Answers
==========================================
Explanation:
AB is a diameter of the circle with point O in the center. This makes angle AOB to be 180 degrees. Consequently, arc ADB makes up 180 degrees of a full 360 degree circle (ie it makes up half of the circle since 180/360 = 1/2)
We're told that arc ADB is 15pi units long. Since arc ADB makes up half the circle, the full circle must therefore be 2*15pi = 30pi. This is the circumference.
------------------
We're also told that angle COB is 60 degrees. Let's find angle COA
(angleCOA) + (angleCOB) = 180
angleCOA = 180-(angleCOB)
angleCOA = 180-60
angleCOA = 120
Angle COA is 120 degrees
This makes up 120/360 = 1/3 of the full circle
So (1/3)*(circumference) = (1/3)*(30pi) = 10pi is the arc length of AC where we take the shorter path from A to C along the circle's edge.
Answer:
AC = 10π
Step-by-step explanation:
Consider arc ADB with length 15π
ADB = circumference of circle × fraction of circle , that is
2πr × [tex]\frac{180}{360}[/tex] = 15π
2πr × [tex]\frac{1}{2}[/tex] = 15π
πr = 15π ( divide both sides by π )
r = 15
∠ AOC = 180° - 60° = 120° ( adjacent angle to 60° )
Thus
AC = 2πr × [tex]\frac{120}{360}[/tex]
= 2π × 15 × [tex]\frac{1}{3}[/tex]
= 30π × [tex]\frac{1}{3}[/tex]
= 10π
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If you are smart enough to use a smart phone then trust me this is peanuts for YOU !
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D=K
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Step-by-step explanation:
hope it helps
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Step-by-step explanation:
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Which statement describes a series of transformationsthat would show that figureA is congruent to figure B.
PLEASE HELP!!!
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Answer:
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O km
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H
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
28.32$
Step-by-step explanation:
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Total: 24+4.32=28.32$
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Answer:
Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Use a calculator lol
Answer:
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Step-by-step explanation:
5,250 divided by 6 is 875
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Answer:
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Answers
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Answers
Answer:
The relation represented by diagram 4 is NOT a function.
Step-by-step explanation:
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According to the fourth diagram, the domains include 1, 2, and 3 while the range includes A, B, and C. Also, the ordered pairs would go as follows according to the arrows:
(1, A), (2, A), (2, B), (3, C)
While the y-values, A and B, are different, they share the same input, 2. Therefore, the relation represented by the 4th diagram is NOT a function.
Hope this helps!
Quadrilateral BECK is known to be a rhombus. Two of the vertices are B(3,5) and C(7,-3).
a. Find one slope of diagonal EK
b. Find an equation of line EK
Answers
Answer:
a. The slope of EK is [tex]\frac{1}{2}[/tex]
b. The equation of line EK is y = [tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
The form of the equation of a line is y = m x + b, where
m is the slope of the lineb is the y-interceptThe rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where
(x1, y1) and (x2, y2) are two points on the lineThe rule of the mid-point is ([tex]\frac{x1+x2}{2},\frac{y1+y2}{2}[/tex])∵ BECK is a rhombus
∵ The diagonal is the line that joins two opposite vertices
∵ B and C are opposite vertices in the rhombus
∵ E and K are opposite vertices in the rhombus
∴ BC and EK are the diagonals of the rhombus BECK
∵ The diagonals of the rhombus are ⊥ and bisect each other
∴ EK is ⊥ bisector to BC
→ Let us find the slope and the mid-point of BC
∵ B = (3, 5) and C = (7, -3)
∴ x1 = 3 and y1 = 5
∴ x2 = 7 and y2 = -3
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{-3-5}{7-3}[/tex] = [tex]\frac{-8}{4}[/tex] = -2
∴ m = -2
∴ The slope of BC = -2
→ To find the slope of EK reciprocal the slope of BC and change its sign
∴ m⊥ = [tex]\frac{1}{2}[/tex]
∴ The slope of EK = [tex]\frac{1}{2}[/tex]
a. The slope of EK is [tex]\frac{1}{2}[/tex]
→ Substitute the value of the slope in the form of the equation above
∵ y = [tex]\frac{1}{2}[/tex] x + b
→ To find b substitute x and y in the equation by the coordinates
of a point on the line
∵ The mid-point of BC is the mid-point of EK
∵ The mid-point of BC = ([tex]\frac{3+7}{2},\frac{5+-3}{2}[/tex]) = ([tex]\frac{10}{2},\frac{2}{2}[/tex]) = (5, 1)
∴ The mid-point of EK = (5, 1)
→ Substitute x by 5 and y by 2 in the equation
∵ 1 = [tex]\frac{1}{2}[/tex](5) + b
∴ 1 = [tex]\frac{5}{2}[/tex] + b
→ Subtract [tex]\frac{5}{2}[/tex] from both sides
∴ [tex]-\frac{3}{2}[/tex] = b
→ Substitute the value of b in the equation
∵ y = [tex]\frac{1}{2}[/tex] x + [tex]-\frac{3}{2}[/tex]
∴ y = [tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{2}[/tex]
b. The equation of line EK is y = [tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{2}[/tex]
What is the slope of the line, what does the slope represent? write an equation for emma’s graph x=time and y=distance
Answers
Answer:
5/2 or 2.5
Step-by-step explanation:
Slope formula:
(y₂ - y₁) / (x₂ - x₁)
Two points are given:
(2, 5) and (6, 15)
x₁ = 2
y₁ = 5
x₂ = 6
y₂ = 15
Substitute and solve:
(15 - 5) / (6 - 2)
10 / 4
5/2 or 2.5
My cookbook says that a salad sauce should be made of 1/3 lemon juice and
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and the total volume is now 70.
How much oil must I now add to have the correct proportions?
Answers
Answer:
50ml
Step-by-step explanation:
as u put 30ml oil and u have 70 so 70-30 is 40 which is 40ml lemon juice. as 1 part is lemon and 2 parts oil out 2x40 so 80ml but as u already have 30 in there only put 50 :)
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The exchange rate one day was $0.82 U.S. $1.00 Canadian.
That day, Sheila exchanged $25 U.S. for Canadian dollars. To the nearest cent, how much Canadian money did Sheila receive?
A. $20.50
В. $25.82
C. $26.82
D. $30.49
Answers
Answer:
$20.50
Step-by-step explanation:
25 / 0.82 = x / 1
