Answers
[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ d=4\\ a_1=-2\end{cases} \\\\\\ \begin{array}{llll} term&value\\ ------&------\\ 2&a_2=-2+(2-1)4\\ 3&a_3=-2+(3-1)4\\ 4&a_4=-2+(4-1)4\\ 5&a_5=-2+(5-1)4 \end{array}[/tex]
----------------------------------------------------------------------------------------
A(n)= 1/4 * A(n) is just a way of saying, you get the next term by multiplying the current one by 1/4, and A(1) = 8, simply means the first term's value is 8.
[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=\frac{1}{4}\\ a_1=8 \end{cases} \\\\\\ \begin{array}{llll} term&value\\ ------&------\\ 2&a_2=8\left( \frac{1}{4} \right)^{2-1}\\\\ 3&a_3=8\left( \frac{1}{4} \right)^{3-1}\\\\ 4&a_4=8\left( \frac{1}{4} \right)^{4-1}\\\\ 5&a_5=8\left( \frac{1}{4} \right)^{5-1}\\ \end{array}[/tex]
Related Questions
Where can the lines containing the altitudes of an obtuse triangle intersect.
Answers
Answer: The lines containing the altitudes of an obtuse triangle intersect at a point which lies outside the triangle called orthocenter.
Explanation:-
A line which passes through a vertex of the triangle and is perpendicular to the opposite side is called an altitude of the triangle.
The point where all three altitudes of the triangle intersect is called its orthocenter .
Orthocenter of acute triangle lies inside the triangle.Orthocenter of right triangle lies on the triangle.Orthocenter of obtuse triangle lies outside the triangle.What is the value of the 30th percentile for the data set 6283, 5700, 6381, 6274, 5700, 5896, 5972, 6075, 5993, 5581?
Answers
The 30th percentile for the given data set is 5758.8, calculated by arranging the data in ascending order and interpolating between the 3rd and 4th values.
To find the 30th percentile for the given data set, first arrange the data in ascending order and then calculate the rank of the 30th percentile. The formula to find the kth percentile for a data set with n observations is:
Rank = (k/100) * (n + 1)
For the given data set of 10 values, the 30th percentile rank would be:
Rank = (30/100) * (10 + 1) = 3.3
Since the rank is not a whole number, the 30th percentile lies between the 3rd and 4th values in the ordered set. After arranging the data:
5581
5700
5700
5896
5972
5993
6075
6274
6283
6381
The 3rd and 4th values are 5700 and 5896. We must interpolate to find the exact 30th percentile:
30th Percentile = 5700 + 0.3 * (5896 - 5700) = 5700 + 0.3 * 196 = 5700 + 58.8 = 5758.8
The 30th percentile is 5758.8.
A gift box has a length of 14 inches, a height of 8 inches, and a width of 6 inches. how many square inches of wrapping paper are needed to wrap the box?
Answers
The surface area of the rectangular box is equal to 488 square inches.
What is surface area?The area of the surface of the rectangular box is equal to the total surface area of the rectangular box.
Given that, a gift box has a length of 14 inches, a height of 8 inches, and a width of 6 inches.
The surface area will be calculated as,
SA = 2(6 x 14) + 2(6 x 8) + 2(14 x 8)
SA = 2(84) + 2(48) + 2(112)
SA = 168 + 96 + 224
SA = 488 square inches of paper to wrap the box.
Therefore, the surface area of the rectangular box is equal to 488 square inches.
To know more about surface area follow
https://brainly.com/question/26759265
#SPJ5
Final answer:
To find the square inches of wrapping paper needed for a gift box, calculate the surface area of the box by using its length, height, and width dimensions.
Explanation:
To calculate the square inches of wrapping paper needed to wrap the box, you need to find the surface area of the box.
Calculate the surface area of each side of the box: 2(length x width) + 2(width x height) + 2(length x height).
Plug in the given dimensions: 2(14 x 6) + 2(6 x 8) + 2(14 x 8).
Calculate the total: 2(84) + 2(48) + 2(112) = 168 + 96 + 224 = 488 square inches needed.
The product of twice a number and three three is the same as the difference of five five times the number and three fourths 3 4. find the number.
Answers
Given,
[tex]2x*3 = 5x - \frac{3}{4} [/tex]
[tex]6x = 5x - \frac{3}{4} [/tex]
[tex]x = - \frac{3}{4} [/tex]
Find the next term in the sequence:
1/3,2/9,3/27,...
A. 4/36
B. 4/54
C. 4/81
D. 4/109
Answers
Now, let's apply this rule to the last fraction. The denominator multiplied by three would be 81.
Therefore, the answer is C. 4/81
A club has 12 members. In how many ways can we select four members to go on a trip?
Answers
12C4 = 12!
----------
4! 8!
= 12*11*10*9 11*5*9 = 495
-------------- =
4*3*2*1
simplify the expression r^-3s^5t^2/r^2st^-2
Answers
(a^b)/(a^c)=a^(b-c) and a^(-b)=1/(a^b)
(r^-3s^5t^2)/(r^2st^-2)
r^(-3-2)s^(5-1)t^(2--2)
r^-5(s^4)t^4
(s^4t^4)/(r^5)
s^5 * t^2 * t^2 / r^3 * r^2 * s
s^4 * t^2 / r^5
The linear function y = 1.2x represents Alberto’s speed, y, in meters per minute, when his stride rate is x steps per minute. Alberto’s average stride rate during a 10-kilometer race is 180 steps per minute.
What is Alberto’s average speed during the race?
Answers
y = meters per minute
x = steps per minute = 180
y = 1.2 (180)
y = 216 meters per minute
Answer:
What is Alberto’s average speed during the race?
216 meters per minute
Based on the linear model, which is the best prediction of how long it will take Alberto to finish the 10-kilometer race?
B. 46 minutes
Follow the process of completing the square to solve 2x2 + 8x - 12 = 0. How will the left side of the equation factor in step 5?
A. (2x + 32)2
B. (4x + 8)2
C. (4x + 16)2
Answers
with form
ax^2+bx+c=0
move c to the other side
2x^2+8x=12
x^2 is multiplied -> divide equation by 2
x^2+4x=6
complete square:
divide b=4 by 2
4*1/2=2
square 2
2^2=4
add 4 to both sides
x^2+4x=6
x^2+4x+4=6+4
x^2+4x+4=10
transform to polynom
(x+2)^2=10
this left side is option B multiplied by a factor of 16 and therefore equal:
(4x + 8)^2
(4*4)x^2+(4*2*8)x+8*8
16x^2+64x+64
x^2+4+4
bonus: calculate root
x+2=+/-sqrt(10)
x=-2+/-sqrt(10)
so it is option B
Complete the square to solve [tex]2x^2 + 8x - 12 = 0[/tex].
Soooooooo, [tex](4x + 8)^2[/tex] is your answer. :)
Samantha wants to use her savings of $1150 to buy shirts and watches for her family. the total price of the shirts she bought was $84. the watches cost $99 each. what is the maximum number of watches that samantha can buy with her savings? (1 point)
Answers
99w = 1150 - 84
99w = 1066
w = 1066/99
w = 10.76......so she can buy 10 watches maximum
Answer:
Maximum number of watches Samantha can buy equals:
10
Step-by-step explanation:
Samantha wants to use her savings of $1150 to buy shirts and watches for her family.
The total price of the shirts she bought was $84.
The watches cost $99 each.
Let she bought x watches
then, 84+99x≤1150
subtracting by 84 on both sides, we get
99x≤1066
dividing both sides by 99, we get
x≤ 10.7676
Hence, maximum number of watches Samantha can buy equals:
10
One pound of feathers would be easier weighing than one pound of iron
Answers
One pound of feathers = One pound of iron
What is the center and radius of the circle with equation x2 + y2 + 6x + 16y + 64 = 0?
Answers
By making factors:
[tex]x^2+y^+2+6x+16y+64=0\\ x^2+6x+9+y^2+16y+64-9=0\\ (x+3)^2+(y+8)^2=9\\ radius=3 [/tex]
Person 1 can do a certain job in twenty-one minutes, and person 2 can do the same job in twenty-eight minutes. When completing the job together, which expression would be used to represent the amount of work done by person 1?
21
1/21
x/21
21x
Answers
r = 1/21
Answer:
[tex]\frac{1}{21}[/tex] would be used to represent the amount of work done by person 1.
Step-by-step explanation:
When someone does a work in x time,
Then, the work done by the person in one day = [tex]\frac{1}{x}[/tex]
Given,
Time taken by person 1 = 21 minutes
Thus, by the above statement,
The one day work of person 1 = [tex]\frac{1}{21}[/tex]
Hence, [tex]\frac{1}{21}[/tex] would be used to represent the amount of work done by person 1.
Second option is correct.
Identify the function as either a constant, direct variation, absolute value or greatest integer function f (x)=-4
Answers
No matter what the input x is, the output f(x) is going to be -4. Therefore, the output is constant.
Note: f(x) can be interchanged with y. So we can say y = -4.
Krystal left the hardware store and traveled toward the recycling plant at an average speed of 61 mph. Scott left at the same time and traveled in the opposite direction with an average speed of 65 mph. Find the number of hours Scott needs to travel before they are 252 mi. Apart
Answers
Since Krystal and Scott is heading on opposite directions, therefore the distance between the two would be the sum of their distances from where they left, so:
total distance (d) = distance covered by Krystal (dK) + distance covered by Scott (dS)
d = dK + dS
We know that the formula for distance is:
distance = velocity * time
So,
d = vK * t + vS * t
where
vK = velocity of Krystal = 61 mph
vS = velocity of Scott = 65 mph
d = 252 miles
Therefore:
252 = 61 t + 65 t
126 t = 252
t = 2 hours
Therefore Scott needs to travel for 2 hours.
An and ac are opposite rays.all of the following are true except
A = A,B,C are collinear
B = A,B,C are coplanar
C = AB = AC
D = A is between B and C
Answers
B = A, B, C are coplanar.
(I believe this should be the answer, but I'm not so sure.)
→It is given that, AB and AC are Opposite rays.
Means point ,A , B and C are collinear that is lying in the same line.
→Points are said to be Coplanar , if they lie in the same Plane.
Line segment Joining Points A, B and C lies on the same surface , so we can say that ,these points are Coplanar.
→As, AB and AC are rays , so point A will be in between C and B.
But, it can be sometimes true that,
→AB=AC
So, Incorrect Statement is:
AB=AC
Which of the following statements is true regarding the relationship between circles and triangles? A. There are many circles that can be circumscribed about a triangle. B. There are many triangles that can be inscribed in a given circle. C. There is only one unique triangle that can be inscribed in a given circle. D. There are many triangles that can be circumscribed about a given circle.
Answers
If you do you'll find that the answer is B.
The true statement regarding the relationship between circles and triangles is option B. There are many triangles that can be inscribed in a given circle.
A circle can be characterized by its center's location and its radius's length.
How to make an inscribed circle in a triangle?There can be many different ways, one can include arc way, one can include angle bisector and perpendicular, and we can even try to discover some.
But usually, (for the angle bisector and perpendiculars), we do the following:
Divide one of the angles in half. Divide another angle in half.
The incenter, or point where they cross, is the inscribed circle's centre.
Construct a perpendicular from the triangle's centre point to one of its sides.
Draw an inscribed circle by placing the compass on the centre point and adjusting the length to where the perpendicular crosses the triangle.
The true statement regarding the relationship between circles and triangles is option B. There are many triangles that can be inscribed in a given circle.
Learn more about inscribing circle here:
https://brainly.com/question/17043518
#SPJ2
what is the reciprocal of 0.25
Answers
convert 0.0000001 to a power of 10.
107
10−7
106
10−6
Answers
Answer:
Its actually 10 to the power of -7.
Step-by-step explanation:
This is because it can be written as:
1/10000000
Because there is 7 0's it becomes -7
Therefore its 10 to the power of -7
Find the domain of f of x equals negative square root of the quantity two x plus four, plus 3?
Answers
The ordered pairs below represent a relation between x and y. (-3,-3), (-2,0), (-1,3), (0,6), (1,9), (2,12).
Could this set of ordered pairs have been generated by a liner function?
A. No, because the y-values decrease then increase
B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x,y) values you use to calculate it
C. No, because the distance between consecutive y-values is different than the distance between consecutive x-values
D. Yes, because the distance between x-values is inconstant
Answers
are matched respectively to -3, 0, 3, 6, 9, 12.
Thus, as the x-coordinate changes by 1, the y-coordinate changes by 3:
We can represent this change by the following picture:
|
|
(2,12) _ |
|
|
(1,9) _ |
|
|
(0,6) _ |
So, the points are on a straight line, because:
B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x,y) values you use to calculate it
The sum of 2 consecutive odd interferes is 92 find the numbers
Answers
92/2 = 46
46-1 =45
46+1 =47
45+47 = 92
numbers are 45 & 47
Which sequence can be defined by the recursive formula f (1) = 4, f (n + 1) = f (n) – 1.25 for n ≥ 1? 1, –0.25, –1.5, –2.75, –4, . . . 1, 2.25, 3.5, 4.75, 6, . . . 4, 2.75, 1.5, 0.25, –1, . . . 4, 5.25, 6.5, 7.75, 8, . . .
Answers
Answer:
[tex]4,2.75,1.5,0.25......[/tex]
Step-by-step explanation:
f (1) = 4, [tex]f (n + 1) = f (n) - 1.25[/tex]
To get the sequence we start with n=1
Plug in n=1 in the formula
[tex]f (n + 1) = f (n) - 1.25[/tex]
[tex]f (1 + 1) = f (1) - 1.25[/tex]
[tex]f (2) = f (1) - 1.25[/tex], replace f(1)=4
[tex]f (2) = 4 - 1.25=2.75[/tex]
n=2
[tex]f (2 + 1) = f (2) - 1.25[/tex]
[tex]f (3) = f (2) - 1.25[/tex], replace f(2)=2.75
[tex]f (3) = 2.75 - 1.25=1.5[/tex]
n=3
[tex]f (3 + 1) = f (3) - 1.25[/tex]
[tex]f (4) = f (3) - 1.25[/tex], replace f(3)=1.5
[tex]f (4) = 1.5 - 1.25=0.25[/tex]
Sequence is [tex]4,2.75,1.5,0.25......[/tex]
Answer:
C.
4, 2.75, 1.5, 0.25, –1
Step-by-step explanation:
If sin 42° =2/3, then cos 48°=
Answers
Then:
sin 42° = cos(90° - 42°) = cos 48°
IF sin 42° = 2/3, the cos 48° = 2/3
if sin42=2/3 then cos(90-42)=2/3 as well (90-42=48)
Janelle is at the movie theater and has $20 to spend.
She spends $8 on a ticket and wants to buy some snacks. Each snack costs $4.99.
How many snacks, x, can Janelle buy?
Inequality: 20≥8 + 4.99x
Please answer, its urgent
Answers
After purchasing a movie ticket for $8, Janelle has $12 left to spend on snacks. Each snack costs $4.99, which means she can buy a maximum of 2 snacks.
Explanation:Janelle started with $20 and has already spent $8 on a ticket, leaving her with $20 - $8 = $12 for snacks. Each snack costs $4.99. To determine how many snacks, represented by x, Janelle can buy, we can set up the inequality 12 ≥ 4.99x. Dividing both sides of the inequality by the cost of one snack (4.99) gives us x ≤ ≈ 2.4. Since Janelle cannot buy a fraction of a snack, she can buy a maximum of 2 snacks with her remaining $12.
Learn more about the Inequality problem here:https://brainly.com/question/15086723
#SPJ12
Choose the correct description of the graph of the compound inequality x - 3 less than or equal to 5
A- open circle on 8, shading to left
B- closed circle on 8, shading to left
C- open circle on 8, shading to right
D- closer circle on 8, shading to right
Answers
x < = 5 + 3
x < = 8
closed circle on 8 (it is closed because there is an equal sign in the problem)...and since it is less then, it will be shaded to the left.
Answer:
B- closed circle on 8, shading to left.
Step-by-step explanation:
We have been given an inequality [tex]x-3\leq 5[/tex]. We are asked to choose the correct description of the graph of the compound inequality.
Let us solve for x.
[tex]x-3+3\leq 5+3[/tex]
[tex]x\leq 8[/tex]
Since we have been given a less than or equal to sign, so we will have a solid dot at [tex]x=8[/tex].
Since the solutions for our given inequality are less than and equal to 8, so we will shade in all values of x that are to the left of 8.
Therefore, option B is the correct choice.
Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, -5). Write the equation of this cubic polynomial function. Recall that the zeros are (2, 0), (3, 0), and (5, 0). What is the y-intercept of this graph?
Answers
So we will let specific cubic polynomial function of the form
[tex]f(x) = a(x - x_1)(x-x_2)(x-x_3)[/tex]
As we know zeros are that point where we will get value of function equal to zero. So it is basically in form [tex](x_n , 0)[/tex]
SO in given question zeros are (2 , 0) , (3, 0) and (5,0)
So we can say [tex]x_1 = 2 , x_2 = 3 , x_3 = 5[/tex]
So required equation is
[tex]f(x) = a (x-2)(x-3)(x-5)[/tex]
[tex]= a[(x^2 - 2x - 3x + 6)(x-5)][/tex]
[tex]= a[(x^2 - 5x+6)(x-5)][/tex]
[tex]= a(x^3 - 5x^2 + 6x- 5x^2 + 25x - 30)[/tex]
[tex]= a(x^3 - 10x^2+31x-30)[/tex]
Now we have one point (0 , -5) from which graph passes.
So we say at x = 0 , f(x) = -5
[tex]-5= a (0-0+0 - 30)[/tex]
[tex]-5 = -30a[/tex]
[tex]a = \frac{-5}{-30} = \frac{1}{6} [/tex]
So required equation of cubic polynomial is
[tex]f(x) = \frac{1}{6}(x^3 -10x^2+31x-30) [/tex]
For finding y - intercept we simply plugin x = 0 in given equation.
As we know at x = 0 , value of function is -5.
So y - intercept is -5.
The equation of the function is [tex]y = \frac 16(x -2)(x -3)(x -5)[/tex], and the y-intercept of the function is -5
A cubic function is represented as:
[tex]y = a(x -x_1)(x -x_2)(x -x_3)[/tex]
The zeros are (2, 0), (3, 0), and (5, 0).
This means that:
(x1, y) = (2, 0)
(x2, y) = (3, 0)
(x3,y) = (5, 0)
So, we have:
[tex]y = a(x -2)(x -3)(x -5)[/tex]
The graph passes through the point (0,-5).
So, we have:
[tex]-5 = a(0 -2)(0 -3)(0 -5)[/tex]
Evaluate the products
[tex]-5 = -30a[/tex]
Solve for a
[tex]a = \frac{5}{30}[/tex]
[tex]a = \frac{1}{6}[/tex]
Substitute 1/6 for a in [tex]y = a(x -2)(x -3)(x -5)[/tex]
[tex]y = \frac 16(x -2)(x -3)(x -5)[/tex]
The y-intercept of the function is when x = 0.
Hence, the y-intercept of the function is -5
Read more about cubic functions at:
https://brainly.com/question/20896994
The graph shows the location of Grant's, Hannah's, and Isobel's houses. Each unit on the graph represents 1 block. A coordinate plane graph is shown. Grants house is located at negative 4 comma 3. Hannahs house is located at 1 comma 3. Isobels house is located at 1 comma negative 4. If Grant walks from his house to Isobel's house, then on to Hannah's house along the path shown, how far will he have walked in blocks? Round your answer to the nearest tenth.
Answers
5^2 + 7^2 = c^2
25 + 49 = c^2
74 = c^2
sqrt 74 = c
8.6 = c
so grant's to Isabelle's is 8.6 blocks, then from there to hannah's house, which is 7 blocks....so he walks a total of 8.6 + 7 = 15.6 blocks
The total distance covered in the graph from Grant to Isobel's house and Isobel's house to Hannah's house is 15.06.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.
As per the given coordinate has been drawn in the graph below,
The locus of the path from Grant's house to Isobel's house and then Hannah's house is making a right-angle triangle.
By Pythagoras' theorem,
Distance from Grant's house to Isobel's house ⇒
√(4² + 7²) = 8.06
The distance from Isobel's house to Hannah's house ⇒ 3 + | -4| = 7
Therefore, 8.06 + 7 = 15.06.
Hence "The total distance covered in the graph from Grant to Isobel's house and Isobel's house to Hannah's house is 15.06".
To learn more about graphs,
brainly.com/question/16608196
#SPJ5
Solve 4a+3=11 plz step by step
Answers
Again, we want to work on isolating the variable a. Let's start doing this by first getting rid of the 3.
We must do the inverse of the operation, which in this case will be subtraction since the 3 is positive. Also, always remember that when we do something on one side of the equation, we must do it on the other.
4a + 3 - 3 = 11 - 3
4a = 8
Since the 4 is multiplying our variable a, this means the inverse of the operation will be division. To fully isolate a by getting rid of the 4, we will divide by 4 on both sides.
4a / 4 = 8 / 4
a = 2
Hopefully, this helps.
The value of solution of expression is, a = 2
We have to give that,
An expression to simplify,
4a + 3 = 11
Now, Simplify the expression by combining like terms as,
4a + 3 = 11
Subtract 3 on both sides,
4a + 3 - 3 = 11 - 3
4a = 8
Divide 4 into both sides,
a = 8/4
a = 2
Therefore, the solution is, a = 2
To learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ6
Find the length of the missing side. The triangle is not drawn to scale.
A. 60
B. 34
C. 169
D. 13
Answers
By the Pythagorean theorem:
a² = 12² + 5² = 144 + 25 = 169
a = √169 = 13 units