Answer:
An=125(1/5)^n-1
Step-by-step explanation:
r=common ratio
A1= first term in the sequence
I hope this helps some
The given series 125, 25, 5, ... is a geometric progression thus the general term will be An=125[tex](\frac{1}{5}}) ^{n-1}[/tex].
What is geometrical progression series?A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.
For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.
The given GP series is 125, 25, 5, ...
First term a = 125
Common ratio = 25/125 = 1/5
The nth term will be given as ar^(n-1)
Thus, An=125[tex](\frac{1}{5}}) ^{n-1}[/tex].
Hence "The given series 125, 25, 5, ... is a geometric progression thus the general term will be An=125".
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PLEASE HELP
A faucet dripped 14 cup of water in 112 hours. What is the rate in cups per hour?
Answer:
8 cups per hour
Step-by-step explanation:
We already have both values, the total sum of hours and the total amount of cups the faucet dripped. We would divide the hours by the cups of water to get an answer of 12. You can also double check this when doing one of these problems on your own, by multiplying your answer by the divisor. (14) 14 times 8 is 112, so we know our answer is correct.
Hope that helps :D
The rate in cups per hour is 8 cups per hour if a faucet dripped 14 cup of water in 112 hours.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
A faucet dripped 14 cup of water in 112 hours.
The total sum of hours and the total amount of cups the faucet dripped.
The rate in cups per hour = 112/14
The rate in cups per hour = 8
Thus, the rate in cups per hour is 8 cups per hour if a faucet dripped 14 cup of water in 112 hours.
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Steel is an alloy of iron and carbon (98% iron, 2% carbon). Stainless steel is steel and chromium, (90% steel, 10% carbon). What amount of iron, carbon, and chromium are needed for 500 kg of stainless steel?
500 kg x 90% = 500x 0.9 = 450 kg of Steel is needed.
450 kg x 98% = 450 x 0.98 = 441 kg of iron needed.
450 x 0.02 = 9 kg of carbon is needed for the steel.
50 kg of chromium is needed.
Chromium is 10% carbon, 50x 0.1 = 5 kg of carbon is needed for the chromium.
Total iron = 441 kg
Total carbon = 9 + 5 = 14 kg
Total chromium = 50 kg
If the imput is -8 then what is the output of y=3x+7
Answer:
output is -17
Step-by-step explanation:
x is input, y is output. You do y = -24 + 7
then y = -17
What is cos 63°? Round your answer to the nearest hundredth.
A. 0.89
B. 0.45
C. 0.17
D. 1.96
Answer:
B. 0.45
Step-by-step explanation:
Use the cos function in a calculator for the degree measure of 63°.
The value of cos 63° is 0.45.
Option B is the correct answer.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
To find cos 63°, we can use a calculator or a table of trigonometric functions.
Now,
cos 63° ≈ 0.447
Rounding to the nearest hundredth, we get:
cos 63° ≈ 0.45
Therefore,
The value of cos 63° is 0.45.
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Suppose that Gx=f(x+11). Which statement correctly describes the graph? please hurry!
Given:
[tex]g(x)=f(x+11)[/tex]
To find:
The correct statement for the given transformation.
Solution:
The translation is defined as
[tex]g(x)=f(x+a)+b[/tex] .... (1)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
We have,
[tex]g(x)=f(x+11)[/tex] ... (2)
On comparing (1) and (2), we get
[tex]a=11>0[/tex]
So, the graph of f(x) translated 11 units to the left.
Therefore, the correct option is A.
The points (5,-2) and (9, r) lie on a line with slope 3/2. Find the missing coordinate r.
Find the percent of decrease from 6 to 5.
Answer:
Use this
Step-by-step explanation:
Which of the following is a solution of x^2 -10x = -36?
-5 - i √10
5 + i √61
-5 - i √11
5 + i √11
geometry unit 4 congruent triangles
Answer:
okay?
Step-by-step explanation:
The four congruent triangles are by SAS, AAA, ASA and RHS.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
The four congruent triangles are,
They can be congruent by side angle and side.
They can be congruent by angle, angle and angle.
They can be congruent by angle side angle.
They can be congruent by one of the legs and the hypotenuse of a
right-angle triangle.
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A candle burned at a steady rate. After 40 minutes, the candle was 12.5 inches. After 70 minutes, the candle was 11.75 inches. Use an equation in point-slope form to determine the height of the candle after 2 hours.
Answer: 8.75 is the correct answer
Step-by-step explanation:
I'm big brain.
HEYYYYYYYYYYY YALLLLLLLLLLLLLLLL ADDDDDDDDD MEHHHHHHHHHHHHHHHHH
Answer:
I think the answer is D
Step-by-step explanation:
A quadrilateral has vertices A(4, 5), B(7, 7), C(6, 8), and D(4, 7). The image of the quadrilateral has vertices A"(–6, 0), B"(–9, –2), C"(–8, –3), and D"(–6, –2).
Which transformations may have taken place?
A. T (-2, 5) r y=x
B. T(-2,5) R 0,180
C. r y=x T(–2, 5)
D. R 0,180 T(-2,5)
Answer:
D
Step-by-step explanation:
Find the value of x.
Group of answer choices
77
34
69
146
Answer:
x = 69Step-by-step explanation:
∠K = 180 - 146 = 34
34 + x + 77 = 180
x = 180 - 77 - 34
x = 69
Julie Myrick has a credit card that has an APR of 15%, applied at a daily
periodic rate to the previous balance. Her previous balance is $567,31. She made
new purchases totaling S128.92, and a payment-of $125 in the month of June.
What is her new balance?
Answer. 332.78
Step-by-step explanation:
I subtracted and as awesome its right trust me.
Determine the future amount if ₱150,000 is deposited in a fund for 5 years at 2.5% compounded annually
Answer:
169,711.23₱
Step-by-step explanation:
compound intrest formula
p(1+r/100)^n
150,000(1+2.5/100)^5
=169,711.23₱
The ratio of the angle measures of the triangle are 3:1:5.if the longest side of the triangle is 15ft .the shortest side of the triangle is?
Answer:
3ft
Step-by-step explanation:
get the ratio of longest side which is 5over9 is equal to 15 what about 1 over 9 then u equate n get 3
Answer:
≈ 5.2 ft
Step-by-step explanation:
sum the parts of the ratio, 3 + 1 + 5 = 9 parts
Divide the angle sum of a triangle by 9 to find the value of one part of the ratio.
180° ÷ 9 = 20° ← value of 1 part of the ratio, then
3 parts = 3 × 20° = 60°
5 parts = 5 × 20° = 100°
The angles of the triangle are 100°, 60° and 20°
The longest side is opposite the largest angle in the triangle
The shortest side is opposite the smallest angle in the triangle.
Thus
the longest side is opposite 100°
the shortest side is opposite 20°
let x represent the shortest side and using the Sine rule
[tex]\frac{x}{sin20}[/tex] = [tex]\frac{15}{sin100}[/tex] ( cross- multiply )
x × sin100° = 15sin20° ( divide both sides by sin100° )
x = [tex]\frac{15sin20}{sin100}[/tex] ≈ 5.2 ( to the nearest tenth )
Thus the shortest side is ≈ 5.2 ft
A prom ticket at Smith high school is $120 time is going to save money for the ticket by walking his neighbors dog for $15 per week.Tom has already saved $15 write an in equality that represents the situation.
Answer:
120 = 15x + 15
Step-by-step explanation:
what you have to do is find the amount of weeks needed to walk the dog until you get around 120. so if two weeks is equal too 30 dollars you can multiply it by that amount. 30 = 2.So 30 times what = 120 or 15 times what = 120. also dont forget that tom has saved thirty dollars in advance
Please help me solve this question will give you braisnlt !
Answer:
[tex]s = 54m +160[/tex]
Step-by-step explanation:
Given: The attachment
Required: Determine the equation
We start by picking any two equivalent points on the table:
[tex](m_1,s_1) = (2,268)[/tex]
[tex](m_2,s_2) = (4,376)[/tex]
Next, we determine the slope, M:
[tex]M = \frac{s_2 - s_1}{m_2 - m_1}[/tex]
[tex]M = \frac{376 - 268}{4-2}[/tex]
[tex]M = \frac{108}{2}[/tex]
[tex]M = 54[/tex]
The equation is then calculated as:
[tex]s - s_1 = M(m - m_1)[/tex]
Where:
[tex]M = 54[/tex]
[tex](m_1,s_1) = (2,268)[/tex]
So, we have:
[tex]s - 268 = 54(m - 2)[/tex]
Open bracket
[tex]s - 268 = 54m - 108[/tex]
Collect like terms
[tex]s = 54m - 108 + 268[/tex]
[tex]s = 54m +160[/tex]
Hence, the equation is: [tex]s = 54m +160[/tex]
Drag the item from them item bank to its corresponding match
Will mark brainless
Answers, in order:
1. Acute
2. Congruent
3. Supplementary angles
4. Vertical angles
5. Adjacent angles
6. Adjacent supplementary angles
7. Alternate interior angles
8. Alternate exterior angles
9. Consecutive interior angles
10. Corresponding angles
11. Straight angle
Farmer Bob wants to build a rectangular pigpen with side lengths of 3x2+4x-1 ft and 2x2-5x+9 ft. How much fencing will he need to
O A 5x2-x+8 ft
OB. 10x2+18x+16 ft
O C. 10x2-2x+16 ft
OD. 5x2+9x+8 ft
Answer:
b
Step-by-step explanation:
Three less than half of a number is - 1. Find the number.
Answer:
x = 4
Step-by-step explanation:
Three less than half of a number is -1
The Half Of A Number means the number can be anything, so we can use "x." However, it is half so it would become: 1/2x.
Three less than means it is minus three, therefore becomes: 1/2x-3
However, three less than half of a number is (or in other words is equal too) -1, so the overall equation is
1/2x - 3 = -1
first, add three on both sides to get:
1/2x = 2
multiply two on both sides to get:
x = 4
help me please!!!!!!!!!
Answer:5.6
Step-by-step explanation:112 divided by 20=5.6
if x =20 and y =40 then x and y are
Answer:
Are directly proportional
Which of these tables represents a function?
Answer:
W
Step-by-step explanation:
The table that will represent a function is the table where every x-value (domain) has exactly one y-value (range).
Table W represents a function because each x-value has exactly only one y-value.
The other tables have two y-values assigned to a one x-value.
Answer:
W
Step-by-step explanation:
A how air ballon roses 474 feet. It then descends 130 feet. Find the elevation of the ballon is it started at sea levels.
Answer:
344 feet
Step-by-step explanation:
474-130=344
PLEASE HELP I GIVE BRAINLIEST
Answer:
y = 11
Step-by-step explanation:
Perimeter = 6 + 5y + y + 2 + 4y + 3
= 10y + 11
10y + 11 = 121
10y = 121 - 11
= 110
y = 110 ÷ 10
y = 11
whats 16, −24, 9, −30, 25 least to greatest?
Answer:
-30, -24, 9, 16, 25
Answer:
30-, -24, 9, 16, 25
Step-by-step explanation:
x + 5y = 8
3x = 24 - 157
Answer:
1) x+5y=8 (that’s a basically simplified already)
2) -44 1/3
Step-by-step explanation:
1) Since its in it’s most simplified form, leave it like that.
2) Solve it, combine like terms, and then just divide 3 on both sides to isolate variable
Harley bought a one year $1000 treasury bond. He paid $950 for the treasury bond. What is his rate of return? Round to one decimal, such as: 6.7%.
0.053%
53%
5.3%
5%
Answer: 5.3%
Step-by-step explanation:
The formula to compute rate of return is given by :-
Rate of return = [tex]\dfrac{\text{Selling price - investing price }}{\text{ investing price}}\times100[/tex]
[tex]=\dfrac{1000-950}{950}\times100\%\\\\=\dfrac{50}{950}\times100\%\\\\=\dfrac{100}{19}\%\\= 5.3\%[/tex]
Hence, his rate of return = 5.3%
What is the actual slope of a line with the points (-4, 9) and (3, -5)?
Answer:
slope=∆y/∆x=9+5/-4-3=14/-7=-2
Answer:
-2
Step-by-step explanation:
slope equation: (y2-y1)/(x2-x1)
lets use (-4, 9) as x1 and y1 and (3, -5) as x2 and y2
when plugged into the equation we get (9+5)/(-4-3) which ultimately equals -2.