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iris [78.8K]
3 years ago
6

Which Statement is true?

Mathematics
1 answer:
antiseptic1488 [7]3 years ago
6 0
A) |-8| \ \textless \  |8| is false. There is no solution.
B) |-2| \ \textgreater \  1 is true. There are infinite solutions.
C) |-7| = -7 is false. There is no solution.
D) |12| \ \textgreater \  |-15| is false. There is no solution. 

Answer: B
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In △ABC, m∠A=57°, m∠B=37°, and a=11. Find c to the nearest tenth.
kykrilka [37]

Answer:

c=13.1\ units

Step-by-step explanation:

step 1

Find the measure of angle C

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

so

A+B+C=180°

we have

A=57°

B=37°

substitute

57°+37°+C=180°

94°+C=180°

C=180°-94°=86°

step 2

Find the measure of side c

Applying the law of sines

\frac{a}{sin(A)}=\frac{c}{sin(C)}

substitute

\frac{11}{sin(57\°)}=\frac{c}{sin(86\°)}

c=\frac{11}{sin(57\°)}sin(86\°)

c=13.1\ units

8 0
3 years ago
In 1984 a locally-owned car company sold 2,743 cars. In 2003, the car sales rose to 4,069. What was the average rate of change f
tatiyna

Answer:

70 cars  per year.

Step-by-step explanation:

Given:

In 1984 a locally-owned car company sold 2,743 cars.

In 2003, the car sales rose to 4,069.

Question asked:

What was the average rate of change for the total number of cars sold?

Solution:

In 2003 number of cars sold = 4069

In 1984 number of cars sold = 2743

Change in the number of car sold = 4069 - 2743

                                                         = 1326

Now, time interval between 2003 and 1984 = 19

The\ average\ rate\ of\ change=\frac{Change\ in\ the\ number\ of\ car\ sold}{Time \ interval}

                                             =\frac{1326}{19} \\=69.789\\\\=70\ cars\ per\ year\  (approx)

Thus, the average rate of change for the total number of cars sold is 70 cars  per year.

7 0
3 years ago
two similar cylinders have surface areas of 40pi square feet and 90pi. What is the ratio of the height of the large cylinders to
Sedbober [7]
The ratio of heights  = ratio of the square roots of the areas because area is 2 dimensional and height is one dimensional.

so required ratio is  sqrt 40pi :   =  sqrt40:sqrt80 =  sqrt1: sqrt2 = sqrt (1/2) = 0.7071  to 4 significant figures 
7 0
3 years ago
Show that cos2x=cosx
PSYCHO15rus [73]

cos (2x) = cos x

2 cos^2 x -1 = cos x   using the double angle formula

2 cos ^2 x -cos x -1 =0

factor

(2 cos x+1) ( cos x -1) = 0

using the zero product property

2 cos x+1 =0    cos x -1 =0

2 cos x = -1       cos x =1

cos x = -1/2       cos x=1

taking the arccos of each side

arccos cos x = arccos (-1/2)         arccos cos x = arccos 1

x = 120 degrees   x=-120   degrees           x=0

remember you get 2 values ( 2nd and 3rd quadrant)

these are the principal values

now we need to add 360

x = 120+ 360n      x=-120+ 360n      x = 0 + 360n  where n is an integer


3 0
3 years ago
What does the equal sign with an arrow mean?
stealth61 [152]
The <span>⇒</span><span> sign means that if the function on the left hand side of the notation is true, then so is the function on the right hand side of the notation.</span>
5 0
3 years ago
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