Given that the external angle formed by the two tangent is 40° and the
part of [tex]m \widehat{LMJ}[/tex] is 138°, we get that [tex]m \widehat{MJ}[/tex] = 87°.
Which property can be used to find [tex]m \widehat{MJ}[/tex] ?Using the two tangent angle theorem, we have;
[tex]m \angle K = \mathbf{ \dfrac{1}{2} \times \left(\widehat{LMJ} - \widehat{LJ} \right)}[/tex]
m∠K = 40°
[tex]m \widehat{ML}[/tex] = 138°
[tex]m \widehat{LMJ}[/tex] = [tex]m \widehat{ML}[/tex] + [tex]m \widehat{MJ}[/tex]
[tex]m\widehat{LJ} = \mathbf{360^{\circ} - \left(m\widehat{ML} + m\widehat{MJ} \right)}[/tex]
Which gives;
[tex]m \angle K = \dfrac{1}{2} \times \left(\widehat{LMJ} - \left( 360^{\circ} - \left(m\widehat{ML} + m\widehat{MJ} \right) \right)\right)[/tex]
Therefore;
[tex]m\angle K= \dfrac{1}{2} \times \left(m \widehat{ML} + m \widehat{MJ} - \left( 360^{\circ} - \left(m\widehat{ML} + m\widehat{MJ} \right) \right)\right)[/tex]
[tex]40^{\circ}= \mathbf{ \dfrac{1}{2} \times \left(138^{\circ} + 2 \cdot m \widehat{MJ} - 232^{\circ} \right) \right)\right)}[/tex]
Which gives;
[tex]m \widehat{MJ}[/tex] = 87°Learn more about two angle tangent theorem here:
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Final answer:
The measure of MJarc in circle C, when MLarc is 138°, is calculated to be 222°, based on the property that the sum of arcs in a circle is 360°.
Explanation:
The question revolves around the properties of a circle and its tangents. We have a circle C with two tangents KJ and KL, touching the circle at points J and L respectively. In addition, we are told that the measure of the arc ML (from M to L) is 138° and we need to find the measure of the arc MJ (from M to J).
According to the properties of circles, a tangent at any point on the circle is perpendicular to the radius at that point. Also, the measure of an angle formed by a tangent and a chord through the point of tangency is half the measure of the intercepted arc. In this scenario, MJ and ML are two arcs that form a complete circle, so the sum of mMJarc and mMLarc should equal 360°. If mMLarc is 138°, then mMJarc, the arc we are trying to find, would be 360° - 138°, which equals 222°.
William runs 5 meters in 20 steps. How many kilometers will he run if he takes 1,000 steps ?
Enrique charges $5 for every 1/5 hour he spends walking dogs.in the morning he walks buttons for 2/5 hour bruno for 1/5 hour and pepper for 3/5 hour. Monday thru friday. On saturdays he takes mimi diva and coco to the dog park for 4/5 of an hour. On wendsday this week it rained and pepper wanted to stay out for only 1/5 hour. How many hours did enrique spend with the dogs this week. Explain your method
Margaret wants to call her friend overseas. There is a connection fee of $2 and a charge of $1.50 per minute. So the cost of the call is 2 + 1.5t dollars for t minutes.
a rectangle that is 2 inches by 3 Inches has been scaled by factor of 7 suppose you want to scale the copy back to its original size what scale factor would you use?
This is about transformation of objects.
Scale factor back to original size = 1/7
We are told that the rectangle was scaled by a factor of 7.What this means is that if the length and width are x and y respectively, then the new scaled measurements will be;
7x and 7y.
Now,for us to scale back to the original size, all we need to do is to divide the new scale measurements by a factor of 7.This means the original size will be;
Length = 7x × 1/7
Width = 7y × 1/7
Thus,the scale factor will be 1/7 back to the original size.Read more at; https://brainly.com/question/17292295
for a rectangular solid with length 12 in width 2 in in height 15 in state the appropriate formula for volume and also find the volume
Shoe store A is having a sale in which every pair of shoes is 40% off the regular price.
Shoe store B is having a sale in which $40 is deducted from the regular price.
Richard is comparing the price of the same pair of shoes in both shoes in both stores.In both stores, the shoes normally sell for $120. Which store has the better bargain?
If changes are made to a signature while using version 5.x signature files, are they visible in the router running the configuration?
which equation is the inverse of y=100-x2
Answer:
Inverse of y = [tex]f^{-1}(x)[/tex] = [tex]\sqrt{100 -x}[/tex].
Step-by-step explanation:
Given : f(x) = y = 100 - x²
To find : Find inverse.
Solution : We have given that :
f(x) = y = 100 - x²
Step1) : Replace every x with a y and replace every y with an x .
x = 100 - y².
Step 2): Solve for y
On subtracting 100 from both sides
x - 100 = -y²
On multiplying both side by -1
100 -x = y²
Taking square root both sides and switching sides
y = ± [tex]\sqrt{100-x}[/tex].
Step3 ) : Replace y with [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].
Therefore, inverse of y = [tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].
Answer:
A on edge
Step-by-step explanation:
which relation defined by mapping diagram is a function
what is the rate of decay, as a percent, for the following function n(x)=7(0.067)^x
Answer: The rate of decay is 93.3%.
Step-by-step explanation:
Since we have given that
The exponential function is given by
[tex]n(x)=7(0.067)^x[/tex]
As we know the general equation of exponential function that is given by
[tex]n(x)=a(1-b)^x[/tex]
Here, a denotes the initial value
1-b denotes the rate of decay.
So, On comparing both the equations, we get that
[tex]1-b=0.067\\\\b=1-0.067\\\\b=0.933=0.933\times 100=93.3\%[/tex]
Hence, the rate of decay is 93.3%.
In a rhombus MPKN with an obtuse angle K the diagonals intersect each other at point E. The measure of one of the angles of a ∆PKE is equal 16°. Find the measures of all angles of ∆PKE and ΔPMN.
Answer:
m∠KEP = 90°
m∠EKP = 74°
m∠EPK = 16°
m∠N PM= 16°
m∠MNP = 16
m∠M = 148°
Step-by-step explanation:
If you do RSM those are the answers
in 3/4 identify the role of 3. Then explain how to read tbis number
Answer:
The 3 is the numerator, To read the number is "three-fourths"
Step-by-step explanation:
I hope this helps!
Find the equation of the plane through the point p=(5,5,4)p=(5,5,4) and parallel to the plane 5x+2y−z=−6.
The diagonal of rectangle ABCD measures 2 inches in length What is the length of line segment AB?
Answer:
Step-by-step explanation:
B on edge
Five hummingbirds drink 7.5 ounces of sugar water a day. How much sugar water is needed for 14 hummingbirds?
A school sold small and large boxes of fruit as a fundraiser. One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Let x represent the price of a small box and y represent the price of a large box. Solve the system to determine the price of each size box of fruit.
A The price of a small box of fruit is $10 and the price of a large box of fruit is $14.
B The price of a small box of fruit is $8 and the price of a large box of fruit is $14.
C The price of a small box of fruit is $10 and the price of a large box of fruit is $16.
D The price of a small box of fruit is $14 and the price of a large box of fruit is $16.
The answer is y=14 and x= 10
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218.
Then we have 5x+13y=232
12x+7y=218
Solving these two equations here we get y=14 and x= 10
Hence, The answer is y=14 and x= 10
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Suppose that the polynomial function A(x) = - 0.0082x2 + 0.06x approximates a person's blood-alcohol level x hours after drinking 5 ounces of 80-proof whiskey. What is the person's blood-alcohol level after 3 hours?
The classroom encyclopedia set seems to fill a shelf that is 24 in long each book is 3/4 in thick how many books are in the classroom set
A vegetable farmer fills 2/3 of a wooden crate with 5/7 pound of tomatoes. How many pounds of tomatoes can fit into one crate?
There are fewer than 8 gallons of gas in the tank how do I write an inequality for that
C=
5\9
(F−32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
I.) A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5\9 degree Celsius.
II.) A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
III.) A temperature increase of 5\9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
For what value of xis the square of the binomial 3x+1 is 9 times greater than the square of the binomial x–2?
Final answer:
The value of x for which the square of the binomial 3x+1 is 9 times greater than the square of the binomial x−2 is obtained by equating (3x + 1)² to 9(x − 2)², which simplifies and solves to x = 5/6.
Explanation:
To find the value of x for which the square of the binomial 3x+1 is 9 times greater than the square of the binomial x−2, we need to formulate and solve an equation based on the given conditions:
(3x + 1)² = 9(x − 2)²
Expanding both sides gives us:
9x² + 6x + 1 = 9x² − 36x + 36
Now, by simplifying and solving for x, we find:
42x = 35
x = 35 / 42
x = 5 / 6
Therefore, the value of x is 5/6.
a triangle has an area of 54 m2 and a height of 9m how long is the base of the triangle entered your answer in the box
2 to the x power equals 512
The diagonals BF and CE divide the hexagon ABCDEF into two equilateral triangles and a square. Find the perimeter of the hexagon if BF = 3 cm. Answer: P = cm
Answer: The perimeter of the hexagon is 18 cm.
Step-by-step explanation: As given in the question, hexagon is shown in the attached figure.
The diagonals g and h divides the hexagon into two two equilateral triangles and one square .
Also, length of diagonal g = 3 cm.
We are to find the perimeter of hexagon.
We know that all the sides of a square are equal, so we have
length of b = length of h = length of e = length of g = 3 cm.
Since the two triangles are equilateral, so all their sides will be equal.
That is, length of a = length of f = length of g =length of c =length of d = length of h = 3 cm.
We know that the perimeter of a polygon is equal to the sum of the lengths of its sides.
Therefore, the perimeter of hexagon is given by
P = a + b + c + d + e + f = 3 + 3 + 3 + 3 + 3 + 3 = 18 cm.
Thus, the perimeter of the hexagon is 18 cm.
which number produces an irrational number when multiplied by 0.5
What is the circumference of a circle circumscribed around a rectangle with sides 10 cm and 24 cm?
A swimmer swam 49 kilometers in d days. what is the value of d if the swimmer swam an average of 3.2 kilometers daily?
How can you find the surface area of a composite solid made up of prisms
9ax+9b-6=21
based on the equation above what is the value of ax+b
The value of equation ax + b is 3.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
To find the value of ax + b, we need to isolate that expression on one side of the equation.
Starting with:
9ax + 9b - 6 = 21
We can add 6 to both sides:
9ax + 9b = 27
Then, we can factor out 9 from the left-hand side:
9(ax + b) = 27
Dividing both sides by 9, we get:
ax + b = 3
Therefore,
The value of equation ax + b is 3.
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