The initial exercise time is 30 minutes, so the y-intercept of the line is 30. The athlete increases their exercise time by 3 minutes each day, which means the slope of the line is 3. The correct answer is option: A.
We use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Using the first day's exercise time as our point, we get (1, 30) as our (x1, y1) values. Substituting these values into the point-slope form and simplifying, we get y - 30 = 3(x - 1), that is option A. Hence option A is correct.
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Find the value of x in the figure below.
Answer:
x = 63° and y =153°
Step-by-step explanation:
a streght line measure 180° so in the given we sum up
90° + x + 27°=180° then solve x
and for y u will sum up 90° and x then u will get by vertical opposite angle
find the volume of the prism below
The volume of the prism with given dimensions in the figure is equal to 612√3 cubic millimeter.
The dimensions of the triangular prism are,
Base of the triangle 'B' = 12mm
let us consider 'h' be the height of the triangle base.
Which intersect base at midpoint
height of the triangle 'h' = √ 12² - 6²
= √108
= 6√3mm
Side length of the prism 'l' = 17mm
Volume of the triangular prism
= ( 1/2 ) × Base × height × length of the side
= ( 1/2 ) × B × h × l
Now , substitute the values we have,
⇒ Volume of the triangular prism = (1/2) × 12 × 17 × 6√3
⇒ Volume of the triangular prism = 612√3 cubic millimeter.
Therefore, the volume of the triangular prism is equal to 612√3 cubic millimeter.
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In ΔABC,
∠BAC = 50° AB = 10cm BC = 9cm
Given that ∠BCA = x°
find the two possible values, to one decimal place, of x
Answer:
86.3
Step-by-step explanation:
To find the two possible values of x, we can use the law of sines, which states that:
asinA=bsinB=csinC
where A, B, and C are the angles of the triangle and a, b, and c are the opposite sides.
In this case, we are given A = 50°, a = 10 cm, and b = 9 cm. We can use the law of sines to find sin B:
10sin50°=9sinB
sinB=109sin50°≈0.6904
Now, we can use the inverse sine function to find B:
B=sin−1(0.6904)≈43.7°
However, this is not the only possible value for B. Since the sine function is positive in both quadrant I and quadrant II, there is another angle with the same sine value but in quadrant II. This angle is the supplement of B:
B′=180°−B≈180°−43.7°=136.3°
This means that there are two possible triangles that satisfy the given information: one with B = 43.7° and one with B = 136.3°.
To find x, we need to find C for each triangle using the fact that the sum of angles in a triangle is 180°:
C=180°−A−B≈180°−50°−43.7°=86.3°
C′=180°−A−B′≈180°−50°−136.3°=−6.3°
However, C’ is not a valid angle for a triangle because it is negative. Therefore, we can ignore this possibility and conclude that there is only one possible value for x:
x=C≈86.3°
Use the dropdown boxes below to complete the statement about the following quadratic function:
g(x)= 2x squared +4x
The function has a minimum value of -2 that occurrs at x = -1
Calculating the minimum or the maximum value?Given that
g(x) = 2x^2 + 4x
This is a quadratic function with a positive leading coefficient (2), which means that it opens upward and so it has a minimum value.
We can find the vertex of the parabola (the point where it changes direction) by using the formula:
x = -b/2a
where a and b are the coefficients of the quadratic function.
In this case, a = 2 and b = 4, so:
x = -4/(2*2) = -1
To find the corresponding y-value (the minimum value of the function), we substitute x = -1 into the function:
g(-1) = 2(-1)^2 + 4(-1) = -2
Therefore, the minimum of the parabola is at the point (-1, -2).
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can yall pls help me?
Answer:
- w - 24
Step-by-step explanation:
- 4(w + 6) + 3w ← multiply each term in the parenthesis by - 4
= - 4w - 24 + 3w ← collect like terms
= (- 4w + 3w) - 24
= - w - 24
Follow the rules to create two number sequences that go to the fifth term each. Rule 1: Multiply by 3 starting from 10. Rule 2: Subtract 7 starting from 58. What is the first term that appears in both sequences? (2 points) a 30 b 55 c 60 d 180
the answer is (a) 30.To find the first term that appears in both sequences, we can simply compare the terms in each sequence until we find a match
what is sequence ?
In mathematics, a sequence is a set of numbers, called terms, arranged in a specific order. Each term in the sequence is obtained by applying a certain rule or formula to the preceding term(s) in the sequence.
In the given question,
Using Rule 1, we can create the first sequence:
10, 30, 90, 270, 810
Using Rule 2, we can create the second sequence:
58, 51, 44, 37, 30
To find the first term that appears in both sequences, we can simply compare the terms in each sequence until we find a match.
We see that the number 30 appears in both sequences as the fifth term of the second sequence and the second term of the first sequence.
Therefore, the answer is (a) 30.
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Euler's formula, V − E + F = 2 relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron. Solve Euler's formula for V.
1. V = 2 − E − F
2. V = 2 + E − F
3. V = −2 + E − F
4. V = −2 − E − F
The Euler's formula solved for the variable V gives . V = 2 + E − F. Option 2
What is subject of formula?The subject of a formula is the variable or variables that represent the quantity being calculated or solved for.
In mathematical formulas, the subject is typically denoted by a letter or symbol, and the formula shows the relationship between the subject and other variables or constants in the equation.
From the information given, we have that;
V − E + F = 2
To make the variable, V, the subject, take the steps
collect the variable E
V + F = 2 + E
Now, collect the F variable
V = 2 + E - F
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PLEASE HELP and add a photo of your work and explain how you got the answer. I WILL MARK YOU BRAINLIEST IF YOU DO!! thanks!
The coordinates for the dilated figure would be A'(-2, 2), B'(-2, -1), C'(2, -1), and D'(2, 2).
The kind of dilation that was done is called a reduction.
What is a reduction dilation ?When you dilate a figure with a scale factor k = 1/3, you are performing a reduction, because the scale factor is between 0 and 1. In this case, the dilation will shrink the original figure by a factor of 1/3.
To find the coordinates of the dilated points, multiply the x and y coordinates of each point by the scale factor (1/3):
A' = (-6 x 1/3, 6 x 1/3) = (-2, 2)
B' = (-6 x 1/3, -3 x 1/3) = (-2, -1)
C' = (6 x 1/3, -3 x 1/3) = (2, -1)
D' = (6 x 1/3, 6 x 1/3) = (2, 2)
The coordinates of the dilated figure are A'(-2, 2), B'(-2, -1), C'(2, -1), and D'(2, 2). This type of dilation is a reduction, as the figure becomes smaller.
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pls help thx your the best
Answer:
(- 2, 16 )
Step-by-step explanation:
y = 8x + 32 → (1)
y = - 8x → (2)
substitute y = 8x + 32 into (2)
8x + 32 = - 8x ( add 8x to both sides )
16x + 32 = 0 ( subtract 32 from both sides )
16x = - 32 ( divide both sides by 16 )
x = - 2
substitute x = - 2 into either of the 2 equations and evaluate for y
substituting into (2)
y = - 8(- 2) = 16
solution is (- 2, 16 )
Given that event E has a probability of 0.31, the probability of the complement of event E
Explanation: We subtract the given value from 1
1-0.31 = 0.69
The complement of an event is the complete opposite.
Example: heads vs tails
Convert the following decimals to percents.
0.956=_%
Answer: 0.956 * 100% = 95.6%
Step-by-step explanation: To convert a decimal to a percent, you can multiply the decimal by 100 and add a percent sign.
So, to convert 0.956 to a percent:
0.956 * 100% = 95.6%
Therefore, 0.956 is equivalent to 95.6%.
Answer:
95.6%
Step-by-step explanation:
In order to solve this, you can just move the decimal point two places to the right to get the answer!
Margo missed 24.6% of her free throw shots in a season. During the season, she shot a total of 90 free throws. Which of the following is the best estimate of the number of free throws Margo missed?
Answer: 22
Step-by-step explanation:
So since Margo missed 24.6% of 90 free throws, you have to find 24.6% of 90. The easiest way to do this is to do 90 multiplied by 0.246.
To multiply by percentages in general, move the decimal point to the left by two places. For example, if it said 82.6, the decimal point would go to the left two places and be 0.826.
Back to the original question...
so 90 multiplied by 0.246 is 22.14. If you can use a calculator, this is easy, if not just do the usual multiplication.
Then, this rounds to 22, and the problem is complete!
An angle measures 51.8 degrees less than the measure of it’s complementary angle, what is the measurement of each angle?
the answer to the problem is that one angle measures 19.1 degrees and its complementary angle measures 70.9 degrees.
How to solve the question?
Let's first define the problem. Complementary angles are two angles whose sum is 90 degrees. Let x be the measure of one of the angles, then the measure of its complementary angle is 90 - x. According to the problem, one angle measures 51.8 degrees less than its complementary angle, so we can write:
x = (90 - x) - 51.8
Simplifying this equation, we get:
2x = 90 - 51.8
2x = 38.2
x = 19.1
Therefore, one angle measures 19.1 degrees and its complementary angle measures 90 - 19.1 = 70.9 degrees.
We can check that these angles are indeed complementary by verifying that their sum is 90 degrees:
19.1 + 70.9 = 90
So the answer to the problem is that one angle measures 19.1 degrees and its complementary angle measures 70.9 degrees.
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Javier buys 0.6 kilograms of sour cream and 1.4 kilograms of butter. What is the total cost?
sour cream
butter
plain yogurt
cream cheese
$2.15/kg
$1.00/kg
$1.19/kg
$2.26/kg
what is the answer?
The calculated value of the total cost of the sour cream and butter is $2.69.
Calculating the total costTo calculate the total cost of sour cream and butter, we need to multiply the weight of each item by its respective price per kilogram and then add the results.
The cost of 0.6 kilograms of sour cream is:
0.6 kg * $2.15/kg = $1.29
The cost of 1.4 kilograms of butter is:
1.4 kg * $1.00/kg = $1.40
Adding these two costs together, we get:
$1.29 + $1.40 = $2.69
Therefore, the total cost of the sour cream and butter is $2.69.
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Students mesured different amounts of water into their beakers for an experiment. If the total amount of water is redistributed equally, how much water will be in the beaker?
1/4 x 6 + 3/4 x 2 + 1/2 + 1 1/4 + 1 1/2 + 1 3/4
However, each beaker would have the following if there were, say, five beakers: 2.5 units of water are equal to 8.5/5.
what is volume ?Typically, it is expressed in geometric units, which including cubic metres (m3), cubic centimetres (cm3), or cubic feet (ft3), depending on the length unit being used. A formula that is based on an object's shape can be used to determine its volume. The volume of such a rectangular prism, for instance, can be determined by utilizing the formula V = lwh, where l stands for length, w for width, and h for height. A cylinder's volume can be calculated using the formula V = r2h, where r denotes the circle of the base and h the height.
given
We can simply sum the numbers supplied to determine the total volume of water in all the beakers:
1/4 x 6 + 3/4 x 2 + 1/2 + 1 1/4 + 1 1/2 + 1 3/4
= 1.5 + 1.5 + 0.5 + 1.25 + 1.5 + 1.75 (converting mixed values to improper fractions)
= 8.5
8.5 units of water are therefore present in all of the beakers.
Each beaker will have 8.5 divided by the number of beakers if this water is distributed equally among them.
We are unable to provide a precise response since we are unsure of the number of beakers.
However, each beaker would have the following if there were, say, five beakers: 2.5 units of water are equal to 8.5/5.
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What is 9 divided by (-3)+6x2-7
A riverboat traveled 2.5 miles per hour for 0.8 hours. How far did it go?
i will give brainliest help
Answer:
[tex]0.42[/tex]÷[tex]7[/tex]
Step-by-step explanation:
First, let's count the number of colored squares in the hundredth-grid.
There are a total of 42 hundredth-squares.
Since this is measured in hundredths, the number it represents is 0.42.
Each of the different colors represents a separate group that 0.42 is being divided into. There are 7 separate groups.
Since 0.42 is being divided into 7 groups, the equation that is being represented is:
[tex]0.42[/tex]÷[tex]7[/tex]
A $1200 bond earns 8.5% simple interest. What is the interest amount earned after 3 years?
As per the concept of simple interest, the interest amount earned after three years is $306.
To calculate the interest amount earned, we can use the formula:
I = P * r * t
Where:
I = interest earned
P = principal amount
r = interest rate per year (as a decimal)
t = time period in years
Plugging in the values from the problem, we get:
I = $1200 * 0.085 * 3
I = $306
This means that after three years, the bond will be worth the principal amount plus the interest earned, which is:
$1200 + $306 = $1506
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Study the solutions of the three equations on the right. Then, complete the statements below.
There are two real solutions if the radicand is
There is one real solution if the radicand is
There are no real solutions if the radicand is
There are two real solutions if the radicand is positive.
There is one real solution if the radicand is zero.
There are no real solutions if the radicand is negative.
What is the radicand about?In mathematics, the radicand refers to the value inside a square root (√) symbol. In the given equations and solutions, we can see that there are square root symbols involved, and we can determine the nature of the solutions based on the sign of the radicand.
For the first equation, y = -16x² + 32x - 10, the solutions for x are given as x = (-32 ± √384) / -32. The radicand in this case is 384. Since 384 is positive, greater than 0, there will be two real solutions for x.
For the second equation, y = 4x² + 12x + 9, the solutions for x are given as x = (-12 ± √0) / 8. The radicand in this case is 0. Since the square root of 0 is 0, there is only one real solution for x in this case.
Therefore, For the third equation, y = 3x² - 5x + 4, the solutions for x are given as x = (5 ± √(-23)) / 6. The radicand in this case is -23. Since the square root of a negative number is not a real number, there are no real solutions for x in this case.
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See full text below
Study the solutions of the three equations on the right. Then, complete the statements below. There are two real solutions if the radicand is There is one real solution if the radicand is There are no real solutions if the radicand is 1. y = negative 16 x squared + 32 x minus 10. x = StartFraction negative 32 plus-or-minus StartRoot 384 EndRoot Over negative 32 EndFraction. 2. y = 4 x squared + 12 x + 9. x = StartFraction negative 12 plus-or-minus StartRoot 0 EndRoot Over 8 EndFraction. 3. y = 3x squared minus 5 x + 4. x = StartFraction 5 plus-or-minus StartRoot negative 23 EndRoot Over 6 EndFraction.
If the triangles are similar, what is the value of x?
Thus, the value of x for the given set of similar triangles is found as: x = 42.
Explain about the similar triangles:Triangles that are similar to one another in terms of shape but not always in terms of size.
Identical triangles always have congruent corresponding angles and proportional corresponding sides. Two angles must share the same measure in order to be congruent.
The triangles both have proportional equivalent sides. Hence, each pair of corresponding sides' ratios is the same. The scale factor is the name of this ratio.
In smaller triangle. applying angle sum property :
Let the unknown angle be y
y + 126 + 16 = 180
y = 180 - 142
y = 38
For the given similar triangles:
The corresponding angles are also equal.
So,
on the straight line:
16 + 3x + 38 = 180 (linear pair)
3x = 180 - 54
x = 126/3
x = 42
Thus, the value of x for the given set of similar triangles is found as: x = 42.
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Using the calculus rule, how could the following derivative be rewritten as 2 partial derivatives?(dx/dz) at constant y
Using the calculus rule, we can rewrite the total derivative (dx/dz) at constant y as the sum of two partial derivatives.
The total derivative (dx/dz) at constant y can be rewritten as the sum of two partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y
Apply the chain rule
The chain rule in calculus allows us to find the derivative of a function with respect to another variable, by considering how the intermediate variables change.
In this case, we want to find (dx/dz) at constant y.
The chain rule states:
(dx/dz) = (dx/dy)*(dy/dz) + (dx/dz) at constant y
Identify the partial derivatives:
Since we want to rewrite (dx/dz) as a sum of two partial derivatives, we will keep the terms (dx/dy) and (dy/dz) as partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y
Final answer
The total derivative (dx/dz) at constant y can be rewritten as the sum of two partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y.
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Pregunta 2 ( 7 points) La raíz cuadrada de un número se identifica cuando el símbolo radical tiene un pequeno dos arriba True False
The small two above the radical symbol indicates that the square root of a mathematical number or expression is being taken, which means that the number under the radical must be squared to obtain the original number
Therefore,the correct answer is True.
What is expression?An expression is a mathematical phrase that combines numbers, variables, and operations to create a value. It can include arithmetic, algebraic, or trigonometric operations and may contain parentheses, exponents, or radicals.
What is square root?The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √ and is a type of radical.
According to the given information:
The correct answer is True.
The radical symbol, which looks like a division bar with a dot on top, is used to denote a root operation in mathematics. The index or degree of the root indicates the number of times the root must be multiplied by itself to obtain the number under the radical. In the case of the square root, the index is 2, which means that the number under the radical must be squared to obtain the original number.
Therefore, when the radical symbol has a small two above it, it is indicating that the square root of the number or expression below the radical is being calculated. The result of the square root operation is always a positive number, since the negative sign is indicated separately outside the radical symbol.
For example, the square root of 25 is written as √25 = 5, since 5 squared is equal to 25. Similarly, the square root of 4 is written as √4 = 2, since 2 squared is equal to 4.
In summary, the small two above the radical symbol indicates that the square root of a mathematical number or expression is being taken, which means that the number under the radical must be squared to obtain the original number.
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which decimal is equivalent to 125/1000?
A. 1.25
B. 0.125
C. 0.0125
D. 0.00125
Answer:
The answer to your problem is, B. 0.125
Step-by-step explanation:
Here is something that is simple so you will not forget easily.
( Just replace the numbers like how you shown in fraction )
= [tex]\frac{125}{1000}[/tex]
= 125 ÷ 1000
= 0.125
Simple but effective
0.125 is the answer.
Thus the answer to your problem is, B. 0.125
Question 7 W
her checking account the must maintain a $500 balance to avoid a fee She wrote a check for $245 50 today Write and solve an
nequality that would be used for the least amount of money she needs to deposit to avoid a fee
-02c
A?
Answer:
500 ≥ 245.50
500 - 245.50 ≥ 0
254.50 ≥ 0
Therefore, she needs to deposit at least $245.50 to avoid a fee.
Step-by-step explanation:
Let x be the least amount of money she needs to deposit to avoid a fee.
The balance in her checking account after writing the check would be (500 - 245.50) = 254.50.
To avoid a fee, the balance must be greater than or equal to 500, so we can write the inequality as:
x + 254.50 ≥ 500
Solving for x, we get:
x ≥ 500 - 254.50
x ≥ 245.50
Which of the following statements contain a variable? Check all that apply
A. Half the height of the building.
B. She arrived at 2 o'clock.
C. There are 12 inches in a foot.
D. The length of the rope.
CO
Answer:
A., D.
Step-by-step explanation:
A. 0.5x
B. 2
C. 12
D. x
Answer: A., D.
Write this trinomial in factored form.
9b^2 + 13b + 4
The factored form of the trinomial 9b² + 13b + 4 is ( 9b + 4 )( b + 1 ).
What is the factored form of the trinomial?Given the trinomial in the question:
9b² + 13b + 4
To factor the trinomial 9b² + 13b + 4, we need to find two binomials whose product equals 9b² + 13b + 4.
We can start by looking for two numbers that multiply to 9 × 4 = 36 and add up to 13. Those numbers are 9 and 4.
Now we need to use these numbers to factor the trinomial.
9b² + 4b + 9b + 4
Factor out the greatest common factor from each group
9b² + 9b + 4b + 4
9b( b + 1 ) + 4( b + 1 )
( 9b + 4 )( b + 1 )
Therefore, the factored form is ( 9b + 4 )( b + 1 ).
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Geometry Homework pls help
angle 1 = 90-( angle 2 ) and angle 2 = 90-( angle 1) ( diagonal property of rectangle)
What is diagonal property of a rectangle?A diagonal of a rectangle divides it into two congruent right triangles. The diagonals of a rectangle are the same length.
If the diagonal of a rectangle diveds it into two congruent triangles, then triangle OST is congruent to Triangle QRT.
Therefore angle 1 = 90-angl2
represent angle 1 by x and angle 2 by y
therefore x = 90-y
and y = 90-x
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what is the probability that all 6 workers are selected from the same shift? again, assume the employees are selected sequentially and not all at once. round your answer to four decimal places. save your answer as p allsame.
For a production company of total 24 workers, who works in different shifts. The probability that all 6 workers are selected from the same shift is equals to the 0.0019.
We have a company with faculty working in different shifts. Total number of workers in company = 10 + 8 + 6 = 24
Number of workers work in day shift = 10
Number of workers work in swing shift= 8
Number of workers work in graveyard shift = 6
Now, 6 workers are randomly selected from among 24. That is any of group of 6 can be selected. Number of possible ways to select 6 out of 24 = ²⁴C₆=134,596.
Number of ways to select a group of 6 workers from morning shift = ¹⁰C₆ = 210
Number of ways to select a group of 6 workers from swing shift = ⁸C₆= 56
Number of ways to select a group of 6 workers from graveyard shift = ⁶C₆ = 1
Now, probability to select the group of 6 from morning shift = [tex]\frac{210}{134596}[/tex]
Probability to select the group from morning shift = [tex]\frac{56}{134596}[/tex]
Probability to select the group from graveyard shift=[tex]\frac{1}{134596}[/tex].
Total probability for selecting a group of 6 workers from same shift [tex]= \frac{210}{134596} + \frac{56}{134596} + \frac{1}{134596} [/tex]
[tex]= \frac{267}{134596}[/tex]
= 0.00198
Hence, required probability is 0.0019.
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Complete question:
a production company factory 10 workers on day shift , 8 workers on swing shift and 6 workers on graveyard shift. A quality control team select 6 workers for in depth interviews.. Suppose the selection made in such a way that any particular group of 6 workers has same chance to selecting as does any other group( drops 6 slips without replacement from among 24 )
what is the probability that all 6 workers are selected from the same shift, again, assume the employees are selected sequentially and not all at once. round your answer to four decimal places. save your answer as p all same.
Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.Write an equation to determine the number of friends (x)left at Jack's party.
Okay so Jack started with 50 chocolates, and ended with 2.
The simple way to calculate it would be by realizing that Jack only distributed 48 chocolates. We can find how many times 3 fits into 48 by dividing [tex]48\div3=16[/tex].
Using algebra, we substitute the value we want to find with [tex]x[/tex]. Here what we want to find is the number of friends that were at Jack's party.
We know that he started with 50 chocolates, then distributed [tex]3\times[/tex] the number of friends present (which is [tex]x[/tex]).
We write that down as [tex]50-3x[/tex]
(It's minus because when chocolates are distributed, Jack is taking away from what he has.)
We know that after this, there were only 2 chocolates left, so it's
[tex]\underline{\bold{50-3x=2}}[/tex]
Then we proceed by moving all the numbers to the right until only [tex]x[/tex] is left:
[tex]-3x=2-50[/tex]
[tex]-3x=-48[/tex]
[tex]x=\dfrac{-48}{-3}[/tex]
[tex]\boxed{\bold{x=16}}[/tex]
Conclusion: The number of people that attended the party was 16.