Answer:
The reference angle is the acute angle formed by the terminal side of an angle in standard position and the x-axis
Step-by-step explanation:
-440° will be in the 1st quadrant
We solve by adding 360° to it till it becomes positive
-440°+360°= -80°
-80°+360°=280°
The equivalent value will become
360°-280°= 80°
Answer:
The reference angle for an angle whose measure is -440° is 80°.
Step-by-step explanation:
The cycles for angles range from the traditional 0° to 360° and subsequent 360° ranges befor and after this traditional intervals, also have the same properties.
So, the ranges that exist and correspond to the traditional 0° to 360° include
0° to 360°
360° to 720°
720° to 1080°
And in the negative direction, we have
-360° to 0°
-720° to -360°
We can see that -440 is in the range of
-720° to -360°
Using the traditional 0° to 360° to compare this range of -720° to -360°, let x represent the reference angle in the traditional range that we require.
-720° ------ 0°
-440° ------ x
-360° ------ 360°
Using interpolation,
[-440° - (-720°)]/[-360° - (-440°)] = (x - 0°)/(360° - x)
(280/80) = x/(360-x)
3.5 = x/(360-x)
3.5(360 - x) = x
1260° - 3.5x = x
4.5x = 1260°
x = (1260°/4.5) = 280°
But, the reference angle is the smallest angle that one can make from the terminal side of an angle (that is, where the angle ends) with the x-axis. It uses the x-axis as its frame of reference.
So, 280° is a fourth quadrant angle, whose equivalent in the first quadrant is 360° - 280° = 80°
Hope this Helps!!!
The volume of the shipping box needs to be 1,144 cubic inches. The equation that models the volume of the shipping box is 8(n + 2)(n + 4) = 1,144.
Answer the following questions about the equation modeling the volume of the shipping box.
Question 1
Solve the equation that models the volume of the shipping box, 8(n + 2)(n + 4) = 1,144. If you get two solutions, are they both reasonable?
Answer:
see below
Step-by-step explanation:
8(n + 2)(n + 4) = 1,144
FOIL
8(n^2 +2n+4n+8) = 1144
Divide each side by 8
8/8(n^2 +2n+4n+8) = 1144/8
(n^2 +2n+4n+8) = 143
Combine like terms
n^2 +6n+8 = 143
Subtract 143 from each side
n^2 +6n+8 -143= 0
Combine like terms
n^2 +6n -135 =0
Factor
What two terms multiply to -135 and add to 6
-9*15 =-135
-9+15 = 6
(n-9) (n+15) =0
Using the zero product property
n-9 =0 n+15=0
n = 9 n=-15
The length cannot be negative so n = -15 cannot be a solution
n =9
Answer:
n = 9
Step-by-step explanation:
8(n + 2)(n + 4) = 1,144
(n + 2)(n + 4) = 143
n² + 2n + 4n + 8 = 143
n² + 6n - 135 = 0
n² + 15n - 9n - 135 = 0
n(n + 15) - 9(n + 15) = 0
(n - 9)(n + 15) = 0
n = 9, -15
since n is a length, it can not be negative
Therefore the only solution is n = 9
Pythagorean Theorem: Jason only has room for a TV that is less than 30^ prime prime wide.
Find the width of the TV
Answer:
Step-by-step explanation:
length² + width² = diagonal²
24² + width² = 40²
576 + width² = 1600
width² = 1600 - 576
width² = 1024
width = √1024 = √32*32
width = 32"
Width of the TV is more than 30"
Answer:
32
Step-by-step explanation:
First off, Bruh, 30" is not prime prime. That's 30 inches.
The base of the TV is 32. This is because A^2+B^2=C^2. 24 is A, 40 is C, and the base is B.
So that means that is we take 24^2 and the base^2, we should get 40^2. 40^2 is 1600. 24 squared is 576. So if we take the base and square it and add 576, we should get 1600. Or we could just take 1600 and subtract 576.
1600-576=1024.
So now, the root of 1024 is the base. Which is 32. Hope that helped.
1. Show work and find the value of the circumference of the circle with a 12 cm radius.
Answer:
75.36
Step-by-step explanation:
3.14(pi) x 24(diameter) = 75.36(circumference)
This pyramid is cut by the plane shown. The plane is parallel to the base of the square pyramid. What is the shape of the cross-
section?
A)
rectangle.
B)
rhombus.
square.
D)
triangle
Answer:
c
Step-by-step explanation:
Answer: THE ANSWER IS c
Step-by-step explanation:
Is (1, -2) a solution of y> -6x – 3?
Choose 1 answer:
Yes
No
Answer:
Yes
Step-by-step explanation:
(1, -2)
y > -6x – 3
-2 > -6(1) - 3
-2 > -6 - 3
-2 > -9 Yes
If you bought a stock last year for a price of $73, and it has risen 7.1% since then, how much is the stock worth now, to the nearest cent?
Answer:
78.18
Step-by-step explanation:
73 times 1.071=78.183
Answer:
$78.11
Step-by-step explanation:
When 800 is increased by 5%, find the amount of increase
Choose the function whose graph is given below.
Y = csc x
Y= tan x
Y= sec x
Y = cot x
The given graph shown in the image is of function y = cotx. Option D is correct.
Given that,
To determine the function whose curve is plotted in the graph.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
Here,
Since the given graph is of cots because only cotx tends to infinity whenever x tends nπ where n is an integer on the number line.
Thus, the given graph shown in the image is y = cotx. Option D is correct.
Learn more about graphs here:
brainly.com/question/16608196
#SPJ2
math question down below
Answer:
whats the question i dont see the link
Step-by-step explanation:
Simplify.
2(m + 11)
2m + 11
2m + 22
24m
22m
Answer:
You distribute the 2 to the m=2m
Then you distribute the 2 to the 11 which gives you 22
ANSWER: 2m+22
Factor this expression.
4x-12
O A. 4(x-4)
OB. 4(x-6)
O C. 4(x-3)
O D. 4(x-8)
Answer:
C. 4(x-3)
Step-by-step explanation:
Use DeMoivre’s Theorem to find (3cis(pi/6))^3.
a.) (27sqrt3)/2 +27/2 i
b.) (9sqrt3)/2 +9/2 i
c.) 27i
d.) 9i
Answer:
C. 27iStep-by-step explanation:
Given the complex number in polar coordinate expressed as
z = r(cos∅+isin∅)
zⁿ = {r(cos∅+isin∅)}ⁿ
According to DeMoivre’s Theorem;
zⁿ = rⁿ(cosn∅+isinn∅)
Given the complex number;
(3cis(pi/6))^3
= {3(cosπ/6 + isinπ/6)}^3
Using DeMoivre’s Theorem;
= 3³(cos3π/6 + isin3π/6)
= 3³(cosπ/2 + isinπ/2)
= 3³(0 + i(1))
= 27i
The right answer is 27i
When 3 is subtracted from 1/3 of a number n, the result is less than 6. Which inequality and solution represent this situation?
A: 1/3n - 3 < 6; n < 27
B: 3 - 1/3n < 6; n > -9
C: 1/3n - 3 < 6; n < 9
D: 3 - 1/3n < 6; n < -9
Answer: A
Step-by-step explanation:
1/3n (variable)
-3 (it says subtracted)
(is less than 6)
(n is less that 27)
Can i get some help ♂️
Answer:
[tex]AC=13.5[/tex]
Step-by-step explanation:
Use the Law of Sines as follows:
[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]
Insert the values (use the steps from the last problem):
[tex]\frac{sin25}{14} =\frac{sin24}{b}[/tex]
Isolate b. Multiply both sides by b:
[tex]b*(\frac{sin25}{14} )=b*(\frac{sin24}{b})\\\\b*\frac{sin25}{14}=sin24[/tex]
Multiply both sides by 14:
[tex]14*(b*\frac{sin25}{14})=14*(sin24)\\\\b*sin25=14*sin24[/tex]
Isolate b. Divide both sides by sin 25:
[tex]\frac{b*sin25}{sin25} =\frac{14*sin24}{ysin25} \\\\b=\frac{14*sin24}{sin25}[/tex]
Insert the equation into a calculator and round to the nearest tenth:
[tex]b=13.5[/tex]
The length of AC is 13.5 units.
:Done
PLEASEEEEE HELPP !!!!!
A lake near Susan's house is predicted to lose water every
day because of a drought. The table shows the estimated
water depth in feet, y, after x days of drought.
Answer:
y = -0.5x + 100
Step-by-step explanation:
Im not really sure what i was supposed to answer but i hope it helped.
Answer:
A. y = −0.5x + 100
Step-by-step explanation:
Lee watches tv for 4 hours per day. During that time , the tv consumes 200 watts per hour. electricity costs (15 cents)/( 1 kilowatt-hour). How much does lee’s tv cost to operate for a month of 30 days?
Answer: $3.6
Step-by-step explanation:
Hi, to answer this question, first we have to calculate watt hours per day:
200 wph x 4 hours = 800 watt hours
Now, we have to convert the watt-hours to kilowatt hours:
800 wh /1000 =0.8 kwh
Since he watches TV 30 days per month:
0.8 kw x 30 days = 24 kwh
Finally we have to multiply that result by the price per kilowatt hour (15 cents)
24 kwh x 15 cents = 360 cents
Converting to dollars:
360/ 100 = $3.6
Lee’s TV cost 3.6 dollars to operate for a month of 30 days
Find , to the nearest tenth of a foot , the height of the tree represented in the accompanying diagram.
Answer:
Height of tree = 28.2 ft (Approx)
Step-by-step explanation:
Given:
Angle from ground to top of the tree = 62°
Distance from a point to base of tree = 15 ft
Height of tree = [tex]X[/tex]
Find:
Height of tree = [tex]X[/tex]
Computation:
Using trigonometric application:
[tex]Tan\ 62 = \frac{Height\ of\ tree}{Distance\ from\ a\ point\ to\ base\ of\ tree} \\\\Using\ calculator\ , Tan62 = 1.88\\\\1.88=\frac{Height\ of\ tree}{15} \\\\Height\ of\ tree=28.2ft[/tex]
Height of tree = 28.2 ft (Approx)
Jack ran 13.5 miles in 1.5 hours. What was his speed in miles per minute?
Answer:
9
Step-by-step explanation:
13.5 / 1.5 = 9
Answer:
[tex] \boxed{Speed = 0.15 \: miles \: per \: minute} [/tex]
Given:
Distance travelled = 13.5 miles
Time taken = 1.5 hours = 1.5 × 60 = 90 minutes
Step-by-step explanation:
[tex]Speed = \frac{Distance \: travelled}{Time \: taken} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{13.5}{90} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 0.15 \: miles \: per \: minute[/tex]
Suppose the equation h =− 16t2 + 35t models the altitude a football will reach t seconds after it is kicked. Is it possible for the football to reach 16 ft in the air? Justify your answer.
Answer:
The ball will be able to reach the 16 ft.
Step-by-step explanation:
In order to calculate if the ball will be able to reach that height, we must make "h" equal to 16, if there's a real positive solution, then the ball will be able to reach it.
16 = -16t² + 35t
16t² - 35t + 16 = 0
t = [-(-35) +- sqrt((-35)² - 4*16*16)]/(2*16)
t = [35 +- sqrt(1225 - 1024)]/32
t = [35 +- sqrt(201)]/32
t = (35 +- 14.177)/32
t1 = 0.65071875
t2 = 1.5367
The ball will reach that height at 0.65 s and 1.53 s.
The length of a planet's orbit around a star is approximately 16,540,000 km.
It takes the planet about 710 Earth days to complete a full orbit.
What is the planet's average speed in kmh-1 to 3sf? ANSWER PLS 15 POINT UP FOR GRABS
Answer:
971 km/h
Step-by-step explanation:
The length of a planet's orbit around a star is approximately 16,540,000 km and it takes the planet about 710 Earth days to complete a full orbit.
Average speed is given as total distance traveled divided by time taken. That is:
S = D / t
Where t is in hours.
We have to convert 710 days to hours:
1 day = 24 hrs
710 days = 710 * 24 = 17040 hours
Therefore, the planet's speed is:
S = 16540000 / 17040 = 971 km/h (to 3 sf)
Given: PK and PE tangents
m∠KPE = 60°,
2KP = PE + 1
Find: EK
Answer:
EK = 1.
Step-by-step explanation:
Here we have KP = PE (tangents from outside the circle)
Therefore, 2KP = PE + 1 = KP + 1
Hence, 2KP - KP = 1 or KP = 1 = PE
Since KE is the base of triangle KPE, where ∡ KPE = 60, and KP = PE, we have an isosceles triangle such that ∡PKE = ∡PEK
Hence, in ΔKPE, ∡KPE + ∡PKE + ∡PEK = 180
Therefore, 60° + ∡PKE + ∡PEK = 180
Hence, ∡PKE + ∡PEK = 180° - 60° = 120°
Because ∡PKE = ∡PEK, (base angles of isosceles triangle), we have;
∡PKE + ∡PEK = 2·∡PEK = 120° which gives
∡PEK = 60° = ∡PKE
Therefore, ∡KPE = ∡PEK = ∡PKE = 60°
Hence, ΔKPE is an equilateral triangle and KP = PE = EK = 1
EK = 1.
math question screen shot down below
Answer:
The correct answer is A, Point P
Step-by-step explanation:
since the additive inverse of 2 is -2 because -2 + 2 = 0 the correct choice must be choice A, Point P.
Which shows how the distributive property can be used to evaluate 7x8 4/5?
Answer:
61 3/5
Step-by-step explanation:
we realize that 8 4/5 can be written as [8 + (4/5)]
hence 7 x 8 4/5
= 7 x [8 + (4/5)]
= 7 [8 + (4/5)] (use the distributive property, see attached for reference)
= 7(8) + 7(4/5)
= 56 + 28/5 (convert 28/5 into mixed fraction)
= 56 + 5 3/5
= 61 3/5 (answer)
How many outcomes are in the sample space of flipping a coin in spinning a spinner with sections labeled 1-4
Answer:
8 outcomes
Step-by-step explanation:
A coin has two possible outcomes: heads or tails.
The spinner has four possible outcomes: 1, 2, 3 or 4.
If we combine then, the number of outcomes will be the product of their number of outcomes:
2 * 4 = 8
So we will have a total of 8 outcomes:
heads, 1 / heads, 2 / heads, 3 / heads, 4 /
tails, 1 / tails, 2 / tails, 3 / tails, 4
3) A box of chocolates contains four milk
chocolates and four dark chocolates. You
randomly pick a chocolate and eat it.
Then you randomly pick another piece.
The first piece is milk chocolate and the
second piece is dark chocolate.
Are the events independent or dependent?
What is the probability?
Answer:
dependent and 2/7
Step-by-step explanation:
dependent because you didn't replace it.
1/2 times 4/7 which is 4/14 which equals to 2/7
Find the volume of the cone
Answer:
12π
Step-by-step explanation:
Volume of the cone is πr^2 * h / 3
r = 3
h = 4
9π * 4 / 3 = 12π
Answer: 37.6991118
Step-by-step explanation:
Which will result in a perfect square trinomial?
Answer:
is there a picture?
Step-by-step explanation:
SOMEONE, PLEASE HELP FAST!!! FOR BRAINLIEST!!!!
Answer:
Volume of rectangular prism:
V1 = base x height = 4 x 6 x 12 = 288 ft3
Volume of triangular prism:
V2 = base x height = 4 x (6/2) x 6 = 72 ft3
Volume of composite prism:
V= V1 + V2 = 288 + 72 = 360 ft3
Hope this helps!
:)
A man wants to hike two trails. The length of one trail is 7.709 km. The length of the other trail is 9.0309 km. What is the total length of the two trails?
Answer:
Its addition I think so the answer would we 16.7399km for both trials
Step-by-step explanation:
plz halp meh!!!!!!!
Answer:
M=25-3D
Step-by-step explanation:
Daniel starts with 25 dollars and spends three dollars per day for a d number of days. So the amount of money in his wallet should be equal to the starting number of dollars minus the amount of money he spends. Therefore we get the equation M=25-3D, where M is the amount of money is his wallet, and D us the number of days he buys a drink and chips.
