2. Verify that cos(360° -0)=cos is an identity.​

Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:

The identity that relates the sine squared and the cosine squared of the angle, as follows:

[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]

In this problem, we have that the sine is given by:

[tex]\sin{\theta} = \frac{1}{3}[/tex]

Hence, applying the identity, the cosine is given as follows:

[tex]\cos^2{\theta} = 1 - \sin^2{\theta}[/tex]

[tex]\cos^2{\theta} = 1 - \left(\frac{1}{3}\right)^2[/tex]

[tex]\cos^2{\theta} = 1 - \frac{1}{9}[/tex]

[tex]\cos^2{\theta} = \frac{8}{9}[/tex]

[tex]\cos{\theta} = \pm \sqrt{\frac{8}{9}}[/tex]

[tex]\cos{\theta} = \pm \frac{2\sqrt{2}}{3}[/tex]

The tangent is given by the sine divided by the cosine, hence:

[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]

[tex]\tan{\theta} = \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}[/tex]

[tex]\tan{\theta} = \pm \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}[/tex]

[tex]\tan{\theta} = \pm \frac{\sqrt{2}}{4}[/tex]

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In order to prove that there are only four of these triangles, we need to first   restate the formula for the perimeter of a triangle which is given as:  P = a + b + c. Hence, we must identify all the triangles that have two or more equal sides, and each side is a whole number.

Step 1 - First, we state all the possible combination three whole numbers which when added together result in fifteen.

The numbers are given as:

Step 2 -  Eliminate options where a side is more than the sum of the other two sides

Hence,

are eliminated. The remaining triangles are four in number.

QED.

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Answer:

Option C

Step-by-step explanation:

Any evening time on a 24 hour clock will be that hour add 12 :

3:50 pm =

3:50 + 12:00 = 15:50

Option C must be the answer

Hope this helped and brainliest please

Answer:

c.1550 hrs

Step-by-step explanation:

It Is military time to it stays going for 12:00 to 13:00 14:00 15:00 and so on

Hope This Helped

The equation of the graphed function is given as follows:

g(x) = (1/7)^x - 4.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The parent function for this problem is given as follows:

f(x) = (1/7)^x.

(which has an asymptote at y = 0).

The function was shifted down 4 units, meaning that the translated function is given as follows:

g(x) = (1/7)^x - 4.

And the correct option is given by the first option.

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The value of x  in order for the two slats to be parallel is 6.

The measure of the indicated angle is 42°

What is an angle?

The angle is the measure of how inclined are the two surfaces, or lines with respect to each other.

For the slats to be parallel. both the given angles must be equal

So,

(3x +24)° = 7x°

Solving this expression, we get

7x -3x = 24

4x =24

x = 6°

The measure of the indicated angle is

(3x +24)° = 3x6 +24

(3x +24)° = 18+24

(3x +24)°  =42°

and 7x = 7x6 =42°

Thus, the measure of the angle is 42°

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Answer:

answer is A - library books by genre and by Adult or Child

Step-by-step explanation:

your column on the left will have different genre of books

your top column will have children or adults

Answer:

2/8

Step-by-step explanation:

there is the 4 sections of a spinner and 2 sides on the coin when you lay it out that leaves 2 opportunities to spin a 3 or a 4 and flipping heads

The value of a dependent variable is dependent on the value of an independent variable. The correct option is C.

Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on other.

The complete question is:

A telephone company charges a $0.25 connection fee, then $0.10 per minute for long distance calls. Which statement is true regarding this situation?

A. The rate of change is $0.25 and minutes are the independent variable.

B. The rate of change is $0.25 and minutes are the dependent variable.

C. The rate of change is $0.10 per minute and minutes are the independent variable

D. The rate of change is $0.10 per minute and minute are the dependent variable.

The cost of making a call is the sum of the cost of connection fee which is one time fee and cost $0.25, and the cost charged for a minute which depends on the number of minute for which the call is been established. Therefore, the total cost can be written for a x minute call is,

Total Cost = $0.25 + $0.10(x)

Since the total cost is dependent on x, therefore, x which is the minute is the independent variable. The rate of change is $0.10 per minute and minutes are the independent variable.

Hence, the correct option is C.

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Answer:

it takes 2 seconds to do one situp

it takes 2 seconds to do one pushup

to do 14 pushups, it takes 28 seconds.

to do 12 situps it takes 24 seconds

to do 12 pushups, it takes 24 seconds

BRAINLIEST PLEASE!

hope this helps :)

Step-by-step explanation:

14x + 12y = 52

12x + 12y = 48

^^^ this is an inequality that we can make.  

x stands for pushups

y stands for situps

if we subtract the second equation from the first, we get

2x = 4

x = 2

now we can place x in one of the equations to solve for y

12(2)+12y=48

24 + 12y = 48

12y = 24

y = 2

Answer:

x = 14

Step-by-step explanation:

given f(x) = 2(3x - 5) and f(x) = 74 , then equating gives

2(3x - 5) = 74 ( divide both sides by 2 )

3x - 5 = 37 ( add 5 to both sides )

3x = 42 ( divide both sides by 3 )

x = 14

Answer:

[tex]\huge\boxed{\sf Speed = 77\ km/hr}[/tex]

Step-by-step explanation:

= 130 km

Speed = 85 km/h

Time = 3 hours

So,

Distance = Speed × Time

Distance = 85 × 3

Distance = 255 km

So,

= 130 + 255

= 385 km

Total distance = 385 km

Time = 5 hours

Speed = Distance / Time

Speed = 385 / 5

Speed = 77 km/hr

[tex]\rule[225]{225}{2}[/tex]

Answer:

1.4375

Step-by-step explanation:

[tex]\frac{10 + (2 x 3)^{2} / (4)(1)}{2^{3}} \\[/tex]

[tex]\frac{10 + (6)^{2} /4}{8} \\[/tex]

[tex]\frac{10 + 36 / 4}{8} \\[/tex]

[tex]\frac{46 /4}{8} \\[/tex] = [tex]\frac{11.5}{8} \\[/tex]

Answer:

The answer is 4

Step-by-step explanation:

The base of 4^5 is 4. The exponent is 5 and 9 & 20 do not work as we are not multiplying 4 and 5 to get 20.

Inequalities help us to compare two unequal expressions. The minimum number of sets of knives Indigo should buy is 8.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Let the number of sets of knives indigo should buy be represented by x.

Given Indigo needs to order some new supplies for the restaurant where she works and the restaurant needs at least 430 knives. Also, There are currently 269 knives. Now, If each set on sale contains 18 knives the inequality that can represent the minimum number of sets of knives Indigo should buy is,

269+18x≥430

18x≥430-289

18x≥141

x≥7.833

x≥8

Hence, the minimum number of sets of knives Indigo should buy is 8.

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Since we know it's quadratic, the n-th term will follow the pattern

[tex]x_n = an^2 + bn + c[/tex]

for some unknown coefficients a, b, and c.

Given that [tex]x_1=-1[/tex], [tex]x_2=2[/tex], and [tex]x_3=7[/tex], we have the following conditions on these coefficients:

[tex]\begin{cases} a + b + c = -1 \\ 4a + 2b + c = 2 \\ 9a + 3b + c = 7 \end{cases}[/tex]

Solve this system to get a = 1, b = 0, and c = -2. Then

[tex]\boxed{x_n = n^2 - 2}[/tex]

To solve the system, use elimination.

[tex](4a + 2b + c) - (a + b + c) = 2 - (-1) \implies 3a + b = 3[/tex]

[tex](9a + 3b + c) - (a + b + c) = 7 - (-1) \implies 8a + 2b = 8 \implies 4a + b = 4[/tex]

[tex](4a + b) - (3a + b) = 4 - 3 \implies a = 1 \implies b = 0 \implies c = -2[/tex]

Answer:
Option c

Step-by-step explanation:

Since tangent = op/adj, in this case the tan37 would be x/1000.

Then, set it up as an algebra problem.

tan37 = x/1000

Multiply both sides by 1000, so 1000tan37=x

that simplifies to x = 753.6

Answer: Option C is correct.

⇒ 4x = 20

⇒ x = 20/4

⇒ x = 5

⇒ x/2 = 8

⇒ x = 8(2)

⇒ x = 16

⇒ x + 8 = 3x

⇒ 3x - x = 8

⇒ 2x = 8

⇒ x = 4

⇒ x = (x + 5)/2

⇒ 2x = x + 5

⇒ 2x - x = 5

⇒ x = 5

Answer: The answer is 7

I did the math

Answer:

7

Step-by-step explanation:

11 - 8(12 + 6) / 6²

Rearrange using the order of operations.

11 - ((8 * (12 + 6)) / (6²))

((8 * (12 + 6)) = 144

(6²) = 36

(6²) / 144 = 4

(11 - 4)

= 7

Using the binomial distribution, it is found that the mean and the standard deviation of variable x are given as follows:

[tex]\mu = 3, \sigma = 0.87[/tex]

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

In this problem, we have that the parameters are given as follows:

n = 4, p = 0.75.

Hence the mean and the standard deviation are given as follows:

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Answer:

(3,4)

Step-by-step explanation:

Hello!

To find the maximum value, we can find the vertex of the graph.

Since the coefficient of x² is negative, the graph opens downwards, meaning that the vertex would be the highest point.

To solve for the vertex, we can convert it to vertex form.

The vertex is (3,4)

A real life example of an acute angle is the angle that's made in letter V.

It should be noted that an acute triangle simply means an angle that measures less than 90 degrees.

In this case, the real life example of an acute angle is the angle that's made in letter V. Other examples include slizing a pizza into different shapes.

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Answer:

see explanation

Step-by-step explanation:

a translation of 4 squares right means add 4 to the x- coordinate

a translation of 2 squares down means subtract 2 from the y- coordinate

then

(1, 1 ) → (1 + 4, 1 - 2 ) → (5, - 1 )

(3, 1 ) → (3 + 4, 1 - 2 ) → (7, - 1 )

(1, 4 ) → (1 + 4, 4 - 2 ) → (5, 2 )

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

x and y are values that represent the angle made by respective arcs on centre of the circle

that is :

Here, Angle x + Angle z = 180°

[ because they form linear pair ]

Now, we can observe that angle made by Arc Y is equal to :

Given the previous length of the bedroom and the current scale factor, the length of the bedroom in the current scale drawing is 1008ft.

Scale factor is simply a measure for similar figures, who look the same but have different scales or measures.

To get new dimension;

New dimension = scale factor × current dimension

Given that;

New dimension = scale factor × current dimension

New length of the bedroom = 112 × 9ft

New length of the bedroom = 1008ft

Therefore, given the previous length of the bedroom and the current scale factor, the length of the bedroom in the current scale drawing is 1008ft.

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Answer:it’s in the explanation

Step-by-step explanation:

a. Each wrap costs $2.00, and each bottle of water costs $6.50.
b. Each wrap costs $4.70, and each bottle of water costs $4.70.
c.Each wrap costs $5.30, and each bottle of water costs $3.00.
d. Each wrap costs $6.50, and each bottle of water costs $2.00.

Answer:

The wraps are $6.50 and the water bottles are $2

Step-by-step explanation:

It will take them exactly 4hours 48 minutes.

Rate is a measure of a given quantity against a known or standard quantity.

Analysis:

If Tanya and Tim cleaned the house in 3 hours. Then either of them would clean the house in 2 x 3 = 6 hours.

If their 3 children cleaned the house in 6 hours, then each child would clean the house in = 3 x 6 = 18 hours

Total time for cleaning the house = 18 hours + 6 hours = 24 hours

If the five people were to do it at once then time taken to clean the house = 24/5 = 4.8 hours = 4 hours 48 minutes

In conclusion, the time for 5 people to clean the house is 4 hours 48 minutes

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Answer:9

Step-by-step explanation:

Use the pythagorean theorem. [tex]a^{2}+b^{2}=c^{2}[/tex]

We know both a and c, so it becomes

[tex]4^{2}+b^{2}=\sqrt{97}^{2}[/tex]=

16+b^2=97=

97-16=b^2=

81=b^2=

9=b

The value of f⁻¹(f⁻¹(7)) is 10

The expression is given as:

f⁻¹(f⁻¹(7))

We start by solving the inner expression f⁻¹(7).

The above means that we determine the x value when y = 7.

So, we have:

f⁻¹(7) = 14

Substitute f⁻¹(7) = 14 in f⁻¹(f⁻¹(7))

f⁻¹(14)

Next, we determine the x value when y = 14

f⁻¹(14) = 10

Hence, the value of f⁻¹(f⁻¹(7)) is 10

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Answer:

20

10

Step-by-step explanation: