Explicit formula [tex]a_{n} =8n+15[/tex]
Recursive formula [tex]\left \{ {{a_{1} =23} \atop {a_{n}=a_{n-1}+8 }} \right.[/tex]
To solve this problem we have to use an arithmetic sequence. The cost of renting a kayak for 1 hour is $23, each additional hour is $8 more. So, the first element of the secuence will be 23 for one hour, then each addittional hour will be 23 + 8, making the secuence:
{23, 31, 39, 47, 55,.....,n}
Writing a recursive formula of the form [tex]a_{n} =a_{n-1} +d[/tex] where [tex]a_{n}[/tex] is the nth term, n the number of terms, and d the common difference in the secuence.
The common difference of the secuence {23, 31, 39, 47, 55,.....,n}. So, the first term is [tex]a_{1} =23[/tex], and the common diffenece is d = 8 which is the difference between each term.
[tex]\left \{ {{a_{1} =23} \atop {a_{n} =a_{n-1}+8 }} \right.[/tex]
Writing a explicit formula of the form [tex]a_{n} =a_{1} +d(n-1)[/tex] where where [tex]a_{n}[/tex] is the nth term, n the number of terms, [tex]a_{1}[/tex] the first term of the secuence, and d the common difference in the secuence.
With [tex]a_{1}=23[/tex], and d = 8:
[tex]a_{n} =23+8(n-1)[/tex]
[tex]a_{n} =23+8n-8[/tex]
[tex]a_{n} =8n+15[/tex]
find the area of the smaller sector (please help me(
Answer:
27
Step-by-step explanation:
If you repeat the perpendicular line segment construction twice using paper folding, you can construct:
A.the midpoint of a line segment.
B.an angle congruent to a given angle.
C.a parallel to a line through a point not on the line.
D.an angle bisector.
Final answer:
By repeating the perpendicular line segment construction twice using paper folding, one can effectively find the midpoint of a line segment, demonstrating the application of geometric principles and theorems related to perpendicular constructions.
Explanation:
If you repeat the perpendicular line segment construction twice using paper folding, you can construct the midpoint of a line segment. This is based on the principle that constructing perpendiculars at the ends of a given line segment and then erecting a third perpendicular midway between them will intercept the line segment at its midpoint. This is affirmed by the theorems that explain the geometrical properties and relationships of constructing perpendicular lines and their midpoints.
To elucidate, let's take a line segment AB of a certain length, and fold the paper to construct a perpendicular line at point A. Next, repeat the same action at point B. Now, fold the paper to find the midpoint of AB, and erect a perpendicular line at this midpoint. This results in the third perpendicular intersecting AB exactly at its midpoint, demonstrating that this method is effective for finding the midpoint of a line segment, thereby validating option A.
You can construct: The midpoint of a line segment.
The correct option is (A).
Paper folding constructions can be used to create geometric shapes and lines based on certain properties. Let's break down each of the given options and see if they can be achieved by repeating the perpendicular line segment construction twice:
A. The midpoint of a line segment: Yes, this can be achieved. Folding a line segment in half will give you its midpoint. By repeating the perpendicular line segment construction twice, you fold the line segment once to find a point equidistant from both endpoints (which is the midpoint), and folding it again should confirm that the resulting point is indeed the midpoint.
B. An angle congruent to a given angle: No, this cannot be achieved. The perpendicular line segment construction does not involve creating or manipulating angles, so it cannot be used to construct an angle congruent to a given angle.
C. A parallel to a line through a point not on the line: No, this cannot be achieved. The perpendicular line segment construction does not involve creating parallel lines.
D. An angle bisector: No, this cannot be achieved. Again, the perpendicular line segment construction does not involve manipulating angles, so it cannot be used to construct an angle bisector.
Therefore, the correct option is:
A. The midpoint of a line segment.
In a singing competition, there are
150 participants. At the end of each
round, 40% of the participants are
eliminated. How many participants
are left after n rounds?
Answer:
150(.40)^n is your equation
Step-by-step explanation:
Answer:
[tex]=150\cdot{0.4^n}[/tex]
Step-by-step explanation:
Let n be the number of rounds. Lets look at n=1 which is round one. Therefore if 40% of the contestants are eliminated then we can write an expression of the number of contestants eliminated:
[tex]=150\cdot{0.4}[/tex]
For round two, n=2:
[tex]=150\cdot{0.4)\cdot{0.4}=150\cdot{0.4^2}[/tex]
Therefore for the n number of rounds:
[tex]=150\cdot{0.4^n}[/tex]
plz answer asap i need to graduate this week
UNIT 3 REVIEW
Circle the correct answer to each of the following questions. All
answers are rounded to the second decimal place,
1. What is the volume of a building that is 18 meters long,
9 meters wide, and 6 meters high?
a. 948 meters b. 972 meters c. 984 meters
2. What is the volume of a fish tank that is 26 inches long,
14 inches wide, and 18 inches high?
a. 6552 inches b. 6844 inches 7208 inches
3. What is the volume of a cube with dimensions that are each
7.2 feet long?
a. 51.84 feet b. 373.25 feet c 2686.39 feet
4. What is the volume of a cube with dimensions that are each
4.5 yards long?
a. 20.25 yards' b. 67.29 yards' C 91.13 yards
Question 1:
For this case we have that by definition, the volume of a prism is given by:
[tex]V = a * b * c[/tex]
Where:
a: It is the long
b: It is the width
c: It is the height
According to the data we have:
[tex]a = 18m\\b = 9m\\c = 6m[/tex]
Substituting:
[tex]V = 18 * 9 * 6\\V = 972[/tex]
Thus, the volume of the building is[tex]972 \m ^ 3[/tex]
Answer:
Option B
Question 2:
For this case we have that by definition, the volume of a prism is given by:
[tex]V = a * b * c[/tex]
Where:
a: It's the long
b: It is the width
c: It is the height
According to the data we have:
[tex]a = 26in\\b = 14in\\c = 18in[/tex]
Substituting:
[tex]V = 26 * 14 * 18\\V = 6552[/tex]
Thus, the volume of the tank is [tex]6552 \in ^ 3[/tex]
Answer:
Option A
Question 3:
For this case we have that by definition, the volume of a cube is given by:
[tex]V = l ^ 3[/tex]
Where:
l: It's the side of the cube
According to the data we have that the cube side is 7.2ft.
Substituting we have:
[tex]V = (7.2) ^ 3\\V = 373.25[/tex]
Rounding off we have that the volume of the cube is [tex]373.25 \ ft ^ 3[/tex]
Answer:
Option B
Question 4:
For this case we have that by definition, the volume of a cube is given by the following formula:
[tex]V = l ^ 3[/tex]
Where:
l: It's the side of the cube
According to the data we have that the cube side is 4.5 yards.
Substituting we have:
[tex]V = (4.5) ^ 3\\V = 91.125[/tex]
Rounding off we have the cube volume is[tex]91.13 \ yd ^ 3[/tex]
Answer:
Option C
Perform the following calculation: 1.9 + 6.25 =
Answer:
8.15
Step-by-step explanation:
Step-by-step explanation:
1.9+6.25=8.15
1.9
+ 6.25
______
8.15
in a concert hall, 250 seats out of 300 were occupied. to the nearest thousand, what part of the hall was not occupied?
Answer: 0.167 is the part of the hall that was not occupied. Or 16.7 %
Step-by-step explanation:
300-250=50 this is the number of seats not occupied since 250 is the amount occupied.
So, 50/300=5/30 which can be converted to a number which is 0.1666666667. It says to round to the thousandths place, which is the 3rd number. That is 0.167
Answer:
0.167 part of the hall was not occupied
Step-by-step explanation:
Given :In a concert hall, 250 seats out of 300 were occupied.
To Find :To the nearest thousand, what part of the hall was not occupied?
Solution:
Total seats = 300
Occupied seats = 250
Unoccupied seats = 300-250 = 50
So, The part of the hall was not occupied = [tex]\frac{\text{unoccupied seats}}{\text{total seats}}[/tex]
= [tex]\frac{50}{300}[/tex]
= [tex]0.167[/tex]
Hence 0.167 part of the hall was not occupied
What is the quotient?
Answer:
4 x [tex]10^{12}[/tex])
Step-by-step explanation:
(6 x [tex]10^{8}[/tex]) / (1.5 x [tex]10^{-4}[/tex])
= ([tex]\frac{6}{1.5}[/tex] x [tex]10^{8}[/tex]) / ([tex]10^{-4}[/tex])
= ([tex]\frac{6}{1.5}[/tex] x [tex]10^{8}[/tex]) x ([tex]10^{4}[/tex])
= [tex]\frac{6}{1.5}[/tex] x [tex]10^{12}[/tex]
= 4 x [tex]10^{12}[/tex]
Step-by-step explanation:
6*10^8 /1.5*10^-4
6/1.5 * 10^8/10^-4
4 * 10^8-(-4)
4*10^8+4
4*10^12
what is the value of x?
Answer:
x = 3Step-by-step explanation:
∠QRT and ∠SRT are supplementary angles,
therefore m∠QRT + m∠SRT = 180°.
(45x)° + m∠SRT = 180° subtract (45x)° from both sides
m∠SRT = 180° - (45x)°
We know: the sum of the measures of the angles of the triangle is equal to 180 °. Therefore we have the equation:
(180 - 45x) + (57 + x) + 25x = 180 combine like terms
(-45x + x + 25x) + (180 + 57) = 180
-19x + 237 = 180 subtract 237 from both sides
-19x = -57 divide both sides by (-19)
x = 3
(29 PTS) Explain how the Quotient of Powers Property was used to simplify this expression. 3^4/9 = 3^2
A/ By simplifying 9 to 32 to make both powers base three and adding the exponents
B. By simplifying 9 to 32 to make both powers base three and subtracting the exponents
C. By finding the quotient of the bases to be 1/3 and simplifying the expression
D. By finding the quotient of the bases to be 1/3 and cancelling common factors
Answer:
B. By simplifying 9 to [tex]3^{2}[/tex] to make both powers base three and subtracting the exponents
Step-by-step explanation:
When you have a division the quotient of powers property states that the exponents should be substracted, and by simplifying 9 to [tex]3^{2}[/tex] you end up with an equation like this:
[tex]\frac{3^{4} }{3^{2} }[/tex]=[tex]3^{2}[/tex]
Then you just have to substract the exponent from the denominator from the numerator´s exponent, which would be:
4-2=2
and the resultant equation would be:
[tex]3^{2} =3^{2}[/tex]
The Quotient of Powers Property allows you to subtract exponents when dividing expressions with the same base. The expression 3^4/9 simplifies to 3^2 because 9 can be expressed as 3^2, therefore their exponents are subtracted (4-2=2).
Explanation:In this question, the Quotient of Powers Property is used. This property states that to divide where the base remains the same, you subtract the exponents. In the expression 3^4/9 = 3^2, we know that 9 can be expressed as 3^2.
Therefore, it becomes 3^4/3^2. According to the Quotient of Powers Property, we subtract the exponent of the denominator from the exponent of the numerator (4-2=2). Hence the expression simplifies to 3^2. The correct choice is B: By simplifying 9 to 3^2 to make both powers base three and subtracting the exponents.
Learn more about Quotient of Powers Property here:https://brainly.com/question/30354557
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Vertical? Obtuse? Straight or acute
Answer:
D. Acute
Step-by-step explanation:
This is an acute angle because the angle is less then 90 degrees.
<FOA is an Acute angle (D).
How I know...
Acute angles are angles are below 90 degrees (aka LESS then a right angle)
Hope this helped!
~Just a girl in love with Shawn Mendes
A parking garage charges $22.50 for the first hour and $2.50 for each additional hour. Write and solve an equation to find how many hours you can park in the garage for $30. Use "x" to represent the number of hours.
Final answer:
To park for $30 in a parking garage that charges $22.50 for the first hour and $2.50 for each additional hour, you can park for 4.2 hours.
Explanation:
The parking garage charges $22.50 for the first hour and $2.50 for each additional hour. Let's use 'x' to represent the number of hours. To find how many hours you can park for $30, we need to write and solve the equation.
Total cost equation:
$22.50 + $2.50(x-1) = $30
$22.50 + $2.50x - $2.50 = $30
$2.50x = $10.50
x = 4.2 hours
Therefore, you can park for 4.2 hours for $30 in the garage.
Which expression is equivalent to (x + 2)(3x – 3)?
Multiply the two brackets together
(x+2)(3x-3)
x(3x)*(-3)(x)+2(3x)(2*-3)
3x^2-3x+6x-6
3x^2+3x-6
Answer is : 3x^2+3x-6
Answer
A. x5y3
Step-by-step explanation:
which is the greatest common factor of 24 and 60
Aloha! My name is Zalgo and I am here to be of assistance to you today. The GCF (Greatest Common Factor) of 14 and 60 would be 12. To the GCF of 24, you need to multiply 2^3 by 3. In order to get the GCF of 60, you need to multiply 2^2 by 3 times 5.
I hope that this info helps! :P
"Stay Brainly and stay proud!" - Zalgo
(By the way, do you think you could mark me as Brainliest? I'd greatly appreciate it! Mahalo! XT)
The greatest common factor of 24 and 60 is 12.
What is the greatest common factor of 24 and 60?To get the greatest common factor, we will list the factors of each number and find the largest one that they have in common.
The factors of 24 are:
1, 2, 3, 4, 6, 8, 12, and 24.
The factors of 60 are:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The largest factor that 24 and 60 have in common is 12.
Read more about common factor
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what are the coterminal angles for an angle of 5 pi over 3 radians
ANSWER
[tex] \frac{5\pi}{3} + 2\pi \: n[/tex]
EXPLANATION
Coterminal angles are angles that have the same terminal side in standard position.
We want find all angles that are coterminal with
[tex] \frac{5\pi}{3} \: \: radians[/tex]
We add or subtract multiples of 2π radians to this angle to obtain all angles that are coterminal with this angle.
The coterminal angles are:
[tex] \frac{5\pi}{3} + 2\pi \: n[/tex]
where n is an integer.
Answer:
-7 Pi/3, -Pi/3, 11 Pi/3
Step-by-step explanation:
What is the answer to 4 • 4.
Answer:
16
Step-by-step explanation:
4 groups of 4 is 16:
[tex]\left\begin{array}{cccc}*&*&*&*\*&*&*&*&*\*&*&*&*&*\*&*&*&*&*\end{array}\right[/tex]
a sequence is a function whose domain is the set of _____ numbers
a sequence is a function whose domain is the set of natural numbers.
natural numbers are all the negative and positive integers
A sequence exists as a function whose domain is the set of natural numbers.
SequenceA sequence exists as a function whose domain is the set of natural numbers or a subset of the natural numbers. Usually use the symbol a to describe a sequence, where n is a natural number and a stands for the value of the function on n. Intuitively, a sequence exists just as an ordered list of (possibly infinitely many) numbers.
Natural numbers stand for the numbers that exist used for counting and are a part of real numbers.A sequence exists as an enumerated collection of objects in which repetitions are permitted and order matters.To learn more about Sequence refer to:
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PLEASE HELP ME! 8 POINTS!
Answer:
720/1681
Step-by-step explanation:
First quadrant so everything is positive for a trig function of just the angle. I would suggest just drawing a right triangle using tan(x)=40/9 (opp/adj). Find the hypotenuse which is sqrt(40^2+9^2)=sqrt(1600+81)=sqrt(1681)=41. So sin(x)=40/41 and cos(x)=9/41.
Therefore sin(2x)=2sin(x)cos(x)=2(40/41)(9/41)=720/1681
1. You have a piece of land where you want to grow a garden. You only
have 20 yards of fencing to surround the garden. Work through the steps
below to figure out the maximum space you can create to grow plants.
A) you decide to make the width 3 yards.
Length: _____ yards
Area: _____ square yards
A gym charges a one-time fee of $75 to join,plus membership dues of $25 per month. Which equation represents the total cost,c, of belonging to the gym for m months
A) C=25m-75
B) C=25m+75
C) C=75m+25
D) C=75m-25
Answer:
the answer is B
Step-by-step explanation:
75 is a one time payment. 25 is the amount that you will pay permonth
Answer:
C=25m+75
Step-by-step explanation:
For what values of y does 125=(1/25)^y-1
[tex]125 = \frac{1}{125} {}^{y - 1} \\ 125 = ( {5}^{ - 2} ) {}^{y - 1} \\ \\ {5}^{3} = {5}^{2 - 2y} \\ 3 = 2 - 2y \\ - 0.5 = y[/tex]
Answer:
The answer is [tex]y=-0.5[/tex]
Step-by-step explanation:
In order to determine the "y" value, we have to change the way of we see the equation.
In these cases, when the variable is in the exponent and it is possible to make two exponents in each side of the equation, we have to equal bases and then we have to make other equation between the exponents of both sides.
So,
[tex]125=(\frac{1}{25})^y^-^1\\(5)^3=(5^-^2)^y^-^1\\(5)^3=(5)^-^2^*^y^+^2\\[/tex]
Then, we have to make an equation between the exponents of both sides:
[tex]3=-2*y+2\\2*y=2-3\\2*y=-1\\y=\frac{-1}{2}=-0.5\\ y=-0.5[/tex]
Finally, the value of "y" is -0.5
Which is the graph of f(x) = 5(2)x?
A is the answer. (0,5) (2,20)
Step-by-step explanation:
This is the correct graph on Desmos, the other user forgot to add x as an exponent.
(0,5) (2,20)
What is the simplified form of the following expression?
Oo oo
Answer:
[tex]\frac{\sqrt[3]{100x}}{5}[/tex]
Step-by-step explanation:
we have
[tex]\sqrt[3]{\frac{4x}{5}}[/tex]
Multiply inside by [tex]\frac{25}{25}[/tex]
so
[tex]\sqrt[3]{\frac{4x*25}{5*25}}[/tex]
[tex]\sqrt[3]{\frac{100x}{125}}[/tex]
Remember that
[tex]\sqrt[3]{125}=5[/tex]
substitute
[tex]\sqrt[3]{\frac{100x}{125}}=\frac{\sqrt[3]{100x}}{\sqrt[3]{125}}=\frac{\sqrt[3]{100x}}{5}[/tex]
Anthony is making A collage for his art class my picking Shapes randomly. He has five squares, two triangles, two ovals, and four circles. find p( circle is chosen first)
I am not sure but I think the probability of a circle being chosen first is 4/13
because 13 is the amount of shapes in total, and 4 is the amount of circles. I hope you found this helpful.
Answer:
The answer is [tex]\frac{4}{13}[/tex].
Step-by-step explanation:
There are five squares, two triangles, two ovals, and four circles.
So, total shapes are = [tex]5+2+2+4=13[/tex]
The probability that the first chosen shape will be a circle is given by :
[tex]\frac{possible outcomes}{total number of outcomes}[/tex]
= [tex]\frac{4}{13}[/tex]
Note: 4 because any 1 out of 4 can be selected.
Help me pleasee , timed
Answer:
The second alternative is correct
Step-by-step explanation:
We have been given the expression;
[tex](x^{27}y)^{\frac{1}{3}}[/tex]
The above expression can be re-written as;
[tex](x^{27})^{\frac{1}{3}}*y^{\frac{1}{3}}\\\\(x^{27})^{\frac{1}{3}}=x^{27*\frac{1}{3}}=x^{9}[/tex]
On the other hand;
[tex]y^{\frac{1}{3}}=\sqrt[3]{y}[/tex]
Therefore, we have;
[tex]x^{9}\sqrt[3]{y}[/tex]
Answer:
Option 2: [tex]x^{9}(\sqrt[3]{y})[/tex]
Step-by-step explanation:
Given
[tex](x^{27}y )^{\frac{1}{3} }[/tex]
The exponent power will be multiplied with the powers inside the bracket
So,
[tex](x^{27 * \frac{1}{3}} y^{\frac{1}{3}})[/tex]
[tex]= x^{\frac{27}{3}} y^{\frac{1}{3} }[/tex]
[tex]= x^{9} y^{\frac{1}{3}}[/tex]
Writing in radical form will give us:
[tex]x^{9}(\sqrt[3]{y})[/tex]
So,
Option 2 is the correct answer ..
The width of rectangular field is x metres.
The length of the field is 30m longer than the width.
The perimeter of the field is less than 500m.
The area of the field is greater than 4000m^2
By writing suitable inequalities, find the possible values of x
Answer:
Possible values of x are 50 < x < 110.
Step-by-step explanation:
Consider the perimeter of the field:
2x + 2(x + 30) < 500
2x + 2x + 60 < 500
4x < 440
x < 110.
Consider the area of the field:
x(x + 30 ) > 4000
x^2 + 30x - 4000 > 0
(x - 50)(x + 80) > 0
The critical values are x = -80 and 50.
As x is a width it must be positive so x > 50.
6. The ratio of red ribbons to green ribbons is 4 to 6. If
there are a total of 30 red ribbons, then how many green
ribbons are there?
Answer:
45
Step-by-step explanation:
The 4 part of the ratio represents 30 red ribbons
Divide 30 by 4 to find the value of one part of the ratio
30 ÷ 4 = 7.5, hence
6 × 7.5 = 45 ← number of green ribbons
Select the correct answer
An air conditioning unit promises to have a cooling capacity of 6,000 British thermal units (Btu). The unit has a maximum variance of y Btu. If x is the
air conditioning unit's actual capacity, which graph could be used to determine variance levels that would cause a unit to be rejected because of its
cooling capacity?
(A,B,C,D)
Answer:
the answer will 100 percent be A
Answer:
The correct option is B.
Step-by-step explanation:
Let x is the air conditioning unit's actual capacity and y is the maximum variance in British thermal units (Btu).
It is given that an air conditioning unit promises to have a cooling capacity of 6,000 British thermal units (Btu).
It means the maximum variance is less than or equal to absolute difference of actual capacity and 6,000.
[tex]y\leq |x-6000|[/tex]
The related equation of this inequality is a V-shaped curve with vertex (6000,0) and y-intercept (0,6000). Related curve is a solid curve because the points on curve included in the solution set.
The shaded region lie below the curve because the sign of inequality is ≤.
Therefore the correct option is B.
The range of the following relation R {(3, -5), (1, 2), (-1, -4), (-1, 2)} is (1 point)
{-4, -5, 2, 2)
{-1, 1, 3)
{-1,-1,1,3)
{-5, -4,2)
Answer:
{-5,-4,2}
Step-by-step explanation:
The domain is the inputs and the range is the outputs
The outputs are the y values
{ -5,2,-4,2}
We only list them once and in order from smallest to largest
{-5,-4,2}
Please answer now and please explain thank you
Hello There!
The answer would be the first one.
This is saying that Tom can not save exactly 50.25 but he must save more than that
| x-3 | < x-3
can someone give a step by step process on how to do this?
Answer:
There are no solutions to the inequality.
Step-by-step explanation:
|x - 3| < x – 3
1. Separate the inequality into two separate ones.
(1) x – 3 < x – 3
(2) x – 3 < -(x – 3)
2. Solve each equation separately
(a) Equation (1)
[tex]\begin{array}{rcl}x - 3 & < & x - 3\\x & < & x\\\end{array}\\\text{This is impossible. No solutions exist.}[/tex]
(b) Equation (2)
[tex]\begin{array}{rcl}x - 3 & < & -(x - 3)\\x - 3 & < & -x + 3\\x & <& -x + 6\\2x & < & 6\\x & < & 3\\\end{array}\\\text{This is impossible. No solutions exist}[/tex]
For example, if x = 0, we get
|0 - 3| < 0 - 3 or
3 < -3