Let the proportion be 3x, 4x and 5x .
We know that sum of all angles of a triangle measures 180°.
So, keeping the values equals to 180°.
⇒ 3x + 4x + 5x = 180°
⇒ 12x = 180°
⇒ x = 180°/12
⇒ x = 15°
Now, finding the each angle measure.
⇒ 3x = 3 × 15 = 45°
⇒ 4x = 4 × 15 = 60°
⇒ 5x = 5 × 15 = 75°
Hence, the measure of each angle is 45°, 60° and 75° respectively.
❒ Required Solution:
It is given that the three angles of the triangle are proportional to 3,4,5. And we are here to find the three angles with the help of the angle sum property (Sum of the angles of a triangle = 180°). So, using this property we can find all the angles.So, Let's assume the angles as 3x, 4x and 5x.
❍ According to the question :
[tex]\\ \tt \implies \: 3 x+ 4x + 5x = 180{}^{ \circ} \\[/tex]
[tex]\\ \tt \implies \: 12 x = 180{}^{ \circ} \\[/tex]
[tex]\\ \tt \implies \: x = \frac{180{}^{ \circ} }{12} \\ [/tex]
[tex]\\ \implies \tt \: x = 15{}^{ \circ} [/tex]
Hence,
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \circ \: \: \: \: \tt \:1st \: \: \: angle \: \: \: \: \: = 3x=3 \times 15=45{}^{\circ} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \circ \: \tt \:2nd \: \: \: angle \: \: \: \: \: = 4x=4\times 15=60{}^{\circ} \: \: \: \: \: \\ \\ \circ \: \: \: \: \tt \:3rd \: \: \: angle \: \: \: \: \: =5 x=5\times 15=75 {}^{\circ} \: \: \\ \\[/tex]
❒ V E R I F I C A T I O N :
Sum of the angles of the triangle = 180°
[tex]\\ \tt \implies \: 3 x + 4x + 5x = 180{}^{ \circ} [/tex]
[tex]\\ \tt \implies \: 45 {}^{ \circ} + 60{}^{ \circ} + 75{}^{ \circ}= 180{}^{ \circ} [/tex]
[tex]\\ \tt \implies \: 180{}^{ \circ} = 180{}^{ \circ} [/tex]
[tex]\\ {\quad { \quad{ \quad{ \textbf{ \textsf{L.H.S = R.H.S}}}}}}[/tex]
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
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)
Warren has money to go see a movie after he pays $8 for the MOVIE he will have $14 left right and solve an equation to show how much money Warren has before paying for the movie
Answer:
$(8+14)
Step-by-step explanation:
Amount of money Warren has at first=$8+$14=$22
help pls pls pls pls pls pls
Is the answer I’ve chosen correct? This is really confusing for my stressed brain :(.
Answer:
X is greater than 5.
Step-by-step explanation:
You choose the correct answer because X > 5.
Meaning that x would be any number over 5.
What is 2x2x4 I’m asking from my big brothers account
Step-by-step explanation:
2×2×4=16
Hope it helps uß
The fox population in a certain region has a continuous growth rate of 7 percent per year. It is estimated that the population in the year 2000 was 14300. (a) Find a function that models the population t years after 2000 (t=0 for 2000). Hint: Use an exponential function with base e. Your answer is P(t)
Answer:
P(t) = 14300e^0.07t
Step-by-step explanation:
Let :
Population as a function of years, t = P(t) ;
Growth rate, r = 7%
Estimated population on year 2000 = Initial population = 14300
The given scenario can be modeled using an exponential function as the change in population is based in a certain percentage increase per period.
P(t) = Initial population*e^rt
P(t) = 14300*e^(0.07t)
P(t) = 14300e^0.07t
Where, t = number of years after year 2000.
Correct answer get brainliest and 5 star
Answer:
B
Step-by-step explanation:
(Slant height)^2= (Radius)^2+(Height)^2
(20)^2= (12)^2+(Height)^2
Height=16
Answer:
B. pls mark me at brainliest and like my answer.
Step-by-step explanation:
⩥ɓeŋʝ⩤
Reza was very sick and lost 15% of his original weight. He lost 27 pounds. What was his original weight?
Answer:
180
Step-by-step explanation:
Let x be the original weight
x* 15% = 27
.15x = 27
Divide each side by .15
.15x/.15 = 27/.15
x =180
Answer:
180 pounds
Step-by-step explanation:
W=27/15%
W=180 pounds
If f(1) = 10 and f(n) = f(n − 1) – 3 then find the value of f(4).
Answer:
f(4) =1
Step-by-step explanation:
f(1) = 10
f(n) = f(n − 1) – 3
Let n=2
f(2) = f(2 − 1) – 3 = 10-3 = 7
Let n =3
f(3) = f(3 − 1) – 3 = f(2) -3 = 7-3 = 4
Let n = 4
f(4) = f(4 − 1) – 3 = f(3) -3 = 4-3 = 1
Answer:
9
Step-by-step explanation:
f(4)=4(4-1)-3
f(4)=4(3)-3
f(4)=12-3
f(4)=9
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.
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
find the interior angle sum for the following polygon.
We know that the interior angle sum of a polygon is (n − 2) × 180°, where n is the number of sides.
Here, number of sides (n) = 12
So, interior angle sum = (n − 2) × 180°
=> interior angle sum = (12 - 2) × 180°
=> interior angle sum = 10 × 180°
=> interior angle sum = 1800°
So, the interior angle sum of this polygon is 1800°.
Uploaded this one again! Hopefully y’all can see it better
Write an equation
in slope y-intercept form A(2,6),m=0
Solve for b:
y = 0x + b
6 = 0 + b
b = 6
The answer is y = 0x + 6
Answer my question
im being timed
Answer:
the third one
Step-by-step explanation:
Part C Next, find the length of BC place point F at (4,4) and draw BF and FC now you hav the right ∆BFC with BC as the hypotenuse find BC and FC ising the coordinates of B,C, and,F then use the Pythagorean theorem to find BC show your work need help ASAP giving thanks and points away I just need these answer fast ???
Answer:
BF = |4 – 1| = 3
FC = |4 – 0| = 4
Using the Pythagorean Theorem to find BC:
BC2 = BF2 + FC2
BC2 = 32 + 42
BC2 = 9 + 16
BC = sqaure root 25
BC = 5
Step-by-step explanation:
The length of BC is 5 unit.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
We need to find the length of BC place point F at (4,4) and draw BF and FC now you have the right ∆BFC with BC as the hypotenuse find BC and FC using the coordinates of B,C, and,F then use the Pythagorean theorem to find BC.
Using the Pythagorean Theorem to find BC:
BC^2 = BF^2 + FC^2
BC^2 = 32 + 42
BC^2 = 9 + 16
BC = √25
BC = 5
So, BF = |4 – 1| = 3
FC = |4 – 0| = 4
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
#SPJ2
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
What is 15.4624 divided by 0.32
Answer:
48.32
Step-by-step explanation:
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
A ladder reaches 6 m up a wall with its foot 2·4 m from the wall. A person standing under the ladder at a point 80 cm from its foot would be able to touch the ladder at a height of _____ m from the ground.
Hey there! I'm happy to help!
We see that the ladder reaches a height of 6m from the ground while being 2.4 m from the wall. The ratio of the height to the length from the wall is 6:2.4 which can actually just simplify to 2.5 because 6m to is 2.4*2.5.
This person is 80 cm from the ladder's base. We just saw that you can take the distance from the wall (in this case, our wall is the human as the human is touching the height) and multiply it by 2.5 to find the height of the ladder at that specific point. So let's do that.
80*2.5= 200
We are looking for meters though. Since there are 100 centimeters in a meter, this is just going to be 2 meters.
Have a wonderful day! :D
Determine the absolute value
Answer:
64000
Step-by-step explanation:
The absolute value is the non-negative number
|64000| = 64000
If s = 6 and t = 4, find the value of x.
x = 4 + s - t
Answer:
x = 6
Step-by-step explanation:
s = 6
t = 4
x = 4 + s - t
Substituting s and t in equation,
x = 4 + 6 - 4
x = 6
Answer:
6
Step-by-step explanation:
s=6
t=4
x= 4+6-4
x=10-4
x=6
Therefore; the final result is 6
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]
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 |x-4| if x>4
Answer:
x-4
Step-by-step explanation:
If x>4, |x-4|>0 which means |x-4|=x-4
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.
9,583,507 to the nearest ten thousand
Answer:
9,580,000
Step-by-step explanation:
The ten thousand place is the 8
look and the thousands place which is 3
This is less than 5 so we leave the ten thousands place alone
9,583,507 becomes
9,580,000
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{9,583,507}[/tex]
[tex]\huge\textsf{= 9,600,000} \leftarrow \huge\textsf{nearest \underline{\underline{HUNDRED}} thousand}[/tex]
[tex]\huge\textsf{= 9,580,000} \leftarrow\huge\textsf{nearest \underline{\underline{TEN}} thousand}[/tex]
[tex]\large\textsf{83 is rounded to 80 because it is closer to 80 than 90. 3 is closer to}\\\large\textsf{0 than 10}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 9,580,000}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day! }[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
value of the pronumeral and describe the rule.
4,1,-2,p,-8,-11
Answer:
p = -5
every element in the sequence is created by subtracting 3 from the pervious element.
Step-by-step explanation:
I am not sure you put every necessary information here.
but I'd the visible information is truly everything, then it's is trivial.
the difference between 4 and 1 is ... well, -3. meaning we subtract 3 from 4 to get 1.
we suspect this is the rule and keep trying.
1 -3 = -2
hey it works.
and -8 -3 = -11
hey, also correct.
and the difference between -2 and -8 is -6, and when we place another item in between (p), we cut that in half again to -3. so, it is all consistent.
therefore,
p = -2 -3 = -5
the rule is
an = an-1 - 3
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
