Answer:
12th term: [tex]a_{12}=5\times 2^{12-1}[/tex]
nth term: [tex]a_n=5\times 2^{n-1}[/tex]
2nd term: [tex]a_{2}=5\times 2^{2-1}[/tex]
4th term: [tex]a_{4}=5\times 2^{4-1}[/tex]
(n-1)th term: [tex]a_{n-1}=5\times 2^{n-2}[/tex]
6th term: [tex]a_{6}=5\times 2^{6-1}[/tex]
Step-by-step explanation:
The first term of GP, a = 5
Common ratio, r = 2
Formula for [tex]n^{th}[/tex] term of a GP, [tex]a_n=ar^{n-1}[/tex].
Putting the values of a and r. So, [tex]n^{th}[/tex] term is:
[tex]a_n=5\times 2^{n-1} ...... (1)[/tex]
[tex]12^{th}[/tex] term is:
Put n = 12 in (1):
[tex]a_{12}=5\times 2^{12-1}[/tex]
2nd term is : (Put n = 2 in (1))
[tex]a_{2}=5\times 2^{2-1}[/tex]
4th term is: (Put n = 4 in (1))
[tex]a_{4}=5\times 2^{4-1}[/tex]
(n-1)th term is, put value of n as (n-1) in equation 1:
[tex]a_{n-1}=5\times 2^{n-1-1}\\a_{n-1}=5\times 2^{n-2}[/tex]
6th term is: (Put n = 6 in (1))
[tex]a_{6}=5\times 2^{6-1}[/tex]
In a certain isosceles triangle, the base is 1 1/2 times as long as each leg and the perimeter is 63. How long is the base?
Answer:
The base is 27 units long.
Step-by-step explanation:
This is a solve the system question. Call the length of the base B and the length of each leg L. We are told:
[tex]B=1.5L[/tex]
and
[tex]B+2L=63[/tex]
Sub the first equation into the second:
[tex]1.5L+2L=63\\3.5L=63\\L=18[/tex]
Now that we have the leg length, sub that into either of the original equations to find the base. I'll use the first equation:
[tex]B=1.5(18)\\B=27[/tex]
Pleaseeeeee helpppppppp i will mark brainlest
Answer:
b
Step-by-step explanation:
The sum of angles in a triangle is 180°. Therefore,
x - 11 + 48 + 90 = 180
x + 127 = 180
x = 53°
Answer:
x = 53
Step-by-step explanation:
Using the information that angles in a triangle add up to 180°, we can set up and equation to find the value of x
⇒ Use the information that angles in a triangle add up to 180°, form an equation
→ x - 11 + 48 + 90 = 180
⇒ Simplify
→ x + 127 = 180
⇒ Minus 127 from both sides to isolate x
→ x = 53
We can substitute the value of x back into x - 11 + 48 + 90 = 180 to see if our value of x is correct, if we end up on 180 on both sides then the value of x is correct
→ x - 11 + 48 + 90 = 180
⇒ Substitute in the value of x
→ 53 - 11 + 48 + 90 = 180
⇒ Simplify
→ 180 = 180
This means that x = 53 is correct
find the square of 2m^2 - 2/3n^2
Answer:
4m^4 - 8/3m^2 n^2 + 4/9n^4
Step-by-step explanation:
(2m^2 - 2/3n^2)(2m^2 - 2/3n^2)
= 2m^2(2m^2 - 2/3n^2) - 2/3n^2(2m^2 - 2/3n^2)
= 4m^4 - 4/3m^2 n^2 - 4/3m^2n^2 + 4/9n^4
= 4m^4 - 8/3m^2 n^2 + 4/9n^4
There is a bag filled with 3 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 blues?
Answer:
2 by 8
I hope this helps you
Angie has a square dog pen with a perimeter of 20 meters. She wants to put a diagonal piece of fencing inside her pen to cut it in half because her 2 dogs have been fighting. How long of a piece of fencing will she need to buy? Hint: The formula for finding the hypotenuse of a right triangle is: a² + b² = c²
Answer: 7.07 miles
Step-by-step explanation:
Hi, to answer this, first, we have to find the length of the square dog pen.
Perimeter of a square = 4 x sides
Replacing with the value given:
20 = 4 s
Solving for s:
20/4=s
Side = 5 meters
Since the situation forms a right triangle (see attachment) we have to apply the Pythagorean Theorem:
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (in this case length of the diagonal) and a and b are the other sides.
Replacing with the values given:
c^2 = 5^2 + 5^2
c^2 = 25+25
c^2 = 50
c = √50
c = 7.07 miles
Feel free to ask for more if needed or if you did not understand something.
which classification best represents a triangle with a side lengths 6 cm,10 cm, and 12 cm ?
Answer:
It would be an obtuse scalene triangle.
EDITED TO ADD:
When given 3 triangle sides, to determine if the triangle is acute, right or obtuse:
1) Square all 3 sides.
2) Sum the squares of the 2 shortest sides.
3) Compare this sum to the square of the 3rd side.
if sum > 3rd side² Acute Triangle
if sum = 3rd side² Right Triangle
if sum < 3rd side² Obtuse Triangle
6^2 = 36
10^2 = 100
12^2=144
36 + 100 = 136 and this is less than 144 so it is an obtuse triangle.
Step-by-step explanation:
Challenger elementary school has 800 students every wendesday 22 percent of the students stay after school for chess club how many students attend chess club on wednesdays
Answer:
176 students attend chess club on wednesdays
Step-by-step explanation:
This question can be solved using a rule of three.
The total number of students(800) is 100% = 1. How many students are 22% = 0.22?
800 students - 1
x students - 0.22
x = 800*0.22 = 176
176 students attend chess club on wednesdays
Answer:
275
Step-by-step explanation:
Your bill at a restaurant is $35.00. There is an 8% meals tax (sales tax). How much is the tax? You want to leave a 20% tip. You should calculate the tip on the $35.00 (not the cost after the tax). How much is the tip? What is the total bill?
Answer:
$44.8
Step-by-step explanation:
The tip:
35*0.2=$7
The total bill:
35*8% = 35*0.08 = 2.8
35 + 2.8 +7 = 44.8
(I added 35 for the price of the actual lunch, and the 7 for the tip)
Alternatively, you can just add the 8% and the 20% and the 100% (for the lunch itself), and then multiply the $35.
8%+20%+100%=0.08+0.2+1= 1.28
1.28*35=$44.8
what is the slope for (6,2) (9,8)
Answer:
3/6
Step-by-step explanation:
The slope is how one number gets to the next, in this instance we have point (6,2) at x=6 y=2 to get from there to the next point x=9 y=8 we would have to count up three and over six. Therefore, the answer is 3/6.
Hope this helps!
Dr. Hester is mailing a package at the post office. The package is 4.75 pounds. The post office charges by the ounce to mail a package. How many ounces does the package weigh?
Answer:
The package weighs 76 ounces.
Step-by-step explanation:
This question can be solved using a rule of three.
Each pound has 16 ounces. How many ounces are 4.75 pounds?
1 pound - 16 ounces
4.75 pounds - x ounces
x = 16*4.75
x = 76
The package weighs 76 ounces.
An is made up of two expressions that are equal in value to each other
Answer:
an what ? this question is a bit confusing to me or im jus not having one of my smart days ..
Step-by-step explanation:
Find the retail sale price of each item below. Round to two decimal places when necessary. Original price : $325.50; Markdown: 15%.
Answer:
Step-by-step explanation:
Answer:
Find the retail sale price of each item below. Round to two decimal places when necessary. Original price : $325.50; Markdown: 15%.
A farmer is tilling a rectangular field that is 65 meters long and 72 meters wide. What is the distance between opposite corners of the farmer's field
Answer:
97m
Step-by-step explanation:
From the image below we solve using pythagoras's theorem
x^2 = 72^2 + 65^2
x^2 = 5184 + 4225
x^2 = 9408
x = 97 m.
Further explanation is shown 8n the image.
What is the volume of the cylinder below? Use 3.14 for pi and I round to the nearest tenth
Answer:
Option (4).
Step-by-step explanation:
Formula to calculate the volume of a cylinder is,
V = πr²h
Here r = radius of the cylinder
h = Height of the cylinder
From the figure attached,
r = [tex]\frac{13}{2}=6.5[/tex] cm
h = 11 cm
Now we substitute the values of h and r in the formula,
V = π(6.5)²(11)
= 464.75π
= 1459.32
≈ 1459.3 cm³
Therefore, volume of the given cylinder is 1459.3 cm³
Option (4) will be the answer.
A card is randomly selected from a standard deck. What is the probability that a club or the queen of hearts is selected?
Answer:1/52 One out of 52 (there are 52 cards in a deck, right?)
Step-by-step explanation:
What is the image point of (3,8) after a translation right 4 units and up 1 unit?
Answer:
its going to be (7,9)
Step-by-step explanation:
Answer:
The image of the point after the translation would land the point at (7, 9).
Step-by-step explanation:
When you're moving a point right, imagine adding the number of units you are going right to the x value. When you're moving a point up, imagine adding the number of units you are going up to the y value.
(3 + 4, 8 + 1)
(7, 9)
So, the image of the point of (3, 8) after a translation right 4 units and up 1 unit is going to be (7, 9).
In April, Phillipa rode 13 . 5 + 8 . 7 + 11 . 1 miles on her bicycle. In March, she rode ( 13 . 5 + 8 . 7 + 11 . 1 ) ÷ 2 miles, and in May, she rode 4 × ( 13 . 5 + 8 . 7 + 11 . 1 ) miles. Determine the month when she rode the most and the month when she rode the least. How many times farther did she ride in the month when she rode the most than in the month when she rode the least?
Answer:
Phillipa rode the most in May and rode the least in March.
Distance travelled by Phillipa on her cycle in May = 8 × Distance travelled by Phillipa on her cycle in March
Step-by-step explanation:
Given:
In April, Phillipa rode 13 . 5 + 8 . 7 + 11 . 1 miles on her bicycle. In March, she rode ( 13 . 5 + 8 . 7 + 11 . 1 ) ÷ 2 miles, and in May, she rode 4 × ( 13 . 5 + 8 . 7 + 11 . 1 ) miles.
To find: the month when she rode the most and the month when she rode the least
Solution:
Distance travelled by Phillipa on her cycle in April = 13 . 5 + 8 . 7 + 11 . 1 = 65 + 56 + 11 = 132 miles
Distance travelled by Phillipa on her cycle in March = ( 13 . 5 + 8 . 7 + 11 . 1 ) ÷ 2 = [tex]\frac{132}{2}=66[/tex] miles
Distance travelled by Phillipa on her cycle in May = 4 × ( 13 . 5 + 8 . 7 + 11 . 1 ) = 4 × 132 = 528 miles
So, she rode the most in May and rode the least in March
Distance travelled by Phillipa on her cycle in May = 8 × Distance travelled by Phillipa on her cycle in March
What is the area of the triangle?
Answer:
The area is 4
Step-by-step explanation:
A=1/2 x b x h
A=1/2 x 4 x 2
A= 4 x 1
A= 4
You conduct an experiment of dice rolling and roll an even number 24 out of 60 rolls. Write both the experimental and theoretical probability as a fraction and a percent.
Answer:
see below
Step-by-step explanation:
The experimental probability is what you actually rolled
24/60 = 2/5 = 40%
The theoretical probability is what we expect to happen
=number of even numbers / total number of numbers
3/6 = 1/2 = 50%
What are the measurements rounded to the nearest hundredth.
Answer:
Step-by-step explanation:
Pedro withdrew some money from his bank account. After giving $15 to his cousin, he spent 1/5 of what was left on a lamp, then he used the remaining $128 to buy a calculator. What percent of Pedro’s money did he give to his cousin?
*Please Show Work*
Answer:
He gave 8.57 % of his money for his cousin.
Step-by-step explanation:
In order to calculate the percent that Pedro gave to his cousin, we first need to calculate his total amount, which is given by "x". This is given by:
x = 15 + (x - 15)/5 + 128
x = 15 + x/5 - 3 + 128
x = x/5 + 140
x - x/5 = 140
(5*x - x)/5 = 140
4*x = 700
x = 175
He had originally $175 and gave $15 to his cousing, therefore we can use a rule of three to calculate the percent that he gave to his cousin:
$175 -> 100%
$15 -> y%
175*y = 1500
y = 1500 / 175
y = 8.57 %
What is the value of the angle marked with x?
Answer:
132°
Step-by-step explanation:
Plssss make me BRAINLIEST PLSSSSSSSS
Liza comes to the swimming pool once every 6 days. Jenny comes once every 4 days and Olga comes once every 10 days. This Monday all of them were in the pool. How many days after this Monday will all of them meet at the swimming pool again?
Answer:
60 days
Step-by-step explanation:
The least common multiple of 6, 4, and 10 is the product of the unique factors ...
6 = 2·3
4 = 2²
10 = 2·5
The LCM is 2²·3·5 = 60.
All of them will meet at the swimming pool again in 60 days.
Answer:
60
Step-by-step explanation:
Explain how to find the median.
Answer:
The median is also the number that is halfway into the set. To find the median, the data should be arranged in order from least to greatest. If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.
Step-by-step explanation:
have a great day
There are two ways to find the median, depending on what situation it is.
The first, is to simply arrange the number set into proper numerical format (least to greatest), then count from both sides towards the middle to find the median or middle number.
The latter, is when we have a number set that has an equal amount of numbers. For this, we would again, arrange it into proper numerical format, and the count from both sides up. However, there will be two numbers at the middle. So, what we do, is that we have to add them up and then divide by 2 since there are only those two numbers at the middle. Once, the numbers are added up and divided by 2, you will get the resulting median.
Example: Find the median of the data set below.
1,2,3,4,5,6,7,8,9,9
There are 10 numbers in this data set.
It's already been arranged into proper numerical format.
So, all we have to do is, find the two middle numbers and then add them up and divide.
The two numbers at the middle are: 5 and 6.
Add them up.
5 + 6 = 11
Divide by 2.
11/2 = 5.5
Thus, the median of the data set is 5.5
Given the definitions of f(x) and g(x) below, find the value of g(f(-1)).
f(x) = -4x – 7
g(x) = x² + 7x – 2
Answer:
(x)=(x-7)(x-4)
g(x)=x(2)+7x - 2
Now find a common denominator. (x+10)(x-4) is a good one.
x-16/(x+10)(x-4)+x-4/(x+10)(x-4)
2x-20/(x+10)(x-4)
The value of function g(f(-1)) is -70.
What is Function?
A relation between a set of inputs having one output each is called a function.
Given that;
The value of functions,
f (x) = -4x - 7
g (x) = x² + 7x - 2
Now, Value of function g(f(-1)) as;
g(f(x)) = g(-4x - 7)
= (-4x - 7)² + 7(-4x - 7) - 2
= (4x + 7)² + 7 × -4 × x - 7 × 7 - 2
= 16x² + 49 + 56x + 28x - 49 - 2
= 16x² + 84x - 2
Thus, g(f(x)) = 16x² + 84x - 2
Now, To find value of g(f(-1)) we can substitute x = -1,
g(f(-1)) = 16(-1)² + 84(-1) - 2
= 16 - 84 -2
= -70
Thus, The value of function g(f(-1)) is -70.
Learn more about the function visit:
https://brainly.com/question/27999415
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WORTH 45 POINTS AND BRAINLIST NO FAKE ANSWERS AND PLAGIARIZING
Ms. Ziolkowski asks her class to write the correct trigonometric function for the triangle shown below.
Two students get into an argument about the correct answer.
Rhianna states that the correct trig function is tan A = 3/4. Christopher insists that the correct trig function is tan C = 4/3. Who is correct? In writing your response, be sure to include the terms opposite side, adjacent side, tangent ratio, and reference angle. Be sure to restate the question and explain your position with at least four sentences.
Answer:
They are both correct
Step-by-step explanation:
tan A = opposite / adjacent = 3/4 >>> A= 36.9 deg
tan C = opposite / adjacent = 4/3 >>> C= 53.1 deg
cheak:
<B+ <A + <C = 180 deg
90 + 36.9 + 53.1 = 180
180 = 180
Answer:
Botn are correct
Step-by-step explanation:
Tan ratio can be obtained by opposite/adjacent
Both students are correct. They have different values only because they have taken different reference angles
Rhianna has taken angle A as the reference angle,
So tanA = opposite/adjacent = BC/AB
tanA = 3/4
Christopher has taken angle C as the reference angle,
So tanC = opposite/adjacent = AB/BC
tanC = 4/3
Logan is doing a handstand dive from a 12 meter platform. The equation that models the path of her dive is given by LaTeX: h=-4.9t^2+12h = − 4.9 t 2 + 12, where t is seconds. After how many seconds will Logan hit the water?
Answer:
Time, t = 2.44 seconds
Step-by-step explanation:
Logan is doing a handstand dive from a 12 meter platform. The equation that models the path of her dive is given by :
[tex]h=-4.9t^2+12t[/tex]
It is required to find the time after which Logan will hit the ground. At this point, h = 0
[tex]-4.9t^2+12t=0\\\\t(-4.9t+12)=0\\\\t=\dfrac{12}{4.9}\\\\t=2.44\ s[/tex]
So, after 2.44 seconds it will hit the water.
Write and solve an equation for .
Answer:
[tex]x = 40 \: \: degrees[/tex]
Step-by-step explanation:
[tex]3x + 20 + x = 180 \\ 4x + 20 = 180 \\ 4x = 180 - 20 \\ 4x = 160 \\ \frac{4x}{4} = \frac{160}{4} \\ x = 40 \: \: degrees[/tex]
pls help to get 100points
The answer is attached to the picture .
Step-by-step explanation:
hope it helps !!
Answer:
Please mark me brainliest and I hope this helped!
7/3
Step-by-step explanation:
To get the answer, we add all of the numerator numbers together since the denominators are all the same. 3 + 4 + 7 = 7 + 7 = 14
The answer is 14/6. We can then simplify it and divide both the numerator and the denominator by 2. That gives us 7/3 and that is our final answer.
Grandma’s chocolate chip cookies calls for 2 cups of flour for 24 cookies. Using the same rate, how many cups of flour is needed if grandma wants to make 36 cookies?
Answer:
C
Step-by-step explanation:
Took the test
Answer:
Grandma needs 3 cups to make 36 cookies
Step-by-step explanation:
If 2 cups is 24 cookies then 1 cup must be 12.
12+24=36 therefore she needs 3 cups to make 36 cookies.