Line AB and BC for a right angle at point B. If A(-3,4) and B(4,4) what is the equation of line BC?
Answers
x=4.
Explanation:
The slope of line AB is given by the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the coordinates of A and B, we have
[tex]m=\frac{4-4}{4--3}=\frac{0}{7}=0[/tex]
Perpendicular lines have slopes that are negative reciprocals. Since the slope of AB is 0/7, the reciprocal is 7/0, which is undefined.
Any line with an undefined slope is a vertical line. This will be a vertical line that passes through point B.
Vertical lines have the equation x=c, where c is a constant; since it runs through B, which has coordinates (4, 4), this means the equation is x=4.
Answer: The required equation of line BC is [tex] x=4.[/tex]
Step-by-step explanation: As shown in the attached figure, lines AB and BC meet at right angle at the point B. The co-ordinates of point A and B are (-3, 4) and B(4, 4).
We are to find the equation of line BC.
We know that the slope of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of the line AB will be
[tex]m=\dfrac{4-4}{4-(-3)}\\\\\Rightarrow m=0.[/tex]
Therefore, the equation of the line AB is
[tex]y-4=m(x-4)\\\\\Rightarrow y-4=0\\\\\Rightarrow y=4.[/tex]
Since y = constant is the equation of a line parallel to X-axis, so its perpendicular line will be parallel to Y-axis.
So, its equation will be of the form
x = constant.
Since the line BC is perpendicular to AB passing through the point (4, 4), so we must have
[tex]x=4.[/tex]
Thus, the required equation of line BC is [tex] x=4.[/tex]
Related Questions
EASY 5POINT MATH QUESTION PLEASE SOLVE
use the relationship between the angles in the figure to answer the question
which equation can be used by find the value of x?
drag and drop the equation into the box
Answers
Answer: x = 180 - (31 + 40)
Hope this helps!
~VERNEX
The hypotenuse of a 45°-45°-90° triangle measures 7√2 units.
What is the length of one leg of the triangle?
A. 7 units
B. 7√2 units
C. 14 units
D. 14√2 units
Answers
Answer:
Option A is correct.
Step-by-step explanation:
Given:
Angle of the right angles triangle are 45° , 45°, 90°
Length of the Hypotenuse = 7√2 units.
To find: Length of the one leg of the triangle.
Since two angles of the triangles are equal.
⇒ Opposite sides to equal angles are also equal.
We have Isosceles right angled triangle.
⇒ both legs are equal.
Let x be the length of the leg
using Pythagoras theorem,
(7√2)² = x² + x²
2x² = 49 × 2
x² = 49
x = ±7
Length cannot be negative so, x = 7
Therefore, Option A is correct.
which of the following expressions is equal to the height, h, of this triangle?
Answers
[tex]25 \cos(56) [/tex]
Determine if the graph of r = 4cos 5θ is symmetric about the x-axis, the y-axis, or the origin.
Answers
Answer:
y-axisStep-by-step explanation:
The function graph is symmetric about
- the y-axis when it is an even function
- the origin when it is an odd function.
A symmetrical graph about the x-axis is not a function graph.
f(x) is an even if and only if f(-x) = f(x).
f(x) is an odd if and only if f(-x) = -f(x).
We have the function r(θ) = 4cos(5θ)
(olny symmetry about the y-axis or about the origin)
Check r(-θ):
r(-θ) = 4cos(5(-θ)) = 4cos(-5θ) = 4cos(5θ)
used cos(-x) = cos x
We have r(-θ) = r(θ). Therefore the graph of r(θ) is symmetric about the y-axis.
Answer:
x-axis
Step-by-step explanation:
if r%28theta%29+=+r%28-theta%29.
Since 4cos%285%2Atheta%29+=+4cos%28-5%2Atheta%29, the graph is symmetric wrt the x-axis.
The graph is symmetric wrt the y-axis if r%28theta%29+=+r%28pi-theta%29.
Since 4cos%285%2Atheta%29+%3C%3E+4cos%285%2A%28pi+-+theta%29%29+=+-4cos%285%2Atheta%29+, the graph is not symmetric wrt the y-axis.
The graph is symmetric wrt the y-axis if r%28theta%29+=+r%28pi%2Btheta%29.
Since 4cos%285%2Atheta%29+%3C%3E+4cos%285%2A%28pi+%2B+theta%29%29+=+-4cos%285%2Atheta%29+, the graph is not symmetric wrt the origin.
Factor the polynomial completely. 4x3 – 12x2 + 7x – 21 4x2(x – 3) + 7(x – 3) Which is the completely factored polynomial? 4x2(x + 4) 3x2(x – 3) (4x2 – 7)(x + 3) (4x2 + 7)(x – 3)
Answers
factor: 4x²(x-3)+7(x-3)
factor again: (x-3)(4x²+7)
The correct answer for this problem would be D. (4x^2 + 7)(x – 3) .
Hope this helps and clears up any confusion!
Which graph shows a line that is perpendicular to line AB?
Answers
Algebra 2 help?
5. A construction explosion has an intensity I of 1.25 x 10–4 W/m2. Find the loudness of the sound in decibels if W/m2. Round to the nearest tenth. (1 point)
81 decibels
161 decibels
82.2 decibels
12.5 decibels
The example question in the textbook is totally different so I'm not sure how to do this. I tried to make the equation and then got confused. An explanation would be great! Thanks
Answers
To solve this, we will use the formula : dB = 10 x log (Isig/Iref)
terms will be:dB= decibels,
Isig = signal's intensity
Iref= softest sound's intensity which is 10^-12.
So the solutions is,dB = 10 x log (1.25 x 10–4 / 10^-12 )
= 80.97 decibels
=81 decibels
Answer:
1. B) logb(q^2t^8)
2. D) None of these (it is actually log (x^4/(x+2)^6) :D)
3. B) log5(7)+5log5(a)
4. C) 6.209
5. A) 81 decibels
Step-by-step explanation:
trust me bro
The Thrill amusement park charges an entry fee of $40 and an additional $5 per ride, x. The Splash water park charges an entry fee of $60 and an additional $3 per ride, x. Based on this information, which system of equations could be used to determine the solution where the cost per ride of the two amusement parks, y, is the same?
Answers
The costs per ride for Thrill and Splash amusement parks can be represented by the equations y = 40 + 5x and y = 60 + 3x respectively. Equating these will give us the number of rides where the costs at both parks will be the same.
Explanation:The cost of visiting each park can be represented as a linear equation. For Thrill amusement park it can be written as y = 40 + 5x, where y is the total cost, 40 is the entry fee and 5x represents the cumulative cost of the rides, with x being the number of rides. For Splash Water Park, the equation is y = 60 + 3x, where 60 is the entry fee and 3x is the cost of the individual rides. To find out when the costs per ride at the two parks will be the same, we solve the system of equations by setting the two equations equal to each other: 40 + 5x = 60 + 3x.
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When triangle ABC is rotated about side AB, what figure is formed?
cylinder
prism
pyramid
cone
Answers
Answer:
Cone
Step-by-step explanation:
We are given that a triangle ABC .
We have to find that what shape is formed when a triangle ABC is rotated about side AB.
A given triangle ABC is a right triangle.
When we rotate the figure about side AB then the figure will be cone .The side AB will be height of cone and side AC will be radius of cone.
Hence, when a triangle ABC is rotated about side AB, the cone is formed.
Answer: Cone
Find the zeros of the polynomial function.
f(x) = x^2 - 12x + 20
I THINK THE ANSWER IS A 2,10
a. 2, 10
b. - 4, -5
c. -2, -10
d. 4, 5
Answers
[tex]given \: equation \: is \: , \\ \\ {x}^{2} - 12x + 20 = 0 \\ \\ using \: quadratic \: formula \: , \\ \\ x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \: \: \: \: = \frac{ - ( - 12) + \sqrt{ { (- 12)}^{2} - 4(1)(20) } }{2(1)} \\ \\ x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \: \: \: \: = \frac{ - ( - 12) - \sqrt{ { (- 12)}^{2} - 4(1)(20) } }{2(1)} \\ \\ x = \frac{12 + 8}{2} \: \: \: \: \: or \: \: \: \: x = \frac{12 - 8}{2} \\ \\ x = 10 \: \: \: \: \: or \: \: \: \: \: x = 2 \: \: \: ans.[/tex]
How many rays intersect at point O
1. 5
2. 4
3. 6
4. 3
Answers
We have then that the lines that contain this point are:
EC
AD
BO
We note that three lines contain point O.
Therefore, three lines intersect at the same point.
Answer:
4. 3
The Hamden board of education wants to know how the community feels about building a new media center for the middle school. They called every tenth person on the registration list of 7,300 voters until they had called a total of 40 voters. Which of the following are true of the sample of 40 voters? Check all that apply.
The sample is not randomly chosen.
The sample should be larger to give more reliable information.
The sample size is too large to make inferences.
The sample size is too small to represent the population.
The sample size is too small and will show larger variation.
The sample is invalid because it randomly chooses voters.
The sample size is too small and can lead to false inferences.
Answers
The sample is not randomly chosen (FALSE)
Given that the statement doesn't tell us anything about the way they choose the sample, it is reasonable to conclude that this is a randomly chosen. They called every tenth person on the registration list until the number of people was 40.
The sample should be larger to give more reliable information (TRUE)
You did not have to use mathematics to determine that you would need more information to get a conclusion. You must increase the sample, that is, the sample must be larger to give a reliable information.
The sample size is too large to make inferences (False)
This is explained in the previous item. If the sample should be lager is because the size is not too large.
The sample size is too small to represent the population (TRUE
This is true because 40 voters represent barely 0.5% of the entire list. This list has 7300 voters, so getting the conclusion from this sample doesn't provide with a strong conclusion.
The sample size is too small and will show larger variation. (FALSE)
Although the sample size is too small, the sample size not necessarily will show variation. In fact, it is possible that it does not show any variation and most of the people feel well about building a new media center for the middle school but it doesn't mean that the whole community does.
The sample is invalid because it randomly chooses voters. (FALSE)
It is false because in probability studies the sample is chosen randomly, so you get conclusions about the whole population always taking samples that represent the population as a whole.
The sample size is too small and can lead to false inferences (TRUE)
You can get false conclusions given that the sample size is too small. It's important to note that the sample size supports the conclusion of the study, so the sample must increase to have a reliable study.
The sampling method used by the Hamden board of education was systematic, not random, and the sample size of 40 voters out of a population of 7,300 is too small to produce reliable conclusions regarding the community's opinion about building a new media center.
Explanation:The quality of conclusions drawn from opinion polls largely depends on the methods used to choose a sample and the sample size. When the Hamden board of education sampled every tenth person from the registration list of 7,300 voters to reach 40 voters, they applied a systematic sampling method, as opposed to a truly random sample. While systematic sampling can be used as an approximation of random sampling, this method still poses a risk of introducing bias if there are hidden patterns in the voter registration list.
The sample size is indeed critical for the reliability of the poll. In this case, surveying only 40 voters out of 7,300 is too small to capture the diverse opinions of the entire voter population, which may lead to false inferences and less confidence in the results. For public opinion polls, especially on matters like building a new media center, a larger sample would provide more reliable information and reduce the potential variation that can arise from a smaller sample. Industry standards suggest varying sizes that can balance the accuracy and cost-effectiveness, often ranging from 500 to 2,500 respondents or more depending on the desired level of accuracy.
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Which rectangle if translated 12 units down and 7 units right will result in rectangle E?
A) Rectangle A
B) Rectangle B
C) Rectangle C
D) Rectangle D
Answers
If we looked at rectangle 'E' and moved it to the left by 7 units (every unit = 1 square on the grid), we would arrive at a point. From then, we can move upwards 12 units and arrive at rectangle 'D'.
Answer:
option D
Step-by-step explanation:
translated 12 units down and 7 units right
(x,y)-> (x+7, y-12)
Lets pick a point on Rectangle A and apply the translation
(-11,4) -> (-11+7, 4-12) ->(-4, -8) That is not in our Rectangle E
Lets pick a point on Rectangle B and apply the translation
(-7,1) -> (-7+7, 1-12) ->(0, -11) That is not in our Rectangle E
Lets pick a point on Rectangle C and apply the translation
(-5,5) -> (-5+7, 5-12) ->(2, -7) That is not in our Rectangle E
Lets pick a point on Rectangle D and apply the translation
(-3,1) -> (-3+7, 1-12) ->(4, -11) That is in our Rectangle E
So option D is correct
The length of a rectangle is 7mm longer than its width. It’s perimeter is more than 62mm. Let W equal the width of the rectangle, write an inequality and solve it
Answers
2(l + w) = p
Since we know the perimeter (p) is greater than 62 we can say:
2(l + w) > 62
It is also given that the length is 7 mm longer than the width, so we know the value of the length in terms of w (the width).
w = w
l = w + 7
Substitute l with (w + 7) into the equation:
2[(w + 7) + w] > 62
Now combine like terms in the parentheses
2(2w + 7) >62
Distribute the 2 into the terms in the parentheses
4w + 14 > 62
Subtract both sides by 14
4w > 62 - 14
Combine like terms
4w > 48
Divide both sides by 4
w > 48
Final answer: w > 48
Hope this helps!
HOW would I go about figuring this out? I need explanation not just answer
Answers
3/4 = x/24
Cross multiply:
4x = 72
Divide by 4:
x = 18
There were 18 clarinets in the music room.
Hope this helps :)
Find an ordered pair (x,y) that is a solution to the equation.
3x-y=3
Answers
One example is (1, 0).
We can see this will work by first selecting any value for x. We'll use the 1 that I gave.
3x - y = 3.
Now sub the value in.
3(1) - y = 3.
Multiply.
3 - y = 3.
Solve for y.
y = 0.
This gives you the ordered pair (1, 0).
Answer: The required ordered pair is (1, 0).
Step-by-step explanation: We are given to find an ordered pair (x, y) that is a solution to the following equation:
[tex]3x-y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find an ordered pair, we should either take a value of x and find the corresponding value of y,
or,
we should take a value of y and find the corresponding value of x.
Let us consider that
x = 1.
Then, from equation (i), we get
[tex]3\times 1-y=3\\\\\Rightarrow 3-y=3\\\\\Rightarrow y=3-3\\\\\Rightarrow y=0.[/tex]
Thus, the required ordered pair is (1, 0).
For every pound a company spends on advertising, it spends £0.26 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.
Answers
If we use the values in the problem, we have a ratio of 1:0.26. The problem is that we have a decimal value and we should use whole numbers.
Start by multiplying each value by 100 to eliminate the decimal.
We have 100:26.
Now, each value contains a factor of 2. So divide by 2 and we get 50:13.
Answer:
50:13
Step-by-step explanation:
25 POINTS to answer question!
Answers
This is because the line would have to cross through -4 on the y-axis on the graph. "A" is the only answer that has a line through -4.
PLEASE HELP
BRAINLIEST AVAILABLE THX
PLEASE ASSIST ME N TRY TO HELP ME
Answers
hope i helped
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Find the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length.
Answers
[tex] {x}^{2} = {1}^{2} + {1}^{2} \\ {x}^{2} = 1 + 1 \\ {x}^{2} = 2 \\ x = \sqrt{2} = 1.41[/tex]
Answer:
The length of the hypotenuse of the isosceles right triangle with leg of length unit is:
√2 units.
Step-by-step explanation:
Let a and b denote the leg of a right triangle and c denote the hypotenuse of the right triangle.
Now we apply the Pythagorean Theorem as:
[tex]c^2=a^2+b^2[/tex]
Now as triangle is isosceles.
Hence, a=b=1 unit
[tex]c^2=1^2+1^2\\\\c^2=2\\\\c=\sqrt{2}[/tex]
Hence, the length of the hypotenuse is:
√2 units.
help please asap! BRAINLIESTTTTT
2 QUESTIONS!
Answers
2nd one Is the vertex is the highest point and would the the max amount of larvae produced. SO this answer is B
what is the answer to 2+2*8
Answers
multiplication is first (in this case) and then addition
2 x 8 = 16
16 + 2 = 18
18 is your answer
hope this helps
Which of the following choices represents the expanded form of the number 38,072?
30,000+800+70+2
30,000+8,000+70+2
30,000+8,000+700+2
3,000+800+70+2
Answers
Final answer:
The expanded form of 38,072 is 30,000 + 8,000 + 70 + 2, where each term represents the digit's value as a product of its place value.
Explanation:
The expanded form of the number 38,072 is written by separating each digit according to its place value and expressing it as the digit multiplied by the power of ten that represents its position. Therefore, the correct expanded form is:
30,000 + 8,000 + 70 + 2
To understand this, we can consider the place value of each digit in the number 38,072. The '3' is in the ten-thousands place, so it is 3 times 10,000, which is 30,000. The '8' is in the thousands place, so it is 8 times 1,000, which is 8,000. The '0' stands for no hundreds, so we skip it. The '7' is in the tens place, so it is 7 times 10, which is 70. Finally, the '2' is in the ones place, which is just 2.
which descriptions from the list below accurately describe the relationship between QRS and TUV
Answers
hope it helps
Answer:
A. Similar
Step-by-step explanation:
We are given the measurements of ΔQRS and ΔTUV as,
QR = RS = 4, QS = 2 with ∠Q = ∠S = 76°, ∠R = 28°
TU = UV = 12, TV = 6 with ∠T = ∠V = 76°, ∠U = 28°
Now, we see that,
These triangles have different side lengths. So, option C i.e. same sides is not correct.
Also, they are different in size. So, option D i.e. same size is not correct.
Since, they do not have same size, they cannot overlap each other. Thus, are not congruent. So, option B is also not correct.
Thus, we see that from SAS Similarity and the measurements,
QR = RS = 4 and ∠R = 28°
TU = UV = 12 and ∠U = 28°
Both the triangles are similar to each other.
Hence, option A is correct.
what is the value of x to the nearest tenth?
Answers
x = 2.546
rounded to nearest tenth x = 2.5
The quality control manager of a peanut butter manufacturing plant want to ensure the quality of the peanut butter in the jars coming down the assembly line.describe a representative sampling method she could use?
Answers
Final answer:
The quality control manager can use a representative sampling method to test jars of peanut butter for quality, with tests such as total plate count and adherence to quality control protocols and good measurement practices for reliable results.
Explanation:
A quality control manager at a peanut butter manufacturing plant can ensure the quality of peanut butter jars using a representative sampling method. This involves selecting jars at regular intervals from the assembly line, and then conducting tests such as total plate count to measure potential bacterial contamination. For accurate quality control, the process should follow good measurement practices and a standardized quality control protocol that includes recording and analyzing the data and evaluating any deviations from set specifications.
The personnel responsible can reject any sample or batch that does not meet the required standards. For continuous quality assurance, statistical process control methods like mean, standard deviation, and coefficient of variation can be utilized to monitor ongoing production. Furthermore, post-production specifications will determine whether to release or reject the final product. Appropriate documentation and adherence to standard operations procedures (SOPs) are crucial throughout the process, maintaining a systematic approach to product quality.
Consider isosceles ΔXYZ.
What is the value of n?
What is the measure of leg XY?
ft
What is the measure of leg XZ?
ft
Answers
1) An Isosceles triangle has three sides, in which two sides are of the same length and the third has a different length. It has two angles of the same value and a third angle with a different value, as well.
In the figure is shown that angles Y and Z are the same, then the sides of this angles must be of the same length. This means that:
XY=XZ
(9n+12)ft=(15n-6)ft
From this equation we have to find n:
9n-15n=-6-12
-6n=-18
[tex]n=\frac{-18}{-6}[/tex]
n=3
2) The measure of the leg XY in ft
XY=(9n+12)ft
Substitute the value of n calculated in the first question:
XY=(9(3)+12)ft
XY=39 ft
3) The measure of the leg XZ in ft
XZ=(15n-6)ft
Substitute the value of n calculated in the first question:
XZ=(15(3)-6)ft
XZ=39ft
A triangle is isosceles triangle when the two sides and two angle of the triangle in equal in measure.
a) the value of n is 3 units.b) the measure of leg XY is 39 feet.c)the measure of leg XZ is 39 feet.What is isosceles triangle?A triangle is isosceles triangle when the two sides and two angle of the triangle in equal in measure.
Given information-
The length of the side [tex]XY[/tex] is ([tex]9n+12[/tex]).
The length of the side [tex]XZ[/tex] is ([tex]15n-6[/tex]).
The measure of angle,
[tex]m\angle Y=m\angle Z[/tex]
a) the value of n-For the isosceles triangle, the two sides and two angle of the equal in measure.
As the measure of angle,
[tex]m\angle Y=m\angle Z[/tex]
Thus the opposite side of this angles must be equal. Thus,
[tex]XY=XZ[/tex]
Put the values as,
[tex]9n+12=15n-6\\15n-9n=12+6\\6n=18\\n=3[/tex]
Hence the value of n is 3 units.
b) the measure of leg XYThe length of the side [tex]XY[/tex] is ([tex]9n+12[/tex]).
Put the value of n,
[tex]XY=9n+12\\XY=9\times3+12\\XY=27+12\\XY=39 \rm ft[/tex]
Hence the measure of leg XY is 39 feet.
c) the measure of leg XZThe length of the side [tex]XZ[/tex] is ([tex]15n-6[/tex]).
Put the value of n,
[tex]XZ=15n-6\\XZ=15\times3-6\\XZ=39\rm ft[/tex]
Hence the measure of leg XZ is 39 feet.
a) the value of n is 3 units.b) the measure of leg XY is 39 feet.c)the measure of leg XZ is 39 feet.Learn more about the isosceles triangle here;
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Given Sin x= 0.5, what is cos x?
Enter your answer as a decimal, round only your final answer to the nearest hundredth.
Answers
sin x = 1/2
sin x = opp/hyp
therefore the ratio of opp/hyp = 1/2, (opp = 1, hyp = 2)
Find the opp side
1² + x² = 2²
1 + x² = 4
x² = 4 -1
x² = 3
x =√3
The opp side is √3
cos x = opp/hyp = √3/2 = 0.87 (round to the nearest hundredths)
If sin x = 0.5, cos x is approximately 0.87.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
To find cos x, we can use the identity: cos² x + sin² x = 1
We are given that sin x = 0.5.
We can substitute this into the identity to solve for cos x:
cos² x + sin² x = 1
cos² x + (0.5)² = 1
cos² x + 0.25 = 1
cos² x = 0.75
cos x = ±√0.75
We take the positive square root since cosine is positive in the first and fourth quadrants.
Evaluating the square root gives:
cos x ≈ 0.87 (rounded to two decimal places)
Therefore,
cos x is approximately 0.87.
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A small fishing boat's outboard motor requires a mixture of gasoline and oil for fuel. The mixture called for in the owner's manual is 1 gallon of oil for every 50 gallons of gas. If the boat's gas tank holds approximately 6 gallons of gas, approximately how much oil must be added to the gasoline?
3 ounces
9 ounces
15 ounces
24 ounces
Answers
What is the area of the polygon given below?
Answers
A = 28 + 117 + 36
A = 181
answer
D. 181 square units