For the given figure, where m and nare relatively prime positive integers. The value of m+n is 32.
Explain Law of Cosines.The law of cosines, also known as the law of cosines, relates all three sides of a triangle to one angle of the triangle. Most useful for searching for missing information in triangles. For example, if you know all three sides of a triangle, you can use the law of cosines to find the measure of the angle. Similarly, if you know two sides and the angle between them, you can find the length of the third side by the law of cosines.
Let X be the intersection of the circles with centers B and E, and Y be the intersection of the circles with centers C and E.
Since the radius of B is 3, AX = 4.
Assume AE = p.
Then EX and EY are radii of circle E and have length 4 + p.
AC = 8, and ∠CAE = 60° because we are given that triangle T is equilateral.
Using the Law of Cosines on Δ CAE, we obtain
(6+p)² =p² + 64 - 2(8)(p) cos 60
The 2 and the cos 60 terms cancel out:
p² + 12p + 36 = p² + 64 - 8p
12p+ 36 = 64 - 8p
p = 28/20
= 7/5
The radius of circle E is 4 + (7/5)
= 27/5,
So, the answer is 27 + 5 = 32
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A highway noise barrier is 120 m long is constructed in 2 pieces. One piece is 45 m longer than the other one. Find the length of each piece. B)If you are to construct a rectangle with each of the sizes of the pieces beingthe length and width then what is the perimeter? C)What would be the area of that rectangle?
Answer:
37.5 and 82.5
Step-by-step explanation:
HELPPP answer A B C D PLEASEE DUE BY MIDNIGHT
Answer:
I'm not exactly sure what you were doing in class but this is what I would do.
I really hope it helps!! :)))
Step-by-step explanation:
for A I would connect the D point of the top angle to the D point of the bottom angle and draw the line across line t. For B the points all share the same angle because the figure is being reflected over line t the position of the figure changes but the size and angles stay the same. use a protractor in B to verify all the angles are the same. For C the only thing that would make sense is that all the lines are parallel because the figure was flipped. and for D just trace one on top of the other
The temperature was recorded at midnight for 5 consecutive days. The
recorded temperatures are: -2°, 4°, 5°, -6°, and 9°. What is the average
temperature?
Two angles of a triangle are same size. The third angle is 12 degrees smaller than the first angle. Find the measure of the third angle.
Answer:
44°
Step-by-step explanation:
Given that :
Two angles are equal sized;
Let the angle = x
Third angle = 12 smaller than first, x - 12
The measure of the third angle ;
Sum of angles in a triangle = 180°
First + second + third angle = 180°
x + x + (x - 12) = 180
2x + x - 12 = 180
3x = 180 - 12
3x = 168°
x = 56°
The third angle :
(x - 12) = 56 - 12 = 44°
Solve for x. 4 48 X 14
can someone solve this for me please?
Answer:
sure, the answer is 50
Step-by-step explanation: Because this is a right triangle, you can use the pythagorean theorem, which is a^2 + b^2 =c^2 so you square 48 and add it to 14 squared and then take the square roo t to get the value of the hypotenuse, note that c will always represent the hypotenuse or longest side, and that pythagorean theorem can only be used on right triangles
please help me :( thank u
It’s simple :(
Answer:
They Have 4 corners.
4 sides.
They are quadrilateral.
If 0° < 0 < 90° or 180° < 0 < 270°, explain why sin 20 is always positive.
The value of sin (20°) will always be positive, because :
0° < 20° < 90°
we know, that 20° lies in first quadrant and values of sin in first quadrant is always positive.
HELPPPPP
Jada rode her bike 5 days in a row. She rode the same distance each day. This model represents the situation. Each column represents one mile and the shaded parts of each column represent the fraction of a mile that Jada rode her bike each day.
Which expression can be used to determine the total distance in miles Jada rode her bike over the 5 days?
(A: 5 × 4/5
(B: 5 + 4/5
(C: 5 × 1/4
(D: 5 + 1/4
PLSSSS HELP
Answer: 5 x 4/5
Step-by-step explanation:
In each column there is 4/5 shaded . There are 5 columns .
So , 5 x 4/5
Answer:
A) 5 × 4/5
Step-by-step explanation:
The shaded part each column in the model represents what fraction of a mile that Jada rode her bike each day.
There are 5 columns.
Therefore, to determine the total distance in miles that Jada rode over the days, we can multiply the distance that she rode each day by the number of days that she rode that distance (5 days):
A) [tex]5 \textrm{ days} \times \dfrac{4}{5} \textrm{ mile each day}[/tex]
A pizza has an 18 inch diameter and is sliced into 12 pieces. What is the length of the crust on the edge of one piece of pizza?
answers:
3 pi
4.5 pi
6 pi
1.5 pi
The required length of the curst on the edge of one piece of pizza 1.5 π. Option D is correct.
What is the perimeter?Perimeter is the measure of the figure on its circumference. The perimeter of a circle is given as 2πr, where r is the radius of the circle.
here,
A pizza has an 18-inch diameter
Circumference of pizza = 18π
The pizza is sliced into 12 pieces, and the length of the crust on the edge of one piece of pizza is given as,
= 18π/12
= 1.5π
Thus, the required length of the curst on the edge of one piece of pizza is 1.5 π.
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A lawn sprinkler located at the corner of a yard rotates through 80 degrees
and sprays water of 20 ft. What is the length of the arc of the sector watered?
(Express your answer to the nearest tenths.)
The length of the arc of the sectored watered is 27.9 feets
What is length of an arc?length of arc is the distance between two points along a section of a curve.In other words, it's the distance from one point on the edge of a circle to another, or just a portion of the circumference
The length of an arc is given by :
L = theta/360 × 2πr
where tetha is the angle substends
r is the radius
Here the radius is the length at which water is sprayed = 20 ft
tetha = 80°
therefore l = 80/360 × 2×3.14 × 20
L = 29feets
Therefore the length of the arc formed by the water is 27.9 feets
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Which of the following is equivalent to 5 a) ²/3 + 2/1/1/0 4 b) 1/2 x 1/1/20 c) / x4 d) / x4 ÷ 4 ? Show your thinking.
Question 1
Solve for x.
x(x + 6) = 0
Write your answers as integers or as proper or improper fractions in simplest form.
X =
|
X =
Answer:
[tex]x=-6, 0[/tex]
Step-by-step explanation:
Using the zero-product property, we know that [tex]x=0[/tex] or [tex]x+6=0[/tex].
This means [tex]x=-6, 0[/tex].
what can 16 and 4 both be divided by
Answer: They can both be divided by 4, 2, and 1
Answer:
1, 2 and 4
explanation:
16/1, 16/2, 16/4
4/1, 4/2, 4/4
/=division sign
A local high school has a student population of 3,020. In a random sample, 42% of the students were female athletes. Approximately how many female athletes can be expected in the entire school population
Answer:
aboout 1268 students
Step-by-step explanation:
Can you please help me solve dis
Answer:
I would say F
Step-by-step explanation:
This is because a rectangle need to have at least one side of parallel sides that are the same length and F confirms that.
A rectangle has the dimensions 2. 4 x 2. 2. If I want a rectangle that has the area
16 times the size of the original rectangle, what will be my new dimensions?
New dimensions:
The new dimensions of the rectangle will be 4.8 x 4.4.
To find the new dimensions, we need to find the area of the original rectangle (2.4 x 2.2 = 5.28), and then multiply it by 16 to find the desired new area (5.28 x 16 = 84.48).
Since the area of a rectangle is determined by the product of its length and width, we can find the new dimensions by taking the square root of the new area and dividing it by the original length.
So, √84.48/2.4 = 4.4 and √84.48/2.2 = 4.8.These are the new dimensions of the rectangle.
We have to make sure that the new dimensions are in the same proportion as the original one, we can use the same factor of multiplying to get the new length and width.
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Evaluate the series. What is the sum?
23(4)*-*
1
DONE
Which shows the terms of the series?
4 + 12 +48 + 192
X 4 + 12 + 36
3 + 12 +48 + 192
O 3 + 12 +48
Answer:
255
Step-by-step explanation:
The summation value of the term in the series will be equal to
3 + 12 +48 + 192 after calculation.
Here, we have,
We know that, summation:
In mathematics, the summation is the addition of a sequence of any kind of numbers, called addends or summands.
Now we have a given term
∑(n = 1 to 4) 3(4)^n-1
By solving the above term;
∑(n = 1 to 4) 3(4)^n-1
=3 + 12 +48 + 192
Hence the value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.
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3 Write an equation for each function, where x is the
number of months and y is the amount owed.
Mr. Allen's plan:
Mr. Jessup's plan:
rriculum Associates, LLC Copying is not permitted.
In
-L-
ODPPY LINAL
The y-intercept represents the loan amount initially. And the rate of change of the function will be negative The equation of Mr. Allen's plan will be y = - 80x + 560 and Mr. Jessup's plan will be y = - 40x + 400.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
From the graph, the y-intercept of the line represents the value of the loan initially.
From the graph, the slope of both lines is negative, then the rate of change of the function will be negative.
Let 'x' be the number of months and 'y' be the amount owed.
The two points are (0, 560) and (1, 480). Then the equation of the line is given as,
(y - 560) = [(560 - 480) / (0 - 1)](x - 0)
y - 560 = - 80x
y = - 80x + 560
And the equation of the line for Mr. Jessup's plan will be given as,
y = - 40x + 400
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2 The displacement of a mass is given by the function
y = sin 3t. 3t is measured in radians.
The tasks are to:
a) Draw a graph of the displacement y against time t
for the time t = 0s to t = 2.s.
b)
Identify the position of any turning points and
whether they are maxima, minima or points of
inflexion.
c) Calculate the turning points of the function using
differential calculus and show which are maxima,
minima or points of inflexion by using the second
derivative.
Compare your results from parts b and c.
The graph is attached and the point of maximum as y"(π/6) < 0 and at point of minimum y"(π/2) > 0.
What is turning point and inflexion point?An inflection point is where a graph's curvature changes, from concave up to concave down or vice versa. It is also known as a turning point, flex, inflection, or "point of diminishing returns."
A concave down graph resembles an upside-down U or a cap, while a concave up graph resembles the letter U (or a "cup"). The intersection of a "cup" and a "cap" marks the inflection point.
Given displacement of mass by function,
y = sin(3t), where 3t is in radians,
the graph for t = 0 and t = 2 sec.
2: The position of turning point,
differentiate the equation we get,
y' = 3cos(3t)
the turning points are t = π/6 and t = π/2
y'(π/6) = y'(π/2) = 0
3: inflexion points,
again differentiate the equation we get,
y" = -9sin(3t)
and inflection at π/3
because y"(π/3) = 0
Maximum and minimum points are π/6 and π/2 respectively,
as the point of maximum t = π/6 as y"(π/6) < 0,
and point of minimum at t = π/2 as y"(π/2) > 0.
Hence the graph is attached and maximum at t = π/6, and minimum at t = π/2, and inflection at π/3.
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Which label on the cone below represents the radius?
Answer:
the radius found on the letter c
Answer:
the radius found on the letter c
1,0032.43+7,543323,4252,34= ?
Answer:
7.5433234e+12 is your answer
Step-by-step explanation:
Answer:
7.5433234e+12
Step-by-step explanation:
On a coordinate plane, a line goes through (negative 12, negative 2) and (0, negative 4). A point is at (0, 6).Which point is on the line that passes through (0, 6) and is parallel to the given line? (–12, 8) (–6, 6) (2, 8) (6, 0)
Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line.
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)
Since, We know that;
Parallel lines have same slopes and different y-intercepts
The formula of the slope of a line which passes through points (x₁ , y₁) and (x₂, y₂) is,
⇒ m = (y₂ - y₁) / (x₂ - x₁)
Since, The given line passes through points (-12 , -2) and (0 , -4)
Hence, Use the formula of the slope above to find the slope of the given line as;
⇒ m = (y₂ - y₁) / (x₂ - x₁)
⇒ m = (-4 - (-2)) / (0 - (-12))
⇒ m = (-2) / 12
⇒ m = - 1/6
Since, The two lines are parallel.
Hence, Their slopes are equal
So, The slope of the parallel line = - 1/6
Here, The parallel line passes through point (0 , 6)
Since, The form of the linear equation is y = mx + b, where m is the slope and b is the y-intercept.
⇒ m = -1/6 and b = 6
Hence, The equation of the parallel line is,
⇒ y = x + 6
Now, Let us check which point is on the line by substitute the x in the equation by the x-coordinate of each point to find y, if y is equal the y-coordinate of the point, then the point is on the line as;
Point (-12 , 8)
Substitute x = -12 and y = 8
⇒ y = (-12) + 6
⇒ y = 2 + 6 = 8
Clearly, The value of y is equal the y-coordinate of the point.
So, Point (-12 , 8) is on the line.
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Use the Pythagorean Theorem to solve for the unknown side length. *
13 cm
12 cm
what’s the unknown side length?
Answer:
13cm
Step-by-step explanation:
Answer: 13cm
Step-by-step explanation:
How do you identify an exponential graph?
Exponential graph is identified by its curve.
An exponential graph is a graph that shows a rapid increase or decrease of a value over time, where the rate of change is proportional to the current value. It is usually represented by a curve that bends upward or downward.
The key characteristic of an exponential graph is that the Y-axis is on a logarithmic scale, and the curve of the graph is a steep curve going either up or down. The equation of an exponential graph is usually of the form y = ab^x, where a is the initial value, b is the growth or decay factor, and x is the independent variable.
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What is the equation for the linear relationship in slope intercept form?
Answer:
y=1/2x-3
Step-by-step explanation:
y=mx+b
y=1/2x-3
1. The accuracy of a pool thermometer is the positive difference between the temperature
reading on the thermometer t and the actual temperature of the pool p. Write two absolute
value expressions equivalent to the accuracy of a pool thermometer.
The two absolute value expressions equivalent to the accuracy of a pool thermometer are |t - p| and |p - t|
How to write absolute value expressions for the accuracy of the thermometer?Absolute value means to remove any negative sign in front of a number and to think of the number as positive. This is indicated by the vertical lines | |
Any expression that contain the vertical lines is called absolute
value expression
Since the accuracy of a pool thermometer is the positive difference between the temperature reading on the thermometer t and the actual temperature of the pool p.
We can write:
accuracy = | t - p|
OR
accuracy = | p - t|
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Answer:
It-pI
Step-by-step explanation:
The sum of H and 188 PLEASE HELP FASTT!!!!! :(
Step-by-step explanation:
50 is your correct Answer
Helppp I’m not sure which one it is !!!
Manny has 5 3/4 cups of sugar to make pies. If each pie uses 1/3 cup of sugar, how many pies can Manny make?
Answer:
well im pretty sure he can make like 7 pies
Step-by-step explanation:
what is 1.65 meters tall measured in centimeters?
Answer:
165 centimeters
Step-by-step explanation:
An example of calculating BMI using the formula: Height = 165 cm (1.65 m), Weight = 68 kg One centimeter is equal to 0.01 meter: 1cm = 0.01m. You are 65 inches tall. 65 * (2.54) = 165.1 cm.
Answer:
165 cm
Step-by-step explanation:
1.65 meters = 1.65 × 100 = 165 centimeters