The angles in a triangle are in the ratio 1:2:3. Show that this triangle is a right-angled triangle. The hypotenuse of the triangle is 19 cm long. Calculate the length of the shortest side in the triangle
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
Sum the parts of the ratio , 1 + 2 + 3 = 6 parts
Divide sum of angles in a triangle by 6 to find the value of one part of the ratio.
180° ÷ 6 = 30° ← value of 1 part of the ratio
2 parts = 2 × 30° = 60°
3 parts = 3 × 30° = 90°
Since there is an angle of 90° then the triangle is right.
(b)
The shortest side is the side opposite the smallest angle of 30°
Using the sine ratio and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opp}{hyp}[/tex] = [tex]\frac{opp}{19}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2 opp = 19 ( divide both sides by 2 )
opp = 9,5
Shortest side in the triangle is 9.5 cm
Related Questions
Divide. Enter the quotient in simplest form.
-
6- +6-=
8 4
Can someone plz explain this.
Answers
Please I will give brainliest!!
Answers
Answer:
A
Step-by-step explanation:
The ribbons length goes highest to lowest from blue, red and yellow
Sam is 5 feet tall. The expression 0.5m+60 can be used to calculate his height in inches if he grows an average of 0.5 inch each month. How tall will Sam be in 6 months?
Answers
Answer: 5ft 8in
Step-by-step explanation:
Which of the following expression is equivalent to (3x^2y^3)^3?
A) 27x^5y^6
B) 27x^6y^9
C) 9x^6y^9
D) 3x^5y^6
Answers
put the following equation of a line into slope intercept form ,simplifying all fractions.
12x-4y = -12
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vertical intercept: (0, 3)
The coefficient of first term of a polynomial written in standard (descending order) form is called the _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ coefficient
Answers
Answer:
The leading coefficient
Step-by-step explanation:
The figure shows Triangle ABC and some of its transformed images on a coordinate grid:
Which of the four triangles was formed by a translation of Triangle ABC? (4 points)
3
2
0 1
04
Answers
Answer:
2
Step-by-step explanation:
it is congruent
Find the midpoint of points A(8,6) and B(0, 3)
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Answer:
Midpoint = (4,4.5) or written as fraction (4,[tex]\frac{9}{2}[/tex])
Step-by-step explanation:
[tex]MP= (\frac{x_1+x_2}{2}),(\frac{y_1+y_2}{2} ) \\MP= (\frac{8+0}{2}),(\frac{6+3}{2} ) \\MP= (\frac{8}{2}),(\frac{9}{2} ) \\MP= (4,4.5)[/tex]
how do I solve 3+k/14=4
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{k = 53}}}}}[/tex]
Step-by-step explanation:
[tex] \bigstar{ \sf{ \: \: \frac{3 + k}{14} = 4}}[/tex]
[tex] \tt{Step \: 1 \: }[/tex] : Do cross multiplication
[tex] \hookrightarrow{ \sf{3 + k = 4 \times 14}}[/tex]
[tex] \tt{Step \: 2}[/tex] : Multiply the numbers : 4 and 14
[tex] \hookrightarrow{ \sf{3 + k = 56}}[/tex]
[tex] \tt{Step \: 3 \: }[/tex] Move 3 to right hand side and change it's sign
[tex] \hookrightarrow{ \sf{k = 56 - 3}}[/tex]
[tex] \tt{Step \: 4 \: }[/tex] Subtract 3 from 56
[tex] \hookrightarrow{ \sf{k = 53}}[/tex]
The value of k is 53
Hope I helped!
Best regards! :D
~TheAnimeGirl
Answer:
Step-by-step explanation:
k/14 + 3 = 4
k/14 = 1
k = 14
5). 3x + y = 13
5x - 2y =7
Simultaneous linear equation
Answers
Answer:
Step-by-step explanation:
6x + 2y = 26
5x - 2y = 7
11x = 33
x = 3
3(3) + y = 13
9 + y = 13
y = 4
(3,4)
Evaluate 42 = (5 – 3). (1 point)
Answers
Answer:(5-3)=42
Step-by-step explanation:
Hello There!!
Your answer is 21.
First, You should do is (5 ₋ 3) = 2.
Then, You need to divide 42/2 =21.
[tex]\sqrt[HopeThisHelps}[/tex][tex]^{HopeThisHelps}[/tex]
[tex]\frac{Loserbrazts}{}[/tex]
An expression has a division symbol and a subtraction symbol. Is there any situation in which you would perform the subtraction before the division
Answers
George has $15. He would like to know if he has enough money to see a movie ($9.00) and buy a pretzel ($2.65), a drink ($1.35), and two veggie cups ($1.74 each). George incorrectly used this numerical expression to decide if he had enough money.
15 - 9 + 2.65 + 1.35 + 2(1.74)
Use the order of operations to simplify this expression.
Answers
Answer:
Yes, he has enough money and your simplified answer is below. If I'm wrong correct me or give me a comment.
Step-by-step explanation:
15 - 9 + 2.65 + 1.35 + 2(1.74) Multiply first.
15 - 9 + 2.65 + 1.35 + 3.48 Then just add or subtract from the left to the right
6 + 2.65 + 1.35 + 3.48
8.65 + 1.35 + 3.48
10 + 3.48
13.48 would be the simplified answer.
Answer:
um i put 13.48 and got it right
Step-by-step explanation:
When reaching mile marker 4 on the trail, Susan uses her GPS to find that her current elevation is 6135 feet. If she follows the trail until its end at mile marker 9, her elevation will be 8290 feet. What is the average change in elevation of Susan's position from mile marker 4 to mile marker 9, in feet per mile marker?
Answers
Answer:
Change in elevation= 431 feet/mile marker
Step-by-step explanation:
given data
Elevation at mile marker 4 = 6135 feet
Elevation at mile marker9 = 8290 feet
to find out
average change in elevation
solution
we get here average change in feet per mile marker that is express as
average change in feet per mile = change in elevation ÷ change in mile marker .....................1
put hree value we get
average change in feet per mile = [tex]\frac{8290-6135}{9-4}[/tex]
average change in feet per mile = 431 feet/mile marker
so
Change in elevation= 431 feet/mile marker
A clock is constructed using a regular polygon with 60 sides. The polygon rotates each minute, making one full revolution each hour. How much has the polygon rotated after 7 minutes?
Answers
Answer:
42
Step-by-step explanation:
D-42 on EDG.
A clock is constructed using a regular polygon with 60 sides. The polygon rotates each minute, making one full revolution each hour. The polygon has rotated 42 times after 7 minutes.
A polygon is known to be a plane figure with at least three equal sides and angles.
From the given information,
the sides of the polygon = 60 sidestime to complete a single rotation for 60 sides = 1 hourIn one full revolution, there are = 360°To estimate the revolution completed in 1 minute, we have:
[tex]\mathbf{= \dfrac{360 \ ^ 0}{60 \ ^ 0} }[/tex]
= 6° per minute
Now, to determine how much the polygon has rotated after 7 minutes, we have:
= (6° / minute) × 7 minutes
= 42°
Therefore, we can conclude that the polygon has rotated 42° in 7 minutes,
Learn more about polygon here:
https://brainly.com/question/3491511?referrer=searchResults
3^2 – 2:3+ x = (3^3 – 3.8) (2) + x
Answers
Answer:
x+46.4
Step-by-step explanation:
A card is picked a random from the following set:
6,7,8,9
What is P(9)? Write as a Percentage
Answers
Answer:
25%
Step-by-step explanation:
There are 4 cards. Each one is a different number.
Only one card is a 9.
p(9) = 1/4 = 0.25 = 25%
What is not a description of slope?
rise over run
the rate of change of a line
change in y over the change in x
the ratio of horizontal change compared to vertical change
Answers
Answer:
Option (d) is wrong.
Step-by-step explanation:
Slope is:
rise over runThe rate of change of a lineChange in y over the change in xThe ratio of vertical change to the horizontal change.It can be given by mathematically as follows :
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{and}\\\\m=\dfrac{dy}{dx}[/tex]
Hence, the option which is not a description of slope is (d) "the ratio of horizontal change compared to vertical change"
Hailey makes a necklace with 24 blue beads and 32 purple beads. She wants to make a bracelet that uses the same ratio of blue beads to purple beads. She plans to use 6 blue beads for the bracelet. How many purple beads should Hailey use
Answers
Answer:
8
Step-by-step explanation:
Ratio of blue beads to purple: 24:32
Reduce it using four and it becomes 6:8
simplify the following: 11^6/11^4
Answers
Answer:
11² or 121
Step-by-step explanation:
simplify the following: [tex]11^6/11^4[/tex]
Remember when bases are the same powers can be subtracted (or added)
[tex]\frac{11^6}{11^4}=11^{(6-4) }\\\\\\11^{2}=121\\[/tex]
:)
buatlah matriks yang terdiri atas 5 baris dan 3 kolom dengan entrinya adalah 15 bilangan prima yang pertama
Answers
[tex]A = \left[\begin{array}{ccccc}2&3&5\\7&11&13\\17&19&23\\29&31&37\\41&43&47\end{array}\right] \\ \\ \\ \\ A^T = \left[\begin{array}{ccccc}2&7&17&29&41\\3&11&19&31&43\\5&13&23&37&47\end{array}\right][/tex]
15 less than the sum of k and 2
Answers
The algebraic expression for the given statement is k-13.
The given statement is "15 less than the sum of k and 2".
We need to form the algebraic expression for the given statement.
What is the algebraic expression?In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.
Now, the sum of k and 2=k+2
15 less than the sum of k and 2=(k+2)-15
=k+2-15
=k-13
Therefore, the algebraic expression for the given statement is k-13.
To learn more about the algebraic expression visit:
https://brainly.com/question/19245500.
#SPJ2
Given b(x) = [X+41, what is b(-10)?
Answers
B(-10) = -10 + 41
B(-10) = 31 [Answer]
Factorize : 3x2 – 10xy + 8y2
Answers
[tex]3x^2-10xy + 8y^2=\\\\=3x^2-6xy-4xy + 8y^2=\\\\=3x(x-2y)-4y(x-2y)=\\\\=(x-2y)(3x-4y)[/tex]
4. What is the value of the expression 3/12÷2/5
Answers
Answer:
(3/12)=0.25
(2/5)=0.40
(0.25/0.40)=0.625
Step-by-step explanation:
i need help w qn 32,, thankyou
Answers
Answer:
a) 9.62m (3 s.f.)
b) 2.58m (3 s.f.)
Step-by-step explanation:
Please see attached picture for full solution.
Please answer sorry I’m dumb
Answers
Answer:
D
Step-by-step explanation:
Hope this helped and have a great day!
(Ur not dumb)
Please help it’s due on Monday!
Answers
The rounded answer is 9.1 hours. The non-rounded answer is 9.11428571429 hours.
First convert all the fractions to decimals, add all the decimals, and then divide by the number of countries to get your answer.
Add in your average use too for the problem.
Which fraction is equal to 6?
Answers
Answer:
12/2
Step-by-step explanation:
what is the equation of the line parallel to the line y=1/4x+5 and passing through the point (2,-1)
Answers
Answer:
The answer is
[tex]y = \frac{1}{4} x + \frac{1}{2} [/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
The equation of the line is
y = 1/4x + 5
Comparing with the general equation above
Slope / m = 1/4
Since the lines are parallel their slope are also the same
Slope of parallel line = 1/4
So the equation of the line using point (2,-1) and slope 1/4 is
[tex]y + 1 = \frac{1}{4} (x - 2) \\ y - 1 = \frac{1}{4} x - \frac{1}{2} \\ y = \frac{1}{4} x - \frac{1}{2} + 1[/tex]
We have the final answer as
[tex]y = \frac{1}{4} x + \frac{1}{2} [/tex]
Hope this helps you