Answer:
6n-5
Step-by-step explanation:
Some different types of sequences
To find sequence patterns, often the sequences are arithmetic (adding by a constant amount) or geometric (multiplying by a constant amount).
To test if something is a geometric sequence, find the quotient of (divide) adjacent terms.
To test if something is an arithmetic sequence, find the difference of (subtract) adjacent terms.
Finding the type of our sequence
Note the following:
19-13=6
13-7=6
7-1=6
So, to get each next term, add 6. However, what is the nth term?
Finding an expression for our sequence
You'll be adding up "n" sixes to get there (expressed with multiplication, because multiplication is shorthand for repeated addition), but we need a starting point so that when n=1, the expression equals 1, and when n=2, the expression equals 7... and so on. This starting point shifts the "6n" piece of our expression so that it lines up on the sequence. I'm going to call this starting point "b" for the base that is supporting this sequence.
So the expression will look something like [tex]6n+b[/tex]
Knowing that the expression needs to equal 1 when n=1, we can set up an equation and solve for "b".
[tex]6n+b=n^{\text{th}} \text{ term}\\6(1)+b=(1)\\6+b=1\\(6+b)-6=(1)-6\\b=-5[/tex]
So, the expression for the nth term of the sequence is [tex]6n-5[/tex]
Verifying
To verify that the expression we found is right, we can test our expression for each of the terms we do know:
The first term (n=1) is 1
[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]
[tex]6(1)-5 \overset{?}{=} (1)[/tex]
[tex]6-5 \overset{?}{=} 1[/tex]
[tex]1 \overset{\checkmark}{=} 1[/tex]
The second term (n=2) is 7
[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]
[tex]6(2)-5 \overset{?}{=} (7)[/tex]
[tex]12-5 \overset{?}{=} 7[/tex]
[tex]7 \overset{\checkmark}{=} 7[/tex]
The third term (n=3) is 13
[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]
[tex]6(3)-5 \overset{?}{=} (13)[/tex]
[tex]18-5 \overset{?}{=} 13[/tex]
[tex]13 \overset{\checkmark}{=} 13[/tex]
The fourth term (n=4) is 19
[tex]6n+b=n^{\text{th}} \text{ term}\\[/tex]
[tex]6(4)-5 \overset{?}{=} (19)[/tex]
[tex]24-5 \overset{?}{=} 19[/tex]
[tex]19 \overset{\checkmark}{=} 19[/tex]
The two dot plots below compare the forearm lengths of two groups of schoolchildren:
Two dot plots are shown one below the other. The title for the top dot plot is Forearm Length, Group A and the title for the bottom plot is Forearm Length, Group B. Below the line for each dot plot is written Length followed by inches in parentheses. There are markings from 9 to 12 on each line at intervals of one. For the top line there are 3 dots above the second mark, 4 dots above the third mark and 3 dots above the fourth mark. For the bottom line there are 3 dots above the first mark, 5 dots above the second mark, and 2 dots above the third mark.
Based on visual inspection of the dot plots, which group appears to have the longer average forearm length?
Group A, because seven children have a forearm length longer than 10 inches
Group B, because two children have a forearm length longer than 10 inches
Group A, because one child in the group has the least forearm length of 9 inches
Group B, because three children in the group have the least forearm length of 9 inches
Answer:
Group A, because seven children have a forearm length longer than 10 inches
Step-by-step explanation:
Create the dot plots based on the given information (please see attached images).
Group A = blue dots
Group B = red dots
From inspection of the attached dot plots, we can see that Group A appears to have the longer average forearm length. This is because 7 children have a forearm length of longer than 10 inches.
To calculate the average forearm length, sum all data values and divide by the total number of data values.
[tex]\textsf{Average of Group A}=\dfrac{ 3 \times 10 + 4 \times 11 + 3 \times 12}{10}=11[/tex]
[tex]\textsf{Average of Group B}=\dfrac{ 3 \times 9 + 5\times 10+ 2\times 11}{10}=9.9[/tex]
Thus proving that Group A has the longer average former length.
According to given text data
Average of both groups
A:-
10(3)+11(4)+12(3)/1030+44+36/1066+44/10110/1011B:-
9(3)+5(10)+11(2)/1027+50+22/1049+50/1099/109.9Group A has bigger average
3. Use the following diagram to solve for x.
The value of x from the given diagram is -6
Lines and anglesLine is defined as the distance between two points. Given the line RP with the following measures
RP = 17
RQ = x + 14
QP = x + 15
Using the expression
RP = RQ + QP
Substitute
17 = x + 14 + x + 15
17 = 2x + 29
Determine the value of x
2x = 17 - 29
2x= -12
x = -6
Hence the value of x from the given diagram is -6
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The diagonals of parallelogram abcd intersect at point e. to prove that bae= dce, all of the following could be used, except for which
a.the sum of measures of the interior angles of abcd is 360 degrees
b. abc = cda by sss
c. abc = cde by sss
d. given two parallel lines by transversal, alternates interior angles are congruent.
The only option that cannot be used to prove that the diagonals of parallelogram abcd intersect at point e is; Option C
How to determine quadrilateral proof?
A) The sum of the interior angles of any quadrilateral is 360° and so this is true about the parallelogram.
B) AB = CD and BC = DA from opposite sides of a parallelogram are equal. Also AC = CA because of reflexive property of congruence. Thus, ∠ABC ≅ ∠CDA
C) This is not true because ∠ABC ≅ ∠CDA instead of ∠ABC ≅ ∠CDE.
D) This is true because of the definition of a transversal.
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this is not a right angled triangle, but how do i find the 3rd side of a triangle if one side is 50 and the other side is 30?
Use the Pythagorean theorem.
Janet solves this equation
log(x-3)+logx=1
She finds the two solutions; x=5 and x=-2
Of Janet’s two solutions, ____ correct because _____
A. Neither x=5 nor x=-2 is
B. Only x=5 is
C. Only x=-2 is
D. Both x=5 and x=-2 are
1. x=5 is an extraneous solution
2. Both x=-2 and x=5 are valid solutions
3. Both x=-2 and x=5 are extraneous solutions
4. x=-2 is an extraneous solution
(TWO DIFFERENT ANSWERS FILL IN THE BLANK)
Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions
Logarithmic functionGiven the log function expressed as:
log(x-3) + logx=1
According to the law of logarithm, addition becomes product to have:
log x(x -3) = log₁₀10
x² - 3x = 10
x² - 3x -10 = 0
x² - 5x + 2x - 10 = 0
x(x-5) + 2(x-5) = 0
(x+2)(x-5)=0
x = -2 and 5
Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions
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The coefficient of 2(3)(6)Q is
The coefficient of the variable Q is 36 , Option A is the correct answer.
The complete question is
The coefficient of 2(3)(6)Q is _____. a.36 b.18 c.12
What is a Coefficient ?Coefficient is the constant term written in front of variable in an expression.
The expression given in the question is
2(3)(6)Q
The coefficient is 2 * 3 * 6 = 36
Therefore , the coefficient of the variable Q is 36 , Option A is the correct answer.
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What is the measure of angle AFR?
O 124 degrees
O 91 degrees
O 13 degrees
O 117 degrees
Answer:
13°Step-by-step explanation:
AFR = VFN (opposite angle rule)
7x + 33 = 9x + 7
33 - 7 = 9x - 7x
26 = 2x
x = 26 : 2
x = 13°
-----------------
check
7 * 13 + 33 = 9 * 13 + 7 (remember PEMDAS)
91 + 33 = 117 + 7
124 = 124
the answer is good
im in summer school and i need to pass this please help me
g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.
Which statement compares the graph of the two functions?
First, a vertical shift of N units is written as:
g(x) = f(x) + N
if N > 0 the shift is upwards.If N < 0 the shift is downwards.A horizontal shift of N units is written as:
g(x) = f(x + N).
if N < 0, the shift is to the right.If N > 0, the shift is to the left.In this case, we have:
g(x) = f(x + 8) + 4
So g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.
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Which point has coordinates (5,-7pi/6)?
Point A
Point B
Point C
Point D
round 68.321 to the nearest tenth
Answer:
When 68.321 rounded to the nearest tenth the result is 68
Select all the correct answers.
Which expressions are equal to
Given the data from the question, the expressions that are equal to 10⁵ are
10³ ⋅ 10²10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10To determine the expressions that are equal to 10⁵, we shall evaluate the options given from the question.
How to evaluate (10⁴)¹Recall
(Aᵐ)ⁿ = Aᵐⁿ
Thus,
(10⁴)¹ = 10⁴
How toevaluate 10³ ⋅ 10²Recall
Aᵐ ⋅ Aⁿ = Aᵐ⁺ⁿ
Thus,
10³ ⋅ 10² = 10³⁺²
10³ ⋅ 10² = 10⁵
How to evaluate 1 / 10⁵Recall
1 / Aᵐ = A⁻ᵐ
Thus,
1 / 10⁵ = 10⁻⁵
How to evaluate (10³)²Recall
(Aᵐ)ⁿ = Aᵐⁿ
Thus,
(10³)² = 10⁶
How to evaluate 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10Recall
Aᵐ ⋅ Aⁿ = Aᵐ⁺ⁿ
10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10¹⁺¹⁺¹⁺¹⁺¹
10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10⁵
SUMMARY
(10⁴)¹ = 10⁴
10³ ⋅ 10² = 10⁵
1 / 10⁵ = 10⁻⁵
(10³)² = 10⁶
10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10⁵
From the above illustrations, only 10³ ⋅ 10² and 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 are equal to 10⁵
Complete question
See attached photo
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What is
-8/15of21/12
Hi, please help me find the volume of this sphere :)
Answer: 8788
Step-by-step explanation:
Use the formula and use 3 for pi
13cm is the radius
[tex]13^{3\\[/tex] = 2197
2197 x 3 = 6591
6591 x 4/3 = 8788
Find the HCF of
x^2 y and y^2
The highest common factor is [tex]\boxed{y}[/tex].
What is this Simplify as √16y¹6
Answer:
[tex]6y^1^6[/tex]
Step-by-step explanation:
I hope this has Helped :)
The fences will be aligned with the exterior angles 1 and 2. what are some other relationships you can see between 1,2,a, and b? (2 points)
please help
1.8.4
The relationships between angles 1, a, b, and 2 can be defined using the angles between parallel lines.
In the diagram, we can see the fences, making angles 1 and 2 with the parallel lines X and Y respectively.
Using the angles among parallel lines, we can state the relationships between angles 1, a, b, and 2 as follows:
Angle 1 and Angle a are adjacent angles, thus their sum is 180°, that is m∠ 1 + m∠ a = 180°.Angle 2 and Angle b are adjacent angles, thus their sum is 180°, that is m∠ 2 + m∠ b = 180°.Angle 1 and Angle b are corresponding angles, thus they are equal, that is m∠1 = m∠ b.Angle 2 and Angle a are corresponding angles, thus they are equal, that is m∠2 = m∠ aAngle 1 and angle 2 are co-exterior angles, thus their sum is 180°, that is, m∠ 1 + m∠ 2 = 180°.Angle a and angle b are co-interior angles, thus their sum is 180°, that is, m∠ a + m∠ b = 180°.These were the relations among angles 1, a, b, and 2, using the parallel lines X and Y.
Refer to the diagram for a better understanding.
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Each statement describes a transformation of the graph of y= x. Which statement correctly describes the graph of y= x+ 9.5?
a. it is the graph of y= x where the slope is increased by 9.5 .
b. it is the graph of y= x translated 9.5 units to the right.
c. it is the graph of y= x translated 9.5 units up.
d. it I'd the graph of y= x translated 9.5 units down.
Answer: C
Step-by-step explanation: The graph is going to go up because the +9.5 isn't in any parentheses. If it was, that would mean it would move horizontally. I hope this helps!
The correct statement:
It is the graph of y = x translated 9.5 units up.
The correct option is c.
The equation y = x represents a straight line passing through the origin with a slope of 1. When we have the equation y = x + 9.5, it means that for every x-value, the corresponding y-value is obtained by adding 9.5 to the original x-value. This translation in the y-direction shifts the entire graph upward by 9.5 units.
To visualize this, imagine the original line y = x. Each point on this line has an x-coordinate and a corresponding y-coordinate, which are the same due to the equation y = x. When we add 9.5 to each y-coordinate, the line shifts vertically by 9.5 units without any change in slope or horizontal position.
The other options can be eliminated because the statement does not mention changing the slope or the horizontal position of the graph. Instead, it specifically describes a vertical translation, indicating a movement in the y-direction. Therefore, the correct answer is c.
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can someone please help and explain these problems ??
Answer:
AAA
Step-by-step explanation:
yesss
Identify the value of a and the length of each secant segment.
x= 10, NL= 8 , NP = 12
What is secant?A secant is a line that intersects a curve at a minimum of two distinct points.
Using secant theorem,
NL* NM = NP* NO
(3+5)*3 = (2+x)*2
24= (2+x)*2
12= 2+x
x= 12-2
x= 10
So, NP= 2+x
NP = 12
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Directions: Find the inverse of each number.
Additive
-2 =
18 =
-30 =
2/5 =
Multiplicative
8/9 =
12/15 =
-6 =
10 =
Answer:
Additive
-2 = 2
18 = -18
-30 = 30
2/5 = -2/5
Multiplicative
8/9 = 9/8
12/15 = 15/12
-6 = -1/6
10 = 1/10
Step-by-step explanation:
an additive inverse is a number you must add to another number to get 0
(think of it as the negative version of the number)
{but WHY? In math, you can imagine comparing numbers on a number line. If we are finding the opposite of a number, we want to find the same distance from 0, but on the opposite side of 0. So, 2 would be two to the right of 0, -2 would be two to the left of 0}
-2 + 2 = 0
18 - 18 = 0
-30 + 30 = 0
2/5 - 2/5 = 0
a multiplicative inverse is a number that you multiply by another number to get 1.
We are finding the "reciprocal" of a number; you are essentially flipping it as a fraction
(reciprocal of 2 = 1/2 {remember, 2 is the same thing as 2/1 } ; reciprocal of 1 / 8 = 8)
note: reciprocal is being used interchangeably with multiplicative inverse here
8/9 · 9/8 = 1
12/15 · 15/12 = 1
-6 · -1/6 = 1 {-6 = -6/1}
10 · 1/10 = 1 {10 = 10/1}
hope this helps!! have a lovely day :)
Answer:
Additive: number that you add to get 0
2
-18
30
-2/5
Multiplicative: number that you multiply to get 1
9/8
15/12
-1/6
1/10
hope this is helpful!! ^u^
What is 10 1/2÷214 ?
Answer:
21/428 or 0.04 906542056074...
Step-by-step explanation:
Which of the following best describes the slope of the line below?
Mike has 63 toys. 18 of them are new and 12 are his favorites, while 4 are new and favorites. Mike is giving away all the toys that are neither new nor favorites. How many toys does mike GIVE AWAY. ASAP ASAP
The geometric sequence graphed shows the number of mold spores in a Petri dish per day (please help!)
Answer:
f(1) = 2
f(n) = 2 × f(n - 1) , n ≥ 2
Step-by-step explanation:
the point of coordinates (1 , 2) is on the graph
Then
f(1) = 2
…………………………
We notice that :
f(2) = 4
f(3) = 8
f(4) = 16
16/8 = 8/4 = 4/2 = 2/1 = 2
________________________
This means the common ratio
of the geo sequence = 2
Hence ,
f(n) = 2 × f(n - 1)
Answer: f(n) = 2 × f(n - 1) , n ≥ 2
Step-by-step explanation:
Which of the following points is NOT visible if the viewing window of a graphing utility is set at:
Xmin : 6
Xmaz: 6
Ymin : —6
Ymaz : 6
The points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible the answers are D, E, and H.
What is graphing utility?A graphing calculator is a portable computer that can plot graphs, solve multiple equations at once, and carry out other variable-related activities.
We have points shown in the coordinate plane.
As the window of a graphing utility is set at:
X(min) : -6
X(max): 6
Y(min) : -6
Y(max) : 6
The points out of 6 will not be visible.
We can draw a square as shown in the attached picture.
The points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible.
Thus, the points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible the answers are D, E, and H.
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NEED HELP ASAP!! In the figure, AC 1 AB and AB 1 BD.
Answer:
d
By the alternate interior angles theorem,
Angles ABD and BAC will be congruentAngles BAD and ABC will be congruentBy the reflexive property, AB is congruent to itself.
Thus, the triangles will be congruent by ASA.
Select the correct answer from each drop-down menu. (Will give brainliest)
(Picture below options are 19.5, 29, 58 for both multiple choice)
The angle BAC will be 29 and the angle BOC will be 58.
What is the circle theorem?The angle in a circle's centre is twice that at its perimeter when two angles are subtended by the same arc. So, angle AOB = 2 angle ACB. Angles that the same arc subtends at its circumference are equal. As a result, angles inside a section are equal.
Here the given angle is ∠BDC = 29 so from the given theorem the angle BEC will be equal to the angle BDC.
∠BDC = 29
The centre angle BOC will be twice the angle at the circumference so the angle will be twice.
∠BOC = 59
Therefore the angle BAC will be 29 and the angle BOC will be 58.
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factorise
answer is (a+c) (ca-b²)
Answer:
Step-by-step explanation:
The loudness, L, measured in decibels (Db), of sound intensity, I, measured in watts per square meter, is defined as L = 10 log StartFraction I Over I 0 EndFraction, where I 0 = 10 Superscript negative 12 and is the least intense sound a human ear can hear. What is the approximate loudness of a dinner conversation with a sound intensity of 10–7?
The correct option is Option D: the approximate loudness of a dinner conversation will be 50Db with a sound intensity 10⁻⁷.
The loudness L, ( which is measured in decibels (Db)), of the sound of the intensity I, can be calculated in watts per square meter,
L = 10 log(I/I₀)
where I₀ = 10⁻¹² which is the least intensity that a human can hear.
The sound intensity of a dinner conversation= I= 10⁻⁷
Loudness L of that conversation = 10 log (10⁻⁷/10⁻¹²)
= 10 log(10⁻⁷⁻⁽⁻¹²⁾)
= 10 log(10⁻⁷⁺¹²)
= 10 log(10⁵)
= 10*5
= 50 Db
Therefore the correct option is Option D: the approximate loudness of a dinner conversation will be 50Db with a sound intensity 10⁻⁷.
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What are the solutions of x^2-3x+3=0
Therefore the solution to this equation is imaginary given by x = [tex]\rm \dfrac { 3 \pm \sqrt{-3}}{2}[/tex]
What is a Quadratic Equation ?A Quadratic equation is an equation that can be written in the form of
ax² +bx+c = 0
The solution of the given quadratic equation
x² -3x +3 = 0
the roots of the equation is given by
[tex]\dfrac { -b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
here a = 1 , b = -3 , c = 3
Substituting the values
The solution is
[tex]\rm \dfrac { 3 \pm \sqrt{(-3)^2 -4*1 *3}}{2}[/tex]
Therefore the solution to this equation is imaginary
given by
x = [tex]\rm \dfrac { 3 \pm \sqrt{-3}}{2}[/tex]
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