Please help 20 Points
This is pretty Easy but I'm dumb so please help me​

Answer:

x=-6, y=-8. (-6, -8).

Step-by-step explanation:

8x-5y=-8

-7x-5y=82

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

-(8x-5y)=-(-8)

-7x-5y=82

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

-8x+5y=8

-7x-5y=82

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

-15x=90

x=90/-15

x=-6

8(-6)-5y=-8

-48-5y=-8

5y=-48-(-8)

5y=-48+8

5y=-40

y=-40/5

y=-8

As the rate of change of function is negative from x=1 to x=2, the function decreases at this interval.

Step-by-step explanation:

We have to find the rate of change of the function

The rate of change of function is given by:

[tex]Rate\ of\ change = \frac{h(b)-h(a)}{b-a}[/tex]

Given function is:

[tex]h(x) = -2x+5[/tex]

Here

a =1

b = 2

So,

[tex]h(2) = -2(2) +5\\= -4+5\\= 1\\h(1) = -2(1) +5\\= -2+5\\= 3[/tex]

Putting the values in the formula

[tex]Rate\ of\ change = \frac{1-3}{2-1} = -2[/tex]

As the rate of change of function is negative from x=1 to x=2, the function decreases at this interval.

Keywords: Functions, rate of change

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Answer:

Velocity equation

[tex]v=\frac{d}{t}[/tex]

Step-by-step explanation:

Given:

Velocity of the car v = 4 units

and time t = 2 seconds

Let d = distance

Find the velocity equation.

The equation of the velocity is given below.

[tex]velocity=\frac{distance\ travelted}{time\ to\ distance\ travel}\ unit/sec[/tex]

[tex]v=\frac{d}{t}[/tex]

The above equation says, the distance travelled in t times is called velocity.

The unknown value in given question is distance. so, we find distance by given value.

[tex]d = v\times t[/tex]

[tex]d = 4\times 2[/tex]

[tex]d = 8\ units[/tex]

Therefore, the distance travelled by car is 8 units.

Formula for velocity: V = d/t

V = velocity

d = distance

t = time traveled

We are given the variables t = 2 and v = 2.

Substitute these values into the formula.

4 = d/2

Solve for d (d = distance).

4 = d/2

4 * 2 = d/2 * 2

8 = d

Therefore, the car traveled a distance of 8 units.

Best of Luck!

The other angles in the isosceles triangle with an angle of 100° will be 40°

Step-by-step explanation:

Lets define an isosceles triangle first.

"An isosceles triangle is a triangle with two equal sides and two equal angles.

Given that an angle of the triangle is 100°

We know that the sum of internal angles of a triangle is 180°

The sum of remaining two angles is:

=180°-100°

=80°

As the triangle is an isosceles triangle, the two angles will be equal.

So the angles will be:

[tex]=\frac{80}{2}\\=40[/tex]

The other angles in the isosceles triangle with an angle of 100° will be 40°

Keywords: Triangle, isosceles triangle

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The values of x are -22 and 10

The dimensions are 4 cm , 11 cm , 21 cm

Step-by-step explanation:

The given is:

We want to show that x² + 12x - 220 = 0, and solve the equation to find its dimensions

The volume of a cuboid is the product of its three dimensions

∵ The dimensions of the cuboid are 4 , (x + 1) , (x + 11)

∴ Its volume = 4(x + 1)(x + 11)

- Multiply the two brackets and then multiply the product by 4

∵ (x + 1)(x + 11) = (x)(x) +(x)(11) + (1)(x) + (1)(11)

∴ (x + 1)(x + 11) = x² + 11x + x + 11 ⇒ add like terms

∴ (x + 1)(x + 11) = x² + 12x + 11

∴ Its volume = 4(x² + 12x + 11)

∴ Its volume = 4x² + 48x + 44

∵ The volume of the cuboid = 924 cm³

- Equate the expression of the volume by 924

∴ 4x² + 48x + 44 = 924

- Subtract 924 from both sides

∴ 4x² + 48x - 880 = 0

- Simplify it by dividing all terms by 4

∴ x² + 12x - 220 = 0

Now let us factorize it into two factors

∵ x² = x × x

∵ 220 = 22 × 10

∵ 22(x) - 10(x) = 12x ⇒ the middle term

∴ x² + 12x - 220 = (x + 22)(x - 10)

∴ (x + 22)(x - 10) = 0

- Equate each factor by 0 to find x

∵ x + 22 = 0 ⇒ subtract 22 from both sides

∴ x = -22

∵ x - 10 = 0 ⇒ add 10 to both sides

∴ x = 10

∴ The values of x are -22 and 10

We can not use x = -22 because there is no negative dimensions, then we will use x = 10

∵ The dimensions are 4 , (x + 1) , (x + 11)

∵ x = 10

∴ The dimensions are 4 , (10 + 1) , (10 + 11)

∴ The dimensions are 4 cm , 11 cm , 21 cm

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Answer: Showed that: [tex]x^2+12x-220=0[/tex].

Both values of x are -22 and 10.

The dimensions are: 4 cm,  11 cm,  21 cm.

The given dimensions are 4cm,(x + 1)cm and (x + 11)cm.

So the volume is = [tex]4(x+1)(x+11)[/tex].

Given that volume= 924 [tex]cm^3[/tex].

Equating the volumes we get:

[tex]4(x+1)(x+11)=924\\4(x^2+12x+11)=924\\x^2+12x+11=\frac{924}{4}\\ x^2+12x+11=231\\x^2+12x+11-231=0\\x^2+12x-220=0\\[/tex]

Then we factor and solve the equation:

[tex]x^2+12x-220=0\\x^2+22x-10x-220=0\\x(x+22)-10(x+22)=0\\(x+22)(x-10)=0\\x=-22,10\\[/tex]

Since x can not be negative, so x = 10.

So the dimensions are: 4 cm, (x + 1) = (10 + 1) = 11 cm, (x + 11) = (10 + 11) = 21 cm.

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Answer:

You would know what people would say by saying that because they mean that you were to match up the letters into a shape in that order

Step-by-step explanation:

Hopefully this helps, give me a brainliest

Answer:

The given angles are

[tex]\angle BOA\\\angle AOC[/tex]

When we write down angles, we have different notations to do it.

In this case, we have angles with three letter, each one indicates a specific element.

The first letter indicate the initial point where the angle starts, for example, [tex]\angle BOA[/tex], beginas at point B, the middle letter indicates the vertex where the angle is at, so [tex]\angle BOA[/tex] indicates is at vertex O, at last, the third letter A indicates the final point where the angle goes.

Having said that, [tex]\angle BOA[/tex] is the opening from point B, then goes to vertex O and finally goes to point A, in the image attached you can see this angle highlighted.

Using the same reasoning, we have that [tex]\angle AOC[/tex] starts at points A, goes to vertex O, and ends at point C. Refer to the image attached.

Answer:

y = 2x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{1}{2}[/tex] x - 4 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2, thus

y = 2x + c ← is the partial equation

To find c substitute (3, 3) into the partial equation

3 = 6 + c ⇒ c = 3 - 6 = - 3

y = 2x - 3 ← equation of perpendicular line

The equation of the line passing through (3, 3) and perpendicular to y = -1/2x - 4, is y = 2x - 3.

To find the equation of a straight line passing through the point (3, 3) which is perpendicular to the line y = -1/2x - 4, follow these steps:

Therefore, the equation of the line passing through the point (3, 3) and perpendicular to the line y = -1/2x - 4 is y = 2x - 3.

Answer:

252 different combinations

Step-by-step explanation:

There are 12 men who may be elected to the council. If there are only 5 members of the council (the order doesn't matter), then there are

[tex]C^{10}_5\\ \\=\dfrac{10!}{5!(10-5)!}\\ \\=\dfrac{10!}{5!\cdot 5!}\\ \\=\dfrac{5!\cdot 6\cdot 7\cdot 8\cdot 9\cdot 10}{5!\cdot 5!}\\ \\=\dfrac{6\cdot 7\cdot 8\cdot 9\cdot10}{1\cdot 2\cdot 3\cdot 4\cdot 5}\\ \\=7\cdot 4\cdot 9\\ \\=252[/tex]

different combinations of council members.

Answer:

3

Step-by-step explanation:

From the given indices

(3a^n)^3 X (1/3a^n)^3

We can rewrite the equation to be

(3a^n)^3 X (3a^-n) ^3

We father simplify;

3a^3n X 3a^-3n

Since we have same base, we add their relative powers, we solve thus,

3a^(3n-3n)

= 3a^0

= 3 X a^0 = 3 X 1

=1

Answer:

Step-by-step explanation:

The percentage is 59 percent males 41 percent females

Answer: 3/15 or 1/5

Step-by-step explanation:

Each person will get 1/15 of each watermelon so 3/15 of watermelon that can be simplified to 1/5

Final answer:

Each of the fifteen friends will receive ⅔ of a watermelon when 3 watermelons are shared equally among them.

Explanation:

If fifteen friends want to share 3 watermelons equally, we need to divide the total number of watermelons by the number of friends to find out what fraction of a watermelon each friend will get.

To find the answer, you start with 3 watermelons and divide them by 15 friends, which is:

3 watermelons ÷ 15 friends = ⅔ of a watermelon per friend.

Thus, each friend will get ⅔ of a watermelon.

Answer:

5x+y=6

Step-by-step explanation:

y=-5x+6

y-(-5x)=6

y+5x=6

5x+y=6

The equation in standard form can be written as; 5x+y=6

An equation is an expression that shows the relationship between two or more numbers and variables.

Suppose the considered polynomial is of only one variable. Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.

We have given the equation as;

y=-5x+6

Now,

y-(-5x)=6

y+5x=6

The equation in standard form can be written as;

5x+y=6

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Answer:

The total area of Tony's vegetable garden is 124 square feet

Step-by-step explanation:

The total area of Tony's vegetable garden is composed by three rectangles.

1st rectangle

Length = 10 feet

Width = 6 feet (14 - 8)

Area = 6 * 10 = 60 square feet

2nd and 3rd rectangles are equals

Length = 4 feet

Width = 8 feet (14 - 6)

Area = 2 * 4 * 8 = 2 * 32 = 64 square feet

Total area

Area of the three rectangles

60 + 64 = 124 square feet

The total area of the vegetable garden is 124 ft.

A rectangle is a quadrilateral in which opposite sides are parallel and congruent to each other.

The area of a rectangle is the product of its length and width. It is given by:

Area = length * width

Area of the vegetable garden = (8 ft * 4 ft) + (8 ft * 4 ft) + (10 ft * (14 - 8)ft)

Area of the vegetable garden = 32 ft + 32 ft + 60 ft = 124 ft.

Therefore the total area of the vegetable garden is 124 ft.

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9514 1404 393

Answer:

  3x +y = 2

Step-by-step explanation:

Standard form is ...

  ax +by = c

where a, b, c are mutually prime integers and the leading coefficient is positive.

We can put the equation in this form by adding 3x to both sides.

  y = -3x +2

  3x +y = 2 . . . . . add 3x to both sides. This is standard form.

Answer:

Sample model as the picture attached, which shows 2/3 of 18 are circled.

Step-by-step explanation:

Here is the correct question: Your class has 18 students. Exactly 2/3

of them say that, out of all their subjects, they like science the most. Which model shows 2/3  of 18 circled?

Given: Total number of student is 18.

           2/3 of the total students like science the most.

Now, calculating the number students like the science the most.

∴ Number of students who like the science most= [tex]\frac{2}{3} \times 18= 12 \ students[/tex]

12 students like the science most out of total students.

Sample model are shown in the picture attached, where out of 18 students only 12 are inside the circle to show they like science the most.

Answer:  The required x-co-ordinate of the point of intersection of two lines is [tex]-\dfrac{2bm}{m^2+1}.[/tex]

Step-by-step explanation:  Given that two perpendicular lines have opposite y-intercept and the equation of one of the lines is

[tex]y=mx+b.[/tex]

We are to express the x-coordinate of the intersection point of the lines in terms of m and b.

Let the slope and y-intercept of the other line be s and c respectively.

Since the product of the slopes of two perpendicular lines is -1 and -b is the opposite of b, so we have

[tex]ms=-1~~~\Rightarrow s=-\dfrac{1}{m}[/tex]

and c = -b.

That is, the equation of the other line is

[tex]y=sx+c\\\\\Rightarrow y=-\dfrac{1}{m}-b.[/tex]

Comparing the equations of both the lines, we get

[tex]mx+b=-\dfrac{1}{m}x-b\\\\\\\Rightarrow mx+\dfrac{1}{m}x=-2b\\\\\\\Rightarrow \dfrac{m^2+1}{m}x=-2b\\\\\\\Rightarrow x=-\dfrac{2bm}{m^2+1}.[/tex]

Thus, the required x-co-ordinate of the point of intersection of two lines is [tex]-\dfrac{2bm}{m^2+1}.[/tex]

Final answer:

The x-coordinate of the intersection point for two perpendicular lines with opposite y-intercepts can be expressed as x = -2b/(m + 1/m), where m is the slope and b is the y-intercept of one of the lines.

Explanation:

When we have two perpendicular lines with opposite y-intercepts, and one of the lines has the equation y = mx + b, we can find the x-coordinate of the intersection point by expressing the other line's equation.

Since the other line is perpendicular, its slope will be the negative reciprocal of m. Therefore, if the first line's slope is m, the second line's slope will be -1/m. Also, if the y-intercept of the first line is b, the y-intercept of the second line will be -b, given that they are opposite.

The equation of the second line will then be y = (-1/m)x - b. To find the intersection point, we set the y-values of both equations equal to each other:

mx + b = (-1/m)x - b

Now, let's solve for x:

mx + (1/m)x = -2b

x(m + 1/m) = -2b

x = -2b/(m + 1/m)

Thus, the x-coordinate of the intersection point in terms of m and b is x = -2b/(m + 1/m).

Answer:390 miles

Step-by-step explanation:

speed*time=distance (keep that in mind)

8 2/3 is also equal to 26/3

take that number and multiply that by 45 min

45*26/3

that equall 390 miles

(I tried my best, I might be wrong)

Answer:

13/2

Step-by-step explanation:

Keep in mind that speed*time=distance

ok so, if you convert 8 2/3 in to a improper fraction you'll get 26/3. Now we have to turn 45 minutes into a fraction so it's easier to multiply, that would be 45/60 because 1 hour has 60 minutes. Now, we would multiply 26/3 and 45/60 and get 78/12. Simplify that and get 13/2

Answer:

A)

Step-by-step explanation:

Answer: 12/13

Step-by-step explanation:

In a deck of cards there are 4 of each number. Therefore there are 4 sevens in the deck. 4/52 are 7, but you want the probability of getting a card that IS NOT 7. That means there are 48 cards that aren’t a 7. 48/52 is the probability. But you can simplify this by finding a number that divides evenly into both, which in this case is 4. This simplifies to 12/13.

Answer:

E) [tex]f(x)=|x-8|+2[/tex]

Step-by-step explanation:

We will check each of the given choices by finding [tex]f(2)[/tex] of the given functions.

In order to find [tex]f(2)[/tex], we plugin [tex]x=2[/tex] in the function.

A) [tex]f(x)=2x+1[/tex]

[tex]f(2)=2(2)+1[/tex]

[tex]f(2)=4+1[/tex]

[tex]f(2)=5[/tex]

B) [tex]f(x)=3x-2[/tex]

[tex]f(2)=3(2)-2[/tex]

[tex]f(2)=6-2[/tex]

[tex]f(2)=4[/tex]

C) [tex]f(x)=x(5x-2)[/tex]

[tex]f(2)=2(5(2)-2)[/tex]

[tex]f(2)=2(10-2)[/tex]

[tex]f(2)=2(8)[/tex]

[tex]f(2)=16[/tex]

D) [tex]f(x)=3x-2x+4[/tex]

[tex]f(2)=3(2)-2(2)+4[/tex]

[tex]f(2)=6-4+4[/tex]

[tex]f(2)=6[/tex]

E) [tex]f(x)=|x-8|+2[/tex]

[tex]f(2)=|2-8|+2[/tex]

[tex]f(2)=|-6|+2[/tex]

[tex]f(2)=6+2[/tex]   [Since absolute value of any number is positive]

[tex]f(2)=8[/tex]

So, the function in E has value =8 for [tex]f(2)[/tex]

Answer:

To build a computer, you need to buy a motherboard for 120 dollars, a CPU for 100 dollars, RAM memory for 45 dollars, storage for 30 dollars, a case for 15 dollars, and a power supply for 50 dollars. What is the cost of building 10 computers? Hope this helps, if so then please mark brainliest.

The distributive property allows for the distribution of multiplication over addition within an expression and is key in algebra and vector operations.

The distributive property is a fundamental algebraic property used in mathematics, especially when dealing with expressions containing variables and constants. This property allows one to distribute multiplication over addition within an expression, helping simplify and solve equations. For example, using the distributive law, the expression A(A + B) can be expanded to AA + AB. Due to the idempotency theorem, which states that A times A is equal to A (AA = A), the result simplifies to A + AB = A. Furthermore, the distributive property is also a key concept in vector operations, such as the cross product, and is critical for proving various mathematical axioms and properties, such as the associative and commutative laws.

43.326 megabytes has been downloaded

Solution:

Given that a file that is 261 megabytes is being downloaded

16.6 % of download is complete

To find: megabytes that have been downloaded

From given question,

16.6 % of 261 megabytes has been downloaded

Let us find 16.6 % of 261

We know that,

a % of b can be written in fraction as [tex]\frac{a}{100} \times b[/tex]

So 16.6 % of 261 is calculated as:

[tex]16.6 \% \text{ of }261 = 16.6 \% \times 261\\\\\rightarrow \frac{16.6}{100} \times 261\\\\\rightarrow 0.166 \times 261\\\\\rightarrow 43.326[/tex]

Thus 43.326 megabytes has been downloaded

The question focuses on Mathematics, specifically Geometry and Calculus. It requires calculating the area of geometric figures especially circles and disks in terms of π, often via the formula A=πr² or integration.

From the question, we are required to find the area of shaded parts, which essentially associates with geometric figures and their properties in Mathematics. Specifically, this question appears to focus on areas related to circles and spheres, as it mentions calculations in terms of π, radius (r) and certain formulas like A=πr², which is the formula for the area of a circle.

When asked to express something in terms of π, it typically means leaving the answer as multiples of π, rather than using its decimal equivalent. So for instance, if we calculated the area of a circle with a radius of 3 using A=πr², we would say that the area is 9π.

Another crucial information that surfaced in the materials provided is the area calculation using integration, which involves adding up the individual areas of 'thin rings' from r=0 to r=R where R is the total radius of the disk or circle. This is an important aspect of finding areas under curves or finding areas enclosed by curves in Calculus.

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The area of the shaded regions is [tex]\(8\pi - 8\)[/tex] square centimeters.

To find the area of the shaded regions in the circle with the inscribed triangle, we'll follow these steps:

1. Calculate the Area of Sector AOC:

  - The sector's central angle is 90° because triangle AOC is right-angled at C.

  - The area of a sector is [tex]\( \frac{\theta}{360} \times \pi \times r^2 \)[/tex], where [tex]\( \theta \)[/tex] is the central angle and [tex]\( r \)[/tex] is the radius.

  - Here, [tex]\( r = 4 \) cm and \( \theta = 90° \).[/tex]

  - So, the area of sector AOC is [tex]\( \frac{90}{360} \times \pi \times 4^2 = \pi \times 4 \) cm^2.[/tex]

2. Calculate the Area of Triangle AOC:

  - The area of a triangle is [tex]\( \frac{1}{2} \times \text{base} \times \text{height} \).[/tex]

  - For triangle AOC, the base and height are both equal to the radius, which is 4 cm.

  - So, the area of triangle AOC is [tex]\( \frac{1}{2} \times 4 \times 4 = 8 \)[/tex] cm².

3. Calculate the Area of the Shaded Segment on the Opposite Side:

  - Subtract the area of triangle AOC from the area of sector AOC.

  - This gives us the area of the shaded segment: [tex]\( \pi \times 4 - 8 \)[/tex] cm².

Combining both shaded areas, the total area of the shaded regions is [tex]\( \pi \times 4 + (\pi \times 4 - 8) \)[/tex] cm², which simplifies to [tex]\( 8\pi - 8 \)[/tex] cm². Therefore, the area of the shaded regions is [tex]\( 8\pi - 8 \)[/tex] cm².

Answer:

$102.30

Step-by-step explanation:

Carlos: 19.80

Shag: 19.80 x 5/6 = 16.5

Deontae: 16.5 x 4 = 66.0

Total: 19.80 + 16.50 + 66.00 = 102.30

The total amount saved by Carlos, Shaq, and Deontae is $102.30.

To find the total amount saved by Carlos, Shaq, and Deontae, we first need to understand how much each of them saved individually. Carlos saved $19.80. Shaq saved 5/6 of the amount that Carlos saved, which we can calculate as (5/6) * $19.80 = $16.50. Deontae saved 4 times as much as Shaq, which we can calculate as 4 * $16.50 = $66. Finally, we add all these amounts together to get the total saved amount.

So, the total saved amount of all three is $19.80 (Carlos) + $16.50 (Shaq) + $66 (Deontae) = $102.30

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Answer:

The decimal point should be placed between the digits 8 and 7 because the quotient should be greater than 56 ÷ 7 and less than 63 ÷ 7.

Step-by-step explanation:

The division of the number 59.50 by 6.8 is equal to 8.75.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The division is one of the four basic operations of arithmetic, which are the methods by which numbers are combined to form new numbers. Addition, subtraction, and multiplication are the other operations.

Given that the number 59.50 is divided by the number 6.8. The division will be done as below,

Division = 59.50/6.8

Division = 8.75

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Answer:

265 Fahrenheit.

Step-by-step explanation:

It is given that,

Highest temperature ever recorded on earth = 136 Fahrenheit

Lowest temperature = -129 Fahrenheit

We need to plot these temperature as an integer on a number line.

136 is a positive integer. So, it lies 136 units on the right side of zero.

-129 is a negative integer. So, it lies 129 units on the left side of zero.

According to absolute values, |x|=|-x|=x.

Absolute value of 136 and -129 are

[tex]|136|=136[/tex]

[tex]|-129|=129[/tex]

The difference between he two temperatures is

[tex]|136-(-129)|=|136+129|=265[/tex]

Therefore, the difference between he two temperatures is 265 Fahrenheit .

Answer:

The cost price of 12 boxes of pudding is $3.96

Step-by-step explanation:

Given as :

The quantity of pudding boxes = 3

The cost price for 3 boxes = $0.99

Again ,

The quantity of pudding boxes = 12

Let The cost price for 12 boxes = $x

Now, According to question

Using Unitary method

∵ The cost price of 3 boxes of pudding = $0.99

or,The cost price of 1 boxes of pudding = [tex]\dfrac{0.99}{3}[/tex] = $0.33

∴The cost price of 12 boxes of pudding =$0.33 × 12

I.e x =$3.96

So,The cost price of 12 boxes of pudding = x =$3.96

Hence,The cost price of 12 boxes of pudding is $3.96 Answer

Answer:

BC/YZ=6/3

Step-by-step explanation:

Doing the quiz rn

The similarities of triangles can be proved using SSS theorem.

The missing mathematical statement is: [tex]\mathbf{\frac{BC}{YZ} = \frac 63}[/tex]

Because the similarities of both triangles is being proved using SSS, then only the sides would be compared

Sides AB, AC, XY and XZ have already been compared.

So, the missing mathematical statement is the ratio of sides BC and YZ

From the question, we have:

[tex]\mathbf{BC = 6}[/tex]

[tex]\mathbf{YZ = 3}[/tex]

So, the missing statement is:

[tex]\mathbf{\frac{BC}{YZ} = \frac 63}[/tex]

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Answer:

310 tickets were sold in advance before school pay and 340 door tickets were sold in advance.

Step-by-step explanation:

Given:

Let number of tickets sold in advance be 'x'.

Cost of advance ticket = $3

Cost of door tickets = $5

Also given:

Thirty more tickets were sold at door in advance

Hence number of door tickets sold = [tex]x+30[/tex]

Total Money Collected = $2630

Now we can say that Total Money Collected is equal to sum of number of tickets sold in advance multiplied by Cost of advance ticket and number of door tickets sold multiplied by Cost of door tickets.

Framing in equation form we get;

[tex]3x+(x+30)5=2630[/tex]

Solving the equation to find the value of x we get;

[tex]3x+5x+150=2630[/tex]

Combining the like terms we get;

[tex]3x+5x=2630-150\\\\8x= 2480[/tex]

Now Dividing 8 on both side using division property we get;

[tex]\frac{8x}{8} =\frac{2480}{8}\\ \\x=310[/tex]

Substituting the value of x to find number of door tickets been sold.

number of door tickets sold = [tex]x+30=310+30 =340[/tex]

Hence, 310 tickets were sold in advance before school pay and 340 door tickets were sold in advance.