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Marianna [84]
3 years ago
13

When 12 is added to a number the result is 32 less than 3 times a number. What is this number?

Mathematics
2 answers:
neonofarm [45]3 years ago
7 0
X - the number

x+12=3x-32 \\
x-3x=-32-12 \\
-2x=-44 \\
x=\frac{-44}{-2} \\
x=22

The number is 22.
seropon [69]3 years ago
4 0
Let the number = x
12 + x = 3x - 32
x = 3x - 44 Subtract 12 from both sides
-2x = -44 Subtract 3x from both sides
<span>x = 22 Divide by -2

SO THE ANSWER IS 22. HOPE THIS HELPS!!!!!!!</span>
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Can someone please explain to me how to get this answer?
SIZIF [17.4K]
Answers:
A = 120
b = 45.0
c = 33.2

Side Note: only one triangle is possible
See attached for a visual. I used GeoGebra to draw the triangle.

-------------------------------------------------------------
-------------------------------------------------------------

Explanation:

We are given the following information
B = 35
C = 25
a = 68

We need to find the following
A, b, c

where the lower case letters represent the side lengths; the upper case letters are the angles. The angles are opposite their corresponding sides. For instance, side lowercase b is opposite angle uppercase B. The other letters are positioned the same way.

-----------------------

First use the idea that for any triangle, the three angles (A,B,C) must add to 180 degrees
A+B+C = 180
Replace B and C with 35 and 25. Solve for angle A
A+35+25 = 180
A+60 = 180
A+60-60 = 180-60
A = 120

Now that we know the three angles A = 120, B = 35, C = 25, we can find the missing sides 'b' and 'c'

-----------------------

We will use the law of sines to find side b
sin(A)/a = sin(B)/b
sin(120)/68 = sin(35)/b
b*sin(120) = 68*sin(35) <<--- cross multiply
b = 68*sin(35)/sin(120)
b = 45.037013350222 <<--- use a calculator; this value is approximate
b = 45.0 <<--- round to the nearest tenth

-----------------------

Do the same for side c
sin(A)/a = sin(C)/c
sin(120)/68 = sin(25)/c
c*sin(120) = 68*sin(25) <<--- cross multiply
c = 68*sin(25)/sin(120)
c = 33.1838323365404 <<--- use a calculator; this value is approximate
c = 33.2 <<--- round to the nearest tenth

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