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) at Jack's party.
Answers
Answer:
3x = 48
Step-by-step explanation:
To easily do this, we'll make the statement in mathematical form.
Let x represent the number of friends at Jack's wedding.
The equation would be:
3 * x = 50 - 2
3x = 48
x = 48 / 3
x = 16
Therefore, the equation to determine the number of friends (x) at Jack's party is expressed as:
3x = 48
Maths is fun!
Answer:
50/3=16
Step-by-step explanation:
Related Questions
What is the area, in square centimeters, of the shape below?
The perimeter of a rectangle is 70 cm. If its length is decreased by 5 cm and its width is increased by 5 cm, its area will increase by 50 cm2. Find the length and the width of the original rectangle.
Which of the following is an arithmetic sequence?-2, 4, -6, 8, ... -8, -6, -4, -2, ... 2, 4, 8, 16, ...
Can u pls explain to me how to do this?
Answers
distribute the 7 to the numbers in the parentheses
7 multiplied by-5v= -35v
7 multiplied by -8= -56
place them: -35v-56
hope i helped (theres a pic too!)
7(-5v) + 7(-8)
-35v - 56
6x + 2y = 22
Which of the following steps could be used to solve by substitution?
6x + 2(−2x + 1) = 22
−2x + 1 = 6x + 2y
6(−2x + 1) + 2y = 22
6(y = −2x + 1)
Answers
Answer:
The steps that could be used to solve by substitution is:
6x + 2(−2x + 1) = 22
Step-by-step explanation:
Substitution method--
The method of substitution states that from a equation the value of one variable is substituted in form of the other variable into the other equation.
From the first equation we have the value of y in terms of x as:
y = -2x + 1
Also, we have equation (2) as:
6x + 2y = 22
Hence, on putting the value of y we have:
6x+(-2x+1)=22
The answer is A
Because this where you gonna start your substitution
and the point P(-3,6) and then answer the following questions:
a. How would you find the line (B) that passes through point P and is perpendicular to line A? What is the equation of that line?
b. How would you find the length of the segment of line B from point P to line A?
c. How would you find the midpoint between point P and the intersection of line A and line B ?
Answers
Answer:
- y = -6/5x +12/5
- distance from P to A: (66√61)/61 ≈ 8.4504
- midpoint: (-18/61, 168/61) ≈ (-0.2951, 2.7541)
Step-by-step explanation:
a. The slope of the perpendicular line is the negative reciprocal of the slope of the given line, so is ...
m = -1/(5/6) = -6/5
Then the point-slope form of the desired line through (-3, 6) can be written as ...
y = m(x -h) +k . . . . . line with slope m through (h, k)
y = (-6/5)(x +3) +6
y = -6/5x +12/5 . . . equation of line B
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b. The distance from point P to the intersection point (X) can be found from the formula for the distance from a point to a line.
When the line's equation is written in general form, ax+by+c=0, the distance from point (x, y) to the line is ...
d = |ax +by +c|/√(a² +b²)
The equation of line A can be written in general form as ...
y = 5/6x -5/2
6y = 5x -15
5x -6y -15 = 0
Then the distance from P to the line is ...
d = |5(-3) -6(6) -15|/√(5² +(-6)²) = 66/√61
The length of segment PX is (66√61)/61.
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c. To find the midpoint, we need to know the point of intersection, X. We find that by solving the simultaneous equations ...
y = 5/6x -5/2
y = -6/5x +12/5
Equating y-values gives ...
5/6x -5/2 = -6/5x +12/5
Adding 6/5x +5/2 gives ...
x(5/6+6/5) = 12/5 +5/2
x(61/30) = 49/10
x = (49/10)(30/61) = 147/61
y = 5/6(147/61) -5/2 = -30/61
Then the point of intersection of the lines is X = (147/61, -30/61).
So, the midpoint of PX is ...
M = (P +X)/2
M = ((-3, 6) +(147/61, -30/61))/2
M = (-18/61, 168/61)
Final answer:
To find line B perpendicular to line A and pass through point P, calculate the negative reciprocal of line A's slope and use it in the line equation along with point P coordinates to find c. The segment length from point P to line A is calculated using the distance formula and involves finding the intersection point between lines A and B. The midpoint is calculated using the midpoint formula.
Explanation:
To answer this question, we need to understand that two lines are perpendicular if the product of their slopes is -1. Line A has a slope of 5/6. Therefore, the slope of line B, perpendicular to line A, is -6/5 (the negative reciprocal). The equation of a line is y = mx + c where m is the slope and c is the y-intercept. As line B passes through point P(-3,6), we can substitute these values into the line equation y = -6/5x + c to solve for c. This will give us the equation of line B.
To find the length of the segment from point P to Line A, we would first need to find the intersection point of Line A and B. Then use the distance formula, which is sqrt[(x2-x1)^2 + (y2-y1)^2].
The midpoint of two points, (x1,y1) and (x2,y2) is given by ((x1+x2)/2, (y1+y2)/2). This formula can be used to find the midpoint between point P and the intersection of line A and line B.
Learn more about Line Equations here:
#SPJ3
The value of a is _____________.
Answers
9x (9x + 4 ) -4 (9x + 4)
81x^2 + 36x - 36x - 16
81x^2 - 16
ax2 - b
therefore the value of a is equal to 81
Answer:
value of a is, 81
Step-by-step explanation:
Using the identity rule:
Given the equation:
Apply the identity rule:
⇒
On comparing both sides we have;
and b = 16
Therefore, the value of a is, 81
Answers
No, he should have taken a random sample of all students at the school to get a good sample of the entire population of the school.
No, he should have surveyed students in his PE class since all grades are represented in that class.
Answers
Answer:
Value of D when t is 8 is:
280
Step-by-step explanation:
If D varies directly with t
⇒ D=kt for some constant k
D is 105 when t is 3
⇒ 105=3k
⇒ k=105/3
⇒ k=35
⇒ D=35t
when t=8
D=35×8
⇒ D=280
Hence, Value of D when t is 8 is:
280