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Naya [18.7K]
3 years ago
8

Which of the following is a solution to 2cos^2x– 2 = 0 ?

Mathematics
2 answers:
Sphinxa [80]3 years ago
8 0

Answer:

A and C

Step-by-step explanation:

Given

2cos²x - 2 = 0 ( add 2 to both sides )

2cos²x = 2 ( divide both sides by 2 )

cos²x = 1 ( take the square root of both sides )

cos x = ± \sqrt{1} = ± 1

cos x = 1 ⇒ x = cos^{-1}(1) = 0°

cos x  = - 1 ⇒ x = cos^{-1}(- 1) = 180°

gogolik [260]3 years ago
5 0

Answer:

2 possible results

0° and 180°

Step-by-step explanation:

2cos² x– 2 = 0  (add 2 to both sides)

2cos² x = 2  (divide both sides by 2)

cos² x = 2/2

cos² x = 1

cos x = ±√1

cos x = ±1

because the range of x is not stated, there are 2 possible results for x  that will cause cos x to be either 1 or -1

0° and 180°

You might be interested in
Which matrix represents the system of equations shown below? 3x-5y=12 4x-2y=15
tatuchka [14]

Answer:

\left[\begin{array}{ccc}3&-5  &|12\\4&-2  &|15\\\end{array}\right]

Step-by-step explanation:

When making a matrix of two equations with the variables x and y, the result will be a matrix with three columns:

  • a column for the values of x in each equation
  • a column for the values of y in each equation
  • a column for the independent values of each equation

since our system of equations is:

3x-5y=12\\ 4x-2y=15

we can see that the value for x in the first equation is 3 and in the second equation is 4, thus the first column will have the numbers 3 and 4:

\left[\begin{array}{ccc}3&&\\4&&\\\end{array}\right]

Now for the values of y we hvae -5 in the first equation and -2 in the second equation, we update the matrix with another column with the values of -5 and -2:

\left[\begin{array}{ccc}3&-5&\\4&-2&\\\end{array}\right]

Finally, the last column is the independent values of each equation (or the results) in the first equation that number is 12 and in the second equation is 15, thus the matrix is:

\left[\begin{array}{ccc}3&-5&12\\4&-2&15\\\end{array}\right]

usually there is a line separating the columns for the values of x and y, and the independent values:

\left[\begin{array}{ccc}3&-5  &|12\\4&-2  &|15\\\end{array}\right]

this is the matrix of the system of equations

6 0
3 years ago
Find all the missing elements : C=120degrees<br> b= 5<br> c=11
mezya [45]

Answer:

A = 36.8°

B = 23.2°

a = 7.6

Step-by-step explanation:

Given:

C = 120°

b = 5

c = 11

Required:

Find A, B, and a.

Solution:

✔️To find B, apply the Law of Sines

\frac{sin(B)}{b} = \frac{sin(C)}{c}

Plug in the values

\frac{sin(B)}{5} = \frac{sin(120)}{11}

Cross multiply

Sin(B)*11 = sin(120)*5

Divide both sides by 11

sin(B) = \frac{sin(120)*5}{11}

sin(B) = \frac{sin(120)*5}{11}

Sin(B) = 0.3936

B = sin^{-1}(0.3936)

B = 23.1786882° ≈ 23.2° (nearest tenth)

✔️Find A:

A = 180° - (B + C) (sum of triangle)

A = 180° - (23.2° + 120°)

A = 36.8°

✔️To find a, apply the Law of sines:

\frac{sin(A)}{a} = \frac{sin(B)}{b}

Plug in the values

\frac{sin(36.8)}{a} = \frac{sin(23.2)}{5}

Cross multiply

a*sin(23.2) = 5*sin(36.8)

Divide both sides by sin(23.2)

a = \frac{5*sin(36.8)}{sin(23.2)

a = 7.60294329 ≈ 7.6 (nearest tenth)

5 0
2 years ago
Integers: what is 10 + (-2)
lapo4ka [179]
10+(-2)=10-2
Therefore 10-2=8
5 0
2 years ago
Read 2 more answers
HELP When does expanding and simplifying a(b + c) result in a positive value for ac?
Reil [10]

Answer:

When c and a are positive or both are negative

Step-by-step explanation:

negative times negative equals positive so if a was negative and c was negative -a*-c= ac

Of course positive times positive equals negative so if a and c were positive we could do

a*c= ac

Hope I could help !

7 0
2 years ago
What is the y-intercept of a line with the equation (y - 3) = 5(x + 2)?
Nookie1986 [14]
The y-intercept would be (0, 13)
7 0
2 years ago
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