The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets.



Part A: Write a system of equations to represent the given scenario. Use the variables "s" for senior citizen tickets and "c" for child.



Part B: Solve the system of equations from Part A algebraically. Show your work.



Part C: Explain what the solution to the system of equations represents in context of the problem. Hint: You will need to put words here, not an equation.

Answer:

Area of rectangular garden = lxb = 10*5

                                             = 50 sq. inch

when area increases by six times

new area = 50*6 = 300 sq inches

now,

let x be increasement in both  length and width

(5+x) (10+x) = 300

50 + 5x + 10x + x² = 300

x² + 15x - 250 = 0

x²+ 25x-10x -250 = 0

x(x+25) - 10 (x+25) = 0

( x-10) (x+25) = 0

either x + 25 =0

x = -25 length can be negative

0r x-10 = 0

x = 10

so 10 inches is increase on both side

Step-by-step explanation:

Answer:

a = 100 + 45t

Step-by-step explanation:

$100 is a one time addition so it will be a constant

100

$15 is added three times a month, so $45 a month

t stands for months as shown in the question

100 + 15(3)t

100 + 45t

Answer:

8 + 2w

Step-by-step explanation:

⇒ Change all signs to addition (subtraction is the same as adding a negative):

5 + 3w + 3 + -w

⇒ Since the expression is now all addition, you can rearrange them in any order. So group the terms together by their type:

5 + 3 + 3w + -w

⇒ Simplify:

8 + 2w

Answer: 8 + 2w

Hope this helps! :)

Answer:

84.6 degrees

Step-by-step explanation:

138.6 - 54 = 84.6

Answer:

56%

Step-by-step explanation:

Let me know if you need an explanation! Hope this helped :)

Answer:

43.75%

Step-by-step explanation:

step 1

16-9=7

7ounce remains

step2

7 of 16 ounce remains

convert into percentge

7/16×100=43.75%

Answer:

24.17

Step-by-step explanation:

Answer:

$24.17 per feet

Step-by-step explanation:

290/12=24.1666...

24.16666 rounds to 24.17

Answer:

-6

Step-by-step explanation:

Answer:

slope is y=10x.

Slope shows that she is consistently burning 10 calories per minute

Step-by-step explanation:

Answer:

the second answer

Step-by-step explanation:

.........

Answer:

$28

Step-by-step explanation:

John and his best friend each got $14, so in total there are $14+$14=$28.

Answer:

$28

Step-by-step explanation:

If they split the money evenly then both of them got half.

So, multiply 14 by 2 to find the answer:

(14)(2) = 28

John and his best friend found a total of $28.

I hope this helps!!

- Kay :)

Answer:

The arc length s = 44 inches

Step-by-step explanation:

We are given:

r = 4 in

Ф = 11 radians

We need to find s

The formula used is: [tex]s=r\theta[/tex]

where s represents arc length, r is radius and Ф is angle in radians

Putting values and finding s

[tex]s=r\theta[/tex]

Put r = 4 and Ф = 11

[tex]s=4\times 11\\s=44[/tex]

So, the arc length s = 44 inches

Answer:

dzxfchgjvhkbjl

Step-by-step explanation:

Answer:

The answer is 75.011

add the given values only make sure the decimal points are in the same line

Answer:

-7

Step-by-step explanation:

7n+5=-44

-5 - 5

7n=-49

7/7 -49/7

n = -7

Answer:

750 miles

Step-by-step explanation:

25+0.05x=40+0.03x

0.02x=15

x=750

Answer/ explanation: -10 for sure :)

The next two terms after -40 in this pattern are 60 and -160.

The difference between every two subsequent words in a sequence is the same; this is known as an arithmetic progression (AP). An equation for the previous block of the AP may be derived from this kind of development. For instance, the sequence 2, 6, 10, 14,... is a mathematical progression (AP) because it fits a pattern where every other number is acquired by adding 4 to the respective period.

The given data is,

-10, 20, -40

From -10 to 20 it is multiplied by 2 with a positive sign, and from 20 to -40 it is multiplied by 2 with a negative sign. Similarly, the next two numbers are 80 and -160.

To know more about reasoning:

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Answer:

p = -8

Step-by-step explanation:

Since, (x - 12) is a factor, then;

x - 12 = 0

x = 12

substitute the value of x in the equation

[tex]x^{2}[/tex] + px - 48 = 0

[tex](12)^{2}[/tex]  + 12p - 48 = 0

144 + 12p -48

12p = -144 + 48

12p = -96

p = -8

So that,

[tex]x^{2}[/tex] +-8x - 48 = 0

[tex]x^{2}[/tex] -12x + 4X- 48 = 0

([tex]x^{2}[/tex] -12x) + (4X- 48)

X(X - 12) + 4(X - 12)

(X - 12) (X + 4)

Therefore, p = -8 and (X - 12) (X + 4) are factors of the equation.

Answer:

Exact Distance = [tex]\frac{4\sqrt{10}}{5}[/tex]

Approximate Distance = 2.529822

============================================

Explanation:

This process is quite involved if you don't know the shortcut formula. I'll go over the long method first, and then show the shortcut in the next section.

First we'll need the equation of the line through points O and M. Use of the slope formula will show line OM has slope -1/3, which you are correct in stating.

Then use point slope form to determine the equation of line OM is y = (-1/3)x+11/3. This converts to the standard form x+3y = 11.

For anything in the form Ax+By = C, the equation perpendicular to this is of the form Bx-Ay = D. The A,B coefficients swap, and one item is negated. This helps form the negative reciprocal slope needed for the perpendicular line.

Compare x+3y = 11 to Ax+By = C. We see that A = 1 and B = 3.

So Bx-Ay = D turns into 3x-y = D. Then plug in the coordinates of H(-3,2) and compute to get

3x-y = 3(-3)-2 = -9-2 = -11. So D = -11

The equation 3x-y = D turns into 3x-y = -11 which is the equation of the line through point H and this line is perpendicular to line OM.

At this point, we have this system of equations

x+3y = 11

3x-y = -11

Solve that system however you wish. Substitution may be the best choice. Doing so leads to the intersection point (-2.2, 4.4)

The last step is to apply the distance formula between the points H(-3,2) and the intersection point (-2.2, 4.4)

The distance you should get is [tex]\frac{4\sqrt{10}}{5} \approx 2.529822[/tex]

I'm skipping steps because listing everything out would take up way too much space in my opinion.

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

The first section goes over a fairly lengthy process of finding the perpendicular distance. Luckily, there's a shortcut.

Consider an equation of the form Ax+By=C, aka standard form. Now consider a point P located at (m,n) that is not on the line Ax+By = C. We can find the distance from P to the line using this formula below

[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}[/tex]

In this case, A = 1, B = 3 and C = 11 found back in the previous section. So you'll still need to calculate the equation of line OM.

Also, we'll use (m,n) = (-3,2) which are the coordinates of point H

From here it's a fairly straightforward computation

[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}\\\\d = \frac{|1*(-3)+3*2-11|}{\sqrt{(1)^2+(3)^2}}\\\\d = \frac{|-8|}{\sqrt{1+9}}\\\\d = \frac{8}{\sqrt{10}}\\\\[/tex]

Optionally we can rationalize the denominator like so

[tex]d = \frac{8}{\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10}\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10*10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{100}}\\\\d = \frac{8\sqrt{10}}{10}\\\\d = \frac{2*4\sqrt{10}}{2*5}\\\\d = \frac{4\sqrt{10}}{5}\\\\d \approx 2.529822\\\\[/tex]

There are different ways to write down the answer, but they all represent the same number.

Answer: No

Step-by-step explanation: 6^2+7^2=85

8^2=64

Answer:

A

Step-by-step explanation:

not sure gusto ko lang tumulong

Answer:

The sketch tool to indicate what Edwin is describing as the parabola's "turning point'' is described below in details.

Step-by-step explanation:

We can see in graph that it intersect X axis and it is open upward it means turning point is below X axis, we can find turning point by find maximum value of Y If open downward and minimum value, if open upward here we can find that minimum point is (3, -5). also you can draw axis of symmetry parabola and finds its intersection with turning point can also be named vertex of parabola.

Answer:

y=¾+8

Step-by-step explanation:

Using the approach y-y1=m(x-x1),where m is the slope defined by ∆y/∆x

So ∆y/∆x=y2-y1/x2-x1

m=6-3/0-(-4)

m=¾

Now plug in m=¾ into the approach and simplify

y-3=¾(x-(-4))

y-3=¾(x+4) Multiply through by 4

4y-12=3x+12 Transpose it for y

4y=3x+12+12

4y=3x+24 divide through by 4

y=¾+8

The first graph shows the x-intercept of -3 and y - intercept of 5.

Option A is true.

What is Intercepts?

The points in which the graph crosses the two axis ( x and y axis) are called Intercepts.

Given that;

The x - intercepts = -3

And, The y - intercepts = 5

Since,

The x - intercepts = -3

That's mean the line cross at the point - 3 on x - axis.

And, The y - intercepts = 5

That's mean the line cross at the point 5 on y - axis.

Clearly, In graph first;

The graph of the line is crosses at the point on x - axis at the point -3 and y - axis at the point 5.

Therefore,

The first graph shows the x-intercept of -3 and y - intercept of 5.

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[tex]b-2<5\\b<5+2\\b<7[/tex]

Therefore, the answer is b < 7.

Answer:

5x+4

Step-by-step explanation:

Answer:

Pretty sure it is c

Step-by-step explanation:

Answer:

It's not A or D it has to be B or C.

Step-by-step explanation: i just took the quiz on edge and it wasn't  A or D.

Answer:

Its B

Step-by-step explanation: