Answers
Answer: [tex]\sum^{24}_{n=1} (4n+5)[/tex]
Step-by-step explanation:
This is an arithmetic series with a common difference of 4, so we can immediately eliminate the two left-hand options.
To determine which of the two options on the right is correct, we can determine the first term of each sum expanded out.
For the top right, the first term is 4(0)+5=5, which does not match the first term of the given sequence.For the bottom right, the first term is 4(1)+5=9, which does match the first term of the given sequence.Related Questions
distance between (-5,1) and (0,-4)?
Answers
Answer:
7.07106781187
5. Identify the sign of the leading coefficient and describe the end behaviour. Using this
information, decide if each function is cubic or quartic.
Answers
The sign of the leading coefficient can be found using the graph of a polynomial function.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have given the graph of polynomial functions:
In the first graph:
The leading coefficient is positive.
x → ∞, f(x) → ∞
x → -∞, f(x) → -∞
Degree of a function = 3
In the second graph:
The leading coefficient is negative.
x → ∞, f(x) → -∞
x → -∞, f(x) → -∞
Degree of a function = 4
In the third graph:
The leading coefficient is positive.
x → ∞, f(x) → ∞
x → -∞, f(x) → ∞
Degree of a function = 4
In the fourth graph:
The leading coefficient is negative.
x → ∞, f(x) → -∞
x → -∞, f(x) → ∞
Degree of a function = 3
Thus, the sign of the leading coefficient can be found using the graph of a polynomial function.
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In how many ways can $9$ friends sit at a circular table if two of them, Anna and Bob, insist on having exactly two people seated between them? (As usual, two seatings are considered the same if one is a rotation of the other.)
Answers
There are 10,080 different ways in which the friends can seat on the circular table.
In how many ways the friends can seat?
There are 9 friends, such that two of them need to be separated by exactly two people.
Because the table is circular, we can consider the first position as the position where Bob is.
Now let's count the number of options for each of the other 8 positions. (counting to the left).
The next two positions have 7 and 6 options respectively (as these can be taken by any of the other 7 friends)
For the next seat, we could seat Anna or one of the remaining 5 friends.
Let's assume we seat Anna there, then for each of the next positions, we will have, respectively, 5, 4, 3, 2, 1 options.
The total number of combinations is given by the product between the numbers of options, so we have:
C = 7*6*5*4*3*2*1
But we also need to consider the case where Anna is on the first position (and Bob on the third), so we just need to add a factor equal to 2.
C = 2*(7*6*5*4*3*2*1) = 10,080
There are 10,080 different ways in which the friends can seat on the circular table.
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Part B
Assume the statement is true for n=k. Prove that it must be true for n=k+1, therefore proving it true for all natural
numbers, n.
Hint: Since the total number of dots increases by n each time, prove that d (k) + (k+1)=d (k+ 1).
Answers
The inductive step is assuming that the statement is true for some n = k , where k is one of the values we want to prove the statement for, it shows that it is also true for n = k+1.
How to carry out Mathematical Induction?Suppose we have the statement 3n > 4n for all positive integers n.
Now, the statement above is false when n = 1 , since 3 is less than 4. However, it will be true for all other positive integers.
In that case, we can still prove this statement by induction for all integers n ≥ 2 .
Thus, the inductive step is assuming that the statement is true for some n = k , where k is one of the values we want to prove the statement for, it shows that it is also true for n = k+1.
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CON PROCESOS POR FAVOR
Answers
Answer:
[tex] \dfrac{149}{40} [/tex]
[tex] \dfrac{38}{15} [/tex]
Step-by-step explanation:
[tex] (\dfrac{7}{8} + \dfrac{4}{5}) - (\dfrac{9}{20} + \dfrac{-5}{2}) = [/tex]
[tex] = (\dfrac{7}{8} \times \dfrac{5}{5} + \dfrac{4}{5} \times \dfrac{8}{8}) - (\dfrac{9}{20} + \dfrac{-5}{2} \times \dfrac{10}{10}) [/tex]
[tex] = (\dfrac{35}{40} + \dfrac{32}{40}) - (\dfrac{9}{20} + \dfrac{-50}{20}) [/tex]
[tex] = \dfrac{67}{40} - (-\dfrac{41}{20}) [/tex]
[tex] = \dfrac{67}{40} + \dfrac{41}{20} \times \dfrac{2}{2} [/tex]
[tex] = \dfrac{67}{40} + \dfrac{82}{40} [/tex]
[tex] = \dfrac{149}{40} [/tex]
[tex] (-\dfrac{6}{4} + \dfrac{3}{2}) + (\dfrac{6}{5} + \dfrac{4}{3}) = [/tex]
[tex] = (-\dfrac{3}{2} + \dfrac{3}{2})+ (\dfrac{6}{5} \times \dfrac{3}{3} + \dfrac{4}{3} \times \dfrac{5}{5}) [/tex]
[tex] = 0 + \dfrac{18}{15} + \dfrac{20}{15} [/tex]
[tex] = \dfrac{38}{15} [/tex]
Angle RSU is complementary to angle UST. Angle QSR is congruent to angle RSU.
Lines Q, R, U, and T extend from point S from left to right. Angle R S T is a right angle.
Which statement is true about angles UST and QSR?
They are complementary.
They are supplementary.
They are congruent.
They are obtuse.
Answers
Answer:
Statement 1 is correct
Angles UST and QSR are complementary.
Step-by-step explanation:
Complementary angles are those angles whose addition gives result of 90°
Congruent angles are those angles which are equal to each other. We can say that there values are same.
Here angle RSU is complementary to angle UST.
Therefore there addition is equal to 90°
∠RSU + ∠UST = 90° - (i)
Here angle QSR is congruent to angle RSU.
Therefore their values are equal.
It means ∠QSR =∠RSU -(ii)
From equation (i) and (ii) we get
∠QSR + ∠UST = 90°
So angles UST and QSR are complimentary angles.
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Answer:
Step-by-step explanation:
A
The temperature is dropping at a rate of five degrees per hour.
Let d represent the number of degrees the temperature drops.
Let t represent the number of hours that pass.
Which is the dependent variable?
Othe number of hours
Othe number of degrees the temperature drops
O the rate at which the temperature drops
the day of the week
Answers
Answer:
The rate at which the temperature drops.
Step-by-step explanation:
In science, the dependent variable is what you are measuring.
In math, the dependent variable is what you are evaluating.
Same idea, different topic.
Answer:
d=temp drop
t=hours
dependent variable is the temperature drops because the number of hours will tell you how much the temprature drops
this is the equation
total temp drops=t x 5
hope this helps!?
Help, Help, Brainliest available to the best Answer!
Find the Variance
Answers
Considering the given data-set, it's mean and the formula, the variance is of 870 lbs².
What is the variance of a data-set?The variance of a data-set is given by the sum of the differences squared between each observation and the mean, divided by the number of values.
The mean is the sum of all observations divided by the number of observations, hence:
M = (145 + 175 + 180 + 205 + 120)/5 = 165.
And the variance, in lbs squared, is given by:
V = [(145-165)² + (175-165)² + (180-165)² + (205-165)² + (120-165)²]/5 = 870.
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how to evaluate 16/81 1/2
Answers
An expression is defined as a set of numbers, variables, and mathematical operations. The value of (16/81)^(1/2) is 4/9.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of the given expression (16/81)^(1/2) can be calculated as shown below,
[tex](\dfrac{16}{81})^{\frac12}\\\\=\sqrt{\dfrac{16}{81}}\\\\= \dfrac49[/tex]
Hence, the value of (16/81)^(1/2) is 4/9.
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Answer:
★The square root of 16/81 = 4/9.
For which value of x is the expression y
=
a. 1
b. -1
C. 5
d. -5
3x-3
x-5
- undefined?
Answers
1
Step-by-step explanation:
when we put 1 in the equation the nominator becomes zero and it becomes undefined
Hii!
___________________________________________________________
[tex]\stackrel\star\rightsquigarrow\circ\boldsymbol{\underbrace{Answer:}}}\circ\leftharpoonup[/tex]
The value of x should be 5! ^^
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation:}}}\circ\leftharpoonup[/tex]
[tex]\boxed{\\\begin{minipage}{7cm} For\,an\,expression \\ \boldsymbol{to\,be\,und efined,} \\ \,its\,denominator\,should\,be\,zero \end{minipage}}}[/tex]
Remember this! ^^
Now let's consider this:
Which value of x will make the denominator equal to 0?
Is it 1? If we stick 1 in, we will not obtain 0.
[tex]\twoheadrightarrow\sf y=\cfrac{3\cdot1-3}{1-5}[/tex]
[tex]\bullet[/tex] Simplify this
[tex]\twoheadrightarrow\sf y=\cfrac{3-3}{-4}[/tex]
---
We will obtain 0 in the numerator, but not in the denominator; if the numerator is 0, then the fraction, or fractional expression, is 0.
Let's try 5. 5-5 is equal to 0, so this sounds promising! ^^
[tex]\twoheadrightarrow\sf y=\cfrac{3\cdot5-3}{5-5}[/tex]
[tex]\bullet[/tex] Look what we obtain when we simplify
Don't we obtain 15-3/0?
Like I said above, if an expression has 0 as its denominator, it's undefined.
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]
--
Graph the equation.
Y= - 3/2x
Answers
Answer:
Step-by-step explanation:
The length of the base of a triangle is twice its height. If the area of the triangle is 16 square kilometers, find the height.
Answers
Answer:
4
Step-by-step explanation:
Area of a triangle = bh/2
B = 2h
16 = 2h × 2/2
h×2 = 16
2h = 16
* put a square root on both sides then u will get the answer which is
Height of the triangle = 4
7
2
3
Mark this and return
f(x)
The functions f(x) and g(x) are graphed.
3
-6-5-4-3-2-1₁-
"AssessmentViewer(Ant
N
5
-2+
-3-
6
g(x)
7
2 3 4 5 6 x
8
Which represents where f(x) = g(x)?
Of(2)= g(2) and f(0) = g(0)
f(2)= g(0) and f(0) = g(4)
Of(2)= g(0) and f(4) = g(2)
Of(2)= g(4) and f(1) = g(1)
Save and Exit
Answers
Answer: Option 1
Step-by-step explanation:
The graphs intersect at x=0 and x=2, meaning f(2)=g(2) and f(0)=g(0).
The functions have the intersecting points at x = 2 and x = 0 and the relation is f ( 0 ) = g ( 0 ) and f ( 2 ) = g ( 2 )
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the first function be represented as f ( x )
Let the second function be represented as g ( x )
Now , the function f ( x ) is a parabolic function and g ( x ) is a linear function
And , the intersecting points of both f ( x ) and g ( x ) are
x = 2 and x = 0
So , both the functions f(x) and g(x) intersect at two points, one at x = 2 at the x-axis in the graph and one at y = 4 at y-axis of the graph
Therefore , f ( 0 ) = g ( 0 ) and f ( 2 ) = g ( 2 )
Hence , the functions are solved
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What percent of 48 listings is 36 listings
Answers
Answer:
75%
Step-by-step explanation:
48x=36
x=36/48
x=3/4
x=0.75=75%
The population of a large city can be calculated using the function P=345,000(1.01). What can you say about the rate of change from year 1 to year 2 compared to the rate of change from year 9 to year 10?
Answers
Rate of change (ROC) refers to how quickly something changes over time.
What is rate of change?The term "rate of change" (ROC) describes the rate at which something changes over time. Thus, it is not the amount of individual changes themselves but rather the acceleration or slowdown of changes (i.e., the pace). Rate of change is a tool used in finance to comprehend price returns and spot trend momentum.Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.The ratio between the change in the values of the y variables and the change in the values of the x variables is known as the rate of change.Given data :
The rate of change will be the same for all years. The rate of change is 7%. The . basic formula for this equation is: I(1+R)^T, where I = Initial amount, R = Rate of growth, and T = Time. So the R here is 0.07, or 7%. The growth RATE is constant, the growth AMOUNT will increase each year.
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Use the graph of the function to find its domain and range. Write the domain and range in interval notation
Answers
Answer:
Step-by-step explanation:
Follow the steps to find the area of the shaded region.
First use the formula below to find the area of the whole sector.
Sector Area= ( angle of sector/360). R2
Sector Area = ? Cm^2
Round to four decimal places.
14 cm
46°
14 cm
Answers
The area of the sector, to 4 decimal places, is 78.6794 cm².
We have given that,
Sector Area= ( angle of sector/360). R2
We have to determine the Sector Area
What is the Area of a Sector of a Circle?
Area of sector = ∅/360 × πr².
We have given the following:
∅ = 46°
Radius (r) = 14 cm
Area of sector = 46/360 × π(14²)
Area of sector ≈ 78.6794 cm²
The area of the sector is approximately 78.6794 cm².
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A pool a possible candidate for a student council consists of 14 freshmen and 8 softwares how many different councils consisting of 5 freshmen and 7 sophomores are possible
Answers
The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.
We have given that,
A pool of possible candidates for a student council consists of 14 freshmen and 8 software.
We have to determine the how many different councils consisting of 5 freshmen and 7 sophomores are possible
What is the combination?[tex]_n C_r=\frac{n !}{r ! (n-r) !}_n C_r = number of combinations\\\n = total number of objects in the set\\\r = number of choosing objects from the set[/tex]
The total number of the council is
[tex]_{10} C_5\times _9 C_7[/tex]
=252(36)
=9216
The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.
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If the volume of the pyramid is 192 yd³; and the area of the base is 64 yd², what is the height measured in yards?
Answers
Answer:
177
Step-by-step explanation:
(x) = x + 0.14x, then find the value of T(290).
A. 300.45
B. 351.2
C. 325.8
D. 330.6
Answers
Answer:
D. 330.6
Step-by-step explanation:
To evaluate the function for a specific value of x, put that value where x is in the function definition, and do the arithmetic.
__
T(x) = x +0.14x . . . . . given function definition
T(290) = 290 +0.14×290 = 290 +40.6 . . . . substitute 290 for x
T(290) = 330.6
The value of T(290) will be 330.6.The relation between them is shown as T(x) is dependent and x is the independent variable. Option D s correct.
What is a function?A connection between independent variables and the dependent variable is defined by the function.
Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.
Given relation;
T(x) = x +0.14x
Substitute the value of x we get;
T(290) = 290 +0.14×290
T(290) = 330.6
Hence, option D s correct.
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Which of the following points would fall on the line produced by the point-slope form equation y - 2 = 3(x - 5) when graphed?
(4, 5)
(6, 5)
(5, 5)
(1, 4)
Answers
The point is (6, 5).
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given :
y - 2 = 3(x - 5)
Those point will satisfy after putting the value of x and y we get LHS= RHS.
take (4, 5)
5-2 = 3(4-5)
3= -3
Hence, not satisfied.
take, (6, 5)
5-2 = 3(6-5)
3= 3
Hence, satisfied.
take, (5, 5)
5-2 = 3(5-5)
3= 0
Hence, not satisfied.
take, (1, 4)
4-2 = 3(1-5)
2= -12
Hence, not satisfied.
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Which is true regarding the graphed function f(x)?
• f(O) = 3
• f(5) = - 1
• f(3) = 2
O f(2) = -2
Answers
Answer:
f(5) = -1
Step-by-step explanation:
The points on the graph are (0,4), (1,3),(2,2), (3,1), (4,0), (5,-1).
The answers are in the form:
f(x) = y
That is, the number in the parenthesis is the x and the number by itself on the right is the y. The only one that is a point on the line is f(5) = -1, which is the point (5,-1)
6(2x²-5) = [?]
x = -3
Answers
Answer:
78
Step-by-step explanation:
plug in -3 as x
6(2(-3)^2-5)
6(2(9)-5)
6(18-5)
6(13)
78
Step-by-Step Solution:
=> 6(2x² - 5) ; when x = -3
Substitute the value of ‘x’ :-
= 6(2x² - 5)
= 6(2(-3)² - 5)
= 6(2(9) - 5)
= 6(18 - 5)
= 6(13)
= 6 * 13
=> 78
Determine the growth defined by the equation y=1.4(3.72)^x.
Answers
Answer:
the type of growth defined by the equation is Exponential growth.
Step-by-step explanation:
Exponential growth :-Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself
expression for exponential growth -
f(x) = k(1+t)^x
f(x) = exponential growth
k = initial amount
t = rate of growth
x = no of time interval
therefor,
the equation shown in the question represents exponential growth with increasing time.
hence, Exponential growth is the correct answer.
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If f(n)= n²-n, then f(-4) is
O-20
12
-12
20
Answers
Answer:
20
Step-by-step explanation:
Plug in -4 for n:
(-4)^2 - (-4) = 16 + 4 = 20
Solve the following word problem.
Money is invested at two rates of interest. One rate is 8 % and the other is 2%. If there is $1300 more invested at 8 % than at 2 %. find the amount invested at
each rate if the total annual interest received is $350. Let x = amount invested at 8% and y = amount invested at 2 %. Then the system that models the problem
[x = y + 1300
is
Solve the system by using the method of addition.
0.08x +0.02y = 350,
Answers
Answer:
at 8%: $3760at 2%: $2460Step-by-step explanation:
You are given a system of equations and asked to solve it by the method of addition. That method requires you add a multiple of one equation to the other so that one of the variables is eliminated. In some cases, this is easier if multiples of both equations are added together. The resulting single-variable equation is then solved in the usual way.
__
lookThe given system of equations is ...
x = y +13000.08x +0.02y = 350We notice the first equation has the variables on opposite sides of the equal sign, and both their coefficients are 1. The second equation has the variables on the same side of the equal sign, and their coefficients are 0.08 and 0.02.
planTo eliminate a variable by the "addition method," we need to have the variable on the same side of the equal sign with opposite coefficients. Or, we need to have the variable on opposite sides of the equal sign with the same coefficient.
Both of the x-variables are on the left side, so we need opposite coefficients. We can get that by multiplying the first equation by -0.08, or by multiplying the second equation by -12.5. We judge the first of these choices to be easier.
The y-variables are on opposite sides of the equal sign, so we need equal coefficients. We can get that by multiplying the first equation by 0.02, or the second equation by 50.
solutionWe choose to multiply the first equation by 0.02, so we can eliminate the y-variable. Here is the result of doing that, then adding the results
(0.02)(x) +(0.08x +0.02y) = (0.02)(y +1300) +(350)
0.10x +0.02y = 0.02y +376 . . . . . eliminate parentheses
0.10x = 376 . . . . . . . . . subtract 0.02y from both sides. y is eliminated
x = 3760 . . . . . . . . . divide by 0.10
y = x -1300 = 2460
__
The amount invested at 8% was $3760; the amount invested at 2% was $2460.
_____
Additional comment
We chose to eliminate y for a couple of reasons. x is the amount at the higher rate. We have found that solving for the higher-rate amount usually works best for preventing errors. The other reason is that multiplying by 0.02 results in smaller numbers, which we consider easier to deal with.
Had we multiplied by -0.08 to eliminate x, we would have ...
-0.08(x) +(0.08x +0.02y) = -0.08(y +1300) +(350)
0.02y = -0.08y +246
We judge -0.08(1300) +350 harder to calculate mentally, than 0.02(1300) +350.
0.10y = 246
y = 2460; x = 2460+1300 = 3760
Express cos A as a fraction in simplest terms.
Answers
Answer:
See below
Step-by-step explanation:
Here is one way
cos^2 + sin^2 = 1
cos^2 = 1 - sin^2
For angle A cos^2 = 1 - (10/26)^2
cos ^2 = 1 - 100/676
= 576/676
cos A = 24/26 = 12/13
Another way would be to use the Pythagorean theorem to find length of AB .... then cos A = length AB / 26
two sides and an angle are given below. determine whether the given information results in one triangle, two triangles, or no triangle at all. solve any resulting triangle(s). b = 8, c= 7, b = 170°
Answers
Answer:
A. single triangle. C = 8.74°, A = 1.26°, a = 1.01
Step-by-step explanation:
When two sides and an angle are given, the possibility of two (or zero) triangles exists only when the given angle is opposite the shorter of the two given sides. That is not the case here, so the given measures define one unique triangle.
Law of SinesThe law of sines tells us the sides and angles have the relation ...
sin(A)/a = sin(B)/b = sin(C)/c
We can use this first to find angle C:
sin(C) = c/b·sin(B)
C = arcsin(c/b·sin(B)) = arcsin(7/8·sin(170°)) ≈ 8.7394°
∠C ≈ 8.74°
Remaining measuresNow that we know two angles, we can find the third:
A = 180° -B -C = 180° -170° -8.74° = 1.26°
∠A = 1.26°
Using the law of sines again, we can find the measure of side 'a'.
a = b·sin(A)/sin(B) = 8·sin(1.26°)/sin(170°) ≈ 1.01346
The measure of segment 'a' is about 1.01 units.
__
Additional comment
If 'a', 'b', and angle A are given, there will be zero triangles if b/a·sin(A) > 1. If b/a·sin(A) < 1 and b > a, there will be two (2) triangles. Otherwise, as here, there will be one unique triangle.
if p = (-1,-1) find the image of p under the following rotation. 90 degrees counterclockwise about the origin
Answers
Answer:
( 1, - 1 )
Step-by-step explanation:
The interior angle of a regular polvgon is 9 times the size of its exterior angle
Work out how many sides the polygon has
Answers
==================================================
Work Shown:
x = exterior angle
9x = interior angle
interior + exterior = 180
9x+x = 180
10x = 180
x = 180/10
x = 18
n = number of sides
n = 360/x
n = 360/18
n = 20
There are 20 sides to the regular polygon.
Side notes:
The formula to determine n only works for regular polygons.A polygon with 20 sides is known as an icosagon.Any pair of adjacent interior and exterior angles are supplementary. They add to 180 degrees.