Answers
Since the value of the function is decreasing exponentially as x decreases ,
The function is of the form [tex] y=ae^{bx}+c,b>0 [/tex].
Since the curve passes through (0,6),
[tex] 6=ae^{0}+c,6=a+c [/tex],
Since the curve passes through (-1,0),
[tex] 0=ae^{-b}+c [/tex].
Since [tex] y=-3 [/tex] is a horizontal asymptote,
[tex] -3=ae^{-\infty}+c,c=-3 [/tex]
From the above 3 equations,
[tex] c=-3,a=9,9e^{-b}=3,e^b=3,b=\ln 3 [/tex].
Therefore, the required function is
[tex] y=9e^{\ln 3 x}-3\\
y=9*3^{ x}-3 [/tex].
It can be verified that the curve [tex] y=9*3^{ x}-3 [/tex] passes through [tex] (-2,-2) [/tex].
Related Questions
Find the area of the following rectangle in square feet. 44 ft 2 11 ft 2 14.7 ft 2 132 ft 2
Answers
we know that
area of rectangle=base*height
in this problem
base is 22 ft
height is 2 yd
convert yd to ft
1 yd is equal to 3 ft
2 yd--------> 2*3-----> 6 ft
area of rectangle=22*6-----> 132 ft²
the answer is
132 ft²
Answer:
132
Step-by-step explanation:
Mind helping someone out?
I've kinda been stuck on this problem and it's my last math problem for the day.
Answers
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
y >-x + 4
y <= 2(x - 1)^2 - 18
Comment
Let's establish what we are talking about. The question says purple and to me purple means the shaded area above the blue and to the upper right of the parabola.
Not so. It is the wine colored area right above the parabola according to the direction of he inequalities.
Second thing: the question is trying to see if you can read all he information you need from a graph.
Step One
Find the equation of the line.
We can read 2 points right away the x and y intercepts.
(4,0) is the x intercept
(0,4) is the y intercept
The general equation for the slope intercept equation is
y = mx + b So when x = 0 then b = y
4 = m*0 + b
b = 4
This far we have
y = mx + 4
when x = 4, y = 0
0 = m*4 + 4 Subtract 4 from both sides.
-4 = m*4 Divide by 4
-4/4 = m
m = - 1
Complete equation is y = -1x + 4
The inequality is y > -x + 4 Top answer block.
Step Two
Find the equation for the parabola
You could just read the minimum point which is (1,-18) There is a catch. (Isn't there always?) This may have a constant in front of the (x - a)^2 term. We'll check that out in the next step.
y = (x - 1)^2 - 18 is the basic vertex solution
Step Three
Find the value of a in
y = a(x - 1)^2 - 18
You have to do this because the answer has a space before the brackets. We need another point. The y intercept might work.
y = a(0 -1)^2 - 18
Use the point (0,-16)
-16 = a(1) - 18
-16 = a - 18 Add 18 to both sides.
2 = a
So the equation of the quadratic is
y <= 2(x - 1)^2 - 18 <<<<<< answer second section down on your question sheet.
what is the surface area of this triangular pyramid
Answers
Equilateral Triangle Height = side * square root (3) / 2 =
12 * 0.8660254038 = 10.3923048454
Triangle Area = 12 * 10.3923048454 * .5
= 62.3538290724
Pyramid Area = 62.3538290724 * 4 sides =
249.4153162896
What is the remainder when the positive integer n is divided by 12 ? (1) when n is divided by 6, the remainder is 1. (2) when n is divided by 12, the remainder is greater than 5?
Answers
The number n would be 31. In this case you could divide it by 6 and get 5 with a 1 remainder and then divide it by 12 and get 2 with a 7 remainder.
What is sin (51)?
Answer Choices : 1.23 , 0.63 , 0.51 , 0.78
Answers
Make sure your calculator is in degrre mode when doing these.
so the answer is 0.78
using his telescope, Tommy watches a bald eagle as it sits on the top of a cliff. the telescope is positioned so that the line of sight to the eagle forms a 38 degree angle of elevation. the telescope sits 1.3 m above the ground and the base of the telescope is 116 m away from the base of the cliff. to the nearest tenth of a meter, how high above the ground is the eagle?
Answers
There are five red marbles eight blue marbles and 12 Green marbles in a bag. What is the theoretical probability of randomly drawing a red marble and then a green marble
Answers
A rectangle has a length of 4 feet and a perimeter of 14 feet. what is the perimeter of a similar rectangle with a width of 9 feet?
a. 36 ft
b. 108 ft
c. 42 ft
d. 126 ft
Answers
Second Rectangle: P= ?, L= ?, W= 9
STEP 1:
solve for the width in the first rectangle using perimeter formula
Perimeter= 2L + 2W
14= 2(4) + 2W
14= 8 + 2W
subtract 8 from both sides
6= 2W
divide both sides by 2
3= W
STEP 2:
Since the two rectangles are similar, they may be different sizes, but they have corresponding angles. We can set up a ratio to compare width and length.
First Rectangle: P= 14, L= 4, W= 3
Second Rectangle: L= ?, W= 9
length/width= length/width
4/3= L/9
cross multiply
4 * 9= 3 * L
36= 3L
divide both sides by 3
12= L
STEP 3:
find perimeter of second rectangle; use length from step 2
Perimeter= 2L + 2W
=2(12) + 2(9)
=24 + 18
=42 feet
ANSWER: (C) 42 feet
Hope this helps! :)
Twenty different statistics students are randomly selected. for each of them, their body temperature ( degrees °c) is measured and their head circumference (cm) is measured. if it is found that r=0, does that indicate that there is no association between these two variables?
Answers
The letter r represents the sample correlation coefficient .The Pearson product-moment correlation coefficient, also known as r, R, or Pearson's r, is a measure of the strength and direction of the linear relationship between two variables that is defined as the covariance of the variables divided by the product of their standard deviations.
The sample correlation coefficient value r is 0 given,so there is no linear relationship between the 2 variables that is the body temperature and head circumference.
Write the expression 5x+4x^2(2x+7)-6x^2-9x as a polynomial in standard form
Answers
5x + 8x³ + 28x² - 6x² - 9x
8x³ + 22x² - 4x
This can be simplified to:
2x(4x² + 11x - 2)
I don't know which of those answers you are looking for.
Answer:
8x^3 + 22x^2 - 4x
Step-by-step explanation:
5x+4x^2(2x+7)-6x^2-9x
Open the bracket
5x + 8x^3 + 28x^2 - 6x^2 - 9x
= 8x^3 + 28x^2 - 6x^2 - 9x + 5x
= 8x^3 + 22x^2 - 4x
In standard form, the polynomial 5x+4x^2(2x+7)-6x^2-9x is 8x^3 + 22x^2 - 4x
Please help me I’m about to cry
Answers
A-Blue
B-Green
C=yellow
D=Grey
E=maroon
Triangle E is not the same as triangle C. This means she was wrong.
Please refer to the attached figure for the drawings, the colors represent the triangles in the order above.
Daniel’s tennis team made $582.85 from running the concession stand at a basketball game. The food and drinks cost the team $64. What expression would model the amount of money each player would receive if the money is divided equally?
Answers
The answer would be
1. (582.85 - 64)/p Or D
And
2. 64.85 Or A
The expression that would model the amount of money each player would receive if the money is divided equally is y = (518.85/x).
What is division?
Division is a operation in mathematics which is used to divide a specific number into equal parts of specific magnitude.
Given is Daniel’s tennis team which made $582.85 from running the concession stand at a basketball game. The food and drinks cost the team $64.
Assume that there are [x] players in the team.
Now, the money left after spending on food = 582.85 - 64 = 518.85
Each player, when divided equally, would receive = y = (518.85/x)
Therefore, the expression that would model the amount of money each player would receive if the money is divided equally is y = (518.85/x).
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multiply and simplify. 5x^2 / y^3 * 4y^2 / 10x
Answers
[tex] \frac{5x^2}{y^3} * \frac{4y^2}{10x} [/tex]
Rewriting the expression we have:
[tex]\frac{20x^2y^2}{10xy^3} [/tex]
Then, simplifying and by properties of exponents we have:
[tex]{2x^{2-1}y^{2-3}} {2xy^{-1}}[/tex]
Rewriting we have::
[tex] \frac{2x}{y} [/tex]
Answer:
The simplified expression is given by:
[tex] \frac{2x}{y} [/tex]
What is the area of the figure to the nearest tenth?
Answers
Area of the full circle = π (6)² = 36π
Area of the sector = 165/360 x 36π = 51.8 in²
Answer: 51.8 in²
3.14 x 36 = 113.04 square inches
the shape is 165 degrees of a full circle which is 360 degrees
so area of the shape would be 165/360 x 113.04
= 51.8 square inches
I WILL MARK BRAINLIEST TO A CORRECT AND EXPLAINED ANSWER!!!!
Look at points C and D on the graph:
What is the distance (in units) between points C and D? Round your answer to the nearest hundredth.
A. 4.54 units
B. 5.00 units
C. 5.83 units
D. 34.00 units
Answers
D(1:0)
Image the right triangle between C, D and the point A(-4,0)
CA is 3-0=3; AD is 1-(-4)=1+4=5
CD is √3²+5²=√34=5.8309...
Answer:
Option C.
Step-by-step explanation:
Coordinates of the points C and D are (-4, 3) and (1, 0)
We have to find the distance CD.
Distance CD = [tex]\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]
CD = [tex]\sqrt{(1+4)^{2}+(0-3)^{2}}[/tex]
= [tex]\sqrt{25+9}[/tex]
= [tex]\sqrt{34}[/tex]
= 5.83 units
Therefore, Option C. distance CD = 5.83 units is the answer.
Given v=(6,3) and w=(1,-2), what is the result of v-w
Answers
I don't believe you need the word "result" here. At first I thought you'd meant "resultant." Here you're finding the "difference" v less w.
The result of v - w is (5, 5).
Explanation:To find the result of v - w, we need to subtract the corresponding components of the two vectors. Given v = (6, 3) and w = (1, -2), we subtract their x-components and their y-components separately.
v - w = (6 - 1, 3 - (-2))
Therefore, v - w = (5, 5).
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What is 3 to the 100th power?
Answers
3 to the 100th power is a very large number with over 47 digits, symbolizing the potential of exponential growth.
Explanation:The question is asking for the computation of the number 3 raised to the 100th power. In mathematics, exponents are used in expressions such as 'a to the power of n', written as an. Here, 'a' is the base and 'n' is the exponent, indicating how many times 'a' is multiplied by itself.
In our case, we have '3' as the base and '100' as the exponent. However, calculating 3100 directly is quite impractical due to the vast result it produces. However, we do know that it's a very large (over 47 digits!) number which could be useful for illustrating the power of exponential growth in mathematical or scientific contexts.
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The population of a town is 20,000 and is decreasing at a rate of 5% per year. What is the population after 23 years?
Answers
A feed bucket holds 12 quarts. How many cups of feed does the bucket hold?
Answers
12 quarts x 4 (cups per quart) = 48 Cups
Use complete sentences to explain how the coordinate plane is a useful tool for geometric proofs.
Answers
Coordinate geometry proofs employ the use of formulas such as the Slope Formula, the Midpoint Formula and the Distance Formula, as well as postulates, theorems and definitions.
The method usually involves assigning variables to the coordinates of one or more points, and then using these variables in the midpoint or distance formulas .
The facilitate verification is a proof of a geometric hypothesis which utilizes "summed up" indicates on the Cartesian Plane make a contention.
The strategy for the most part includes doling out factors to the directions of at least one focuses, and afterward utilizing these factors in the midpoint or separation equations .
For instance, the accompanying is an arrange evidence of the Triangle Midsegment Theorem , which expresses that the fragment interfacing the midpoints of two sides of a triangle is parallel to the third side and precisely a large portion of the length.
The coordinate plane is an essential tool in geometry, allowing for a visual representation of shapes and aiding in geometric proofs, such as the Pythagorean Theorem. It allows abstract geometric concepts to be more concrete and easier to understand.
Explanation:The coordinate plane is a pivotal instrument in the field of Mathematics for conducting geometric proofs. The coordinate plane enables us to visually represent geometric shapes and articulate the different points, distances, and areas which helps us in proving geometric theorems and statements.
For instance, the Pythagorean Theorem, a fundamental theorem in Geometry can be illustrated efficiently and proven right on the coordinate plane. By placing a right-angled triangle on the coordinate plane, the lengths of the sides can be calculated using the coordinates of the vertices. Then, by applying the theorem, we can demonstrate that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Overall, the coordinate plane provides a graphical representation of the geometric shapes, making the abstract ideas more concrete and easier to understand, thus aiding in geometric proofs.
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Share 450 in the ratio of 4:5
Answers
4n + 5n = 450
9n = 450
n = 50
Now we multiply into the ratio:
200:250
Or
200 and 250
450 : 9 = 50
4 · 50 = 200
5 · 50 = 250
Answer: 200 and 250.
Maria works at a bookstore. On Wednesday, she sold three times as many books as she did on Tuesday. On Thursday, she sold 8 fewer books than she did on Wednesday. During the three days, Maria sold 20 books. Create an equation that can be used to find m, the number of books Maria sold on Tuesday.
Answers
Tuesday - m
Wednesday - 3m
Thursday - 3m - 8
Show all of these in an addition problem with a total of 20 and simplify.
m + 3m + (3m - 8) = 20
7m - 8 = 20; You can solve this equation to find the number of books Maria read.
Helllllppppp MEEEEEEE
Answers
To find the distance the player runs, we have to use pythagorean formula, which is
[tex] a^2 + b^2 = c^2 [/tex]
In the question , value of a is 64 meters and value of b is 100 meters .
Substituting the values of a and b , we will get'
[tex] 64^2 +100^2=c^2
\\
c^2 = 14096
\\
c = 119meters [/tex]
Find the inverse function of h(x) = - 2/3x + 6.
h -1(x) = -3/2x + 9
h -1(x) = -3/2x - 6
h -1(x) = -2/3x + 9
h -1(x) = -2/3x - 6
Answers
A group of 12 people attend a meeting. Every pair of people shook hands with each other. How many handshakes were there?
Answers
So there will be 11+10+9+8+7+6+5+4+3+2+1=66 handshakes.
Hope this helped!
Bob can type 2 letters in 4 hours while Bill can do it in 6. How many hours would it take them, working together, to type six letters?
Answers
r1 = 2/4 = 1/2 letter / hour
The production rate of Bill is given by:
r2 = 2/6 = 1/3 letter / hour
Thus, the production rate of both is:
r1 + r2 = 1/2 + 1/3 = 5/6 letter / hour
Then, the production of 6 letters is given by:
rate * time = letters
(5/6) t = 6
t = (6/5) 6
t = 36/5 = 7 1/5 hours = 7hr 12 min
Answer:
it would take them, working together, to type six letters about:
7hr 12 min
Answer:
It would take them 7.2 hours.
Which set of ordered pairs could be generated by an exponential function?
(0, 0), (1, 1), (2, 8), (3, 27)
(0, 1), (1, 2), (2, 5), (3, 10)
(0, 0), (1, 3), (2, 6), (3, 9)
(0, 1), (1, 3), (2, 9), (3, 27)
Answers
For this case we must find the set of ordered pairs that form an exponential function.
When observing, the last set of ordered pairs is an exponential function of the form:
[tex]y = 3 ^ x[/tex]
For x = 0:
[tex]y = 3 ^ 0 = 1[/tex]
We have the ordered pair:
[tex](x, y): (0, 1)[/tex]
For x = 1:
[tex]y = 3 ^ 1 = 3[/tex]
We have the ordered pair:
[tex](x, y): (1, 3)[/tex]
For x = 2:
[tex]y = 3 ^ 2 = 9[/tex]
We have the ordered pair:
[tex](x, y): (2, 9)[/tex]
For x = 3:
[tex]y = 3 ^ 3 = 27[/tex]
We have the ordered pair:
[tex](x, y): (3, 27)[/tex]
Answer:
The set of ordered pairs that form an exponential function is:
[tex](0, 1), (1, 3), (2, 9), (3, 27)[/tex]
Answer:
D
Step-by-step explanation:
If 7 is subtracted from the product of 3 and a number, the result is 5 more than the number.
Answers
suzie divided a 3-pound bag of apples into 2 equal piles. How many lbs of apples are in each pile
Answers
3 pounds divided by 2 piles = 1.5 pounds per pile
Suzie's 3-pound bag of apples divided into two equal piles will result in each pile weighing 1.5 pounds. This is a basic arithmetic problem often referred to as equal distribution.
Explanation:Suzie is dividing a 3-pound bag of apples into two equal piles. This is a simple division problem where the total weight of apples (3 pounds) is distributed equally into two piles. Therefore, we simply divide the total weight by the number of piles.
To calculate the weight of apples in each pile, we divide the total weight (which is 3 lbs) by the number of piles (which is 2). So, 3 lbs ÷ 2 = 1.5 lbs. Each pile would weigh 1.5 lbs.
This type of problem is often referred to as an equal distribution problem in mathematics. It falls under the category of basic arithmetic and is typically taught in lower grades.
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