Consider line A which is defined by the equation:
y=5/6x-5/2
and the point P(-3,6) and then answer the following questions:
a. How would you find the line (B) that passes through point P and is perpendicular to line A? What is the equation of that line?
b. How would you find the length of the segment of line B from point P to line A?
c. How would you find the midpoint between point P and the intersection of line A and line B ?
Answers
Answer:
y = -6/5x +12/5distance from P to A: (66√61)/61 ≈ 8.4504midpoint: (-18/61, 168/61) ≈ (-0.2951, 2.7541)Step-by-step explanation:
a. The slope of the perpendicular line is the negative reciprocal of the slope of the given line, so is ...
m = -1/(5/6) = -6/5
Then the point-slope form of the desired line through (-3, 6) can be written as ...
y = m(x -h) +k . . . . . line with slope m through (h, k)
y = (-6/5)(x +3) +6
y = -6/5x +12/5 . . . equation of line B
__
b. The distance from point P to the intersection point (X) can be found from the formula for the distance from a point to a line.
When the line's equation is written in general form, ax+by+c=0, the distance from point (x, y) to the line is ...
d = |ax +by +c|/√(a² +b²)
The equation of line A can be written in general form as ...
y = 5/6x -5/2
6y = 5x -15
5x -6y -15 = 0
Then the distance from P to the line is ...
d = |5(-3) -6(6) -15|/√(5² +(-6)²) = 66/√61
The length of segment PX is (66√61)/61.
__
c. To find the midpoint, we need to know the point of intersection, X. We find that by solving the simultaneous equations ...
y = 5/6x -5/2
y = -6/5x +12/5
Equating y-values gives ...
5/6x -5/2 = -6/5x +12/5
Adding 6/5x +5/2 gives ...
x(5/6+6/5) = 12/5 +5/2
x(61/30) = 49/10
x = (49/10)(30/61) = 147/61
y = 5/6(147/61) -5/2 = -30/61
Then the point of intersection of the lines is X = (147/61, -30/61).
So, the midpoint of PX is ...
M = (P +X)/2
M = ((-3, 6) +(147/61, -30/61))/2
M = (-18/61, 168/61)
Related Questions
What is the length of the shortest altitude in a triangle, if the lengths of the sides are 24 cm, 25 cm, 7 cm?
Answers
Answer:
The shortest altitude is 6.72 cm
Step-by-step explanation:
Given that the side lengths are
24 cm, 25 cm, 7 cm
The area of a triangle =
[tex]A = \sqrt{s \cdot (s-a)\cdot (s-b)\cdot (s-c)}[/tex]
Where;
s = Half the perimeter = (24 + 25 + 7)/2 = 28
A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²
We note that 84/7 = 12
Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7
To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude
Altitude = A/(1/2 ×base)
Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;
We set the base to 25 cm to get;
Area of the triangle A = 1/2 × base × Altitude
84 = 1/2 × 25 × Altitude
Altitude = 84/(1/2 × 25) = 6.72 cm
The shortest altitude = 6.72 cm.
Haley is at the store buying some supplies for an art project. She decides to buy some colored pencils for $3.95 and a drawing tablet. The total cost of the supplies before sales tax is $6.94. What is the cost of the drawing tablet? $2.99 $1.76 $10.89 $3.01
Answers
Its $2.99 because 6.94-3.95=2.99 so $2.99
Answer:
$2.99
Step-by-step explanation:
To find the value of the drawing tablet, we can use the known total cost and the cost of the pencils. Let's build an equation, where x represents the cost of the drawing tablet:
x + 3.95 = 6.94
Now let's solve the equation for x to find the cost of the tablet.
x + 3.95 = 6.94
x + 3.95 - 3.95 = 6.94 - 3.95
x = 2.99
So the cost of the drawing tablet is $2.99.
Cheers.
what expression is equivalent to this Expression?
(-5cd-4)(2cd2)2
Answers
Answer:
[tex]-40c^{2} d^{2} -32cd[/tex]
Step-by-step explanation:
-20c³ is the expression which is equivalent to (-5cd⁻⁴)(2cd²)².
To simplify the given expression, (-5cd⁻⁴)(2cd²)², we can apply the power of a product rule, which states that (ab)² is equal to a²b².
Let's break down the expression step by step:
(-5cd⁻⁴)(2cd²)²
First, let's square the expression (2cd²)²:
(2cd²)² = (2)²(c)²(d²)² = 4c²d⁴
Now, we substitute this result back into the original expression:
(-5cd⁻⁴)(4c²d⁴)
To simplify further, we can multiply the coefficients and combine the variables:
(-5)(4) = -20
(c)(c²) = c³
(d⁻⁴)(d⁴) = 1
Putting it all together, the expression (-5cd⁻⁴)(2cd²)² simplifies to -20c³.
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0.00000007834= blank ×10^2 in scientific notation
Answers
Answer:
7.834 × 10^-8
Step-by-step explanation:
= 7.834 × 10^-8
(scientific notation)
= 7.834e-8
(scientific e notation)
= 78.34 × 10^-9
(engineering notation)
(billionth; prefix nano- (n))
= 0.00000007834
(real number)
^ means the number after is exponent.
Helpp me pleaseeeeee
Answers
Answer:
On-time Buses: 75%
Running late Buses: 13.46%
Step-by-step explanation:
Part 1: Solve for the probability of Jerry owning an "on-time" bus
Of the 48 buses that run on time, Jerry owns 36 of them. Therefore, the probability of a bus running on time being owned by Jerry will be solved with the ratio of 36 buses to 48 buses.
This is represented by the fraction 36/48. Simplifying this fraction will give us 3/4. Convert to a decimal and then multiply by 100 to get a percentage - 75%.Part 2: Solve for the probability of Jerry owning a "running late" bus
Of the 52 buses that run late, Jerry owns 7 of them. Therefore, the probability of a bus running late & being owned by Jerry will be solved with the ratio of 7 buses to 52 buses.
This is represented by the fraction 7/52.Simplifying this fraction will give us 7/52 (cannot be simplified).Convert to a decimal and then multiply by 100 to get a percentage - 13.46%.Is the function f(x) increasing or decreasing over the interval -2 < x <-1?
Answers
Answer:
increasing
Step-by-step explanation:
a function is increasing when y increases as x increases
Since the graph goes up as x increases, the function f(x) is increases between -2 and -1
A parabola has an x-intercept of -1, a y-Intercept of -3, and a minimum of -4 at x = 1.
Which graph matches this description?
Answers
Answer:
A
Step-by-step explanation:
Looking for the graph which
crosses the x- axis at x = - 1 ( x- intercept )
crosses the y- axis at y = - 3 ( y- intercept )
has a minimum value of - 4 at x = 1, that is vertex = (1, - 4) and minimum U
The required graph is A
The graph A should match the description.
Graph:Here we look the graph which crosses the x- axis at x = - 1 ( x- intercept )And, crosses the y- axis at y = - 3 ( y- intercept )Now we considered those that contain a minimum value of - 4 at x = 1, that is vertex = (1, - 4) and minimum Ulearn more about the graph here: https://brainly.com/question/19661552
Clifton drove for 3 hours at 52 mph. How fast must he drive during the next hour in order to have an average speed of 55 mph?
Answers
Answer:
64 mph
Step-by-step explanation:
Given that:
Speed for the first 3 hours = 52 mph
Average speed for 4 hours = 55 mph
To find:
Speed for the next hour = ?
Solution:
Formula for average speed is given as:
[tex]Average\ Speed = \dfrac{Total\ Distance}{Total \ Time \ Taken}[/tex]
Formula for Distance:
[tex]Distance =Speed \times Time[/tex]
Distance traveled in first 3 hours:
[tex]Distance =52\times 3 = 156\ miles[/tex]
Let the speed for the next hour = u mph
Distance traveled in 1 hour = [tex]u \times 1 = u\ miles[/tex]
Total distance traveled = (156 + u) miles
Total time = 4 hours
Average Speed = 55 mph
Putting the values in formula:
[tex]55 = \dfrac{156+u}{4}\\\Rightarrow 220 = 156+u\\\Rightarrow \bold{u = 64\ mph }[/tex]
So, the answer is: 64 mph
Write an expression for 267 multiplied by x
Answers
Answer:
267x
Step-by-step explanation:
Multiplication means times
267 * x
267x
Answer:
267x
when you multiply a number by a variable, you can combine the terms if there is no coefficient for the variable.
Graphing Linear Equations
Answers
Answer:
Kyra=15 points
Liam=20 points
30 points=y=4/3x+5
Step-by-step explanation:
I graphed each equation and point on the graph given
HOPE THIS HELPS!!! :)
PLEASE CORRECT ME IF IM WRONG
The probability that a civil servant own a car is 1/6,if two civil servants are selected at random.Find the probability that a.Each own a carb.Only one owns a car
Answers
Answer:
Step-by-step explanation: Given that a civil servant own a car is 1/6.
A) The Pr. that each own a car = Pr of each multiplied by the other.
Pr = 1/6 ×1/6
P = 1/36
B) Pr that only one owns a car
= 1/6 × (1-1/6) + 1/6 × (1-1/6)
= 1/6 × 5/6 + 5/6 × 1/6
= 5/36 + 5/36
= 10/36
= 5/18
If A has a 3 letter name, but the name doesn’t contain a vowel what would be A’s name?
Answers
A is vowel.
first condition prevents any vowels, thus there will be no A at all
Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If Beth places the swings at point D, how could she prove that point D is equidistant from the jungle gym and monkey bars?
Answers
Answer:
Following are the answer to this question:
Step-by-step explanation:
Some of the information is missing which is defined in the attached file, and the solution to this question can be defined as follows:
When the point AC ≅ BC point is in the equal distance from point A and Point B then Point A is perpendicular and the bisector point is in equally distant from the endpoints of that intersects points.
please find the attachment of the full question:
Answer:
If segment AC ≅ segment BC, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
Step-by-step explanation:
X
5x – 3y = -20
4x + 5y = -2
Answers
Answer:
x=-106/37
y=70/37
Step-by-step explanation:
I chose to set up the problem as a matrix to solve here.
(Another way to do this would be to isolate one variable in one of the equations, substitute it into the other equation, solve for that, and then plug it back in to get the final variable.)
My work is in the attachment. Lmk if you have any questions.
Answer:
[tex]\huge\boxed{\left\{\begin{array}{ccc}x=-\dfrac{106}{37}\\y=\dfrac{70}{37}\end{array}\right}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}5x-3y=-20&\text{multiply both sides by 5}\\4x+5y=-2&\text{multiply both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}25x-15y=-100\\12x+15y=-6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad37x=-106\qquad\text{divide both sides by 37}\\.\qquad\boxed{x=-\dfrac{106}{37}}[/tex]
[tex]\text{Substitute it to the first equation}\\\\5\left(-\dfrac{106}{37}\right)-3y=-20\\\\-\dfrac{530}{37}-3y=-20\qquad\text{multiply both sides by (-37)}\\\\(-37\!\!\!\!\!\diagup)\left(-\dfrac{530}{37\!\!\!\!\!\diagup}\right)-(-37)(3y)=(-37)(-20)\\\\530+111y=740\qquad\text{subtract 530 from both sides}\\\\111y=210\qquad\text{divide both sides by 111}\\\\y=\dfrac{210}{111}\\\\y=\dfrac{210:3}{111:3}\\\\\boxed{y=\dfrac{70}{37}}[/tex]
Drag each tile to the correct box.
Arrange the functions in increasing order of their periods.
y=-3tan(x+2pi)
y = 2/3csc(x/4)+6
y=-1/2cos(5x/6+pi)
y=5sec(3x) +6
y =-1/3sin(x/3)
y=-10cot(x/2-2pi)
Answers
Answer:
y=5sec(3x) +6
y=-3tan(x+2pi)
y=-10cot(x/2-2pi)
y=-1/2cos(5x/6+pi)
y =-1/3sin(x/3)
y = 2/3csc(x/4)+6
The functions in increasing order of their periods are given below.
y=5sec(3x) +6
y=-3tan(x+2pi)
y=-10cot(x/2-2pi)
y=-1/2cos(5x/6+pi)
y =-1/3sin(x/3)
y = 2/3csc(x/4)+6
As y = 2/3csc(x/4)+6 gives a high value than the other, it is considered the highest.
What are increasing order and decreasing order?Ascending order way going up from small value to excessive cost and textual content from A to Z. Descending order manner arranging the numbers from largest to smallest and textual content from Z to A. while the names are arranged for a list, then it is usually arranged in A to Z order, alphabetically.
Steps to find the Period of a Function
If a function repeats over a constant period we say that is a periodic function.It is represented like f(x) = f(x + p), p is the real number and this is the period of the function.Period means the time interval between the two occurrences of the wave.Learn more about functions here: https://brainly.com/question/2833285
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round off 3867 in nearest 100
Answers
Answer:
3900
Step-by-step explanation:
since its to the nearest 100th we use the common rule that if the number is greater than half way then we round up otherwise if it is less then we round down. In the number 3867, 867 is greater than 850 so we round up. It becomes 3900 then.
The winning times (in seconds) in a speed-skating event for men can be represented by the formula T = 46.97 - 0.099x, where x represents the year, with x = 0 corresponding to 1920. (For example in 1992, x would be 1992 - 1920 = 72.) According to the formula, what was the winning time in 1997? Round to the nearest hundredth. * 1 point 40.34 sec 39.35 sec 3609.07 sec 41.33 sec
Answers
Answer:
39.35 sec
Step-by-step explanation:
Given that:
The winning time is represented by the function:
T = 46.97 - 0.099x
Where x = year ; x = 0 corresponding to 1920
According to the formula, what was the winning time in 1997?
first find the value of x;
x = 1997 - 1920 = 77 years
Nowing plugging the value of x in the function :
T = 46.97 - 0.099(77)
T = 46.97 - 7.623
T = 39.347 seconds
T = 39.35 s
Find the product of 0.3×0.23.
Answers
Answer:
0.069
Step-by-step explanation:
0.3*0.23=0.069
if jane has 3 apple then buys 4 times as much as that how much does she have
Answers
Answer:
12 apples
Step-by-step explanation:
3*4=12
I really need help Please help me please
Answers
Which of the following is the solution of 5x – 6 = 44?
O x=-10
38
X=--
5
38
X = 10
Answers
Answer:
x = 10
Step-by-step explanation:
5x - 6 = 44
Add 6 on both sides of the equation.
5x = 50
Divide by 5 on both sides of the equation.
x = 10
So, the value of x is equal to 10
Answer:
x=10
Step-by-step explanation:
5x-6=44
grouping constants and numbers with coefficient of x we get
5x=44+6
5x=50
5x/5=50/5
x=10
explanation please! thx!
Answers
Answer:
63°
Step-by-step explanation:
complement means that the two angles add to 90°
90 - 27 = 63°
Answer:
Step-by-step explanation:
complement angles have sum of angles=90°
∠AOC=27
∠BOC=90-27=63°
ASAP PLZ ANSWER!!! Can you tell me step by step to this question 8,595 ÷ 24?
Answers
Answer:
358 and remainder of 3
Step-by-step explanation:
1. Divide it like any other problem
24 goes into 85, 3 times with 13 left overBring down the 9 and 24 goes into 139, 5 times with 19 left overThen bring down the 5 and 24 goes inside 195, 8 times with 3 left overSo your remainder would be 3Hope this helps
Please answer quickly, what is the measure of c
Answers
===================================================
Explanation:
The only given number here is the 20 degree angle. So we'll start with that. This is an inscribed angle, which doubles to 2*20 = 40, and this is the measure of the arc the inscribed angle cuts off (inscribed angle theorem). Consequently, it means that central angle b is also 40 degrees.
With b = 40, we can see that c = 180-b = 180-40 = 140. This is because b+c = 180 as the two angles are supplementary.
Answer:
140 degrees
Step-by-step explanation:
If the given angle is 20 degrees then the other unknown angle would also be 20 degrees because this triangle is an isosceles triangle. 20+20+20=180 proving the triangle sum theorem.
Population data from three towns is displayed in the tables below. Which
town has growth that follows an exponential model?
Answers
Answer:
Rushmont
Step-by-step explanation:
Trenton can be ruled out due to its constant increase rate of 1.5. Rushmont can be ruled out because it goes from an increase rate of ~1.8 to an increase rate of 1.4 to an increase rate of 1.3 (exponential decay, not growth, so possibly...). Springville has a rate of ~1.9, then 1.475, then 1.3, also exponential decay. However, y\ =\ x\frac{38}{10}-185 goes through all of springville's points (or close to it), so Rushmont must be the answer.
The town that has growth that follows an exponential model is Town B, Rushmont where the population increases or decreases at a consistent rate over time.
In this case, analyze the population data from the three towns to determine which one exhibits exponential growth.
Let's go through each option briefly:
A. Springville:
The population of Springville in 1960 is 42, and in 1990 it is 156.The difference in population over 30 years is 156 - 42 = 114.The average increase per year is 114 / 30 = 3.8.The growth in Springville does not follow a consistent exponential pattern, as the average increase is not constant over time.B. Rushmont:
The population of Rushmont in 1960 is 38, and in 1990 it is 131.The difference in population over 30 years is 131 - 38 = 93.The average increase per year is 93 / 30 = 3.1.The growth in Rushmont exhibits a consistent increase of approximately 3.1 per year, indicating a possible exponential model.C. Trenton:
The population of Trenton in 1960 is 32, and in 1990 it is 108.The difference in population over 30 years is 108 - 32 = 76.The average increase per year is 76 / 30 = 2.5.The growth in Trenton does not follow a consistent exponential pattern, as the average increase is not constant over time.Based on the analysis above, the town that shows growth following an exponential model is Rushmont (B). It exhibits a consistent increase in population over time, suggesting exponential growth.
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Aaron and his 2 friends found some money and split it even. Each received $5.00. How much did they find? a. $1000 b. $100 c. $15 d. $1500
Answers
Answer:
15
Step-by-step explanation:
Aaron and his 2 friends = 3 people
Each received $5.00 = 3 people*5 each = 15 total
Find the value of cotA x sinA x secA.
Answers
Answer:
The value = 1
Step-by-step explanation:
Here in this question, we are interested in calculating the product of the trigonometric identities given.
To adequately calculate this correctly, we shall need to express the trigonometric identities in their normal division form which is as follows ;
Mathematically;
cotA = 1/tanA
let’s leave sin A
sec A = 1/cos A
So inputing the values of the following, we have ;
1/tan A * sin A * 1/cos A
This can be written as;
1/tan A * sin A/cos A
Mathematically; sinA/cos A = tan A
making that substitution, we have;
1/tan A * tan A
= tan A/tan A = 1
Find the length of the base and the height and calculate the area
Answers
Answer:
44
Step-by-step explanation:
base = 3- -5 = 8
height = 8 - -3 = 11
1/2 bh
1/2(8)(11) = 44
1+cos(8x)= A.4cos(2x) B.2cos^2(4x) C.4sin(2x) D.2sin^2(4x)
Answers
Answer:
bro please send in a picture format so that it could be more easier
What is the answer??
c — 10 ≥ 15
Answers
Answer:
Step-by-step explanation:
c - 10 ≥ 15 =
c ≥ = 15 + 10
c ≥ = 25
c = 26 ( or numbers above 26)
