Nate wants to visit his friend Mac before going to the park. Nate's house is located at (-2, 4), while the park is located at (10, 2). Find the bacation of Mac's house if it is of the distance from Nate's house to the park.
Answers
Answer:
Step-by-step explanation:
Using the formula for calculating the distance between two points as shown;
D = √(x2-x1)²²+(y2-y1)²
Given the coordinates (-2, 4) and (10,2)
x1 = -2, y1 = 4, x2 = 10 and y2 = 2
substitute into the formula;
D = √(10+2)²+(2-4)²
D = √(12²+(-2)²
D = √144+4
D = √148
D = 12.17 units
Hence the distance of Mac,s house from Nate's house is 12.17 units
Final answer:
To find the coordinates of Mac's house, we use the section formula in mathematics. By substitifying the given locations of Nate's house and the park into the formula, we conclude that Mac's house is located at approximately (2, 3.33) which is one third the distance from Nate's house to the park.
Explanation:
In this math problem, we are dealing with points in a 2D cartesian coordinate system. Nate's house is at (-2, 4) and the park is at (10, 2). Mac's house is located one third of the distance between these two points. Following the formula for the coordinates of a point dividing a line segment in a given ratio, we can find Mac's house location.
Let the coordinates of Mac's house be (x, y). We use the formula for section formula which is:
x = [(m*x2 + n*x1) / (m+n)] and y = [(m*y2 + n*y1) / (m+n)]
Here, x1, y1 (-2, 4) are the coordinates of Nate's house, x2, y2 (10, 2) are the coordinates of the park and the ratio m:n is 1:2 since it's one third of the distance from Nate's house to the park.
By substituting these values in the formula, we get x = [(1*10 + 2*-2) / (1+2)] = 2 and y = [(1*2 + 2*4) / (1+2)] = 3.33
So, the coordinates of Mac's house are approximately (2, 3.33).
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Related Questions
Write the equation of the line that passes through (2, 3) and is parallel to the line 12x – 5y = 2.
If a car travels 340 miles on 20 gallons of gas how far can it travel on 25 gallons of gas
HELP ME PLS PLS PLSZLZLDBFKSBJZBABS
Slope for -8,18 and -14,-3
A.
Jane
B.
Peter
Answers
Jane = 400/8=50mph
Therefore Peter drove at a faster speed, so B.
Answers
Answer:
36
Step-by-step explanation:
6+6+(4)(6)
12+24
36
Answer:
36
Step-by-step explanation:
Insert the given values:
Simplify multiplication:
Simplify addition:
:Done
Answers
Given choices:
(1) division property of equality
(2) factoring the binomial
(3)completing the square
(4)subtraction property of equality
Answer : (2) factoring the binomial
Step 1:
Step 2:
In step 2, 'a' is taken out from . when we take out 'a' we divide each term by 'a'. so it becomes
'a' is factored out in step 2. we call it as factoring a binomial.
Answer:
answer is B
Step-by-step explanation:
x = 3; the diver hits the water 3 feet away horizontally from the board
x = 10; the diver jumps in the pool at 10 feet per second
x = 3; the diver jumps in the pool at 3 feet per second
Answers
-x2 -7x +30 =0
The roots of this quadratic equation are:
x = 3 and -10
Since the diver is on a diving board, the -10 is somewhere behind him. We use the root x = 3 since this distance is in front of the board.
Therefore, the answer is:
x = 3; the diver hits the water 3 feet away horizontally from the board
The diver hits the water 3 feet away horizontally from the board.
The correct option is (b)
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0 with a ≠ 0 .
Given function: f(x)= -x² -7x +30
Factorising f(x), we get
-x² -7x +30 =0
x² +7x -30 =0
x² +10x - 3x -30 =0
x(x+10)-3(x+10)=
(x+10)(x-3)=0
The roots of this quadratic equation are x = 3 and -10.
As, the diver is on a diving board we will not use -10.
Hence, the diver hits the water 3 feet away horizontally from the board.
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B. the points scored by a basketball player compared to his minutes played
C. the height of a woman compared to her age
D. the hours of daylight in a city throughout the year
Answers
The hours of daylight in a city throughout the year represent the negative linear correlation coefficient. Then the correct option is D.
What is a negative linear correlation coefficient?
Independent quantities with an inverse relationship tend to move in different directions.
In essence, any figure between 0 and -1 denotes an opposing movement of the equity stocks.
When the correlation coefficient becomes less than 0, there is a negative (opposite) correlation. This suggests that both parameters are moving in the obverse direction.
The hours of daylight in a city throughout the year represent the negative linear correlation coefficient
Then the correct option is D.
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Answer:
D. the hours of daylight in a city throughout the year
Step-by-step explanation:
Answers
The value of the fraction is given by equation A = 6 7/12
What is a Fraction?
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the simplified fraction be represented as A
Now , let the first fraction be p
The value of p = 12 1/4
Let the second fraction be q
The value of q = 5 2/3
On simplifying , we get
A = p - q
A = 12 1/4 - 5 2/3
A = ( 49/4 ) - ( 17/3 )
Taking the LCM of the denominators , we get
A = [ ( 49 x 3 ) - ( 17 x 4 ) ] / 12
A = ( 147 - 68 ) / 12
A = ( 79/12 )
On further simplification of the fraction , we get
A = 6 7/12
Therefore , the value of A is 6 7/12
Hence , the simplified fraction is A = 6 7/12
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5 2/3 = 17/3
49/4 = 147/12
17/3 = 68/12
14/12 - 68/12 = 79/12
6 5/12