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3 years ago

Which Statement is true?

1 answer:

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

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

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

$c=\frac{11}{sin(57\°)}sin(86\°)$

$c=13.1\ units$

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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

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

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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

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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>

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3 years ago