We are given:
Money on the fifth day (a₅) = $80
Money on day 21 (a₂₁) = $160
To Find:
Money in the bank on the first day (a₁) = ?
Money being added to the account per day (d) = ?
Money in the bank on day 30 (a₃₀) = ?
__________________________________________________________
Finding the money on day one and the money added:
Solving for equations
Since we are adding a constant amount to our account every day, the amount of money in the bank can be represented by an AP
We know that the formula for the nth term of an AP is:
aₙ = a₁ + (n-1)d
So, we can write the amount of money on day 5 as:
a₅ = a₁ + (5-1)d
a₅ = a₁ + 4d
80 = a₁+ 4d [We are given that a₅ = 80]
We are also given the amount of money on day 21:
a₂₁ = $160
Money on day 21 can be rewritten as:
a₂₁ = a₁ + (21-1)d
160 = a₁ + 20d [Since a₂₁ = 160]
Solving the equations:
Now we have 2 equations. We will now solve them to get the values of a₁ and d
160 = a₁ + 20d ----------------------(1)
80 = a₁ + 4d--------------------------(2)
From equation (2), we can say that:
a₁ = 80 - 4d [subtracting 4d from both sides]
Now, we will use this value of a₁ in the equation (1):
160 = a₁ + 20d
160 = (80-4d) + 20d
160 = 80 + 16d
80 = 16d [subtracting 80 from both sides]
d = 5 [dividing both sides by 16]
Now that we know the value of d, we can use it in any of the 2 equations:
80 = a₁ + 4d
80 = a₁ + 4(5) [since d=5]
80 = a₁ + 20
a₁ = 60 [subtracting 20 from both sides]
Now, we know the values of the initial amount of money and the money added to the account everyday
Initial money in the bank = $60
Money added everyday = $5
__________________________________________________________
Money in day 30:
We will use the AP formula to find the value of money on day 30
a₃₀ = a₁ + (30-1)d
We know that a₁ = $60 , d = $5
a₃₀ = 60 + 29(5)
a₃₀ = 60 + 145
a₃₀ = $205
Money on day 30 = $205
Answer:
started with $55
adds $5 each day
$205 on the 30th day
Step-by-step explanation:
21-5 = 16
160-80 = 80
80 divided by 16 = 5
5 * 5 = 25
80 - 25 = 55
9 * 5 = 45
160 + 45 = 205
Given: AABC = ADEF
Determine the perimeter of A ABC.
A) 7 units
B) 12 units
C) 15 units
D) 21 units
Answer: Its C!( 15 units)
Step-by-step explanation:
HELP WILL MARK BRAINLIST!!!!!!!!!!! DUE TODAY 10:52 Write 1/8% as a decimal number. Enter your answer in the box.
Answer:
12.5
Step-by-step explanation:
Answer:
.125
Step-by-step explanation:
divide 1 by 8
or divide 1 by 4 then divide by 2
PLEASE HELP QUICK!!! WILL GIVE BRAINLIEST
In two or more complete sentences, explain the theorem used in solving for the range of possible lengths of the third side, AB of ABC.
Answer:
Step-by-step explanation:
You can use the Pythagorean Theorem to find the length of the third side AB (Identified as "x" in the figure attached in the problem), which says that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs:
a² = b²+c²
As we can see the figure, the triangle does not have an angle of 90°, but it can be divided into two equal parts, leaving two triangles with a right angle. We already have the values of the hypotenuse and a leg in triangle "A" , so we can find the value of the other leg:
b = √(a²-c²) b = √(10²-4²) b = 9.16
With these values, we can find the hypotenuse in the triangle "B": x = √b²+c² x = √(9.16)²+(4)² x = 10
7. The ratio of width to length of the United States flag is 10:19.
If the width of the flag at Emersen's school is 4 feet, what is its length in feet?
Does this graph represent a function? Why or why not?
10+
8
8+
4+
2+
- 1084
4
-10
A. Yes, because it passes the vertical line test.
B. No, because it is not a straight line.
C. Yes, because it has two straight lines.
D. No, because it fails the vertical line test
the answer is D. I hope that helps
helppppppppppppp meeeeeeeeeeeeeeeeee plzzzzzzzzzzzzzzzzzz wrong or right?
Answer:
Yes you are right.
Step-by-step explanation:
Once you divide 128.25 by 3 you will get 42.75
Then you multiply 42.75 by 5 and you will get 213.75.
Callie pays for a cat toy with a $10 bill and receives $2.55 in change. The equation 10 - c = 2.55 gives the cost in dollars for the cat toy. Determine whether c=6.45, c=7.45 or c=8.45 is a solution of the equation, and tell what the solution means. The
Answer:
c = 7.45
Step-by-step explanation:
its easy and im smart that's why i got it
Select the correct graph of linear function shown in each table below
I REALLY NEED HELP.It’s due at 3:30 today
Answer:
from top to bottom it is b c a
Penny reads 10
pages in
hour. What is the unit rate for pages per hour? For hours per page?
The unit rate is 30 page(s) per hour.
(Simplify your answer. Type an integer, proper fraction, or mixed number.)
The unit rate is hour(s) per page.
(Simplify your answer. Type an integer, proper fraction, or mixed number.)
Answer:
Hr/p is 1/30 Or 1hr every 30pg
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Jeremy opened a bank account depositing $1,950 initially. He withdraws a fixed amount every month. At the end of the first month, account balance is $1,800. Which equation could model the situation?
Answer:
1800 = 1950 - m
Step-by-step explanation:
Lets call the fixed amount he withdraws every month m. He starts with $1950 and withdraws a certain amount, m, every month. At the end of the first month, he has withdrawn 1m amount of money and ends up with $1800. Therefore, 1950 - 1m = 1800. We can get rid of the 1 and get 1950 - m = 1800, or 1800 = 1950 - m. If the answer choices do not have "m" as a variable, you can substitute "m" for any variable.
can you help with this? and explain.
Answer:
C
Step-by-step explanation:
Answer:
C. x < -175
Step-by-step explanation:
-1/5x + 4 < 39
minus 4 on both sides
= -1/5 < 35
multiply by -5 because we want the X to be positive, always. And when we multiply or divide by a negative number, the sign will always flip.
X > -175
PLEASE HELP ASAP
how do you solve this?
Answer:
every 2 x's the y goes down 6 so the slope is -3 and at 0 for x the y is at 18
Step-by-step explanation:
Question 6
Given h(x) = -8(x - 5), what is the value of h(-6)?
Previous
Answer:
h(-6) = 88
Step-by-step explanation:
h(-6) = -8(-6 - 5)
= -8(-11)
= 88
Puzzle 3 - Perfect Squares
Directions: Using the digits 1 - 9 at most one time each, fill in the boxes to make each expression evaluate as a perfect square number. Example: 16 4 * 4 also equals 8 * 2.
Please help
(4x^2-2x-3)+(-3x^2+x+7) i know the answer i just need to show the work
Answer:
x² - x + 4
General Formulas and Concepts:
Algebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define
(4x² - 2x - 3) + (-3x² + x + 7)
Step 2: Simplify
Combine like terms (x²): x² - 2x - 3 + x + 7Combine like terms (x): x² - x - 3 + 7Combine like terms (Z): x² - x + 4a(7x+3)=14x+b
What are the values of A and B?
Answer:
24
Step-by-step explanation:
I think there the same for each but I hope I helped
How long will it take to get $250 in interest if $2500 in invested at a 7% interest rate?
Answer:
If it is an annual percentage rate: 8.4 months
Step-by-step explanation:
2500 x .07 = 175
175 / 250 = .7 / 12months = 8.4 months
Which of the following is not a solution to the inequality
4x + 1 ≤ 18
A. 4
B. 4.23
C. 4.25
D. 4.27
Answer: A 4
step by step explmationn
Answer:
C. 4.25
Step-by-step explanation:
You would want to subtract the one so you could subtract it to 18 then divide 4 by 17 to get 4.25
Convert this words into actual number
A. seventy and one thousand, four hundred three ten-millionths
B. seventy-two and one thousand, six hundred forty-two-hundred-thousandths
Answer:
i think it's a= 70.0000001403 b=72.00001642
Step-by-step explanation:
hope this helps! please mark as brainliest!
Which expression has a value of −10?
A (−3)−(−7)
B 2−(−8)
C 10−(−10)
D (−2)−8
Answer:
D
Step-by-step explanation:
What is the y-intercept of the graph of y = 5x - 12?
Answer:
y=5
Step-by-step explanation:
y=5x-12
x+12/5
5x-12
y=5
Someone help!!! for finals
8. Solve the formula K = 3M - 7 for M
Answer:
m = [tex]\frac{k + 7}{3}[/tex]
Step-by-step explanation:
k = 3m - 7
k + 7 = 3m - 7 + 7
k + 7 = 3m
[tex]\frac{k + 7}{3}[/tex] = m
(I'm not 100% sure fyi)
What should you do during the editing stage of the writing process?
A triangle has a base of x^1/3 m and a height of x^1/2 m. If the area of the triangle is 16 m^2, what are the base and height of the triangle?
The base is....and the height is......
The base of the triangle is 4 m and the height of the triangle is 8 m.
What is the area of the triangle?The are of the triangle is A = 1/2 × b × h
where 'b' is the base and 'h' is the height
For given example,
A triangle has a base of x^1/3 m and a height of x^1/2 m.
Also, the area of the triangle is 16 m^2
⇒ [tex]b = x^{\frac{1}{3}} ~m,h=x^{\frac{1}{2} }~m, A=16~m^{2}[/tex]
Using the formula for area of the triangle,
[tex]\Rightarrow A=\frac{1}{2}\times b\times h\\\\\Rightarrow 16=\frac{1}{2}\times x^{\frac{1}{3} }\times x^{\frac{1}{2} }\\\\\Rightarrow 16\times 2=x^{\frac{1}{3} + \frac{1}{2} }\\\\\Rightarrow 32=x^{\frac{5}{6} }\\\\\Rightarrow 32^6=(x^{\frac{5}{6} })^6\\\\\Rightarrow 32^6=x^5\\\\\Rightarrow x=32^{\frac{6}{5}}\\\\\Rightarrow x=64[/tex]
So, the base of the triangle would be,
[tex]\Rightarrow b=x^{\frac{1}{3} }\\\\\Rightarrow b=64^{\frac{1}{3} }\\\\\Rightarrow \bold{b=4}[/tex]
and the height of the triangle would be,
[tex]\Rightarrow h=x^{\frac{1}{2}}\\\\\Rightarrow h=64^{\frac{1}{2} }\\\\\Rightarrow \bold{h=8}[/tex]
Therefore, the base of the triangle is 4 m and the height of the triangle is 8 m.
Learn more about the area of the triangle here:
https://brainly.com/question/27683633
#SPJ2
HELPPPL!!!!!JVVHjamsk
Winter Wonderland buys items at wholesale, then marks them up to set a retail price. They buy snow globes for $9.20 and mark them up by 95%. What is the retail price or selling price of the snow globes?
Answer:
$17.94
Step-by-step explanation:
Step one:
given
the cost price of snow globes = $9.20
mark up percent= 95%
Required:
the retail selling price
Step two:
let us find 95% of $9.20
=95/100*9.20
=0.95*9.20
=$8.74
Hence the retail selling price is = 9.20+8.74
=$17.94
Help questions 1, 3, 4 and 8 please? It’s due In 30 mins
Answer:
For number one I forget what it is called but I know that its not right because the left side can't be connected to 2 numbers on the right side. For number 3 I honestly have no idea I have never seen or done that equation in my life. For number 4 all you have to do is count up then how many left or right that goes to the line crossing a place where a point could be. For example you rise 3 and go over two it would be 3/2. Though that isn't the answer I hope this helps. Also I don't know number 8 either I am sorry but I also hope this helped a little bit.
The length is 30 feet and the width is 13 feet. What is the area in feet? (TIMED TEST)
Answer:
390 ft2 so 390 ft but put the feet as squared
Step-by-step explanation:
its just 30×13
PLEASE HELP!! Urgent!!
Answer:
Step-by-step explanation: