As proportional relationship, the amount decreasing at a rate milligrams per hour can be written in expression P(t) = 500 + e⁻⁰²ˣ
What is Proportional relationship?In math, the relationships between two variables where their ratios are equivalent is known as proportional relationship.
Given that P(t) represent the amount of a certain drug, in milligrams, that is in the bloodstream at time t hours.
Here we have the rate at which the drug leaves the bloodstream proportional to the amount of the drug bloodstream.
The amount of the drug in the bloodstream can be modeled by dP/dt = kP, where k is a constant and t is time, in hours.
Here we need to find the expression.
Bloodstream = 500 milligrams
So, the expression for this proportional relationship is written as;
P(t) = 500 + e⁻⁰²ˣ
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Please help!! :) Thank you!
Let's complete the square
f(x) = x^2 + 6x + 8
y = x^2 + 6x + 8
y-8 = x^2 + 6x
y-8+9 = x^2+6x+9 .... see note below
y+1 = (x+3)^2
y = (x+3)^2-1
note: I added 9 to both sides due to taking half of the 6, and then squaring that result.
We'll restrict x such that [tex]x \ge -3[/tex] to ensure that this function is one-to-one.
Now we need to swap x and y, and solve for y to get the inverse
y = (x+3)^2 - 1
x = (y+3)^2 - 1
x+1 = (y+3)^2
(y+3)^2 = x+1
y+3 = sqrt(x+1)
y = sqrt(x+1)-3
g(x) = sqrt(x+1)-3 is the inverse
The graph is shown below. The original function is in red. The inverse is in blue. The inverse is the result of reflecting the red curve over the dashed line y = x. So this explains why x and y swap places. Consequently, the domain and range also swap as well.
The original selling price of a share of stock was d dollars. The selling price for a share of the same stock at a later date was represented by the expression 1.15(0.95d). Which description could explain what happened to the price of the share of stock?
Group of answer choices
Answer:
96
Step-by-step explanation:
Tammy made 12 paper cranes in 3 days. Find the unit rate. Please provide a tape diagram
Answer:
To find the unit rate, we must find how many cranes Tammy made in one day.
12 (cranes) 4 cranes
_________ = ________, he makes 4 cranes per day.
3 days 1 day
Tape diagram provided;
PLEASE ANSWER QUICK. LOTS OF POINTS
By graphing the system of constraints, find the values of x and y that maximize the objective function.
2=
1=
x+y=<8
maximize for P=3x+2y
A) (2, 1)
B) (6, 2)
C) (2, 5)
D) (3, 5)
Answer:
c is the answer I'm sure
whats the sum to 4/6 4/6
In the given problem, the sum of [tex]\frac{4}{6}[/tex] and [tex]\frac{4}{6}[/tex] is [tex]\frac{4}{3}[/tex].
The sum is the result of adding two or more numbers or terms. In other words, it is the process of bringing two or more numbers together to produce a new result or total. The symbol for the sum is "+".
The sum can be performed on any kind of number, including whole numbers, integers, rational numbers, real numbers, and complex numbers. The rules for addition are the same for all types of numbers.
To find the sum of [tex]\frac{4}{6}[/tex] and [tex]\frac{4}{6}[/tex],
[tex]\frac{4}{6}[/tex] + [tex]\frac{4}{6}[/tex] = 2 [tex]\times \ \frac{4}{6}[/tex]
= [tex]\frac{4}{3}[/tex].
So, [tex]\frac{4}{6}[/tex] + [tex]\frac{4}{6}[/tex] = [tex]\frac{4}{3}[/tex].
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True or False: When converting a percent to a decimal you can multiply by 100 or move the decimal two spaces to the right. *
Answer:
true
Step-by-step explanation:
true
Answer: True
Step-by-step explanation:
Henry enjoys watching his pet frog hop.
Each time his frog hops, Henry skip-counts backward by 100s.
Henry starts his first count at 815.
How many times does his frog have to jump to get to 15?
Explain your thinking below.
8 times does his frog have to jump to get to 15.
Why do frogs hops?The frog jump is a plyometric exercise that primarily works your quads, glutes, and hip flexors. This exercise strengthens the wrists, ankles, knees, hips, and ligaments in the joints. It also stretches your hips and ankles while strengthening your legs and lower back muscles.Frogs jump and hop around using their long, strong legs. Toads, on the other hand, prefer to walk rather than hop. They only move modest distances when they jump or hop. As a result, they don't require long legs like a frog, hence their legs are quite short.The starting number is 815.
the frog hops once (715)
2nd (615)
3rd (515)
4th (415)
5th (315)
6th (215)
7th (115) and
one last time (15) there are 8 numbers.
No. of Times = (815-15)/100 = 8 times.
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what is the value of this
Answer:
I believe the value is equal to 8
Find the slope of the line passing through the points (-4, -4) and (2, 5)
Answer: The slope is 3/2
Step-by-step explanation:
To find the slope, you need to find the difference between the y coordinates and divide it by the difference in the x coordinates.
The y coordinates are -4 and 5
The x coordinates are -4 and 2
-4 -5 = - 9
-4 - 2 = -6
-9/-6 = 3/2
What is the center of the circle x ^ 2 + y ^ 2 + 14 = 9x
Find the slope of the line drawn below
Answer:
slope is undefined
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (1, - 3)
m = [tex]\frac{-3-2}{1-1}[/tex] = [tex]\frac{-5}{0}[/tex]
Since division by zero is undefined then the slope of the line is undefined
Compute... 2x + 5 = 11
Answer:
Your answer is x=3
Step-by-step explanation:
So you have the equation 2x+5=11
First, subtract 5 from 5 and from 11.
Then you will cancel out the 5's.
After that, you should have "2x=6"
Now divide 2 from 2x and from 6.
Your answer is x=3
What is substitution?
Answer:
to put a letter in the place of a number
Step-by-step explanation:
Please! I need help! ASAP!
2 solutions (2 intersection points)
and the solutions
(4 ; 5) and (0 ; - 3)
What is 5(y-2)-2=2(y+1)-5? Solve for y and show your work please.
Answer:
y = 3
Step-by-step explanation:
Let's start with the left side of the equation.
5(y-2)-2= 2(y+1)-5
5y-10-2= 2(y+1)-5
Now let's solve the right side
5y-10-2= 2y+2-5
5y-12= 2y-3
-2y -2y
3y-12=-3
+12 +12
3y = 9
3y/3 = 9/3
y = 3
hope this helps!
DOES ANYONE KNOW THIS????
Answer:
9/10, 1 3/15, 1 6/10, 2 2/9
Step-by-step explanation:
Let's make all the numbers a fraction.
1 6/10, 1 3/15, 9/10, 2 2/9
Find the LCD of the fractions.
1 6/10 = 144/90
1 3/15 = 108/90
9/10 = 81/90
2 2/9 = 200/90
Order the fractions least to greatest.
9/10, 1 3/15, 1 6/10, 2 2/9
Can I get some help?
A. 48
B. 55
C. 77
D. There is not enough information given to find the value of x
Look for Relationships Does this system have one solution, no solutions,
or infinitely many solutions?
Write another system of equations with the
same number of solutions that uses the first equation only.
12x + 51y = 156
-8x - 34y = -104
simultaneous equations
While evan and sam are fishing 12kms from shore, their boat springs a leak, and water comes in at a constant rate of 3 gallons per minute. Same starts rowing towards the shore at a constant rate of 24kms per hour while evan bails water out of the boat. What is the slowest rate, in gallons per minute, at which evan can bail if they are to reach the shore with out sinking?
Based on the calculations, the slowest rate is equal to 4 gallons per minute.
Given the following data:
Distance from shore = 12 km.In-rate = 3 gallons per minute. Rowing rate = 24 km per hour.How to calculate the slowest rate.Let's assume the boat would sink if it takes in more than 20 gallons of water.
Conversion:
24 km/h to km/min = [tex]\frac{24 }{60}[/tex] = 0.4 km/min.Translating the word problem into an algebraic expression, we have;
[tex]\frac{12}{0.4} \times 3 - \frac{12}{0.4} \times x\geq 30\\\\\frac{36}{0.4}-\frac{12x}{0.4} \geq 30\\\\90-\frac{12x}{0.4} \geq 30\\\\\frac{12x}{0.4} \geq90+30\\\\\frac{12x}{0.4} \geq120\\\\12x \geq120 \times 0.4\\\\12x \geq 48\\\\x\geq 4[/tex]
Therefore, the slowest rate is equal to 4 gallons per minute.
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Someone pls help????????????????????????????
Answer:
The answer is 32 square inches.
Step-by-step explanation:
A square has 4 sides, and each side is 8 square inches. So the area of an object if the space of it. That means 8 x 4 which is 32.
Have a nice day!
Hannah opened a bank account. She placed $120 into the bank account and added $30 per week. Now she has $450 in her account. A. Write an equation that represents her savings. B. Find the number of weeks that have passed since she opened her savings account. Explain how you arrived at your answer
The equation that represents her savings is $450 = $120 + $30n.
The number of weeks that have passed since she opened her savings account is 11 weeks.
What equation represents her savings?Total amount saved = amount initially deposited + (amount added weekly x number of weeks)
$450 = $120 + $30n
Where n = number of weeks
In order to determine the value of n, take the following steps:
Combine similar terms = $450 - $120 = 30n
$330 = 30n
Divide both sides by 30
n = 11 weeks
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The set of ordered pairs
below has a linear relationship
between x and y. Which one of the
following functions can represent
this set of ordered pairs?
{(0,-5), (2, 3). (3,7). (5,5)}
A: y= 4x - 5
B: y= 4x + 5
C: y= -4x - 5
D y= -4x + 5
Answer:
Recommendation: Try using the online graphing calculator Desmo and try to see if you can get your answer by entering the equations. desmo is free.
Work out the size of an interior angle of a regular polygon with 24 sides.
Answer:
165°
Step-by-step explanation:
First, we need to find the sum of all the interior angles in the 24-sided polygon.
The equation for that is: 180 (n-2)
[n represents the number of sides]
180 (24-2)
180 (22)
3960
Then to find the measure of a single interior angle, just divide 24 from 3960.
3960 ÷ 24 = 165
Rounded to the nearest whole degree, what is the measure of angle boa? ° rounded to the nearest tenth of a centimeter, what is the length of arc bac? cm
1) The measure of ∠BOA is 60.16°.
2) the length of arc BAC is 14.68cm.
What is the formula for arc length?
Arc length = Central Angle(in radian) * Radius
So, length of arc AC = (45π/180) * 8
Arc AC = 2π
Arc AC = 6.28cm
So, length of arc BAC = arc AC+ arc AB
Arc BAC = 6.28 +8.4
Arc BAC = 14.68cm
∠BOA = length of Arc AB / Radius
∠BOA = 8.4/8 = 1.05 radian
∠BOA= 1.05 *(180/π)°
∠BOA=60.16°
Therefore, 1) The measure of ∠BOA is 60.16°.
2) the length of arc BAC is 14.68cm.
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Answer:
BOA= 60
BAC= 14.7
Step-by-step explanation:
i did it
Which statement about a right triangle is NOT true
The hypotenuse is the longest side of the triangle.The square of the hypotenuse is equal to the sum of the squares of the other two lengths.
The sum of the length of the two legs is equal to the length of the hypotenuse.
The hypotenuse is always opposite the largest angle of the triangle.
Answer:
The sum of the length of the two legs is equal to the length of the hypotenuse.
Solve for x, given the perimeter = 40 cm.
2x+1+x+4
I need fast please help me
106.5 divided by 3 partial quotients pls Answer ASAP
Answer:
35.5
Step-by-step explanation:
Hopefully this is what you mean
Please help me!! Il give u brainliest(:
Answer: f^-1(x)= 2-4x/3
This is because the power of f is -1
Answer:
A. Answer: f^-1(x)= 2-4x/3
Step-by-step explanation:
This is because the power of f is -1, all you would do is solve the 4x-2 divided by 3 to get the answer pls give brainiest thank you.
Part E
Now check your work by using the GeoGebra geometry tool to repeat parts A through D. Open GeoGebra e, and complete
each step below. If you need help, follow these instructions for using GeoGebra. You'll take a screenshot of your work when
you're through, so be sure to clearly label your construction as you work.
1. Plot points A, B and C, and draw a polygon, AABC, through the points.
2. Draw a line perpendicular to AC through point B. 3. Label the intersection of the line perpendicular to AC through Band AC point D.
4. Measure and display the slopes of AC and BD.
5. Display the equations of AC and BD in the Algebra margin.
6. Measure and display the lengths of AC and BD.
7. Calculate and display the area o Part F
Compare the calculations displayed in GeoGebra with the calculations you completed in parts A through D. Look in the Algebra
margin too. Do the results in GeoGebra match the results you obtained earlier? If not, where do the discrepancies occur? You
might have to rearrange equations algebraically to determine whether two equations match. Part 6
You've seen two methods for finding the area of AABC-using coordinate algebra (by hand) and using geometry software.
How are the two methods similar? How are they different? Why might coordinate algebra be important in making and using
geometry software?
Answer:
Part E is the pic
Part F is the triangle
sorry if it is kinda blurry
Part 6:
You've seen two methods for finding the area of AABC-using coordinate algebra (by hand) and using geometry software.
How are the two methods similar?
They both apply the fundamentals of triangle geometry in solving the area of a triangle using the formula for the area of triangle 1/2×base of triangle×height of the triangle.
How are they different?
Using coordinate algebra in finding the area of a triangle, you would have to measure coordinates(XY coordinates) of a triangle manually on the graph and find y coordinates based on x. If you used geometry software, it would get these coordinates automatically(based on your graph on the software) and calculate the area of the triangle using the formula.
Why might coordinate algebra be important in making and using geometry software?
A solid grasp of coordinate algebra allows you to understand how the geometry software works because it makes use of the same geometry fundamentals, making it easier for you to tweak and get the best value out of the software for your geometry calculations.
Hope it helps!!!Brainliest pls!!!Daniel had 1,868 in his bank account before he left for North Carolina. He wrote a check for $710 to pay his monthly truck payment. He also wrote a check for $224.89 to Farm Bureau Insurance Company for his truck insurance. When he got home from North Carolina he deposited his paycheck in the amount of $4,020.67. What was the balance in his bank account after he deposited his paycheck?
Answer:
4,953.78 dollars. I think