Answer:
The Coordinates of Point C are C(5,2)
The slope of CD is 3
The possible coordinates of point D(a,b) are (6, 5) and (4, -1)
Step-by-step explanation:
According to the Question,
Given, The end points of AB are A(2,3) and B(8,1). The perpendicular Bisector of AB is CD, and point C lies on AB. The length of the CD is √10 units.Now, Let The Coordinates of Point C are C( x , y ) .
Thus, C( x , y ) = [tex]\frac{(8+2)}{2} , \frac{(1+3)}{2}[/tex]The Coordinates of Point C are C( x , y ) = [tex]\frac{(10)}{2} , \frac{(4)}{2}[/tex] ⇒C(5, 2).
And, The slope of AB = [tex]\frac{(1-3)}{(8-2)}[/tex] ⇒ [tex]\frac{-2}{6}[/tex] ⇔ [tex]\frac{-1}{3}[/tex] .Thus, The slope of CD is [tex]\frac{-1}{The slope of AB}[/tex] = [tex]\frac{-1}{\frac{-1}{3} }[/tex] ⇔ 3.
Let the coordinate of D be (a, b) then⇒ √{ (b - 2)² +(a - 5)² } = √10
on squaring both sides we get,
⇒ a² - 10a + 25 + b² - 4b + 4 = 10
⇒ a² + b² - 10a - 4b = - 19 ⇔⇔ (Equation 1)
We Know, the slope of CD = 3⇒Thus, (b - 2)/(a - 5) = 3
⇒ b - 2 = 3a - 15
⇒ b = 3a - 13 ⇔⇔ (Equation 2)
Putting value of Equation 2 into Equation 1, We get⇒a² + (3a - 13)² - 10a - 4(3a - 13) = - 19
⇒a² + 9a² - 78a + 169 - 10a - 12a + 52 = - 19
⇒10a² - 100a + 240 = 0
⇒a² - 10a + 24 = 0
⇒(a - 4)(a - 6) = 0
⇒a = 4 or a = 6
Now,
When a = 4 , b = 3(4) - 13 ⇒ 12 - 13 ⇒ b = -1When a = 6, b = 3(6) - 13 ⇒ 18 - 13 ⇒ b = 5Therefore, the possible coordinates of point D(a,b) are (6, 5) and (4, -1).
The mean sustained wind velocity, v, can be determined by the equation v = 6.3 StartRoot 1013 minus p EndRoot, where p is the air pressure, in millibars, at the center of the hurricane. What is the approximate air pressure at the center of a hurricane when the mean sustained wind velocity is 64 meters per second? 103 millibars 194 millibars 363 millibars 910 millibars
Answer:
910 millibars
Step-by-step explanation:
According to the Question,
Given That, The mean sustained wind velocity equation [tex]v=6.3*\sqrt{1013-p}[/tex] And The mean sustained wind velocity is 64m/s (v=64) . where, p is the air pressure(in millibars).Now, the air pressure at the center of a hurricane when the mean sustained wind velocity is 64 m/s is
[tex]64=6.3*\sqrt{1013-p}\\\frac{64}{6.3} = \sqrt{1013-p}\\[/tex]
on squaring both sides we get,
(10.1587)² = 1012 - p ⇒ p = 908.80≈910millibar
p = 910millibars air pressure .
Answer: 910
Step-by-step explanation: Did the review and got it right
How many solutions does the system have?
4x−6y=−24
2x−3y=−6
Answer:
none
Step-by-step explanation:
if we plot it, it's clear, but you might also spot that the plotted lines will be parallel in the equation
because x and y in line two are the same multiple of these in line one (both values are just the half)
plotted with desmoes
10 points!
If you are going to answer, actually answer!
Answer:
1/27
Explanation:-
(1/3)^3=(1x1x1)/(3x3x3)=1/27
Answer:
0.03703703703 or
²/27
sorry i am late but still hope I helped
Step-by-step explanation:
Please help me ASAP and i mean ASAP
Answer:
no
Step-by-step explanation:
no
I NEED HELP ASAP IM STRESSJNG OUT
Answer:
A
Step-by-step explanation:
Using the Sine rule in Δ ABC
∠ B = 180° - (30 + 50)° = 180° - 80° = 100° ( sum of angles in triangle ) , then
[tex]\frac{13}{sin100}[/tex] = [tex]\frac{BC}{sin30}[/tex] ( cross- multiply )
BC × sin100° = 13 × sin30° ( divide both sides by sin100° )
BC = [tex]\frac{13sin30}{sin100}[/tex] ≈ 6.6 ( to the nearest tenth )
f(x) = x^2. What is g(x)?
Answer:
This becomes way easier if you have the knowledge of inverse functions.
Let me make this clear. You have f(x)=x2+1 f(x)=x2+1 and g(f(x))=1/(x2+4)g(f(x))=1/(x2+4). Now pause and think about the second function. The function is defined as g(f(x))g(f(x)), right. now what if there is some way that you could manipulate this function and some how change it to g(x)g(x). Or think about with what other function should you multiply f(x)f(x) [the function in g(f(x))g(f(x)) ] to get xx [so that the function would be g(x)g(x)]. It is f(x)−1f(x)−1 right.
So let us find f(x)f(x) inverse. f(x)=x2+1f(x)=x2+1 then f(x)−1=x−1−−−−−√f(x)−1=x−1 right [ just swipe the xx with f(x)
more help im dum lol
Answer:
32780
Step-by-step explanation:
Answer:
32,780
Step-by-step explanation:
It should be 30,000
I need help with angles in a triangle to find x
I need help with these. please :(
Answer:
[tex]a. \: \: x = {60}^{o} [/tex]
[tex]b. \: \: x = {24}^{o} [/tex]
Step-by-step explanation:
Hint :Sum of angles = 180°
Simplify :[tex]a. \: \: {x}^{o} + {40}^{o} + {80}^{o} = {180}^{o} [/tex]
[tex] {x}^{o} + {120}^{o} = {180}^{o} [/tex]
[tex] {x}^{o} = {180}^{o} - {120}^{o} [/tex]
[tex] {x}^{o} = {60}^{o} [/tex]
[tex]b. \: 96+(x+12)+2x=180[/tex]
[tex]x+108+2x=180[/tex]
[tex]3x+108=180[/tex]
[tex]3x=180−108[/tex]
[tex]3x=72[/tex]
[tex]x = \frac{72}{3} [/tex][tex]x = 24[/tex]
Hope it is helpful...Given the linear equation 5x+3y-9=0. Write another linear equation in two variables such that the geometrical representation of the pair so formed are parallel lines
Answer:[tex]5x+3y+1=0[/tex]
Step-by-step explanation:
Given
The linear equation is [tex]5x+3y-9=0[/tex]
The other linear equation parallel to the given line can be represented by
[tex]5x+3y+c=0[/tex]
Here, c can take any value . for example c=1, line becomes
[tex]\Rightarrow 5x+3y+1=0[/tex]
Sean and sarah spend $70 a month eating out how much money would they have after 15 years if they invested the money instead at 4 percent compounded monthly round your answer to the nearest hundredth
Answer:
Future Value= $17,170.12
Step-by-step explanation:
Giving the following information:
Monthly deposit (A)= $70
Interest rate (i)= 0.04/12= 0.0033
Number of periods (n)= 15*12= 180 months
To calculate the future value (amount saved), we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= monthly deposit
FV= {70*[(1.0033^180) - 1]} / 0.0033
FV= $17,170.12
Over 5 straight plays, a football team gained 8 yards, lost 4 yards, gained 7 yards, gained 3 yards, and lost 11 yards. What is the team's position no compared to their starting position? WILL GIVE BRAINLIEST ALSO BE CORRECT PLS THX
find hcf and LCM of 40 ,60 and 80
hear here is your answer in attachment attach
Answer:
Step-by-step explanation:
40 = 2*2*2*5
60 = 2 * 2 * 3 * 5
80= 2 * 2 * 2 * 2 * 5
LCM = 2 * 2 * 2 * 2 * 5 * 3 = 240
HCF = 2*2*5= 20
Given the following system of equations, what value of x makes the equations true?
x+y= 3.25
x-y= 1.75
someone help me answer these two
What is a solution of -8x+5>=11
A.-1/2
B.3
C.0.25
D.-1
Answer:
i got -2
Step-by-step explanation:
1 step; 8*x-5-(11)=0
2 step; 8x - 16 = 8 • (x - 2)
3 step; Solve : 8 = 0
4 step; Solve : x-2 = 0
final part Add 2 to both sides of the equation :
x = 2
The following graphs have no scales assigned to them. Which of them could
not possibly be density curves for a continuous random variable if they were
provided with the right scale?
Check all that apply.
A. Graph A
B. Graph B
C. Graph C
D. Graph D
E. Graph E
The graph A , graph C, could not possibly be density curves for a continuous random variable is they were provided with the right scale.
Given four graphs of different nature as options.
We are required to find the graph that is not continuous variable.
Continuous lines are those lines which when decreases, decreases with continuity and when increases,increases with continuity.
When we observe the graph A,graph C. In these graphs the value of function keeps increasing and decreasing a lot and not in continuity.
Hence graph A, graph C could not possibly be density curves for a continuous random variable is they were provided with the right scale.
Learn more about continuity at https://brainly.com/question/24637240
#SPJ1
Answer:
The answer is A, D, and E.
Step-by-step explanation:
What is the height of the pyramid ???
Answers:
A: 7cm
B: 5cm
C: 14 cm
D: 10 cm
Given:
[tex]m\angle ACD=45^\circ[/tex]
Point B is the center of the base.
Each side of the base = 10 cm
To find:
The height of the pyramid.
Solution:
It is given that the measure of each side of the base is 10 cm. It means the base is square. The length of the diagonal of a square is:
[tex]d=a\sqrt{2}[/tex]
Where, a is the side length of the square.
Putting [tex]a=10[/tex] in the above formula, we get
[tex]d=10\sqrt{2}[/tex]
It is given that point B is the center of the base. It means point B bisect each diagonal of a base. So,
[tex]BC=\dfrac{d}{2}[/tex]
[tex]BC=\dfrac{10\sqrt{2}}{2}[/tex]
[tex]BC=5\sqrt{2}[/tex]
In a right angle triangle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
In triangle ABC,
[tex]\tan (45^\circ)=\dfrac{AB}{BC}[/tex]
[tex]1=\dfrac{h}{5\sqrt{2}}[/tex]
[tex]5\sqrt{2}=h[/tex]
[tex]7.0710678=h[/tex]
Round the value to the nearest integer.
[tex]h\approx 7[/tex]
The height of the pyramid is about 7 cm. Therefore, the correct option is A.
The slope is ____ and the y-intercept is ___?
Answer:
The slope is -1 and the y-intercept is -1 ?
[tex]slope = \frac{ - 6 - 1}{5 - ( - 2)} \\ = \frac{ - 7}{7} \\ = - 1 \\ y - intercept : \\ y = mx + c \\ 1 = ( - 1 \times - 2) + c \\ c = - 1 \\ [/tex]
Answer:
slope -1 and y intercept is -1
hope this helps
have a good day :)
Step-by-step explanation:
Como se encuentra la mediana?
Answer:
Para encontrar la mediana: Organice los puntos de datos de menor a mayor. Si el número de puntos de datos es impar, la mediana es el punto de datos intermedio de la lista. Si el número de puntos de datos es par, la mediana es el promedio de los dos puntos de datos intermedios de la lista.
Step-by-step explanation:
que tenga un lindo día
help me solve for m<4 and m<5 and x
Answer:
x = 18
Angle 4 = 31 degree
Angle 5 = 59 degree
Step-by-step explanation:
According to the question, angle 3 is 90 degree and the sum of angle 4 and 5 is equal to the angle 3 as they are vertically opposite angles.
Angle 4 + angle 5 = 90 degree
Angle 4 = 2 x - 5
angle 5 = 4 x - 13
So, according to the question,
2 x - 5 + 4 x - 13 = 90
6 x - 18 = 90
6 x = 108
x = 18
So, angle 4 = 2 (18) - 5 = 31 degree
So, angle 5 = 4 (18) - 13 = 59 degree
To make a profit, a company’s revenue must be greater than its operating costs. The company’s revenue is modeled by the expression 7.5x – 100, where x represents the number of items sold. The company’s operation costs are modeled by the expression 79.86 + 5.8x. How many items does the company need to sell to make a profit?
Answer:
106 items
Step-by-step explanation:
We are actually finding the "break even" point, where revenue = costs.
Set the revenue 7.5x - 100 equal to the costs 79.86 + 5.8x:
7.5x - 100 = 79.86 + 5.8x
Group the x terms together:
1.7x - 100 = 79.86
and then group the constants together on the right side:
1.7x = 179.86
Solving for x, we get 105.8 (items)
Round this up: 106 items
The company will begin making a profit as production passes 106 items.
Answer:
first one : 7.5x -100 > 79.86 + 5.8x
second one : x > 105.8
last one : 106
Step-by-step explanation:
✨Please help me :) ✨
Answer:
Jaden would have to save $25 each week for next 6 weeks to get the $290 bike.
Step-by-step explanation:
What do we know:
He has $140 to start withHe saves $25 each weekHis bike costs $290What are we solving for;
We are solving for x (number of weeks it would take Jaden to buy a $290 bike), when y = 290Equation would be:
y = 25x + 140So for Jaden to buy a $290 bike, y would have to be replaced with 290, and solve for x;
y = 25x + 140=> 290 = 25x + 140
=> 290 - 140 = 25x
=> 150 = 25x
=> 150 / 25 = x
=> 6 = x
Therefore, Jaden would have to save $25 each week for next 6 weeks to get the $290 bike.
Hope this help!
WILL MARK BRAINILIEST
are the angles corresponding, alternate interior, alternate exterior, or constructive interior
Answer:
maybe it is corresponding
Identify the slope and y-intercept for the line y = -2x -3.
Answer:
The slope is -2 and the y intercept is -3
Step-by-step explanation:
y = -2x -3
This equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is -2 and the y intercept is -3
write this expression using numbers and symbols two less then six times a number
a. 2n-6
b.2n+6
c.6n-2
d.6-2
Answer:
d
Step-by-step explanation:
becaus ei did
Which function graph is shown
Answer:
A) y=3cos(-x)
Step-by-step explanation:
Because the amplitude of the graph is 3, this eliminates options C and D as their amplitudes are different. With the period of the graph being 2π, B cannot be correct because that would have a period of π/2. Therefore, A is correct.
Convert 5 km 36 m into km
Answer:
5.036 km
Step-by-step explanation:
36 m ÷ 1000 = 0.036 km
5 km + 0.036 km = 5.036 km
Find the value of x.
Answer:
x = 82°
Step-by-step explanation:
The opposite angles of a cyclic quadrilateral are supplementary, sum to 180°
x + 98° = 180° ( subtract 98° from both sides )
x = 82°
a nuber to be multiplied is called
Answer:
7×5 4×5 777⁷7777777777×7
Answer:
it is called factors
Step-by-step explanation:
Pls help me solve pls show how you got the answer
Answer:
48 length units
Step-by-step explanation:
area of each squre = 9
side length of each square = sqrt(9) = 3
Length of each side of grid = 4*3 = 12
Perimeter of grid = 4 sides = 4*12 = 48 length units
