GIVEN circle P with arc AE = 53 , arc BA =68 and arc CB =72
match the following angles with their corresponding measurements
Answers
the sum of the internal angles of a triangle is 180°.
when the angles of arcs have been given(e.g: BA) that means from the centre of the circle to point B has been rotated by 53° to point A.
Next from point A to point E, the angle rotated is 68°
the addition of these 2 angles give the angle rotated from point B to point E,
that is angle no.7
m∠7 = 53° + 68° = 121°
consider ΔPBE,
PB and PE are radii therefore isosceles triangles
In isosceles triangles the angles opposite equal sides are equal
if the angle is x°, then there are 2 angles with values x each
x° +x° + 121° = 180°
2x° = 59°
x = 29.5°
therefore m∠3 = 29.5°
next connect PC and consider ΔPCB,
according to given information, C∠PB = 72°
as PC and PB are radii ΔPCB is an isosceles triangle, then the angles (y°) opposite radii are equal
2y° + 72° = 180°
y° = 54°
then consider ΔPCD, again an isosceles triangle
as a straight line has an angle of 180°
B∠PC + C∠PD = 180°
72° + C∠PD = 180°
C∠PD = 108°
as ΔPCD is an isosceles triangle, P∠CD and P∠DC are equal (take this angle as z°)
2z° + 108° = 180°
z° = 36°
B∠CD is a sum of y and z angles
therefore m∠8 = y + z
m∠8 = 54° + 36° = 90°
there is also a tangent line that cuts point D of the circle. this tangent cuts D and is perpendicular to the PD radius
this indicates that lines PD and HD are perpendicular to each other
hence, forms a right angle where it cuts each other.
therefore H∠DP / m∠4 = 90°
C∠DH /m∠5 is the difference between P∠DH and P∠DC
m∠5 = 90° - 36° = 54°
m∠1 and m∠6 together make a straight line therefore the sum of these 2 angles is 180°
by looking at the options of answers given the 2 angle values given that add up to 180° are 116.5° and 63.5°.
m∠1 is the acute angle therefore m∠1 = 63.5°
m∠6 is the obtuse angle therefore m∠6 = 116.5°
consider ΔDFB
D∠FB is 180° - m∠1 = 180° - °63.5 = 116.5°
D∠FB + F∠DB(w°) + D∠BF (m∠3)= 180°
116.5 + w° + 29.5° = 180°
w° = 34°
m∠2 = m∠4 + w°
= 90° + 34°
= 124°
finally all the answers are
m∠1= 63.5°
m∠2 = 124°
m∠3 = 29.5°
m∠4 = 90°
m∠5 = 54°
m∠6 = 116.5°
m∠7 = 121°
m∠8 = 90°
All the answers are
m∠1= 63.5°
m∠2 = 124°
m∠3 = 29.5°
m∠4 = 90°
m∠5 = 54°
m∠6 = 116.5°
m∠7 = 121°
m∠8 = 90°
The theory that is mainly used to find out the angles of the above diagram is that;
the sum of the internal angles of a triangle is 180°.
when the angles of arcs have been given(e.g: BA) that means from the centre of the circle to point B has been rotated by 53° to point A.
Next from point A to point E, the angle rotated is 68°
the addition of these 2 angles give the angle rotated from point B to point E,
that is angle no.7
m∠7 = 53° + 68° = 121°
consider ΔPBE,
PB and PE are radii therefore isosceles triangles
In isosceles triangles the angles opposite equal sides are equal
if the angle is x°, then there are 2 angles with values x each
x° +x° + 121° = 180°
2x° = 59°
x = 29.5°
therefore m∠3 = 29.5°
next connect PC and consider ΔPCB,
according to given information, C∠PB = 72°
as PC and PB are radii ΔPCB is an isosceles triangle, then the angles (y°) opposite radii are equal
2y° + 72° = 180°
y° = 54°
then consider ΔPCD, again an isosceles triangle
as a straight line has an angle of 180°
B∠PC + C∠PD = 180°
72° + C∠PD = 180°
C∠PD = 108°
as ΔPCD is an isosceles triangle, P∠CD and P∠DC are equal (take this angle as z°)
2z° + 108° = 180°
z° = 36°
B∠CD is a sum of y and z angles
therefore m∠8 = y + z
m∠8 = 54° + 36° = 90°
there is also a tangent line that cuts point D of the circle. this tangent cuts D and is perpendicular to the PD radius
this indicates that lines PD and HD are perpendicular to each other
hence, forms a right angle where it cuts each other.
therefore H∠DP / m∠4 = 90°
C∠DH /m∠5 is the difference between P∠DH and P∠DC
m∠5 = 90° - 36° = 54°
m∠1 and m∠6 together make a straight line therefore the sum of these 2 angles is 180°
by looking at the options of answers given the 2 angle values given that add up to 180° are 116.5° and 63.5°.
m∠1 is the acute angle therefore m∠1 = 63.5°
m∠6 is the obtuse angle therefore m∠6 = 116.5°
consider ΔDFB
D∠FB is 180° - m∠1 = 180° - °63.5 = 116.5°
D∠FB + F∠DB(w°) + D∠BF (m∠3)= 180°
116.5 + w° + 29.5° = 180°
w° = 34°
m∠2 = m∠4 + w°
= 90° + 34°
= 124°
finally all the answers are
m∠1= 63.5°
m∠2 = 124°
m∠3 = 29.5°
m∠4 = 90°
m∠5 = 54°
m∠6 = 116.5°
m∠7 = 121°
m∠8 = 90°
Related Questions
Sean divides 8 cups of granola into 1/4-cup servings. How many servings of granola does he have?
Answers
8 cups make x
x = 8*4
x = 32 servings
Two runners are to race one lap on a circular track, the radius to the inside circle is 50m.the radius on the outside lane is 51m. How much of a head start should the runner on the outside get?
Answers
Tmuch of a head start should the runner on the outside get would be = 2πm.
How to calculate the length of head start for the runner outside?
To calculate the length of head start for the runner outside against the inside runner, the following steps should be taken as follows:
The formula for circumferential of circle = 2πr
Circumference of inner circle;
= 2× π×50
= 100π
Circumference of outer circle;
= 2×π×51
= 102π
The length of head start for the runner outside = 102π-100π = 2πm
find the product of 80x^4/y^3 ×xy/5x^2
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In a shipment of 400 parts, 14 are found to be defective. How many defective parts should be expected in a shipment of 1,000? Really need this I'm giving you maximum points
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If an object is dropped from a height of 55 feet, the function d=-16t^2+55 gives the height of the object after t seconds. Graph this function. Approximately how long does it take the object to reach the ground (d=0)
Answers
[tex]\bf \stackrel{d}{0}=-16t^2+55\implies 16t^2=55\implies t^2=\cfrac{55}{16}\implies t=\sqrt{\cfrac{55}{16}}[/tex]
that's when.
as far as its graph, is more or less like the picture below, now, notice that if we put the quadratic in "vertex form", it'd look like
[tex]\bf d=-16t^2+55\implies d=-16(t-\stackrel{h}{0})^2+\stackrel{k}{55}\qquad vertex~(h,k)[/tex]
so its vertex is at (0, 55), so just pick one point to the left of the vertex, and one to the right of the vertex, and draw it away
Which number completes the inequality? -5.13< ?< -4.8
Answers
what do you call an object with one fixed endpoint that extends to infinity
Answers
Complete the square to write y = 3x2 + 12x + 7 in vertex form, y = a(x - h)2 + k. y = 3(x2 + 4x) + 7 y = 3(x2 + 4x +4) + 7 -
Answers
Answer:
A. 12
B. 3
C. -2
D. -5
Step-by-step explanation:
Verified on edge, just finished it
The Vertex form is y= 3(x+ 2)² -5 and a= 3, h= -2, k= -12.
What is Vertex Form?The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants.
Vertex form, one of the usual forms for quadratic functions, emphasises the coordinates of the vertex of the function's graph.
Given:
y = 3x² + 12x + 7
Now writing the equation in vertex form
y = 3x² + 12x + 7
y = 3x(x + 4) + 7
Adding and subtracting 12 on both side
y= 3(x²+ 4x) + 7 -12 + 12
y= 3(x² + 4x + 4) + 7- 12
y= 3(x+ 2)² -5
Now, Comparing it with y = a(x - h)² + k we get
a= 3
h= -2
and, k= -12
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A rectangular prism has a length of 212 meters, a width of 4 meters, and a height of 214 meters.
What is the volume of the prism?
Enter your answer in the box as a simplified mixed number or a decimal.
m³
Answers
The volume of the rectangular prism is 22 1/2 m³
What is the volume of the rectangular prism?A rectangular prism is a three-dimensional object. It is made up of six faces, twelve sides and six vertices.
Volume = length x width x height
2 1/2 x 4 x 2 1/4
5/2 x 4 x 9/4 = 720 / 32 = 22 1/2 m³
Here is the complete question: A rectangular prism has a length of 21/2 meters, a width of 4 meters, and a height of 21/4 meters.
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In the standard (x,y) coordinate plane below, the points ( 0,2), (8,2), (3,6), and (11,6) are the vertices of a parallelogram. What is the area, in square units, of the parallelogram
Answers
The area of the parallelogram is 32 square units.
What is a parallelogram?Parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
First, we can plot the points on the coordinate plane to get a better visual understanding of the parallelogram:
| (3,6) (11,6)
| *-----------*
| / /
| / /
| / /
| / /
| *-----------*
| (0,2) (8,2)
|
Now,
We can see that the base of the parallelogram is the line segment connecting (0,2) and (8,2), which has a length of 8 units.
To find the height of the parallelogram, we can observe that the line segment connecting (0,2) and (3,6) is perpendicular to the base, and has a length of 4 units.
Therefore,
The height of the parallelogram is 4 units.
Now,
The area of a parallelogram is given by the formula:
Area = base x height
Plugging in the values we found, we get:
Area = 8 x 4
Area = 32
Therefore,
The area of the parallelogram is 32 square units.
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Express the complex number in trigonometric form.
-5i
A) 5(cos 270° + i sin 270°)
B) 5(cos 180° + i sin 180°)
C) 5(cos 90° + i sin 90°)
D) 5(cos 0° + i sin 0°)
Answers
It is in the form a+bi where a = 0 and b =-5
So the point (a,b) is (0,-5)
The distance from the origin to this point is 5 units, therefore r = 5. This is the magnitude.
The angle is 270 degrees as shown in the attached image. You start on the positive x axis and rotate until you reach the point (0,-5)
This is why the answer is choice A) 5(cos(270) + i*sin(270))
During each minute of a comedy show, Carlin laughs 555 times. Carlin watches 333 comedy shows every day, and each show is 404040 minutes long. How many times does Carlin laugh every day due to the comedy shows?
Answers
Answer: 600
Step-by-step explanation:
Given : The number of times Carlin laughs in each minute = 5
The number of comedy show Carlin watched = 3
The length of each comedy show = 40 minutes
Total minute she watched Comedy show will be :-
[tex]40\times3=120\text{ minutes}[/tex]
Then , the total number of times Carlin will be :-
[tex]120\times5=600[/tex]
Hence,Carlin laughs 600 times every day due to the comedy shows.
An arrangement of marbles has 12 marbles in the first row and 10 rows in all. In each successive row one marble is added.
What is the explicit rule for this situation, and how many marbles will be in the 10th row?
Drag and drop the answers into the boxes to match the situation.
Explicit rule
Number of marbles in the 10th row
An = 11 + 11n, An = 12 + n, An = 11 + n, An = 12 + 10n, 19, 20, 21,
Answers
Explicit rule: An = 12 + n
Number of marbles in the 10th row: 22
The explicit rule for this situation is An = 12 + n, where "n" represents the row number.
To find the number of marbles in the 10th row, you can plug in n = 10 into the explicit rule:
A10 = 12 + 10
A10 = 22
So, there will be 22 marbles in the 10th row.
Matching the answers:
Explicit rule: An = 12 + n
Number of marbles in the 10th row: 22
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convert 39/5 to a mixed number written in lowest terms
Answers
39 ÷ 5 = 7.8
A N S W E R:
7.8 = 7 4/5 (This is in lowest terms)
10x - 4 = 2 ( ? ) is it a) 5x - 4 b) 5x - 2 c) 10x - 4 d ) 10x - 8
Answers
10x - 4 = 2 ( ? )
I proceed to replace the missing value with the given expression
case a-------------> 5x - 4
then
10x - 4 = 2 (5x-4 )--------> 10x - 4 = 10x-8--------> is not solution
case b-------------> 5x - 2
then
10x - 4 = 2 (5x-2 )--------> 10x - 4 = 10x-4--------> is solution
case c-------------> 10x - 4
then
10x - 4 = 2 (10x - 4 )--------> 10x - 4 = 20x-8--------> is not solution
case d-------------> 10x - 8
then
10x - 4 = 2 (10x - 8 )--------> 10x - 4 = 20x-16--------> is not solution
the answer is the option b) 5x - 2
Sierra sawed 10 1/2 inches off the end of a board. the remaining board was 37 1/2 inches long. how long was the boared that sierra started with? please explain answer
Answers
48 inches is your answer ;)
If the asymptotes of a hyperbola are the x- and y-axes, it is known as a rectangular hyperbola?
Answers
Final answer:
A rectangular hyperbola is defined by the angle between its asymptotes being 90°, with its Equation represented as x'y' = a².
Explanation:
Rectangular Hyperbola: When the angle between the asymptotes of a hyperbola is 90°, it is called a rectangular hyperbola. In this case, b = a and the eccentricity is √2. The Equation to a rectangular hyperbola is x'y' = a².
Andy has 9 math books and 6 reading books if you wants to distribute them evenly among some bookshelves so that each has the same combination of books with none left over what is the greatest number of bookshelves Andy can use
Answers
6/3=2(reading books per shelf)
9/3=3(math books per shelf)
Every shelf there are two reading books and 3 math books
6 reading books
First we need to find the greatest common factor.
in this case it would be 3.
9 ÷ 3 = 3
6 ÷ 3 = 2
Here we have our answer
since 3 is not an even number it cannot be split evenly which means each bookcase will have at least 3 math books on it - and 2 reading books as well
*bookcase 1:
3 (math)
2(reading
*bookcase 2:
3 (math)
2 (reading)
*bookcase 3:
3 (math)
2 (reading
Write the time another way 23 minutes after 4
Answers
Would be the answer
what fractions are equivalent to 8 over 12
Answers
56. exercise. for natural numbers a and b, give a suitable definition for "least common multiple of a and b", denoted lcm(a, b). construct and compute some examples.
Answers
LCM(6, 9) = 6*9/3 = 18 . . . . . . . (2 [ 3 ) 3] = 18 . . . ( ) product = 6; [ ] product = 9
LCM(2,5) = 2*5/1 = 10 . . . . . . . . (2 [ 1 ) 5 ] = 10
LCM(27, 45) = 27*45/9 = 135 . . (3 [ 9 ) 5] = 135
_____
In the above LCM products, the number in [ ) brackets is the GCD.
Simplify: (–5) • (7) – (6) • (–2)
Answers
hope this helped PLEASE ADD ME BRAINIEST :-)
The correct answer is -23.
To simplify the given expression, we need to perform the indicated operations and follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
Given expression: (–5) • (7) – (6) • (–2)
Step 1: Perform the multiplications inside the parentheses.
(–5) • (7) = –35
(6) • (–2) = –12
Step 2: Perform the subtraction operation.
–35 – (–12) = –35 + 12 = –23
Therefore, the simplified expression is:
[tex](-5) \cdot (7) - (6) \cdot (-2) = -35 + (-12) = -23[/tex]
Choose the correct simplification of the expression (−2x + 4y)(3x − 7y). −6x2 − 2xy − 28y2 6x2 + 26xy − 28y2 −6x2 + 26xy + 28y2 −6x2 + 26xy − 28y2
Answers
Answer:
[tex] - 6 {x}^{2} + 26xy - 28 {y}^{2} [/tex]
Step-by-step explanation:
The given expresion is:
(−2x + 4y)(3x − 7y)
We expand using the distributive property: (a+b)(c+d)=a(c+d)+b(c+d)
We apply this property to get:
[tex]( - 2x + 4y)(3x - 7y) = - 2x \times(3x - 7y) + 4y(3x - 7y)[/tex]
We expand further to obtain:
[tex] - 6 {x}^{2} + 14xy + 12xy - 28 {y}^{2} [/tex]
[tex] - 6 {x}^{2} + 26xy - 28{y}^{2} [/tex]
Answer:
[tex](-2x+ 4y)(3x - 7y)=-6x^2+26xy-28y^2[/tex]
Step-by-step explanation:
We multiply each term in the parentheses, by those of the other parenthesis:
[tex](-2x+ 4y)(3x - 7y)=(-2x)(3x)+(-2x)(-7y)+(4y)(3x)+(4y)(-7y)\\=-6x^2+14xy+12xy-28y^2[/tex]
Now, we simplify.
We have two terms that contain xy:
[tex]=-6x^2+26xy-28y^2[/tex]
Wich will be the correct simplification of the expressionn [tex](-2x+ 4y)(3x - 7y)[/tex]
Natasha had d dollars. She bought two ice creams which cost x dollars each. How much money does she have left?
Answers
By connecting two non-intersecting vertices of a regular pentagon, the figure can be split into a triangle and a quadrilateral. Always Sometimes Never
Answers
A quadrilateral has four sides.
See attached figure.
If you cannot find another way of subdividing the pentagon, then you have found that the pentagon is always split into a triangle and a quad.
Jessica grows two types of tomato plants in her garden. For each type, she records the heights, in inches, of five plants.
What can she infer about the heights of the plants?
Type 1: {42, 56, 44, 60, 48}
Type 2: {62, 59, 68, 55, 66}
Type 1 plants and Type 2 plants do not have similar height distributions.
Type 1 and Type 2 plants have similar height distributions.
Type 1 plants and Type 2 plants have identical height distributions.
Type 1 and Type 2 plants have somewhat similar height distributions.
Answers
Type 1 Type 2 plants have somewhat similar height distributions
The inference that can be made is that D. Type 1 and Type 2 plants have somewhat similar height distributions.
What is Inference?This refers to a statement or assertion that is made about something, which may or may not be true.
Hence, we can see that based on the height of the plants, there is a similarity in the heights of Type 1 and Type 2 plants, hence it can be inferred that Type 1 and Type 2 plants have somewhat similar height distributions.
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you deposit 2800 in a savings account that earns 1% annual intrest compounded semiannually.Write a function that represents the balance after t years
Answers
Amount = Initial amount * ( 1 + (r/n) ) ^ (nt)
where r = interest rate per year, n = period per year
n = 2, r = 0.01
Answer: F(t) = 2,800 * [ 1 + (0.01/2) ] ^ 2t
The function which represent the given situation for Amount by compound interest is [tex]A = 2800 X 1.005^{2t}[/tex]
What is Compound Interest?Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
Here, P = $2800
I = 1 % compounded semiannually = 0.5 % = 0.005
Time = t years
n = 2t semi-years
We know that,
[tex]A = P(1+i)^n[/tex]
[tex]A = 2800 ( 1 + 0.005 )^{2t}[/tex]
[tex]A = 2800 X 1.005^{2t}[/tex]
Thus, The function which represent the given situation for Amount by compound interest is [tex]A = 2800 X 1.005^{2t}[/tex].
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37.5 x 10(-6) in scientific notation?
Answers
a rectangular park is 4 miles long and 2 miles wide. how long is pedestrian route that runs diagonally across the park
Answers
[tex]{x}^{2} = {4}^{2} + {2}^{2} [/tex]
Now solve for x
[tex] {x}^{2} = 16 + 4 \\ {x}^{2} = 20 \\ x = \sqrt{20} [/tex]
Now you can simplify this to
[tex]x = \sqrt{5 \times 4} \\ x = \sqrt{5} \sqrt{4} \\ x = \sqrt{5 } \times 2 \\ x = 2 \sqrt{5} [/tex]
And that's your answer
what is the average of -10.25 and 125.75
Answers
125.75+(-10.25)=115.5
115.5/2= 57.75
the mean is 57.75