A sector of a circle has a central angle of 60∘ . Find the area of the sector if the radius of the circle is 9 cm.
Answers
Step-by-step explanation:
area of a sector is theta ÷360 ×πr²
Related Questions
match the system of equations with the solution set.hint: solve algebraically using substitution method.A. no solutionB. infinite solutionsC. (-8/3, 5)D. (2, 1)
Answers
We will solve all the systems by substitution method .
System 1.
By substituting the second equation into the first one, we get
[tex]x-3(\frac{1}{3}x-2)=6[/tex]which gives
[tex]\begin{gathered} x-x+6=6 \\ 6=6 \end{gathered}[/tex]this means that the given equations are the same. Then, the answer is B: infinite solutions.
System 2.
By substituting the first equation into the second one, we have
[tex]6x+3(-2x+3)=-5[/tex]which gives
[tex]\begin{gathered} 6x-6x+9=-5 \\ 9=-5 \end{gathered}[/tex]but this result is an absurd. This means that the equations represent parallel lines. Then, the answer is option A: no solution.
System 3.
By substituting the first equation into the second one, we obtain
[tex]-\frac{3}{2}x+1=-\frac{3}{4}x+3[/tex]by moving -3/4x to the left hand side and +1 to the right hand side, we get
[tex]-\frac{3}{2}x+\frac{3}{4}x=3-1[/tex]By combining similar terms, we have
[tex]-\frac{3}{4}x=2[/tex]this leads to
[tex]x=-\frac{4\times2}{3}[/tex]then, x is given by
[tex]x=-\frac{8}{3}[/tex]Now, we can substitute this result into the first equation and get
[tex]y=-\frac{3}{2}(-\frac{8}{3})+1[/tex]which leads to
[tex]\begin{gathered} y=4+1 \\ y=5 \end{gathered}[/tex]then, the answer is option C: (-8/3, 5)
System 4.
By substituting the second equation into the first one, we get
[tex]-5x+(2x-3)=-9[/tex]By combing similar terms, we have
[tex]\begin{gathered} -3x-3=-9 \\ -3x=-9+3 \\ -3x=-6 \\ x=\frac{-6}{-3} \\ x=2 \end{gathered}[/tex]By substituting this result into the second equation, we have
[tex]\begin{gathered} y=2(2)-3 \\ y=4-3 \\ y=1 \end{gathered}[/tex]then, the answer is option D
3 166.40 266.24 3. Consider the following functions which all have an or decay? By what percent? Rewrite as (1+r) or (1-r) f(t) = 30(1.04) p(x) = 30(0.65)Solve f(t)
Answers
ANSWER
Function f(t) represents a growth by 4%
EXPLANATION
If the function represents a decay it is written as:
[tex]f(t)=a(1-r)^t[/tex]and if it represents a growth it's:
[tex]f(t)=a(1+r)^t[/tex]We can see if it's a growth or decay by looking at the number we have between parenthesis: if it's greater than 1, then it's a growth and if it's less than 1 then it's a decay.
For function f(t) we have
[tex]1+r=1.04[/tex]Therefore, r = 0.04 which, expressed as a percent is 4%
A half-marathon has 53 runners. A first-, second-, and third-place trophy will be awarded. Howmany different ways can the trophies be awarded?
Answers
Let's use the combination formula:
[tex]\begin{gathered} C(n,k)=nCk=\frac{n!}{k!(n-k)!} \\ n=53 \\ k=3 \\ C(53,3)=53C3=\frac{53!}{3!(50)!}=23426 \end{gathered}[/tex]Can you please help me because I don’t understand this and I would like to really understand it
Answers
Answer:
Explanation:
Given the expression:
[tex]\sqrt{12(x-1)}\div\sqrt{2(x-1)^{2}}[/tex]By the division law of surds:
[tex]\sqrt[]{x}\div\sqrt[]{y}=\sqrt[]{\frac{x}{y}}[/tex]Therefore:
[tex]\sqrt[]{12(x-1)}\div\sqrt[]{2(x-1)^2}=\sqrt[]{\frac{12(x-1)}{2(x-1)^2}}[/tex]The result obtained can be rewritten in the form below:
[tex]=\sqrt[]{\frac{2\times6(x-1)}{2(x-1)(x-1)^{}}}[/tex]Canceling out the common factors, we have:
[tex]=\sqrt[]{\frac{6}{(x-1)^{}}}[/tex]An equivalent expression is Opt
solving systems by graphing and tables : equations and inequalities
Answers
Given,
The system of inequalitites are,
[tex]\begin{gathered} 2x+3y>0 \\ x-y\leq5 \end{gathered}[/tex]The graph of the inequalities is,
The are three possible solution for the inequality.
For (0, 0),
[tex]\begin{gathered} 2x+3y>0 \\ 2(0)+3(0)>0 \\ 0>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 0-0\leq5 \\ 0\leq5 \end{gathered}[/tex]For (3, -2),
[tex]\begin{gathered} 2x+3y>0 \\ 2(3)+3(-2)>0 \\ 0>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 3-(-2)\leq5 \\ 5=5 \end{gathered}[/tex]For (5, 0),
[tex]\begin{gathered} 2x+3y>0 \\ 2(5)+3(0)>0 \\ 5>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 5-(0)\leq5 \\ 5=5 \end{gathered}[/tex]Hence, the solution of the inequalities is (5, 0).
Find five soloutions of the equation select integer values for X starting with -2 and ending with 2. Complete the table of value below y=6x-8
Answers
The five solutions of the equation y = 6x - 8 for x starting with -2 and ending with 2 are: (-2, -20), (-1, -14), (0, -8), (1, -2) and (2, 4)
In this question, we have been given an equation y = 6x - 8
We need to find five solutions of the equation select integer values for x starting with -2 and ending with 2.
For x = -2,
y = 6(-2) - 8
y = -20
For x = -1,
y = 6(-1) - 8
y = -14
For x = 0,
y = 6(0) - 8
y = -8
For x = 1,
y = 6(1) - 8
y = -2
For x = 2,
y = 6(2) - 8
y = 4
Therefore, five solutions of the equation y = 6x - 8 for x starting with -2 and ending with 2 are: (-2, -20), (-1, -14), (0, -8), (1, -2) and (2, 4)
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“Use the properties to rewrite this expression with the fewest terms possible:3+7(x - y) + 2x - 5y”
Answers
Expanding 7(x - y) in the above expression gives
[tex]-5y^{}+2x+7x-7y+3[/tex]adding the like terms (2x+ 7x) and (-5y-7y) gives
[tex](-5y-7y)+(2x+7x)+3[/tex][tex]\rightarrow\textcolor{#FF7968}{-12y+8x+3.}[/tex]The last expression is the simplest form we can convert our expression into.
An airplane is taking off at angle of 9 degrees and traveling at a speed of 200 feet per second in relation to the ground. If the clouds begin at an altitude of 4,000 feet, how many seconds will it take for the airplane to be in the clouds?
Answers
ANSWER
[tex]\begin{equation*} 127.85\text{ }seconds \end{equation*}[/tex]EXPLANATION
First, let us make a sketch of the problem:
To find the time it will take the airplane to be in the clouds, we first have to find the distance flown by the airplane in attaining that height, x.
To do this, apply trigonometric ratios SOHCAHTOA for right triangles:
[tex]\sin9=\frac{4000}{x}[/tex]Solve for x:
[tex]\begin{gathered} x=\frac{4000}{\sin9} \\ x=25,569.81\text{ }ft \end{gathered}[/tex]Now, that we have the distance, we can solve for the time by applying the relationship between speed and distance:
[tex]\begin{gathered} speed=\frac{distance}{time} \\ \Rightarrow time=\frac{distance}{speed} \end{gathered}[/tex]Substitute the given values into the formula above and solve for time:
[tex]\begin{gathered} time=\frac{25569.81}{200} \\ time=127.85\text{ }seconds \end{gathered}[/tex]That is the number of seconds that it will take.
What is the measure of EDH?EHFO 10°O 40°50°90
Answers
To find the measure of angle EDH we must solve for x first. Formulating an equation to find x, we have:
5x + 4x= 90 (Given that the sum of the angles EDH and HDG is equal to 90°)
9x = 90 (Adding like terms)
x= 90/9 (Dividing on both sides of the equation by 9)
x= 10
Replacing in the expression for angle EDH, we have:
m∠EDH = 5*(x) = 5*(10) = 50° (Multiplying)
The answer is m∠EDH =50°.
Help me with my schoolwork what is the slope of line /
Answers
The two points given on the line are
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(-2,9) \\ (x_2,y_2)\Rightarrow(6,1) \end{gathered}[/tex]The slope of line that passes through (x1,y1) and (x2,y2) is gotten using the formula below
[tex]\begin{gathered} m=\frac{\text{change in y}}{\text{change in x}} \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{1-9}{6-(-2)} \\ m=-\frac{8}{6+2} \\ m=-\frac{8}{8} \\ m=-1 \end{gathered}[/tex]Therefore,
The slope of the line = -1
A psychology test has personality questions numbered 1, 2, 3, intelligence questions numbered 1, 2, 3, 4, and attitudequestions numbered 1,2. If a single question is picked at random, what is the probability that the question is an intelligence question OR has an odd number?
Answers
Answer:
7/9.
Step-by-step explanation?
Total number of questions: 3 + 4 + 2 = 9.
Number of Intelligence questions: 4
Number of questions that have an odd number: 5
The probability of a question is Intelligence questions = 4/9
The probability a question has an odd number = 5/9
The probability a question is Intelligence questions and has an odd number = 2/9
The probability a question is Intelligence question OR has an odd number is:
4/9 + 5/9 - 2/9 = 7/9.
If a and b are the measure of two first quadrant angles, find the exact value of the functioncsc a =5/3 and tan 5/12 find the cod (a+b)
Answers
Input data
[tex]\begin{gathered} \cos a=\frac{5}{3} \\ \tan b=\frac{5}{12} \end{gathered}[/tex]
Now for cos(a+b)
[tex]\begin{gathered} a=\csc ^{-1}(\frac{5}{3})^{} \\ a=36.87 \end{gathered}[/tex][tex]\begin{gathered} b=\tan ^{-1}(\frac{5}{12}) \\ b=22.62 \end{gathered}[/tex][tex]\begin{gathered} \cos (a+b) \\ \cos (36.87+22.62) \\ \cos 59.5 \\ \frac{33}{65}=0.507 \end{gathered}[/tex]an acre is one chain multiplied times one furlong. I know from horse racing that there are 8furlongs in one mile. I remember that there are 640acres in one square mile. How many feet are in one chain?
Answers
Based on the acres in one square mile and the number of furlongs, the number of feet in one chain is 66 feet.
How to find the number of feet?First, find the number of feet in 1 furlong:
8 furlongs = 1 mile
This means that 1 furlong is 1/8 miles. In feet this is:
= 1/8 x 5,280 feet per mile
= 660 feet
Then, it is said that an acre is equal to a Chain x a Furlong.
This means that 1 chain is:
= Number of acres per square feet / Number of feet in chain
= 43,560 / 660
= 66 ft
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Ms. Mistovich and Ms. Nelson are having a competition to see who can get morestudents to bring in extra tissues for their classroom. Ms. Mistovich starts with 4 boxesand each week she gets two more boxes from her students. Ms. Nelson starts with 1box and each week she gets 3 more boxes from her students. Write a system ofequations to represent the situation. (1 pt)y=2x+4y=3x+1Ooy=2x+4y=2x+3y=4x+2y=3x+1y=2x+3y=4x+1o
Answers
To write an equation, it is enough to know the rate of change (slope) and the initial value (y-intercept).
The equation of a line of slope m and y-intercept b is:
[tex]y=mx+b[/tex]For Ms. Mistovich, the initial value is 4 and the rate of change is 2.
For Ms. Nelson, the initial value is 1 and the rate of change is 3.
Therefore, the equations that model this situation, are:
[tex]\begin{gathered} y=2x+4 \\ y=3x+1 \end{gathered}[/tex]hannah paid 15.79 for a dress that was originally marked 24.99 what js the percent of discount
Answers
The percentage of discount is 37%
Here, we want to calculate the percentage of discount
The first thing we need to do here is to calculate the discount amount
Mathematically, we have this as;
[tex]24.99-15.79\text{ = 9.2}[/tex]Now, we find the percentage of 24.99 is this discount
We have this as;
[tex]\frac{9.2}{24.99}\text{ }\times100\text{ \% = 36.8\%}[/tex]The percentage of discount is approximately 37%
w=3? What is the value of the expression below when w = 5w+ 2
Answers
Answer:
The value of the expression at w=3 is;
[tex]17[/tex]Explanation:
Given the expression;
[tex]5w+2[/tex]Then when w=3, the value of the expression is;
[tex]\begin{gathered} 5w+2 \\ =5(3)+2 \\ =15+2 \\ =17 \end{gathered}[/tex]The value is gotten by replacing/substituting w with 3 in the expression;
Therefore, the value of the expression at w=3 is;
[tex]17[/tex]3/5 ÷ 1/3 = ?????????
Answers
Change the division sign to multiplication and then invert 1/3
That is;
[tex]\frac{3}{5}\times3[/tex][tex]=\frac{9}{5}\text{ =1}\frac{4}{5}[/tex]Calculate Sse for the arithmetic sequence {a,}5sequence {1,3 ={}+}=Ο Α. 1463OB. 91220 C. 8,6716D. 9,26767
Answers
Answer:
[tex]\frac{8,671}{6}[/tex]Explanation:
Here, we want to get the sum of the 58 terms in series
Mathematically, we have the formula to use as:
[tex]S_n\text{ = }\frac{n}{2}(a\text{ + L)}[/tex]where a is the first term and L is the last term
The first term is when n is 1
We have this calculated as:
[tex]\text{ a}_{}\text{ = }\frac{5}{6}+\frac{1}{3}\text{ = }\frac{5+2\text{ }}{6}\text{ = }\frac{7}{6}[/tex]The last term is the 58th term which is:
[tex]\text{ a}_{58}\text{ = }\frac{290}{6}\text{ + }\frac{1}{3}\text{ = }\frac{292}{6}[/tex]We finally substitute these values into the initial equation
Thus, we have it that:
[tex]S_{58}\text{ = }\frac{58}{2}(\frac{292}{6}+\frac{7}{6})\text{ = 29(}\frac{299}{6})\text{ = }\frac{8671}{6}[/tex]
The function is defined by h(x) = x - 2 . Find h(n + 1) .
Answers
SOLUTION:
Case: Functions
Method:
The function
[tex]\begin{gathered} h(x)=x-2 \\ Hence \\ h(n+1)=(n+1)-2 \\ h(n+1)=n+1-2 \\ h(n+1)=n-1 \end{gathered}[/tex]Final answer:
[tex]h(n+1)=n-1[/tex]i need help, plotting the ordered pair (0, 0.5) and I need to state in which quadrant or on which axis the point lies.
Answers
The ordered pair:
[tex](x,y)=(0,0.5)[/tex]it is located at:
Since the point lies on the y-axis it doesn't not lie in any quadrant
Which representation does not show y as a function of x?1.II.€9> 10III.x 1 3 5 7y -6 -18 -30 -42IV. {(-2,3), (-1,4), (0,4), (3, 2)}a) I and IIb) I, II, and IIIc) I and IVd) All of the above are functions
Answers
We can say that I is not a function because inputs can only have one output.
II it's not a function since if you draw an horizontal line through the function intersect in two points, then it's not a function.
The answer is A.
Jina opened a savings account with $600 and was paid simple interest at an annual rate of 3%. When Jina closed the account, she was paid $54 in interest. How long was the account open for, in years?
Answers
Answer: The account has been open for 3 years
Step-by-step explanation:
3% of $600 is 18
18*3 = 54
Answer:
3 years
have $600
interest $54
annual rate 3%
600 - 3% = 582 that is the money she has in bank without interest
600-582 = 18
54÷ 18= 3 years
Which of the following statements about the table is true?
Select all that apply.
The table shows a proportional relationship.
All the ratios for related pairs of x and y are equivalent to 7.5.
When x is 13.5, y is 4.5.
When y is 12, x is 4.
The unit rate of for related pairs of x and y is .
26
22 Undertond Proportional Relationships: Fouivalent Ratios
C
C
y
10.5 3.5
15.9 5.3
22.5 7.5
27
9
3
Answers
Answer:
there is a lot of ratios here, but I will try my best. A proportional relationship is the relationship that is proportional obviously. and if the ratio is related, pairs are equivalent to 7.5 then that must mean that the proportional relationship is fuevalent
If TW =6, WV =2, and UV =25, find XV to the nearest hundredth.
Answers
TW = 6
WV = 2
UV = 25
XV = ?
XV/UV = WV/TV
XV/25 = 2 /(6 + 2)
XV = 2(25)/7
XV = 50/7
XV = 7.1428
Rounded to the nearest hundredth
XV = 7.14
why does a cubic graph have both an x intercept and a y intercept
Answers
Answer:
All cubic function has domain (-∞,∞) and range (-∞,∞)
Step-by-step explanation:
Raphael has an odd-shaped field shown in Figure 13-2. He wants to put a four-strand barbed wire fence around it for his cattle.A. What is the perimeter of the field?b. How many 80-rod rolls of barbed wire does he need topurchase?c. How many acres will be fenced?
Answers
Answer: Total perimeter = 9, 962.01 feet
The figure is a composite structure
It contains a rectangle and triangle
The perimeter of a rectangle is given as
Perimeter = 2( length + width)
length of the rectangle = 1500ft
Width of the rectangle = 1390 ft
Perimeter = 2( 1500 + 1390)
Perimeter = 2(2890)
Perimeter = 5780 ft
To calculate the perimeter of a triangle
[tex]\begin{gathered} \text{Perimeter = a + b + }\sqrt[]{a^2+b^2} \\ a\text{ = 1050ft and b = 1390 ft} \\ \text{Perimeter = 1050 + 1390 + }\sqrt[]{1050^2+1390^2} \\ \text{Perimeter = 2440 + }\sqrt[]{1,102,\text{ 500 + 1, 932, 100}} \\ \text{Perimeter = 2400 + }\sqrt[]{3,034,600} \\ \text{Perimeter = 2440 + 1,742,01} \\ \text{Perimeter = }4182.01\text{ f}eet \end{gathered}[/tex]The total perimeter of the field = Perimeter of the rectangle + perimeter of the right triangle
Total perimeter = 5780 + 4182.01
Total perimeter = 9, 962.01 feet
Question 13 of 18Graph the solution to the following inequality on the number line.x² - 4x ≥ 12
Answers
Step 1
Given; Graph the solution to the following inequality on the number line.
x² - 4x ≥ 12
Step 2
[tex]\begin{gathered} x^2-4x\ge \:12 \\ Rewrite\text{ in standard form} \\ x^2-4x-12\ge \:0 \\ Factor\text{ the inequality} \\ \left(x+2\right)\left(x-6\right)\ge \:0 \end{gathered}[/tex][tex]\begin{gathered} Identify\text{ the intervals} \\ x\le \:-2\quad \mathrm{or}\quad \:x\ge \:6 \end{gathered}[/tex]Thus, the number line will look like
Answer; The solution to the inequality graphed on a number line is seen below
[tex]x\le \:-2\quad \mathrm{or}\quad \:x\ge \:6[/tex]Some airlines charge a fee for each checked luggage item that weighs more than 21,000 grams. How many kilograms is this?
Answers
The value of 21,000 grams to kilograms is 21 kilograms
How to convert kilograms to grams ?1000 grams = 1kg
The first step is to convert 21,000 grams to kilograms
It can be calculated as follows;
= 21000/1000
= 21
Hence the value of 21,000 grams in kilograms is 21 kilograms
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Determine the minimum and maximum value for f(x) = -5x²-3x+7 over interval [-1, 3].
Answers
The maximum and minimum value of the equation "f(x) = -5x²-3x+7" over the interval [-1, 3] is 5 and -47.
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. A number that can be entered for the variable to produce a true number statement is the solution to an equation. 3(2)+5=11, which states that 6+5=11, is accurate. The answer is 2, then. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the minimum and maximum values when x are -1 and 3:
(1) When x = -1:
f(x) = -5x²-3x+7f(x) = -5(-1)²-3(-1) +7f(x) = -5(1) + 3 +7f(x) = -5 + 10f(x) = 5(2) When x = 3:
f(x) = -5x²-3x+7f(x) = -5(3)² -3(3)+7f(x) = -5(9) -9 +7f(x) = -45 -9 +7f(x) = - 54 + 7f(x) = - 47Therefore, the maximum and minimum value of the equation "f(x) = -5x²-3x+7" over the interval [-1, 3] is 5 and -47.
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Find the area of the circle. Use 3.14 or 227for π . thxQuestion 2
Answers
Step 1
State the area of a circle using the diameter
[tex]\frac{\pi d^2}{4}[/tex]Where d=diameter=28in
[tex]\pi=\frac{22}{7}[/tex]Step 2
Find the area
[tex]A=\frac{22}{7}\times\frac{28^2}{4}=616in^2[/tex]Answer;
[tex]Area\text{ = }616in^2\text{ when }\pi\text{ =}\frac{22}{7}[/tex]