Answers
Answer:
a) m∠BPD = 120°
b) m∠BC + m∠AD = 120°
Step-by-step explanation:
a) To solve for question a, we make use of a theorem called the intersecting chord theorem. This states that:
The measure of the angle formed by two chords that intersect inside a circle is the average of the measures of the intercepted arcs.
The Interior angle =( The larger exterior arc + The smaller exterior arcs) ÷ 2
The larger exterior arc (m∠BD) = 170°
The small exterior arc (m∠CA) = 70°
m∠BPD = m∠BD + m∠CA/2
m∠BPD = 170° + 70°/2
= 240°/2
= 120°
b) We are to find m∠BC + m∠AD
The sum of exterior angles in a circle = 360°
360° = m∠BD + m∠CA + m∠BC + m∠AD
360° = 170° + 70° + m∠BC + m∠AD
360° = 240 + m∠BC + m∠AD
360 - 240° = m∠BC + m∠AD
Thererefore,
m∠BC + m∠AD = 120°
Answer:
1. m∠BPD = 120°
2. m∠BC + m∠AD = 120°
Related Questions
If v=5 and w=24, what is 5v+w?
Answers
Answer:
49
Step-by-step explanation
5v + w
5(5) + 24
25 + 24
49
First you have to substitute the variables with numbers given (v=5 ; w=24)
Start with multiplying 5*5 which equals 25, then finish off with adding the two numbers.
Answer:
5v+w = 5(5)+24 = 49
Step-by-step explanation:
As you can see we have two variables
v & w
And we have no coefficient to w but we do to v which is...
5
So... we must replace the variables (v & w) replacing them with the numbers you gave us, 5 for v and 24 for w.
The sentence is
5v+w= ?
If you replace v with 5 it becomes...
5(5)+w
When seeing a number & a variable or numerous variables that placed right next to each other, it means that the number and the variable(s) are to be multiplied together.
So now we have 5(5)+w meaning 5 times 5 plus the variable w
The second value you gave us is 24 which is supposed to be subbed in for w.
So... when we replace w with 24 we get...
5(5)+24
Now we evaluate the expression.
According to PEMDAS... since we have no parenthesis or exponents we do m, multiplication first. 5*5=25
We are now left with...
25+24
25 + 24 = 49.
So...
5v+w is now 5(5)+24 which is equal to...
49
Hopefully this helped you!
Have a good day!
NEEDDD HELPPPP ASAPPPPPPPPPP !!
Answers
Answer:
42 = 8x + 13x
42 = 21x
x = 2
8 = 8c -4(c + 8)
8 = 8c - 4c - 32
8 = 4c - 32
40 = 4c
c = 10
Answer:
42 = 8x + 13x42 = 21x
42/21 = x
x = 2
check:
42 = 8*2 + 13*2
42 = 16 + 26
8 = 8c - 4(c+8)8 = 8c -4*c -4*8
8 = 8c - 4c - 32
8 + 32 = 4c
40 = 4c
40/4 = c
c = 10
Check:
8 = 8*10 - 4(10+8)
8 = 80 - 4*18
8 = 80 - 72
It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches. Which function models the horizontal displacement as a function of time in seconds? y = 5 cosine (StartFraction 2 pi Over 3 EndFraction x) y = 5 cosine (StartFraction 4 pi Over 3 EndFraction x) y = 10 cosine (StartFraction 2 pi Over 3 EndFraction x) y = 10 cosine (StartFraction 4 pi Over 3 EndFraction x)
Answers
Answer:
Step-by-step explanation:
Given functions are
y = 5 cos ( 2π / 3 ) t
y = 5 cos ( 4π / 3 ) t
y= 10 cos ( 2π / 3 ) t
y = 10 cos ( 4π / 3 ) t
The pendulum half oscillation from left extreme to right extreme takes 1.5 s
So its time period of oscillation T = 1.5 x 2 = 3 s .
standard equation of oscillation is
y = A cos ω t where A is amplitude and ω is angular frequency .
Amplitude of oscillation A = 10 / 2 = 5 inch .
Among the given equation of motion only first two has amplitude equal to 5 . So both the last two are ruled out .
The angular frequency of first motion as per given equation
ω = 2π / 3
If time period is T
2π / T = 2π / 3
T = 3 s
So it matches with the time period of oscillation of pendulum .
Hence the first equation truly represents the oscillation of pendulum.
The function models the horizontal displacement as a function of time in seconds is [tex]\rm y = 10 sin(\dfrac{2\pi}{3})t[/tex] and this can be determined by using the given data.
Given :
It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches.
For the oscillation the standard equation is given below:
[tex]\rm y = A\;cos \;\omega t[/tex]
where A is the amplitude, [tex]\omega[/tex] is the angular velocity, and t is the time.
Now, determine the time period that is:
T = 1.5 [tex]\times[/tex] 2
T = 3sec
Now, the angular frequency is given by:
[tex]\omega = \dfrac{2\pi}{3}[/tex]
So, the function models the horizontal displacement as a function of time in seconds is given below:
[tex]\rm y = 10 sin(\dfrac{2\pi}{3})t[/tex]
Therefore, the correct option is C).
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Find x. A. 332–√ B. 113–√ C. 33 D. 443–√
Answers
Answer:
C. 33.
Step-by-step explanation:
The sides of a 45-45-90 triangle are in the ratio 1:1:√2 so the side opposite to 45 degrees = 11√6 / √2.
Consider the larger triangle containing the 60 degree angle:
tan 60 = x / (11√6 / √2).
x = tan 60 * 11√6 / √2
x = 33.
The value of the variable x will be 33 units. Then the correct option is C.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The diagram is shown below.
Let h be the height of the triangle.
The value of h is given by the sine of angle 45°. Then the value of the height h will be
sin 45° = h / 11√6
h = 11√6 × 1/√2
h = 11√3 units
The value of h is given by the tangent of angle 60°. Then the value of the height h will be
tan 60° = x / h
x = 11√3 × √3
x = 11 × 3
x = 33 units
Thus, the value of the variable x will be 33 units.
Then the correct option is C.
More about the right-angle triangle link is given below.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each value to the correct expression.
Answers
The answer is shown below:
What is expression?An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. Let us understand how to write expressions. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression.
1+5.2 + (1+3)²
=1+10 + 16
=27
0.25*4³-1
=0.25*64-1
=16-1
=15
4+8(1/4+2)
=4+8(9/4)
=4+2*9
=4+18
=22
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Mummy shade has three children one is Ade, the one second is sumbo. WHAT IS THE NAME OF THE THIRD ONE
just to think wisely about it.
Answers
Answer:
Shade
Step-by-step explanation:
she's called Mummy shade, so I think her other child's name is shade
Answer:
Shade
Step-by-step explanation:Her name is Mummy shade
A business tenant has a percentage lease stating rent payment is greater of 2% of the business's total gross sales volume or a minimum base rental of $1,000.00 per month. In the past year, sales totaled $435,000. How much rent did the business pay?
Answers
Answer:
The answer is $12,000. 12 months × $1,000 per month = $12,000 minimum annual base rent; $435,000 gross sales × 2% = $8,700. The tenant paid $12,000 because the minimum base rent was more than the percentage of gross sales.
Step-by-step explanation:
At Horatio's machining company, it takes 2 minutes to manufacture each part and 10 minutes to pack all the parts for an order. Write an expression that shows how many minutes it will take to complete an order, assuming there are x parts in an order.
Answers
Answer:
f(x) = 2x + 10
Step-by-step explanation:
Let's call this function f(x), where f(x) is time to get the order ready and x is the number of parts:
f(x) = 2x + 10 Is the expression of this function.2x is the time to manufacture all parts of the order and 10 min is the time to pack them.
Answer:
2x + 10 is the correct answer :)
Probability ~
The probability of selecting a white chocolate from a box is 1/5 and the probability of selecting a dark chocolate from the same box is 1/3. The other chocolates are milk chocolates.
A. Find the probability of selecting a milk chocolate.
B. How many chocolates in total could be in the box? Give reasons. Is there more than one answer?
Answers
A.
A - selecting a milk chocolate
[tex]P(A)=1-\dfrac{1}{5}-\dfrac{1}{3}=\dfrac{15}{15}-\dfrac{3}{15}-\dfrac{5}{15}=\dfrac{7}{15}[/tex]
B.
The number of the chocolates must be a multiple of 15, so there can be 15,30,45,... etc. chocolates in the box.
If each of the 4 shelves holds 14 movies, how many movies does Betty have on her shelving unit? Show your work.
Answers
Answer:
62
Step-by-step explanation:
4x + 6
4(14) + 6 (substituting x = 14)
56 + 6
62
PLS SIMPLIFY b3·b^−5·b^11
A) b^9
B) b^15
C) b^19
D) b^-165
Answers
Answer:
a) b⁹
Step-by-step explanation:
b³ • b⁻⁵ • b¹¹
add the exponents
b³ ⁺ ⁽⁻⁵⁾ ⁺ ¹¹
b⁹
Answer:
b^9
Step-by-step explanation:
b^3·b^−5·b^11
Since the bases are the same, and we are multiplying, we can add the exponents
b^(3+-5+11)
b^9
Which expression is equivalent to the product of p+7/3 and6/p , where p0? PLZZZZ HELPPPPPPP
Answers
Answer: [tex]6+\dfrac{14}{p}[/tex] .
Step-by-step explanation:
To find : The expression is equivalent to the product of [tex]p+\dfrac73\text{ and }\dfrac6p[/tex], where p ≠0.
Product of [tex]p+\dfrac73\text{ and }\dfrac6p[/tex] = [tex](p+\dfrac73)\times\dfrac6p[/tex]
Using distributive property: [tex](b+c)a= ba+ca[/tex]
[tex](p+\dfrac73)\times\dfrac6p=p\times\dfrac6p+\dfrac73\times\dfrac6p\\\\= 6+\dfrac{7}{1}\times\dfrac2p\\\\=6+\dfrac{14}{p}[/tex]
Hence, the required expression is [tex]6+\dfrac{14}{p}[/tex] .
Answer:
B!!!
Step-by-step explanation:
Multiply then divide every number by 2 to simplify.
What axis does the independent quantity go on?
Answers
The Axes. The independent variable belongs on the x-axis (horizontal line) of the graph and the dependent variable belongs on the y-axis
NEEEEDDDD ASSAAAAPPPPP NEED ANSWER NOWWWW
Answers
Answer:
w=10
Step-by-step explanation:
-2=-(w-8)
2=w-8
w=10
Question:
-2=-(w-8)
Answer:
-2=-w+8
w=8+2
w=10
Step-by-step explanation:
A tank contains 15,000 L of brine with 24 kg of dissolved salt. Pure water enters the tank at a rate of 150 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate.How much salt is in the tank after t minutes
Answers
Answer:
Step-by-step explanation:
Let y(t) be the amount of salt in the tank after time t.
(A) Incoming rate = 0 (due to Pure water having no salt)
(B) Mixed solution comes out at 150 L/min. Initially the tank has 15,000 L of brine with 24 kg of salt.
concentration of salt at time t = y(t) / 15000 kg/L
Outgoing rate = y(t)/15000 * 150 = y(t) / 100
(C) we know that,
[tex]\frac{dy}{dx} =(incoming\ rate) - (outgoing\ rate)[/tex]
[tex]\frac{dy}{dx} =0-\frac{y(t)}{100} = \frac{-y(t)}{100}[/tex]
Separate variable and integrate
[tex]\int {\frac{dy}{y} } = - \int {\frac{1}{100} } \, dt[/tex]
[tex]ln|y|=-\frac{1}{100}t + D[/tex]
[tex]y=e^{D} e^{\frac{-t}{100} }[/tex]
[tex]y= Ce^{\frac{-t}{100} }\ [C=e^{D} ][/tex]
At t= 0 , y(0) = 24 kg
[tex]24=C\ e^{0}[/tex]
C= 24
(D) Therefore, the amount of salt in the tank after time t :
[tex]y(t)=24e^{\frac{-t}{100} }\ kg[/tex]
Let f(x) = 7x − 13. Find f−1(x)
Answers
Step-by-step explanation:
let f(x)=y
y=7x-13
y+13=7x
y+13/7=x
f-1(x)=x+13/7
A group of people buys 5 pounds of corn meal to divide equally among 6 families write a fraction or mixed number that shows how many pounds of corn meal each family gets'.
Answers
Answer:
5/6 pounds
Step-by-step explanation:
A group of people buys 5 pounds of corn meal to divide equally among 6 families write a fraction or mixed number that shows how many pounds of corn meal each family gets'.
Given the following :
Amount of corn meal purchased = 5 pounds
Number of people to share = 6 families
Assume, it is divided equally among them;
Then; each family gets ;
(Pounds of corn meal purchased/number of families) ;
5 / 6 pounds of corn meal will be distributed to each family.
The cost to rent a car at one agency is $24.50 per day plus an additional $15.99 fee for insurance. At a different agency, the cost to rent a car is $27.50 per day, but the insurance is only an additional $3.99 fee. Which equation could be used to find the number of days, d, at which the rental fee is the same for both agencies?
Answers
Answer:
d=4
Step-by-step explanation:
Agency 1:
Total cost of renting a car=24.50d + 15.99
Agency 2:
Total cost of renting a car=27.50d + 3.99
Where, d=No. of days of renting the car
Which equation could be used to find the number of days, d, at which the rental fee is the same for both agencies?
The equation is by equating agency 1 and agency 2 equation
24.50d + 15.99 = 27.50d + 3.99
Collect like terms
24.50d - 27.50d = 3.99 - 15.99
-3d = -12
Divide both sides by -3
d= -12 / -3
=4
d=4
Check
Agency 1:
24.50d + 15.99
= 24.50(4) + 15.99
= 98 + 15.99
= 113.99
Agency 2:
27.50d + 3.99
= 27.50(4) + 3.99
= 110 + 3.99
= 133.99
Answer:
24.5d + 15.99 = 27.5d + 3.99
Step-by-step explanation:
The other person who answered this question was correct, they just explained it all the way through and since you guys skim through everything instead of reading, I'll put the answer. :)
draw a graph of 2x - 3y = 6
Answers
Answer:
Slope:[tex]\frac{2}{3}[/tex]
y-intercept:-2
Step-by-step explanation:
A club has 16 members, included Mary and Peter. If two representative are
randomly selected from those members, find the probability that
(d) Mary or Peter is chosen.
Answers
Answer:
12.5 percent; 2/16; 1/8
Step-by-step explanation:
Peter and Mary make up 2 of the clubs members, so the probability that they are chosen is 2/16. This simplifies to 1/8, and in decimal form is .125. Therefore, the percentage form of the probability they are chosen is 12.5 percent.
The 3 question please with explained
Answers
Answer:
Step-by-step explanation:
Rectangle:
length = l = 12 cm
Width = w = 0.8 cm
Use Pythagorean theorem to find the diagonal
Diagonal² = l² + w²
= 12² + 0.8²
= 144 + 0.64
= 144.64
Diagonal = √144.64 = 12.03 cm
Diagonal of square = diagonal of rectangle
= 12.03 cm
To find the side of square again use Pythagorean theorem,
side² + side² = 12.03²
2 sides² = 144.64
side² = 144.64/2
side² = 72.32
side = √72.32
Side = 8.50 cm
reduce 63/72 to its lowest terms
Answers
Answer:
7/8
Step-by-step explanation:
63 ÷ 9/72 ÷ 9
= 7/8
Answer:
7/8
Step-by-step explanation:
63/9 = 7
72/9 = 8
then:
63/72 = 7/8
how to find y in this equation 11=12-14y
Answers
(Subtract 12 from both sides)
-1 = -14y
(Divide both sides by -14)
1/14 = y
solve for x 7x - 3/4 = 6x - 5/8
Answers
Answer: x=0.125 or 1/8
Step-by-step explanation:
[tex]7x-\frac{3}{4}=6x-\frac{5}{8}[/tex]
add 3/4 on both sides
[tex]7x-\frac{3}{4}+\frac{3}{4}=6x-\frac{5}{8}+\frac{3}{4}[/tex]
[tex]7x=6x+\frac{1}{8}[/tex]
subtract 6x on both sides
[tex]x=\frac{1}{8}[/tex]
Answer:
x = 1/8
Step-by-step explanation:
7x - 3/4 = 6x - 5/8
7x - 3/4 + 3/4 = 6x - 5/8 + 3/4
7x = 6x + 1/8
7x - 6x = 6x + 1/8 - 6x
x = (6x - 6x) + 1/8
x = 1/8
Need help how to find this slope
Answers
Answer:
slope = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, 1)
m = [tex]\frac{1-2}{3-0}[/tex] = - [tex]\frac{1}{3}[/tex]
Evaluate the expression 52 + 2x when x = 5. Choose the phrase below that describes the resulting number.
Answers
Answer:
62
Step-by-step explanation:
hope that helps! if it is an answer
The Phrase is: "The resulting number is 62."
We have the expression as
52 + 2x
Now, To evaluate the expression 52 + 2x when x = 5,
we substitute the value of x into the expression and simplify:
=52 + 2(5)
= 52 + 10
= 62.
Thus, The resulting number is 62.
Learn more about Expression here:
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Please answer this question now
Answers
Answer:
373.66 cm².
Step-by-step explanation:
The following data were obtained from the question:
Pi (π) = 3.14
Radius (r) = 7 cm
Slant height (l) = 10 cm
Surface Area (SA) =?
The surface area of the cone can be obtained by using the following formula:
SA = πr² + πrl
SA = (3.14 × 7²) + (3.14 × 7 × 10)
SA = (3.14 × 49) + 219.8
SA = 153.86 + 219.8
SA = 373.66 cm²
Therefore, the surface area of the cone is 373.66 cm².
1/2x+1/3y=2
1/3x+1/2y=13/6 (x is not equal to 0, y is not equal to 0)
by substitution method,
step by step
Answers
Answer:
x=2
y=3
Step-by-step explanation:
x/2+y/3=2 so
3x/6+2y/6=12/6
then multiply by 6
3x+2y=12
equation number 2
x/3+y/2=13/6
2x/6+3y/6=13/6
multiply by 6
2x+3y=13
so the system is now
3x+2y=12
2x+3y=13
from the first equation 2y=12-3x, y=6 - 3x/2
then put y in the second equation
2x+3*(6-3x/2)=13
2x+18-9x/2=13
2x-9x/2=13-18
4x/2-9x/2=-5
-5x/2=-5
*(-1/5) *(-1/5)
x/2=1
*2 *2
x=2
so y=6-3*2/2=6-3
y=3
Step-by-step explanation:
Given that:
(1/2x)+(1/3y) = 2 --------(1)
(1/3x)+(1/2y) = 13/6-----(2)
Put 1/x = a and 1/y = b then
(1) becomes
(a/2 )+( b/3) = 2
⇛ (3a+2b)/6 = 2
⇛ 3a+2b = 2×6
⇛ 3a+2b = 12 --------(3)
(2) becomes
(a/3)+(b/2)=13/6
⇛ (2a+3b)/6 = 13/6
⇛ 2a+3b=13----------(4)
On adding (3)&(4) then
3a+2b=12
2a+3b=13
(+)
_________
5a+5b = 25
_________
⇛ 5a+5b = 25
⇛ 5(a+b)=25
⇛ a+b=25/5
⇛ a+b=5 -------------(5)
On subtracting (3) from (4)
2a+3b=13
3a+2b=12
(-)
_________
-a+b = 1
_________
⇛ -a+b = 1
⇛ b = 1+a --------(6)
On Substituting the value of b in (5) then
a+1+a = 5
⇛2a+1 = 5
⇛ 2a = 5-1
⇛ 2a = 4
⇛ a = 4/2
⇛ a = 2
On Substituting the value of a in (6) then
b = 1+2
b = 3
Now,
a = 2
⇛ 1/x=2
⇛ “x” = 1/2
and
b= 3
⇛ 1/y = 3
⇛“y” = 1/3
Answer:- Hence, the value of x and y with be 1/2 and 1/3 respectively.
The solution for the given problem is (1/2,1/3)
Check:-
If x = 1/2 and y = 1/3 then
LHS = (1/2x)+(1/3y)
= 1/2(1/2)+1/3(1/3)
= 1/(2/2)+1/(3/3)
= (1/1)+(1/1)
= 1+1
=2
= RHS
LHS=RHS is true
and
LHS=(1/3x)+(1/2y)
⇛ 1/3(1/2)+ 1/2(1/3)
⇛ 1/(3/2)+1/(2/3)
⇛ (2/3)+(3/2)
⇛ (4+9)/6
⇛ 13/6
⇛ RHS
LHS = RHS is true
also read similar questions: Simultaneous equations: 1. 2x+2y=10 X+2y=6 2. 3x+y=18 2x+y=13 3. X+y=1 X-y=5 4. 3x+4y=29 X-4y=-17 5. 4c+3y=11 2x+y=7
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Maureen plants tulips in a rectangular flower bed that is 2 cubed feet wide and 2 Superscript 4 feet long.
Answers
Answer:
The area would be 128ft^2
2^4 i= 2x2x2x2
2^3 = 2x2x2
multiply them and you get 128ft6^2
Answer:
128ft^2
Step-by-step explanation:
took the quiz just now :D
In circle L, arc MNOP is 120° and the radius is 5 units. Which statement best describes the length of arc MNOP? one half the area of circle L one third the area of circle L one half the circumference of circle L one third the circumference of circle L
Answers
Question
In circle L, arc MNOP is 120° and the radius is 5 units. Which statement best describes the length of arc MNOP?
• one half the area of circle L
• one third the area of circle L
• one half the circumference of circle L • one third the circumference of circle L
Answer:
• one third the circumference of circle L
Step-by-step explanation:
In the question, we are told that:
In circle L, arc MNOP is 120° and the radius is 5 units.
We are asked to find the statement amongst the options that describes the arc length MNOP of Circle L
Step 1
Find the Area of circle
Area of a circle = πr²
r = 5 units
Area of a circle = π × 5²
Area of a circle = π × 25
Area of a circle = 78.53981634 square units
Step 2
Find the arc length of a circle
Arc length = 2πr × θ /360
r = 5 units
θ = 120°
Arc length = 2 × π × r × 120/360
Arc length = 2 × π × r × (1/3)
Arc length = 2 × π × 5 × (1/3)
Arc length = 10.47198 units
Step 3
Circumference of a circle = 2πr
= 2 × π × 5
= 31.415926536 units
Since the Circumference of a circle = 2πr
Arc length of the circle for the above calculation, = 2πr × 1/3
Therefore, the statement that best describes the arc length MNOP of Circle L is:
" the arc length MNOP is one third the circumference of circle L"
Answer:
the arc length MNOP is one third the circumference of circle L
Step-by-step explanation:
i fishie yupo
