Answer:
sinΘ = √5/3
Step-by-step explanation:
Mathematically, we know that the cos of an angle is the ratio of the adjacent to the hypotenuse
The sine of an angle is the ratio of the opposite to the hypotenuse
So in this case, from the cosine given; adjacent is 2 and hypotenuse is 3
From the Pythagoras’ theorem, we can get the opposite
Mathematically, the square of the hypotenuse equals the sum of the squares of the two other sides
Let us have the opposite as x
3^2 = 2^2 + x^2
9 = 4 + x^2
x^2 = 9-4
x^2 = 5
x = √5
This root can be positive or negative
But since the sine is positive, we shall be considering only the positive root
Thus;
sine theta = √5/3
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Difference between a 1 inch button and ⅜ inch button
[tex] = 1 \: inch - \frac{3}{8} \: inch \\ = \frac{8}{8} \: inch - \frac{3}{3} \: inch \\ = \frac{(8 - 3)}{8} \: inch \\ = \frac{5}{8} \: inch[/tex]
Answer:
5/8
Step-by-step explanation:
To determine the difference, we do:
1 - 3/8
8/8 - 3/8
5/8
A 1 inch button is 5/8 inches longer than a 3/8 inch button.
if a hexagonal prism has a volume of 539 cubic meters and is 16 meters tall, find the area of the hexagonal base
Base Area= ___ m^2
9514 1404 393
Answer:
33 11/16 m² = 33.6875 m²
Step-by-step explanation:
The volume of a prism is given by ...
V = Bh
where B is the area of the base, and h is the height. Solving for B, we find ...
B = V/h
B = (539 m³)/(16 m) = 33 11/16 m² = 33.6875 m²
Find the number of all the 2-digit numbers satisfying the
following congruences x = 3(mod7), x = 2(mod5).
OLEASE HELP
Use the Chinese remainder theorem.
Start with x = 3×5 + 2×7 = 15 + 14 = 29. Now,
• 29 ≡ 15 ≡ 1 (mod7)
• 29 ≡ 14 ≡ 4 (mod5)
Adjust for this by multiplying the first term in x by 3, and the second term by 3 (because 4×3 ≡ 12 ≡ 2 (mod5)).
So now x = 3×5×3 + 2×7×3 = 45 + 42 = 87, and
• 87 ≡ 45 ≡ 3 (mod7)
• 87 ≡ 42 ≡ 2 (mod5)
The CRT then says that x ≡ 87 (mod(7×5)) ≡ 87 (mod35), which is to say any number x = 87 + 35n satisfies both congruences (where n is any integer).
So there are 3 possible 2-digit numbers that work: {17, 52, 87}.
To confirm:
• 17 ≡ 15 + 2 ≡ 2 (mod5) and 17 ≡ 14 + 3 ≡ 3 (mod7)
• 52 ≡ 50 + 2 ≡ 2 (mod5) and 52 ≡ 49 + 3 ≡ 3 (mod7)
• 87 ≡ 85 + 2 ≡ 2 (mod5) and 87 ≡ 84 + 3 ≡ 3 (mod7)
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Answer:
hope this help you
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A point is chosen randomly on KN. Identify the probability that the point is on KL or MN.
Answer:
11/18
Step-by-step explanation:
KL + MN = 11
Total = 18
Probability of KL or MN = 11/18
hello could you please help me with this math problem with full explanation which I am unable to solve?
Answer:
b) 27
Step-by-step explanation:
sum of angles in triangle = 180
a + 63 + 90 = 180
a = 27
Answer:
27 degrees
Step-by-step explanation:
since angle B is 68 and you know that angle c is a right angle it is 90. so yhu take 90 and 63 and add them together and subtract that number from 180 and you find angle A
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Answer my question
im being timed
Answer:
the third one
Step-by-step explanation:
Determine the absolute value
Answer:
64000
Step-by-step explanation:
The absolute value is the non-negative number
|64000| = 64000
what is |x-4| if x>4
Answer:
x-4
Step-by-step explanation:
If x>4, |x-4|>0 which means |x-4|=x-4
The perimeter of a rectangle is 74 inches. If the length is five more than the width, what are the rectangle's measurements?
Answer:
P=2(74)+2(5)
148+10=158
Darias bought 5 school binders that cost $8.00 per
binder. If a back-to-school discount of 40% was
applied to his purchase, and then a 6% sales tax was
added, what was the total cost of the binders?
Answer:
$25.44
Step-by-step explanation:
First, find the original cost of the binders:
5(8)
= $40
Find the cost with the 40% discount:
40(0.6)
= $24
Find the cost with the 6% sales tax:
24(1.06)
= $25.44
So, the total cost of the binders was $25.44
Rae earns $60 for playing music on Saturday nights at the local coffee house. She makes an average of $5.25 in tips per hour. Write the function of Rae's earnings, and solve for how much she would make after 4 hours. (1 point) a y
A garrison of 120 people had provisions for 30 days. If 20 people leave the garrison after 10 days, how long does the remaining provisions last?
Answer:
24 days
total units = 120* 30 = 3600
used after 10 days = 120*10 = 1200
remaining units after 10 days = 3600-1200 = 2400
2400/100 people = 24 days that the provisions will last
Step-by-step explanation:
7.
For which discriminant is the graph possible?
A. b2 – 4ac = 0
B. b2 – 4ac = –1
C. b2 – 4ac = 4
Answer:
C. b2 – 4ac = 4
Step-by-step explanation:
Answer:
The graph is possible for
Step-by-step explanation:
we know that
The discriminant of a quadratic equation of the form
is equal to
If D=0 the quadratic equation has only one real solution
If D>0 the quadratic equation has two real solutions
If D<0 the quadratic equation has no real solution (complex solutions)
In this problem , looking at the graph, the quadratic equation has two real solutions (the solutions are the x-intercepts)
so
therefore
The graph is possible for
...............................................................................................................................................
Answer:
b^2 – 4ac = 4
...............................................................................................................................................
x^5+x-1
x^5+x-1
x^5+x-1
Step-by-step explanation:
x⁵+x-1
(2x-x+1) ( x³+x²-1 )
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.................................
X = [?]°
Dr.
X Х
As
140°
B
C
Answer:
40°
Step-by-step explanation:
x+140=180°(angle on a straight line)
x=180-140
x=40°
∠DBA and ∠DBC are making linear pair.
Linear pair of angles are formed when two lines intersect each other at a single point.
The sum of angles of a linear pair is always equal to 180°[tex] \rm \large\longrightarrow \: \: x \: + \: 140 \degree \: = \: 180 \degree[/tex]
[tex]\rm \large\longrightarrow \: \: x \: = \: 180 \degree \: - \: 140 \degree \: [/tex]
[tex]\rm \large\longrightarrow \: \: x \: = \: 40 \degree[/tex]
It cost 2.10 for a gourmet coffee shop to make a small latte.The price of a small latte is 2.94.What is the percent markup on the latte
Answer:
40%
Step-by-step explanation:
Given that :
Cost of production of small latte = 2.10
Sale price of small latte = 2.94
The Markup = Sale price of small latte - cost of production of small latte
The Markup = 2.94 - 2.10 = 0.84
Percentage Markup = (0.84 / 2.10) * 100%
Percentage Markup = 0.4 * 100% = 40%
Question 13 of 46
What is the remainder for the synthetic division problem below?
Answer:
Step-by-step explanation:
Let's do this out as best as we can here. Here's the problem:
2 | 3 1 2 -7
___________
The rule is to bring down the first term, whatever it is (ours is a 3), and multiply it by the number "outside" which is a 2. Put that product up under the number next to the 3:
2 | 3 1 2 -7
6
3
Then add straight down, and multiply that sum by the 2 outside and put that product under the next number (the 2 "inside" the box):
2 | 3 1 2 =7
6 14
3 7
And do the same thing. Add straight down, multiply the sum by 2 and put the product up under the next number, -7, and add again. The final is shown below:
2 | 3 1 2 -7
6 14 32
3 7 16 25
The last number in the very bottom row, the depressed polynomial row, is the remainder. Ours is a 25. This is the super easy way to divide polynomials, as long as our divisor is a linear (first degree) term.
Laura brought some fish; salt water ($2 each) and fresh water ($1 each). If she has 15 fish - how many of each did she buy?
Answer:
are you sure there is no further info
Step-by-step explanation:
What is the value of X? Enter your answer in the box.
Answer:
x =4
Step-by-step explanation:
First we need to find the length of RT
Since the triangle on the left (RST) is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 60 = 2 sqrt(3) / RT
RT sin 60 = 2 sqrt(3)
RT = 2 sqrt(3) / sin 60
RT = 2 sqrt(3) / (sqrt(3)/2)
RT = 4
Now we can find x
Since the triangle on the right (QRT) is a right triangle, we can use trig functions
tan theta = opp /adj
tan 45 = x/ RT
tan 45 = x / 4
4 tan 45 = x
4 (1) = x
4 =x
What is the length of AC?
Answer:
B) 4 miles
Step-by-step explanation:
the big triangle CAB and small triangle CED are simular (given)
this means the ratio between their corresponding sides will be the same.
find corresponding sides with alternate interior angle theorem
m CDE= m CBA
vertical angles theorem
m ACB = m DCE
therefore, AC corresponds to CE
find ratio of sides
7 miles = 36960 feet
36960/ corresponding side 21 ft
36960/ 21= 1780 ft
multiply by 1780 to get from small side to big side
small side CE = 12 ft
12*1780
=21120 ft =AC (in ft)
convert to miles (ft to miles is ft/5280)
21120/5280
=4 miles
hope this helps
What is the value of x in the equation 1/5x - 2/3y
=
30, when y = 15?
Answer:
x = 200
Step-by-step explanation:
Plug in 15 as y into the equation and solve for x:
1/5x - 2/3y = 30
1/5x - 2/3(15) = 30
1/5x - 10 = 30
1/5x = 40
x = 200
So, when y = 15, x = 200
Find the measure of b.
please help!
=======================================================
Explanation:
The inscribed angle 20 degrees doubles to 2*20 = 40 which is the measure of the central angle, and the arc in which the inscribed angle subtends (or cuts off). This is due to the aptly named inscribed angle theorem.
------------
A slightly longer alternative path would be to do this:
The triangle with interior angles 20 and c is isosceles. Note how the missing angle up top is one of the congruent base angles, so the missing angle is 20 degrees. That means angle c is...
20+20+c = 180
40+c = 180
c = 180-40
c = 140
Then angle b is supplementary to this
b+c = 180
b+140 = 180
b = 180-140
b = 40
This path leads to the same answer. It's slightly longer, but it's a path you can take if you aren't familiar with the inscribed angle theorem.
In fact, this line of thinking is effectively how the inscribed angle theorem is proved as shown in the diagram below.
Find the Measure of one interior angle for each polygon
Answer:
5 corners : 108 degrees
6 corners : 120 degrees
Step-by-step explanation:
there are (at least) 2 different views to get the result :
officially (usually the teachers' preferred method) you consider a polygon as a combination of non-overlapping triangles. a polygon with n corners or edges we can split into n-2 such triangles.
each triangle has an angle sum of 180 degree.
so, the polygon angle sum is (n-2)×180 degrees.
and each (internal) angle is then (n-2)×180/n
n = 5 : (5-2)×180/5 = 3×36 = 108 degrees
n = 6 : (6-2)×180/6 = 4×30 = 120 degrees
the second approach (I prefer) goes after the external angles of the polygon.
the sum of all external angles in any polygon is 360 degrees (a full circle).
for n corners/edges each external angle is 360/n.
and the internal angle is then the complement to 180 degrees = 180 - 360/n
n = 5 : 180 - 360/5 = 180 - 72 = 108 degrees
n = 6 : 180 - 360/6 = 180 - 60 = 120 degrees
There is a distance marker every 100 m and a pole every 80 m along a straight road. There is a distance marker and a pole together at the start of the road. How far along the road will there be a distance marker and a pole together again?
Answer:
At a distance of 400 m.
Step-by-step explanation:
From the information in the given question, a distance marker and pole are together at the start of the road.
Thus,
the distance marker would mark the road 100 m, 200 m, 300 m, 400 m, 500 m etc.
Also,
the pole would be located 80 m, 160 m, 240 m, 320 m, 400 m, 480 m etc.
Comparing the distance of location of the marker and pole, it would be observed that the next location where the two would be together is 400 m from the starting point.
Therefore, there would be a distance marker and a pole together at 400 m from the stat of the road.
What is 15.4624 divided by 0.32
Answer:
48.32
Step-by-step explanation:
I need help right now!!!ASAP
Answer:
Points Q, J and M are not collinear
Step-by-step explanation:
Three points cannot be collinear if they are not coplanar (on the same plane), and M is on a different plane than Q. J is located on both planes.
an obtuse angle is an angle which is _______
Answer:
an obtuse angle is an angle that is more than 90 degrees
Step-by-step explanation:
