9514 1404 393
Answer:
A. the x-coordinate of the intersection point
Step-by-step explanation:
If you are solving ...
f(x) = g(x)
the solution is one or more values of x. That is still true if you rewrite the equation to be a system of equations ...
y = f(x)
y = g(x)
The value of y tells you the value of each side of the original equation where the solution causes the functions to be equal. That is largely irrelevant. What you're looking for is the value of x.
The solution is the x-coordinate of the intersection point.
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If the height of the bounce follows geometric progression, find the general term that represent the situation in term of k. [2 marks] Hence, if the ball dropped from a height of 235ft, determine i. the highest height achieved by the ball after six bounces ii. the total distance travelled by the ball when it strikes the ground for 12th time [2 marks] [3 marks b) The number of cell double after each process of cell division every 2 hours. If there are 120 bacteria initially, how many bacteria will be there after one and half day? [4 marks]
The movement of the ping pong ball follows a exponential progression.
The expression for the k-th bounce is: [tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]The height after the 6th bounce is 41.82 ftThe total distance after the 12th bounce is 1584.84ft.There will be 31457280 bacteria after a day and a half.1. Ping pong ball
The given parameters are:
[tex]\mathbf{a = 235}[/tex] --- the initial height
[tex]\mathbf{r = 75\%}[/tex] --- the common ratio
(a) The expression after bouncing k times
To do this, we make use of
[tex]\mathbf{T_n = a \times r^n}[/tex]
So, we have:
[tex]\mathbf{T_n = 235 \times (0.75)^n}[/tex]
In this case; k = n.
So, the equation becomes
[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]
Hence, the expression for the k-th bounce is: [tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]
(b) The height after bouncing 6 times
This means that k = 6.
So, we have:
[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]
[tex]\mathbf{T_6 = 235 \times (0.75)^6}[/tex]
[tex]\mathbf{T_6 = 41.82}[/tex]
Hence, the height after the 6th bounce is 41.82 ft
(c) The total distance after the 12th bounce
First, we calculate the total height after the 12th bounce using:
[tex]\mathbf{S_k = \frac{a(1 - r^k)}{1 - r}}[/tex]
So, we have:
[tex]\mathbf{S_k = \frac{235 \times (1 - 0.75^{12})}{1 - 0.75}}[/tex]
[tex]\mathbf{S_k = \frac{235 \times (0.968)}{0.25}}[/tex]
[tex]\mathbf{S_k = 909.92}[/tex]
So, the total distance is:
[tex]\mathbf{Distance = 2 \times S_k - a}[/tex]
[tex]\mathbf{Distance = 2 \times 909.92 - 235}[/tex]
[tex]\mathbf{Distance = 1584.84}[/tex]
Hence, the total distance after the 12th bounce is 1584.84ft.
(2) Cell division
The given parameters are:
[tex]\mathbf{r = 2/2hr}[/tex] --- rate
[tex]\mathbf{a = 120}[/tex] --- initial number of cells
[tex]\mathbf{t = 18}[/tex] --- number of 2 hours is a day and a half
So, the number of bacteria is:
[tex]\mathbf{T_t = ar^t}[/tex]
This gives
[tex]\mathbf{T_t = 120 \times 2^{18}}[/tex]
[tex]\mathbf{T_t = 31457280}[/tex]
Hence, there will be 31457280 bacteria after a day and a half.
Read more about exponential functions at:
https://brainly.com/question/11487261
Evaluate the expression 6^2-(8–4^2+7
Answer
11
you can confirm from by yourself or tell
please mark this answer as brainlist
Camille is 7 years older than Donny, and Donny is 4 years younger than Tommy.
Write an expression for the total ages of the three people, in simplest form.
11
Step-by-step explanation:
first you add seven plus four and then you get your answer that is eleven
evaluate f(m-5) and simplify if f(x)=5x-9
Answer:
f(m-5) = 5m-34
Step-by-step explanation:
f(x)=5x-9
Replace x with m-5
f(m-5) = 5(m-5) -9
Distribute
= 5m-25 -9
= 5m-34
Answer:
answer is 5m - 34
Step-by-step explanation:
!!!!!!!!!!!!!!!!!!!!!!!!
An academy requires there to be 3 teachers for every 72 students and 5 tutors for every 60 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 132 students?
__% of 4 is 7
Please answer its due today
Answer:
175%
hope that helps. :)
x^2-6x+13 step by step to vertex form
I’m doing my math homework and I don’t understand it all. I did most of it in class but I don’t get it still so here’s the question
Question:
-4/3(3q -10)
Answer:
-4q+ 40/3
Step-by-step explanation:
Aashi buys
2 packets of bread rolls costing £1.40 for each packet
1 bottle of ketchup costing £1.80
3 packets of sausages
Aashi pays with a £10 note.
She gets 45p change.
Work out the price in pounds (£) of one pack of sausages.
(you will get brainliest) !! :D
Price of one unit Sausage = 1.65
Sum ( Price x Quantity) = Total Expenditure
Price of Bread x Quantity of Bread + Price of Ketchup x Quantity of Ketchup + Price of Sausage x Quantity of Sausage
Total Expenditure Value = 10 - 0.45 = 9.55
Let price of sausage = P
Therefore, 2 (1.40) + 1 (1.80) + 3 P = 9.55
2.80 + 1.80 + 3 Ps = 9.55
4.6 + 3 P = 9.55
3P = 9.55 - 4.60 = 4.95
P = 4.95 / 3 = 1.65
To learn more, refer https://brainly.com/question/16910784?referrer=searchResults
Can someone help me please
Answer:
The financial aid covers $ 1,875
Student needs to pay out-of-pocket $635
Step-by-step explanation:
(2,500) * (3/4) = 7500/4 = 1,875
2,500 - 1,875 = 635
Find the volume of the composite solid.
Answer:
volume________
7 ft 8 ft 7.5 ft 7 ftX-6y=6 find an ordered pair
Answer:
(6,0) or (0,-1)
Step-by-step explanation:
X-6y=6
X=6+6y
X/6=1+y
X/6-1=y
y=X/6-1
We'll use substitution to solve the ordered pair. Let's say Y = 0. We'll insert it back into our equation.
0=X/6-1
1=X/6
6=X
(6,0)
We can also start with X being = 0.
y=0/6 -1
y=-1
(0,-1)
I've attached what that would look like as a graph.
please ans very easy question
Answer:
what is the question please tell me on comment
Solve pls branliest!
Answer:
1 23 then 70 .2 corrected
what is the approximate length of segment PR?
25
11
125
18
Answer:
18
correct me if I'm wrong❌
Show how to use a power of 10 to write 42.66 / 2.97 as an equivalent expression with a whole number divisor
PLEASE HELP DUE TONIGHT!!
WILL MARK BRAINLIEST!!
Expressing the given equation as a power of 10 with the divisor expressed as an whole number can be written as [tex] \frac{42.66 \times 10^{2}}{297}[/tex]
Given the expression :
42.66/2.97Expressing the numbers as a power of 10 :
Dividend = 42.66 Divisor = 2.97To convert the divisor to a whole number :
Multiply both by 100
Dividend = 42.66 × 100Divisor = 2.97 × 100 = 297Expressing dividend as a power of 10 :
Dividend = 42.66 × 100 = 42.66 × 10²Hence, the equivalent equation would be : [tex] \frac{42.66 \times 10^{2}}{297}[/tex]
Learn more : https://brainly.com/question/18796573
pls help meeeee
pls....
Answer:
1→10
Step-by-step explanation:
12
27
45
105/4
49/2
2/15
2/9
22/45
7/12
1/3
help #2 #4 #6 #8 #10 #12
Same value as 40% of 84
Answer:
33.6
you are welcome :)
Step-by-step explanation:
If the sales tax rate is 8.9%, how much tax will be paid on a $457 tv?
State your answer in terms of dollars, rounded to the nearest cent (hundredth).
Do not include a $ sign with your response.
Write the equation in function form:
8x + 4y = 20
if y varies inversely as x, when y=20 and x=2 find the equation for y. then, find y when x=4
Answer:
the equation for y=20=1/2
Step-by-step explanation:
y=1/4
y=0.25
Please help I’m timed thank you!!!
Answer:
BAP=12
ABP=32.5
BCP=45.5
help with 14 please!!! please also explain!!
Answer:
f = ab/(a + b)Step-by-step explanation:
#14Given:
1/f = 1/a + 1/bSolving for f:
1/f = b/ab + a/ab1/f = (a + b)/ab cross - multiplyf(a + b) = ab divide by (a + b)f = ab/(a + b)Pls help can’t figure it out
See the question
Help
I’ll give a brainliest
1 , 2 , 3 , or 4 ?
Answer:
the answer is 3 I think if not than 2
2. Mack buys a gourmet pizza for $50. The shop increases its purchase price by 50%? What is the new price of the pizza?
Answer:
$75
Step-by-step explanation:
50% is half of the total, meaning that we can take half of $50, then add it to 50. Half of 50 is 25, so 50 + 25 = 75 dollars.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
should be 40
1.6[3(5(2))-5]
1.6[30-5]
1.6[25]
40
What is the largest multiple of 9 whose negation is greater than -100?
Answer:
99
Step-by-step explanation:
Its negation is greater than -100. Hope this helps!
~Just a joyful teen
[tex]SilentNature[/tex]
Answer:
99
Step-by-step explanation: