By using Pythagoras theorem and distance formula the length of CP is obtained as 3.43 units.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
To find the length of CP, first find the coordinates of point P, and then use the distance formula to calculate the length of CP.
Let A be at the origin (0, 0), and let B be on the positive x-axis at (6, 0). Then we can find the coordinates of C using the Pythagorean theorem -
AC² + BC² = AB²
AC² + (3√3)² = 6²
AC² = 9
AC = 3
So C is located at (3, 3√3). We can find the coordinates of M by taking the average of the coordinates of A and B, which gives -
M = ((0+6)/2, (0+0)/2) = (3, 0)
Similarly, find the coordinates of N by taking the average of the coordinates of B and C, which gives -
N = ((6+3)/2, (0+3√3)/2) = (4.5, 1.5√3)
Now find the equation of the line passing through M and C, which is the line containing median AM -
slope = (3√3 - 0)/(3 - 0) = √3
y - 0 = √3(x - 3)
y = √3x - 3√3
And find the equation of the line passing through N and A, which is the line containing median CN -
slope = (0 - 3√3)/(0 - 6) = √3/2
y - 0 = (√3/2)(x - 6)
y = (√3/2)x - 3√3
Now, find the intersection point of these two lines, which is point P -
√3x - 3√3 = (√3/2)x - 3√3
x = 6/3.5
x = 12/7
y = √3(12/7) - 3√3
y = 3√3/7
So P is located at (12/7, 3√3/7).
Now use the distance formula to find the length of CP:
CP² = (12/7 - 3)^2 + (3√3/7 - 3√3)²
CP² = (33/7)^2 + (6√3/7)^2
CP² = 1089/49 + 72/49
CP² = 1161/49
CP = √1161/7
Therefore, the length of CP is (approximately) 3.43.
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Graph the line with the equation y = 6/5x-2
Answer:
Step-by-step explanation:
The graph of equation is shown in figure.
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The equation of line is,
⇒ y = 6/5x - 2
Now,
Since, The equation of line is,
⇒ y = 6/5x - 2
Clearly, The slope = 6/5
And, The y - intercept = - 2
Thus, The graph of equation is shown in figure.
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Conor earns $9 an hour for yard work. He raked leaves one afternoon and earned $29.25.
How much does Conor earn for each minute he does yard work?
Hint: There are 60 minutes in 1 hour.
29.25 divided by 9 is 3.25. You have to take the total amount of money he made $29.25 and divide it by the amount he gets every hour $9. So 29.25 divided by 9 is 3.25 or 3 hours and 15 minutes.
Answer:
15 cents a minute
Step-by-step explanation:
9 ÷ 60 = $0.15
Martin charges $10 for every 5 bags of leaves he rakes. Last weekend, he raked 28 bags of leaves. How much money did he earn?
Answer:
$48
Explanation:
24 Divided by 5 = 4.8 times 10 =48
Answer:
$56
Step-by-step explanation:
$10 divided 5＝$2
one bag $2
28bags＝$2 multiply 28＝$56
please help me with this. I will give brainliest to whoever gets the question right. attachment below.
Answer:
22100
Step-by-step explanation:
First you would add the truckloads of concrete for both playgrounds (3 5/8 + 3 5/8 + 1 9/10). Then you would divide that by 1/2. Finally multiply that number by 2000. (Pls mark me the brainliest)
If represents the number of entry tickets sold and the hours of space rental, which inequality represents the constraints in the situation
2000000000017827272626728182
Answer:
no question or any number or question available
Please help me!!!!!!
Answer:
do you know what the question is asking?
Step-by-step explanation:
An arithmetic sequence is given below.
15, 19, 23 ,27 …
Write an explicit formula for the nth term an
Step-by-step explanation:
arithmetic sequence means every new term is the previous term plus a certain constant.
as we can see, this constant is +4 in our case.
15 + 4 = 19
19 + 4 = 23
23 + 4 = 27
...
so, we have
a1 = 15
a2 = a1 + 4 = 15 + 4 = 19
a3 = a2 + 4 = a1 + 4 + 4 = a1 + 2×4 = 15 + 8 = 23
...
an = an-1 + 4 = a1 + (n-1)×4 = 15 + (n-1)×4
I’ll give brainliest, thanks and 5 stars.
Answer:
First, you can break 6 into 3 * 2.
[tex]\frac{6^4*15^3}{3^3*2^4} =\frac{3^4*2^4*15^3}{3^3*2^4}[/tex]
Then, cancel out the common factor of [tex]3^3[/tex]:
[tex]\frac{3^4*2^4*15^3}{3^3*2^4} =\frac{3*2^4*15^3}{2^4}[/tex]
Next, cancel out the common factor of [tex]2^4[/tex].
[tex]\frac{3*2^4*15^3}{2^4} =3*15^3[/tex]
You can evaluate it as 10125 if you'd like.
why does math included things we will never use
Answer:
To make students question their existence
Step-by-step explanation:
a break on the earth crust that is a result of movement or shaking refers to
Answer:
A fault
Step-by-step explanation:
A fault is a crack in the Earth's crust that allows chunks of the crust to move relative to one another along its length.
Find the inverse function in slope-intercept form (mx+b):
f(x) = -x - 5
Answer:
In order to find the inverse of a function, we flip it over the line y=x, or we switch the x and y values in the equation and solve it for y. So let's do the latter:
m(x) = 5x - 5
y = 5x - 5
x = 5y - 5
5y = x + 5
y = (x + 5)/5
Step-by-step explanation:
hope this is helpful
Answer: f ^−1(x)=x+5
Zach goes on holiday. The ratio of the costsflights: hotels = 3 : 8. The cost of the flightsis $861. Workout the total cost of flightsand hotels.
total cost of the hotels is 2,296
Answer:
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PLEASE HELP IT’S DUE TMR!!
4856
1.07
12.9
7.00
0.00199 (199)
0.000660 (660)
:)
can somebody tell me if these answers are correct?
Is 1/3 greater than, less than, or equal to 1?
Answer:
1/3 is less than 1
Step-by-step explanation:
3/3=1
1/3<1
Solve for Z:
4 > 5Z + 34
help me so hard
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
Z < − 6
Interval Notation:
( − ∞ , − 6 )
Step-by-step explanation:
Answer:
z<-6
Step-by-step explanation:
4-5Z>34
-5z>34-4
-5z>30
z<-6
Give coordinates for three possible pairs of points for the other two verticies...
Answer:
A) (-1,3) and (4,3)
B) (-1,-7) and (4,-7)
C) (1.5, .5) and (1.5, -4.5)
Step-by-step explanation:
For 1 and 2, because the y-values of the points are the same, the length of the square can be found by subtracting the x-coordinates.
4-(-1)=4+1=5
The length of the side of the square is 5.
1. For the first set of points, the square is above the two given points so just add 5 to the y-values
-2+5=3
This gives you the points:
(-1,3) and (4,3)
2. For the second set of points, the square is below the two given points so subtract 5 from the y-values.
-2-5=-7
This give you the points:
(-1,-7) and (4,-7)
3. The third answer is when the two given points are on opposite corners
of the square.
Here the diagonal is equal to 5 since they are on opposite corners of the square.
The diagonal of a square can be found with the pythagorean theorem
Since we have the diagonal we can find the side lengths we need.
[tex]2s^2=25[/tex]
s=[tex]\sqrt{\frac{25}{2} }[/tex]
s=3.5355
We want the new vertices to be in the middle of the other vertices x-coordinates
[tex]\frac{4-(-1)}{2} =\frac{5}{2} =2.5[/tex]
The new vertices will be 2.5 units away from the other vertices
-1+2.5=1.5
The new vertices will be at x=1.5
Now we need the pythagorean theorem again to find the y-values
[tex](2.5)^2+h^2=(3.5355)^2[/tex]
[tex]6.25+h^2=\frac{25}{2}[/tex]
[tex]h=\sqrt{\frac{25}{2} -6.25}[/tex]
h=2.5
The new vertices will be:
(1.5, -2+2.5)=(1., .5)
(1.5, -2-2.5)=(1.5, -4.5)
According to the scatterplot, what would you predict would be the crime index for a city with a population of 220,000? A. 450 B. 465 C. 500 D. 550
Answer:
Step-by-step explanation:
500
kate has $2.95 in quarters and nickels and the total number of ocins is 23 how many quarters and how many nickels does kat have
Answer: 9 quarters and 14 nickels
Step-by-step explanation:
9*25=225
14*5=70
225+70=295
The total number of nickels is 14 and the total number of quarters is 9 and this can be determined by forming the linear equation.
Given :
kate has $2.95 in quarters and nickels and the total number of coins is 23.
The following steps can be used in order to determine the total number of quarters and nickels Kat have:
Step 1 - Let the total number of quarters be 'x' and the total number of nickels be 'y'.
Step 2 - Remember one quarter is equal to $0.25 and one nickel is $0.05.
Step 3 - The total amount of money Kat has:
0.25x + 0.05y = 2.95 --- (1)
Step 4 - Total number of coins is given by:
x + y = 23
x = 23 - y --- (2)
Step 5 - Substitute the value of 'x' in equation (1).
0.25(23 - y) + 0.05y = 2.95
5.75 - 0.25y + 0.05y = 2.95
2.8 = 0.20y
y = 14
Step 6 - Now, substitute the value of 'y' in equation (2).
x = 23 - 14
x = 9
So, the total number of nickels is 14 and the total number of quarters is 9.
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the distance between town A and town B is 123 km. Two buses begin their journey and move directly toward each other. From town A, the bus is moving at a speed of 45 km/hr and from town B, the bus is moving at a speed of 67 km/hr. Assuming the buses started at the same time, find how far is their meeting point from town A?
Answer:
Speed of slower bus = 50mph and
speed of faster bus = 60 mph
Step-by-step explanation:
Let speed of first bus be x mph
Then speed of second bus = x+10 mph.
Let A and B have a distance d.
Then given that faster bus reached in 3.5 hours.
i.e. ... i
THe other bus was away from B by 1/6 times d.
Distance travelled by slower bus = 1-1/6 = 5d/6
Time taken = 3.5 hours
i.e. ... ii
Divide i by ii to eliminate d.
ie Speed of slower bus = 50mph and
speed of faster bus = 60 mph
Use ii equation
miles
Given: AB is perpendicular to BD. Find m<1
See picture for full problem. Please and thank you!
Step-by-step explanation:
angle 5 = supplementary to 89 = 180-89 = 91°
the sum of all angles in a triangle is always 180°.
so,
angle 3 = 180 - 51 - 91 = 38°
angle 2 = complementary to 38 = 90-38 = 52°
therefore,
angle 1 = 180 - 38 - 52 = 90°
Find the slope of the line that passes through each pair of points (8,2) (8, -1)
Answer:
Undefined
Step-by-step explanation:
Use the following formula to solve for slope:
[tex]\frac{y_2-y_1}{x_2-x_1} =m[/tex]
[tex]m=\frac{(-1)-2}{8-8}[/tex]
[tex]m=\frac{-3}{0}[/tex]
The equation is not a function and therefore the slope is undefined because there are multiple y values for a single x value.
I need help with my Geometry. Can you help?
Thanks.
Answer:
1. 32 units
2. C(-15, -4) and D(17, -4)
Step-by-step explanation:
1.The midpoint divides CD into two segments that are the same length:
CM = MD
8(x -2) = 4(5x -16)
8x -16 = 20x -64 . . . eliminate parentheses
48 = 12x . . . . . . . . . add 64 -8x
x = 4 . . . . . . . . . . . divide by 12
Then the length of CD is ...
CD = 2·CM = 2(8(x -2)) = 2(8(4-2))
CD = 32
__
2.If we put C and D on the same horizontal line as M, their coordinates are ...
C = M -(16, 0) = (1,-4) -(16, 0) = (-15, -4)
D = M +(16, 0) = (1, -4) +(16, 0) = (17, -4)
Coordinates C and D that have M(1, -4) as a midpoint are ...
C(-15, -4) and D(17, -4).
please I need immediate help
Answer:
sorry what? the photo is not clear
Step-by-step explanation:
dude the photo
plz brainliest
7+(4x8)-9
i need help this is weird
Answer:
30
Step-by-step explanation:
7+(4*8)-9
Multiply first inside the parentheses
7+(32)-9
Then add and subtract from left to right
39 - 9
30
Answer:
If x is a variable then the answer is 4x⁸ - 2
If x is a multiplication representation then the answer is 30
Step-by-step explanation:
If x is a variable:
1) Eliminate redundant parentheses
[tex]7+(4x^{8} )-9\\7+4x^{8} -9[/tex]
2) Subtract the numbers
[tex]7+4x^{8} -9\\-2+4x^{8}[/tex]
3) Rearrange Terms
[tex]-2+4x^{8} \\4x^{8} -2[/tex]
ANSWER ASAP PLEASE!!!!!
What is the domain of the square root function graphed below?
A. x is greater than 1
B x is greater or equal to 1
C. x is greater than 3
D. x is greater or equal to 3
Answer: the answer is D hope it helps.
Just took the test. Edge
I'M GIVING BRAINLIEST!!!!!!!!!!!
Answer:
i dont know
Step-by-step explanation:
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6 * 2 /( -1)4* 5-(8+3)
Answer:
-251
Step-by-step explanation:
Following BEDMAS/PEMDAS
6*2/(-1)4*5-(8+3); first simplify the brackets/parenthesis
= 6*2/(-1)4*5-11; now do divisons and multiplications going from left to right
= 12/(-1)4*5-11 = -12*4*5-11 = -48*5-11 = -240-11
= -251
What is the y-intercept in the equation y = 4x-3?
Answer:
-3
Step-by-step explanation:
y = mx + b
b is the y-intercept
Answer:
(0,-3)
This the answer hope this help