Enrique is selling a drop leaf table and wants to include the area of the table when the leaves are down is his ad.
What is the area of the center section when the leaves are down? Explain how you found your answer. HELPPP
Answers
Answer:
drop-leaves 38 in "U SE 22 1 19 0 o Let the center of the table be O and the chord of length 38 in.be AB Drop a perpendicular from to AB meeting it at C. Since the diameter of the circle is 44 in., the radius of the circle must be 22 in. and thus, OA= = in. By the definition of the sine function, AC sin 500-Twice that gives ZAOB, so the area of OA sector AOB is about in and the area of AAOB is 1 OA. OB sin 20-in? Subtracting the area of the triangle from the area of the sector shows that the area of the segment bounded by chord AB is about in (Type integers or decimals rounded to four decimal places as needed.) 19 22 B 2
Step-by-step explanation: i really hope this is what your looking for, and helps!! love you have an amazing day:)) -marina mae
The area of the center section when the leaves are down is evaluated being of 932.84 in.²
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
The simplified figure is attached below.
We need to find the area PQRS.
Area(PQRS) = 4(Area(DOQ) + Area(QOB)) (by symmetry.
The line OD and OT are perpendiculars on those 38 inch chords, and therefore D and T are bisecting them(by a theorem that perpendicular from center of a circle to its chords bisect them).
Finding Area of DOQ:Using Pythagoras theorem, we get:
[tex]|DO| = \sqrt{|OQ|^2 -|DQ|^2 } = \sqrt{22^2 - 19^2} = \sqrt{123}[/tex]
Thus, we get:
[tex]\text{Area DOQ} = \dfrac{1}{2} \times 19 \times \sqrt{123} \approx 105.36 \: \rm in^2[/tex]
Finding Area of QOB:Since angle ∠DQO and ∠QOB are alternate interior angle, they are of same measure.
From triangle DOQ, from the perspective of ∠DQO, we get the sine ration as:
[tex]\sin(m\angle DQO) = \dfrac{|DO|}{|OQ|}\\m\angle DOQ = \sin^{-1}\left( \dfrac{\sqrt{123}}{22}\right) \approx 30.27^\circ \: \text{(chose acute angle)}[/tex]
Thus, we get:
[tex]m\angle QOB \approx 30.27^\circ[/tex]
360 degrees cover full area of circle,
1 degree will cover full area /360 of the circle
Thus, we get:
Aera of the sector QOB = Area covered by central angle ∠QOB[tex]\approx 30.27 \times \dfrac{\pi (22)^2}{360} \approx 127.85 \: \rm in^2[/tex]
Thus, as we have:
Area(PQRS) = 4(Area(DOQ) + Area(QOB))
we get:
Area(PQRS) ≈ 4(105.36 + 127.85) ≈ 932.84 in.²
Thus, the area of the center section when the leaves are down is evaluated being of 932.84 in.²
Learn more about Pythagoras theorem here:
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Related Questions
Simplify the expression by removing symbols of grouping and combining like terms.
4t[5 − (t − 4)] + t(t + 3)
Answers
Answer: -3t^2 + 39t
Step-by-step explanation:
Answer the following questions.
1) Match the descriptions with the properties.
If you multiply or divide both sides of an inequality by a negative number, you must change the direction of the inequality symbol.
If you divide the terms of one side of an inequality by a positive number, you must divide the terms of the other side of the inequality by the same number for the inequality to remain true.
If you add a value to one side of an inequality, you must add the same value to the other side of the inequality for the inequality to remain true.
Addition Property of Inequality
Division Property of Inequality
Inequality Property of Multiplication or Division by a Negative Number
Multiplication Property of Inequality
Subtraction Property of Inequality
Answers
Answer:
B. If both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality symbol must be reversed.
Step-by-step explanation:
please help :( A large rectangle has a length of 30 inches and a width of 27 inches. A smaller rectangle has a length of 10 inches and a width of question mark inches. The diagram represents the process of enlarging a rectangle using a scale factor of 3. The width of the original rectangle must be: 9 in. 11 in. 12 in. 17 in.
Answers
Answer:
9in
Step-by-step explanation:
I´m telling you I just got it Right
Answer:
It’s A
Step-by-step explanation:
GOT IT RIGHT
BRAINLIEST ASAP!! Find the focus of the parabola: f(x) = 1/4(x – 3)^2 + 1
Answers
Question: Find the focus of the parabola: f(x) = 1/4(x – 3)^2 + 1
Answer: Focus: (3, 2)
Step-by-step explanation:
Use the vertex form to find the focus. Hope this helps!
8.
Use the graph to
write an equation of the line
and interpret the slope.
Answers
= -60
y-y1 = m(x-x1)
y-180 = -60 (x-5)
y-180=-60x+300
y= -60x + 480
Good Luck.
shylas resreach shows that 8 empty cans can make 1/4
Answers
8 cans equal 2 and not 1/4
Evaluate the following function when x = 2: f(x) =x^2-x+2
Answers
Answer: 4
Step-by-step explanation:
First you do the exponent because of "order of operation", which in this case is 2 to the 2nd power or 2 squared. Then you substract the answer you got by doing 2 squared, which is supposed to give you an answer of 4 which then gets substracted by 2, which leads to the answer being 2 and then you add 2 + 2 and the final answer is 4
6. (01.03 LC)
An item originally priced for $51.99 is on sale for 15% off. What is the discounted price of the item? (4 points)
$7.80
O $44.19
$45.21
d
$61.16
Answers
Answer:
$44.19 it is correct answer
Solution set for -8y<72
Answers
Answer:
y < -9
Step-by-step explanation:
-8y < 72
~Divide -8 to both sides
y < -9
Best of Luck!
What is the the independent quantity and the dependent quantity.
If Sam buys the pair of shoes for $64, he will have to pay a sales tax of $5. 28
Answers
Hey there!
Total = Price+ Sale s tax
=> $64 + $5. 28
=> $69.28
Therefore, Total cost is $69.28
The independent quantity would be the cost of the shoes ($64) and the dependent quantity would be the amount of sales tax ($5.28).
What is the independent and dependent variable?In mathematics, independent and dependent variables are values that vary in relation to one another. The dependent variable is dependent on the independent variable, which means that if the value of the independent variable changes, so will the dependent variable.
In this scenario, the independent quantity would be the cost of the shoes ($64) and the dependent quantity would be the amount of sales tax ($5.28).
The cost of the shoes is the independent variable because it is the value that is being used to calculate the amount of sales tax, which is the dependent variable.
The amount of sales tax depends on the cost of the shoes, hence the name "dependent variable."
To learn more about the independent and dependent variables click here:
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what is rebooting computer?
Answers
https://en.m.wikipedia.org/wiki/Reboot
Hope this helps. If you need any more help please comment. Good luck in your learning journey and have a wonderful day/night!! :)
What is the range of the following relation
(9,-2) (4,3) (8,10) (-4,8)
A- 2,3,8,10
B-(9, -2) (4,3)
C - -4,4,8,9
D- (8,10) (-4, 8)
Answers
Which is bigger -2.5 or -3/1
Answers
Answer:
-2.5
Step-by-step explanation:
-2.5 is greater.
Find the value (6° -2°) x (6° +2°)
Answers
Answer:
0
Step-by-step explanation:
using the identity
[tex]a^{0}[/tex] = 1 , then
([tex]6^{0}[/tex] - [tex]2^{0}[/tex] ) × ([tex]6^{0}[/tex] + [tex]2^{0}[/tex] )
= (1 - 1) × (1 + 1)
= 0 × 2
= 0
a^0 = 1
6^0-2^0 = 1-1
= 0
(6^0 -2^0)*(6^0+2^0) = 0*(1+1)
= 0
SOMEONE PLS HELP ASAP
Answers
Answer: h(3) = 1
Step-by-step explanation: If x = 3, draw a straight horizontal line at it. It crosses 1 at y, so h(3) = 1.
Solve the equation for y.
(15y+24)/a =f PLEASE DO NOT HELP ME IF YOU DO NOT KNOW WHAT YOU ARE DOING!! Everyone on this app who has helped me have been getting me wrong on all my work.
Answers
Answer:
y = [tex]\frac{fa - 24}{15}[/tex]
Step-by-step explanation:
[tex]\frac{15y + 24}{a}[/tex] = f
multiply both sides by a
(15y + 24) = fa
the parenthesis can be removed
15y + 24 = fa
subtract 24 from both sides
15y = fa - 24
divide both sides by 15
y = [tex]\frac{fa - 24}{15}[/tex]
someone pls answer this!!
Answers
Answer:
line p
Step-by-step explanation:
Line p forms both angle 3 and angle 5 by passing through other lines. It is also a transversal because it passes through a system of lines (line n and l).
What is the slope of this problem.
Answers
Answer:
Slope of the line= -1
Step-by-step explanation:
The given line is of equation y= -x
Slope of any line= y/x
= -x/x= -1
1. What is the degree of
the polynomial
below?
x^3 + 2x - 3x^4 + 5 +
3х^2
Answers
Answer:
4
Step-by-step explanation:
The highest power(exponent) of the variable 'x' is the degree of the polynomial.
In this sum the highest power of x is 4
Degree = 4
Involves sine/cosine rules
Answers
Answer:
44.47 cm² (nearest hundredth)
Step-by-step explanation:
Area of ΔABC = 1/2 x base x height
⇒ 21 = 1/2 x 7 x BC
⇒ BC = 6 cm
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
⇒ AB² + BC² = AC²
⇒ 7² + 6² = AC²
⇒ AC² = 85
⇒ AC = √85 cm
Cosine rule to find length AD:
c² = a² + b² - 2 ab cosC
⇒ DC² = AD² + AC² - 2(AD)(AC)cos(DAC)
⇒ 9.2² = AD² + (√85)² - 2(AD)(√85)cos 73°
⇒ AD² - 5.39106...AD + 0.36 = 0
⇒ AD = 5.323442445, 0.06762541414
⇒ AD = 5.323442445
Area of a triangle ADC: (1/2)absinC
(where a and b are adjacent sides and C is the angle between them)
⇒ area = (1/2) × AC × AD × sin(DAC)
⇒ area = (1/2) × √85 × 5.323442445 × sin(73°)
⇒ area =23.4675821... cm²
Area of quadrilateral = area of ΔABC + area of ΔADC
= 21 + 23.4675821...
= 44.47 cm² (nearest hundredth)
How many solutions does the system of equations have?
y = 9x - 4
y = -6x + 6
Answers
Answer:
1 solution (2/3, 2)
Step-by-step explanation:
A ribbon is cut into 2 pieces so that piece x is half as long, in feet, as piece y. Which table represents this situation?
y
y
24
12
24
8
24
6
24
0
38
18
36
12
36
9
36
48
24
48
16
48
12
48
10
60
30
60
20
60
15
60
Answers
Answer:B; (12,24) (18,36), etc
Step-by-step explanation:divide y and x, in this case 24÷2=12
The ribbon cuts into the pieces are (12,24) (18,36), (24, 48), and (30, 60) which satisfy the equation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
A ribbon is cut into 2 pieces so that piece x is half as long, in feet, as piece y.
x = y/2
or
2x = y
Based on the above equation the pairs of (12,24) (18,36), (24, 48), and (30, 60) satisfy the equation.
Thus, the ribbon cuts into the pieces are (12,24) (18,36), (24, 48), and (30, 60) which satisfy the equation.
Learn more about the arithmetic operation here:
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GIVING 50 POINTS 42 + 49 - 9023 + 34830 =
Answers
What is 42 + 49 - 9023 + 34830?
Answer: 25898
Explanation:
1. 42 + 49 = 91
2. 91 + -9023 = -8932
3. -8932 + 34830 = 25898
-20:2+(15)=
Simplify
Answers
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
help me pls pls pls
nonsense=report
nice answer=brainles
pls dont waste my points
Answers
G) The softball diamond is 25 meters long on each side
O) Multiplication
N) Twenty-five meters times 4 sides
S) 25 meters * 4 = 100 meters
A) 100 meters
I NEED HELP. I MAY MARK BRAINLEIST
Answers
Complementary Angles
Explanation:
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.[1] Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles. Two intersecting curves define also an angle, which is the angle of the tangents at the intersection point. For example, the spherical angle formed by two great circles on a sphere equals the dihedral angle between the planes containing the great circles.
An angle formed by two rays emanating from a vertex.
1/5a+5=21, what is the value of a
Answers
Answer:
the value of a is 80
A=80
Step-by-step explanation:
Answer: A=100
Step-by-step explanation: You multiply 1/5A by 5 and 21 by five. A+5=105 and then you subtract 5 giving you 100
helppppppppp meeeeeeeeee
Answers
Answer:
R'(-15, 1.5)
S'(-6, 3)
T'(-6, -4.5)
U'(-15, -4.5)
Step-by-step explanation:
Multiply every coordinate by the scale factor k = 3/2 which also 1.5.
R(-10, 1) ---> R'(-15, 1.5)
S(-4, 2) ---> S'(-6, 3)
T(-4, -3) ---> T'(-6, -4.5)
U(-10, -3) ---> U'(-15, -4.5)
what is the domain? What is the range
Answers
Answer:
domain: -∞ < x < ∞range: -∞ < y ≤ 4Step-by-step explanation:
The domain is the horizontal extent of the function graph. The range is its vertical extent. The arrows on the ends of the lines indicate they extend to negative infinity in the vertical direction, and to ± infinity in the horizontal direction. The maximum value of the function is y=4.
The domain of the function is -∞ < x < ∞.
The range of the function is -∞ < y ≤ 4.
Find the area plllllllllssssss
Answers
Answer:
A = 25 ft²
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 10 and h = 5 , then
A = [tex]\frac{1}{2}[/tex] × 10 × 5 = 5 × 5 = 25 ft²