Answer:
K = (-5, 14)
Step-by-step explanation:
For writing equations of parallel and perpendicular lines, it is convenient to start with equations in general form:
ax +by +c = 0
Rewriting the given equations, we have ...
y = 1/2x -1
x -2y -2 = 0 . . . . . line d
y = -3x +2
3x +y -2 = 0 . . . . . line d'
__
A parallel line will have the same coefficients, but a constant appropriate to the required point on the line.
Parallel to d' through A(-1, 2):
3(x -(-1)) +(y -2) = 0
3x +y +1 = 0 . . . . . . . . simplify
__
A perpendicular line will have the coefficients swapped and one of them negated. Again, the constant is appropriate to the required point.
Perpendicular to d through B(3, -2):
2(x -3) +(y -(-2)) = 0
2x +y -4 = 0 . . . . . . . . simplify
__
The solution to this system of equations can be found by subtracting the second equation from the first:
(3x +y +1) -(2x +y -4) = (0) -(0)
x +5 = 0
x = -5
Substituting into the second equation gives ...
2(-5) +y -4 = 0
y -14 = 0
y = 14
The coordinates of point K are ...
K = (-5, 14)
_____
Additional comment
The general line through the origin ...
ax +by = 0
can be translated to go through point (h, k) by the usual method for translating functions. The variable x is replaced by (x -h), and the variable y is replaced by (y -k). Using the general form equation means we can keep the variables and constants all on the same side of the equal sign, saving a bit of work and confusion.
a(x -h) +b(y -k) = 0 . . . . . . line through point (h, k)
__
The graph is drawn by a geometry program capable of drawing parallel and perpendicular lines through given points. It confirms the equations and th solution.
Provide the missing reasons for the proof.
Given: (AB) || (RS)
Prove: QA/QR= QB/QS
Answer:
Step-by-step explanation:
1) Given
2) <Q is congruent to <Q by reflexive prop of congruence
3) <QBA is congruent to <QSR by alternate interior angles theorem
4) Triangle QBA is similar to triangle QSR by AA theorem
5) QA/QR=QB/QS by CPSP (corresponding parts of similar polygons are proportional)
What is the distance formula
Thus option C is correct.
[tex]\sf Distance \ between \ points\sf : \ \ \ d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
Option C
Let's look up at an example
(3,4)(1,2)Distance:-
√(3-1)²+(4-2)²√2²+2²√4+4√82√216-2t=5t+9
Answer
equation
Answer:
t=1
Step-by-step explanation:
16-2t=5t+9
step 1 :group like term to the same side
16-9=5t+2t
step 2 : combine
7=7t
step 3: solve for t
t=7/7
t=1
A buoy starts at a height of 0 in relation to sea level and then goes up. its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds. which of the following equations can be used to model h, the height in feet of the buoy in relation to sea level as a function of time, t, in seconds? h = 4 sine (startfraction pi over 6 endfraction t) h = 4 sine (startfraction pi over 3 endfraction t) h = 6 sine (startfraction pi over 4 endfraction t) h = 6 sine (startfraction pi over 2 endfraction t)
The equation of the model h will be h = 6 × sin(2πt/8). Then the correct option is C.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
A buoy starts at a height of 0 in relation to sea level and then goes up.
Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds.
Then we have
[tex]h=A \times \sin \omega t, \ \ at=0, \ \ h =0[/tex]
The maximum displacement of the buoy in either direction is 6 ft, then we have
[tex]h=6 \times \sin \omega t[/tex]
The time it takes the buoy to get from the lowest to the highest point is 4 seconds then the oscillation time period will be 8 seconds.
Then we have
[tex]\omega T = 2\pi\\\\\omega = \dfrac{2\pi}{8}[/tex]
Then the h will be given as
[tex]h =6\times \sin (\dfrac{2\pi}{8}t)[/tex]
More about the function link is given below.
https://brainly.com/question/5245372
Type the missing number that makes these fractions equal: 1 2 = 2
Answer:
4
Step-by-step explanation:
[tex]\frac{1}{2} * 4[/tex] = 2
i do not know this answer
Answer:
15 miles
Use the Pythagoras theorem
Answer: 15
Step-by-step explanation:
Let's start by stating what we are given
The perimeter is 36
One side length is 12
And the other given side is 9
Finally we have an unknown side x
The value of all the sides added together is the perimeter.
So add all the sides
12+9+x=36
21+x=36
Subtract both sides by 21
21-21+x=36-21
x=15
Use the two-way frequency table at the right to find the probability P(7th-grade boy).
(Simplify your answer.)
Answer:
8/50
Step-by-step explanation:
find the total number of 7th grade boys
put that in the numerator
I'm assuming you're trying to get the probability of picking a 7th grade boy out of all the kids in the soccer camp so 50
select the correct answer
what is the solution for x in the equation
5/3x+4=2/3x
Answer:
x = -4
Step-by-step explanation:
4 = 2/3x - 5/3x
4 = -3/3x
4 = -x
-4 = x
I Need Help! Please!
A local grocery store buys fresh carrots from a nearby farm for $0.65 per pound and sells them for $0.88 per pound. What markup rate does the grocery store use? Round to the nearest whole percent.
The markup rate that the grocery store uses is _____ % (Round to the nearest whole percent.)
Answer:
35%
Step-by-step explanation:
I'm sorry if it isn't right but I tried.
help me with this math question please its find the area <3
Answer:
9.628 cm²
Step-by-step explanation:
Let A be the area of the sector OAB
Let a be the area of the sector OCD
The shaded area = A − a
[tex]\begin{aligned}A &=\frac{1}{12} (\pi \times 7^{2}) \\&=12.828 \ldots\end{aligned}[/tex]
[tex]\begin{aligned}a & = \frac{1}{12}\left(\pi \times 3.5^{2}\right) \\&=3.2 \ldots\end{aligned}[/tex]
The shaded area ≈ 12.828 - 3.2 ≈ 9.628 cm²
bryson collects data on the depth of a river at various points and the velocity of the river at those points. his data has a correction coefficient of -0.94. which scatterplot represents brysons data ?
The scatterplot that represents Bryson's data is the scatterplot that is downward sloping.
What is negative correlation?
Correlation is a statistical measure used to measure the relationship that exists between two variables.
Negative correlation means that the two variables move in opposite directions. If one variable increases, the other variable decreases. When there is a negative correlation, the graph of the variables is downward sloping
Please find attached the graph representing the negative correlation. To learn more about negative correlation, please check: https://brainly.com/question/14436361
Select the correct answer.
an experiment observing the growth of two germ strand populations finds these patterns.
• the population of the first germ is represented by the function a(x) = (1. 3)+9
• the population of the second germ is represented by the function b(t) = (1. 3)45+1
which function best represents function r, the ratio of the population of the second germ to the population of the first germ?
Answer:
the
• the population of the first germ is represented by the function a(x) = (1. 3)+9
what is the mean of this data set
56,87,90,42,36,77
Answer:
64.7 when rounded up to one decimal place
Step-by-step explanation:
I really need help on this! No download answer scam link
Answer:
y=x^2 - 8x +8:
(1.8,0) and (6.8)
y=-x^2-4x+7:
(-5.3,0) and (1.3,0)
Step-by-step explanation:
If you go to desmos graphing calculator online, you can type the equation in and click on the zeros.
I have attached the following graphs to show what I did to find them.
Solve for m
[tex]n=\frac{4}{5} (m+7)[/tex]
Answer:
Step-by-step explanation:
How many miles can be driven with 5.5 gallons of gas
Answer:
About 198 miles.
Step-by-step explanation:
The average car can drive with an MPG ratio of 36 miles per gallon. Using this and other observations. This would make this equation rather facile and result in equation 36(MPG) × 5.5(Gallons). Therefore, the result led to the remedy as 198 miles.
An angle measures 142° more than the measure of its supplementary angle. What is the measure of each angle?
Answer:
161° and 19°
Step-by-step explanation:
supplementary angles =180
(142+x)+(x)=180
142+2x=180
2x=180-142
2x=38
x=19
142+19=161
What is 3 1/2 + (-6) - (-1 1/2-9 3\4 ) simplified?
Answer:
8.75
Add everything together
PLEASE HELP ASAPPP IM TIMED
[tex]\textbf{a).}\\\\r^2-12r+32\\\\=r^2 -8r-4r+32\\ \\=r(r-8) -4(r-8)\\\\=(r-8)(r-4)\\\\\textbf{b).}\\\\5a^2-7a-6\\\\=5a^2-10a+3a-6\\\\=5a(a-2)+3(a-2)\\\\=(a-2)(5a+3)\\\\\textbf{c).}\\\\16g^2+40g+25\\\\=(4g)^2 +2\cdot 5\cdot 4g+5^2\\\\=(4g+5)^2\\\\=(4g+5)(4g+5)[/tex]
Solve for x and round to nearest tenth for both please and Thankyou:)
Answer:
For the first picture, 57.14
For the second picture, 27.04
18.
Is the data point, P, an outlier, an influential point, both, or neither?
A. Neither
B. Influential point
C. Outlier
D. Both
The number of reviews for each of the local restaurants is counted. The results are normally distributed with a mean of 25 and a standard deviation of 4.
What percentage of restaurants have between 20 and 25 reviews?
10.6%
50.0%
16.0%
39.4%
Using the normal distribution, it is found that 39.4% of restaurants have between 20 and 25 reviews.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem, the mean and the standard deviation are given, respectively, by [tex]\mu = 25, \sigma = 4[/tex].
The proportion of restaurants that have between 20 and 25 reviews is the p-value of Z when X = 25 subtracted by the p-value of Z when X = 20, hence:
X = 25:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25 - 25}{4}[/tex]
Z = 0.
Z = 0 has a p-value of 0.5.
X = 20:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 25}{4}[/tex]
Z = -1.25.
Z = -1.25 has a p-value of 0.106.
0.5 - 0.105 = 0.394 = 39.4%.
Hence, 39.4% of restaurants have between 20 and 25 reviews.
More can be learned about the normal distribution at https://brainly.com/question/24663213
heath records the number of winners of three ring toss games. According to heaths experiments, what is the probability a player will win the game
help :(
“x is less than -3”
- The inequality translated in numerical form
- The solution in interval notation
Answer:
-2x
Step-by-step explanation:
x-(-3)
-2x
answer will be -2x ok follow me
please help I don't know the median give an answer and explanation
Answer:
Median is the middle of the data set. For example this data set is 4, 6, 7, 9, 10. First you take out 4 and 10. The you take out 6 and 9 to get a median of 7. But if there is an even amount of numbers like in this data set, 1, 2, 4, 5. Then you take out 1 and 5 and then find the middle point in between 2 and 4 which is 3.
100 points
The ratio of students polled in 6th grade who prefer lemonade to iced tea is 8:4. If there were 39 students in 6th grade polled, explain how to find the number of students that prefer lemonade and the number of students that prefer iced tea using a ratio table. If you wish, you may upload a copy of your ratio table.
Answer:
Step-by-step explanation:
So, the total unit number of sixth graders polled is 12.
39/12=3.25
So, you'd do 8x3.25=26 students like lemonade
13 students like iced tea
7. Are the given functions inverses? Why or why
not?
y = (x - 2)2 + 4
f-1(x) = +Vx – 4 + 2
Answer:
x=1 it is not inverse
a dartboard has a diameter of 16 inches. What are its radius and circumstance? Round to the nearest hundredth. Use 3.14 for pi
Which list shows the fractions in order from greatest to least? *
pls help i give brainliest
3/6, 2/5, 1/4, 2/5
2/3, 3/6, 1/4, 2/5
1/4, 3/6, 2/5, 2/3
2/3, 3/6, 2/5, 1/4
Answer:
1/4, 3/6, 2/5, 2/3.........
1.
The area of a circle is 25m^2, what would be its diameter?
2.
The perimeter of a circle is 30 cm, what would be its radius?
3.
What would be the area of a circle with a perimeter of 12 feet.
HELP
Answer:
1. diameter=5.54m
2. radius=9.55cm
3. area=11.46feet²
Step-by-step explanation:
1. The formula of the area of a circle is: A=[tex]\pi r^{2}[/tex]
A: area of the circle=25m²
[tex]\pi[/tex] : Pi≈3.14
r: radius of the circle= unknown
Solve the equation to find r:
25=(3.14)r²
r²=[tex]\frac{25}{3.14}[/tex] =7.69m²
r= √7.69= 2.77m
diameter d= 2 x r =2 x 2.77 =5.54m
2. The formula of the perimeter of a circle is: P=2[tex]\pi r[/tex]
P: perimeter of the circle= 30cm
[tex]\pi[/tex] : Pi≈3.14
r: radius of the circle= unknown
Solve the equation to find r:
30=(3.14)r
r= [tex]\frac{30}{3.14}[/tex] = 9.55cm
radius r = 9.55cm
3. First we have to find r (radius) from the equation of perimeter:
P=2[tex]\pi r[/tex]
r= [tex]\frac{P}{2\pi }[/tex] = [tex]\frac{12}{2(3.14)}[/tex] = [tex]\frac{12}{6.28}[/tex] =1.91 feet
Substitute r in the equation of area to get the area:
A= [tex]\pi r^{2}[/tex] = 3.14 (1.91)² = 3.14(3.65) = 11.46 feet²