Answers
The area of the circle is given by:
[tex]A=\pi r^2[/tex]So, the area of a circle is basically:
[tex]A=\frac{1}{2}\times2\pi r\times r[/tex]It can be seen as the number of squares inside of the circle
Related Questions
A boat is heading towards a lighthouse, where Dalvin is watching from a vertical distance of 138 feet above the water. Round your answer to the nearest tenth of a foot if necessary.
Answers
To find the first distance we use:
[tex]\begin{gathered} tan13=\frac{138ft}{x} \\ x=\frac{138ft}{tan13º} \\ x=\frac{138ft}{0.23} \\ x=\text{ 600ft} \end{gathered}[/tex]For the second distance, we change 13º to 45º and 77º to 45º as well.
So:
[tex]\begin{gathered} tan45=\frac{138ft}{x} \\ 1=\frac{138ft}{x} \\ x=138ft \end{gathered}[/tex]So the distance from point A to B is=600ft - 138ft = 462ft
PLSS HELP Find a formula for the exponential function passing through the points (-3, 3/8) and (3,24)
Answers
The exponential function is of the form:
[tex]y=ab^x[/tex]Given the two points, we can plug each point into the equation and see:
1.
[tex]\begin{gathered} y=ab^x \\ \frac{3}{8}=ab^{-3} \end{gathered}[/tex]2.
[tex]\begin{gathered} y=ab^x \\ 24=ab^3 \end{gathered}[/tex]Let's divide the the 2nd equation by the 1st one:
[tex]\begin{gathered} \frac{24}{\frac{3}{8}}=\frac{ab^3}{ab^{-3}} \\ 24\times\frac{8}{3}=\frac{b^3}{b^{-3}} \\ 64=b^{3+3} \\ b^6=64 \end{gathered}[/tex]Note: we used the property of exponents, 1/a^x = a^ -x to simplify it.
Now, we can solve for b:
[tex]\begin{gathered} b^6=64 \\ b=\sqrt[6]{64} \\ b=2 \end{gathered}[/tex]The second equation, now, becomes:
[tex]\begin{gathered} 24=ab^3 \\ 24=a(2)^3 \end{gathered}[/tex]Now, we can easily find a:
[tex]\begin{gathered} 24=a(8) \\ a=\frac{24}{8} \\ a=3 \end{gathered}[/tex]We know b = 2 and a = 3.
So, the final equation will be:
[tex]\begin{gathered} y=ab^x \\ y=3(2)^x \end{gathered}[/tex]in the figure below, points D, E, and F are the midpoints of sides ABC. suppose AC =58, DF =26, and AB =38. find the following lengths. DE, BC, and CE
Answers
The values of the lengths DE, BC, and CE are 29, 52, and 26 respectively which can be found out by using the relations for mid-points of triangle.
In the figure, it is given to us that -
Points D, E, and F are the midpoints of sides AB, BC, and AC of the ΔABC respectively.
AC = 58
DF = 26
and, AB = 38
We have to find out the values of the lengths DE, BC, and CE.
Now, AC = 58 is parallel to the mid-segment DE
=> The mid-segment DE is half of the AC.
=> DE = AC/2
=> DE = 58/2
=> DE = 29
Similarly, the mid-segment DF = 26 is parallel to BC
=> BC = Twice the mid-segment DF
=> BC = 2*26
=> BC = 52
Now, E is the midpoint of BC of the ΔABC.
=> CE = BC/2
=> CE = 52/2
=> CE = 26
Through the formulas for mid-points of triangle, we find out that the values of the lengths DE, BC, and CE are 29, 52, and 26 respectively.
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what is the area of a square with side of 14 millimeters
Answers
The formula for determining the area of a square is expressed as
Area = length^2
If the length of each side of the given square is 14 millimeters, then
Area = 14^2
Area = 196 mm^2
In the figure XYZ ~ ABC.Find cosB, tanB, and sinB.Round your answers to the nearest hundredth.
Answers
we have the following;
1. Cos B:
[tex]\begin{gathered} CosB=\frac{a}{h} \\ CosB=\frac{15.4}{17}=0.91 \end{gathered}[/tex]2. Tan B:
[tex]\begin{gathered} TanB=\frac{o}{a} \\ TanB=\frac{7.2}{15.4}=0.48 \end{gathered}[/tex]1. Sin B:
[tex]\begin{gathered} SinB=\frac{o}{h} \\ SinB=\frac{7.2}{17}=0.42 \end{gathered}[/tex]A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function =ht−80t16t2. After how long will it reach its maximum height?
Answers
over Thanksgiving break Joshua drove from Connecticut to Ohio which is 422 Mi this trip took Jason and his family 6 hours how fast was Joshua driving be sure to round your answer to the nearest whole number
Answers
In this case the answer is very simple. .
Step 01:
Data
total distance = 422 mi
total time = 6 hours
Step 02:
[tex]\frac{total\text{ distance}}{\text{total time}}=\frac{422mi}{6\text{ hour}}\text{ = }70.33\text{ mi / hour}[/tex]The answer is:
Joshua's speed was 70 mi/hours
What are the magnitude and direction of w = ❬–5, –14❭? Round your answer to the thousandths place.
Answers
To solve the question, we will have to determine the quadrant within which the point falls
Since both values are negative
[tex](x,y)=(-5,-14)[/tex]So the values are in the third quadrant
So we will have to get the magnitude first
[tex]\begin{gathered} \text{Magnitude}=\sqrt[]{x^2+y^2} \\ \text{Magnitude}=\sqrt[]{(-5)^2+(-14)^2} \\ \text{Magnitude}=\sqrt[]{25+196} \\ \text{Magnitude}=221 \\ \text{Magnitude}=14.866 \end{gathered}[/tex]Next, we will have to get the direction
[tex]\begin{gathered} \text{direction}=\tan ^{-1}(\frac{y}{x}) \\ \text{direction}=\tan ^{-1}(\frac{-14}{-5}) \\ \text{direction}=\tan ^{-1}(2.8) \\ \text{direction}=70.346^0 \end{gathered}[/tex]So, since we know that the point is on the third quadrant, then
We will add 180 degrees (90 degrees from first and 90 degrees from the second quadrant)
So we will have
[tex]180^0+70.346^0=250.346^0[/tex]Thus the answer is
[tex]\mleft\Vert w\mleft\Vert=\mright?\mright?14.866,\theta=250.346^0[/tex]Solve the equation. 6x = 96a16b576c90d102
Answers
Answer
Option A is correct.
x = 16
Explanation
We are asked to solve the equation
6x = 96
Divide both sides by 6
(6x/6) = (96/6)
x = 16
Hope this Helps!!!
A. Show all of your work to solve each equation and to check for extraneous solutions:4. [√(2x^2 - 1)]=x
Answers
ANSWER:
x = 1
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]\sqrt{2x^2-1}=x[/tex]We solve for x:
[tex]\begin{gathered} 2x^2-1=x^2 \\ \\ 2x^2-x^2=1 \\ \\ x^2=1 \\ \\ x=\sqrt{1}=\pm1 \\ \\ \text{ we check:} \\ x=1 \\ \\ \sqrt{2\left(1\right)^2-1}=1 \\ \\ \sqrt{2-1}=1 \\ \\ 1=1 \\ \\ x=-1\rightarrow\text{ true} \\ \\ \sqrt{2\left(-1\right)^2-1}=-1 \\ \\ \sqrt{2^-1}=-1 \\ \\ 1=-1\rightarrow\text{ false} \end{gathered}[/tex]Therefore, the solution of the equation is x = 1
Type the equation for the graphbelow.Pi/3 2piy = [?] sin([ ]x)
Answers
To find the equation of the graph, what we do is to recognize some characteristics of a sine function:
- Amplitude: The amplitude of the sine function is the distance from the middle value or line running through the graph up to the highest point. In this case, the amplitude is 1.
- Period: The period of a sine function is defined as the length of one complete sine wave or one complete cycle of the curve. It can be found using the equation: P=2pi/B.
Why are these characteristics important?
Because the sine function has the following general form:
In this problem, we have A=1 and we know that the period equals 2pi/3. So,
Therefore, the equation of the graph is:
On a set of architectural drawings for a new school building the scale is 1/4 inch = 2 feet. Find the missing lengths of the rooms.
Answers
We have a scale for the drawing that is 1/4 inch = 2 feet.
This means that 1/4 inch in the drawing represent 2 feet in the real world.
1. Lobby.
The actual length is 16 feet.
If 2 feet are drawn in 1/4 inch (0.25), the drawing length is 2 inches
[tex]\frac{16*0.25}{2}=\frac{4}{2}=2[/tex]2. Principal's office
The drawing length is 1.25 inches.
We can calculate the actual length as:
[tex]1.25\cdot\frac{2}{0.25}=\frac{2.50}{0.25}=10[/tex]3. Library
The actual length is 20 feet.
We have discovered that we can transform this in drawing units (inches) multypling by 0.25/2=0.125.
[tex]20\cdot0.125=2.5[/tex]The drawing length is 2.5 inches.
4. School room
The drawing length is 3 inches.
We have discovered that we can transform this in actual length units by dividing by 0.125, or multiplying by 2/0.25=8:
[tex]3\cdot8=24[/tex]The actual length is 24 feet.
5. Science lab.
In the drawing has 1.5 inches, so we multiply by 8 and we get 1.5*8=12 feet.
The actual length is 12 feet.
6. Cafeteria
The actual length is 48 feet.
Then, the drawing length is 48*0.125=48/8=6 inches.
7. Music room
The drawing length is 4 inches.
Then, the actual length is 4*8=32 feet.
8. Gymnasium
The drawing length is 13 inches, so the actual length is 13*8=104 feet.
9. Auditorium
The actual length is 56 feet, so the drawing length is 56/8=7 inches.
10. Teachers lounge
The drawing length is 1.75 inches, so the actual length is 1.75*8=14 feet.
We can calculate the scale factor drawing to actual length as:
[tex]\frac{\text{drawing}}{\text{actual}}=\frac{\frac{1}{4}in}{2\text{ feet}}=\frac{1}{8}\cdot\frac{in}{\text{ feet}}\cdot\frac{1\text{ feet}}{12\text{ in}}=\frac{1}{96}[/tex]The scale is 1:96.
12) If the scale is 12 inches = 1 foot, the scale factor is:
[tex]\frac{\text{drawing length}}{\text{actual length}}=\frac{12\text{ in}}{1\text{ ft}}\cdot\frac{1\text{ ft}}{12\text{ in}}=1[/tex]The scale in this case is 1:1 (the drawing has the same size as the actual object).
14) We have a road which length is 30 cm.
The scale is 1 cm = 3.5 m.
We can calculate the actual length of the road as:
[tex]\text{Actual length}=30cm\cdot\frac{3.5\text{ m}}{1\text{ cm}}=105\text{ m}[/tex]The actual legth of the road is 105 meters.
What is the positon of the letter E on the number line and how can i write it as a fraction or mixed number
Answers
We are asked to identify the position of the letter E on the number line.
First of all, count the total number of spacings between 2 and 3.
There are a total of 7 spacings.
The letter E is at the 6th spacing.
So, we can write the position of the letter E in the mixed form as
[tex]2\frac{6}{7}[/tex]We can also re-write the above mixed number as a fraction
[tex]2\frac{6}{7}=\frac{2\times7+6}{7}=\frac{14+6}{7}=\frac{20}{7}[/tex]So, the position of the letter E on the number line as a fraction is 20/7
The cost in dollars of a class party is 59+13n, where n is the number of people attending. What is the cost of 44 people?
Answers
The function is:
C(n) = 59 + 13n
where n is the number of people, and C(n) is the cost of a class party.
To determine the value of C(n) where n = 44, just replace this value of n into the previous formula, and simplify the expression, just as folow:
C(44) = 59 + 13(44)
C(44) = 59 + 572
C(44) = 631
Hence, the cost for 44 people is 631 dollars.
A tailor cut 1/2 inch off a skirt and 1/6 inch off a pair of pants. which garment had the greater amount cut off
Answers
The garment that had the greater amount cut off is the skirt
Explanation:
Amount cut off from skirt = 1/2
Amount cut off from pants = 1/6
To determine the grament witht he greater cut, we need to find the LCM of the fractions
[tex]\text{LCM of the denominator, 2 and 6 = 12}[/tex][tex]\begin{gathered} \frac{1}{2},\frac{1}{6}=\frac{6(1),2(1)}{12}=\frac{6,\text{ 2}}{12} \\ \text{the fraction with higher number of numerator had the greater amount cut off} \end{gathered}[/tex]The fractor with higher number in the numerator = 1/2 has it has 6 has the numerator
In other words, 1/2 > 1/6
The garment that had the greater amount cut off is the skirt
What is the value of 2x in this equation?3(2x-5)-4x+8=-2x+1a. 8 b. -1c. 4d. -4
Answers
The value of (2x) after the solving the equation
[{3(2x-5) - 4x + 8} = (-2x + 1)] for the variable "x" will be 4.
As per the question statement, we are provided with an equation:
[{3(2x-5) - 4x + 8} = (-2x + 1)],
And we are required to calculate the value of (2x) from the solution of the above mentioned equation.
Given, [{3(2x-5) - 4x + 8} = (-2x + 1)]
Or, [{(6x - 15) - 4x + 8)} = (-2x + 1)]
Or, [{(6x - 4x) + (8 - 15)} = (-2x + 1)]
Or, [(2x - 7) = (-2x + 1)]
Or, [(2x + 2x) = (7 + 1)]
Or, (4x = 8)
Or, [x = (8/4)]
Or, (x = 2)
Or, [2x = (2 * 2)]
Or, (2x = 4)
Equation: An equation is a mathematical statement that determines the relation of equality among two or more expressions, by a connector "equal to" sign in between.To learn more about Equations, click on the link below.
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1. Which of the following is the value of -13 - 51 – 3? (A) -5 (B) -1 (C) 0 (D) 1 M
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The value of -|3-5|-3 is,
[tex]\begin{gathered} -|3-5|-3=-|-2|-3 \\ =-2-3 \\ =-5 \end{gathered}[/tex]Hence, Option A is right.
The graph of function fis shown.YA-10X-5g(x)ENTEENENEN-10-2-325(0,-2)-5Function g is represented by the table.-10(2,8)-1-16BUDETETIEREDIVITETITENTENTENDEUREN MEDIOEMED MERDENDENDIENTEDETETTETTEN VEDIMENMEDITED RENDUER TRENINEEEEE5ENITEDIOUS0-8101-42-2
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For function f:
According to the graph in the interval [0,2] the function is increasing.
Rate: 8 - 0 = 8
For function g:
According to the table g function is increasing.
Rate: -2 - ( -8) = -2 + 8 = 6
Answer: C. both functions are increasing but f is increasing faster
Use the formula t= ln2 over k that gives the time for a population, with growth rate k, to double, to answer the following questions. The growth model A=6e^0.001t describes the population, A, of a country in millions, t years after 2003. A. What is the country's growth rate? B. (After answering A I will assistance for question B following question A)
Answers
Answer:
A. k = 0.001
B. 693 years
Explanation:
An exponential function has the following form:
[tex]y=a\cdot e^{kt}[/tex]Where a is the initial value and k is the growth or decay rate.
So, if the equation is:
[tex]A=6e^{0.001t}[/tex]Therefore, the growth rate is 0.001.
Now, to know how long will it take the country to double its population, we can use the equation:
[tex]t=\frac{\ln 2}{k}[/tex]Where k is the growth rate. So, replacing k by 0.001, we get:
[tex]\begin{gathered} t=\frac{\ln 2}{0.001} \\ t=693.14\approx693\text{ years} \end{gathered}[/tex]Therefore, the country will double its population 693 years after 2003
1. Given triangle ABC, what is the length of the line segment connecting the midpoints of AC and BC?
A = (1,6)
B = (3,1)
C = (8,3)
Answers
The length of the line segment connecting the midpoints of AC and BC is 2.69 units.
We are given a triangle. The vertices of the triangle are A, B, and C. The coordinates of the vertices are A (1, 6), B (3, 1), and C (8, 3). We need to find the length of the line segment connecting the midpoints of AC and BC.
Let the midpoints of AC and BC be E and F.
The coordinates of the midpoint E are calculated below.
E = [(1 + 8)/2, (6 + 3)/2] = (4.5, 4.5)
The coordinates of the midpoint F are calculated below.
F = [(3 + 8)/2, (1 + 3)/2] = (5.5, 2)
The length of the line segment EF can be calculated by using the distance formula. Let the length of EF be represented by "L".
L = √[(4.5 - 5.5)² + (4.5 - 2)²]
L = √(1 + 6.25)
L = √7.25
L = 2.69
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James and Susan wish to have $10,000 available for their wedding in 2 years.
How much money should they set aside now at 6% compounded monthly in
order to reach their financial goal?
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They need to set aside $8871.86
Writing rational numbers as a decimal
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2. Let's convert the rational number as a decimal
[tex]-2\frac{4}{5}[/tex]The given number is a mixed number, so we need to convert it to rational.
[tex]-2\frac{4}{5}=-2+\frac{4}{5}=-\frac{6}{5}[/tex]Then: To convert -6/5 into a decimal number, divide 6 by 5:
6 divide by 5
5*1 = 5, then 6-5 = 1
6 l 5
1
--------------
6 l5
5 1
-------------
1 l 5
1
We add
Drag the preimage to the correct location on the graph.
Quadrilateral 2 is a reflection of a quadrilateral across line m. Where is the preimage for quadrilateral 2 located and what is its orientation?
Answers
It is true that the preimage of the quadrilateral labeled 1 is reflected across line M to produce 2. The preimage for quadrilateral 2 is located at exactly below the position of quadrilateral 2 as indicated in the attached image. Its orientation is °180 the current location of image 2.
What is a preimage?Preimage refers to a collection of some input set items that are handed to a function to get some output set elements. It is the opposite of the Image. Domain = all valid independent variable values. This is the input set of a function, also known as the set of departure.
The orientation (that is angular position or attitude or bearing, or direction) of an object, such as a line, plane, or rigid body, is described in geometry as part of how it is positioned in the space it inhabits.
Hence quadrilateral 2 is 180° reflected from the preimage, given that it was reflected across line m.
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took me an hour to figure it out
Step-by-step explanation:
A dilation by a scale factor od 2 centered at (2,-1) is performed on the triangle shown draw the resulting triange
Answers
Explanation:
The vertices of the triangle are:
• (2, -1)
,• (-3, -1)
,• (1,2)
The triangle is dilated by a scale factor of 2 with the center of dilation at (2, -1).
The coordinates of the image triangle are (-2,1), (0,5) and (-8, -1).
Answer:
The triangle and its image are attached below:
A group of people were asked "What time do you prefer to see a movie? The two way tablebelow represents the results by their age.Morning 4 2 12 25 4316-20 21-25 26-30 Over 30 TotalsAfternoon 8 12 18 32 70EveningTotals28 34 28 11 101Late Night 34 18 21 4 7774 66 79 72 291What the approximate probability that a person will be over 30 given they prefer afternoonmovies?
Answers
From theinformation given,
total number of people = 291
Number of persons over 30 that prefer afternoon movies = 32
Number of persons that prefer afternoon movies = 70
This is a conditional probability.
Recall, Probability of event A given event B = P(A and B)/P(B)
Thus,
Probability that a person will be over 30 given that they prefer afternoon movies = 32/70
By multiplying by 100, it becomes
32/70 x 100
= 46%
Probability that a person will be over 30 given that they prefer afternoon movies = 46%
Quadrilateral QRST with vertices Q (1,2), R(3,4), S(5,6) and T(2,7), is dilated by a factor of 2 with the center of dilation at the origin. what are the coordinates of the quadrilateral QRST
Answers
SOLUTION
Now, since the center of dilation is at the origin, to get the new coordinates of the vertices of the quadrilateral, we will simply multiply the coordinates by a the scale factor of 2. This becomes
d
[tex]undefined[/tex]Could you please help me out with this question ??
Answers
Given the polynomial function:
[tex]x^3-2x^2-x+2[/tex]Group the functions:
[tex](x^3-2x^2)-(x-2)[/tex]Factor out the greatest common factor from the parenthesis
[tex]\begin{gathered} x^2(x-2)-1(x-2) \\ (x^2-1)(x-2) \end{gathered}[/tex]Simplify fully to have:
[tex]\begin{gathered} (x^2-1)(x-2) \\ \lbrack(x^2-1^2)\rbrack(x-2) \\ (x+1)(x-1)(x-2) \end{gathered}[/tex]This gives the factored form of the given polynomial.
How many routes does this function have Y= -2x^2+12x-10
Answers
We have that the equation is equal to
[tex]-2(x-1)(x-5)[/tex]So the equation have two roots, x = 1 and x = 5.
A community service group spent Planet summer planting trees in City park the table shows the total of number of trees after a certain number of weeks how many trees were already planted in the park before the community group started to plant?
Answers
If we consider the number of weeks equals 0 as the moment where the group started to plant, we can notice that at this point there were already 16 trees, then the answer is 16 trees
Reflect the vector (-3,5) acrossthe x-axis.([?],[])
Answers
1) When we reflex across the x-axis we must follow this rule:
Pre-image Image
(x, y) ----------------> (x,-y)
2) Since we have a vector <-3,5> then reflecting it across the x-axis we'll have
Pre-image Image
<-3,5>---------> <-3, -5>
3) So the vector after the reflection is < -3,-5>