Answer:
See explanation
Step-by-step explanation:
We have that;
P(t) = (25t2 + 150t + 100)/(t2 + 6t + 24)
a) rate at which Glen Cove's population is changing with respect to time.
dP/dt = (t^2 + 5t + 40) (50t + 125) - (25t^2 + 125t + 200) (2t + 5)/(t^2 + 5t + 40)^2
dP/dt = 1000t + 3000/(t^2 + 6t + 24)^2
b) population after 10 years
P(t) = (25t2 + 150t + 100)/(t2 + 6t + 24)
P(t) =(25(10)^2 + 150(10) + 100)/((10^2 + 6(10) + 24)
P(t) = 4100/184
P(t) = 22283
c) when t = 10
dP/dt = 1000t + 3000/(t^2 + 6t + 24)^2
dP/dt = 1000(10) + 3000/(10^2 + 6(10) + 24)^2
dP/dt = 13000/33856
dP/dt = 0.384
determine the area of mrs wests backyard that is coverd grass and show ur work!!
Answer:
150 ft^2
Step-by-step explanation:
The formula is (30*10)/2 which is equal to 150.
Find the value of q which will make the quadratic expression 9x ^2-12x+q a perfect square
Answer:
The value of q that makes the expression a perfect square is q = 4.
Step-by-step explanation:
Perfect square:
A perfect square expression has the following format:
[tex](a - b)^2 = a^2 - 2ab + b^2[/tex]
In this question:
[tex]9x^2 - 12x + q[/tex] is a perfect square, we have to find the value of q.
First we have to find the value of a, looking at the equivalent formula above. So
[tex]a^2 = 9x^2[/tex]
[tex]a = \sqrt{9x^2}[/tex]
[tex]a = 3x[/tex]
Since the second term, which is -2ab, is -12x, we have that:
[tex]-2ab = -12x[/tex]
[tex]-2(3x)b = -12x[/tex]
[tex]-6xb = -12x[/tex]
[tex]6b = 12[/tex]
[tex]b = \frac{12}{6}[/tex]
[tex]b = 2[/tex]
q is b squared. So
[tex]q = b^2 = 2^2 = 4[/tex]
The value of q that makes the expression a perfect square is q = 4.
what are the next 3 terms in this:O,T,T,F,F
Answer:
Step-by-step explanation:
S, S, E.
Come on, do I have to spell it out for you? :)
Leann wants to gift wrap a present she got for her little brother how many square inches of gift wrap will be needed to cover a box that is 4in by 6in by 2in
Answer:
48 square in.
Step-by-step explanation:
so first off you do 4x6 and you get 24 now you want t do 24x2 and get 48
Yuri thinks that 3/4 is a root of the following function.
q(x)=6x^3+19x^2-15x-28
Explain to Yuri why 3/4 cannot be a root.
Given:
The polynomial function is
[tex]q(x)=6x^3+19x^2-15x-28[/tex]
Yuri thinks that [tex]\dfrac{3}{4}[/tex] is a root of the given function.
To find:
Why [tex]\dfrac{3}{4}[/tex] cannot be a root?
Solution:
We have,
[tex]q(x)=6x^3+19x^2-15x-28[/tex]
If [tex]\dfrac{3}{4}[/tex] is a root, then the value of the function at [tex]\dfrac{3}{4}[/tex] is 0.
Putting [tex]x=\dfrac{3}{4}[/tex] in the given function, we get
[tex]q(\dfrac{3}{4})=6(\dfrac{3}{4})^3+19(\dfrac{3}{4})^2-15(\dfrac{3}{4})-28[/tex]
[tex]q(\dfrac{3}{4})=6(\dfrac{27}{64})+19(\dfrac{9}{16})-\dfrac{45}{4}-28[/tex]
[tex]q(\dfrac{3}{4})=3(\dfrac{27}{32})+\dfrac{171}{16}-\dfrac{45}{4}-28[/tex]
[tex]q(\dfrac{3}{4})=\dfrac{81}{32}+\dfrac{171}{16}-\dfrac{45}{4}-28[/tex]
Taking LCM, we get
[tex]q(\dfrac{3}{4})=\dfrac{81+342-360-896}{32}[/tex]
[tex]q(\dfrac{3}{4})=\dfrac{-833}{32}\neq 0[/tex]
Since the value of the function at [tex]\dfrac{3}{4}[/tex] is not equal to 0, therefore, [tex]\dfrac{3}{4}[/tex] is not a root of the given function.
Please Answer This question.
Answer:
K = 15
Step-by-step explanation:
From the question given above, the following data were obtained:
Sine x = 1/4
Cos² x = K / 16
K =?
Next, we shall determine the 3rd leg (i.e the adjacent) of the right angle triangle. This can be obtained as follow:
Sine x = 1/4
Sine x = Opposite / Hypothenus
Opposite = 1
Hypothenus = 4
Adjacent =?
Hypo² = Opp² + Adj²
4² = 1² + Adj²
16 = 1 + Adj²
Collect like terms
16 – 1 = Adj²
15 = Adj²
Take the square root of both side.
Adj = √15
Next, we shall determine Cos² x.
Adjacent = √15
Hypothenus = 4
Cos² x =?
Cos x = Adjacent / Hypothenus
Cos x = √15 /4
Square both side
Cos² x = (√15 /4)²
Cos² x = 15 / 16
Finally, we shall determine the value of K. This can be obtained as follow:
Cos² x = K / 16
Cos² x = 15 / 16
K / 16 = 15 / 16
K = 15
Becky made 63 carnival masks, which is 30% less than the number
her brother made. How many carnival masks did Becky and her
brother make in total?
Answer:
273
Step-by-step explanation:
63 ÷ 30% = 210
210 + 63 = 273
therefore your total is 273
hope this is right, and that it helps :)
Answer:
Becky and her brother made 90+63=153 masks in total
Step-by-step explanation:
Percentages
Let's call x=number of masks Becky's brother made.
We know Becky made 30% less than the number of masks her brother made.
30% of x is calculated by:
30*x/100 = 0.3x
Now subtracting from x:
x - 0.3x = 0.7x
Becky made 63 carnival masks, this means that:
0.7x = 63
Dividing by 0.7:
x = 63/0.7 = 90
Becky's brother made 90 masks.
Becky and her brother made 90+63=153 masks in total
Identify if the equation is growth
or decay and the rate.
Answer:B
Step-by-step explanation:m is the slope and m=-3
50 points I WILL ALSO MARK BRAINLIEST ITS TIMED PLZ HURRY
The coordinates of the vertices of a polygon are shown on the graph below.
On a coordinate plane, point A is at (negative 4, 3), point C is at (0, negative 3), and point B is at (negative 4, negative 3).
What is the name of the polygon?
octagon
pentagon
quadrilateral
triangle
Answer:
Triangle
Step-by-step explanation:
Option D. triangle
Please include the steps that took you to get your answer. I am very confused on what to do with the 1/2.
First let's review how to expand this!
(ax+b)^2=a^2*x^2+2abx+a^2
In this case
(2x^2+1/2)^2=2^2*x^2+2*1/2*2x+(1/2)^2
=4x^2+2x+1/4
Done!
Using the diagram below, what is the length of PR (Please answer within 10 min it's on a time limit.)
Answer:
oof
Step-by-step explanation:
Question- What method would you happen to be using to solve this problem?
Factorise fully 18j + 30jk
Answer:
6j(5k+3)
Step-by-step explanation:
18j+30jk
Factor out 6.
6(3j+5jk)
Consider 3j+5jk. Factor out j.
j(3+5k)
Rewrite the complete factored expression.
6j(5k+3)
Someone please help me!!:(
solve each equation for given variable
- 12 = 6i- 6
Please help me I’m giving brainliest!
=====================================================
Work Shown:
Applying the tangent-secant theorem will allow us to solve for x
x*(x+5) = (x+2)^2
x^2+5x = (x+2)*(x+2)
x^2+5x = x^2+4x+4
5x = 4x + 4 ..... subtracting x^2 from both sides; terms cancel
5x-4x = 4
x = 4
------------------
Check:
Plug in x = 4
x*(x+5) = (x+2)^2
4*(4+5) = (4+2)^2
4*(9) = (6)^2
36 = 36
The answer is confirmed.
What is the equation of the line that passes through the point (-3,2) and has a slope of -2/3
Answer: Y=2/3x+4
................................................
What is the velocity of a car that’s traveled 306 kilometers northeast in 3.4 hours
Answer : -302.6
Step-by-step explanation:
Solve the proportion: 9 is to 16 as M is to 32.
(please show working out!)
Answer:
Step-by-step explanation:
9 : 16 :: M : 32
Means of extremes = means of means
= 9 x 32 = 16 x M
= 288 = 16M
288/16 = M
18 = M
PLEASE HELP THIS IS URGENT
Kayla is thinking of a 3-digit number. * It is divisible by 18. * It is a palindrome (It reads the same left-to-right as it does right-to-left, like 252 and 848). * It is one less than a multiple of 5. What is Kayla’s number?
Answer: 414
Step-by-step explanation: 414 is a palindrome that is divisible by 18 because it’s an even number and that it’s one less than 415 which is a multiple of 5.
Kayla's number is 414 and this can be determined by using the given data and also by using the arithmetic operations.
Given :
Kayla is thinking of a 3-digit number. It is divisible by 18.It is a palindrome.It is one less than a multiple of 5.The following steps can be used in order to determine Kayla’s number:
Step 1 - Remember palindrome means 'reads the same left-to-right as it does right-to-left'.
Step 2 - The digit should be between 0 to 9 and according to the given data, the number is one than a multiple of 5 that is, the first and last digit must be 4 or 9.
Step 3 - So, the number which is divisible by 18 is 414.
For more information, refer to the link given below:
https://brainly.com/question/25277954
can someone help this is kinda confusing i’ll mark you as brainlilest.
Answer:
The answer is A, good luck on the test! :D
Step-by-step explanation:
Answer:
Step-by-step explanation:
A. In geometry, a cylinder is a three-dimensional shape with a circular base, ... So using the volume of cylinder formula we can find the volume of i
50 points
Yolanda received her telephone bill on July 27th and paid it three weeks later. What was the date that Yolanda paid her electric bill? A. July 6 B. July 17 C. August 17 D. August 18
Answer:
Aug 16th
Step-by-step explanation:
is it complementary, supplementary, vertical, or none of the above? i need this right now!!!!
Answer:
d. None of these
Step-by-step explanation:
Hope it helps you in your learning process.
[tex] m\angle 1 + m\angle 2 + 90\degree = 360\degree [/tex]
[tex] m\angle 1 + m\angle 2 = 360\degree- 90\degree [/tex]
[tex] m\angle 1 + m\angle 2 = 270\degree [/tex]
Answer:
D. None of the above.
Step-by-step explanation:
Complementary are 90 degrees and supplementary are 180 degrees.
A full circle is 360 degrees, and since there is a right angle, that means that angle 1 and 2 make up 270 degrees total.
This means it is neither.
The height of a standard coffee cup
would be about
7 meters
B
7 kilometers
7 centimeters
D
7 millimeters
Answer:
7 centimeters
Step-by-step explanation:
Standard size of a coffee cup is 7 centimeters
7 meters is too big
7 kilometers is bigger than 7 meter
7 millimeters is too small
do's and donts in handling measuring tools
Answer:
I need answer too
Pleaseee help us
Lindsay invest $250 in a bank account that pays 3% interest each year how much money will be in her account after one year?
which word describes the slope of line ?
What is the answer please
Look at this expression.
-3xfy
x3y2
Which of the following is the simplest form of this expression?
OA
-3x²y2
ОВ. -3x?у?
Ос. -3°у?
OD. -3x® yo
Answer:
‐3×2y2 is the most common correct answer
Pippin went to a game room that charged $4 admission, plus $0.25 per token. The equation which represents his total cost is y = 0.25x + 4.What are the ordered pairs for the equation when you use these x-values: 5, 10, 20?(5, 5), (10, 8), (20, 15)(5, 8), (10, 10), (20, 15)(5, 5.25), (10, 6.50), (20, 9)(5, 5.50), (10, 8.50), (20, 13)
Answer:
(5, 5.25) , (10, 6.50) , (20, 9)
Step-by-step explanation:
As given ,
y = 0.25x + 4
Now,
if x = 5
⇒ y = 0.25(5) + 4
= 1.25 + 4
= 5.25
⇒ y = 5.25
∴ the ordered pair be (x, y) = (5, 5.25)
if x = 10
⇒ y = 0.25(10) + 4
= 2.5 + 4
= 6.50
⇒ y = 6.50
∴ the ordered pair be (x, y) = (10, 6.50)
if x = 20
⇒ y = 0.25(20) + 4
= 5 + 4
= 9
⇒ y = 9
∴ the ordered pair be (x, y) = (20, 9)
Elena is designing a paint can with thickness ttt millimeters and height hhh centimeters. She calculates that the thickness of the can in milimeters must be at least 0.1, point, 1 times the height of the can in centimeters in order to withstand pressure. Due to cost constraints, the cost of material used, (0.2 + t+ 0.5h)cents, must be at most 12.2, point, 2 cents. Which system of inequalities best models the relationship between height and thickness?
Answer:
[tex]t \ge h[/tex] and [tex]t + 0.5h \le 12.0[/tex]
Step-by-step explanation:
Given
[tex]t= thickness[/tex]
[tex]h =height[/tex]
From the first statement, we have that:
[tex]t\ mm \ge 0.1 * h\ cm[/tex]
Convert mm to cm
[tex]t\ * 0.1*cm \ge 0.1 * h\ cm[/tex]
[tex]t\ *0.1 \ge 0.1 * h[/tex]
Divide both sides by 0.1
[tex]t \ge h[/tex]
From the second statement, we have that:
[tex]Cost \le 12.2[/tex]
Substitute 0.2 + t + 0.5h for Cost
[tex]0.2 + t + 0.5h \le 12.2[/tex]
Collect Like Terms:
[tex]t + 0.5h \le 12.2-0.2[/tex]
[tex]t + 0.5h \le 12.0[/tex]
So, the inequalities are:
[tex]t \ge h[/tex] and [tex]t + 0.5h \le 12.0[/tex]
Answer: it's a, the answer
Step-by-step explanation: