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).
Which of the following identifies the individuals in the
set?
The individuals of a set are the various data or variable of a data set.
The study's participants or study subjects are referred to as individuals. The trait of the person being measured or observed is known as a variable. For instance, if we were to do a research on climbers of Mount Everest, the participants would be the real climbers who succeeded in reaching the summit.
A categorical variable places each individual in to a category such as male or female.
A quantitative variable has numerical values that measure some characteristic of each individual, such as height in centimeter or salary in dollars.
The problem deals with the concept of types of variables. We use the definition of variables to identify/determine the type variable from the known information.
The individuals in the data set are vehicles or cars.
The given information is related to the different types of cars and its model, and specifications. Hence, the vehicles or cars are individuals in the data set.
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A man drove 14 mi directly east from his home, made a left turn at an intersection, and then traveled 9 mi north to his place of work. if a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
If a road was made directly from his home to his place of work, its distance will be 16.6 mi.
If a man drives east from his home, makes a left turn at an intersection, and then travels north to his place of work, then the path he travels resembles the sides of a right triangle (see attached photo).
if a road was made directly from his home to his place of work, then this path will be the hypotenuse of the triangular path.
Using Pythagorean theorem, we can solve for the distance of the road.
c^2 = a^2 + b^2
where c is the distance of the road
a is the distance he travels to the east
b is the distance he travels up north
c^2 = a^2 + b^2
c^2 = (14 mi)^2 + (9 mi)^2
c^2 = (196 + 81) mi^2
c^2 = 277 mi^2
c = 16.64331698 mi
distance of the road = c = 16.64331698 mi
Rounding off to the nearest tenth of a mile:
distance of the road = 16.6 mi
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Jenna works in an ice cream shop. When she starts her shift, the tub of chocolate ice cream is 23 full. When she finishes her shift 612 hours later, there is only 16 of the tub left. What was the average hourly change in tub fullness?
The average hourly change in tub fullness is ₋1/13.
Jenna she starts her shift, the tub of chocolate ice cream is 2/3 full.
After she finishes her shift 6 1/2 hours , there is only 1/6 of tub left.
the average hourly change in tub fullness = ?
subtract the initial quantity from the quantity left after 6 1/2 hours.
⇒ 2/3 ₋ 1/6
= 1/2
Divide the quantity by 6 1/2 hours.
time is represented in improper fraction, convert it into proper fraction.
6 1/2 = 12 ₊ 1/2
= 13/2
⇒ 1/2 ÷ 13/2
= 1/13
the statement says the quantity decreases,
so ₋1/13
therefore the average hourly change in tub fullness is ₋1/13
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The function y=x+3 is what type of function?
1. linear
2. quadratic
3. cubic
4. rational
5. radical
Answer: the type of function is linear.
I hoped this helped!
mark me the brainliest :)
Help I need some help due tomorrow
Answer:
Angle 1: 141 degrees
Angle 2: 39 degrees
Angle 3: 141 degrees
Step-by-step explanation:
Angle 2 and Angle 4 are equal since they are vertical angles. This means that Angle 2 is equal to 39 degrees.
Angle 1 and Angle 4 add up to 180 degrees. We call these supplementary angles. This means that Angle 1 is equal to 180-39=141 degrees.
Angle 1 and Angle 3 are vertical angles, so Angle 3 is also equal to 141 degrees.
rewrite the following statements less formally, without using variables. determine, as best as you can, whether the statements are true or false
All of the statements are True when the expressions are evaluated using appropriate illustrations.
What are Real numbers?Real numbers are made up of both rational and irrational numbers. Real numbers include integers (-2, 0, 1), fractions (1/2, 2.5), and irrational numbers such as 3, (22/7), and so on.STATEMENT: 1
Real numbers have both rational and irrational values and can thus be manipulated using arithmetic operators like addition.
As a result, the statement is correct.
[tex]1+\frac{1}{2}=1 \frac{1}{2}[/tex]
STATEMENT: 2
Real numbers can be expressed or raised to the power of another number in a variety of ways, including being squared.
2² = 4; (1/3)² = 1/9STATEMENT: 3
All positive integers have a squared value that is greater than or equal to the value.
n = 2; n² = 2² = 44 > 2STATEMENT: 4
A sum's absolute value is always less than or equal to the sum of two numbers' absolute values.
a = 3 ; b = - 4|a + b | = |3-4| ≤ |-3|+|4||-1| ≤ 3 + 4-1 ≤ 7Therefore, all of the statements are True when the expressions are evaluated using appropriate illustrations.
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The complete question is given below:
Rewrite the following statements less formally, without using variables. Determine, as best as you can, whether the statements are true or false.
a. There are real numbers u and v with the property that u+v b. There is a real number x such that x2 c. For all positive integers n,n2≥n.
d. For all real numbers a and b,|a+b|≤|a|+|b|
• Liz fue a comprar un Kilo de Papas tres cuartos
de Kilo de tomate y medio Kils de aguacate Yob
Cuarto de kilo de cebolla ¿Cuantos Kilos Pesaba
toda la verdura que compro?
Liz went to the store to get a kilo of papas, three kilo tomatoes, and a half kilo of aguacate. Yob Cuarto de Kilo de Cebolla, How Many Kilograms Were All the Vegetables You Bought Weighed
2,40
Dejar:
T = Tomate
n = cebolla
(2 kilograms of t) plus 1 kilogram of n = 8.40
(1 kilogram plus 2 kilograms) equals 7.80.
2t + n = 8,40 - -
t + 2n = 7,80 - -
De (2);
t = 7,80 - 2n
Toggata = 7.80 - 2n en
2 (7,80 - 2n) + n = 8,40
15,6 - 4n + n = 8,40
15,6 - 3n = 8,40
-3n = 8,40 - 15,6
-3n = - 7,2
n = 2,4
t = 7,80 - 2
t = 7,80 - 4,80
t = 3
As a result, the price of 1 kg of celery is $2.40.
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How many triangles exist with the given side lengths? 7 in, 7 in, 7 in A. No triangle exists with the given side lengths. B. Exactly one unique triangle exists with the given side lengths. C. More than one triangle exists with the given side lengths.How many triangles exist with the given side lengths? 7 in, 7 in, 7 in A. No triangle exists with the given side lengths. B. Exactly one unique triangle exists with the given side lengths. C. More than one triangle exists with the given side lengths.
Answer:
B. Exactly one unique triangle exists with the given side lengths
Step-by-step explanation:
A triangle has three sides. So if all three sides are the same in length then it is a equilateral triangle. Which means that only one triangle can be formed.
I hope this helps!! Have a good day :D
PLEASE HELPPPP. WILL GIVE BRAINLIEST AND 5 STR RATINGGG
For each complex number z, find arg z
z = 4/5 + 3/5i
The argument of complex number ([tex]\frac{4}{5}[/tex]+i[tex]\frac{3}{5}[/tex] ) is [tex]tan^{-1}[/tex]([tex]\frac{3}{4}[/tex])
Complex number:
A complex number is a result of adding a real and an imaginary number. A complex number has the formula a + ib and is usually represented by the symbol z. Both a and b are real numbers in this case. The value 'a' is known as the real part, which is denoted by Re(z), and the value 'b' is known as the imaginary part Im (z). ib is also known as an imaginary number.
Argument:
A complex number is represented in polar form by the equation r(cos[tex]\theta[/tex] +isin[tex]\theta[/tex]), where [tex]\theta[/tex] is the argument. Arg(z) denotes the argument function, where z is the complex number, i.e. z = x + iy. The complex argument can be determined by the following formula:
arg (z) = arg (x+iy) = [tex]tan^{-1}[/tex](y/x)
Here the given complex number is ([tex]\frac{4}{5}[/tex]+i[tex]\frac{3}{5}[/tex] )
arg (z) = arg ([tex]\frac{4}{5}[/tex]+i[tex]\frac{3}{5}[/tex] )= [tex]tan^{-1}[/tex]([tex]\frac{3}{4}[/tex])
Therefore,the argument of complex number ([tex]\frac{4}{5}[/tex]+i[tex]\frac{3}{5}[/tex] ) is [tex]tan^{-1}[/tex]([tex]\frac{3}{4}[/tex])
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Statistics on women in politics highlight that women - who make up over 50 percent of the u.s. population - are ________ in high government positions.
Statistics on women in politics highlight that woman - who make up over 50 percent of the U.S. population - are substantially lag in high government positions.
In U.S. the population of Women are 50.8 percent. Approximately, 60 percent of women have their undergraduate degree, and 60 percent of women have their master's degree. They are very well educated. They earn almost 60 percent of law degrees.
But, when it comes to representation in high government positions, they substantially lag behind men. There are only 14.6 percent of executive officers, they hold only 24.2 percent of state legislative seats. They hold only 18.5 percent of congressional seats, and they are just 20 percent of U.S. senators.
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Type the expression that results from the following series of steps:
Start with
n
, add 5, multiply by 4, then subtract 7.
Answer:
n + 5 x 4 - 7
Step-by-step explanation:
Answer:
4(n+)7
Step-by-step explanation:
n+5
(n+5) x 4 = 4 ( n + 5)
4( n+5)-7
Triangle T R S has centroid Z. Lines are drawn from each point to the midpoint of the opposite side to form line segments T W, R V, and S U.
In triangle TRS, VZ = 6 inches. What is RZ?
In triangle TRS, VZ = 6 inches. Then the length of the line segment RZ will be 12 inches.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The centroid Z of the triangle TRS. Line sections TW, RV, and SU are created by drawing lines from every point to the center of the opposing side.
We know that the centroid divides the median of the triangle in a ratio of 2: 1.
In triangle TRS, VZ = 6 inches. Then the length of the line segment RZ will be
RZ / ZV = 2 / 1
RZ / 6 = 2
RZ = 6 x 2
RZ = 12 inches
In triangle TRS, VZ = 6 inches. Then the length of the line segment RZ will be 12 inches.
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Pls help my homework is due in 7mins
Find the area of a circle with a 15inch diameter in terms of pie
Answer:
56.25π in²
Step-by-step explanation:
The area of a circle is given by πr², where r is the radius of the circle.
Given that the diameter is 15 inch, let's calculate the radius.
Diameter= 2 ×radius
Radius
= 15 ÷2
= 7.5 in.
Applying the formula for area of circle,
area of circle
= π(7.5)²
= 56.25π in²
Since the question requires for the answer to be in terms of π, we have arrived at our answer.
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3. Which statement is true about a translation?
A) A translation takes a line to a parallel line or itself.
B) A translation takes a line to a perpendicular line.
C) A translation requires a center of translation.
D) A translation requires a line of translation.
A) A translation takes a line to a parallel line or itself.
Answer: A) A translation takes a line to a parallel line or itself.
Step-by-step explanation:
Find the surface area of the cube shown below. A. 66 cm2 B. 121 cm2 C. 726 cm2 D. 1,331 cm2
Answer:
66
Step-by-step explanation:
Find the solution to the system: -5/7-11/7x=-y and 7+5x=2y
The solution to the system of equation is x = 1 / 5 and y = 4
How to solve system of equation?The system of equation can be solved as follows:
- 5 / 7 - 11 / 7 x = - y
7 + 5x = 2y
let's rearrange the equations
Therefore,
- 11 / 7 x + y = 5 / 7
5x - 2y = -7
Let's multiply equation(i) by 7 to eliminate the fractions
Hence,
-11x + 7y = 5
5x - 2y = -7
Therefore, using substitution method
5x = -7 + 2y
x = -7 / 5 + 2 / 5 y
Hence,
-11(-7 / 5 + 2 / 5 y) + 7y = 5
77 / 5 - 22 / 5 y + 7y = 5
- 22 / 5 y + 7y = 5 - 77 / 5
-22y + 35y / 5 = 25 - 77 / 5
13y / 5 = -52 / 5
cross multiply
65y = -260
y = -260 / 65
y = 4
Hence,
5x - 2(4) = -7
5x - 8 = -7
5x = -7 + 8
x = 1 / 5
Therefore, the solution to the system of equation is x = 1 / 5 and y = 4
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someone help please!!!!
Answer:
x = -2
TU = 4
UB = 2
Step-by-step explanation:
you can add x^2 with 4x+10 and equate it to 6:
x^2 + 4x + 10 = 6
x^2 + 4x + 4
then u can use the roots formula : x = (-b ± √ (b2 - 4ac) )/2a
so it'll be x = {-4±[√16 - 4(4)]}/2
x= -2
then u can substitute it and find TU and UB
TU= (-2)^2 = 4
UB= 4(-2)+10 = 2
Is 168 divisible by 2,3,4,5,6,8,9 or 10 explain why please
Help ASAP
Answer:
2,3,4,6,8
Step-by-step explanation:
prime factorization: 2^3×3×7 which has: 2, 3, 4, 6, 8
Answer:
It is divisible by 1, 2, 3, 4, 6, 7, 8
Step-by-step explanation:
Everything is divisible by one, so this is obvious.
168 is an even number, therefore being able to be divided by 2
1+6+8=15 which is in the 3 times tables (3x5=15)
If the last two digits are divisible by 4 (which 68 is) then you can divide it by 4.
168 doesn't end in 5 or 0 so it can't be divided by 5
This number can be divisible by 2 and 3 so it can be divided by 6
160 is divisible by 8 so if you add 8 it is divisible.
1+6+8=15 again which is not divisible by 9
It doesn't end in 0 meaning it cannot be divisible by 10
Hope this helped! <3
The diagram shows a solid triangular prism with a cylindrical hole of radius r cm drilled through it. (i) The ratio of the volume of solid removed : volume of remaining solid is 1 : 6. Find the value of r. Using your answer in part (i), find the total surface area of the solid shown.
The value of the radius r is 9.35 cm.
The dimensions of the triangular prism is 62 cm × 62 cm × 85 cm.
The volume of the prism will be:
Volume = (1/2) × 62 × 62 × 85
Volume = 163370 cm³
Now,
The volume of solid removed: The volume of remaining solid = 1 : 6
Therefore,
The solid removed = ( 1 / 7 ) of the total volume
Solid removed = ( 1 / 7 ) × 163370
Solid removed = 23338.57 cm³ which is the volume of the cylindrical hole.
Now, the volume of the cylinder is:
V = π (r)² h
23338.57 = π (r)² × (85)
23338.57 = (3.142) × (r)² × (85)
23338.57 = 267.1 r²
r² = 87.38
r = √(87.38)
r = 9.35 cm
The surface area of the triangular prism:
A = (1/2) (b) (h)
A = (1/2) (85)(62)
A = 2653 cm²
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What feature in excel allows you to begin with a 1 in a1 and a 2 in a2 and complete the sequence through the number 30 in a30 without having to type in the entire sequence?
Answer:
type 1 in a1 type 2 in a2, (or whatever ur preferred no.s are),then heighlight both cells, then go to the bottom right corner of a2 and drag down or double click
Step-by-step explanation:
Drag down or double-click the bottom right corner of a2 to begin with a 1 in a1 and a 2 in a2 and complete the sequence.
What is excel?Excel is a software in which we can process large amount of data and data handling easily and effectively, Excel can be used in Data analysis.
in a1 type 1 Type 2 in cell a2 (or whatever your chosen numbers are), highlight both cells, and then drag down or double-click the bottom right corner of a2.
Thus, drag down or double-click the bottom right corner of a2 to begin with a 1 in a1 and a 2 in a2 and complete the sequence.
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Translate (3x-1,y+5)
Answer: Three times x minus y is five times the sum of y and two times x.
Step-by-step explanation:
the given equation is: (3x-1,y+5)
The left hand side of the equation may be written as: "Three times x minus y."
The right hand side of the equation may be written as: "Five times the sum of y and two times x."
Hence, the correct option is:
In 8 years Jack will be three times as old as he is now. How old is he now?
Answer:
4 years old
Step-by-step explanation:
3x = x + 8
2x = 8
x = 4
Answer:
4 y/o
Step-by-step explanation:
x = age now
add 8 years
x+8 and this equals 3 times as old as he is now, or 3x
x+8 = 3x subtract 'x' from both sides
8 = 2x divide both sides by 2
x = 4 y/o
the 5th term of an A.P is 9 and the 8th term is 27.Find the 31st term
Answer:
189
Step-by-step explanation:
The difference between consecutive terms of an arithmetic sequence, known as the common difference is given by
d = a(k) - a(k-1) where k = 1,2,3 ....n
We have the 5th term as a(5) = 9
The 6th term is 9 + d
The 7th term is 9 + 2d
The 8th term is 9 + 3d
Each successive term adds a d to the previous term
We have 8th term = 27
So 9 + 3d = 27
3d = 27 - 9 (subtract 9 from both sides)
3d = 18
Divide above by 3 on both sides to get
d = 18/3 = 6
So the common difference is 6
Let's figure out how to calculate the 31st term
We can see that the 5th term can be expressed as
9 + 0d = 9 + 0.6 = 9
The sixth term is
9 + 1d = 9 + 1(6) = 9 + 6 = 15
The seventh term is 9 + 2d = 9 + 12 = 21 and so on
Therefore the general equation for the nth term, given the 5th term
is
a(n) = a(5) + (n - 5)(6) 9 + 6(n - 5)
So the 31st term is
a(31) = 9 + 6(31-1) 9 + 6 x 30 = 9 + 180 = 189
Answer: 31st term is 189
I really need help in this question
The height of the isosceles triangle is 8.08 cm.
Given the sides of the triangle are:
a = 9 cm (one side of the triangle)
b = 8 cm ( base of the triangle)
Therefore, height of the triangle =?
An isosceles triangle's height is determined by measuring perpendicularly from one vertex to the other's triangle base. A triangle's height is one of its crucial parameters since it enables us to determine the triangle's area.
we know that h = √a²₋ b²/4
substitute a and b values in the above formula, to find height:
h = √9² ₋ 8²/4
h = √81 ₋ 64/4
h = √(81 × 4) ₋ 64 / 4
h = √324 ₋ 64/4
h = √260/4
h = √65
h= 8.06 cm
Therefore the height of the isosceles triangle is 8.06 cm.
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Need help asap
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A scientist uses a submarine to study ocean life.
She begins 174 feet below sea level.
After traveling down for 15 seconds, she's 252 feet below sea level.
Find the rate of change in the submarine's elevation in feet per second. Round your answer to the nearest tenth.
The rate of change in the submarine's elevation in feet per second is 5.2
According to the question ,
She starts 174 feet below sea level
after 15 minutes she reaches 252 feet below sea level
distance travel in 15 minutes = [tex]\frac{252 - 174}{15}[/tex]
= [tex]\frac{78}{15}[/tex]
= [tex]\frac{26}{5}[/tex]
Round off [tex]\frac{26}{5}[/tex] = 5.2
There are certain rules to follow when rounding a decimal number. Put simply, if the last digit is less than 5, round the previous digit down. However, if it’s 5 or more than you should round the previous digit up. So, if the number you are about to round is followed by 5, 6, 7, 8, 9 round the number up. And if it is followed by 0, 1, 2, 3, 4 round the number down.
Here some Rounding Examples :
Consider the number 8.9163
8.9163 rounded to the nearest tenth is 8.9
Because 9 is followed by 1 and 1 is less than 5.
8.9163 rounded to the nearest hundredth is 8.92
Because 1 is followed by 6 and 6 is greater than 5.
8.9163 rounded to the nearest thousandth is 8.916
Because 6 is followed by 3 and 3 is less than 5.
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me is needing help ok
Answer:
50.96 days can be rounded to 51
73381
1223
51
Step-by-step explanation:
Too bad I can't see the choices. I will give the numbers both as exact figures rounded to integers and you have to choose the closest to these.
Part A
50.96 days
Part B
6.6043 x 10⁵ gallons at 9 gallons per minute = (6.6043 x 10⁵)/9 = 660,430/9 = 73,381.11 gallons per minute rounded to 73,381 minutes
73,381 minutes = 73,381 /60 = 1223.02 hours 1223 hours
1223 hours = 1223/24 = 50.96 days rounded to 51 days
Hope that helps. Ask if you need further info
Find the equation of the line that passes through (1,3) and is perpendicular to y = 2x + 3.
Leave your answer in the form ax + by = c Where a, b and c are integers.
The equation of the line that passes through (1,3) and which is perpendicular to y = 2x ₊ 3 is x ₊ 2y = 7.
Given the equation of the which passes through the point is (1,3)
the line is perpendicular to y = 2x ₊ 3
first we need to determine the slope of the equation.
line is perpendicular to y = 2x ₊ 3
perpendicular means slope (m) = ₋1
but given the in the line equation we have
y = mx ₊ c
m = 2
therefore ₋1 = 2
hence slope m = ₋1/2
Then the line passing through (1,3), substitute the coordinates of the point in the equation of the line:
y ₋ y₁ = m(x ₋ x₁)
take (1,3) as (x₁,y₁)
y ₋ 3 = ₋1/2 (x ₋ 1)
y ₋ 3 = ₋1x/2 ₊ 1/2
y ₋ 3 = ₋x ₊ 1/2
2y ₋ 6 = ₋x ₊ 1
2y ₊ x ₋ 6 ₋ 1 = 0
2y ₊ x ₋ 7 = 0
2y ₊ x = 7
x ₊ 2y = 7
which is in the form ax ₊ by = c
Hence we derived the equation of the line as x ₊ 2y = 7 which is in the form of ax ₊ by = c.
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