Answers
The first five terms of a geometric sequence are 5, 10, 20, 40, 80.
A geometric sequence is also known as Geometric Progression (GP) is a non-zero numerical series whereby each term succeeding the very first is determined by multiplying the preceding one by a fixed, non-zero value designated as the common ratio.
It can be expressed by using the formula:
[tex]\mathbf{a_n = ar^{n-1}}[/tex]
where;
[tex]\mathbf{a_n=}[/tex] [tex]\mathbf{n^{th}}[/tex] term of the sequencea = first termr = common ratioGiven that;
the first term a₁ = 5the common ratio r = 2∴
The second term of the sequence is:
[tex]\mathbf{a_2 = 5 \times 2^{2-1}}[/tex]
[tex]\mathbf{a_2 = 5 \times 2^{1}}[/tex]
[tex]\mathbf{a_2 = 10}[/tex]
The third term of the sequence is:
[tex]\mathbf{a_3 = 5 \times 2^{3-1}}[/tex]
[tex]\mathbf{a_3 = 5 \times 2^{2}}[/tex]
[tex]\mathbf{a_2 = 20}[/tex]
The fourth term of the sequence is:
[tex]\mathbf{a_4 = 5 \times 2^{4-1}}[/tex]
[tex]\mathbf{a_3 = 5 \times 2^{3}}[/tex]
[tex]\mathbf{a_4 = 40}[/tex]
The fifth term of the sequence is:
[tex]\mathbf{a_5 = 5 \times 2^{5-1}}[/tex]
[tex]\mathbf{a_3 = 5 \times 2^{4}}[/tex]
[tex]\mathbf{a_4 = 80}[/tex]
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Related Questions
(-11, 12),(-4,-9) what is the slope
Answers
Answer:
m = -21 / 7 = -3 / 1 = -3
Step-by-step explanation:
i think im not sure but i hope it helps and good luck!
In the example function, could one side length ever
produce two different perimeters? Explain.
Answers
Answer:
no
Step-by-step explanation:
Express the ratio as a fraction in simplest form. 10 yards to 10 feet
Answers
Answer:
The ratio is 3:1
Step-by-step explanation:
[tex]\frac{10 yards}{10 feet}[/tex]
We know, 1 yard is equal to 3 feet
So, [tex]\frac{10 yards X 3}{10 feet}[/tex] is equal to [tex]\frac{30 feet}{10 feet}[/tex] is equal to 3:1
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Including a 5% sales tax, an inn charges $189 per night. Find the inn's nightly cost before the tax is added.
Answers
Light bulbs cost £3.40 each.
Yasmin buys as many as she can with £30.
How much change should she get?
Give your answer in pounds, £.
Answers
======================================================
Work Shown:
x = number of light bulbs
3.40x = total cost to buy x light bulbs, cost is in pounds
3.40x = 30
x = 30/(3.40)
x = 8.823529 approximately
Rounding down, we get 8
Note that,
3.40*8 = 27.20 pounds which is under budget3.40*9 = 30.60 pounds which is over budgetTherefore, the highest number of bulbs that can be bought is 8.
The change given will be 30-27.20 = 2.80 pounds
Write an equation in slope intercept form for the line perpendicular to y = 2x - 3 that passes through the point (-3, -3)
Answers
Answer:
y=-1/2x-9/2
Step-by-step explanation:
check picture
The equation of the line perpendicular to y = 2x - 3 that passes through the point (-3, -3) is y = (-1/2)x - 9/2 in slope-intercept form.
To find the equation of a line perpendicular to y = 2x - 3, we need to determine the slope of the original line and then find the negative reciprocal of that slope.
The original line has a slope of 2. The negative reciprocal of 2 is -1/2.
Now, we have the slope (-1/2) and the point (-3, -3) that the perpendicular line passes through.
We can use the point-slope form of a linear equation to write the equation of the line:
y - y1 = m(x - x1)
Substituting the values:
y - (-3) = (-1/2)(x - (-3))
y + 3 = (-1/2)(x + 3)
Expanding and simplifying:
y + 3 = (-1/2)x - 3/2
y = (-1/2)x - 3/2 - 3
y = (-1/2)x - 3/2 - 6/2
y = (-1/2)x - 9/2
Therefore, the equation of the line perpendicular to y = 2x - 3 that passes through the point (-3, -3) is y = (-1/2)x - 9/2 in slope-intercept form.
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find the point of the line segment joining the points (-2,-1) and (-10,4)
(type an ordered pair)
the midpoint is ____
Answers
Answer:
( - 6, 1.5 )
Step-by-step explanation:
( x1, y1 ) = ( - 2, - 1 )
Here,
x1 = - 2
y1 = - 1
( x2, y2 ) = ( - 10, 4 )
Here,
x2 = - 10
y2 = 4
Formula : -
Mid - point = ( x1 + x2 ) / 2, ( y1 + y2 ) / 2
Mid - point = ( - 2 - 10 ) / 2, ( - 1 + 4 ) / 2
= - 12 / 2, 3 / 2
Mid - point = ( - 6, 1.5 )
You are buying a new camera. The table shows the prices of cameras in a store
advertisement. You are willing to pay the mean price with an absolute deviation of at most
$102.
$890 $750
$650 $370
$660 $670
$450 $650
$725 $825
Your friend helped you with a list of steps to follow so you’ll find how many of the camera
prices meet your condition?
Step 1:
Find the mean of the given data.
(Search for: How to find the mean of a given data set?
Answers
$980 $670 Step-by-step explanation:
please help me with this
Answers
Answer:
42.5 square units
Step-by-step explanation:
To solve, we can split this shape up into 4 known shapes:
2 unit by 2 unit triangle
2 unit by 2 unit square
2 unit by 5 unit triangle
3.5 unit by 9.0 unit rectangle
Now let's solve these areas:
2 x 2 = 4 / 2 = 2
2 x 2 = 4
2 x 5 = 10 / 2 = 5
3.5 x 9.0 = 31.5
Then add all these values together:
2 + 4 + 5 + 31.5 = 42.5
Joseph owes his mother $12.25. He borrows $6.50 more from his mother. Which of the following best represents Joseph's debt to his mother?
Answers
Answer:
18.75.
Step-by-step explanation:
If he already owes his mother 12.25 and borrows 6.50, we can add those numbers up to get the total amount of how much he owes his mother.
12.25 + 6.50 = 18.75
Therefore, Joseph's debt to his mother can be represented using the equation above.
Identify the type of function explain
Answers
Step-by-step explanation:
it is a quadratic function
it is because it satisfies the equation f(x)= -3-5x+4x^2
The length of a square table is 1.25m. An ant walks around the edge of the table.How far does the ant walk?
Answers
Answer:
5m
Step-by-step explanation:
1.25m multiply by 4 sides equals 5m
The length of which ant walk will be the same as the perimeter of the square thus it will be 5 meters.
What is the perimeter?Perimeter is the addition of an external measure of sides it will always positive.
Perimeter of square = side + side + side + side
Given a table in form of a square,
Side of square = 1.25 m
The external measure of side = length of ant walk
1.25 + 1.25 + 1.25 +1.25 = Length of ant walkt
Length of ant walk = 5 meters.
Hence "The length of which ant walk will be the same as the perimeter of the square thus it will be 5 meters".
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Use the polygon tool to draw a right triangle with hypotenuse AB?
Answers
Answer:
in the -1,-1
Step-by-step explanation:
t midnight, a candle was lit. At 15 minutes past midnight, the candle was 4 inches tall, and you notice that it burns at a rate of 0.75 inches per hour.
(a)Write the point–slope form of the function that gives the height of the candle, h, in inches, as a function of time, t, in minutes past midnight, as the candle burns.
(b)When is the candle 1 inch tall?
Answers
Answer:
a) t-4 = 3 (i - 1/4h) = h = 3i - 3 3/4h
= t = -0.75
= h = 4
b) 3.30am = 1 inch.
Step-by-step explanation:
a) formula for point slope form = y - y1 = m(x-x1)
a) t-4 = 3(i - 1/4h) converts to t-4 = 3i - 3/4h = t = 3i- 3 3/4
x = - 0.75 y = 4 = t= -0.75 and h = 4
b) 12.15am = 4 inches
1.15am = 3.25 inches
2.15am = 2.5 inches
3.15am = 1.75inches
3.30 = 1 inches
3.15 + 15mins = 1 inch
Answer:
Step-by-step explanation:
Someone please answer this?
Answers
Answer:
y = 2x + 5
Step-by-step explanation:
First, you must choose two ordered pairs from the table to solve for the slope (m):
Let (x1, y1) = (0, 5)
(x2, y2) = (1, 7)
Substitute the given values into the following slope formula:
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{7 - 5}{1 - 0} = \frac{2}{1} = 2[/tex]
Therefore, the slope (m) = 2.
The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates (0, b ). It is also the value of y when x = 0. Looking at the given table, (0, 5) reflects the description of the y-intercept. The y-intercept (b) is the y-coordinate of (0, 5).
Given the slope (m) = 2, and y-intercept (b) = 5, the linear equation is:
y = 2x + 5
Please mark my answers as the Brainliest if you find my explanations helpful :)
Slop is 2, y-intercept is (0,5) and equation is 2x+5
a sum of money is divided among ethan June way and Raj in the ratio of 5:6:9 after eating gave $50 to his mother the ratio becomes 3:4:6 find the amount of money ethan has after giving $50 to his mother
Answers
Last year a popular app was downloaded 2.47 x 10 to the 8th power write the number of time the app was downloaded in standard form.
Answers
Answer:
247,000,000 times
Step-by-step explanation:
Đa thức P= 4x^2 -12x+9
Answers
Answer:
kciyyyyfdttftuttdciiiiifffffccccccutyyttttdccccckkff
hcucickkciffiiiiifiyffyysuatyyggHZZ£;YYYYYRRtrTyY56644%55646776-755522#3435%5$$4
HELP Please Will give Brainliest to first correct answer
Answers
Answer:
choose B......B is the right answer
Answer:
B. -(x - 1)/5 + 13
Step-by-step explanation:
combine like terms: 9 - (x - 1)/5 + 4 --> - (x - 1)/5 + 4 + 9--> - (x - 1)/5 + 13
What is the slope of the line passing through the points (-3, 4) and (2, - 1)? A -1
B 1
C 3/5
D - 5/3
Answers
Answer:
A
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 4 ) and (x₂, y₂ ) = (2, - 1 )
m = [tex]\frac{-1-4}{2-(-3)}[/tex] = [tex]\frac{-5}{2+3}[/tex] = [tex]\frac{-5}{5}[/tex] = - 1 → A
Determine the relationship between the two triangles and whether or not they can be proven to be congruent.
Answers
Answer:
If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
Step-by-step explanation:
[tex]\sf HELP \: ME\:!!!![/tex]
[tex]\sf (-5x+1)(-2)[/tex]
Answers
Answer:
=>10x-2
Step-by-step explanation:
=>(-5x+1)(-2)
=>-2(-5x+1)
=>-2(-5x+1)
=>10x-2
Answer:
10x-2Step-by-step explanation:
(-5x+1)(-2)
-2×-5x-2
10x-2
Evaluate:
bx(b – X) – b if b=5 and x = 3
Answers
Solve for the input variable.
h(x) = –2x + 15 when h(x) = – 45
Answers
-60 = -2x
divide by -2
answer is 30
Answer:
-45=-2x+15
-45-15=-2x
-60=2x
x=30
Question 8 of 10
Solve 4x- c= k for x.
A. x= 4(k+ c)
B. x=k-c/4
C. x = 4(k-c)
D. x=k+c/4
SUBMIT
Answers
Answer:
D. x=k+c/4
because:
4x-c= k
4x=k+c
x=k+c/4
pls help this is so harddd for meee
Answers
Answer:
B
Step-by-step explanation:
Tell me if im right
:)
B because its on the y axis and thats what there asking for and its positive
What are the coordinates of Point A (-2,-6) after a rotation 270° Counter Clock-Wise?
Answers
Answer:
(2,-2) or (0,4)
Step-by-step explanation:
Tell whether the fraction is in the simplest form. Write yes or no
(Please answer all of them in order!!)
4 over 10
2 over 8
3 over 5
4 over 12
6 over 10
3 over 6
Answers
2.No
3.Yes
4. No
5. Yes
6. No
Answer: 4/10 = 2/5
2/8 = 1/4
3/5 = 3/5
4/12 = 1/3
6/10 = 3/5
3/6 = 1/2
Step-by-step explanation:
4/10 = 2/5
4/10 is not in its simplest form.
Both 4 and 10 can be divided by 2.
Therefore, 4/10 = 2/5
2/8 = 1/4
2/8 is not in its simplest form
2 / 2 = 1
8 / 2 = 4
Both 2 and 8 can be divided by 2, therefore, 2/8 = 1/4
3/5 = 3/5
3/5 is in its simplest form
3 and 5 are prime, so they don’t have any factors other than 1 and itself so they wouldn’t be able to be simplified.
4/12 = 1/3
4/12 is not in its simplest form
4 / 4 = 1
12 / 4 = 3
4 and 12 can be divided by 4, resulting in 1 and 3. Therefore, 4/12 = 1/3.
6/10 = 3/5
6/10 is not in its simplest form
6 / 2 = 3
10 / 2 = 5
6 and 10 can both be divided by 2, resulting in 3/5. Therefore, 6/10 = 3/5
3/6 = 1/2
3/6 is not in its simplest form
3 / 3 = 1
6 / 3 = 2
Both 3 and 6 can be divided by 3, resulting in 1/2
Therefore, 3/6 = 1/2
Short Answers:
4/10 = 2/5
2/8 = 1/4
3/5 = 3/5
4/12 = 1/3
6/10 = 3/5
3/6 = 1/2
Which value of y makes the equation 7.2 - y=6?
SELECT ONE:
y=43.2
y=1.2
y=0.2
y=13.2
Answers
Answer:
y=1.2
Step-by-step explanation:
7.2-1.2=6
A music store originally purchased a piano at a cost of $892.03 and marked it up 125%. After a few weeks, however, the store discounted the piano 50% in order to make room for new merchandise. What was the discounted price?
Answers
Answer:
$557.52
Step-by-step explanation:
1. Find the marked up price.
125% = 1.25
$892.03 x 1.25 = $1,115.04
2. Find the discounted price.
50% = 0.5
$1,115.04 x 0.5 = $557.52
Answer:
1003.54
Step-by-step explanation:
Hope this helps! ;)