Answers
[tex]a_{n}=a_{1}+d(n-1)\\a_{n}=2+3(n-1)\\a_{n}=3n-1[/tex]
The graph shows the first 8 terms.
Related Questions
There are five apples and you take three away. how many apples do you have?
Answers
You can get this by subtracting the 3 from the 5 you originally had.
Answer: 2 apples
Step-by-step explanation:
Logic
Which accurately shows how to use inverse operations to find the value of a in a + 5 = 14?
Answers
a+5=14
using the additive inverse property we shall have:
a+5+(-5)=14+(-5)
simplifying the above we get:
a+5-5=14-5
a+0=9
thus
a=9
Write the partial fraction decomposition of the given rational expression. startfraction 5 x plus 2 over x superscript 4 baseline minus 4 x squared endfraction
Answers
Answer:
Step-by-step explanation:
Given is a rational algebraic expression in x as
[tex]\frac{5x+2}{x^4-4x^2}[/tex]
First let us factorize the denominator.
[tex]x^2(x^2-4)\\=x^2(x+2)(x-2)[/tex]
Let the given term be
[tex]\frac{A}{x} +\frac{B}{x^2} +\frac{C}{x-2} +\frac{c}{x+2} \\\\=\frac{Ax(x^2-4)+B(x^2-4)+cx^2(x+2)+Dx^2(x-2)}{x^4-4x^2}[/tex]
Equate the numerator to get
[tex]Ax(x^2-4)+B(x^2-4)+cx^2(x+2)+Dx^2(x-2)[/tex]=[tex]5x+2[/tex]
Substitute x =-2
[tex]4D (-4) = -8\\D=\frac{1}{2}[/tex]
Now substitute x =2
We get
[tex]16C=12\\C=\frac{3}{4}[/tex]
Put x=0
[tex]-4B=2\\B=\frac{-1}{2}[/tex]
Next equate X cube terms to 0 on right side
[tex]A+C+D=0\\A=\frac{-5}{4}[/tex]
Hence partial fraction is
[tex]\frac{-1}{2x^2} -\frac{5}{4x} +\frac{1}{2(x+2)} +\frac{3}{4(x-2)}[/tex]
To decompose the rational expression startfraction 5x + 2 over x4 - 4x2 endfraction into partial fractions, we need to factor the denominator. The partial fraction decomposition of the given rational expression is startfraction A over x + B over x2 + C over (x - 2)2, where A, B, and C are the determined coefficients.
Explanation:To decompose the rational expression startfraction 5x + 2 over x4 - 4x2 endfraction into partial fractions, we need to factor the denominator. The denominator can be factored as x2(x2 - 4) which gives us two distinct linear factors x and x + 2, and a repeated linear factor x - 2. Therefore, we can express the rational expression as follows: startfraction A over x + B over x2 + C over (x - 2)2.
To find the values of A, B, and C, we can use the method of equating coefficients. By multiplying both sides of the equation by the common denominator, we can eliminate the fractions and solve for the unknowns. Finally, we substitute the values of A, B, and C back into the partial fraction decomposition expression.
Therefore, the partial fraction decomposition of the given rational expression is startfraction A over x + B over x2 + C over (x - 2)2, where A, B, and C are the determined coefficients.
The diagonal of the floor of a square room is 6 meters.what is the length of a side of the room? round to the nearest tenth.
Answers
From the right triangle, where sides of the square are legs of the right triangle, and the diagonal of the square is a hypotenuse of the right triangle.
x²+x²=6²
2x²=36
x²=18
x=√18 =√(2*9)=3√2≈4.2m
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 3 - 4 sin θ
Answers
Explanation:
The equation r = 3 - 4 sin θ may be graphed using cartesian coordinates (i.e. x and y) or polar coordinates.
The logical way is to graph in polar coordinates. I did it using a graphing software and obtained the attached graph.
Also, I attached the graph in cartesian coordinates.
Here you have a table that you can build by your self and use the pairs to draw the graph (either cartesian or polar coordinates).
θ (rad) r = 3 - 4 sin θ
0 3
π/8 2.61731657
π/4 2.29289322
3π/8 2.07612047
π/2 2
5π/8 2.07612047
3π/4 2.29289322
7π/8 2.61731657
π 3
9π/8 3.38268343
5π/4 3.70710678
11π/8 3.92387953
3π/2 4
13π/8 3.92387953
7π/4 3.70710678
15π/8 3.38268343
2π 3
In both of the attached graphs you can see that the left side is equal to the right side, but the upper side is not equal to the bottom side.
Therefore, the graph is symmetric about the y-axis.
Answer:
y-axis... just look at the graph on desmos.com
Rafael has ridden 14 miles of a bike course. The course is 40 miles long. What percentage of the course has Rafael ridden so far
Answers
Answer: 35%
What is the degree of the polynomial function f(x) = 2x3 + 7x5 − 4x − 12?
Answers
The three undefined terms in geometry are point , line, and plane. True or false
Answers
Hope this helps :)
Divide 420 in the ratio of 2:1
Answers
420 / 3 = 140
so we have 140 * 2 = 280
and 140 * 1 = 140
Answer 280 and 140
∠ABD is formed by a tangent and a secant intersecting outside of a circle. If minor arc AC = 72° and minor arc CD = 132°, what is the measure of ∠ABD?
A) 30°
B) 36°
C) 42°
D) 48°
Answers
m∠ABD=1/2(mCD-mAC)
m∠ABD=1/2(132-72)
m∠ABD=1/2(60)=30
Answer:
c 42 degrees
Step-by-step explanation:
A grocer stacks oranges in a four-sided pyramid that is 7 layers high. How many oranges are in the pile?
A.504 B.840 C.140 D.120
Answers
Answer:
Option C. 140
Step-by-step explanation:
Base of a pyramid which has four triangular sides is four sided.
If pyramid contains seven layers of oranges then the layer at the bottom will have 7 oranges.
Since base is a square then other side of the square base will have the same number of oranges = 7.
Therefore number of oranges at the first layer will be = 7×7
Similarly other layers above this layer will have the same sequence
6×6, 5×5, 4×4, 3×3, 2×2, 1×1
Therefore total number of oranges = 7×7 + 6×6 + 5×5 + 4×4 + 3×3 + 2×2 + 1×1 = 49 + 36 + 25 + 16 + 9 + 4 + 1 = 140
Option C. 140 is the answer.
A grocer stacks oranges in a four-sided pyramid that is 7 layers high. Many oranges are in the pile are C.140
Further explanationThe orange is the fruit of the citrus species Citrus and sinensis in the family Rutaceae, native to China. Orange is also called sweet orange, to distinguish it from the related Citrus and aurantium, referred to as bitter orange.
The proper name of four-sided pyramid is a "tetrahedron". The tetrahedron has the extra interesting property of having all four triangular sides congruent
1st Layer: The 1st layer contains only 1 orange so it has only 1 orange
2nd layer: The 2nd layer has total 4 oranges. Calculation: [tex]2*2=4[/tex]
3rd layer: The 3rd layer has total 9 oranges. Calculation: [tex]3 * 3 = 9[/tex]
4th Layer: The 4th layer has total 16 oranges. Calculation: [tex]4 * 4 = 16[/tex].
5th layer: The 5th layer has total 25 oranges. Calculation: [tex]5 * 5 = 25[/tex]
6th layer: The 6th layer has total 36 oranges. Calculation: [tex]6 * 6 = 36[/tex]
7th layer: The 7th layer has total 49 oranges. Calculation: [tex]7 * 7 = 49[/tex].
Sum of all layers:
[tex]1+4+9+16+25+36+49 = 140[/tex]
Learn moreLearn more about oranges https://brainly.com/question/10744522Learn more about pyramid https://brainly.com/question/10262815Learn more about pile https://brainly.com/question/9094265Answer detailsGrade: 9
Subject: mathematics
Chapter: pyramid
Keywords: oranges, pyramid, four-sided, layers, pile
NEED HELPPPPPPP!!!!!!! PLEASE!!!!!!!!
Which statement best describes the graph of -x3 - x2 + 4x + 4?
A. It starts down on the left and goes up on the right and intersects the axis at x = -2, 2, and 4.
B.It starts down on the left and goes up on the right and intersects the axis at x = -2, -1, and 2.
C.It starts up on the left and goes down on the right and intersects the x-axis at x = -2, -1, and 2.
D.It starts up on the left and goes down on the right and intersects the axis at x = -2, 2, and 4.
Answers
Firstly, simplife the function [tex] -x^3-x^2+4x+4 [/tex] in the following way:
[tex] -x^3-x^2+4x+4=-(x^3+x^2)+4(x+1)=-x^2(x+1)+4(x+1)=(x+1)(4-x^2)=(x+1)(2-x)(2+x)=-(x+2)(x+1)(x-2) [/tex].
There are three x-intercepts: x=-1; x=2 and x=-2 (therefore, options A and D are incorrect).
Since before brackets is sign "-", you should state that graph starts down on the left (you can check this substituting smaller negative number than -2 into function expression. For example, if x=-10, then f(-10)=-(-10+2)(-10+1)(-10-2)=-(-8)(-9)(-12)>0) and goes up on the right (you can check this substituting greater positive number than 2 into function expression. For example, if x=10, then f(-10)=-(10+2)(10+1)(10-2)=-(12)(11)(8)<0).
Answer: correct choice is B.
A biology class of 24 students decides to measure the height of each student and then calculate the average height for the class. which of these is a possible source of error in this activity?
Answers
Answer: The possible source of error in this activity is " the accuracy of making and recording measurements"
The height of each and every student in the class has to be taken very accurately. Even if there was a single error in either making the calculation or even recording it, the average height will take a hit and will result in the entire exercise being a failure.
Hence, it’s very important to accurately measure the height and record and even have a second person do the same activity so that the numbers recorded are accurate.
This is Josh’s solution for the equation
x2-6x-7=0:
x2-6x-7=0
x2-6x=7
x2-6x+9=7+9
(x-3)2=16
x=19
x-3=-16
x=-13
Is Josh’s solution correct? Explain
Answers
x - 3 = 4 OR x - 3 = -4
And the result answer would have been x = 7 or x = -1
A plane intersects one cone of a double-napped cone such that the plane is neither parallel to the generating line nor perpendicular to the axis. What conic section is formed?
circle
hyperbola
ellipse
parabola
Answers
ellipse
Hope this Helped!
;D
please help will give brainiest!!!
Answers
How: Re-arrange formulae knowing tan(theta) = sin(theta)/cos(theta)
such that it become: cos(theta) -sin(theta)/cos(theta) x cos(theta) = 0.
From there; cos (theta) = sin(theta) (by re-arranging). Now, substitute figures of b), pie/4 = 45 degrees. At 45 degrees, sin(45) = cos(45) = 1/square root of 2. Also, 5pie/4 = 235 degrees. At 235 degrees, sin(235) = cos(235) = -1/square root of 2
b. [tex] \frac{ \pi }{4} or \frac{5 \pi }{4} [/tex]
Explanation:
Before we begin, remember that:
tan α = [tex] \frac{sin \alpha }{cos \alpha } [/tex]
Now for the given, we have:
cos θ - tan θ * cos θ = 0
cos θ - [tex] \frac{sin theta }{cos theta } [/tex] * cos θ = 0
cos θ - sin θ = 0
cos θ = sin θ
Now, divide both sides by cos θ, we get:
1 = tan θ
Following the ASTC rule, we know that the tan function is positive in the first and third quadrants.
This means that:
either θ = [tex] \frac{ \pi }{4} [/tex]
or θ = π + [tex] \frac{ \pi }{4} [/tex] = [tex] \frac{ 5 \pi }{4} [/tex]
Hope this helps :)
Manuel bought a balloon (that is a perfect sphere) with a radius of 2 \text{ cm}2 cm2, space, c, m. He wanted his balloon to be bigger, so he blew 222 big breaths of air into the balloon. Each big breath increased the balloon's radius by 1 \text{ cm}1 cm1, space, c, m. What is the ratio of the current volume of the balloon to the original volume of the balloon?
Answers
Answer:
8 times
Step-by-step explanation:
I found the volume of the sphere. Then increased it how many times he blew. That was the ratio.
Also, Khan :)
The ratio of the current volume of the balloon to the original volume of the balloon is 8.
What is the volume of a sphere?The volume of a sphere is given by (4\3)πr³ where r is the radius of the sphere.
The initial volume of the balloon = [tex]\frac{4}{3} \pi 2^{3}[/tex]
The initial volume of the balloon =[tex]\frac{32}{3} \pi[/tex]
Radius of the balloon after first breath = 2+1 =3cm
The Radius of the balloon after the second breath = 2+2=4cm
So, the new volume of the balloon = [tex]\frac{4}{3} \pi 4^{3}[/tex]
The new volume of the balloon = [tex]\frac{256}{3} \pi[/tex]
The ratio of new volume to the initial volume = [tex]\frac{\frac{256}{3 } \pi }{\frac{32}{3}\pi }[/tex]
The ratio of new volume to the initial volume =8
Hence, the ratio of the current volume of the balloon to the original volume of the balloon is 8.
To get more about sphere visit:
https://brainly.com/question/10171109
What is the volume of the coffee in a can if the can has a radius of 4 inches and a height of 9 inches? (use 3.14 for π.) 113.04 in.3 226.08 in.3 339.12 in.3 452.16 in.3?
Answers
your answer is here...
we know that almost all cans are cylindrical.
given the radius of the coffee can is 4 in and height is 9 in.
volume of the coffee can = πr²h
= 3.14 × 4 × 4 × 9
= 452.16 in³
cheers!!
The volume of the coffee in the can if the can has a radius of 4 inches and height of 9 inches is 452.16 inches³.
The can must be in the shape of a cylinder.
The formula to find the volume of the cylinder is,
Volume of cylinder = π r² h
Here r is the radius of the base of the cylinder and h is the height of the cylinder.
Given, Radius, r = 4 inches and Height, h = 9 inches
Volume of the coffee = π (4)² (9)
= 144 π
= 144 × 3.14
= 452.16 inches³
Thus, the volume of the coffee in the can is 452.16 inches³.
Learn more about Volume here :
https://brainly.com/question/16134180
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Classify each polynomial by its degree and number of terms
Answers
1) 7x/4+3 (Name using degree: First degree polynomial),(Name using number of terms:binomial)
2) 5.2x^2-4x+2.5 (Name using degree: Quadratic polynomial),(Name using number of terms:trinomial)
3) 3/5 (Name using degree: zero degree polynomial),(Name using number of terms:monomial)
4) 0.75x^2 (Name using degree: Quadratic degree polynomial),(Name using number of terms:monomial).
Answer with explanation:
We know that a polynomial is classified based on the degree as follows:
Constant-
If it has a degree zero.
and the equation of such a polynomial is:
p(x)=a
Linear--
It has degree 1.
and the equation of such a polynomial is: p(x)=ax+b
Quadratic--
If it has degree two and the equation of the polynomial is given by:
[tex]p(x)=ax^2+bx+c[/tex]
Based on number of Terms--
Monomial--
If it has just one term.
Binomial--
If it has two terms.
Trinomial--
If it has three terms.
How do do a 3/4 as a fraction, decimal, and percent?
Answers
Answer:
3/40.7575%Step-by-step explanation:
How do do a 3/4 as a fraction, decimal, and percent?
1) 3/4 is just a fraction
2) 3:4 = 0.75 (0.75 = 75%)
3) 75%
let f(x)=1-x*2 and g(x)=1-x find (fg)(x)
Answers
(fg)(x) = (1-x^2)*(1-x) = 1 - x - x^2 + x^3 (answer)
A sphere has a radius of 12 meters. What is the approximate volume of the sphere? Use 3.14 for π . Round your answer to the nearest whole number.
Answers
Solve the system of equations y = 40x2 and y = 19x + 3 algebraically.
Answers
We have been given a system of nonlinear equations.
[tex]\\y=40x^{2},y=19x+3[/tex]
In order to solve this system we can first equate the two equations in order to get a quadratic in x.
[tex]\\40x^{2}=19x+3[/tex]
Our next step is to bring all the terms on one side.
[tex]\\40x^{2}-19x-3=0[/tex]
Now we have to solve this equation. We can solve it by factoring using the splitting middle term method.
[tex]\\40x^{2}-24x+5x-3=0[/tex]
[tex]\\8x(5x-3)+(5x-3)=0[/tex]
[tex]\\(8x+1)(5x-3)=0[/tex]
Upon setting each of these factors equal to zero using zero product property we get
[tex]\\8x+1=0 \text{ or } 5x-3 = 0[/tex]
Upon solving both these equations we get
[tex]\\x=-\frac{1}{8} \text{ or } x=\frac{3}{5}[/tex]
Now we can substitute these values of x in the equation
[tex]y=19x+3[/tex]
We get
[tex]\text{For }x=- \frac{1}{8} \Rightarrow y=19(- \frac{1}{8})+3= \frac{5}{8}\\[/tex]
[tex]\text{For }x= \frac{3}{5}\Rightarrow y=19( \frac{3}{5})+3= \frac{72}{5}\\[/tex]
Therefore, our final set of solutions are
[tex](x,y)=(- \frac{1}{8},\frac{5}{8}) \text{ and } ( \frac{3}{5}, \frac{72}{5})[/tex]
Which transformation will be equivalent to rotating a figure 270° counterclockwise? A) reflecting over the x-axis and the y-axis
B) translating left 3 units and down 5 units
C) Reflecting over the y-axis and then reflecting over the line y = x
D) Reflecting over the y-axis and then reflecting over the line y = -x
Answers
(x, y) ⇒ (-x, y)
Reflection of that over the line y = x:
(-x, y) ⇒ (y, -x)
Rotation counterclockwise by 270°:
(x, y) ⇒ (y, -x) . . . . . . equivalent to reflection over y, then over y=x.
The appropriate choice is ...
C) Reflecting over the y-axis and then reflecting over the line y = x.
Answer:
D) Reflecting over the y-axis and then reflecting over the line y = -x
Step-by-step explanation:
When the figure is rotate clock-wise or anti clock-wise then the coordinate of figure is get changed and this new coordinate can be find on the basis of degree of rotation.
The rules of rotation is:
When rotation = 90° clock-wise, the vertices is get changed to (-y, x) from (x, y).When rotation = 180° clock-wise, the vertices is get changed to (-x, -y) from (x, y).When rotation = 270° clock-wise, the vertices is get changed to (y, -x) from (x, y).Thus, Option (D) is correct option.
Area of figure? Geometry help???
Answers
[tex] A = \dfrac{172^\circ}{360^\circ} \times 3.14159 \times (4~in.)^2 [/tex]
[tex] A = \dfrac{172^\circ}{360^\circ} \times 3.14159 \times 16~in.^2 [/tex]
[tex] A = 24.0~in.^2 [/tex]
If BC is tangent to circle O and OB is a radius, what kind of triangle is OBC?
Answers
Triangle OBC is a right triangle. This is because where the radius and the tangent meet creates a right angle. A right angle is created due to the theorem that states that a radius is perpendicular to its tangent.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
What is the first step to solve the following equation? x^2-2x=0
Answers
x^2-2x=0
Δ = b^2-4ac
a = 1; b = - 2; c=0
Δ = 4-0=4
X1,2 = -b+ or - rad Δ / 2 a
X1,2 = 2 + or - 2 / 2
X1 = 2 and X2 = 0/2 = 0
So the solutions are 2 and 0
I hope it helped!
A number is chosen at random from the first 100 positive integers. Find the probability that the number is a multiple of 7.
Answers
Probability is 14/100=7/50
[tex] |\Omega|=100\\
|A|=14\\\\
P(A)=\dfrac{14}{100}=\dfrac{7}{50}=14\% [/tex]
A plane intersects a double-napped cone only at the cone's vertex.
Which terms describe the degenerate conic section that is formed?
Select each correct answer.
degenerate parabola
degenerate ellipse
line
degenerate hyperbola
point
pair of intersecting lines
Answers
In addition to ...
degenerate ellipse
point
it is also a degenerate circle (special case of ellipse).
___
The vertex of a double-napped cone is a point. So, the intersection of only the vertex with a plane is a point, not a degenerate parabola (a line) or degenerate hyperbola (pair of crossing lines).
Essentially, the plane must intersect at an angle greater than the angle of the edge of the cone with the axis of the cone. If the plane is not at the vertex, such an intersection angle will result in a circle or ellipse. As the plane gets closer to the vertex, the ellipse gets smaller, degenerating to a single point.
Answer:
The answer is:
Degenerate ellipse.
Point.
Step-by-step explanation:
We know that when a plane intersects a double-napped cone only at the cone's vertex then the cross-section that is obtained is the point.
Also we know that a point is also considered as a circle with radius 0.
and a circle is also a kind of a ellipse when the length of both the transverse and conjugate axis are equal.
Hence, the term that best describe the degenerate conic section that is formed is:
degenerate ellipse
point
Pleaseee helpppp!!!!!!!!!!!!!!!!
Answers
(change in y)/(change in x) = (-18 -(-20))/(1 - 0) = 2
so can be written in slope-intercept form as
g(x) = 2x -20
The x-intercept of this line is at x=10.
0 = 2x -20 . . . . the x-intercept is where g(x) = 0
20 = 2x
10 = x
The circle also intersects the x-axis at x=10, so that will be one point that is shared by the circle and g(x). A graph shows there is also another point of intersection, (6, -8).
Yes, the linear function g(x) will intersect the circle at 2 points with positive x-coordinates.