To calculate the x-intercepts we replace y=0 and solve for x
[tex]x^2-8x+12=0[/tex]where a is 1, b is -8 and c 12
so factor the expression using
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]replacing
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(12)^{}}}{2(1)} \\ \\ x=\frac{8\pm\sqrt[]{64-48}}{2} \\ \\ x=\frac{8\pm\sqrt[]{16}}{2} \\ \\ x=\frac{8\pm4}{2} \\ \\ x=4\pm2 \end{gathered}[/tex]so x have two solutions because there are two x-intercepts
[tex]\begin{gathered} x_1=4+2=6 \\ x_2=4-2=2 \end{gathered}[/tex]then the x-intercepts are 6 and 2, the corrdinates are
[tex]\begin{gathered} (6,0) \\ (2,0) \end{gathered}[/tex]Vertex
the vertex is a point (x,y) to calculate x we use
[tex]x=\frac{-b}{2a}[/tex]and replace
[tex]\begin{gathered} x=\frac{-(-8)}{2(1)} \\ \\ x=\frac{8}{2}=4 \end{gathered}[/tex]now replace x=4 on the equation of the parable to find y
[tex]\begin{gathered} y=x^2-8x+12 \\ y=(4)^2-8(4)+12 \\ y=16-32+12 \\ y=-4 \end{gathered}[/tex]the coordinate of the vertex is
[tex](4,-4)[/tex]is y=2x+4 a linear equation
Answer:
A linear equation is always of the form:
y = mx + c
Where m = the slope
and c = the intercept
The equation given is y = 2x + 4
and it takes the form y = mx + c
where m = 2 and
c = 4
Therefore, the equation y = 2x + 4 is a linear equation
What is mZADB in Circle D? 57° 85.5° 28.5° 114°
We want to know the measure of the angle ADB on the circle D.
For doing so, we remember that:
• The measure of an inscribed angle is ,half ,of the measure of the arcs it intercepts.
,• The measure of an arc is ,equal ,to the measure of the central angle it generates (whose vertex is the center of the circle).
In the graph, we see that the angle ACB is inscribed, and thus, the measure of the arc AB is given by:
[tex]\hat{AB}=2m\angle ACB=2\cdot(57^{\circ})=114^{\circ}[/tex]But, the arc AB is equal to the central angle it generates, this is:
[tex]\hat{AB}=m\angle ADB=114^{\circ}[/tex]This means that the measure of ∠ADB is 114°.
What would be 2 radians converted into degrees? Need help cant include square units in my answer
REQUIRED:
We are required to convert an angle measure of 2 radians into degrees.
Step-by-step solution;
First thing to note is that the formula for conversion from radians to degrees is an inverse of degrees to radians. The formula for conversion is;
[tex]\begin{gathered} Radians\Rightarrow Degrees: \\ r\times\frac{180}{\pi} \\ \\ Degrees\Rightarrow Radians: \\ d\times\frac{\pi}{180} \end{gathered}[/tex]For the angle given as 2 radians, we now have;
[tex]\begin{gathered} r\times\frac{180}{\pi} \\ \\ =2\times\frac{180}{\pi} \\ \\ =114.591559026 \end{gathered}[/tex]ANSWER:
[tex]2radians=114.59\degree[/tex]What is the value of x?12 units15 units20 units25 units
Explanation
Step 1
set the equations:
we have three rectangles triangles,so
Let
triangle STR and triangle RTQ
so,
a) for triangle STR
let
[tex]\begin{gathered} \text{ hypotenuse: RS} \\ \text{adjacent side;RT}=x \\ \text{opposite side:ST=9} \\ \text{angle:m}\angle R \end{gathered}[/tex]so, we can use the Pythagorean theorem,it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
so
[tex]\begin{gathered} (RS)^2=(ST)^2+(RT)^2 \\ (RS)^2=(9)^2+(x)^2\rightarrow equation(1) \end{gathered}[/tex]b) for triangle RTQ
[tex]\begin{gathered} \text{ hypotenuse: RQ} \\ \text{adjacent side;TQ}=16 \\ \text{opposite side:RT=x} \\ \text{angle:m}\angle Q \end{gathered}[/tex]again, let's use the P.T.
[tex]\begin{gathered} (RQ)^2=(RT)^2+(TQ)^2 \\ (RQ)^2=(x)^2+(16)^2\Rightarrow\text{equation}(2) \end{gathered}[/tex]c)
we know the triangles STR and SQR are similar, so
[tex]m\angle R=m\angle Q[/tex]also,
[tex]\begin{gathered} \tan m\angle R=\tan m\angle Q \\ \frac{oppositeside_R}{\text{adjacent sideR}}=\frac{oppositeside_Q}{\text{adjacent sideQ}} \\ \frac{9}{x}=\frac{SR}{RQ}\rightarrow equation\text{ (3)} \end{gathered}[/tex]finally, we can set a new equation with triangle SQR
d)again, let's use the P.T.
[tex]\begin{gathered} (SQ)^2=(SR)^2+(RQ)^2 \\ \text{replace} \\ (9+16)^2=(SR)^2+(RQ)^2 \\ (25)^2=(SR)^2+(RQ)^2\rightarrow equation(4) \end{gathered}[/tex]Step 2
solve the equations
[tex]\begin{gathered} (RS)^2=(9)^2+(x)^2\rightarrow equation(1) \\ (RQ)^2=(x)^2+(16)^2\Rightarrow\text{equation}(2) \\ \frac{9}{x}=\frac{SR}{RQ}\rightarrow equation\text{ (3)} \\ (25)^2=(SR)^2+(RQ)^2\rightarrow equation(4) \end{gathered}[/tex]solution:
a)
[tex]\begin{gathered} \text{isolate (x) in equation(1) and (2) and set equal } \\ (RS)^2=(9)^2+(x)^2\rightarrow equation(1) \\ (RS)^2-(9)^2=(x)^2 \\ \text{and} \\ (RQ)^2=(x)^2+(16)^2\Rightarrow\text{equation}(2) \\ (RQ)^2-\mleft(16\mright)^2=(x)^2 \\ (RQ)^2-(16)^2=(x)^2 \\ \text{hence} \\ (RS)^2-(9)^2=(RQ)^2-(16)^2 \\ \text{isolate (RS)}^2 \\ (RS)^2=(RQ)^2-(16)^2+(9^2) \\ (RS)^2=(RQ)^2-175\rightarrow equation(5) \end{gathered}[/tex]b) now using equation (4) and equation(5) we can set system of 2 equations and 2 unknown values, so
[tex]\begin{gathered} (25)^2=(RS)^2+(RQ)^2\rightarrow equation(4) \\ (RS)^2=(RQ)^2-175\rightarrow equation(5) \\ replce\text{ eq(5) into equation (4)} \\ (25)^2=(RS)^2+(RQ)^2\rightarrow equation(4) \\ so \\ (25)^2=(RQ)^2-175+(RQ)^2 \\ 625+175=(RQ)^2+(RQ)^2 \\ 800=2(RQ)^2 \\ \mleft(RQ\mright)^2=\frac{800}{2} \\ (RQ)^2=400 \\ RQ=20 \end{gathered}[/tex]so
RQ=20
now, replace in equation (5) to find RS
[tex]\begin{gathered} (RS)^2=(RQ)^2-175\rightarrow equation(5) \\ (RS)^2=(20)^2-175 \\ (RS)^2=225 \\ RS=\sqrt[]{225} \\ RS=15 \end{gathered}[/tex]RS=15
finally, replace RS in equation (1) to find x
[tex]\begin{gathered} (RS)^2=(9)^2+(x)^2\rightarrow equation(1) \\ (15)^2=(9)^2+(x)^2 \\ 225-81=x^2 \\ 144=x^2 \\ \sqrt[]{144}=\sqrt[]{x^2} \\ 12=x \end{gathered}[/tex]therefore, the answer is
12 unitsI hope this helps yuo
Question 5 of 15
Which statement is true?
A. All rational numbers are either integers or whole numbers.
B. All rational numbers can be written as integers.
C. All irrational numbers can be written as integers.
D. All real numbers are either rational or irrational.
Answer:
D. All real numbers are either rational or irrational.
Step-by-step explanation:
You want to know the true statement about the sets of rational, irrational, integer, and whole numbers.
Rational numbersA rational number is one that can be written as the ratio of two integers. All integers and whole numbers are rational, but not all rational numbers are integers.
3 = 3/1 . . . . an integer that is written as a rational number
1/2 . . . . . . . a rational number that is not an integer
Irrational numbersAn irrational number is a number that cannot be written as a ratio of two integers. √2 is an example of an irrational number. Its decimal representation has a fractional part that is never-ending and never-repeating.
The decimal part of any real number either terminates, repeats, or neither. If the number terminates or repeats, it is a rational number. If it doesn't, then it is an irrational number.
D. All real numbers are either rational or irrational.
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These three pizzas are all the same size. Which one has the greatest number of equal pieces?
Given the following question:
It tells us that these pizzas are the same size
We are trying to find out which one of these pizza's have the greatest number of equal pieces.
For first pizza
It's cut up in four different pieces and these four pieces are equal
For the second pizza it is cut up in three different pieces and these three pieces are equal.
For the third pizza it is cut up in two pieces, these pieces are indeed equal.
Again the question is asking us which one has the GREATEST NUMBER of equal pieces
4, 3, 2
4 > 3
4 > 2
= 4
Your answer is the first pizza.
Factor completely. 4x^2+44x+72
4(x + 2)(x + 9)
Explanation:4x² + 44x +72
a = 4, b = 44, c = 72
a(c) = 4(72) = 288
The factors of 288 whose sum gives 44 are 36 and 8
4x² + 36x + 8x +72
4x(x + 9) + 8(x + 9)
(4x + 8)(x + 9)
To factorise completely, 4 is common to the first parenthesis:
(4x + 8) = 4(x + 2)
The factorisation of 4x² + 44x +72:
4(x + 2)(x + 9)
Find the coordinates of the midpoint of HX1H4-1X34324
We need to find the midpoint of a segment HX given the endpoints:
H = (4.5, -4.25) and X = (3.25, -2.75)
where we have written the coordinates (initially in mixed number form) in decimal form for ease of handling operations.
4 1/2 = 4.5
-4 1/4 = -4.25
etc.
Now we apply the formula for the midpoint (in the x and y coordinates separately):
x coordinate of midpoint = (4.5 - 3.25)/2 + 3.25 = 3.875
y coordinate of midpoint = (-2.75 - (-4.25))/2 + (-4.25) = -3.5
So we can write the coordinates of themidpoint as:
(3.875, -3.5) or in mixed number form as: (3 7/8, -3 1/2)
0.001×4= Possible answers: a),1/100×4/4 b),1/10×4/1000 c),1/4×4/4 d)1/1000×4/1
Explanation:
0.001×4:
[tex]\begin{gathered} 0.001\text{ = }\frac{1}{1000} \\ we\text{ know these by looking at the place value of the last number.} \\ \text{place value is thousandth} \end{gathered}[/tex][tex]\begin{gathered} 4\text{ = }\frac{4}{1} \\ 0.001\times4\text{ = }\frac{1}{1000}\times\frac{4}{1} \\ \text{(option D)} \end{gathered}[/tex]Each of 7 students reported the number of movies they saw in the past year. Here is what they reported. 7,12,12,16,13,19,14.
Answer:
13.3
Explanation:
To calculate the mean number of movies, use the formula below:
[tex]\text{Mean}=\frac{\text{Sum of the number of movies seen}}{\text{Number of students}}[/tex]Substituting the data gives:
[tex]\begin{gathered} \text{Mean}=\frac{7+12+12+16+13+19+14}{7} \\ =\frac{93}{7} \\ =13.3 \end{gathered}[/tex]The mean number of movies that the students saw is 13.3 (correct to the nearest tenth).
The location of a point moved from (1, - 3) to (-2, -1) by translation. Find the translation rule
moved from (1, - 3) to (-2, -1)
x'= x -3
y=
-2x - 14 =-2(Solve for x)
Explanation
[tex]-2x-14=-2[/tex]Step 1
add 14 in both sides,
[tex]\begin{gathered} -2x-14=-2 \\ -2x-14+14=-2+14 \\ -2x=12 \end{gathered}[/tex]Step 2
divide both sides by -2
[tex]\begin{gathered} -2x=12 \\ \frac{-2x}{-2}=\frac{12}{-2} \\ x=-6 \end{gathered}[/tex]I Hope this helps you
what is the ratio of dried fruit to sunflower seeds in the granola recipe?If you need to triple the recipe,will the ratio change?Explain.
We have to the ratio between the dried fruit and the sunflower seeds.
We know that the recipe requires 1/2 cup of dried fruit, and 1/8 of sunflower seeds. The ratio would be
[tex]\frac{\frac{1}{2}\text{fruit}}{\frac{1}{8}seeds}=\frac{1\cdot8}{1\cdot2}=4[/tex]So, the ratio of dried fruit to sunflower seeds in the granola recipe is 4, which means there must be 4 cups of dried fruits per each cup of sunflower seeds.If we triple the recipe, the ratio won't change, because ratios are constant, that way no matter if you do ten times more of the recipe, the result will be the same, because the ratios is the same too.
Divide using synthetic division (m^4 + 7m^3 + m +13) = (m + 7)
Quotient:
[tex]m^3+1[/tex]Remainder:
[tex]6[/tex]Result:
[tex](m^3+1)\times(m+7)+6[/tex]Determine the range for the relation below
Answer:
Assuming the scale of the graph is 1, the range would be just -1
Step-by-step explanation:
The graph is just a single horizontal line, so the range (what y can be) will always be that one constant. It appears that the scale of the graph is by 1s, so the Range would be -1
Graph quadrilateral ABCD with vertices A(−4,1) B(−3,3) C(0,1) D(−2, 0) and its image after the translation.(x,y)→(x+4, y−2)
To find:
The graph of quadrilateral ABCD and its translation.
Solution:
Plot the points A(−4,1) B(−3,3) C(0,1) D(−2, 0) on the graph and join the points.
The translation is (x,y)→(x+4, y−2). So, the image after translation is given below:
A window shaped like a parallelogram has an area of 31 square feet. The height of the window is 33 feet. How long is the base of the window?
The area of a parallelogram can be determined by multiplying its height by its base following the formula:
[tex]A=h\cdot b[/tex]If you know the area and the height of the parallelogram you can determine the length of the base. To do so, you have to divide the area by the height:
[tex]b=\frac{A}{h}[/tex]We know that the area of the window is A=31ft² and the height is h=33ft, you can calculate the length of the base as follows:
[tex]undefined[/tex]A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 98 m long and 70 m wide,Find the area of the training field. Use the value 3.14 for I, and do not round your answer. Be sure to include the correct unit in your answer.98 m
We are asked to determine the area of the given figure. The figure is composed of two semi-circles and a rectangle, therefore, the total area of the figure is:
[tex]A=A_s+A_r+A_s[/tex]The area of the semicircle is given by:
[tex]A_s=\frac{1}{8}\pi D^2[/tex]Where "D" is the diameter. Replacing the values we get:
[tex]A_s=\frac{1}{8}(3.14)(70m)^2[/tex]Solving the operations:
[tex]A_s=1923.25m^2[/tex]Now we determine the area of the rectangle using the following formula:
[tex]A_r=wh[/tex]Where "w" and "h" are the dimensions of the rectangle. Replacing the values we get:
[tex]\begin{gathered} A_r=(98m)(70m) \\ A_r=6860m^2 \end{gathered}[/tex]Now we replace the values in the formula for the total area:
[tex]A=1923.25m^2+6860m^2+1923.25m^2[/tex]Solving the operations:
[tex]A=10706.5m^2[/tex]Velasquez, Miguel, Juan, and Pablo score a total of 36 points in a game of basketball. They score a consecutive even number of points from smallest to greatest in respect to the order of the names mentioned. How many points does Juan score?A6 pointsB12 pointsC8 pointsD10 points
Take into account that the scores are three even consecutive numbers. Being x a missing value we can write:
2x, 2(x+1), 2(x+2), 2(x+3)
where each of the previous expressions corresponds to the score of Velasquez, Migule, Juan and Pablo respectivelly.
Now, due to the sum of all scores are 36 point, we can write:
2x + 2(x+1) + 2(x+2) + 2(x+3) = 36
By applying distribution property left side and by ordering like terms we get:
2x + 2x + 2x + 2x + 2 + 4 + 6 = 36
8x + 12 = 36
Now, by subtracting 12 both sides, simplifying and dividing by 8 we obtain:
8x = 36 - 12
8x = 24
x = 24/8
x = 3
Then, we can replace the previous value into the expression which represents Juan score:
2(x + 2) = 2(3 + 2) = 2(5) = 10
Hence, Juan scored 10 points (option D)
A helicopter hovers 550 feet above a small island. The figure shows that the angle of depression from the helicopter to point p is 43°. How far off the coast, to the nearest foot, is the island? (Round the answer to the nearest whole number.)
The angle of depression and angle P are alternate interior angles, then:
∠P = 43°
By definition:
tan(angle) = opposite/adjacent
In this case,
tan(43°) = 550/d
d = 550/tan(43°)
d = 590 ft
cuatro multiplicado por la suma de ocho y un numero.la suma de nueve y el numero
Definiendo como x al número desconocido.
la suma de ocho y un numero: 8 + x
cuatro multiplicado por la suma de ocho y un numero: 4(8 + x)
la suma de nueve y el numero: 9 +x
la suma de estas dos cantidades es igual a: 4(8 + x) + (9 + x)
To pay for a 15,300 car, Tony made a down payment of $3900 and took out a loan for the rest. On the loan , he paid monthly payment payment of $252.34 for 4 years.A:what was the total amount Tony end up paying for the car.(including the down payment and monthly payment.B: how much interest did Tony pay on the loan.
Down Payment = 3900
Loan Amount - 15,300 - 3900 = $11,400
Total Paid on Loan = $252.34 (monthly) for 4 years (4 x 12 = 48 months).
So, he paid
[tex]252.34\times48=\$12,112.32[/tex]So, total amount Tony paid for the car is "downpayment (3900) + loan amount with interest (12,112.32)".
So,
[tex]3900+12,112.32=\$16,012.32[/tex]Answer: $16,012.32
B)The interest is the excess amount on the loan.
Loan amount = $11,400
Loan + Interest amount = $12,112.32
Thus, the interest amount is 12,112.32 - 11,400 = $712.32
Answer: $712.32
Hi! I have a question and I don't understand it's answer. Could you help me?It's in the attachment below.
To solve this question, we just need to evaluate our set of points in the standard form equation of a Hyperbola, and find the coefficients. This will give to us the equation for our Hyperbola. The standard form is
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]Let's start with the easier points, the x-intercepts (5, 0) and (-1, 0).
Since this hyperbola has two x-intercepts, we're dealing with a horizontal hyperbola, and the center is the midpoint between the x-intercepts.
[tex]\begin{gathered} \bar{x}=\frac{x_1+x_2}{2}=\frac{-1+5}{2}=2 \\ \bar{y}=\frac{y_1+y_2}{2}=\frac{0+0}{2}=0 \end{gathered}[/tex]The center coordinates are (2, 0), then, our equation is
[tex]\frac{(x-2)^2}{a^2}-\frac{y^2}{b^2}=1[/tex]To find the missing coefficients, we can just substitute the remaining points and solve the system for a and b. Our final equation is
[tex]\frac{(x-2)^2}{9^{}}-\frac{y^2}{4}^{}=1[/tex]What is the solution of 5/2xminus7=3/4xplus14А. x=-6 B. x=6 C. x= 8 D. x=12
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
[tex]\frac{5}{2}x\text{ - 7 = }\frac{3}{4}x+14[/tex]Step 02:
We must apply algebraic properties.
[tex]\begin{gathered} \frac{5}{2}x-\frac{3}{4}x=14+7 \\ \frac{20x-6x}{8}=21 \\ \frac{14x}{8}=21 \\ 14x=21\cdot8 \end{gathered}[/tex]x = 168 / 14
x = 12
The answer is:
x = 12
Frogs lay spherical eggs that are 1.2 millimeters in diameter. Nutrients are absorbed through the egg's surface. What is the approximate area ofa frog egg's surface?ОА. 15.1 mm2OB. 18.1 mm2OC. 86.8 mm2OD. 4.5 mm2
Surface Area of a Sphere
For a sphere of radius r, the surface area can be calculated as:
[tex]A=4\pi r^2[/tex]A frog's egg has a diameter of d = 1.2 mm. The radius is half the diameter, thus:
r = 1.2 mm/2 = 0.6 mm
Calculating the surface area:
[tex]A=4\pi(0.6mm)^2[/tex][tex]A\approx4.5mm^2[/tex]Choice D
Bob reads 1/2 of a 200 page book in 4 days. How long would it take him to read 600 page book
24 days
1) Consider that Bob reads at a regular pace. So, we can write out a pair of ratios. Note that if Bob reads half of a 200 pages book so he does 100 pages in 4 days
[tex]\begin{gathered} pages--------days \\ 100---------4 \\ 600---------x \end{gathered}[/tex]2) So writing out a pair of ratios we have:
[tex]\frac{100}{600}=\frac{4}{x}[/tex]Now, we can cross multiply them:
[tex]\begin{gathered} 100x=600\cdot4 \\ 100x=2400 \\ \frac{100x}{100}=\frac{2400}{100} \\ x=24 \end{gathered}[/tex]A. Input 3, output 0B. Input 4, output 5C. Input -3, output 0D. Input 2, output 3
The only valid pair is B.
To determine this we need to remember that the input is the value of x and the output is the value of y.
For the input 4, that is x=4, the graph passes through the output is 5, that is y=5. This means that the graph passes through the point (4,5).
Which of the following is a simple event?Getting a spade cardGetting a numbered cardAll of the choicesGetting an ace of diamond card
Explanation
A simple event is one that can only happen in one way - in other words, it has a single outcome.
A compound event is more complex than a simple event, as it involves the probability of more than one outcome.
Getting a spade card is a simple event
Also, Getting a numbered card is a simple event
Getting an ace
Write the quotient for 5/6 ÷ 1/3 and the multiplication equation used to solve for the quotient. A) 2 1/2 5/6 × 3B) 2 1/25/6 × 1/3C) 2/31/3 × 5/6D) 2/33 × 5/6
We can write the quotient as:
[tex]\frac{\frac{5}{6}}{\frac{1}{3}}[/tex]We can use the fact that:
[tex]\frac{a}{b}=a\cdot\frac{1}{b}[/tex]to transform the quotient into a multiplication.
If b=1/3, then 1/b=3/1.
Then the expression becomes:
[tex]\frac{\frac{5}{6}}{\frac{1}{3}}=\frac{5}{6}\cdot\frac{3}{1}=\frac{15}{6}=\frac{5}{2}=2.5[/tex]The fraction 5/2 can be expressed as mixed number as:
[tex]\frac{5}{2}=\frac{2\cdot2}{2}+\frac{1}{2}=2\frac{1}{2}[/tex]Answer: the result is 2 1/2 or 2.5.
The quotient becomes the multiplication 5/6 * 3.
[Option A]
A committee has raised $230 in fundraising and continues toraise 30 dollars at each event they throw.-- Identify your independent and dependent variables- Write an equation to model the situationDetermine how much money will be raised after 10 events!Answer here:
Let's denote by x = the number of events.
and let's denote by y = the dollars raised.
Because the dollars raised to depend on the number of events, we can say that the dependent variable is y, and the independent variable is x. Now, we have the following data:
first event: 1, and the dollars raised is 230. That is, our first point is:
[tex](x_0,y_0)\text{ = ( 1,230 )}[/tex]second event: 2, and the dollars raised is 230 + 30. That is, our second point is
[tex](x_1,y_1_{\text{ }})=(2,230+30)=(2,260)_{}[/tex]Now, let's calculate the slope of the graph:
[tex]m\text{ = }\frac{y_1-y_0}{x_1-x_0}=\frac{260-230}{2-1}_{}_{}_{}[/tex]that is equivalent to say:
[tex]m\text{ = }\frac{260-230}{2-1}\text{ = }\frac{30}{2}\text{ = 15}[/tex]The equation for a line is y = mx + b. Now, let's calculate b
y = mx + b
so
b = y- mx
but m = 15, so the previous equation is equivalent:
b = y - 15x
if we choose the point (x,y) =(1,230) and we replace it in the previous equation we have:
b = 230- 15(1) = 230 - 15 = 215.
So, our equation of the line is :
y = 15x + 215
if x = 10 events we have :
y = 15(10) + 215 = 365 dollars
then, to the question: how much money will be raised after 10 events?, the answer is 365 dollars.