textdegree\ =300\textdegree\}[/tex]

                                           [tex]AB=y.[/tex]

             [tex]\cos{\theta=\frac{ads}{h}p}\\ cos\ G\begin{matrix}0\\0\\\end{matrix}=\frac{x}{25}[/tex]

                     [tex]x=25\times cos\ 60\textdegree[/tex]

                        [tex]=12.5\ mle[/tex]

             [tex]cos\ 30\textdegree=\frac{xe}{y}=\frac{12.5}{y}[/tex]

                    [tex]\because\ y=\frac{12.5}{cos\ 30\textdegree}[/tex]

                            [tex]=14.Fmm'_\mathcal{i}(es[/tex]

I hope this helps you

:)

What will happen to you and your sister's motion if you push against each other Is; ( A ) You move forward and your sister moves backward at a faster rate.

Force is the product of a mass and an acceleration due to gravity while Motion is a change in position with respect to time.Because you are bigger you will alter her movement by making her go in your direction. you impose more force on here which will make her go faster. But because of that collision, your force will reduce, thereby reucing your speed.

In conclusion the one with the higher mass have the greater force. Therefore What will happen to you and your sister's motion Is that You move forward and your sister moves backward at a faster rate.

Learn more about motion: https://brainly.com/question/453639

#SPJ1

Answer:

To find the inverse of:

[tex]f (x)=\dfrac{4}{x-2}-1[/tex]

Set the function to y:

[tex]\implies y=\dfrac{4}{x-2}-1[/tex]

Rearrange to make x the subject:

[tex]\implies y+1=\dfrac{4}{x-2}[/tex]

[tex]\implies (y+1)(x-2)=4[/tex]

[tex]\implies xy-2y+x-2=4[/tex]

[tex]\implies xy+x=2y+6[/tex]

[tex]\implies x(y+1)=2y+6[/tex]

[tex]\implies x=\dfrac{2y+6}{y+1}[/tex]

Swap x and y:

[tex]\implies y=\dfrac{2x+6}{x+1}[/tex]

Change y to the inverse of the function sign:

[tex]\implies f[/tex][tex]\:^{-1}(x)=\dfrac{2x+6}{x+1}[/tex]

Rewrite g(x) as a fraction:

[tex]g(x)=\dfrac{3}{x+2}-2[/tex]

[tex]\implies g(x)=\dfrac{3}{x+2}-\dfrac{2(x+2)}{x+2}[/tex]

[tex]\implies g(x)=\dfrac{3-2(x+2)}{x+2}[/tex]

[tex]\implies g(x)=\dfrac{3-2x-4}{x+2}[/tex]

[tex]\implies g(x)=-\dfrac{2x+1}{x+2}[/tex]

Therefore, as the inverse of f(x) ≠ g(x), the functions are NOT inverses of each other

Answer:

a b

Step-by-step explanation:

Answer:

All of these transformations are equivalent to reflection across the line y=x:

A. a reflection across the y-axis followed by a clockwise rotation 90° about the origin

C. a clockwise rotation 90° about the origin followed by a reflection across the x-axis

D. a counter-clockwise rotation 90° about the origin followed by a reflection across the y-axis

E. a reflection across the x-axis followed by a counter-clockwise rotation 90° about the origin

Step-by-step explanation:

EDGE

Answer:

125 kg

Step-by-step explanation:

500 kg * 25 %  =

500 * .25 = 125 kg

Answer:

125 kg

Step-by-step explanation:

500/100 × 25 = 125

..........

Answer:

45 degrees

Step-by-step explanation:

Since this angle is a right angle (1/4 of a full circle, or 360 degrees) its angle is 90. Since one part of it is 45 degrees. A=90-45=45

Answer:

D. 16

Step-by-step explanation:

16 because 4 * 2 * 2= 16 there are 4 shirts and 2 pants so that is 8 combos and then two pairs of shoes so 16 combos. hope that helps.

Answer:

16 or 48

Step-by-step explanation:

i dont think this is the correct answer