Mathematics High School

In a​ circle, a 225 degrees sector has area 490pi in2. What is the radius of the​ circle?

Answers

Answer 1
we know that

area of a sector=(∅*pi/360°)*r²--------> when ∅ is in degree
r=√[360°*(area of a sector)/(∅*pi)]

area of a sector=(∅/2)*r²--------> when ∅ is in radians
r=√[2*(area of a sector)/∅]

let's calculate the radius of the two ways

1) r=√[360°*(area of a sector)/(∅*pi)]
area of a sector=490*pi in²
∅=225°
 r=√[360°*(490*pi)/(225°*pi)]-------> r=√784-----> r=28 in

2) r=√[2*(area of a sector)/∅]
area of a sector=490*pi in²
∅=225°-----> convert to radians-----> ∅=225°*pi/180-----> ∅=1.25*pi
r=√[2*(490*pi)/(1.25*pi)]----> r=√[980/1.25]---> r=√784----> r=28 in

the answer is 
the radius is 28 in

Related Questions

You bought 2 pairs of pants at $28.99 each, and one shirt at $21.34. If the tax rate is 5%, what is the total cost of your purchase?

Show how you got the answer

Question 3 options:



$79.32



$58.98



$69.32



$83.29

Answers

So, first let's add the prices together before we calculate the tax rate:
28.99*2 + 21.34
Multiply:
79.32
Now we find the tax rate:
79.32 * 0.05 = 3.966 ( we can round up to 3.97)
Add tax and total:
79.32 + 3.97 = 83.29
The total price is $83.29

The total cost of purchase on 2 pants and 1 shirt is $76.986.

Given that, you bought 2 pairs of pants at $28.99 each, and one shirt at $21.34.

What is the sales tax?

Calculating the sales tax applied to a purchase is a matter of simply multiplying the tax rate by the purchase price using the equation sales tax = purchase price × sales tax rate. Adding the sales tax to the original purchase price gives the total price paid with tax.

Now,

The cost of 2 pairs of pants

= 2 ×28.99

= $57.98

Total cost of two pants and a shirt

= 21.34+51.98

= $73.32

Tax =5% of 73.32

= 5/100 ×73.32

= 0.05 ×73.32

= $3.666

Total cost of purchase =73.32+3.666

= $76.986

Therefore, the total cost of purchase on 2 pants and 1 shirt is $76.986.

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classify 4x^5+2x^4-5x^3+12 by number of terms

Answers

That is 4 terms long. 

The polynomial 4x⁵ + 2x⁴ - 5x³ + 13 has a degree of five and a quadrinomial (four terms).

What is a polynomial?

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.

Polynomials can be classified based on degree as linear, quadratic, cubic and so on. Polynomials can also be classified based on number of terms.

The polynomial 4x⁵ + 2x⁴ - 5x³ + 13 has a degree of five and a quadrinomial (four terms).

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Two similar cones have volumes of 8pi and 64pi find the ratios of the radio

Answers

we have that
volume larger cone=64*pi unit³
volume smaller cone=8*pi unit³

we know that
volume larger cone=[scale factor]³*volume smaller cone
[scale factor]³=volume larger cone/volume smaller cone
[scale factor]³=64*pi/(8*pi)-----> 8
[scale factor]=∛8------> [scale factor]=2

Find the ratios of the radio 
[radio larger cone/radio smaller cone] is equal to the scale factor
so
[radio larger cone/radio smaller cone]=2
or 
[radio smaller cone/radio larger cone]=1/2

neil tried to simplify an expression step by step 5^-6/5^-4

Answers

The simplified form of the given expression is 1/25.

The given expression is [tex]\frac{5^{-6} }{5^{-4} }[/tex].

We need to simplify the given expression.

What are exponents and how do solve exponents questions?

The exponent of a number shows how many times the number is multiplied by itself. The properties of exponents or laws of exponents are used to solve problems involving exponents. These properties are also considered major exponents rules to be followed while solving exponents.

Using quotient law [tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex].

Now, [tex]\frac{5^{-6} }{5^{-4} }[/tex] can be written as [tex]\frac{5^{4} }{5^{6} }[/tex]

By using the quotient rule, we get [tex]\frac{5^{4} }{5^{6} }=5^{4-6}[/tex]

[tex]=5^{-2}=\frac{1}{5^{2}}[/tex]

=1/5×5=1/25

Therefore, the simplified form of the given expression is 1/25.

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Katherine invested $140.she earned a simple interest of 4% per year on the initial investment. If no money was added or removed from the investment what was the amount of interst katherine received at the end of two years?

Answers

Interest per year = 4% x $140 = $5.60

Interest for 2 years = $5.60 x 2 = $11.20

Total amount at the end of 2 years = $11.20 + $140 = $151.20

Answer: $151.20

HIGH AMOUNT OF POINTS! MATH QUESTION! IF YOU DON'T KNOW IT, DON'T ANSWER!

Answers

Solving the equations by graphing requires plotting the given functions.
y=x^2-3
x-y=1
thus the plot will be as shown in the picture. The solutions are:
(-2,-1) and (2,1)


angle 0 is in quadrant 1 with sin0 = 2/5. Use the Pythagorean identity, sin^2 0 + cos^2 0 = 1, to calculate the value of cos0 as a radical.

Answers

we know that
sin²x+cos²x=1
so 
clear cos x
cos x=(+/-)√[1-sin²x]

in this problem
Angle 0 is in quadrant 1 -----> cos o and sin o are positive
sin o=2/5
cos x=√[1-(2/5)²]----> cos o=√[1-4/25]----> cos o=√[21/25]---> cos o=√21/5

the answer is
cos o=√21/5

One of the angles of a parallelogram is equal to 40°. Find the rest of the angles.

Answers

angles a and b must add up to 180 degrees. So the angles are 40, 140, 40, 140

The angles of parallelogram are 40°, 140°, 40°, 140°.

What is parallelogram?

A parallelogram is a type of quadrilateral. It is a two-dimensional figure with four sides. The most important properties of a parallelogram are that the opposite sides are parallel and congruent and the opposite angles are also equal.

For the given situation,

One angle of parallelogram = 40°

Let the unknown angle be 'x'

The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees.

⇒ [tex]40+x=180[/tex]

⇒ [tex]x=140[/tex]

The opposite interior angles are equal.

Hence we can conclude that the angles of parallelogram are 40°, 140°, 40°, 140°.

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In spherical geometry, what is the term used for the shortest distance between two points?

Answers

The correct answer for the question shown above is: Geodesic.

 The explanation of is shown below:
 1. You have that ,by definition, the spherical geometry studies figures on the surface of the spheres.
 2. And the termn known as "Geodesic" is define as the shortest distance between two points on the surface of a sphere or a curved surface. 

A sum of money is divided among peter paul and jane in ratio 13:12:7 calculate how much paul gets if amount peter gets more than jane is 78$

Answers

First we define variables:
 x: Money Peter receives
 y: Money Paul receives
 z: Money Jane receives
 We write the system of equations:
 x / y = 13/12
 x / z = 13/7
 x = z + 78
 Solving the system we have:
 x = $ 169
 y = 156 $
 z = 91 $
 Answer:
 Paul gets 156 $

How do you find the inverse of y=2x-3

Answers

Subtract 3 from each side

y - 3 = 2x

 

Divide through by 2

y/2 - 3/2 = x

or x = y/2 - 3/2

 

Now simply switch labels: x↔y

y = x/2 - 3/2

The domain of this graph is {x | x≥−2}.

True.
False.

Answers

The correct answer is:  [B]:  " True ".
_____________________________________________________
Note:  From visual inspecton of the graph shown — [Note:  all images attached refer to the same graph.] :
 
→  We can see that when "x = -2"  ;  there is only one value for "y" ;  and then the "line" of the graph stops for any coordinate corresponding to any "x-value" LESS THAN "-2" ; 

 →  and that there are corresponding "y-coordinates" corresponding to any "x-value that is equal to "-2" and "GREAT THAN  "-2" .
_________________________________________________________



The domain of the graph is {x|x>= - 2}

So the answer is TRUE

The area of a rectangular knitted blanket is 14 x^2 - 17 x -6. What are the possible dimensions of the​ blanket? Use factoring.

Answers

It's unlikely that it the dimensions are either 14 and 1 in front of the x or 6 and 1 for the 6, but this is math, so you never know. I would try 7 and 2 and 3 and 2 and see what comes of it.

(7x        2)(2x     3 ) That looks promising. We'll put the 3 with the 2x. That leaves us with the signs. We need 17 to  be minus

(7x        2)(2x - 3) that gives you - 21 x So the 2 with the seven has to be plus.

(7x + 2)(2x - 3) should be the the factored answer.
7x + 2 = 0 has no meaning. Measurements cannot be minus.

2x - 3 = 0
2x = 3
x = 3/2

If there are choices, please list them.  That's as far as is possible.

Find the quotient. Write your answer USING A DECIMAL and ROUNF TO THE NEAREST HUNDREDTH.


8,426÷82

Answers

This is my work hope it is correct. Do not add 0 at the end. Hope this helps!
the quotient is 102.76

In the figure, what is the value of x?

Answers

1. C 2. B 3. D 4. B 5. C

Answer:x=90 °


Step-by-step explanation:

In any circle the exterior angle formed is half of the major arc - minor arc .

Angle formed by tangents or secants = [tex]\frac{1}{2}(Major arc - minor arc )[/tex]

The sum of measure of arcs inany circle is 360°.

Minor arc is given as x°.So Major arc = 360-x.

Substituting the given values in the formula :

[tex]x=\frac{1}{2}(360-x-x)[/tex]

[tex]x=\frac{1}{2}(360-2x)[/tex]

x=180-x

Adding x both sides we have:

2x=180.

Dividing both sides by 2.x= 90.

Suppose that in a large company, 30% of the computers are infected by adware. if 6 computers are randomly selected and tested, what is the probability that 2 of the computers are infected by adware?

Answers

it's either 1.8 or 0.9

Tracy solved the system of equations by making a substitution for x in the second equation.

What equation did she get as a result of that substitution?

x = –2y – 2
2x + 3y = –6

–2y – 2 = –6
–2y + 1 = –6
–4y – 2 + 3y = –6
–4y – 4 + 3y = –6

Answers

Tracy put (-2y-2) where x is in the second equation. This resulted in
  2(-2y-2) +3y = -6
After eliminating parentheses, Tracy had
  -4y -4 +3y = -6

The 4th selection is appropriate:
  -4y - 4 + 3y = -6

Find the surface area of the equilateral triangular pyramid.

Answers

C is the correct answer



good luck

Answer:

i think the answer is C.

GOOD LUCK!!!

What would “x” be ?

Thanks you

Answers

cos x = 16/21

So x would equal  to 40.37 degrees

Step-by-step explanation:

[tex]cos \: x = \frac{a}{h} \\ cos \: x = \frac{16}{21} = 0.76 \\ cos \: x = 40.36degrees[/tex]

Assuming the cost of cement blocks is $75 per 1,000, how much will it cost for the blocks to build a wall 7ft. tall by 20 ft. long if the block is 6 inches thick and 10 blocks are needed for 1 cubic foot.

Answers

First, we are going to convert the thick of the block from inches to feet. To do that we are going to take advantage of the fact that 1 foot=12 inches to create a multiplier:
[tex]6in* \frac{1ft}{12in} =0.5ft[/tex]

Since the thickens of the wall will be equal to the thickness of each block, the thick of the all is 0.5 feet. 
Now, to find the volume of the wall, we are going to use the formula:
[tex]V_{w}=hlt[/tex]
where
[tex]V_{w}[/tex] is the volume of the wall 
[tex]h[/tex] is the height of the wall
[tex]l[/tex] is the length of the wall 
[tex]t[/tex] is the thickness of the wall
We know for our problem that the wall is 7ft. tall by 20 ft. long, so [tex]h=7ft[/tex] and [tex]l=20ft[/tex]. We also know from our previous calculation that the thickness of the wall is 0.5ft, so [tex]t=0.5ft[/tex]. Lets replace those values in our formula:
[tex]V_{w}=hlt[/tex]
[tex]V_{w}=(7ft)(20ft)(0.5ft)=70ft^3[/tex]

Now we know that the volume of the wall is 70 cubic feet. We also know that 10 blocks are needed for 1 cubic foot, so to find the total numbers of blocks needed, we are going to multiply the volume of the wall by the number of blocks needed for 1 cubic foot:
[tex]TotalBlocks=70ft^3* \frac{10blocks}{1ft^3 } =700 blocks [/tex]

Finally, to find the total cost, we are going to multiply the number of blocks needed by the cost of 1000 blocks:
[tex]TotalCost=700blocks* \frac{75}{1000} =52.5[/tex]

We can conclude that the cost of the wall will be $52.5

true, false, or open. Explain. 45/x-14=22

Answers

45/x - 14 = 22 
add 14 to both sides

45/x -14 +14 = 22 +14
45/x = 36
36 x = 45
x = 45/36 = 5/4 = 1.25

What is the value of x?

132√ cm

526√3 cm

262√ cm

263√ cm

Answers

30 60 90 right triangle on the right
ratio of short leg: long leg :hypo = a: a√3: 2a
So if hypo = 52 cm then short leg = 52/2 = 26 cm

The other right triangle on the left is 45 45 90 because it has 2 equal sides
ratio of leg: leg :hypo = a: a: a√2

the leg = 26 cm
so hypo x = 26√2

Answer
26√2 cm

[tex]\huge \boxed{\sf 26\sqrt{2}\ cm } \\\\\\\sf Using\ trigonometric\ functions \\\\\displaystyle cos \theta = \frac{adj}{hyp} \\\\cos(60)=\frac{adj}{52} \\\\adj=cos(60) \times 52=26 \\\\Using\ the\ Pythagorean\ theorem \\\\x=\sqrt{26^2+26^2} =26\sqrt{2}[/tex]

A TV has a listed price of $ 899.99 before tax. If the sales tax rate is 7.25 % , find the total cost of the TV with sales tax included.

Answers

Your price for this TV with its tax will be 965.24 dollars

Bruce has 97 sports cards. 34 of them are football cards. Which equation can be used to find the number of sports cards y that are not football cards

Answers

Answer: 34 + y  = 97

Step-by-step explanation:

According to the question,

Total number of sport cards = 97

In which some are foot ball cards and some are non football cards.

Let y be the number of sports cards.

Given, 34 cards are football cards.

Therefore, total number of cards = 34 + y

⇒ 34 + y = 97

Which is the equation that will use to find the number of non football cards.


To find the number of sports cards that are not football cards, you subtract the number of football cards from the total number of sports cards. The equation is y = 97 - 34.

To determine the number of sports cards that are not football cards, you need to subtract the number of football cards from the total number of sports cards.

Step-by-Step Explanation:

The total number of sports cards is 97.

The number of football cards is 34.

The number of sports cards that are not football cards can be found by subtracting the number of football cards from the total number of sports cards: y = 97 - 34.

Therefore, the equation y = 97 - 34 can be used to find the number of sports cards that are not football cards.

Suppose you want to build a rectangular sandbox where the width is 5 feet less than the length and the diagonal is 5 feet longer than the length. what are the dimensions of the sandbox?

Answers

Let L = length
     W = L - 5 ←5 feet less than (reverse order - ) the length (L)
     D = L + 5
These 3 lengths form a right triangle with D being the hypotenuse, c.
Using the Pythagorean Theorem, a² + b² = c²
L² + (L - 5)² = (L + 5)²
L² + L² - 10L + 25 = L² + 10L + 25
L² - 20L = 0
L = 0 (can't use this answer) or L = 20 (this is a usable answer)
Dimensions of the sandbox 20 ft by 15 ft 
Length = 20 ft
Width = 15 ft
Diagonal = 25 ft

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Given: x - 5 > -10.

Choose the solution set.

{x | x R, x < -15}

{x | x R, x > -5}

{x | x R, x < 5}

{x | x R, x > 15}

Answers

Answer:

{x | x R, x > −5}

Step-by-step explanation:

x - 5 > -10

+ 5 + 5

__________

x > −5

I am joyous to assist you anytime.

The pyramid shown below has a square base, a height of 7, and a volume of 84. what is the length of the side of the base?

Answers

Volume of a pyramid is (length * width * height) / 3

So we plug in the given information and solve. Let x = length and width since it's a square their measurements are the same.

84 = (x * x * 7) or 84 = 7x²

Divide both sides by 7 to isolate the squared variable. 

x² = 12

Now square root both sides to isolate the variable

x = √12 which simplifies to x = 2√3

The measurements for the length and width of the base are 2√3 units or approximately 3.464 units. 

The length of the side of the base is 6 units.

What is the volume of the pyramid?

The volume of the pyramid is;

[tex]\rm Volume \ of \ pyramid=\dfrac{1}{3}\times height \times Base[/tex]

The pyramid shown below has a square base, a height of 7, and a volume of 84.

Substitute all the values in the formula

[tex]\rm Volume \ of \ pyramid=\dfrac{1}{3}\times height \times Base\\\\\rm84 =\dfrac{1}{3}\times height \times 7\\\\Height = \dfrac{84\times 3}{7}\\\\ Height = \dfrac{252}{7}\\\\Height =36[/tex]

The length of the side of the base is;

[tex]\rm Side\ length^2=height\\\\ Side\ length^2=36\\\\Side\ length^2=6^2\\\\Side\ length=6[/tex]

Hence, the length of the side of the base is 6 units.

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Bryant collects a set of 20 data representing the lengths of worms he found in the garden. The variance of the set of measurements is 36. What is the standard deviation from the mean? millimeters

Answers

Answer:

6 millimeters

Explanation:

The standard deviation is the square root of the variance.

Since the variance is 36, the standard deviation would be

√36 = 6

Answer:6

Step-by-step explanation:

i’m sure this is easy but i'm gonna ask anyway

Answers

No, it's always okay to ask if you don't understand a question.  Anyway, for this problem, we just have to plug in the value for V to solve for P :

[tex]P = 4V^{ \frac{1}{3}} \\ P = 4(125)^{ \frac{1}{3}}[/tex]

A number to the power of 1/3 is the same as taking a cube root.

[tex]P = 4(125)^{ \frac{1}{3}} \\ P = 4(5) \\ P=20[/tex]

The perimeter of one face of the cube is 20m.

What is the surface area of the cylinder in terms of pi? The diagram is not drawn to scale.

Answers

Surface Area = 2πr² + 2πrh 

Surface Area = 2π(7)² + 2π(7)(15) = 308π in²²

Answer: 308π in²

The solution is, 308π in² is the surface area of the cylinder in terms of pi.

What is surface area?

Surface area is the amount of space covering the outside of a three-dimensional shape. The surface area of a solid object is a measure of the total area that the surface of the object occupies.

here, we have,

from the given diagram , we get,

the cylinder has,

radius = r = 7

height = h = 15

we know that,

Surface Area = 2πr² + 2πrh

so, we get,

r = 7

h = 15

substituting the values, we get,

Surface Area

= 2π(7)² + 2π(7)(15)

= 308π in²²

Answer: 308π in²

Hence, The solution is, 308π in² is the surface area of the cylinder in terms of pi.

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