The image below is a triangle drawn inside a circle with center O:

A triangle is shown inscribed inside a circle. The leg of the triangle labeled 6 inches passes through the center of the circle, O. The other two legs are labeled as 4 inches and 3 inches.

Which of the following expressions shows the area, in square inches, of the circle?

(π = 3.14)

3 ⋅ 3.14 ⋅ 22
3.14 ⋅ 32
3.14 ⋅ 22
3.14 ⋅ 3

Quick answer, it's B.

For this case we must rationalize the following expression:

[tex]\frac {2 \sqrt {5}} {- 3 \sqrt {50}}[/tex]

Multiply the numerator [tex]\sqrt {50}:[/tex]

[tex]\frac {2 \sqrt {5} * \sqrt {50}} {- 3 \sqrt {50} * \sqrt {50}} =\\\frac {2 \sqrt {5 * 50}} {- 3 (\sqrt {50}) ^ 2} =\\\frac {2 \sqrt {250}} {- 3 * 50} =\\\frac {2 \sqrt {250}} {- 150}[/tex]

Answer:

Option B

The function 2x + 3 is equivalent to g(x) + f(x) if the g(x) = (9x + 1) and f(x) = (-7x + 2)

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

h(x) = (3x - 4)

f(x) = (-7x + 2)

g(x) = (9x + 1)

Find h(x) + g(x):

= (3x - 4) + (9x + 1)

= 12x -3

Find g(x) + f(x):

= (9x + 1) + (-7x + 2)

= 2x + 3

Thus, the function 2x + 3 is equivalent to g(x) + f(x) if the g(x) = (9x + 1) and f(x) = (-7x + 2)

Learn more about the function here:

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#SPJ2

Answer: B. Unimodal

Unimodal- having or involving 1 mode

Answer:

90

Step-by-step explanation:)

To obtain [tex]S_{4}[/tex] , sum the first 4 terms, using n = 1 to n = 4

[tex]S_{4}[/tex]

= 6[tex](2)^{0}[/tex] + 6[tex](2)^{1}[/tex] + 6(2)² + 6(3)³

= (6 × 1) + (6 × 2) + (6 × 4) + (6 × 8)

= 6 + 12 + 24 + 48

= 90

Answer:

90

Step-by-step explanation:

Answer:

A = 7552.866242 ft^2

Step-by-step explanation:

Circumference = 2 * pi *r

308 = 2 * pi *r

Divide each side by 2

154 = pi *r

Divide each side by pi

154/pi = pi *r/ pi

154/pi = r

The area of a circle is given by

A = pi r^2

A = pi * (154/pi)^2

A = pi * 154/pi * 154/pi

A = 154*154 /pi

A =23716/pi

Let pi be approximated by 3.14

A = 23716/3.14

A = 7552.866242 ft^2

Answer:

Area of circular platform is 7549.25 feet ².

Step-by-step explanation:

in the given question we have to find the area of Circle, where circumference of circle is given.

Area of Circle A = πr²

and Circumference of circle C = 2πr => r = C/2π

Putting value of r in area of circle:

A = π (c/2π)²

A = C²/4π

Putting value of C = 308 feet and π = 3.1415

A = (308)² / 4*3.1415

A = 7549.25 feet ²

So, Area of circular platform is 7549.25 feet ².

Answer:

2x2,2+2=4

Step-by-step explanation:

2*2=4

2+2=4

Answer:

g(x) has the greater max:  11 versus 6

Step-by-step explanation:

One can readily discern the max value of the graph; it is 6 and occurs at x =1.

Regarding the function g(x) = (-1/2)x^2 + 4x + 3:  Find the vertex, which also represents the max value:

Here the coefficients are a = -1/2, b = 4 and c = 3, so that the axis of symmetry is:

x = -b/(2a), which here is   x = -4 / ( 2·[-1/2] ) = -4 / (-1) = 4

At x = 4, the function (y) value is

g(4) = (-1/2)(4)² + 4(4) + 3, or

g(4) =    -8  +   16 + 3, or 11

This is greater than the max value of the graphed function.

To assess which function has a larger maximum value, analyze their critical points or endpoints, using the derivative and evaluating the function's values at those points, which reveal the function with the higher maximal value.

To determine which function has the larger maximum value, we must analyze the behavior of the functions and examine their critical points, endpoints, or any given constraints. For polynomial functions, the extreme value theorem ensures the existence of a maximum, provided the function is continuous over a closed interval. In many cases, finding where the derivative equals zero can indicate the location of a maximum. However, if the derivative does not equal zero at any real number, it suggests that the maximum may occur at the endpoints of the given interval.

When calculating the maximum, it's crucial to evaluate the function at the endpoints, which often reveal the highest value, especially when the turning points are not located within the interval of interest. This approach is validated through both algebraic manipulation, such as the application of the quadratic formula, and graphical analysis of the function.

In comparing two functions for their maximum values, we analyze each function similarly, derive their respective derivatives, solve for critical points, and evaluate the endpoints. Deductions are then made based on the calculated values to determine which function has the greater maximum value.

Answer:

4

Step-by-step explanation:

Given in the questions

-8 * [tex]\frac{-1}{2}[/tex]

Step 1

[tex]\frac{-(-1)8}{2}[/tex]

Step 2

[tex]\frac{8}{2}[/tex]

Step 3

4

Answer:

16

Step-by-step explanation:

I had it on a test and i got it right this is 100% correct.

Answer:

6/25, or 0.24

Step-by-step explanation:

There are 25 numbers from which to choose, each equally likely to be chosen.

Multiples of 4 that are between 1 and 25 are {4, 8, 12, 16, 20, 24}

There are 6 such multiples of 4, out of 25 numbers total.

Thus, the probability of choosing a number from 1-25 that is a multiple of 4 is 6/25, or 0.24.

Answer:

r = 3/4

Step-by-step explanation:

Area of circle = Volume of sphere.

pi*r^2 = 4/3 pi r^3                   Divide by pi r^2

1 = 4/3 r                                    Divide by 4/3

1//4/3 = 4/3 r / 4/3

3/4 = r

27.5

Follow the order of operations and start by solving the parentheses.

18 + 19 / 2

Now, do the division.

18 + 9.5

Finally, solve the addition.

27.5

Answer:

-6.05-3.611=-9.661

Step-by-step explanation:

Answer: -9.661

i used khan academy and make sure to add the - sign otherwise it will be wrong

For this case we have that by definition, the area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

A: It is the radius of the circle.

If they tell us that the diameter is 17 inches, then the radius is 8.5 inches. Substituting:

[tex]A = \pi * (8.5) ^ 2\\A = 226,865[/tex]

If we round up, we have that the area is:

226.87 square inches

Answer:

Option C

16 flowers per arrangement

Answer:

The arc PS would be a minor arc

Step-by-step explanation:

As a minor arc is one that is less that 180 degrees, it would be the only viable solution.

Line SO is not an arc, so it cannot be chosen

the measures of arcs SQ and PSR are each 180 degress, so they would not be minor.

The arc which is a minor arc  is:

                      Arc PS.

Minor arc--

A minor arc is a arc which subtend an angle of measure less than 180 degree in the center.

i.e. such a arc should be smaller than a semicircle.

1)

Arc SQ

This arc subtend an angle of 180 degree in the center,

This means it is a semicircle and not a minor arc.

2)

arc PSR

This is again a semicircle and not a minor arc.

Since  PR is the diameter of the circle and hence the arc so formed will be a semicircle.

3)

arc PS

The angle subtended at the center of the circle by this arc is less than 180 degree and hence it is a minor arc.

4)

Line SO

O is the center of the circle and S is a point on the circumference of the circle and hence it denotes the radius of the circle.

ANSWER

[tex]2 ( { \cos \: 56 \degree + i \sin \:56 \degree) }[/tex]

EXPLANATION

The complex number given to us is in the polar form,

32(cos 280° + i sin 280°)

The fifth root is

[tex] {32}^{ \frac{1}{5} } ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } [/tex]

This is equal to:

[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } [/tex]

According to the DeMoivre's Theorem,

[tex]( { \cos \theta \: \degree + i \sin\theta \degree) }^{ \frac{p}{q} } = ( { \cos \frac{p}{q} \theta \degree + i \sin \frac{p}{q} \theta \degree) }[/tex]

We now use the DeMoivre's Theorem to obtain:

[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } = 2 ( { \cos \: \frac{1}{5} \times 280 \degree + i \sin \:\frac{1}{5} \times 280 \degree) }[/tex]

[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } = 2 ( { \cos \: 56 \degree + i \sin \:56 \degree) }[/tex]

Answer:

trey

Step-by-step explanation:

he reads one page per every 2.5 minutes

Answer:

Roderick

Step-by-step explanation:

Just divide the number of pares by the time it too then to read them.

The final probability is the weighted average of the playing probabilities calculated over the possible weather options:

P(john practices cello; given that it rains) * P(it rains) +

P(john practices cello; given that it does not rain) * P(it does not rain) =

0.6 * 0.7 + 0.4 * 0.3 = 0.54

The probability is 54%

The probability that John will practice his cello is 54%.

If it rains ​tomorrow, the probability is 0.6. If it does not rain ​tomorrow, there is only a 0.4 chance. And, the chance of rain tomorrow is 70​%.

Calculation of probability:

= 0.6 (0.7) + 0.4 (0.3)

= 0.54

= 54%

Learn more about the probability here: https://brainly.com/question/3974756

Answer: Second Option

[tex]C = 16\pi[/tex]

Step-by-step explanation:

We are evaluating aarco lengths

The formula for the arc length is:

[tex]C = 2\pi r[/tex]

We want to know what is the arc length for a radius of r = 8

Then we substitute r = 8 in the equation and solve

[tex]C = 2 \pi * 8[/tex]

[tex]C = 16\pi[/tex]

The correct answer is the second option

Answer:

Correct choice is [tex]C=16 \pi [/tex].

Step-by-step explanation:

Given equation is [tex]C=2 \pi r[/tex].

Now we need to find the value of C using given equation [tex]C=2 \pi r[/tex] and [tex]r=8[/tex].

To find that, we just need to plug [tex]r=8[/tex] into [tex]C=2 \pi r[/tex] and simplify.

[tex]C=2 \pi r[/tex]

[tex]C=2 \pi \times 8[/tex]

[tex]C=16 \pi [/tex]

Hence correct choice is [tex]C=16 \pi [/tex].

Answer:

Step-by-step explanation:

To find the equation of directrix of the parabola, we need to identify the axis of the parabola i.e, parabola lies in x-axis or y-axis.

We have 4 parts in this question i.e.

For each part the value of directrix will be different.

For x²  = 12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = -a

So, we need to find the value of a.

The general form of equation for y-axis parabola having positive co-efficient is:

x² = 4ay  eq(i)

and our equation in question is: x² = 12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

4ay = 12y

a= 12y/4y

a= 3

Putting value of a in equation of directrix: y = -a => y= -3

The equation of the directrix of the parabola x²= 12y is y = -3

For x²  = -12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = a

So, we need to find the value of a.

The general form of equation for y-axis parabola having negative co-efficient is:

x² = -4ay  eq(i)

and our equation in question is: x² = -12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

-4ay = -12y

a= -12y/-4y

a= 3

Putting value of a in equation of directrix: y = a => y= 3

The equation of the directrix of the parabola x²= -12y is y = 3

For y²  = 12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = -a

So, we need to find the value of a.

The general form of equation for x-axis parabola having positive co-efficient is:

y² = 4ax  eq(i)

and our equation in question is: y² = 12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

4ax = 12x

a= 12x/4x

a= 3

Putting value of a in equation of directrix: x = -a => x= -3

The equation of the directrix of the parabola y²= 12x is x = -3

For y²  = -12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = a

So, we need to find the value of a.

The general form of equation for x-axis parabola having negative co-efficient is:

y² = -4ax  eq(i)

and our equation in question is: y² = -12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

-4ax = -12x

a= -12x/-4x

a= 3

Putting value of a in equation of directrix: x = a => x= 3

The equation of the directrix of the parabola y²= -12x is x = 3

Answer: second option

Step-by-step explanation:

To find the inverse function of the given function f(x):

[tex]f(x)=2x[/tex]

You need to:

Substitute [tex]f(x)=y[/tex] into the function:

 [tex]y=2x[/tex]

Now, you need  to solve for "x", to do this, you must divide both sides of the function by 2:

[tex]\frac{y}{2}=\frac{2x}{2}\\\\\frac{y}{2}=x[/tex]

Now, replace "x" with "y" and replace "y" with "x":

[tex]\frac{x}{2}=y[/tex]

Therefore, substituting [tex]y=f^{-1}(x)[/tex] you get:

[tex]f^{-1}(x)=\frac{x}{2}[/tex] or  [tex]f^{-1}(x)=\frac{1}{2}x[/tex]

Since the smaller pieces are all equal.

Then, X1=X2=X3...=1/10.

Therefore, the sum of the whole pieces should give you 3/4 back.

X1+X2+X3...=3/4

Therefore, (3/4÷n)=1/10

where n is the number of all the pieces.

I hope this helps

Answer: The answer to the first question is C(20%)

Step-by-step explanation: 1. you need to find the absolute decrease which is subtracting 350-280= 70.

2. now you need to find the percent decrease which is dividing the absolute decrease by the whole price.. so.. 70/350= .20

3. now just multiply .20 *100 = 20%

Since we're trying to find out how much the price was reduced by, first you will do this

[tex]350 - 280 = 70[/tex]

The price was dropped by $70.

Then we find out how much $70 is of the original price which is 350

[tex]70 \div 350 = 0.2[/tex]

Then you convert 0.2 into a percentage which is 20%.

The price of the digital camera was reduced by 20%.

Answer:

it is 11/6 and the second one I have no idea. sorry

Step-by-step explanation:

Answer:

The ratio of the perimeters is 11/6

The ratio of the areas is 121/36

Step-by-step explanation:

For the area, you need to do 11/6 squared which means 11 * 11 / 6 * 6 which = 121/36

And for the perimeter it's 11/6 = 11/6 because you cannot really do anything with that so it stays the same

if you are wondering why it is 11/6 is because the red = original and blue = image so since red is the original it goes on top.

I hope this helped  

They can be described as a horizontal movement, a vertical movement, or a combination of the two (horizontal and vertical.)

Answer:

In this case, the median would be the best measure since there is the outlier of 14 in the data. This set of data will have the median of 1.5.

Step-by-step explanation:

The median would be 1.5

Answer:

2(3x + 7)(2x - 1)

Step-by-step explanation:

You can see it a little easier if you take out a common factor of 2

2(6x^2 + 11x - 7)

The 6 leaves you with a lot of factors, the 7 does not. It only has 2 factors.

Let 6 factor into 2 and 3 and the 7 into 7 and 1

2(3x - 1 )(2x + 7)

Now remove the brackets.

2(6x^2 + 21x - 2x - 7) This obviously does not work but we'll combine like terms anyway.

2(6x^2 + 19x - 7)

So we'll try it again

2(3x + 7)(2x - 1)

2(6x^2 + 14x - 3x - 7)    Looks like we have it.

2(6x^2 + 11x - 7)

So the right factors are

2(3x + 7)(2x - 1)

Answer:

x = 0.7

Step-by-step explanation:

To solve this, simply find the square root of 0.49

x^2 = 0.49

(Finding the square root will cancel out the ^2 on x, to get x alone)

x = 0.7

You can double check this too to see if this is the right answer.

0.7 x 0.7 = 0.49

I hope this helps!!! :)

0.7 x 0.7 = 0.49 i think this is it

Answer:

b. -33

Step-by-step explanation:

The question is about finding the determinant of a 2×2 matrix

General formula; when given matrix A =[  b  c ]

                                                                  [ d   e]

the determinant of A = (e×b)-(c×d)

Evaluate

(3  -3)

(-5  -6)  = (-6×3) - ( -5×-3)

            = (-18)- ( 15) = -33    

Answer:

It depends on whether you are accounting for inflation. If not taking that into  account, you do not lose money because your friend pays you the full amount back.