The next term in the sequence is -1.
Given a sequence is defined recursively by the formula f(n+1)=f(n)+3.
An ordered list of integers that frequently follows a pattern or function is known as a sequence. Sequences can have a finite or indefinite length. Terms refer to the distinct components of a sequence. The individual numbers or parts that make up a sequence are known as its terms.
The first term of the sequence is -4.
That means f(1)=-4 .......(1)
When compare f(1) with f(n+1), we get
n=0
So, when n=0 then it is the first term of the sequence.
When n=1 then substituting this in the given formula, we get
f(1+1)=f(1)+3
f(2)=f(1)+3
Now, Substitute the value of f(1) from equation (1), we get
f(2)=-4+3
f(2)=-1
Hence, the next term in the sequence when the sequence is defined recursively by the formula f(n+1) = f(n)+3 and the first term of the sequence is –4 is -1.
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A circle has a circumference of 6. It has an arc of length 1.
What is the central angle of the arc, in degrees?
Answer:
Central Angle (Radians)=
1.0482
Central Angle (Degrees)=
6.0058e+1
Sector Area Equals
0.477
Step-by-step explanation:
To wire the entire new addition, max and fred have 6 rolls of wire with 9 2/5 feet per roll and 7 rolls of wire with 16 3/4 feet per roll. how many feet of additional wire do they need in order to complete the job if it requires 200 feet of wire? write the result as a mixed number.
Additional wire of 26 7/20 feet, in the form of a mixed fraction, is required to complete the job.
What is the length of additional wire required, in the form of a mixed fraction?A mixed fraction is represented by both its quotient and remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
Max has total 6*9 2/5feet of wire, that is, 282/5 feet of wire.
Fred has total 7*16 3/4 feet of wire, that is, 469/4 feet of wire.
The total amount of wire required=200 feet
The total amount of wire available=282/5+469/4
=3473/20
An additional amount of wire is required=200-3473/20
=(4000-3473)/20
=527/20
Thus, the additional amount of wire required is expressed as a mixed fraction= 26 7/20 of feet.
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A bucket is in the shape of a frustum with top diameter 20cm and bottom diameter 12cm. If the height of the bucket is 8cm, calculate the volume of the bucket
Answer: V≈1642 cm³.
Step-by-step explanation:
D=20 cm d=12 cm h=8 cm V=?
[tex]R=\frac{D}{2}=\frac{20}{2} =10 \ (cm).\\ r=\frac{d}{2}=\frac{12}{2}=6 \ (cm).\\ \boxed {V=\frac{1}{3} *\pi *h*(R^2+R*r+r^2)} \ \ \ \ \ \Rightarrow\\V=\frac{1}{3}*\pi *8*(10^2+10*6+6^2)\\V=\frac{1}{3}*\pi *8*(100+60+36)\\ V=\frac{8}{3} *\pi *196\\V=\frac{8*196*\pi }{3} \\V\approx1642\ cm^3.[/tex]
The population of a town grows at a rate proportional to the population present at time t. the initial population of 500 increases by 20% in 10 years. what will be the population in 20 years? (round your answer to the nearest person.)
The population in 20 years is 719 people.
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
According to the question
[tex]\frac{dP}{dt} = kP[/tex] where P is population at any time
solving equation,
[tex]\int[/tex][tex]\frac{dP}{dt} =\\[/tex] [tex]\int kP[/tex]
[tex]lnP=kt+C[/tex] -(1)
Applying the conditions,
at t=0, P = 500
[tex]ln500=C[/tex] -(2)
at t=10, P= 600
putting it in equation gives
[tex]ln(600) = k(10)+ln(500)[/tex]
ln(6/5) = k(10)
[tex]k = \frac{ln(6/5)}{10}[/tex]
at t=20 , P= ?
[tex]lnP=(\frac{ln(6/5)}{10})20 + ln500[/tex]
[tex]lnP=({ln(6/5)}{2 + ln500[/tex]
On putting the values of ln(6/5) , ln(500)
[tex]lnP=0.182(2) + 6.214[/tex]
[tex]P = e^{6.578}[/tex]
P = 719.099
On rounding off
P ≈ 719 people
Thus the population in 20 years is 719 people.
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ion 9
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ed out of
g
ion
Given circle A with radius 15, find the length of arc FD. Give your answer rounded to the nearest hundredth.
Answer:
20°
156°
46°
my
E
D
B
The length of arc FD with a radius of 15 and angle of 120° is 10π units.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The length of an arc is given by:
arc length = (Ф/360) * 2π*radius
Let us assume that the angle is 120°
arc FD = (135/360) * 2π(15) = 10π
The length of arc FD with a radius of 15 and angle of 120° is 10π units.
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help me find the answer plss
Answer:
about 8.2 cm
Step-by-step explanation:
The key is to realize that the volume never changes.
The formula for the volume of a sphere is (4/3)*pi*radius^3
22/7 is being substituted in place of pi in this problem
The volume of one of the small spheres is
(4/3)*(22/7)*2^3 is about 33.524 cm^3
64 of those spheres would have a volume of 33.524*64, or about 2145 cm^3
Now, the problem is to find a sphere with a volume of 2145 cm^3
Volume = (4/3)*(22/7)*radius^3
plug in and solve
2145 = 4.1905*r^3
r^3=511.87
r is about equal to 8.2 centimeters
Please help me Ill mark you brainlest
Answer:
Step-by-step explanation:
By rounding each number to 1 significant figure,
estimate the answers to:
a)763 x 42
_______
82
b)39 × 52
_______
3.8 x 4.9
Answer:
see explanation
Step-by-step explanation:
rounding each number to 1 significant figure
(a)
763 × 42
≈ 800 × 40
= 32000
(b)
39 × 52
≈ 40 × 50
= 2000
(c)
3.8 × 4.9
≈ 4 × 5
= 20
A dilation is a nonrigid transformation that can produce enlarged or reduced images from a given pre-image. How do you know that a dilation will produce similar figures? Explain
The dilation will produce similar figures because the image and pre image will have congruent corresponding angles.
What is dilation?It should be noted that dilation simply means a transformation to resize an object
In this case, the dilation will produce similar figures because the image and pre image will have congruent corresponding angles.
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Answer:
The dilation will produce similar figures because the image and pre image will have congruent corresponding angles.
Step-by-step explanation:
What is the area of a square with radius 7.5m
Answer:
48.375
Step-by-step explanation:
Area of square- area of circle
Side^2 - pieR^2
(15)^2 - 3.14*7.5*7.5
225 - 176.625
= 48.375
Hope this helps
The area of the square is 56.25 m².
The area of the square is:
Area = Side²
Area = (7.5 m)²
Area = 56.25 m²
{ Pisces04 }
what postulate is this?
A. SSS (side side side)
B. SAS (side angle side)
C. ASA (angle side angle)
D. AAS (angle angle side)
Answer:
the answer is c ASA
Step-by-step explanation:
i think I. not sure
Can someone help with these geometry questions? I gotta have answers fast, it’s urgent:(
Can't answer 1-6 cause I have no idea what you need
7) A triangle with two congruent sides is isosceles.
8) [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex]
9) [tex]\angle C[/tex]
10) [tex]\overline{AB}[/tex]
11) [tex]\angle A, \angle B[/tex]
12) isosceles triangle
help me please U_U......
Distance traveled = dependent variable
Gasoline left in tank = independent variable
PLEASE HELP!!!
Determine the measure of the angle formed by the line y=3/2x and the positive x-axis.
Answer:
the angle = ~56.3 degrees
Step-by-step explanation:
1. y=3/2(x) and y=0
2. say x is equal to 4. the length along the x axis is 4. you would plug x=4 into y=3/2x to get the length along the y axis (which would be 6). then you would use these lengths to find the angles value with tan. tan^-1(6/4), so the answer would be ~56.3 degrees
Select all the correct answers.
3x
If the measure of angle is 4, which statements are true?
The measure of the reference angle is 60°.
□ sin(0) = 2
The measure of the reference angle is 45°.
Otan(8) = 1
cos(8) = √2
The measure of the reference angle is 30°.
If the measure of angle θ is 3π/4, the true statements are:
sin(θ) = √2/2.The measure of the reference angle is 45°.How to determine the true statements?In Trigonometry, an angle with a magnitude of 3π/4 (radians) is equivalent to 135° (degrees) and it's found in the second quarter. Thus, we would calculate the reference angle for θ in second quarter as follows:
Reference angle = 180 - θ
Reference angle = 180 - 135
Reference angle = 45°.
Also, a terminal point for this angle θ is given by (-√2/2, √2/2) which corresponds to cosine and sine respectively. This ultimately implies that sin(θ) = √2/2.
tan(θ) = cos(θ)/sin(θ)
tan(θ) = [(-√2/2)/(√2/2)]
tan(θ) = -1
In conclusion, we can logically deduce that only options A and B are true statements.
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Complete Question:
If the measure of angle θ is 3π/4, which statements are true. Select all the correct answers.
A. sin(θ)=sqrt2/2
B. The measure of the reference angle is 45
C. The measure of the reference angle is 30
D. The measure of the reference angle is 60
E. cos(θ)=sqrt2/2
F. tan(θ)=1
what does I mean in a equation
Iota, also known as the symbol , is denoted as being the square root of -1. Since square roots of negative numbers do not exist, there is a variable that represents it complexly. In fact, every real number (a) can be represented using the form (a) + (0).
On occasion, variables can also use and it does not have to be talking about the square root of -1. However, this rarely ever happens to avoid confusion. Check instructions in questions to see how is defined.
if p is a prine number greater than 5 and q is an odd number greater than 5 whihc of the following is true
The first statement p + q is not a prime number is a true option (A) correct.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
First statement:
p + q is not a prime number.
Let p = 7
q = 9
= 7 + 9 = 16 (16 is not a prime)
= 7×9 = 63 (no factor of 63)
p = 7, q = 7
q/p = 7/7 = 1 (1 is integer)
Thus, the first statement p + q is not a prime number is a true option (A) correct.
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Robert, Richard and David were working on a project to redesign coke cans. First, Robert measured the original coke can and found the circumference to be 8.6 inches. Richard measured the height to be 15.2 cm.
David calculated the volume to be 131.3 cm3.
Choose the true statement(s) below.
Select one or more:
a.David's calculations are incorrect, he needed to convert centimeters to inches before finding the radius then use the area of the base times the height .
b.David is correct.
c.David's calculations are incorrect, he used the circumference and the height to find the volume.
The true statement is David's calculations are incorrect, he used the circumference and the height to find the volume.
VolumeCorrect calculation:
Height = 15.2 cmCircumference = 8.6 inchesC = 2πr
8.6 = 2 × 3.14 × r
8.6 = 6.28r
r = 8.6/6.28
r = 1.36942675159235 inches
convert 1.36942675159235 inches to cm
= 3.478343949044569 cm
Approximately,
r = 3.5 cm
Volume = πr²h
= 3.14 × 3.5² × 15.2
= 3.14 × 12.25 × 15.2
= 584.668 cm³
Approximately,
volume = 584.7 cm³
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22/11,594 I need a step by step answer
Answer:
1.89753
Step-by-step explanation:
22/11,594
Multiply the numerator and denominator by 1000 to remove decimal[tex]\frac{22}{11.594} * 1000 = \frac{22000}{11594}[/tex]
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Solve The Following
( Solving equations)
Answer:
a) x = 4
b) x = 1
Step-by-step explanation:
a) [tex]\frac{4x-1}{2} = x + 7[/tex] multiply both sides by 2 so we can simplify the fraction by getting rid of 2
4x - 1 = 2x + 7 transfer like terms to the same side of the equation
4x - 2x = 7 + 1
2x = 8 divide both sides by 2
x = 4
b) [tex]3x + 2 = \frac{2x+13}{3}[/tex] again, get rid of the fraction by multiplying both sides by 3
9x + 6 = 2x + 13 transfer like terms to the same side of the equation
9x - 2x = 13 - 6
7x = 7 divide both sides by 7
x = 1
(LOOK AT IMAGE)
The diagram shows a circle with a tangent.
a) What is the size of angle x?
b) Choose the theorem below which allows you to find x.
a) By the alternate segment theorem, [tex]x=53^{\circ}[/tex]
b) Alternate angles are equal
Select the correct answer. The steps for solving the given equation are shown below. -3-7 T 11 C 4 Steps 7 4 114 -3x7 44 -3x7 + 7 = 44 + 7 -3x = 51 3r = I = -17 Justifications 1. multiplication property of equality 2. simplification 3. 777 4. simplification 5. division property of equality 6. simplification Select the correct property for the missing justification in the table. addition property of equality division property of equality multiplication property of equality subtraction property of equality Select the correct answer . The steps for solving the given equation are shown below . -3-7 T 11 C 4 Steps 7 4 114 -3x7 44 -3x7 + 7 = 44 + 7 -3x = 51 3r = I = -17 Justifications 1. multiplication property of equality 2. simplification 3. 777 4. simplification 5. division property of equality 6. simplification Select the correct property for the missing justification in the table . addition property of equality division property of equality multiplication property of equality subtraction property of equality
The property for the missing justification is: A. addition property of equality.
What is the Addition Property of Equality?If b - a = c, based on the addition property of equality, we can isolate b by adding a to both sides, i.e. b - a + a = c + a, to give us b = c + a.
Using the addition property of equality, 7 was added to both sides of the equation as shown in step 3.
Therefore, the missing justification is: A. addition property of equality.
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How many times could you expect to roll a number that is not 5 if you rolled a standard die 360 times?
The number of times I would expect to roll a number that is not a 5 is 300 times.
What is the number of times a 5 won't be rolled?A standard die has 6 faces. There are 5 numbers that are not 5 on a standard die. They are 1, 2, 3, 4, 6.
The number of times a 5 won't be rolled = (5/6) x 360
5 x 60 = 300 times
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Which choices are equivalent to the expression below? Check all that apply.
√8√8
A. √8
B. 8
C. √√8.8
D. 64
E. √16
F. 64
I hope this photo will help you.
HELP PLSSSSS! 10 points for whoever and good ratings
Answer:
Hello! The answer is 19.25 m²
Step-by-step explanation:
A = 1/2(4 + 7)3.5
A = 1/2(11)3.5
A = (5.5)3.5
A = 19.25 m²
Answer:
19.25 m²
Step-by-step explanation:
A = (1/2)(b1 + b2)h
A = (1/2)(7 m + 4 m)(3.5 m)
A = 19.25 m²
Select the correct answer.
Which statement is true about function f, which is shown in the graph?
The graph shows a cubic function. The curve is drawn using the points (minus 1, 8), (minus 1, minus 3.5), (0, 0), (1, 3.5), and (1, minus 8) which intercepts (1, 0), and (minus 1, 0)
A.
Function f is neither even nor odd.
B.
Function f is odd.
C.
Function f is both even and odd.
D.
Function f is even.
A triangle has one side length of 2x
2 + 5x + 3. The other two sides of the triangle have lengths x
2 + 2x and
3x − 2. Determine the simplified expression that represents the total perimeter of the triangle.
The simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x + 3
How to determine the perimeter?The side lengths are given as:
2x^2 + 5x + 3, 2 + 2x and 3x - 2
Add these lengths to determine the perimeter (P)
P = 2x^2 + 5x + 3 + 2 + 2x + 3x - 2
Collect like terms
P = 2x^2 + 5x + 2x + 3x + 3 + 2 - 2
Evaluate the like terms
P = 2x^2 + 10x + 3
Hence, the simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x + 3
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Use synthetic division to find the expression for the area of the base of a rectangular prism with height x 4 and volume x3 2x2 – 17x – 36. 2x2 – 9x x2 6x – 24 x2 – 2x – 9 –4x2 8x 36
The expression for the area of the base of Prism is x2 – 2x – 9
The volume of a rectangular prism is this
Volume = Area x Height
Substituting the given expressions
x3 + 2x2 - 17x - 36 = Area x (x + 4)
Area = (x3 + 2x2 - 17x - 36) / (x + 4)
Now, let's use synthetic division
-4 | 1 2 -17 -36
---- __-4___8___36
1 -2 -9 0
The expression for the area is
Area = x2 - 2x - 9
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in each of the following graphs, the two given polygons are similar. write precisely a single dilation (coordinated of center and coefficient) by which the image (labled with primed letters) was obtained.
The single dilation of the shape is a dilation by a scale factor of 1.5 with center R
How to determine the dilation rule?From the graph, we have the center of dilation to be point R.
This is so because R = R'
Also, we have:
R = (-1, -4)
S = (2, 0)
S' = (3.5, 2)
Calculate the distance RS and RS' using
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
This gives
[tex]RS = \sqrt{(0 + 4)^2 + (2+ 1)^2} = 5[/tex]
[tex]RS' = \sqrt{(2 + 4)^2 + (3.5+ 1)^2} = 7.5[/tex]
Divide RS' by RS to determine the scale factor (k)
k = 7.5/5
k = 1.5
Hence, the single dilation of the shape is a dilation by a scale factor of 1.5 across point R
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Solve the system of equations:
8x + 3y = 13
3x + 2y = 11
Answer:
1.x=13/8-3y/8
2.x=11/3-2y/3
Step-by-step explanation: