keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{3} x + 3\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{3\implies\cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}[/tex]
so we're really looking for the equation of a line whose slope is -1/3 and that is passes through (3 , 2)
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{3}) \\\\\\ y-2=- \cfrac{1}{3}x+1\implies {\Large \begin{array}{llll} y=- \cfrac{1}{3}x+3 \end{array}}[/tex]
1. By what factor does organism A's population grow in the first five days? Express your answer as an exponential expression. (2 points)
2. The expression showing organism A's decrease in population over the next 3 days is
(
1
2
)
3
(
2
1
)
3
. This can be written as (2–1)3.
Write (2–1)3 with the same base but one exponent. (2 points)
3. By combining the increase and decrease, find an exponential expression for the total change in organism A's population after 8 days. Show your work. (2 points)
Using an exponential function, it is found that:
a) During the first five days, the population of organism A grew by a factor of 2^5.
b) During the next three days, the population of organism B decayed by a factor 2^(-3).
c) The expression for the total change is of 2².
What is an exponential function?An exponential function is modeled according to the following rule:
[tex]y = ab^x[/tex]
In which:
a is the initial value of the exponential function.b is the rate of change of the exponential function.For the first five days, the population doubles each day, hence the rate of change is of:
b = 2.
The growth factor will be of:
y = 2^5 = 32
During the next three days, the population cuts in half each day, hence the rate of change is of:
b = 0.5.
Then the decay factor is of:
y = (0.5)³ = (1/2)³ = 2^(-3).
Applying properties of exponents, over the entire period, the change in the population will be of:
2^5 x 2^(-3) = 2^(5 - 3) = 2².
As when we multiply two terms with the same base and different exponents, we keep the bases and add the exponents.
What is the missing information?The problem is given by the image at the end of the answer.
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A 3 lb (1.36 kg) bag of carrots cost $3.25, a 75 lb (ca. 34 kg) bag of carrots cost $4.75, which is the better deal?
Answer:
The second bag (4.75)
Step-by-step explanation:
Domain and Range, please help!!
Answer:
Step-by-step explanation:
Increasing
Domain: (-∞,∞)
Domain: -∞<x<∞
Range: (-∞,∞)
Range: -∞<y<∞
Which function's graph has a vertex at (3, 5) and contains the point (5, 13)?
The equation y = 2x² - 12x + 23 describes the function graph that includes a vertex at (3, 5) and passes through the point (5, 13).
What does a parabolic equation look like in vertex form?The vertex of a parabolic equation is at the point and the vertex form is y = a(x - h)2 + k, where a, h, and k are constants (h, k).
How do you answer this dilemma?Find the function whose graph has the vertex at (3, 5) and passes through the point in the question (5, 13).
Assuming it to be a parabolic function, we know that a parabolic equation's vertex form is y = a(x - h)2 + k, where a, h, and k are constants, and the vertex is located at the position (h, k).
As the vertex of the necessary function is at the position (3, 5), we may substitute h = 3 and k = 5 to obtain the following equation in the above equation:
y = a(x - 3)² + 5
Now that we know that the graph passes through the point (5, 13), we can change the original equation to read:
13 = a(5 - 3)² + 5,
or, 13 = 4a + 5,
or, 4a = 13 - 5 = 8,
or, a = 2.
We obtain the following from the equation y = a(x - h)2 + k by inserting a = 2, h = 3, and k = 5:
y = 2(x - 3)² + 5,
alternatively, y = 2(x² - 6x + 9) + 5,
alternatively, y = 2x² - 12x + 18 + 5,
Alternatively, y = 2x² - 12x + 23.
As a result, the function graph with the vertex at (3, 5) and the point of intersection (5, 13) yields the equation y = 2x² - 12x + 23.
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approximate √86 as a decimal to the tenths place.
Find the surface area of a cylinder with a height of 8 inches and base radius of 4 inches
The surface area of the cylinder is 118.76 square inches if the height is 8 inches and base radius is 4 inches.
What is a cylinder?A cylinder is defined as a solid geometric figure with straight parallel sides and a circular or oval cross section.
What is Surface Area ?Surface area is the amount of space covering the outside of a three-dimensional shape.
Surface area of the cylinder is calculated as : - 2πr² + 2πrh
We have:
Height of the cylinder h = 8 inches
The radius r = 4 inches
π = 3.14
Surface Area = 2(3.14)(4)² + 2(3.14)(4)(8)
surface Area = 2x 3.14 x 16 + 18.28
surface Area = 100.48 + 18.28
surface Area = 118.76 square inches
Therefore , the surface area of the cylinder is 118.76 square inches if the height is 8 inches and base radius is 4 inches.
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9. Solve
x(c- b) = g solve for x
For the given equation, on rearranging, the value of x becomes = x = g / (c-b)
What does the math term "rearranging" mean?
Rearranging parts is the act of rearranging counters, numbers, etc. to alter the way a number is shown visually; for instance, the number "4" could be shown in either of the two ways shown below.
A formula's components must be rearranged so that a different variable is the subject in order to change the formula's subject. Understanding inverse operations and how to solve equations is really helpful.
Given,
x(c- b) = g
On rearranging the equation,
x = g / (c-b)
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-2,-14) and (h,28) slope is 6
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-14})\qquad (\stackrel{x_2}{h}~,~\stackrel{y_2}{28}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{28}-\stackrel{y1}{(-14)}}}{\underset{run} {\underset{x_2}{h}-\underset{x_1}{(-2)}}} \implies \cfrac{28 +14}{h +2}~~ = ~~\text{\LARGE 6}\implies \cfrac{42}{h+2}=6 \\\\\\ 42=6h+12\implies 30=6h\implies \cfrac{30}{6}=h\implies \boxed{5=h}[/tex]
E
In the diagram, WY, and XZ are diameters of OT, and WY=XZ = 6.
If mXY = 140°, what is the length of YZ? Select all that apply.
47
A. 4
B. T
3
C. 3
D. 4T
E. 6
E
BD
B
W
N
The arc YZ represented in the diagram, its length is :
2π/3 or 4π/6
Explanation:A circle's arc can be formed by any two points on its circumference.
A circle's arc length (S) = r(θ), where r is the radius and theta is the central angle in radians.
Given WY = XZ = 6,
So YZ = TZ = 3radius
and m∠XY = 140°.
so, m∠YZ = 180° - 140°. (As a semicircle with a central angle of 180°.)
m∠YZ = 40°.
then, m∠YZ = (40/180)°×π rad.
m∠YZ = 2π/9 rad.
then, Arc length of YZ = = 3×(2π/9).
YZ = 6π/9.
YZ = 2π/3 or 4π/6
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For each sequence, decide whether it could be arithmetic or geometric or neither. 200, 40, 8
Answer:
geometric sequence
Step-by-step explanation:
an arithmetic sequence has a common difference d between consecutive terms.
40 - 200 = - 160
8 - 40 = - 32
no common difference thus not arithmetic
a geometric sequence has a common ratio r between consecutive terms
[tex]\frac{40}{200}[/tex] = [tex]\frac{4}{20}[/tex] = [tex]\frac{1}{5}[/tex]
[tex]\frac{8}{40}[/tex] = [tex]\frac{1}{5}[/tex]
thus there is a common ratio so sequence is geometric
y = x + 3
y = x^2 + 5x - 2
solve simultaneous equation
By solving the simultaneous equation value of x = -5, -2 and y = 1, 4.
How to solve simultaneous equation?
1. Use the elimination method to get rid of one of the variables.
2. Find the value of one variable.
3. Find the value of the remaining variables using substitution.
Given that,
y = [tex]x[/tex]+3
y = [tex]x^{2} +5x-2[/tex]
First both equation are equal
[tex]x+3 = x^{2} +5x-2\\x^{2} +4x-5 =0\\x^{2} +5x-x-5=0\\x(x+5)-1(x+5)=0\\x=1, -5[/tex]
Then, substitute the value of x in y =x+3
y = x+3
at x= -5
y= -2
at x= 1
y = 1+3
y = 4
Hence, By solving the simultaneous equation value of x = -5, -2 and y = 1, 4.
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Solve the equation below for x. 100 = 25e3 In4 O A. 4 B. 3 e O C. X=In4 - 3 c In100 3. In25 O D.
Dividing the given equation by 25 we get:
[tex]\begin{gathered} \frac{100}{25}=\frac{25e^{3x}}{25}, \\ 4=e^{3x}\text{.} \end{gathered}[/tex]Applying the natural logarithm to the above equation we get:
[tex]\ln (4)=\ln (e^{3x})=3x\ln (e)=3x\text{.}[/tex]Finally, solving for x we get:
[tex]x=\frac{\ln (4)}{3}\text{.}[/tex]Answer: Option A.
0.01p + 0.05(22 – p) = 0.54
Ari has a total of 22 coins consisting of pennies and nickels. The total value of the coins is $0.54.
How many of each type of coin does Ari have?
pennies and
nickels
The number of pennies that Ari has is 14.
The number of nickels that Ari has is 8.
How many of each type of coin does Ari have?The linear equations that represent this question are:
0.01p + 0.05n = $0.54 equation 1
p + n = 22 equation 2
Where:
p = number of pennies n = number of nickelsIn order to determine the number of nickels, multiply equation 2 by 0.01
0.01p + 0.01n = 0.22 equation 3
Subtract equation 3 from equation 1:
0.04n = 0.32
Divide both sides by 0.04
n = 0.32 / 0.04
n = 8
Substitute for n in equation 2:
8 + p = 22
p = 22 - 8
p = 14
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Question 1 of 10
The following graphs have no scales assigned to them. Which of them could
be density curves for a continuous random variable if they were provided with
the right scale?
Check all that apply.
B.
my
nh
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Graph A, and graph C could not possibly be density curves for a continuous random variable if they were provided with the right scale.
What is variable?A symbol (often a letter) used in algebra to represent an unknowable numerical value in an equation. Variables can have a wide range of values, which is why they are called variables. Thus, a variable can be thought of as a quantity that can take on different values depending on the circumstances of a given issue. As the program executes, we may store, modify, and access this data thanks to variables. All types of information can be stored in variables.
Four graphs of different nature as options.
We are required to find a graph that is not a continuous variable.
What is continuity?In mathematics, a continuous function is a function such that a continuous variation of the argument induces a continuous variation of the value of the function.
Continuous lines are those lines that when decreased, decrease with continuity and when increased, increase with continuity.
Given that,
When we observe graph A, graph C. In these graphs, the value of the function keeps increasing and decreasing a lot and is not in continuity.
Hence, graph A, and graph C could not possibly be density curves for a continuous random variable if they were provided with the right scale.
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30 POINTS!!!!
Please turn this into an EQUATION
One-half times the difference of twenty and a variable is two thirds
Here are the possible answers
Write a simplified equation in point-slope form.
Line 2: contains (1,2) and (4, -7)
Answer:
y = -3x + 5
Step-by-step explanation:
(1, 2) and (4, -7)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -7 - 2 -9
m = ------------- = ------------- = -------- = -3
x₂ - x₁ 4 - 1 3
y - y₁ = m(x - x₁)
y - 2 = -3(x - 1)
y - 2 = -3x + 3
+2 +2
----------------------
y = -3x + 5
I hope this helps!
HELP IM CONFUSED. NEED HELP ASAP
Answer:
Yeah good job! u got it right :)
Step-by-step explanation:
How to find perimeter?
Frist you will add up all the sides
then thats your answer :)
In this case the same logic applies
Hope this helps :3
You bike 11 1/4 miles from your house to a. State park. You travel 1/6 of that distance in the woods. You bike along the bank of a stream for the last 2/5 of the woods. On how many miles of your trip do you bike along the bank of the stream?
Answer:
9/10 mile
Step-by-step explanation:
Distance from house to state park = 11 1/4 miles = 45/4 miles
Distance through woods
[tex]\dfrac{1}{6}\cdot \dfrac{45}{4}\\\\=\dfrac{9}{4} \text { miles}\\[/tex]
Since the distance along the stream is 2/5 of the distance in the woods,
the distance biked along the stream
= 9/4 x 2/5 = 18/20 = 9/10 mile
Write as a percent
23 out of 100.
Answer:
%23
Step-by-step explanation:
23/100
Answer:
23%
Step-by-step explanation:
HELPPP WHICH NUMBER IS EQUIVALENT TO 4/5??!!
Answer:0.8
Step-by-step explanation:
80/100= 8/10= 4/5
Use the Distance Formula to write an equation of the parabola with vertex (0,0) and directrix y = -6
An equation of the parabola is y=
Answer:
x^2 + y^ = 36
Step-by-step explanation:
See attached worksheet.
if y = 10x^2, find the value of y when x = 3
evaluate the given expression for the given value of y
x-2
when x=4 =
when x=-7 =
Where x = 3, and the value of y = 90;
For the expression y = x -2, when x = 4, y = 2, when x = -2, y = -9
What is the computation for the above?Given:
y = 10x²................................1
Where x = 3, We make the required substitution
y = 10 x (3)²
y = 10 x 9
Hence,
y = 90
For the given expression:
Y = x -2.....................................2
Where x = 4, We make the required substitution
= 4 -2
hence,
y = 2
Where x = -7, We make the required substitution
y = 7
y = -7-2
Hence
y = -9
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Write an equation of the line in point-slope form that passes through the given points.
(4,-5) and (-4,-8)
Answer: y+5=3/8*(x-4)
Step-by-step explanation: Find the slope using m = y2-y1/x2-x2 which is the change of y over change of x, so the slope is m=3/8. Use the slope 3/8, and a given point (4, -5) to substitute for x1 and y1 in point slope form y -y1 = m(x-x1). So y-(-5)=3/8*(x-(4)). Now we simplify the equation so it's y+5=3/8*(x-4).
Kiley and her parents traveled to visit her grandmother. They drove 24.3 miles from their house to the airport in 12 hour. At the airport, they exited the car and walked for 34 hour to the waiting area by the gate to board their plane. Their walk covered 1.2 miles. From the waiting area, they walked another 0.1 mile to board the plane. The plane left the gate 45 minutes after they arrived at the waiting area. The plane flew 346 miles in 214 hours. After the plane landed, Kiley and her parents walked for 30 minutes, covering 1.1 miles, before they found a cab. It was a 15-minute cab ride to get to Kiley’s grandmother’s house, which was 12.3 miles away.Answer the following questions about Kiley’s trip. All questions are written in terms of an average rate. Assume that an average rate includes the time that Kiley is at rest (that is, not moving).In this task, you will write the ratio of miles to hours for each leg of Kiley’s trip. You will then, express the ratio as a decimal number. Next, you will find the unit rate in miles per hour (mph) for each leg of the trip. If your unit rate includes a repeating decimal number, you must indicate which digits repeat (for example, write 0.3¯when the 3 repeats.) A description of each leg is listed below in parts A through F.
Given:
The car ride from Kiley's house to the airport.
Distance =24.3 miles.
Time =1/2 hour.
We know that
[tex]\text{Average rate =}\frac{\text{Distance}}{\text{time}}[/tex]Substitute Distance =24.3 miles and time =1/2 hour to compute the average rate of the car ride from Kiley's house to the airport.
[tex]=\frac{24.3\text{ miles}}{\frac{1}{2}\text{hours}}[/tex][tex]\text{ Use }\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}\text{.}[/tex][tex]=24.3\times\frac{2}{1}\text{ miles per hour}[/tex][tex]=24.3\times2\text{ miles per hour}[/tex][tex]=48.6\text{ miles per hour}[/tex]Hence the average rate of the car ride from Kiley's house to the airport is 48.6 miles per hour.
2)
Given that they walked 3/4 hours to the waiting area and covered the distance of 1.2 miles.
Distance =1.2 miles.
Time =3/4 hours.
we know that
[tex]\text{Average rate =}\frac{\text{Distance}}{\text{time}}[/tex]Substitute distance =1.2 miles and time =3/4 hours to compute the average rate of the walk from the car to the waiting area by the gate, at the airport.
[tex]=\frac{1.2\text{ miles}}{\frac{3}{4}\text{ hours}}[/tex][tex]=1.2\times\frac{4}{3}\text{ miles per hour.}[/tex][tex]=\frac{1.2\times4}{3}\text{ miles per hour.}[/tex]Multiplying 1.2 and 4, we get 4.8
[tex]=\frac{4.8}{3}\text{ miles per hour.}[/tex]Dividing 4.8 by 3, we get 1.6
[tex]=1.6\text{ miles per hour.}[/tex]Hence at the airport, the average rate of the walk from the car to the waiting area by the gate is 1.6 miles per hour.
*PLEASE SOLVE!!!*
In late 1897, Amos Dolbear published an article called “The Cricket as a Thermometer." He had determined that the outside temperature (in Fahrenheit) shared a linear relationship with the number of times the snowy tree cricket would chirp per . If you count the number of cricket chirps per (while sitting inside your warm house), then you can find the temperature outside. In his research, Dolbear concluded that for every extra cricket chirp per second, the temperature was 1/4*F higher. Furthermore, he found that when the number of cricket chirps per minute was 120, the temperature outside was 70*F.
What are the quantities in this scenario?
What in the problem suggests or indicates that the relationship between the temperature and the number of chirps per minute should be linear?
If you graph the relationship, what will be the value of the slope of the graph?
What is the y-intercept?
Answer:
The equations is t = 1/4n + 40
The slope is 1/4 and the y-intercept is 40
t is the temperature.
n is the number of chirps per minute.
Step-by-step explanation:
(6z³ + 3z² - 4x + 8) - (4z²-3z + 2)
A. 6z-z²-z+6
B.
10z³ + 3z² - 4z + 10
C. 6z³-z² - 4z + 10
D. 10z³ +7z² - 4z+6
Which is equivalent
Answer:
6z³ -z² - z + 6
Step-by-step explanation:
By using the negative sign to open the bracket and collecting like terms, we have:
6z³ + 3z² - 4z + 8 - 4z² + 3z - 2 I'm guessing it suppose to be 4z and not 4x.
= 6z³ -z² - z + 6
Option A is correct.
How do I do this question?
Round 673,432 to the place of the underlined digit , enter the rounded number in the box. The thousands place =3 is underlined.
Answer: 673, 43
Step-by-step explanation:
As the next digit coming after the underlined digit is 2, the rounded number becomes 673,43. If instead of 2 we had 5 or above, the number should have become 673,44.
Pls help asap for math
write 600 as the product of prime factors
Give your answer in index form
The value of 600 as the product of prime factors will be 2³ × 3 × 5².
What's prime number?It should be noted that a prime number simply means the number that can be multiplied by itself and 1.
Therefore, it should be noted that 600 will be expressed thus:
600 = 2 × 2 × 2 × 3 × 5 × 5
600 = 2³ × 3 × 5².
Therefore, the value is 2³ × 3 × 5².
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Consider the function f(x) = 10(x2 â€"" 7x). what are the additive and multiplicative inverses? the additive inverse is g(x) = 10(x2 7x) and the multiplicative inverse is h(x) =startfraction 1 over 10 (x squared minus 7 x) endfraction. the additive inverse is g(x) = â€""10(x2 â€"" 7x) and the multiplicative inverse is h(x) =startfraction 1 over 10 (x squared minus 7 x) endfraction. the additive inverse is g(x) = 10(x2 7x) and the multiplicative inverse is h(x) =startfraction 1 over 10 endfraction (x squared minus 7 x) . the additive inverse is g(x) = â€""10(x2 â€"" 7x) and the multiplicative inverse is h(x) =startfraction 1 over 10 endfraction (x squared minus 7 x) .
The Additive inverse of f(x) is 70x – 10x² and the multiplicative inverse of f(x) is [tex](x^{2} -7x)[/tex] x [tex](1/10)[/tex]
We have, f(x) = 10(x² – 7x).The additive inverse of a number is a value that on adding to the given number gives zero.The multiplicative inverse of a number is a number when multiplied by a given number gives 1.According to the question,We have,f(x) = 10( x² – 7x)Assume that the additive inverse of f(x) is g(x).Thereforef(x) + g(x) = 010x² - 70x + g(x) = 0g(x) = 70x - 10x²and,Let’s assume that the multiplicative inverse of f(x) is h(x).Thereforef(x) x h(x) = 110(x² – 7x) x h(x) = 1h(x) = [tex](x^{2} -7x)[/tex] x [tex](1/10)[/tex]Hence, the additive inverse of f(x) is g(x) = 70x - 10x² and the multiplicative inverse of f(x) is h(x) = [tex](x^{2} -7x)[/tex] x [tex](1/10)[/tex]Solve more questions on Additive inverse and multiplicative inverse -https://brainly.com/question/17142610#SPJ4