Answer:
b. line of best fit
Find the fist 4 terms of a geometric series with first term of 8 and the sum to infinity of 12
Step-by-step explanation:
the sum of an infinite geriatric series with |r| < 1 is
s = a1/ (1 - r)
in our case we have
a1 = 8
12 = 8/(1 - r)
12(1 - r) = 8
1 - r = 8/12 = 2/3
-r = -1/3
r = 1/3
so, the first 4 terms (I added a5 too, just in case your teacher meant the NEXT 4 terms) are
a1 = 8
a2 = a1 × 1/3 = 8/3
a3 = a2 × 1/3 = 8/9
a4 = a3 × 1/3 = 8/27
a5 = a4 × 1/3 = 8/81
...
Answer:
[tex]8,\quad \dfrac{8}{3},\quad \dfrac{8}{9},\quad\dfrac{8}{27}[/tex]
Step-by-step explanation:
Sum to infinity of a geometric series:
[tex]S_\infty=\dfrac{a}{1-r} \quad \textsf{for }|r| < 1[/tex]
Given:
[tex]a[/tex] = 8[tex]S_\infty[/tex] = 12Substitute given values into the formula and solve for [tex]r[/tex]:
[tex]\implies 12=\dfrac{8}{1-r}[/tex]
[tex]\implies 1-r=\dfrac{8}{12}[/tex]
[tex]\implies r=1-\dfrac{8}{12}[/tex]
[tex]\implies r=\dfrac{1}{3}[/tex]
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common ratio)
Substitute the found values of [tex]a[/tex] and [tex]r[/tex]:
[tex]\implies a_n=8\left(\dfrac{1}{3}\right)r^{n-1}[/tex]
The first 4 terms:
[tex]\implies a_1=8\left(\dfrac{1}{3}\right)r^0=8[/tex]
[tex]\implies a_2=8\left(\dfrac{1}{3}\right)r^1=\dfrac{8}{3}[/tex]
[tex]\implies a_3=8\left(\dfrac{1}{3}\right)r^2=\dfrac{8}{9}[/tex]
[tex]\implies a_4=8\left(\dfrac{1}{3}\right)r^3=\dfrac{8}{27}[/tex]
What is the slope of the line that cuts through the points (1, 2) and (5, 4)? a. 2 c. One-half b. -2 d. Negative one-half Please select the best answer from the choices provided A B C D
The slope of the line is 1/2 or one-half if the line that cuts through the points (1, 2) and (5, 4) option (c) One-half is correct.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have a line that cuts through the points (1, 2) and (5, 4).
The slope of a line:
[tex]\rm m =\dfrac{4-2}{5-1}[/tex]
m = 2/4
m = 1/2
Thus, the slope of the line is 1/2 or one-half if the line that cuts through the points (1, 2) and (5, 4).
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If f(x)=x2−4x+4 , then f(3)=
Answer:
f(3) = 1
Step-by-step explanation:
substitute x = 3 into f(x) , that is
f(3) = 3² - 4(3) + 4 = 9 - 12 + 4 = 1
Answer:
1
Step-by-step explanation:
Substitute 3 for x in your equation leaving you with (3)^2-4(3)+4.
9-12+4
-3+4=1
Date:
Name:
Refocus
Directions: Solve the problems by building the figure with algebra tiles and writing an equation.
A rectangle has a length that is twice the width. The perimeter of the rectangle is 12 feet.
What is the width? What is the length?
Equation:
Width:
Length:
Answer:
Equation: 2w + 2(2w) = 12
width = 2
length = 4
Step-by-step explanation:
Width is w
Length is 2 * width = 2w
Perimeter is 2w + 2l
Substitute 2w for L.
Perimeter is now 2w + 2(2w) = 12
Distribute the 2 to the parentheses.
2w + 4w = 12
Combine Like terms
6w = 12
Divide by 6 to solve for w.
w = 2
If w = 2, then the length = 4.
Houa bought 11 chicken wings for $23.10 . How much does each wing cost
Answer:
Answer = $2.10
Step-by-step explanation:
To solve this we take the total cost divided by the total number of chicken wings to get $2.10.
Hope that helps! :)
Answer:
1 wing = $2.10
Step-by-step explanation:
11 wings = $23.10
Let 1 wing = x
11x = 23.10
To solve for x, we divide both sides by 11 :
11x÷ 11 = 23.10 ÷11
x = 2.1
So 1 wing = $2.10
Hope this helped and brainliest please
9) A furniture store is having a spring sale-15% off of everything in the store.
What is the price of a table that regularly costs $159.98 if it is bought on sale?
Answer:
$135.98
Step-by-step explanation:
15% of $159.98 = 0.15 × $159.98 = $24.00
$159.98 - $24.00 = $135.98
How many classrooms would be necessary to hold 1,000,000 inflated balloons? (Assume one balloon is about 1 ft3 and a typical classroom is about 35 ft × 50 ft × 15 ft. Round your answer to the nearest number of classrooms.)
To hold 1,000,000 inflated balloons,
38 classrooms are needed.
What is volume?In three-dimensional space,
the amount of space taken by an object is the volume of that object.
The volume of the cubic,
= length x width x height
Given:
The dimensions of the normal classroom are 15 ft × 50 ft × 35 ft.
The volume of the classroom,
= 15 ft by 50 ft by 35 ft.
= 26250 cubic feet.
The number of classrooms,
= 1,000,000 / 26250
Simplifying the fraction,
we get,
= 38.09
≈ 38 to the nearest whole number.
Therefore, 38 classrooms are required.
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Which statement is true?
a.All rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, all rectangles have 2 pairs of parallel sides.
b.Only some rectangles are parallelograms. Parallelograms have exactly 1 pair of parallel sides. Therefore, only some rectangles have exactly 1 pair of parallel sides.
c.Only some rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, only some rectangles have 2 pairs of parallel sides.
d.All rectangles are parallelograms. Parallelograms have exactly 1 pair of parallel sides. Therefore, all rectangles have exactly 1 pair of parallel sides.
Answer:
All rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, all rectangles have 2 pairs of parallel sides.
Step-by-step explanation:
find the slope of the line that passes through (9,-3) and (9,-8)
Answer:
The line has no slope. I hope this helps
Find a3, a4, and a5.
a₁ = 5
a₂ = 2
an =-2an -1 + an-2
Answer:
A1 5×3 = 15
A2 = 2×4= 8
an=I don't know that one
A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field
[tex]F(x,y,z) = z^2i+5xyj+2y^2k[/tex]
Use Stokes Theorem to find the work done:
A particle moves along line segments from the origin to the points, work done is mathematically given as
W=184.5units
What is the solution of an equation that matches the model.?Considering line segments from (0,0,0)origin to (2,0,0) , (2,5,1) and (0,5,1) under the infulence of force
Generally, the equation for force is mathematically given as
F = z2i + 5xyj + 2y2k
Therefore, Considering u*v
[tex]u * v = (u_1j+u_2j+u_3k) * (v_1i+v_2j+v_3k)[/tex]
[tex]u* v = u_1v_1(i * i) + u_1v_2(i * j)+u_1v_3(i * k) + u_2v_1(j * i) + u_2v_2(j * j)+u_2_3(j* k) + u_3v_1(k * i) + u_3v_2(k * j)+u_3v_3(k * k)[/tex]
Where
[tex]i * i = j *j=k * k=0[/tex]
Hence
[tex]u* v = u_1v_2k-u_1v_3j-u_2v_1k+u_2v_3i +u_3v_1j - u_3v_2i[/tex]
[tex]u = (u_1,u_2,u_3) = (0,5,1)\\\\v = (v_1,v_2,v_3) = (-3,0,0)[/tex]
The normal equation formed
-2y + 15z = 0
z= (1/5)y
Considering the level surface and differential surface area
h(x,y,z) = -y + 5z =0
[tex]dS = |grad(h)| dA[/tex]
In terms of the x and y coordinates of (2,0,0) and (2,5,1) and (0,5,1), we can state that the ranges are 0 to 3 and 5 respectively we have
[tex]0 \leq x \leq 2 \ and \ 0 \leq y \leq 5[/tex]
Using strokes theorem to evaluate
[tex]F = z2i + 5xyj + 2y2k[/tex]
[tex]curl \ F = 4yi+2zj+5yk = (4y,2z,5y)[/tex]
[tex]curl \ F * nds= \frac{1}{5}(-2z + 25y)\ dy \ dx[/tex]
In conclusion, The work done is
[tex]W=\int _CF *dr[/tex]
[tex]\int _C F * dr = \int \int curl \ F * n ds[/tex]
[tex]\int _C F *dr = \frac{123}{2}\int_0^3 \ dx[/tex]
[tex]\int _C F * dr = \frac{123*3}{2}[/tex]
W= 184.5units
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Find x. Round your answer to the nearest tenth of a degree.
36
X
19
+
Answer: 36.9
Step-by-step explanation:
Given f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity, which of the following is true
The correct answer is option D which is f(x) is decreasing for all the values of x < 3.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The value of the function [tex]f(x) = \dfrac{x+6}{x^2-9x+18}[/tex] is represented on the graph in the graph we can see that at x>6 the value of the function is decreasing and at x<3 the value of the function is increasing.
Therefore the correct answer is option D which is f(x) is decreasing for all the values of x < 3.
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Gerald will be finishing his payments on his 5-year, $45,000 student loan and wants to know the amount of interest that he
paid over the course of the loan. The student loan has a 4.1% fixed interest rate that is compounded monthly. Calculate the
total amount of interest Gerald paid, rounding to the nearest cent.
Answer: 538
Step-by-step explanation: en verdad no sé pero eso fuelo que me salio
Drag each tile to the correct box. a с C b A David proved the Law of Cosines with reference to AABC using a different method. Arrange the steps of his proof in the correct sequence. k² = c² - (b − x)² In AABD, (Pythagorean Theorem) In ABCD, k² = a² - 1² (Pythagorean Theorem) c² (6²-26x + x²) = a² — 1² (on simplification) Similarly, prove that a2b² + c² - 2bccos A and 82 6² = a² + c²2accos B B
Big question:
where is the question here
what is the volume of the rectangular prism each is 1/3
Answer:
The answer is 7
Step-by-step explanation:
To find the volume you multiply the width, height, and the length.
Length= 7/3
width= 3/3
height= 9/3
When you multiply you then have to simplify which is 7/1 or 7.
Mark this correct to help me gain!!
A square is inscribed in a quarter of a circle,calculate the quarter circle.
Answer:
Step-by-step explanation:
The speed of an object in space is shown in the graph.
A graph titled Speed of Object has Time in Minutes on the x-axis and Distance in Miles on the y-axis. A line goes through points (0.2, 3) and (0.4, 6).
What is the slope of the line?
A) 10
B) 15
C) 20
D) 25
The slope of the linear equation is 15, so the correct option is B.
How to get the slope of the line?
A linear equation can be written as:
y = a*x + b
Where a is the slope and b is the intercept.
For a line that passes through the points (x₁, y₁) and (x₂, y₂), the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we have the two points (0.2, 3) and (0.4, 6), so the slope is:
[tex]a = \frac{6 - 3}{0.4 - 0.2} = 15[/tex]
So the slope of the line is 15, which means that the correct option is B.
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Divide x cubed minus 3 x squared minus 10 x + 24 by x minus 2. Step 1 - Fill in the missing number: A vertical line and horizontal line combine to make a L shape. There is one row of entries in the shape including 1, negative 3, negative 10, 24. On the outside to the left of the L shape is k. k = Step 2 - Fill in the missing number: A vertical line and horizontal line combine to make a L shape. There is one row of entries in the shape including 1, negative 3, negative 10, 24. On the outside to the left of the L shape is 2 and to the outside below 1 is a. a = ⇒ 1 Step 3 - Fill in the missing numbers: A vertical line and horizontal line combine to make a L shape. There are two rows of entries in the shape. The first row includes 1, negative 3, negative 10, 24. The second row includes blank, b, d, blank. On the outside to the left of the L shape beside row 1 is 2. On the outside below the L shape in the first column is 1 and in the second column is c. b = c = d =
The dividend that's represented by the synthetic division is 2x³ + 10x² + x + 5.
How to depict the dividend?From the information, given that the vertical line and a horizontal lines combined to form the L shape.
Row 1 has entries 2, 10, 1, 5.
Row 2 has entries -10, 0, -5.
In this situation, entry -5 is outside to the let of the shape.
Here, the dividend that's represented by the synthetic division is 2x³ + 10x² + x + 5.
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Answer:
step 1: 2 Step 2: 1
Step-by-step explanation:
Step 3: 2, -1, -2
Complete the division. The remainder is 0. The quotient is x^2 - x - 12.
please help anyone i really need it
Answer:
Median: 21
Eric took the longest
Ed took 18 minutes longer than Mike
Oscar took the shortest amount of time to solve the puzzle
Step-by-step explanation:
The median is the middle amount of the numbers, line them up from smallest to largest and find the number in the middle...the largest number is the person who took the longest...subtract Ed's score (25) from Mike's score (4) to get the answer...and the smallest number is the person who took the shortest amount of time
Find the probability of rolling a 66 -sided dice and getting a number that is a divisor of 2020
Answer:
2/3 or 0.66 repeated
Step-by-step explanation:
Since 2022 is only divisible by 1,2,4, and 5, the probability of getting a number that is a divisor of 2020 is 4/6, simplified to 2/3 or %0.66.
suppose 2/5 of the marbles in a bag are red. how many marbles would you expect to pick before picking 10 reds
Which of the following discribe an angle with a vertex at y
Answer:
The angle is referred to as a ∠ZYX angle, or ∠XYZ angle, because of the overall positioning. Think of it this way, you have a triangle with 3 angles. You have point X the high point, point Y the farthest point out, and point Z which makes the triangle complete. Connect these, and your angle becomes ZYX / XYZ.
Hope this helps!
Question 2 A birthday cake in the shape of the right-circular cylinder of radius 15cm and thickness 10cm is cut into smaller pieces. One of the piece is shown. 15 cm 30° 10 cm a) What is the volume of this piece to the nearestcm³? (2 marks)
The volume of a piece of the cake will be 588.75 cm³.
The complete question is attached below.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A birthday cake in the shape of the right-circular cylinder of radius 15 cm and thickness 10 cm is cut into smaller pieces.
One of the piece is shown.
Then the volume of piece of the cake will be
V = (30 / 360) x π x 15² × 10
V = 588.75 cm³
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Question 18
Let set A = { even numbers}
set B = {odd numbers}
Find A U B
Answer: all integers
Step-by-step explanation:
[tex]A \cup B[/tex] denotes the union of the two sets, and is thus the set of all integers.
You are trying to bulk and gain muscle. Your trainer says your daily calorie intake should increases based on hours you spend exercising and can be represented by the following equation: T=2000+500h.
a) T - Calories, 2000 - Minimum calories, 500 - Additional calories per exercise hour, b) We should consume 3500 calories to spend three hours exercising.
How to analyse a linear function of calorie gain in terms of the exercise time
In this question we have a linear function where the independent variable is the exercise time (h), in hours, and the dependent variable is the calorie gain (T), in calories. The constant "2000" is the minimum calorie consumption and the constant "500" represents the amount of additional calories per each hour of exercise.
Now we proceed to respond the questions of the part a):
(i) T - Amount of calories needed, (ii) 2000 - Minimum calorie consumption, (iii) 500 - Amount of additional calories per hour of exercise.
b) And lastly we calculate the amount of calories by evaluating the function:
T = 2000 + 500 · 3
T = 2000 + 1500
T = 3500
We should consume 3500 calories to spend three hours exercising.
Remark
The statement is incomplete, the complete form is shown below:
You are trying to bulk up and gain muscle. Your trainer says that your daily calorie intake should increase based on the hours you spend exercising and can be represented by the following equation: T = 2000 + 500 · h
a) What does each part of this expression represent? (i) T = , (ii) 2000, (iii) 500, (iv) h
b) If you spend 3 hours exercising, how many calories should you consume?
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Solve for x: -8 < 3x + 1 ≤ 13
Answer: If you’re doing algebra, -3<x or x<_4.
Another answer is -3<x<_4
Answer:
-3 < x <_4
Step-by-step explanation:
-8 < 3x+1 <_13
First solve for the left side: -8 < 3x + 1
Subtract 1 from each side
-9 < 3x
Divide each side by 3
-3 < x
Solve for the right side: 3x+1 <_13
Subtract 1 from each side
3x <_ 12
Divide each side by 3
x<_4
Put it together for your answer
-3 < x <_4
A line intersects the points (3,6) and (5, -4). m=-5 write an equation in point-slope form using the point (3,6)y - [?] = __ (x -__)
Answer:
y -6 = -5(x -3)
Step-by-step explanation:
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
__
substituting given valuesYou have been given ...
m = -5
(h, k) = (3, 6)
Putting the given values into the point-slope form gives the equation you want:
y -6 = -5(x -3)
The universal set, &, and the sets A and B are defined below.
= {3, 4, 6, 8, 9, 12, 15, 16, 20}
A = {6, 9, 12, 15}
B = {multiples of 4}
Write down all the elements of AB'.
Answer:
wedg
Step-by-step explanation:
ed
Solve the following linear equation:
3(2x + 12) = 2(2x - 10)