JL is a common tangent to circles M and K at point J. If angle MLK measures 61ᵒ, what is the length of radius MJ? Round to the nearest hundredth. (Hint: Show that triangles LMJ and LKJ are right triangles, and then use right triangle trigonometry to solving for missing sides of the right triangles.)
To find the length of radius MJ, we can use right triangle trigonometry. Firstly, we can show that triangles LMJ and LKJ are right triangles. Then, we can use the given angle MLK of 61ᵒ to find the length of radius MJ, using the sine function. The equation to find MJ is MJ = rM * sin(29ᵒ).
Explanation:To find the length of radius MJ, we can use right triangle trigonometry. Firstly, we can show that triangles LMJ and LKJ are right triangles. Since JL is a common tangent, it is perpendicular to the radii of the circles at points J. Therefore, angle LMJ and angle LKJ are right angles. Now, we can use the given angle MLK of 61ᵒ to find the length of radius MJ.
Let's call the radius of circle M rM and the radius of circle K rK. In triangle LMJ, we have the following relationships:
angle LMJ = 90ᵒ (since it is a right triangle)angle MLJ = angle MLK - angle JLK = 61ᵒ - 90ᵒ = -29ᵒ (since angle JLK is a right angle)angle MJL = angle JML = 90ᵒ - angle MLJ = 90ᵒ - (61ᵒ - 90ᵒ) = 119ᵒUsing the sine function, we can find the length of side MJ:
sin(angle MLJ) = length of side MJ / length of side LJ
sin(-29ᵒ) = MJ / rM
Since sin(angle MLJ) = -sin(angle MJL), we can rewrite the equation as:
sin(29ᵒ) = MJ / rM
Now, we can rearrange the equation to solve for MJ:
MJ = rM * sin(29ᵒ)
Since we are not given the values of rM or rK, we cannot find the specific value of MJ. However, we can use this equation to find the length of radius MJ if we are given the values of the radii of the circles and the given angle MLK.
Remember to round the answer to the nearest hundredth as specified in the question.
The length of the shadow of a flagpole was found to be 72 feet. the shadow of a 3 foot picket fence in line with the flagpole was 4 feet. what is the height of the flagpole?
We can solve this problem by simply using ratio and proportion. Let us call the height of the flagpole to be X. Therefore the ratio and proportion would be:
3 ft is to 4 ft and X ft is to 72 ft
3 / 4 = X / 72
X = (3 / 4) * 72
X = 54 ft
The height of the flagpole is 54 ft.
Mary, who is sixteen years old, is four times as old as her brother. how old will mary be when she is twice as old as her brother? explained
Use basic identities to simplify the expression. sin2θ + tan2θ + cos2θ
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just need to check these answers
Answers for 1.2.1 how can I describe a graph
PLEASE HELP!! Use the following image↓
which one is it? need help please
Explain how the GCF helps with the distributive property. Why is it so important to use the GCF when factoring a sum of two numbers?
GCF is the greatest common factor, that divides two number and the distributive property is that when a number multiplied with each number in the bracket and then perform addition or subtraction etc.
GCF help with distributive property and it is important to use when factoring a sum of two numbers. For example we have to add fractions 2/3 and 4/9, now the GCF is 9
2/3 + 4/9
= 2(3) + 4 (1) / 9
Now 2 is the common factor, so it allow us to use the distributive property.
= 2 (3 + 2) / 9
= 2(5) /9
=10 / 9 is the answer.
(04.01 LC)
Which of the sets of ordered pairs represents a function?
A = {(2, −2), (5, −5), (−2, 2), (−5, 5)}
B = {(4, 2), (4, −2), (9, 3), (9, −3)}
Only A
Only B
Both A and B
Neither A nor B
Answer:
Only A
Step-by-step explanation:
Let's remember the definition of a function:
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
In A, each input has exactly one output so it's a function.
But in B, the inputs 4 and 9 have two different outputs, it can't represent a function.
The answer is only A.
1,226 days late to answer this question but that will not stop me!
The answer is... drumroll please ... Only A :]
Find the area of a regular hexagon whose side length is 16 in. and the apothem is 8 square root of 3 in
Find the measure of each interior angle and each exterior angle of the following regular polygons. Show your work
Answer:
Step-by-step explanation:
As we know for a regular polygon sum of all interior angles is represented by n A = 180 (n-2)
and sum of all exterior angles is represented by n A' = 360°
Here n represents number of sides of the polygon.
Now we will go for each options given.
(A) Decagon : (Having 10 sides)
(1) 8A = 180 ( 8-2 )
8A = 180 × 6
A = [tex]\frac{1080}{8}[/tex] = 160° ( interior angle )
(2) n A' = 360°
8 A' = 360°
A = 45° ( exterior angle )
(B) Pentagon ( having 5 sides )
(1) 5A = 180 ( 5-2 )
5A = 180 × 3 = 540
A = 108° ( interior angle )
(2) 5A' = 360
A' = 72° (exterior angle )
(C) Dodecagon : ( having 12 sides )
(1) 12A = 180 (12-2)
12 A = 180 × 10 = 1800
A = 150° ( interior angle )
(2) 12 A' = 360
A' = 30° ( exterior angle )
(D) 16-gon ( having 16 sides )
(1) 16 A = 180 ( 16 - 2 )
16A = 180 × 14
16 A = 1520
A = 157.5° ( interior angle )
(2) 16 A' = 360
A' = 22.5°
(E) 25-gon ( having 25 sides )
(1) 25 A = 180 ( 25-2)
25A = 180 (23)
A = 165.6° ( interior angle )
(2) 25A' = 360
A = 14.4° ( exterior angle)
A phone company offers two monthly plans. Plan A costs $30 plus an additional $0.15 for each minute of calls. Plan B costs $16 plus an additional $0.20 for each minute of calls.
For what amount of calling do the two plans cost the same?
What is the cost when the two plans cost the same?
Plan A = 30 +0.15x
Plan B = 16 +0.20x
30+0.15x = 16+0.20x
subtract 16 from each side
14 +0.15x = 0.20x
subtract 0.15x from each side
14=0.05x
x = 14/0.05 = 280 minutes
280*0.15 = 42 +30 = $72
280 * 0.20 = 56 +16 = 72
280 minutes and cost $72 each
The course for the frog hopping race is 59 inches long. Max's frog has jumped 2 feet and 3 inches. How much further does Max's frog need to jump in order to reach the finish line?
To find the remaining distance Max's frog needs to jump in the race, convert the initial jump to inches, and subtract it from the total race length.
The frog hopping race's course is 59 inches long. Max's frog has jumped 2 feet and 3 inches. To find out how much further Max's frog needs to jump to reach the finish line, convert 2 feet and 3 inches to inches and subtract it from 59 inches.
The conversion is: 2 feet x 12 inches = 24 inches. Adding 24 + 3 inches gives 27 inches. Subtract 27 inches from 59 inches to find the remaining distance Max's frog needs to jump.
The distance Max's frog still needs to jump is 32 inches.
What is the length of CF? look at image attached
The domain of the function is given. Find the range.
f(x) = 2x - 1
Domain: {-2, 0, 2, 4}
12.38 in expanded form
A doorway is 8 feet high and 4 feet wide. A square piece of plywood needs to be moved through the doorway. The plywood is 10 feet long and 10 feet wide. The door is a rectangle with a height of 8 feet, and a width of 4 feet. A dotted line shows the diagonal.
Will the piece of plywood fit through the door if it is tilted diagonally?
A. No, because the length of the diagonal is close to 9 feet.
B. No, because the height of the door is less than 10 feet.
C. Yes, because the length of the diagonal is close to 11 feet.
D. Yes, because the sum of the height and width of the door is greater than 10 feet.
After calculating the diagonal of the doorway to be approximately 8.944 feet using the Pythagorean theorem, it's clear that the 10-foot square piece of plywood will not fit diagonally through the door. Thus, the correct answer is option (A).
The question is whether a 10-foot square piece of plywood can fit through an 8-foot by 4-foot doorway when tilted diagonally. To determine if the plywood can fit, we need to calculate the diagonal of the doorway using the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as c² = a² + b² where c is the hypotenuse, and a and b are the other two sides.
Let's apply the theorem to our doorway:
Height (a) = 8 feet
Width (b) = 4 feet
Diagonal (c) = ?
We calculate the diagonal:
c² = a² + b²
c² = 8² + 4²
c² = 64 + 16
c² = 80
c = sqrt(80)
c = 8.944 feet (approx)
The diagonal of the doorway is approximately 8.944 feet, which is less than the 10 feet length of the plywood. Therefore, the correct answer is:
No, because the length of the diagonal is close to 9 feet.
The option (A) is correct.
What are the exact solutions of x2 − 3x − 1 = 0?
Select one:
a. x = the quantity of 3 plus or minus the square root of 5 all over 2 Incorrect
b. x = the quantity of negative 3 plus or minus the square root of 5 all over 2
c. x = the quantity of 3 plus or minus the square root of 13 all over 2
d. x = the quantity of negative 3 plus or minus the square root of 13 all over 2
The point (–3, –5) is on the graph of a function. Which equation must be true regarding the function?
f(–3) = –5
f(–3, –5) = –8
f(–5) = –3
f(–5, –3) = –2
Answer:
Option 1st is correct
[tex]f(-3) = -5[/tex]
Step-by-step explanation:
If any point [tex](x, y)[/tex] is on the graph then we can write the function as:
[tex]y= f(x)[/tex]
where
x is the independent variable and
y is the dependent variable.
As per the statement:
The point (–3, –5) is on the graph of a function.
⇒x = -3 and y = -5
By above definition we have;
[tex]f(-3) = -5[/tex]
Therefore, the equation must be true regarding the function is, [tex]f(-3) = -5[/tex]
Please help!! Will give medal!!
Compare the following functions:
(see attachment)
Which function has the smallest minimum?
A. All three functions have the same minimum
B. f(x)
C. g(x)
D. h(x)
Answer:
Step-by-step explanation:
We are given three functions and we have to find which one has the smallest minimum.
I function is
[tex]f(x) = -5sin(2x-\pi) +2[/tex]
Since sine varies from -1 to 1, we get this function has a minimum when sine takes value 1.
Minimum of f(x) =1(-5)+2 =-3
II function is
a graph of parabola with minimum at x=3 and y =-2
III function is shown in tabular form.
From the table we find that minimum is x=1 y=3
Tabulating we have
f(x) (3pi/4, -3)
g(x) (3,-2)
h(x) (1,3)
Smallest is for f(x) with least value of -3
Which of the following is true when probability answer is written in the form of a fraction
In probability, a fraction does not need to be simplified but converting to a percentage or decimal can aid in interpretation, with percentages being fractions with a denominator of 100. (First option)
When a probability answer is written in the form of a fraction, it is important to know how to handle the result. Simplifying the fraction is not generally required, especially in Probability Topics, where the focus is on understanding the probability itself rather than the arithmetic of fractions.
However, converting the probability to a percentage is a common practice that can help with interpretation. This is done by writing the value of the percent as a fraction with a denominator of 100 and then simplifying it if possible.
Converting a fraction to a decimal is another common step, which involves dividing the numerator by the denominator. It's also important to note that for rounding answers to probability problems, the convention is to round to four decimal places.
Suppose a study estimated that 85% of the residents of a town (with an error range of ±12 percentage points at 95% confidence) favor building a new community center. Which of the following percentages of the town's residents may favor building a new community center?
A. 69%
B. 79%
C. 59%
D. 99%
The confidence interval for a given sample value can be calculated using the following formula:
Confidence interval = Average value ± Margin of error
Which in this case the values are:
Average value = 85%
Margin of error = 12%
Therefore substituting the given values into the equation will give us:
Confidence interval = 85 ± 12
Confidence interval = 73, 97
Therefore the percentage of the residents of the town who are favour of building a new community center ranges from 73% to 97%.
Based from the given choices, only letter B 79% is within this range:
Answer:
B. 79%
Answer:
B. 79%
Step-by-step explanation:
yes
in the system shown below, what are the coordinates of the solution that lies in quadrant I? x^2-y^2=25, x+y=25
Can anyone please help ASAP, will give thanks and all that fun stuff
Answer:
The answer is B!!!!
8% of x is equal to 48
divide 48 by 8%
48/0.08 = 600
check
600*0.08 = 48
x=600
Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?
Stanfing in your tree house 50ft off the ground you look down at a 60 degree angle how many feet from the base of the tree is the frisbee
multiply 50 x tan(60) = 86.6 feet.
round your answer as needed
2 Questions~
Evaluate the expression.
38+16⋅12÷2−(30⋅2)
Simplify this expression.
5 + 10 ÷ 5
3
7
10
15
Your answer would be a.
Answer: 3
hope this helps! :)
~Izzie