Answer:
21
Step-by-step explanation:
1. Contaminated water is subjected to a cleaning process. The concentration of the pollutants is initially 5 mg per liter of water. If the cleaning process can reduce the pollutant by 10% each hour, define a function that can represent the concentration of pollutants in the water in terms of the number of hours that the cleaning process has taken place.
Answer:
[tex]C(t)=5\cdot(0.9)^t[/tex]
Step-by-step explanation:
The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function is expressed as:
[tex]C(t)=C_o\cdot(1-r)^t[/tex]
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
The concentration of the pollutants starts at Co=5 mg/lt. We also know the pollutant reduces its concentration by 10% each hour. This gives us a value of r = 10% / 100 = 0.1
Substituting into the general equation:
[tex]C(t)=5\cdot(1-0.1)^t[/tex]
Operating:
[tex]\boxed{C(t)=5\cdot(0.9)^t}[/tex]
y(n) = 5(0.9)ⁿ
To answer this, we will make use of the exponential decaying function which is given by;y(n) = a(1 - b)ⁿ
where;
y is the final amount at time n,
a is the original amount
b is the decay factor
x is the amount of time that has passed.
We are told that the initial concentration of the pollutants is 5 mg/LThus;
a = 5 mg/L.
We are told that the pollutant reduces its concentration by 10% each hour. Thus; b= 10%
b = 0.1
Therefore Plugging in the relevant values into y(n) = a(1 - b)ⁿ, we have;y(n) = 5(1 - 0.1)ⁿ
y(n) = 5(0.9)ⁿ
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Write a linear equation that is parallel to
line below and passes through the point
(-4,-13)
Answer:
y = 3x - 1
Step-by-step explanation:
Original line: y = 3x + 5
Parallel line has the same slope, so use the point-slope form.
y - (-13) = 3(x - (-4))
y + 13 = 3x +12
y = 3x -1
The equation of the line that is parallel to the line shown in the graph and passes through the point (-4,-13) is y = 2x - 5.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given the graph of the linear equation:
From the graph:
The line passes through (-3, -1) and (0, 5)
The slope of the line is shown in the graph:
m = (5+1)/(0+3)
m = 2
The equation of the line that has slope -2 and passes through (-4, -13):
[y - (-13)] = 2[(x - (-4)]
y + 13 = 2(x + 4)
y + 13 = 2x + 8
y = 2x + 8 - 13
y = 2x - 5
Thus, the equation of the line that is parallel to the line shown in the graph and passes through the point (-4,-13) is y = 2x - 5.
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If ΔABC = ΔDEF, angle m∠A = 50, and angle m∠E = 30, what is angle m∠C?
When you indicate triangle congruency, the order of the letters matter. As you see these statements, look at how the side length names correspond to how the letters are written in its order, ΔABC ≅ ΔDEF. (By the way, triangles aren't equal with an = sign. It's a ≅ congruency sign.)
AB is congruent or the same length as DE.
BC is congruent or the same length as EF.
AC is congruent or the same length as DF.
In the same way, all of the angles in the corresponding order are ALSO congruent. By the way, we say that angles are congruent and angle MEASURES (like 30 degrees) are equal.
m∠A = m∠D
m∠B = m∠E
m∠C = m∠F
In the same way, we can try to find m∠C, or measure C!
1. Let's find the missing angle!
So, we know that m∠A is 50 degrees and m∠E is 30 degrees. Since we know that m∠E = m∠B because of the order of the triangles, now we know two of the angles in triangle ABC.
m∠A = 50 degrees
m∠B = 30 degrees
m∠C = 180 degrees - (50 + 30) = 100 degrees
(We minus from 180 degrees because 180 degrees is the sum of the angles in a triangle!)
And that's it! If you have any questions, please feel free to ask questions. I'm not here to judge, and I'm only here to help. Again, ask questions if you need help. It's crucial that you know the basics of geometry!
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question in the picture
Answer:
The answer is B
Step-by-step explanation:
Answer:
2 divided by 3
Step-by-step explanation:
6c.) Consider the functions f(x) = -2x + 1 and g(x) = 4x - 5
Now find g(3).
Answer:
7
Step-by-step explanation:
g(x)=4x-5
g(3)= 4(3)-5
=12-5
=7
Answer:
g(3)=4x-3
Step-by-step explanation:
put 3 into x
know g(3)=4x-3=4×3-1=12-1=11
11 will be the answer
Which choice represents 673.983 rounded to nearest hundredth
Answer: 673.98
Step-by-step explanation: The 8 is the hundredth place, and anything less than five you don't round up
Simplify -|-5 + 2|
7, 3, -7,-3
Answer:
-3
Step-by-step explanation:
what is the answer? pls help
Answer:
Undefined
Step-by-step explanation:
The x value is always 5 so the slope is undefined
Answer:
The slope of the line is undefined.
Step-by-step explanation:
To solve this problem, we should use the formula for slope, which is given below:
m = slope = (y2-y1)/(x2-x1)
If we plug in two of the points that are given in the table, we get:
m = slope = (6-3)/(5-5)
If we perform the subtraction in the parentheses in both the numerator and the denominator, we get:
slope = 3/0
Since we cannot divide by 0, this means the slope is undefined.
Hope this helps!
You notice a hot air balloon descending. The elevation h
(in feet) of the balloon is modeled by the function h(x)=−8x+360,
where x
is the time (in seconds) since you first noticed the hot air balloon.
Graph the function and specify its domain and range. Then interpret the slope and intercepts of the graph.
Answer:
the domain is 0 x 45 and the range is 0 h 360. The slope is -8, so the change in the height of the ballon is -8 feet per second. The h-intercept is 360, so the height of the ballon when the first noticed it was 360 feet. The x-intercept is 45, so the time it took the hot air balloon to reach the ground was 45 seconds.
Step-by-step explanation:
The descending balloon is an illustration of a linear function.
The balloon spent 45 seconds in air The balloon was at a height of 360 feet when you noticed it.The balloon descends 8 feet per seconds.[tex]\mathbf{Domain=[0,45]}[/tex].[tex]\mathbf{Range=[0,360]}[/tex]The function is given as:
[tex]\mathbf{h(x) = -8x + 360}[/tex]
See attachment for the graph of h(x)
From the graph, we have the following observations
The y value ranges from 0 to 360The x value ranges from 0 to 45The function crosses the graph at x = 45 and y = 350The above highlights mean that:
[tex]\mathbf{Domain=[0,45]}[/tex][tex]\mathbf{Range=[0,360]}[/tex][tex]\mathbf{x-intercept = 45}[/tex][tex]\mathbf{y-intercept = 360}[/tex]The x intercept means that:
The balloon spent 45 seconds in air
The y-intercept means that:
The balloon was at a height of 360 feet when you noticed it.
A linear function is represented as:
[tex]\mathbf{y = mx + c}[/tex]
Where:
m represents the slope
By comparison with [tex]\mathbf{h(x) = -8x + 360}[/tex]
[tex]\mathbf{m = -8}[/tex]
The above value of slope means that:
The balloon descends 8 feet per seconds
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Please help me. I have no idea how to solve this.
Answer:
its either D or C
Step-by-step explanation:
A makes no sense because u only moving 2 and for B too and E it not it
please help me with the domain and range of the graphs.?part 5
Problem 5
Domain = [tex]-4 \le x \le 3[/tex]
This is because the smallest x value allowed is x = -4 as shown by the left-most point. The right most point has x coordinate x = 3, so this is the largest value in the domain.
The domain in interval notation is [-4, 3]. The square brackets include the endpoint.
--------------
Range = [tex]-4 \le y \le 5[/tex]
We're now looking at the possible y values. The lowest point happens when y = -4 and the highest point is when y = 5. We can have any y value between those endpoints.
The range in interval notation is [-4, 5]
=============================================================
Problem 6
Domain = [tex]-2 \le x < 2[/tex]
Same idea as the previous problem. This time the left most point has x = -2 and the right most point has x coordinate x = 2.
The big difference here is that the open hole says to not include the endpoint. The domain in interval notation is [-2, 2) where we use a parenthesis to not include the endpoint.
-------------
Range = [tex]-4 \le y < 4[/tex]
The smallest possible y value is y = -4. The ceiling for the y values is y = 4, but we can't actually reach this value due to the open hole.
The range in interval notation is [-4, 4)
=============================================================
Problem 7
Domain = [tex]-4 < x \le 2[/tex]
Same idea as earlier. Now the open hole is at the left endpoint. The right most point occurs not at an endpoint this time.
The domain in interval notation is (-4, 2]
-------------
Range: [tex]-4 < y < 4[/tex]
Both endpoints are open holes, so we exclude both endpoints.
The range in interval notation is (-4, 4). Unfortunately in this case, interval notation looks identical to ordered pair notation.
=============================================================
Problem 8
Domain = [tex]-5 < x < 3[/tex]
Domain in interval notation = (-5, 3)
The graph is too blurry to be able to determine the range.
ANSWER ASAP WILL GIVE EXTRA POINTS AND BRAINLIEST
Answer: 2/7 will be more
Step-by-step explanation:2/7 times 11 each then gets 22/77 then 3/11 times 7 gives it 21 over 77 22 is more than 21
Answer:
common denom is 77 so 2/7=22/77 and 3/11=21/77
>
One apple contains 80 calories. What
percent of a 2000-calorie diet is
contained in one apple?
a) 42
b) 80
c) 96
d) 20
What expression is equivalent to (24+9)
Answer:
welol its in parentheses and no matter what you always do parentheses first and it shows
(24+9) and the answer to that is 33
bc your simply just adding 24+9
Step-by-step explanation:
or if your looking for something similar do
(11+22)
Determine weather or not the following is a function:{-2,9)
Answer:
THis is a function
Step-by-step explanation:
Each x value corresponds to one y-value. It is a function.
Modeling Real-World Scenarios with Sine and Cosine Functions
The table below shows the illuminated percentage of the moon on a lunar cycle of 28 days. The relationship can be described using a cosine function.
Answer:
0 and 0
Step-by-step explanation:
it stays the same 7 to 17 is 7
14 to 21 is 7 etc...
The amplitude of the function is 48 units.
The period of the function is 28 units.
The graph has a vertical shift of 48 unit.
To determine the amplitude and period of the cosine function that describes the relationship between the day (d) and the illuminated percentage of the moon (%), we can analyze the given data:
d %
0 48
14 96
21 48
28 0
Amplitude:
The amplitude of a cosine function represents half the difference between the maximum and minimum values of the function.
So, (96 - 0) / 2
= 48 units.
Period:
The period of a cosine function is the length of one complete cycle.
Therefore, the period of the function is 28 units.
Vertical shift:
The vertical shift represents the displacement of the graph vertically.
The graph has a vertical shift of 48 unit.
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How do you build a triangle if you are given 3 numbers like 3,4,5. Provide an example besides 3,4,5 or a non-example.
Pattern:
Example:
Answer:
3, 4, and 5 make a right triangle (Pythagorean triple). 3 and 4 are the legs, 5 is the hypotenuse. Another example is 9, 12, 15, with 9 & 12 as the legs and 15 as the hypotenuse on a right triangle.
Step-by-step explanation:
Pythagorean triples (measurements are whole numbers) are always in a 3:4:5 ratio; the longest side is always hypotenuse; the right angle is always opposite of the hypotenuse; the legs will be perpendicular (making right angle)
Find the equation of the line
Answer the question with y= mx+c
What is the slope of the line
Answer:
-3/4x
Step-by-step explanation: Since the line going top left to bottom right you know that it is a negative slope. Remember to do rise over run. It's easier if you start at a point like (1, -1) and then rise up 3 and run left 4.
PLEASE HELP MEEEEEEEEEEEEEEEEEEEEE
Answer:
D
Step-by-step explanation:
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition SubtractionStep 1: Write expression
[tex](\frac{7}{2}-\frac{1}{3} )(-2)^2+\frac{1}{2}[/tex]
Step 2: Evaluate
Exponents: [tex](\frac{7}{2}-\frac{1}{3} )(4)+\frac{1}{2}[/tex]Parenthesis: [tex](\frac{19}{6} )(4)+\frac{1}{2}[/tex]Multiply: [tex]\frac{38}{3} +\frac{1}{2}[/tex]Add: [tex]\frac{79}{6}[/tex]Answer:
13 1/6
Step-by-step explanation:
Follow PEMDAS:
(7/2-1/3) * (-2)^2 +1/2
P: parenthesis... 7/2 - 1/3 is 19/6
then you do E: exponents... (-2)^2 is basically -2 * -2 which a negative multiplied by a negative is a positive so its 4.
19/6 * 4+1/2
PE M DAS... M: multiply... 19/6 *4 is 38/3 which simplifies to 12 2/3
Lastly you add 12 2/3 with 1/2 and you get 13 1/6
The marketing department of a local shoe company found that approximately 550 pairs of running shoes are sold monthly when the price of each pair is $100. It was also observed that, for each $1 reduction in price, an additional 20 pairs of
running shoes are sold monthly. What price should the shoe store charge for a pair of running shoes in order to maximize revenue?
Answer:
The price that maximizes the revenue is $63.75
Step-by-step explanation:
Analyzing the statement one after the other.
[tex]Initial\ Quantity = 550[/tex] ---- When ----- [tex]Initial\ Price = \$100[/tex]
When there's a reduction of $1, we have:
[tex]Quantity = 550 + 20x[/tex] and [tex]Price = 100 - x[/tex]
Where x represents the maximum reduction
At this point, we need to calculate the revenue (R)
[tex]R = Quantity * Price.[/tex]
[tex]R = (550 + 20x) * (100 - x)[/tex]
Open Brackets
[tex]R = 55000 - 550x + 2000x - 20x^2[/tex]
[tex]R = 55000 +1450x - 20x^2[/tex]
Differentiate both sides with respect to x
[tex]\frac{dR}{dx} = 0 + 1450 - 40x[/tex]
[tex]\frac{dR}{dx} = 1450 - 40x[/tex]
To maximize revenue;
[tex]\frac{dR}{dx} = 0[/tex]
So:
[tex]1450 - 40x = 0[/tex]
[tex]1450 =40x[/tex]
Solve for x
[tex]x = 1450/40[/tex]
[tex]x = 36.25[/tex]
Recall that:
[tex]Price = 100 - x[/tex]
Substitute [tex]x = 36.25[/tex]
[tex]Price = 100 - 36.25[/tex]
[tex]Price = 63.75[/tex]
Hence:
The price that maximizes the revenue is $63.75
Ian and Ruth volunteer at the community center. Ian works every fifth day and Ruth works every seventh day. They both worked on Wednesday, October 24th. What is the DATE when they will work together again?
Answer:
11/29/2020
Step-by-step explanation:
Every seventh and fifth day, both numbers are prime, 5 x 7 = 35, so 35 days after October 24th is November 29th because October has 30 days.
State the zero of 3x+4y=24
Answer:
jdjcnsixjkskzmdmdmxndm
please hurry I need this fast
Answer:
option #2
Step-by-step explanation:
solve this: F(x) = 1/x+6
Answer:
Step-by-step explanation:(F)=1/F+6
We move all terms to the left:
(F)-(1/F+6)=0
Domain of the equation: F+6)!=0
F∈R
We get rid of parentheses
F-1/F-6=0
We multiply all the terms by the denominator
F*F-6*F-1=0
We add all the numbers together, and all the variables
-6F+F*F-1=0
Wy multiply elements
F^2-6F-1=0
a = 1; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·1·(-1)
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
F1=−b−Δ√2aF2=−b+Δ√2a
The end solution:
Δ‾‾√=40‾‾‾√=4∗10‾‾‾‾‾‾√=4√∗10‾‾‾√=210‾‾‾√
F1=−b−Δ√2a=−(−6)−210√2∗1=6−210√2
F2=−b+Δ√2a=−(−6)+210√2∗1=6+210√2
A line has a slope of -3 and passes through the point (-3, 8). What is the equation of the line?
o y=-3x+6
o y--3x+8
o y=bx-
o y=8x-3
Answer:
y= -3x + 8
Step-by-step explanation:
In one day's work at the nursery, Dale and Mary together potted 74 plants. If Dale potted 48, how many did Mary pot?
Answer: 26
Step-by-step explanation: Assuming this a regular subtraction, 26
what is six less than the product six and eight
Answer:
six less than the product six and eight in numerical form= (6*8)-6
and 6*8-6=48-6=42
PLEASE HELP ASAP
Is the function y=x- 5/4 linear or nonlinear
Answer:
Linear
Step-by-step explanation:
y=x-5/4 is a linear equation.
