Mathematics High School

The sector of a circle with a diameter of 20 inches has a central angle measure of 36°. What is the area of the sector?

40π in²

10π in²

2π in²

π in²

plz explain what you did to get the answer so that i vcan understand and do it alone in the future

Answers

Answer 1
We need the radius to find the area of sector.

radius = 20/2 = 10

Area of sector:

πr²(x/360) = x is the central angle in degrees.
π(10)²(36/360)
10π in²

Hope this helps :)

Related Questions

PLEASE HELP ME ON THIS....
thx

Answers

parallel means the lines have same slope and they never intersect. So no point lies on both lines. It means no solution

answer
There is no solution

While Playing Yahtzee and rolling 5 dice, Mei gets the result shown at right (the numbers are 2, 4, 4, 4, and 1). Mei decides to keep the three fours and reroll the other 2 dice. a. what is the probability that Mei will have 5 of a kind? b. What is the probability that she will have 4 of a kind? c. what is the probability that she will have exactly three 4's?

Answers

A. The probability is 1/36. There are 36 combinations of the first and second dice and only one of them is 2 - 4s.

B. 10/36. Ten of the options contain exactly 1 - 4. 

C. The remaining 25/36 options do not include a 4. 

Find the value of a. The diagram is not to scale. a. 36 b. 144 c. 54 d. 126 **I believe the answer is B

Answers

i agree with you to the answer being B

The value of a in the diagram is 144°.

The correct option is B.

What is a trapezoid?

An open, flat object with four straight sides and one set of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases.

Given:

A trapezium has parallel bases and that one of its characteristics is that the two angles on a single side are supplementary, meaning that the total of the angles on two neighboring sides is 180°.

So,

∠a = 180 - 36

∠a = 144

∠b = 180 - 113

∠b = 67

Therefore, the value of a is 144°.

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The complete question is given in the attached image.

A lighthouse is 15m above sea level.
The lighthouse operator sights a boat at an angle of depression of 25 degrees.
How far is the boat from the lighthouse?
Round your answer to the nearest tenth.

Answers

For this you will use the tangent function. You have the adjacent side and have to find the opposite side.

tan x = opposite/adjacent
tan 25 = x/15
15 (tan 25) = x
6.9946 = x

So the boat is approximately 6.9946 m away from the lighthouse.

Answer:

41.2

Step-by-step explanation:

The length of a shadow of a building is 32 m . the distance from the top of the building to the tip of the shadow is 38 m . find the height of the building. if necessary, round your answer to the nearest tenth.

Answers

For this case the first thing you should realize is that you have a rectangle triangle where you have two of the three sides.
 Therefore, to solve the problem, you must find the third side using the
 Pythagorean theorem.
 We have then:
 h ^ 2 + 32 ^ 2 = 38 ^ 2
 We cleared h:
 h = root (38 ^ 2 - 32 ^ 2)
 h = 20.49390153
 round to the nearest tenth
 h = 20.5 m
 Answer: 
 the height of the building is: 
 h = 20.5 m

daniel is standing 100ft from a tower and sees a bird land on top of the tower. if the angle of elevation from daniel to the top is 84.6, how tall is the tower

Answers

check the picture below.

make sure your calculator is in Degree mode.

Catie is trying to determine the height that a ladder reaches as it leans against a wall. She walks under the ladder and touches her forehead to it as shown. If her feet are 16 inches from the ladder's base, the ladder's base is 4.5 feet from the bottom of the wall, and Catie is 5 feet 6 inches tall, then come up with an estimate for how high the ladder reaches up the wall to the nearest tenth of a foot. Watch your units on this problem and show all work

Answers

18.56 feet
Catie creates a similar triangle with the ladder so we can create a proportion to solve for the height.  
[tex] \frac{baseto feet}{base to wall} = \frac{catie height}{wall height} [/tex]
Convert all values to feet . 16in = 1.33 ft . 5ft 6 in = 5.5 ft 
Insert values into proportions
[tex] \frac{1.33}{4.5} = \frac{5.5}{x} [/tex]
Cross multiply to get
24.75=1.33x
divide both sides by 1.33
x=18.56ft

To find the height the ladder reaches up the wall, set up a proportion using similar triangles and Catie's height as the ladder's height. The estimate for the ladder's height up the wall is 6.8 feet.

Given information:

Catie is 5 feet 6 inches tall.Her feet are 16 inches from the ladder's base.The ladder's base is 4.5 feet from the bottom of the wall.

To find the height the ladder reaches up the wall, we can set up a proportion using similar triangles. Catie's height can be considered as the ladder's height, and the distance on the wall can be related to the ladder's base and height.

Using the information provided and performing the calculations, the estimate for the height the ladder reaches up the wall would be approximately **6.8 feet** to the nearest tenth of a foot.

sin 4 theta

hey, how do you simplify sin 4 theta? using double angle theory?

Answers

Yes, you do use double-angle formulas. 
You begin with double-angle formula for sine:

sin(4θ) = sin(2·2θ) = 2·sin(2θ)·cos(2θ)

Then, double-angle formula for sine again:

2·sin(2θ)·cos(2θ) = 2·2·sinθ·cosθ·cos(2θ) = 4·sinθ·cosθ·cos(2θ)

Then double-angle formula for cosine:

4·sinθ·cosθ·cos(2θ) = 4·sinθ·cosθ·(cos²θ - sin²θ)

Last, multiply:

4·sinθ·cosθ·(cos²θ - sin²θ) = 4·sinθ·cos³θ - 4·sin³θ·cosθ




What is the difference of the two polynomials?

(7y2 + 6xy) – (–2xy + 3)

Answers

(7y2 + 6xy) – (–2xy + 3)

7y^2 + 6xy +2xy +3

7y^2 +8xy +3

8xy + 7y^2 +3
 7y^{2} + 8xy-3 Answer B

How much more interest is owed on $900 for 9 months then for 6 months? 6 months = 2.4% rate 9 months = 2.9% rate

Answers

keeping in mind that 6 months is not even a year, since there are 12 months in a year, then 6 months is really 6/12 years, and 9 months is 9/12 years, then


[tex]\bf ~~~~~~ \textit{Simple Interest Earned on 9 months}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$900\\ r=rate\to 2.9\%\to \frac{2.9}{100}\to &0.029\\ t=years\to \frac{9}{12}\to &\frac{3}{4} \end{cases} \\\\\\ I=900(0.029)\left( \frac{3}{4} \right)\\\\ -------------------------------[/tex]

[tex]\bf ~~~~~~ \textit{Simple Interest Earned on 6 months}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$900\\ r=rate\to 2.4\%\to \frac{2.4}{100}\to &0.024\\ t=years\to \frac{6}{12}\to &\frac{1}{2} \end{cases} \\\\\\ I=900(0.024)\left( \frac{1}{2}\right)[/tex]

check their difference, that much.

The interest is $8.77 owed in the amount of $900 for 9 months more than for 6 months.

What is the simple interest?

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, The rate of interest is in percentage r% and is to be written as r/100

To  determine interest on the amount of $900 for 9 months

Here P = $900, R =  2.9% = 2.9/100, and T = 9/12 year

Interest  = P × R × T

Interest  = 900 × 2.9/100 × 9/12

Interest  = $19.57

To  determine interest on the amount of $900 for 6 months

Here P = $900, R =  2.4% = 2.4/100, and T = 6/12 year

Interest  = P × R × T

Interest  = 900 × 2.4/100 × 6/12

Interest  = $10.80

The difference of interest is owed on $900 for 9 months then for 6 months: $19.57 - $10.80 = $8.77

Therefore, the interest is $8.77 owed in the amount of $900 for 9 months more than for 6 months.

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If the discriminant of a quadratic equation is greater than zero, which of the following is true of the equation?

A. It has two complex solutions.
B. It has one real solution.
C. It has two real solutions.

Answers

C. It has two real solutions. The discriminant in solving a quadratic equation is b^2-4ac. If this is greater than zero it has two real solutions.

Given the following linear function, identify the slope and y-intercept of the function: x= 1/6x+7

Answers

the slope is 1/6 and the y intercept is 7
hope it helps
please mark as brainliest
the slope is 1/6 and the y intercept is 7

identify the image of xyz for a composition of two 270 degree rotation and a 90 degree rotation both about point x.

Answers

I believe The Answer is C

Answer:

The answer is D

Step-by-step explanation:


Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?

Answers

Factoring by grouping usually pairs up the first 2 sets of expressions with the second 2 sets.  Ours looks like this, then:  [tex](x^3-9x^2)+(5x-45)=0[/tex].  If we factor out the common x-squared in the first set of parenthesis, along with factoring out the common 5 in the second set, we get this:  [tex]x^2(x-9)+5(x-9)[/tex].  Now the common expression that can be factored out is the (x-9).  When we do that, here's what it looks like:  [tex](x-9)(x^2+5)[/tex].  I'm not sure how far you are going with this.  You could set each of those equal to 0 and solve for x in each case.  The first one is easy.  If x - 9 = 0, then x = 9.  The second one involves the imaginary i since x^2 = -5.  In that case,  [tex]x=i \sqrt{5},-i \sqrt{5} [/tex].  Hopefully, in what I have given you, you can find what you're looking for.

Answer:

x(x2 + 5) – 9(x2 + 5)

Step-by-step explanation:

You receive $1,000 to put in the bank. You place it in an account that pays 4% annual interest compounded continuously. How much will you have in 15 years? Round the answer to the nearest dollar.

Answers

(1.04^15)(1000)= $1,800.94

The perimeters of two similar quadrilaterals are 48 cm and 60 cm, respectively. If the area of the smaller quadrilateral is 96 cm2, find the area of the larger quadrilateral.

Answers

To answer this question set up a ratio of the perimeter to the area for the small quadrilateral (48 cm:96 square cm). Create an equivalent ratio with the perimeter of the larger quadrilateral to the area of the larger a quadrilateral (60 cm:x square cm). Use cross products to answer this. See the attached work.

The area of the larger quadrilateral is found by using the scale factor derived from the ratio of the perimeters of the similar quadrilaterals, which comes out to 150 cm².

The question involves finding the area of a larger quadrilateral given the perimeters of two similar quadrilaterals and the area of the smaller one. In similar figures, the ratio of their areas is the square of the ratio of their corresponding linear dimensions, such as side lengths or perimeters in this case. Since the perimeters are 48 cm and 60 cm, the ratio of the perimeters (also the scale factor) is 48/60, or 4/5. Consequently, the ratio of the areas is the square of the scale factor, which is (4/5)² or 16/25. Knowing the area of the smaller quadrilateral is 96 cm², we find the area of the larger quadrilateral by dividing the area of the smaller by the scale factor squared and then multiplying by the larger scale factor squared. This gives us (96 / (16/25)) cm² = (96 * 25/16) cm² = 150 cm².

So, the area of the larger quadrilateral is 150 cm².

How many minutes greater is the software company's median than the bank's median?



Enter your answer in the box.


Answers

The software company's median is 25 and the bank's median is 15, so 25 - 15 equals 10. So, the software company's median would be 10 minutes greater than the bank's median. Hope this helped! <3
Yes the answer is 10!

PLEASE HELP! What is the area of triangle BCD in exact form? 35 points!

Answers

This is a 30-60-90 triangle. The short leg is given to us as 5 

The long leg is equal to sqrt(3) times the short leg

long leg = sqrt(3)*(short leg)
long leg = sqrt(3)*5
long leg = 5*sqrt(3)

The base is 5. The height is 5*sqrt(3)
b = 5
h = 5*sqrt(3)

Use this to find the area
A = b*h/2
A = 5*5*sqrt(3)/2
A = 25*sqrt(3)/2
which is the exact area in terms of a radical

You can write it out as [tex]\frac{25\sqrt{3}}{2}[/tex]

The real part of the complex number –5 + 3i is

Answers

A complex number is a number of the form a + bi, where i = and a and b are real numbers. For example, 5 + 3i, - + 4i, 4.2 - 12i, and - - i are all complex numbers. a is called the real part of the complex number and bi is called the imaginary part of the complex number.

Real part of the complex number [tex]-5 + 3i[/tex] is -5.

What is complex number?

" Complex numbers are such numbers which expressed in form of [tex]a+ i b[/tex], where 'a' represents the real part and b represents the imaginary part containing [tex]i[/tex] . Value of [tex]i = \sqrt{-1}[/tex]."

According to the question,

Given complex number,

 

 [tex]-5 + 3i[/tex]

Compare it with general form of complex number [tex]a+ i b[/tex] we get,

Real value of( [tex]-5+ 3i[/tex])  = -5

Imaginary value of [tex]-5+ 3i[/tex] = 3

Hence, real part of the complex number [tex]-5 + 3i[/tex] is -5.

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Three times the number of blue marbles exceeds twice the number of red marbles by 18 also 5 times the number of blue marbles is 2 less than 6 times the number of red marbles how many of each are there?

Will give brainliest please answer quickly

Answers

There are 12 red and 14 blue.

The first equation would be
3B=2R+18.

The second equation would be
5B=6R-2.

To get the coefficients of R the same we will multiply the first equation by 3:
3(3B=2R+18)
which gives us
9B=6R+54

Now our system is
9B=6R+54
5B=6R-2

We will subtract the bottom equation to eliminate R:
9B=6R+54
-(5B=6R-2)

which gives us
4B=56

Divide both sides by 4:
4B/4=56/4
B=14

Substitute this into our first original equation:
3(14)=2R+18
42=2R+18

Subtract 18 from both sides:
42-18=2R+18-18
24=2R

Divide both sides by 2:
24/2=2R/2
12=R

Final answer:

By creating and solving a system of equations based on the given information, we find that there are 10 blue marbles and 8 red marbles.

Explanation:

To solve this problem, we set up two equations based on the information given:

3 times the number of blue marbles (3B) exceeds 2 times the number of red marbles (2R) by 18: 3B - 2R = 18.

5 times the number of blue marbles (5B) is 2 less than 6 times the number of red marbles (6R): 5B = 6R - 2.

Now, we can solve these equations using substitution or elimination. Using substitution, solve the second equation for B:

B = ⅜(6R - 2)

Then substitute this expression for B in the first equation:

3(⅜(6R - 2)) - 2R = 18

Solve for R:

R = 8

Now substitute R back into the equation for B:

B = ⅜(6(8) - 2) = 10

Thus, there are 10 blue marbles and 8 red marbles.

A car has a 12-volt battery. The engine has a resistance of 0.22 ohms. How many amps will be drawn from the battery when the key is turned? I (to the nearest hundredth)

Answers

Answer:

54.54 amps.

Step-by-step explanation:

Amps refers to the electrical current.

We have to find the electrical current when the car has a 12-volt battery and the engine has a resistance of 0.22 ohms.

The relation between these magnitudes is

[tex]V=I\times R[/tex]

Where [tex]V[/tex] is the voltage, [tex]I[/tex] is the electrical current and [tex]R[/tex] the resistance.

We know that [tex]V=12; R=0.22[/tex]. Replacing these values in the formula and solving for [tex]I[/tex]

[tex]V=I\times R\\\frac{V}{R}=I\\ I=\frac{12}{0.22}\\ I\approx 54.54 amp[/tex]

Therefore, the answer is around 54.54 amps.

The current drawn from the battery when the key is turned is approximately 54.55 amps.

To determine the current drawn from the battery, we can use Ohm's Law, which states that the current (I) is equal to the voltage (V) divided by the resistance (R):

[tex]\[ I = \frac{V}{R} \][/tex]

Given that the voltage (V) of the battery is 12 volts and the resistance (R) of the engine is 0.22 ohms, we can plug these values into the equation:

[tex]\[ I = \frac{12 \text{ volts}}{0.22 \text{ ohms}} \][/tex]

[tex]\[ I = \frac{12}{0.22} \][/tex]

[tex]\[ I \approx 54.5454 \][/tex]

Rounding to the nearest hundredth, we get:

[tex]\[ I \approx 54.55 \text{ amps} \][/tex]

PLEASE ANYONE
HELP
I think its 120 + 15x ≤ 360
IS that Correct!!??

Answers

Hello there! I can help you! So the centerpieces take 15 minutes to make, and x equals the amount of centerpieces. That part makes 15x. Just by looking at the answers, A and C are already eliminated. We are adding up the time. the florst has already spent 2 hours, which equals 120 minutes. She will spend no more than 6 hours or 360 minutes on creating the centerpieces. We add the time, not subtract. B is the only one that shows that. 120 + 15x ≤ 360. The answer is B. Your answer is correct.

How do I find the holes of this function?

Answers

Factor the numerator and then the denominator as well. If there are any holes in the function, they will be where the numerator and denominator are the same... (x-1)
The holes in this function are the points where you can cancel factors from the numerator and denominator.

We factor the function.

[tex]y= \dfrac{3x^2-7x+4}{x^2-1} = \dfrac{3x^2-3x-4x+4}{x^2-1}= \dfrac{3x(x-1)-4(x-1)}{x^2-1} \\\\\\ y = \dfrac{(3x-4)(x-1)}{(x+1)(x-1)} = \dfrac{3x-4}{x+1}, \ x \neq -1, \ x \neq 1[/tex]

We canceled (x-1) from the numerator and denominator, so when this factor is equal to zero, there is a hole on the graph, that is, at the point [tex](1, \frac{-1}{2})[/tex].

Giving a test to a group of students, the grades and gender are summarized below. if one student was chosen at random, find the probability that the student was female. male total 39 female total 26

Answers

Answer: 40% of the total population is female.

To find the probability that a student is female, first add up both the number of males and females.

39 + 26 = 65

Now, divide the total number of females by 65 and multiply by 100.

26 / 60 = 0.4 x 100 = 40%

A rectangle is drawn on a coordinate plane. Three vertices of the rectangle are points L(−3,10) , M(6,10) , and P(−3,−6) . Point N is the fourth vertex of the rectangle. How long is the side of the rectangle connecting points M and N?

Answers

Hello!
----------
The answer is 16.
----------
Hope this helps and have a great day!

Answer:

answer 16 or 1.6

Step-by-step explanation:

Calculate.

0 = x² + 10x + 16

Enter your answers in the boxes.

Answers

x = -2 and x = -8. 

You can get this by factoring the polynomial and solving for x or by using the quadratic formula. 

find the geometric mean between 18 and 2,

Answers

The Anser is 6


Formula: 

Geometric Mean = ((X₁)(X₂)(X₃)........(Xₙ))^1/ⁿ
Where, 
X = Individual score 
N = Sample size (Number of scores)
The geometric mean is defined the nth root of the product of n number. The formular is given as n√ a1 * a2 * a3 * ... where an are the the values of the sample. Here there are 2 numbers so n = 2 Our geometric mean = 2√ 18 * 2 = 2 √36 = √36 = 6

Carlos plots a circular planter's wall on a computer. He determines that the circle that defines the part of the planter wall that gets watered by the sprinkler is (x−10)2+(y+12)2=36.

What is the diameter, in meters, of the circular area that gets watered by the sprinkler?

Answers

1. You have that the circle that defines the part of the planter wall which gets watered by the sprinkler is: (x−10)²+(y+12)²=36.
 
 2. The standard form for the equation of a circle is:
 
 (x-h)²+(y-k)²=r²
 
 (h,k) is the center point.
 r is the radius.
 
 3. Keeping this on mind, you can find the value of the radius, as below:
 
 r²=36
 r=√36
 r=6 m
 
 4. Then, the diameter of the circle is:
 
 D=2r
 D=2(6m)
 D=12 m
 
 What is the diameter, in meters, of the circular area that gets watered by the sprinkler?  
 
 The answer is: 12 m

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. if the cardboard is 17 in. long and 12 in. wide, find the dimensions of the box that will yield the maximum volume. (round your answers to two decimal places.)

Answers

The maximum value that could be reached would be about 211.05 cubic inches.

The initial measurements of the box are:
Length: 17
Width: 12
Height: 0

Right now, the volume is zero. However, if we let the height equal 0 (the amount of the cut out), we can write the following equation for the volume.

Volume = (17 - 2x)(12 - 2x)x

If you graph this, you will find a maximum value of 211.05, keeping in mind that the cut out must be less than 6.

A sum of _________ can be factored according to the pattern (a + b)(a2 - ab + b2).

Answers

it is cubes, sorry so late.

Solution:

we are given with [tex] (a + b)(a^2 - ab + b^2) [/tex]

we have been asked to find the representation of the given factor as a Sum.

As we know that

[tex] (a^3+b^3)= (a + b)(a^2 - ab + b^2) [/tex]

Because

[tex] (a + b)(a^2 - ab + b^2)=a(a^2 - ab + b^2)+b(a^2 - ab + b^2)\\
\\
(a + b)(a^2 - ab + b^2)=a^3-a^2b+ab^2+ba^2-ab^2+b^3\\
\\
(a + b)(a^2 - ab + b^2)=a^3+b^3\\ [/tex]



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