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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HELP ASAP!!!
What are the exact solutions of x2 − 3x − 1 = 0 using x equals negative b plus or minus the square root of the quantity b squared minus 4 times a times c all over 2 times a?
x = the quantity of 3 plus or minus the square root of 5 all over 2
x = the quantity of negative 3 plus or minus the square root of 5 all over 2
x = the quantity of 3 plus or minus the square root of 13 all over 2
x = the quantity of negative 3 plus or minus the square root of 13 all over 2
Explanation:
The given equation is in the form [tex]ax^2+bx+c=0[/tex], where,
a = 1b = -3c = -1Use the quadratic formula to get the following
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-3)\pm\sqrt{(-3)^2-4(1)(-1)}}{2(1)}\\\\x = \frac{3\pm\sqrt{9+4}}{2}\\\\x = \frac{3\pm\sqrt{13}}{2}\\\\[/tex]
The last equation matches with choice C.
Find the range of the following group of numbers: 1, -8, -10, 11, 19
simplify the expression.
20a^4 × (1/2 a^3 )^2
Answer:
5a^10
Step-by-step explanation:
Please man, I need this answer as fast as possible. Thank You!!!!
Answer:
-5f
and
2g
Step-by-step explanation:
1,2
2,6
3,12
4, 20
Is the function Linear or Nonlinear, and explain why
Explanation:
The variable x increases by 1 each time we move down the rows. This increase is constant or the same jump each time.
However, the variable y increases by different amounts. From y = 2 to y = 6, we have +4. Then from y = 6 to y = 12 is +6. This mismatch of increases is sufficient to prove we don't have a linear function. The function is nonlinear.
Visually, we can plot all of the points on the same xy grid. Notice that a straight line does not go through all four points. Rather, a parabola does, and the equation of the parabola is y = x^2+x which is the same as y = x(x+1).
Find the perimeter. Simplify your answer.
Answer:
wild guess, 50
Step-by-step explanation:
10s+3+10s+3+3s+9+3s+9= 50
Megan spent half of her paycheck on an iPad. Over the weekend she earned $12 from babysitting. If she has $514.50 now. Write and equation and solve to find out how much was her paycheck
the price of a pair of shoes increases from $58 to $61 What is the percent increase to the nearest percent?
please help I will mark brainliest
Answer:
23.08
Step-by-step explanation:
What is the greatest common factor of 48, 72 and 52? A.2 B.4 C.8 D.16
the answer is 4 since 4 is common in all the three digits
B).4
i have to explained it in words pls help
9514 1404 393
Answer:
slope: cost per miley-intercept: fixed base costStep-by-step explanation:
The y-intercept is the value of y when x=0. The problem statement tells you that x is the number of miles driven, and y is the rental cost.
When the number of miles driven is zero, the rental cost is ...
y = 2.25×0 +70
y = 70
The cost of renting the truck is $70 when it isn't driven anywhere. The y-intercept ($70) is the basic, fixed cost of truck rental.
__
If x=1 (1 mile driven), then 2.25 is added to the cost of the truck rental. The slope (2.25) is the cost per mile driven. (That mileage cost is added to the basic rental cost.)
Please help. Been stuck on this for days.
Answer:
At least 8.333 km/hr
Step-by-step explanation:
Using the inequality setup, we have
5/r + 1.25 + .75 + .9 ≤ 3.5
5/r ≤ .6
5 ≤ .6r
r ≥ 25/3 = 8.333
Simplify 38 - 32
-
A. 34
B. 36
c. 310
D. 3-6
Answer:
38 - 32 = 6
Step-by-step explanation:
subtract the question
points (4, 3) and (0, 6) Mid point
Answer:
(3.5,3)
Step-by-step explanation:
Midpoint= (x¹+x²/2, y¹+y²/2)
x¹=4
x²=3
y¹=0
y²=6
Put your values into the formula
(4+3/2,0+6/2)
(7/2, 6/2)
(3.5,3)
Complete the recursive formula of the arithmetic sequence -1, -13, -25, -37
a ( 1 ) =
a ( n ) = a ( n-1 ) +
Answer:
see explanation
Step-by-step explanation:
A recursive formula allows the next term in a sequence by adding the common difference d to the previous term.
d = a₂ - a₁ = - 13 - (- 1) = - 13 + 1 = - 12 , then
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 12 with a₁ = - 1
8x -2 + (4x - 1)(4x+1) = 0
Answer:
8x - 1 + 16x²
Step-by-step explanation:
8x - 2 + (4x - 1)(4x+1) = 0
=> 8x - 2 + 16x² + 4x - 4x - 1
=> 8x - 2 + 16x² - 1
=> 8x - 1 + 16x²
Therefore, 8x - 1 + 16x² is our answer
What is Arithmetic ?
Answer:
Arithmetic is a branch of mathematics that consists of the study of numbers, especially concerning the properties of the traditional operations on them - addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Answer:
The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.
Step-by-step explanation:
a man earn $6 in two hours. how much does he earn in 5 hours
Answer:
$15
Step-by-step explanation:
6 divided by 2 is 3
3 multiplied by 5 is 15
A circle is divided into equal parts. An angle turns through one of the parts, as
shown below. Which equation shows a way to find the measure of the angle?
Answer:
1/6 = 60/360
Step-by-step explanation:
The circle is split into 6 parts and a circle equals 360°
1/6 = x/360
Cross Multiply...
6x = 360
Divide to isolate x...
x = 60
The equation measures the angle that will be 1 / 6 = x / 360. Then the correct option is D.
What is a circle?It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.
A circle is divided into equal parts. An angle turns through one of the parts, as shown below.
Then the equation shows a way to get the measure of the angle that will be
The arc of the circle makes 360°. And the circle is divided into six equal parts, and then the angle of each section will be equal.
Let x be the angle of each section.
Then the ratio of the area of the complete circle and one-sixth circle. Then we have
A₁ = 6A₂
Then we have
A₂ / A₁ = [(x/360) πr²] / [πr²]
A₂ / 6A₂ = x / 360
1 / 6 = x / 360
Then the value of x will be
x = 60°
More about the circle link is given below.
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what is rt5 x rt3
yeah do that plz
Answer:
3(2r+1)
Step-by-step explanation:
5r+1 is 6
Then you factor out 3 and get 3(2r+1)
5x-4=9x+6 please put explanation
is 5,7,9 a pythagorem theorem? pls help me due rn
Answer:
No
Step-by-step explanation:
a^2+b^2=c^2
5^2= 25
7^2 = 49
25+49=74
square root of 74 does not equal 9
Answer:
No.
Step-by-step explanation:
Pythagorean Theorem: a²+b²=c²
5²+7²=9²
5²=25, 7²=49, 9²=81
25+49 does not equal 81.
phân tích đa thức x^3 - x thành phân tử
Answer:
1
Step-by-step explanation:
A recipe calls for
23
cup of sugar for every 4 teaspoons of vanilla. How much vanilla should be used for every 1 cup of sugar?
Answer:
.....
Step-by-step explanation:
PLEASE HELPPPPPPPPPPPPPPPP!!!
Answer:
6 years
Step-by-step explanation:
5% of 1000 is 50
1. $1050
2. $1100
3. $1150
4. $1200
5. $1250
6. $1300
For each gallon of gas Sean puts in his truck, the truck will go $\frac{8}{3}$ miles. Suppose Sean's tank is empty, and he puts in $\frac{7}{5}$ gallons. How far can Sean go with his truck?
Answer:
56/15
Step-by-step explanation:
All we have to do is 8/3 x 7/5 and 8x7 is 56,5x3 is 15
So the answer is 56/15.
Answer:
56/15
Step-by-step explanation:
If the perimeter of a rectangle is 6x^2-2x+14 and the length is x^2-x+8 what is the measure of the width?
Please help!!
Answer:
w = 2x^2-2x+15
Step-by-step explanation:
Since the formula to find the perimeter is P=2l+2w, use this to set up your equation:
6x^2-2x+14 = 2(x^2-x+8) + 2w
Then, distribute the 2 to everything inside the parentheses.
6x^2-2x+14 = 2x^2-2x+16 + 2w
Subtract 2x^2-2x+16 from both sides, leaving you:
4x^2-4x+30 = 2w
Divide 2 from both sides.
2x^2-2x+15
The answer is 2x^2-2x+15
HELP 25 POINTS LIKE HELP SOLVE THIS ASAP!!!
Answer:
nahhhh why did you report me I did nun wrong
Step-by-step explanation:
Help me urgently i have to submit a t today
Answer:
6/5
Step-by-step explanation:
He reads 1.2 page every 1 minute, 1.2X15(mins)=18 page.
Select the function that is odd.
A. f (x) = sin (x)
B. f (x) = cos (x) + sin (x)
C. f (x) = cos^3 (x)
D. f (x) = sin^2 (x)
easy one for you folks.
Answer:
if its easy do it
Step-by-step explanation:
Answer:
7.5/15 or something because yes