Why are two lines with the same y intercept are perpendicular?
Answers
If you want to know why 2 lines are perpendicular or parallel you have to look @ the slope
Perpendicular: The slope is the negative reciprocal of the slope of the original equation (other line slope) what this means it that you flip the numerator and denominator and make it negative (or positive, depending if it's already negative)
Parallel: The slope is the same (see 2nd picture as an EX).
Two lines with the same y-intercept are perpendicular because they are only perpendicular if their slopes are the reciprocals of each other's negative values.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The standard form of the lines are:
y = mx + c
Here m is the slope and c is the y-intercept of the line
mM = -1
The M is the slope of the second line which is perpendicular to the first one.
y = Mx + c (with the same y-intercept)
Thus, two lines with the same y-intercept are perpendicular because they are only perpendicular if their slopes are the reciprocals of each other's negative values.
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Related Questions
The lengths of the base and legs of an isosceles triangle are in the ratio of 3;2 the perimeter of triangles is 105 find the length of the base
Answers
Anyhow,
The sides of isoceles triangle are leg, leg , base
each leg =2
while the base =4
To find the number you have to divide the ratio by total and multiply into 105
The base
3/7 × 105 = 45
The leg
2/7 × 105 = 30
Therefore, The length of the base = 45 cm
The sum of two numbers is 50 . the smaller number is 12 less than the larger number. what are the numbers?
Answers
31
50/2 is 25. since one # is 12 less than the other, we add and subtract 6 which is half of 12.
The two numbers are 31 and 19, where 31 is the larger number and 19 is the smaller number which is 12 less than the larger number.
The sum of two numbers is given to be 50, and the question states that the smaller number is 12 less than the larger number. To find these numbers, let's denote the larger number as x and the smaller number as x - 12. According to the problem, the sum of these two numbers is 50, so we can write the equation:
x + (x - 12) = 50
Simplifying the equation gives us:
2x - 12 = 50
Adding 12 to both sides gives us:
2x = 62
Dividing both sides by 2 gives us:
x = 31
Now that we know the larger number is 31, we can find the smaller number by subtracting 12:
x - 12 = 31 - 12
x - 12 = 19
Therefore, the two numbers are 31 and 19.
What would be equation would be perpendicular to p(1,3), y = 2x - 1?
Answers
y=2.×-1
The vertex form of the equation of a parabola is x=8(y-1)^2-15. What is the standard form of the equation?
Answers
Standard form looks like this, x^2 -6x + 8, or y^2 - 6y + 8
To convert your equation into standard form all we have to do is expand it fully:
x = 8(y-1)^2 - 15
x = 8(y-1)(y-1) - 15
x = 8(y^2 -2y + 1) - 15
x = 8y^2 -16y + 8 - 15
x = 8y^2 -16y - 7
The standard form of the equation is:
[tex]x=8y^2-16y-7[/tex]
Step-by-step explanation:We know that the standard form of a quadratic equation is given by the expression:
[tex]x=ay^2+by+c[/tex]
where a,b and c are real numbers.
and a≠0
Here we are given the vertex form of the equation of a parabola by:
[tex]x=8(y-1)^2-15[/tex]
Now, on expanding the parentheses term by using the formula:
[tex](a-b)^2=a^2+b^2-2ab[/tex]
Here a=y and b= 1
Hence, we have:
[tex]x=8(y^2+1-2y)-15\\\\i.e.\\\\x=8\times y^2+8\times 1-2y\times 8-15\\\\i.e.\\\\x=8y^2+8-16y-15\\\\i.e.\\\\x=8y^2-16y+8-15[/tex]
( Since, in the last step we combined the constant term i.e. 8 and -15 )
Hence, we get the standard form of the equation as:
[tex]x=8y^2-16y-7[/tex]
Which equation represents a line which is parallel to the line y=4x-8y=4x−8?
Answers
The equation that makes it parallel to the line is y=4x+[Any number]
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Answers
Find the median of the data: 206, 194, 198, 172, 190
Answers
For what values of x and y must each figure be a parallelogram?
Answers
6x = 360
x = 60
2y + 4y = 180
6y = 180
y = 30
The required values are x = 60 and y = 30 for the given parallelogram.
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal. A parallelogram is a square and a rhombus is a square.
The parallelogram is represented in the given figure
A parallelogram has two pairs of adjacent sides that are congruent.
As per the given figure, we have
x + 5x - 180 = 180
6x = 360
x = 360/6
Apply the division operation, and we get
x = 60
2y + 4y = 180
Apply the addition operation, and we get
6y = 180
y = 180/6
y = 30
Thus, the required values are x = 60 and y = 30
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Solve for t. −5t≥65
a. t≥13
b. t≤13
c. t≤−13
d. t≥−13
Answers
−t≥13
Multiply - throughout and change direction of arrow
c. t≤−13
Mike and Kate plan to save money for their wedding over a 20 month period. They will need to save $8,000 to help pay for the wedding. They set aside the same amount each month. After a year they saved $4,000. Mike and Kate know they must adjust their plan in order to meet their goal, so they came up with the following options: Option A: Stay with saving the same amount they've been saving each month but postpone the wedding 2 months. Option B: Increase the amount of money they save each month by $80 from what they've been saving. Which of the following is a true statement? a. Only option A will allow them to meet their goal. b. Only option B will allow them to meet their goal. c. Both options A and B will allow them to meet their goal. d. Neither option A nor option B will allow them to meet their goal.
Answers
I would say b.
Hope this helps!
What can be used as a reason in a two-column proof?
Select each correct answer.
a true premise
a conjecture
a definition
a theorem
Answers
Answer :- A definition and a theorem can be used as a reason in a two-column proof.
Explanation:-
A two column proof is assembled into statement and reason columns, where each statement should have verified reason. The reason in a two column proof are usually given information, vocabulary definitions, postulates and previously proved theorems.
Therefore, from the given options a definition and a theorem can be used as a reason in a two-column proof.
A definition and a theorem can be used as a reason in a two-column proof.
Further explanation:
Given:
The options are as follows,
(a). A true premise
(b). A conjecture
(c). A definition
(d). A theorem
Explanation:
True premise is an assumption about something is true. It is not proved.
Conjecture is a statement that has not been proved.
Definition is a statement which tells us the meaning of the word.
Theorem is a statement that has been proved.
A definition and a theorem can be used as a reason in a two-column proof.
Conjecture and true premise cannot be used as a reason in a two-column proof as they are not proved.
Option (a) is not correct as a true premise cannot be used as reason in two-column proof.
Option (b) is not correct as a conjecture cannot be used as reason in two-column proof.
Option (c) is correct can be used as a reason in a two-column proof.
Option (d) is correct can be used as a reason in a two-column proof.
Learn more:
1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Simple interest
Keywords: two-column proof, a true premise, a conjecture, a definition, a theorem, correct answer, reason.
Find the dimensions of a right circular cylindrical can with both a top and a bottom that holds 5832 cubic cm and is constructed with the least amount of material possible.
Answers
The dimensions of a right circular cylindrical can that holds 5832 cubic cm and uses the least amount of material are a radius of approximately 10.614 cm and a height of approximately 16.526 cm.
Explanation:The question asks for the dimensions of a right circular cylindrical can that holds 5832 cubic cm of liquid and is designed to use the least amount of material. This scenario fits into the realm of mathematical optimization. Here, we’re being asked to identify dimensions that minimize the surface area of the cylinder while holding a fixed volume. This kind of problem is typically addressed using calculus.
The volume V of a cylinder is given by the formula V = πr²h where r is the cylinder radius and h is the cylinder height. The surface area A of a cylinder closed at both ends is given by A = 2πrh + 2πr².
From the volume equation, we can express h in terms of V and r, h = V/πr². Substituting this into the surface area equation yields: A = 2πr(V/πr²) + 2πr² = 2V/r + 2πr².
To find the radius that minimizes the surface area, we would set the derivative of the surface area with respect to r equal to zero and solve for r. After these calculations, we find that r = (V/(2π))^(1/3). For V = 5832 cubic cm, this yields r ≈ 10.614 cm.
Substitute r ≈ 10.614 cm back into the equation h = V/πr² to find h ≈ 16.526 cm. So, the dimensions of the can that minimizes the material used are radius 10.614 cm and height 16.526 cm.
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To find the dimensions of the cylindrical can that holds a specific volume and is made from the least material, utilize the volume and surface area formulas for a cylinder. Using calculus, find the radius that minimizes the surface area, then find the corresponding height.
Explanation:This problem is a classic calculus optimization problem. The volume of the cylindrical can is given by the formula V = πr²h, where r is the radius and h is the height of the cylinder. To minimize the amount of material used in constructing the can, we need to minimize the surface area, given by the formula [tex]A = 2\pi rh + 2\pi r^2[/tex] (which includes both top and bottom of the can).
From the volume formula, we can express h as h = V/πr² = 5832/πr². Substituting this value into the surface area equation, we get A = [tex]2\pi r(5832/\pi r^2) + 2\pi r^2 = 11664/r + 2\pi r^2.[/tex] Differentiating this equation with respect to r and setting the derivative equal to zero, will provide the radius that minimizes the material used. The height can be obtained by substituting this radius value back into the equation h = 5832/πr².
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find m<p the diagram is not to scale
Answers
Determine the vertex point, domain, and range of the following function
y = -|x| + 2
Answers
Now we need to see each change done to it.
y = -|x| makes every y-coordinate its additive inverse, so y = -|x| still has the vertex at (0, 0), but now is turned downward.
y = -|x| + 2 can be changed to
y - 2 = -|x|
Now y was replaced by y - 2. When y is replaced by y - k, the graph shifts vertically k units. In this case, k = 2, so the graph shifts up 2 units. The vertex is now at (0, 2).
Vertex: (0, 2)
Domain: all real numbers
Range: all real numbers less than or equal to 2.
Two classrooms are sharing seven packages of unit cubes if the packages are split evenly how many packages with each classroom receive
Answers
This means we need to divide the seven packages in half (two pieces).
7packages ÷ 2 classrooms = 7/2 = 3.5 packages per class
(three and a half packages)
belinda has twice as many nickels as dimes. how many of each does she have if they total
A) 80 cents
B) $1.20
Show all work using an equation
Answers
.40+ .40=.80
How many 5 pound bags of apples can be made from 400 apples each weighing 1/4 pound?
Answers
Answer:
You can make 20 - 5 pound bags
Step-by-step explanation:
You first find the number of total pounds that the 400 applying ratios :
400 apples * ¼ pound / 1 apple = 100 pounds by simplifying units
Then we find the number of bags as:
100 pounds* (1 bag/5 pounds ) = 20 bags by simplifying units
So the final answer is 20 bags for this problems by using ratios
what is the estimate 5% of 59
Answers
hope this helps
Regina took out a 30-year loan for $190,000 at 4.5% interest, compounded monthly. If her monthly payment on the loan is $962.70, and if $712.50 of her first payment went toward interest, how much of her second payment went toward interest?
A.$962.70
B.$712.50
C.Less than $712.50
D.More than $712.50 but less than $962.70
please please please help
Answers
Answer:
C.Less than $712.50
Step-by-step explanation:
Given details are :
Loan amount = $190,000
Rate = 4.5% or 0.045 compounded monthly.
Time = [tex]30\times12=360[/tex] months
Monthly payments are = $962.70
First month interest = $712.50
I have calculated this using excel sheet and the answer is - C.Less than $712.50 .
Please find attached the excel sheet to see the working. You can see the highlighted interest that is less than first month interest.
Answer:Less than $712.50
Step-by-step explanation:
Two–thirds of the children in the fourth–grade class are girls. if there are 18 girls, what is the total number of children in the class?
Answers
If there are 18 girls that mean half this number is the boys which is 9.
Therefore, total number is 27.
Find the value of x. Then find the measure of each labeled angle
Answers
2x - 32 = 180
2x = 212
x = 106
x - 32 = 106 - 32 = 74
the other 2 angles = 90
Answer:
x=107
[tex]x-34=107-34=73[/tex]
Step-by-step explanation:
Sum of angles in a quadrilateral is 360 degree
right angle is 90 degree
[tex]90 +90+x+x-34= 360[/tex]
[tex]180+x+x-34=360[/tex]
subtract 180 from both sides
[tex]x+x-34=180[/tex]
[tex]2x-34=180[/tex]
add 34 on both sides
[tex]2x=214[/tex]
divide by 2 on both sides
x=107
[tex]x-34=107-34=73[/tex]
PLEASE HELP ME WITH THIS! WILL MARK BRILLIANT!!! ✨✨
Answers
Answer:
b. linear; y +2 = -5/4(x +9)
Step-by-step explanation:
From the first line of the table to the second, we have ...
slope = (change in y)/(change in x) = (-7-(-2))/(-5-(-9)) = -5/4
Only one equation shows a slope of -5/4: the second one.
__
We know the relation is linear because the same slope can be computed from any pair of lines of the table. In particular, from one row to the next, x changes by the constant value +4 and y changes by the constant value -5.
The solutions to the inequality y<-x+1 are shaded on the graph. Which point is a solution?
Answers
B) (3, –2)
Explanation:
The inequality is y ≤ –x + 1
There are two ways to do this. You can try the four options by seeing where they lie on the graph, or by inputting them into the inequality and seeing if they check out. I am going to do a bit of both.
I know that the solution cannot have two positive coordinates because the first quadrant is not part of the solution, so I won't guess A or C.
I'll try (3, –2) (which is option B).
On the graph, (3, –2) is on the line, which means it is part of the solution because the line is solid and the inequality is a greater than or equal to sign.
Try it in the inequality:
y ≤ –x + 1
–2 ≤ –3 + 1
–2 ≤ –2 yes this checks out.
Answer:
the answer is B
Step-by-step explanation:
A segment with endpoints X Left parenthesis negative 6 comma 2 right parenthesis and Y Left parenthesis negative 1 comma negative 3 right parenthesis is rotated 90º about the origin. What are the coordinates of X Prime and Y Prime?
A. X prime Left parenthesis negative 1 comma negative 3 right parenthesis and Y prime Left parenthesis negative 6 comma 2 right parenthesis.
B. X prime Left parenthesis 2 comma 6 right parenthesis and Y prime Left parenthesis negative 3 comma 1 right parenthesis.
C. X prime Left parenthesis negative 2 comma negative 6 right parenthesis and Y prime Left parenthesis 3 comma negative 1 right parenthesis
D. X prime Left parenthesis 6 comma negative 2 right parenthesis and Y prime Left parenthesis 1 comma 3 right parenthesis
Answers
Answer:
The correct answer is C.
Step-by-step explanation:
This can be done using complex numbers and its relations with plane geometry. The endpoints of the segment are X(-6,2) and Y(-1,-3). These points can be seen as complex numbers, just recall the geometric interpretation of complex numbers.
So, the complex counterpart of [tex]X(-6,2) is x=-6+2i[/tex], and the complex counterpart of [tex]Y(-1,-3) = -1-3i[/tex]. Moreover, a rotation about the origin has an interpretation as multiplication by a complex number of modulus 1. In this particular case, a rotation of 90 degrees is equivalent to multiply by the complex unit: [tex]i=\sqrt{-1}[/tex].
Then,
[tex] x' = (-6+2i)\times i = -2-6i[/tex] which gives the point [tex]X'(-2,-6)[/tex]
[tex] x' = (-1-3i)\times i = 3-1i[/tex] which gives the point [tex]Y'(2,-1)[/tex].
The other option is to use a software to make geometrical constructions as Geogebra. Bellow there is an image attached made with Geogebra with the solution of the exercise.
Today a car is valued at $42000. The value is expected to decrease at a rate of 8% each year. What is the value of the car expected to be 6 years from now?
Answers
A=p (1-r)^t
A future value?
P current value 42000
R rate of decreases 0.08
T time 6 years
A=42,000×(1−0.08)^(6)
A=42000 (0.92)^6
A=25,466.91 round your answer to get 25467
Hope it helps!
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. Which property justifies this statement?
If x = −2, then 5x = −10.
A. Symmetric Property of Equality
B. Multiplication Property of Equality
C. Subtraction Property of Equality
D. Transitive Property of Equality
2. Drag a statement or reason to each box to complete the proof.
If 3(x−4)=x+4, then x=8.
Statement: Reason:
1. 3(x−4)=x+4 ----> Given
2. 3x−12=x+4 ----> ________
3. 3x−12+12=x+4+12 ----> ________
4. 3x=x+16 ----> Simplifying
5. 3x−x=x+16−x ----> ________
6. 2x=16 ----> Simplifying
7. 2x2=162 ----> ________
8. x=8 ----> Simplifying
A. Subtraction Property of Equality
B. Distributive Property
C. Addition Property of Equality
D. Division Property of Equality
Answers
This is irrelevant, but was THAT many exclamation points necessary?
Anyway, these aren't that hard, you gotta just use your brain a bit. These problems use a bit of simple common sense if you put 2-and-2 together and look into it. Look for signs and just use your head, it's hard to explain but just try. ^^
wilson jarred 45 liters of jam after 5 days. how much jam did wilson jar if he spent 7 days making jam? solve using unit rates.
Answers
x/7 = 9
x= 63 jams a day
Hope this helps!
Select the correct product.
(2x + 9)(x + 1)
2x^2 + 11x + 9
3x^2 + 11x + 9
2x^2 - 7x + 9
2x^2 + 11x + 10
Answers
F = First
O = Outer
I = Inner
L = Last
Step 1: Multiply the First terms of each binomial
2x * 2 = 2x^2
Step 2: Multiply the Outer terms
2x * 1 = 2x
Step 3: Multiply the Inner terms
9 * x = 9x
Step 4: Multiply the Last terms of each expression
9 * 1 = 9
Step 5: List the results of FOIL in order
2x^2 + 2x + 9x + 9
Step 6: Combine like terms to get your final answer
2x^2 + 11x + 9
If there is 20 students and 20 chairs how many way for a student to sit
Answers
Answer:
40. Just add 20+20 and you will get your answer.
Calculate δe, if q= 0.764 kj and w= -830 j . express your answer using two significant figures.
Answers
When calculating the change in internal energy (δe) using the First Law of Thermodynamics, first convert all units to the same kind, then apply the formula δe = q + w. In this case, the answer is -0.07 kJ or -70 J.
Explanation:This is a Chemistry question involving the calculation of change in internal energy (δe) using the First Law of Thermodynamics, which states that the change in internal energy is equal to heat (q) added to the system plus the work (w) done on the system. Specifically, the formula is: δe = q + w.
In this case, you have a value for heat (q) of 0.764 kJ and a value for work (w) of -830 J, but these values are not in the same units. In order to add them, you need to convert work (w) to kJ:-830 J * (1 kJ / 1000 J) = -0.83 kJ.
Now you can put these values into the formula: δe = 0.764 kJ + (-0.83 kJ) = -0.07 kJ, which may also be written as -70 J.Therefore, using two significant figures, the answer is -0.07 kJ or -70 J.
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The change in internal energy (ΔE) is -0.07 kJ. Since ΔE is negative, this indicates that the system has lost internal energy.
Given:
q = 0.764 kJ
w = -830 J
We can calculate the change in internal energy (ΔE) using the following equation:
ΔE = q + w
where:
ΔE is the change in internal energy (kJ)
q is the heat absorbed by the system (kJ)
w is the work done by the system (kJ)
First, convert the work from joules to kilojoules:
w = -830 J * (1 kJ/1000 J) = -0.830 kJ
Now, plug in the values for q and w to calculate ΔE:
ΔE = 0.764 kJ + (-0.830 kJ) = -0.066 kJ
Round the answer to two significant figures:
ΔE ≈ -0.07 kJ
Therefore, the change in internal energy (ΔE) is -0.07 kJ. Since ΔE is negative, this indicates that the system has lost internal energy.