Find the complete perimeter of the sector that intercepts arc AC.
Round to the nearest hundredth.
Answers
Calculate for the circumference of the circle with the equation,
C = 2πr
where C is circumference and r is radius. Substitute the known value for r,
C = 2π(7) = 43.98
Then, multiply the obtained value by the ratio of the angle intercepted and the whole revolution.
Arc = 43.98 x (45°/360°)
Arc = 5.5
The whole perimeter of the sector includes the arc and 2 radii. Hence, the equation for the whole perimeter is,
Perimeter = Arc + 2r
Substituting the values,
Perimeter = (5.5) + 2(7)
Perimeter = 19.50
ANSWER: 19.50 units
Related Questions
Need help with this please
Answers
A. Move the graph of y=[x] UP 3 units
B. Move the graph UP 1 unit
C. Move the graph DOWN 1 unit
D. Move the graph DOWN 3 units
The graph you're given on the problem screen is not a very good one, I think. Would it help to draw y = [x] on a piece of graph paper where one square = 1 unit? The graph you're shown has one square = 2 units, which could lead to some confusion.
So, draw the graph of y = [x], then figure out which way the graph was moved -- and how far -- to get the graph in the problem.
Here is a link to a YouTube video that might help a lot.
https://youtu.be/UQ3a2QH_-GU
Avery can run at 10 uph. The bank of a river is represented by the line 4x + 3y = 12, and Avery is at (7, 5). How much time does Avery need to reach the river?
Answers
4x+3y=12
3y=-4x+12
y=-4x/3+12/3
So a line perpendicular to the bank will be:
y=3x/4+b, and we need it to pass through (7,5) so
5=3(7)/4+b
5=21/4+b
20/4-21/4=b
-1/4=b so the perpendicular line is:
y=3x/4-1/4
So now we want to know the point where this perpendicular line meets with the river bank. When it does y=y so we can say:
(3x-1)/4=(-4x+12)/3 cross multiply
3(3x-1)=4(-4x+12)
9x-3=-16x+48
25x=51
x=51/25
x=2.04
y=(3x-1)/4
y=(3*2.04-1)/4
y=1.28
So now that we know the point on the river that is closest to Avery we can calculate his distance from that point...
d^2=(x2-x1)^2+(y2-y1)^2
d^2=(7-2.04)^2+(5-1.28)^2
d^2=38.44
d=√38.44
d=6.2 units
Since he can run at 10 uph...
t=d/v
t=6.2/10
t=0.62 hours (37 min 12 sec)
So it will take him 0.62 hours or 37 minutes and 12 seconds for him to reach the river.
How many three digit numbers can be made from the digits 1,\ldots,9 if repetitions of digits are not allowed?
Answers
9*8*7 = 504
Look at a simpler example, with 1, 2, 3:
123
132
213
231
312
321
6 numbers
3*2*1 = 6
There are 84 three digit numbers can be made from the digits 1, ..., 9
What is Combination?
A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
The numbers are,
⇒ 1, 2, ..., 9
Now,
All the three digit numbers can be made from the digits 1, ..., 9 are;
⇒ [tex]^{9} C_{3}[/tex]
⇒ 9! / 3! 6!
⇒ 9 × 8 × 7 / 6
⇒ 84
Thus, There are 84 three digit numbers can be made from the digits
1, ..., 9.
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Toby gets 78 votes, which is 52% of the total votes cast. How many students voted in Toby’s grade?
Answers
52% = 0.52
78/0.52 =150
150 students voted
Find the probability of at least 2 girls in births. Assume that male and female births are equally likely and that the births are independent events. Round to three decimal places.
Answers
Male and FemaleMale and Male Female and Male Female and Female
All four variants are equally likely.Probability of each one is 1/4 = 0.25.So, Result "Female and Female"
are probability = 0.250 --- if round to three decimal places.
What value of x makes the denominator of the function equal zero? y= 6/4x-40
Answers
4x - 40 = 0
Add 40 to both sides.
4x = 40
Divide both sides by 4
x = 10
The value of x makes the denominator of the function equal zero is 10
what is an equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
Given that:
y = [tex]\frac{6}{4x-40}[/tex]
Now the denominator is: 4x - 40
So, 4x =40
x =40/4
x =10
So, make the denominator 0, put x= 10.
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It costs $35$35 per hour to rent a boat at the lake. You also need to pay a $25$25 fee for safety equipment. You have $200$200. For how long can you rent the boat?
Answers
During one year about 163 million adults over 18 years old in the United States spent a total of about 93 billion hours online at home. On average, how many hours per day did each adult spent online at home?
1. How do you write each number in scientific notation?
2 How do you convert the units to hours per day.
Answers
[tex]\bf 163,000,000\implies 163\times 10^6 \\\\\\ 93,000,000,000\implies 93\times 10^9\\\\ \cfrac{93\times 10^9}{163\times 10^6}\impliedby \textit{hours per year for one adult} \\\\\\ \cfrac{93\times 10^9\times 10^{-6}}{163}\implie
s \cfrac{93\times 10^{9-6}}{163}\implies \cfrac{93\times 10^3}{163}[/tex]
that's how many hours each adult spent a year... now, how many hours is that per day? well, there are 365 days a year, so, we simply divide it by 365
[tex]\bf \cfrac{\frac{93\times 10^3}{163}}{365}\implies \cfrac{\frac{93\times 10^3}{163}}{\frac{365}{1}}\implies \cfrac{93\times 10^3}{163}\cdot \cfrac{1}{365}\implies \cfrac{93\times 10^3}{163\cdot 365}\quad \cfrac{hours}{day}[/tex]
Final answer:
To write each number in scientific notation, express it as a product between 1 and 10 and a power of 10. Each adult spent an average of 570.55 hours per day online at home.
Explanation:
To write each number in scientific notation, we need to express it as a product of a number between 1 and 10 and a power of 10.
163 million can be written as 1.63 x 10⁸
93 billion can be written as 9.3 x 10¹⁰
To convert the units to hours per day, we need to divide the total number of hours by the number of adults.
So, each adult spent an average of (93 x 10¹⁰) / (163 x 10⁸) = 570.55 hours per day online at home. Scientific notation simplifies large numbers, facilitating computations and providing a concise representation of quantities in mathematical contexts.
Solve the following system by graphing.
x - y = 4
x + y = 2
What is the solution of the system?
(3, -1)
(3, 1)
(-1, 3)
Answers
the solution is : (3, -1)
put x= 3 and y = -1
you have : 3-(-1) = 4 and 3+(-1) = 2 ..... right
The solution for the system of equation x - y = 4 and x + y = 2 is (3, -1).
What is an equation ?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given pair of equations,
x - y = 4 (1)
And x + y = 2 (2)
To find the solution of the equations,
Add both the equations,
x - y + x + y = 4 + 2
2x = 6
x = 3,
Substitute the value of x = 3 in equation (1),
3 - y = 4
y = -1
The values of x and y are 3 and -1 respectively.
Hence, option (A) is correct.
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Answer please math isn't my forte
Answers
x + 5 < 14
Subtract 5 on both sides
x + 5 - 5 < 14 - 5
x < 14 - 5
x < 9
Answer is D.
5)
< (less than) and > (greater than) have empty circles because the number is not included.
For example, x > 5
5 is not a solution because we are looking for all x that is greater than 5.
≤ (less than or equal to) and ≥ (greater than or equal to) have a closed circle because the number is included.
For example, x ≤ 7
7 is a solution because we are looking for all x that is less than or equal to 7.
Answer is C.
6)
4(x-1) ≥ 8
Divide 4 on both sides
(x-1) ≥ 2
Add 1 on both sides
x ≥ 3
Answer is D.
Rationalize the denominator
Answers
Answer:
[tex]\frac{60 - 10\sqrt10-6\sqrt3+\sqrt30}{97}[/tex]
Step-by-step explanation:
Hello!
To rationalize the denominator, we have to remove any root operations from the denominator.
We can do that by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate simply means the same terms with different operations.
Rationalize[tex]\frac{6 - \sqrt10}{10 + \sqrt3}[/tex][tex]\frac{6 - \sqrt10}{10 + \sqrt3} * \frac{10 - \sqrt3}{10 - \sqrt3}[/tex][tex]\frac{(6 - \sqrt10)(10 - \sqrt3)}{100 - 3}[/tex][tex]\frac{60 - 10\sqrt10-6\sqrt3+\sqrt30}{97}[/tex]The answer is [tex]\frac{60 - 10\sqrt10-6\sqrt3+\sqrt30}{97}[/tex].
Find all complex solutions of 3x^2+3x+4=0.
(If there is more than one solution, separate them with commas.)
Answers
Now we can compare it with general form of quadratic equation ([tex]ax^2 + bx + c = 0[/tex])
a = 3 , b = 3 and c = 4
Now we can apply quadratic formula which is given as
[tex]x =\frac{ -b+/- \sqrt{b^2-4ac} }{2a}[/tex]
Now we can plugin value of a , b or c
[tex]x = \frac{-3+/- \sqrt{(3)^2 - 4*3*4} }{2*3} [/tex]
[tex]= \frac{-3+/- \sqrt{9 - 48} }{6} = \frac{-3+/- \sqrt{-39} }{6} [/tex]
In general we know [tex] \sqrt{-1} = i [/tex]
So we can write [tex] \sqrt{-39 } = \sqrt{-1} * \sqrt{39} = i \sqrt{39} [/tex]
So
[tex]x = \frac{-3+/-i \sqrt{39} }{6} [/tex]
So [tex]x = \frac{-3+i \sqrt{39} }{6} [/tex] or [tex]x = \frac{-3- \sqrt{39} }{6} [/tex]
The complex solutions to the equation[tex]3x^2+3x+4=0 are x = (-3 + i\sqrt{39})/6 and x = (-3 - i\sqrt{39})/6.[/tex]
Explanation:To find all complex solutions of the quadratic equation [tex]3x^2+3x+4=0[/tex]e the quadratic formula:
[tex]x = \((-b \pm \sqrt{b^2-4ac})/(2a)\).[/tex]
Here, a = 3, b = 3, and c = 4. Plugging these values into the formula, we get:
[tex]x = \((-3 \pm \sqrt{3^2-4 \cdot 3 \cdot 4})/(2 \cdot 3)\).[/tex]
This simplifies to:
[tex]x = \((-3 \pm \sqrt{-39})/6\).[/tex]
Since the discriminant (under the square root sign) is negative, we know that the solutions will be complex. Using i to represent the square root of -1, we can write the solutions as:
[tex]x = \((-3 \pm i\sqrt{39})/6\).[/tex]
So, the complex solutions are [tex]x = (-3 + i\sqrt{39})/6 and x = (-3 - i\sqrt{39})/6.[/tex]
Write 11•47 using the distributive property. Then simplify.
Answers
a (b+c) = ab + bc
Try writing 47 = 50-3 or 47 = 40+7.
11 x 47 = 11 x (50-3) = 11 x 50 - 11 x 3 = 550 - 33 = 517
or
11 x 47 = 11 x (40+7) = 11 x 40 + 11 x 7 = 440 + 77 = 517
Four less than a number is greater than -28
Answers
Any number which is larger than -28 by at least 5 would work.
Examples, -23, 0, 99 etc.
Hope this helps!
How do I solve this
Answers
so, hmm which are those? let's check, let's set the denominator to 0, and solve for "x".
[tex]\bf x^2+6x-7=0\implies (x+7)(x-1)=0\implies x= \begin{cases} -7\\ 1 \end{cases} \\\\\\ \textit{let's check, } x=-7\quad \cfrac{(-7)+2}{(-7)^2+6(-7)-7}\implies \cfrac{-5}{49-42-7}\implies \cfrac{-5}{0} \\\\\\ x=1\quad \cfrac{(1)+2}{(1)^2+6(1)-7}\implies \cfrac{3}{1+6-7}\implies \cfrac{-3}{0}[/tex]
Write 5000 = 12 as an order pair
Answers
Which expression is equivalent to (cos x)(tan(–x))?
A. -sin x
B. sin x
C. -csc x
D. csc x
Answers
[tex][cos(x)][tan(-x)][/tex] is the same as [tex][cos(x)][ -\frac{sin(x)}{cos(x)}] [/tex]
We can now cancel out the cos(x), which leaves us only with -sin(x) remaining. So your answer is A.
A quadratic equation has a discriminant of 0. which describes the number and type of solutions of the equation?
Answers
Discriminant 0 in quadratic equation means 1 real solution—a repeated root where parabola touches x-axis once.
When the discriminant of a quadratic equation is 0, it means that the quadratic equation has exactly one real solution. This solution is considered a "double root" or "repeated root," meaning that the parabola defined by the quadratic equation touches the x-axis at exactly one point. Mathematically, this occurs when the quadratic equation has two identical roots.
The general form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex], and the discriminant, denoted by [tex]\(b^2 - 4ac\),[/tex] helps determine the nature of the roots.
When the discriminant is zero [tex](\(b^2 - 4ac = 0\))[/tex], the quadratic equation has one real root. This happens when the parabola defined by the equation just touches the x-axis at one point. The solution is given by:
[tex]\[x = \frac{{-b \pm \sqrt{b^2 - 4ac}}}{{2a}}\][/tex]
The following conditions are:
D < 0 ; there are two non-real or imaginary roots which are complex conjugates
D = 0 ; there is one real root and one imaginary (non-real)
D > 0 ; there are two real distinct roots
Therefore the answer to this question is:
The solution has one real root and one imaginary root.
A cone has a volume of about 28 cubic inches. Which are possible dimensions for the cone?
Answers
So, as you see you have two variables, radius and height, which means that there are different combinations of radius and height that lead to the same volume.
That implies that your questions is missing some information.
I searched for it and found that the question has a list of answer choices. This is the list:
a) radius 6 inches, height 3 inches
b) diameter 6 inches, height 3 inches
c) diameter 4 inches, height 6 inches
d) diameter 6 inches, height 6 inches
Now you can probe those options to see which leads to an approximate volume of 28 cubic inches.
a) radius 6 in, height 3 in
=> V = (1/3)*3.14*(6in)^2 * 3in = 113.04 in^3 => not possible
b) diameter 6 in, height 3 inc
diameter 6 in => radius 3 in
=> V = (1/3)*3.14*(3in)^2 * 3in = 28.26 in^3 => this is the answer
The other options lead to values far from 28 in^3.
Answer: diameter 6 inches, height 3 inches.
what is the slope of a line that passes through (-4,-13) and (19,11)
Answers
m (gradient) = (y1 - y2) / (x1 - x2)
where (x1, y1) is the coordinate of the first point, and (x2, x2) is the coordinate of the second point
in your question:
x1 = -4
x2 = 19
y1 = -13
y2 = 11
m = (-13 -11) / (-4 -19) = -24 / -23 = 24/23 or 1.04 (2d.p.)
hope that helps :)
Answer:
24/23
Step-by-step explanation:
- vs - = + after -24,-23 =
Answer = 24, 23
What is the factored form of the expression k^2 - 9h^2
Answers
a^2 - b^2 = (a+b) (a-b)
So, what we need to do here is apply this equation:
k^2 - 9h^2 =
k * k - (3h)^2 =
(k + 3h) (k - 3h)
What kind of transformation is illustrated in this figure ?
Answers
PLEASE CAN SOMEONE HELP!!!????
Use elimination to solve for x and y:
−2x−y=9
2x−9y=1
My Choices are....
a. (−4,−1)
b. (−1,−4)
c. (5,1)
d. (−1,−7)
Answers
-2x-y=9
2x-9y=1 +
0x-10y=10
-10y=10
divide by -10
y=-1
sub back
-2x-y=9
-2x-(-1)=9
-2x+1=9
-2x=8
divide by -2
x=-4
y=-1
(x,y)
(-4,-1)
A
The values of x and y after solving both the equations by the elimination method are -4 and -1. So option A is correct
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
Two linear equations
−2x − y = 9
2x − 9y = 1
by using elimination method,
−2x − y = 9
2x − 9y = 1
0 - 10y = 10
y = -1
2x − 9× -1 = 1
2x = -8
x = -4
Hence, the values are, -4 and -1
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Explain what needs to happen to the inequality sign when dividing or multiplying by a negative number. a. nothing happens c. change the inequality sign to an equals sign b. flip the inequality sign d. the inequality needs to be graphed on a number line
Answers
so the answer is B
Answer:
(B) flip the inequality sign.
Step-by-step explanation:
If we consider an inequality such that [tex]-x\leq7[/tex], then if we multiply the inequality with a negative number such as [tex]-1[/tex], then the inequality becomes [tex]x\geq-7[/tex].
Also, if we divide the above inequality [tex]-x\leq7[/tex], by a negative number that is [tex]-1[/tex], then the inequality becomes [tex]x\geq-7[/tex].
Therefore, if we multiply or divide an inequality by a negative number, then it flips the inequality sign.
Hence, option (B) is correct.
Jake has proved that a function, f(x), is a geometric sequence. How did he prove that?
A He showed that an explicit formula could be created.
B He showed that a recursive formula could be created.
C He showed that f(n) ÷ f(n − 1) was a constant ratio.
D He showed that f(n) − f(n − 1) was a constant difference.
Answers
C. He showed that f(n)/(f(n-1) was a constant ratio.
Factor completely 36x2− 121.
Answers
Factorising (a² - b²) gives (a+b)(a-b)
Factorising 36x² - 121 gives (6x+11)(6x-11)
Find the volume of revolution bounded by the curves y = 4 – x2 , y = x, and x = 0, and is revolved about the vertical axis.
Answers
The rest of solution in the attachment.
There's a mistake in the picture
It shoud be
[tex]V=\pi\left(\dfrac{289\sqrt{17}-521}{60}\right)\approx35[/tex]
If XYZ measures 75, what is the measure of XWZ ? A. 285 B. 210 C. 75 D. 150
(Its a circle, and its saying that the arc is 775 and wants to know what the rest of the circle is)
Answers
The measure of XWZ is 285
what is arc?The arc of a circle is defined as the part or segment of the circumference of a circle.
Given:
<XYZ = 75
As, we know central angle of 360
So, arc(XWZ) + <XYZ = 360
arc (XWZ) = 360 - 75
arc(XWZ) = 285
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Permutations!!
If 9 actors must sit together how many ways are there to seat 13 people around the table?
Answers
To calculate the number of ways to seat 13 people around a table with 9 actors sitting together, we treat the 9 actors as one unit and then arrange the five units around the table, resulting in (4! * 9!) different possible arrangements.
Explanation:The question asks us to calculate the number of ways to seat 13 people around a table if 9 actors must sit together. This can be approached as a permutations problem in combinatorics.
Firstly, treat the 9 actors as one unit since they must sit together. With this in mind, we effectively have 5 units to arrange: the group of 9 actors and the remaining 4 individuals. As the seating arrangement is around a circular table, we can fix one person's seat and arrange the remaining units. As a result, there are (5-1)! ways to arrange these units since circular permutations eliminate the concept of a distinct 'starting' point that linear permutations have.
Now we need to consider the arrangements of the 9 actors within their group. Since their relative positions to each other matter, they can be permuted in 9! ways.
Therefore, the total number of seating arrangements would be the product of the two permutations: (5-1)! * 9!.
Calculating this gives us (4!) * 9! = (4*3*2*1) * (9*8*7*6*5*4*3*2*1) different possible arrangements.
in a certain county, the number of charter schools is 4 less than twice the number of alternative schools. We know that there are 48 charter schools in the county. How many alternative schools are in the county?
Answers
Answer:
There are [tex]26[/tex] alternative schools in the country
Step-by-step explanation:
Let
x------> the number of charter schools
y-----> the number of alternative schools
we know that
[tex]x=48[/tex]
[tex]x=2y-4[/tex] -----> equation A
substitute the value of x in the equation A and solve for y
[tex]48=2y-4[/tex]
[tex]2y=48+4[/tex]
[tex]2y=52[/tex]
[tex]y=26[/tex]