Find the radius of a circle with an x-intercept of -2 if the circle’s center is (2,3) on a coordinate plane.

5
25
16
9

x = number

the equation to use is: 3x+4=28

3x+4=28

3x=24

x-24/3 =8

x=8

Answer:

286.5 degrees

Step-by-step explanation:

We want to change radians to degrees

2 pi radians = 360 degrees

5 radians * 360/ 2 pi

900/pi degrees

286.4788976 degrees

286.5 degrees

Answer: 286.48 degrees

Step-by-step explanation: We are trying to find the number of degrees. The equation to convert radians to degrees radian x 180/π. Plug in 5 for x.

5 x 180/π = 286.48

5 radians is the same as 286.48 degrees.

Final answer:

The remainder when 5k is divided by 3 is 2. This is because k can be represented as 6n + 1 where n is the quotient, and when 5 is multiplied by k and then divided by 3, after simplifying, only the term +5 contributes to the remainder.

Explanation:

When a positive integer k is divided by 6, the remainder is 1. Thus, we can write k as 6n + 1 where n is a quotient. To find the remainder when 5k is divided by 3, we must first multiply k by 5, resulting in 5(6n + 1) = 30n + 5.

Breaking down 30n + 5, we see that 30n is divisible by 3 since 30 is a multiple of 3. Hence, it will not contribute to the remainder when divided by 3. All that is left to consider is the +5 part. The closest multiple of 3 to 5 is 3 itself, meaning 5 divided by 3 will leave a remainder of 2. Therefore, the remainder when 5k is divided by 3 is 2.

The exact values for sinθ, cscθ, and cotθ given the point (-3, -8) are sinθ = -8/√73, cscθ = √73/-8 (because sinθ and cscθ are negative in the third quadrant), and cotθ = 3/8 (positive since sin and cos signs cancel out).

The question involves finding the values of sinθ, cscθ, and cotθ given a point (-3, -8) on the terminal side of an angle θ. To find these values, we first need to determine the radius (r) of the corresponding right triangle formed by the point (-3, -8) and the origin (0, 0). The radius can be calculated using the Pythagorean theorem:

r = √((-3)2 + (-8)2) = √(9 + 64) = √73

Using the definitions of the trigonometric functions:

Note that θ is in the third quadrant where both sine and cosine are negative; hence, sinθ and cscθ are negative, while cotθ is positive due to both the numerator and denominator being negative.

opposite angles = 180

180-49 = 131

 angle 2 = 131 degrees

The distance between the friends changing with the rate of 7√15/4 meter per sec.

Let B represents the position of runner, A represents the position of the friend and C represents the position of centre of the circular track. ( shown  below ),

We need to find: dc/dt

By the cosine law,

[tex]c^2 =a^2+b^2+2abcosC[/tex]

Differentiating with respect to t ( time ),

[tex]2c \frac{dc}{dt}=2absinC \frac{dc}{dt}[/tex]

[tex]\frac{dc}{dt}=\frac{2absinC\frac{dc}{dt}}{2c}[/tex]..(1)

Now, by arc length formula,

Radius( say r ) × angle = arc length ( say l )

r × ∠C= l

Differentiating w. r. t. t,

[tex]r \times \frac{dC}{dt} + \angle C \times \frac{dr}{dt} = \frac{dl}{dt}[/tex]

Here dl/dt=7 m per sec

dr/dt=0

r=110

dC/dt=7/110

Now again , [tex]C^2= a^2+b^2-2abcosC[/tex]

[tex]220^2 = 110^2 + 220^2 -2(110)(220)cosC[/tex]

[tex]48400=12100+48400-48400cosC[/tex]

[tex]-12100=-48400cosC[/tex]

[tex]1/4=cosC[/tex]..(2)

[tex]sinC=\frac{\sqrt{15}}{4}[/tex] ...(3)

From equation (1), (2) and (3),

[tex]dC/dt = \frac{(110)(220)\sqrt{15}/4. 7/110}{220}[/tex]

=7√15/4 meter per second.

Hence, the distance between the friends changing with the rate of 7√15/4 meter per sec.

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When the runner's distance from his friend is same as the distance from the friend to center of the track, the runner is moving in a way that the distance between him and his friend isn't changing. Hence, at those specific moments, their relative speed is zero m/s.

This problem involves the concept of relative velocities in a plane. Since the runner is moving along a circular path with a constant speed of 7 m/s, the runner's speed towards or away from his friend depends on the runner's location on the track. However, when the runner is at a distance of 220 m from his friend (which is also the distance from the friend to the center of the track), the runner is moving perpendicular to the line joining the runner and his friend. This is because, in this particular case, the runner is moving along a tangent to the circle that intersects the friend's location. Therefore, the distance between the friends isn't changing at all during those moments - their relative speed is zero m/s.

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Answer:

The solutions are:  [tex]x= 3.72, -6.72[/tex]

Step-by-step explanation:

[tex]x^2+ 3x = 25\\ \\ x^2+3x+(\frac{3}{2})^2 = 25 +(\frac{3}{2})^2\\ \\ (x+\frac{3}{2})^2 = 25+\frac{9}{4}\\ \\ (x+\frac{3}{2})^2 =27.25\\ \\ \sqrt{(x+\frac{3}{2})^2} =\pm \sqrt{27.25} \\ \\ x+1.5= \pm \sqrt{27.25} \\ \\ x= -1.5 \pm \sqrt{27.25}\\ \\ x=-1.5+ \sqrt{27.25}=3.72015... \approx 3.72\\ \\ or\\ \\ x=-1.5-\sqrt{27.25} =-6.72015...\approx -6.72[/tex]

So, the solutions are:  [tex]x= 3.72, -6.72[/tex]

Answer:

the songs downloaded in  10 seconds

DEEZNUTS

Step-by-step explanation:

The data in the form of the equation can be written as a + c = 1200 and 7a + 3c = 6400. The correct option is A.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a movie theatre sold 1200 tickets and made $6400 in one night. If an adult ticket costs $7 and a children's ticket costs $3.

The expression in the form of the equation can be written as below,

a + c = 1200

7a + 3c = 6400

The correct system of equations will be option A.

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Answer:

The correct simplification of the given expression  [tex]tan(-x){\times}cos(-x)[/tex] is [tex]-sinx[/tex].

Step-by-step explanation:

The given expression is:

[tex]tan(-x){\times}cos(-x)[/tex]

Now, simplifying the above given expression, we get

=[tex]\frac{sin(-x)}{cos(-x)}{\times}cos(-x)[/tex] (because [tex]tanx=\frac{sinx}{cosx}}[/tex])

=[tex]sin(-x)[/tex]

Also, we know that [tex]sin({-\theta})=-sin{\theta}[/tex], tehrefore teh expression becomes

=[tex]-sinx[/tex]

Hence, the correct simplification of the given expression  [tex]tan(-x){\times}cos(-x)[/tex] is [tex]-sinx[/tex].

Answer:

  0.65 square inch

Step-by-step explanation:

Each triangle has an area given by ...

  A = 1/2bh = 1/2·(0.5 in)(0.4 in) = 0.10 in²

The square base has an area given by ...

  A = s² = (0.5 in)² = 0.25 in²

The total area is that of the square base and 4 triangles:

  S = 0.25 in² + 4×0.10 in² = 0.65 in²

Answer:

0.65 square inch

Step-by-step explanation:

Answer:

The total number of codes is found with

[tex]P_{n}^{r} =n^{r}[/tex]

This formula is applied when we have to find combinations where the order matters, and each element can be used more than once, as happens with codes, there can be repetitions of numbers.

So, [tex]n[/tex] represents the total number of elements which are 6, and [tex]r[/tex] represents the total digits per code, which are 4.

Replacing these values, we have

[tex]P_{6}^{4} =6^{4}=1296[/tex]

This means there are 1296 possible codes.

Now, if the owner doesn't remember the code, the probability of entering the correct code on the first try would be

[tex]P=\frac{1}{1296}=0.0008 (or \ 0.08\%)[/tex]

This means that it's nearly impossible to enter the right code at once.

Using the tangent function of trigonometry, the height of the South Carolina State House is calculated to be approximately 180.2 feet. When rounded, the building stands at an estimated 180 feet tall.

To calculate the height of the South Carolina State House, we can use trigonometry. Given that Issac is standing 174 feet from the base and the angle of elevation to the top of the building is 46°, we can use the tangent function to determine the height of the building. The tangent of an angle in a right triangle is the ratio of the opposite side (the height of the building in this case) to the adjacent side (the distance from Issac to the building).

Using the formula:

tangent (angle) = opposite/adjacent

The equation would be:

tangent (46°) = height of building / 174 feet

Solving for the height of the building:

height of building = 174 feet * tangent (46°)

Using a calculator with the tangent function:

height of building = 174 * 1.035530 (approx value of tangent (46°))

So:

height of building ≈ 180.2 feet

Rounded to the nearest foot, the height of the South Carolina State House is approximately 180 feet.

Answer:

the answers are c and e 1,1 and 2,2

Step-by-step explanation:

Answer:

(1,1) (2,2)

Step-by-step explanation: