Answer:
The given point satisfies both equations of a line, hence is common to the two lines.
Step-by-step explanation:
Given two lines, one joining the points (6,-7,0) to (16,-19,-4), and the other joining the points (0,3,-6) to (2,-5,10), you want to show that the point (1, -1, 2) is common to those lines.
Equation of a lineThe equation of a line through points (x1, y1, z1) and (x2, y2, z2) can be written:
(x -x1)/(x2 -x1) = (y -y1)/(y2 -y1) = (z -z1)/(z2 -z1)
For the first pair of points, the equation of the line is ...
(x -6)/(16 -6) = (y +7)/(-19 +7) = (z -0)/(-4 -0)
(x -6)/10 = -(y +7)/12 = -z/4 . . . . . line 1
For the second pair of points, the equation of the line is ...
(x -0)/(2 -0) = (y -3)/(-5 -3) = (z +6)/(10 +6)
x/2 = -(y -3)/8 = (z +6)/16 . . . . . line 2
Point on the line?If the given point is on each of these lines, then it will satisfy each of the equations.
Line 1: (1 -6)/10 = -(-1 +7)/12 = -2/4 ⇒ -5/10 = -6/12 = -2/4 . . . true
The given point is on Line 1.
Line 2: (1)/2 = -(-1-3)/8 = (2+6)/16 ⇒ 1/2 = 4/8 = 8/16 . . . true
The given point is on Line 2.
The given point is common to both lines.
__
Alternate solution
For points A and B and parameter p, we can write the parameterized equation of each line as ...
(x, y, z) = A +p(B -A)
Using parameters t and s for the two lines, we get ...
Line 1: (x, y, z) = (6, -7, 0) +t(16 -6, -19 +7, -4 -0) = (6 +10t, -7 -12t, 0 -4t)
Line 2: (x, y, z) = (0, 3, -6) +s(2 -0, -5 -3, 10 +6) = (0 +2s, 3 -8s, -6 +16s)
A common point will be found where (x, y, z) for some value of t matches (x, y, z) for some value of s. We can find those values of s and t by solving simultaneous equations for any pair of the variables (x, y, z). The equations are ...
6 +10t = 2s-7 -12t = 3 -8s-4t = -6 +16sBy any of your favorite methods, these equations have the solution (t, s) = (-0.5, 0.5). The point the lines have in common is ...
(6 +10(-0.5), -7 -12(-0.5), 0 -4(-0.5)) = (6 -5, -7 +6, 2) = (1, -1, 2)
The common point to the two lines is (1, -1, 2).
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01:52 / 08:00
When this expression is simplified, what is my final answers
-5(2x - 5)
O 10x + 25
O 52x - 25
O-7x + 25
O-10x + 25
Answer:
-10x + 25
Step-by-step explanation:
We will distribute the - 5 in to 2x which is - 10x
Then distribute - 5 to - 5 which is 25
Ed’s class went on a class picnic. Ed’s teacher packed 20 sports drinks in a cooler for Ed and his classmates. Eight of the sports drinks were orange-flavored. What is the ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler? Choose from the numbers listed below to create the correct ratio.
The ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler is 3 : 5.
What is Ratio?
In mathematics, Ratio is a term that is used to compare two or more numbers.
Given that their are 20 sports drinks in a cooler out of which 8 are orange flavored. Therefore, we can write that -
Number of orange flavored bottles = n[O] = 8
Total number of bottles = n[T] = 20
We can calculate the ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler as follows -
Total number of non - orange flavored bottles will be -
n[C] = n[T] - n[O]
Now, the ration of non - orange bottles to the total number of bottle's can be written as -
n[C] / n[T]
(n[T] - n[O]) / n[T]
(20 - 8) / 20
12 / 20
3 / 5
Assume that the ratio is denoted by R. Therefore -
R = 3 : 5
Hence, the ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler is 3 : 5.
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5 6 7 8 9 10
TIME REMAINING
10:31
What is true about the completely simplified sum of the polynomials 3x2y2 − 2xy5 and −3x2y2 + 3x4y?
The sum is a trinomial with a degree of 5.
The sum is a trinomial with a degree of 6.
The sum is a binomial with a degree of 5.
The sum is a binomial with a degree of 6.
Answer:D) the sum is a binomial with a degree of 6
Step-by-step explanation:
A plane leaves the airport and travels east for 2.5 hours at a speed of 240 miles per hour. It then travels south for 500 miles. a)Calculate the distance of the plane from the airport. b)Calculate the bearing of the plane from the airport.
a) The distance of the plane from the airport is approximately 781.025 miles.
b) The bearing of the airplane in standard position is approximately 320.194°.
How to calculate the distance and the bearing of the bearing from the airport
Let the location of the airport be the origin and the orthogonal axes are oriented to the east and north, respectively. Beside, let consider that the plane moves at constant speed. a) Thus, the distance of the plane can be found by using the Pythagorean Theorem:
d = √[[(240 mi / h) · (2.5 h)]² + (500 mi)²]
d ≈ 781.025 mi
b) And the bearing in standard position is determined by the following inverse trigonometric function:
θ = tan⁻¹ [(- 500 mi) / [(240 mi / h) · (2.5 h)]]
θ ≈ 320.194°
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Smallest
437.55
437.49
437.15
437.5
437.05
Largest
Answer:
smallest to largest will be:
437.05 , 437.15, 437.49, 437.5, 437.55
Step-by-step explanation:
an easier method i use is to simply check the 1st digit rhat comes after the decimal point if the whole numbers are similar.
in a case where there is only one number after the decimal while the rest have 2, for example 437.5, simply add a 0 to make it even as the rest
What does the pair of equations y = 1, z = 7 represent? in other words, describe the set of points (x, y, z) such that y = 1 and z = 7.
The intersection of two plans is represented by the pair of equations y = 1, z = 7. The set of points is (0,1,7) and the line is parallel to the x axis.
What is intersection of planes?In geometry, a plane is a flat plate which extends in all directions to infinity.
Intersecting planes are non-parallel planes that always intersect in a straight line.The two planes cannot cross more than one line.A good illustration of intersecting planes is the two connecting borders, the binding side of a book, where all of the papers (planes) meet.Now, as per the question;
Consider the following equation.
y = 1 denotes a vertical plane in the xy plane.
Z = 7 denotes a horizontal plane parallel to the xy plane.
Both planes intersect and are perpendicular to each other.
y = 1 and z=7 is the intersection of two plans where x is zero and y = 1 and z = 7.
Therefore, the points are (0,1,7), and also the line is parallel to the x axis.
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A flagpole makes a 15-foot long shadow. The angle of elevation with the end of the shadow and the ground
makes a 65° angle. What is the height of the flagpole?
Answer:
12.5988 feet.
Step-by-step explanation:
Length of shadow = 15 feet.
Height of flagpole = A.
We know the angle of elevation is 40∘. Using this angle and the tangent ratio, we can find A.
Hope this helps! :)
How do you calculate the X and Y coordinates of the vertex when the equation is in standard form?
If the quadratic is y = a*x^2 + b*x + c
the coordinates of the vertex are:
x = -b/2a
y = (1/2a)*( -0.5*b^2 + c)
How to find the coordinates of the vertex?For a quadratic equation in standard form:
y = a*x^2 + b*x + c
The x-value of the vertex is given as:
x = -b/2a
Once we get the x-value of the vertex, we can get the y-value by evaluating the quadratic equation in x = -b/2a, we will get:
y = a*(-b/2a)^2 + b*(-b/2a) + c
y = b^2/(4a) - b^2/2a + c = (1/2a)*(b^2/2 - b^2 + c)
y = (1/2a)*( -0.5*b^2 + c)
Then the coordinates of the vertex are:
x = -b/2a
y = (1/2a)*( -0.5*b^2 + c)
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Simplify: (2 3/5)+(-3 3/4)
Answer:
-23/20
Step-by-step explanation:
The lines 4x+6y-5=0 and 2x+4y-3=0 intersect at N. Find the equation of the line through N perpendicular to the line x+2y=0.
4x+6y=5 and 2x+4y=3 are the 2 supplied lines. We must solve two simultaneous equations in order to determine the location at where these two lines cross.
When we multiply the second equation by two, we obtain the result 4x+8y=6. Next, we subtract this from the first equation to get -2y = -1, which equals y=1/2. N's coordinates are therefore (+1/2, +1/2).
The line we need to identify now goes through this point and is perpendicular to the line x+2y=0; its slope is -1/2 (the slope of the line [tex]ax+by+c=0[/tex] is -a/b). With m1*m2=-1, the line perpendicular to this one has a slope of 2. Consequently, the line that we must identify The slope of the equation is 2, and it goes through N. In order to simplify the equation, (y-1/2) = 2*(x-1/2), which results in 2y-1 = 2*(2x-1) and 2y-1 = 4x-2 and 4x-2y-1=0. The necessary equation is as follows.
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How would you write 730,812 in word form?
Answer Seven hundred and thirty thousand eight hundred twelve
convert 574 inches to yards foot and inches
Answer:
Firstly, you need to divide by 36! That'll tells you how many yards there are. Then, divide the remainder by 12! That'll tells you how many feet are there. The final remainder tells you the number of inches!
4=2x+y
-6x-3y=-12
Elimination
Answer:
infinitely many solutions
Step-by-step explanation:
4=2x+y
-6x-3y=-12
First, line up the variables in the right place
4=2x+y
-12=-6x-3y
Choose the variable you want to eliminate, I will do x
Multiply everything in the first equation by 3
3(4)=(2x+y)3
-12=-6x-3y
Simplify
12=6x+3y
-12=-6x-3y
If we combined everything, it would all cancel
This means there are infinitely many solutions
The black graph is the graph of y=f(x)
HELPPPPP PLEASE. PLEASE TELL ME THE BLANKS IN ORDER.
At a certain bookstore you get a $5 dollar coupon for every four books you buy. what is the least number of books you can buy to get $15 dollars in coupons.
The function h(x) = x^2 - x - 2 / x^2 - x - 6 has a vertical asymptote at x =
A. 6
B. 3
C. -2
D. -1 and 2
E. -2 and 3
Answer:
The function h(x) =x^2-x-2/ x^2-x-6=
E.-2 and 3
Options are
A. (-3, -1)
B. (3,1)
C. (6,4)
D. (2,6)
Answer: D
Step-by-step explanation: 2,6
what is the median of 0,4,8,5,3,5,5,5,1
Answer:
The median is: 5
Hope this helps! <3
Answer:
Step-by-step explanation:
5
We can calculate the depth d of snow, in centimeters, that accumulates in Harper's yard during the first h hours of a snowstorm using the equation d=5h.
How many hours does it take for 1 centimeter of snow to accumulate in Harper's yard?
How many centimeters of snow accumulate per hour?
Please helpppp.Will vote the brainliest?I don't understand
Answer:
1.5
2.1/5
Step-by-step explanation:
Farfalla kites owns 3 factories around the globe. In one year, the original factory can make 600 kites, and each of the other factories can make 900 kites. How many kites does Farfalla produce every year
Farfalla produces 2,400 kites every year.
The number of factories Farfalla owns around the globe = 3;
The number of kites produced by original factory every year = 600;
The number of kites produced by each of other 2 factories every year = 900;
Then the total kites produced by both other factories will be = 2 × 900 = 1800;
Now, the number of kites Farfalla produces every year is = 600 + 1800 = 2400;
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What is the value of a?
Answer:
15 units
Step-by-step explanation:
By using the Pythagoras Theorem,
C^2 = A^2 + B^2
Substitute in the given values,
25^2 = a^2 + 20^2
625 = a^2 + 400
625 - 400 = a^2 + 400 - 400
a^2 = 225
[tex]a = \sqrt{225} [/tex]
= 15
Hope this too helped! ^^
I'd recommend watching a video or two on the topic of Pythagoras Theorem, if this explanation isn't clear enough.
Find the difference of -6-(-7)
Answer:
1
Step-by-step explanation:
When you simplify, the answer is 1.
Answer:
1
Step-by-step explanation:
answer the photo
please do it correctly
Answer:
65
Step-by-step explanation:
180 -( 95 + 20 )
=180 - 115
= 65
Solve d = rt for r
Practice problems algebra
Answer: r=d/t
Step-by-step explanation:
d=rt
d/t=rt/t
r=d/t
Answer:
[tex]r=\frac{d}{t}[/tex]
Step-by-step explanation:
[tex]d=rt[/tex]
Divide both sides by [tex]t[/tex]:
[tex]\frac{d}{t}=r[/tex]
[tex]r=\frac{d}{t}[/tex]
In+a+recent+poll,+64%+of+the+respondents+supported+stricter+gun+laws.+is+this+an+example+of+statistic+or+a+parameter?
In a recent poll, 64% of the respondents supported stricter gun laws is statistic.
What is an example of a parameter?
To describe the entire population under study, a parameter is utilized. For instance, we are interested in learning the typical length of a butterfly. This information about the total butterfly population makes it a parameter.What is an example of a population parameter?
A parameter is a descriptive measure applied to a whole population. Numerous population parameters exist. For instance, the population size (N) is one parameter, while other parameters that relate to continuous variables are the population's mean diastolic blood pressure or mean body weight.Learn more about population parameter
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PLEASE HELP! Need help quick!
Joaquin started an online music collection with 105 songs. Each week, Joaquin purchases 4 new songs to add to his collection.
Which inequality can be used to find w, the number of weeks after starting his collection, when Joaquin will have more than 200 songs in his collection?
A- 105w+4<200
B- 105w+4>200
C- 4w+105<200
D- 4w+105>200
Answer: The answer will be D
Step-by-step explanation: I think the answer will be C because you can multiply this as I did to get the answer so its C
50 < = x >= 1000 inequality
The solution to the given inequality is x≥50.
The given inequality is 50≤x≥1000.
What is inequality?Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Now,
Move all terms not containing x from the centre section of the inequality.
Inequality Form: x≥50
Interval Notation: [50,∞)
The solution to the inequality is marked on the number line.
Therefore, the solution to the given inequality is x≥50.
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A fraction is equivalent to 2/3. The product of its numerator and denominator is 216. What is the fraction?
Suppose that y is directly proportional to x. use the given information to find the constant of proportionality k. then use y = kx to find y for the given value of x. y = 30 when x = 10;find y given x = 14
The the value of constant proportionality k is 3 and the value of y is 42 when the value of x is 14.
Constant proportionality:
Constant proportionality means the ratio of two proportional values at a constant value.
Directly Proportional:
In direct proportion, if one quantity is increased or decreased then the other quantity increases or decreases, respectively.
Given,
Suppose that y is directly proportional to x.
And y = kx.
Here we need to find the value of k when the value of x = 10 and the value of y = 30.
And we also need to find the value of y when the value of x = 14.
First, we have to find the value of k by apply the given value of the equation,
=> 30 = k x 10
=> 30 /10 = k
=> k = 3
Now the value of y when the value of x = 14 and the value of k = 3,
Then
=> y = 3 x 14
=> y = 42.
Therefore, the value of constant proportionality k is 3 and the value of y is 42 when the value of x is 14.
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