Final answer:
The function f(x) = 4(2)^(-x) - 3 approaches -3 as x approaches infinity and decreases without bound as x approaches negative infinity, with a horizontal asymptote at y = -3.
Explanation:
The end behavior of a function describes what happens to the function's values as x approaches infinity or negative infinity. For the function f(x) = 4(2)^(-x) - 3, as x approaches infinity, the term 2^(-x) approaches zero, because any non-zero base raised to the power of negative infinity is zero. Thus, the function approaches -3. Conversely, as x approaches negative infinity, the term 2^(-x) grows exponentially, and the function's values decrease without bound, heading towards negative infinity. However, since f(x) involves a negative exponential function, the graph ultimately will approach the horizontal asymptote y = -3.
In 1990, the rate of change of the world population was approximately 0.09125 billion per year (or approximately 1 million people every four days). The world population was estimated to be 5.3 billion in 1990.
Write an equation to model the population, P (in billions), in terms of t, where t is the number of years since 1990 (t = 0 corresponds to 1990)
A. P= 5.3 + 0.09125t
B. P= 5.3t + 0.09125
C. P= -5.3 + 0.09125t
D.P= -5.3t + 0.09125
Answer: Option A
[tex]P = 5.3 + 0.09125t[/tex]
Step-by-step explanation:
Note that for the initial year, 1990, the population was 5.3 billion.
The exchange rate is 0.09125 billion per year. In other words, each year there are 0.09125 billion more people.
In year 2 there will be 0.09125 * 2 billion people
In year 3 there will be 0.09125 * 3 billion people
In year 4 there will be 0.09125 * 4 billion people
In year t there will be 0.09125 * t billion of people
So the equation that models the number of people that there will be as a function of time is:
[tex]P = P_0 + rt[/tex]
Where [tex]P_0[/tex] is the initial population
[tex]P_0 = 5.3[/tex] billion
r is the rate of increase
[tex]r = 0.09125[/tex] billion per year
finally the equation is:
[tex]P = 5.3 + 0.09125t[/tex]
The correct answer is option A.
Cheryl is planning a garden that will be
8x7 feet. She wants it to be raised by 6 inches.
How many cubic feet of topsoil will she need
to add?
Hello There!
Great Question!
To calculate the area of a rectangular prism, you would multiply the length, the width, and the depth. As we want to measure this in cubic feet, we should convert all of the measurements to feet to begin with.
How wide is the garden? (either 7 or 8 feet)
How long is the garden? (Whichever of 7 or 8 wasn’t used)
How deep is this garden? 6 inches.
Well, that’s not feet, right?
How many inches are in a foot? 12.
Divide 6 by 12, what is the answer? .5.
Rob ran 27.2 miles less than Jasmine last week. Rob ran 10 miles. How many miles did Jasmine run?
Answer:
Jasmine ran last week 37.2 miles
Step-by-step explanation:
Let
x ----> number of miles Rob ran last week
y ----> number of miles Jasmine ran last week
we know that
x=y-27.2 ----> equation A
x=10 ----> equation B
Substitute equation B in equation A and solve for y
10=y-27.2
y=10+27.2
y=37.2 miles
If a+b = 11 and a−b = 7, then ab
Answer is..
ab= 18
Explanation..
a + b = 11...---> a= 11-b
a -b = 7
11 - b - b = 7
11 - 2b = 7
2b = 18
b = 9
and a = 11 - 7
a = 2
So
ab = 2 * 9 =18
-2x = 16–8y
x+4y= 25
Solve by substitution
Answer:
([tex]\frac{17}{2}[/tex], [tex]\frac{33}{8}[/tex]
Step-by-step explanation:
Given the 2 equations
- 2x = 16 - 8y → (1)
x + 4y = 25 → (2)
Rearrange (2) expressing x in terms of y by subtracting 4y from both sides
x = 25 - 4y → (3)
Substitute x = 25 - 4y into (1)
- 2 (25 - 4y) = 16 - 8y ← distribute left side
- 50 + 8y = 16 - 8y ( add 8y to both sides )
- 50 + 16y = 16 ( add 50 to both sides )
16y = 66 ( divide both sides by 16 )
y = [tex]\frac{66}{16}[/tex] = [tex]\frac{33}{8}[/tex]
Substitute this value into (3) for corresponding value of x
x = 25 - 4 × [tex]\frac{33}{8}[/tex] )
= [tex]\frac{50}{2}[/tex] - [tex]\frac{33}{2}[/tex] = [tex]\frac{17}{2}[/tex]
Solution is ( [tex]\frac{17}{2}[/tex], [tex]\frac{33}{8}[/tex] )
To solve the given system of equations using substitution, solve one equation for one variable and substitute that expression into the other equation. The solution to the system is x = 17 and y = 6.25.
Explanation:To solve the system of equations using substitution, we need to solve one equation for one variable and substitute that expression into the other equation. Let's solve the first equation for x:
-2x = 16 - 8y
Adding 2x to both sides, we get:
0 = 16 - 8y + 2x
Now, we solve the second equation for x:
x + 4y = 25
Substituting the expression for x into the second equation, we get:
16 - 8y + 2x + 4y = 25
Simplifying the equation:
-4y + 16 + 25 = -2x + 2(25)
Combine like terms:
41 - 4y = 50 - 2x
Now, let's isolate x:
-2x = 41 - 4y - 50
Simplifying the equation:
-2x = -4y - 9
Dividing by -2, we get:
x = 2y + 4.5
Now we have the expression for x, which we can substitute into either of the original equations to find the value of y. Let's substitute it into the first equation:
-2(2y + 4.5) = 16 - 8y
Simplifying the equation:
-4y - 9 = 16 - 8y
Adding 8y to both sides:
4y - 9 = 16
Adding 9 to both sides:
4y = 25
Dividing by 4, we get:
y = 6.25
Now that we have the value of y, we can substitute it into the expression for x:
x = 2(6.25) + 4.5
Simplifying the expression:
x = 12.5 + 4.5
Simplifying further:
x = 17
So, the solution to the system of equations is x = 17 and y = 6.25.
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Describe the journey graphs maths PLZZZZ help
One is going up and then going down and then going up and all the way up. You’re welcome
Please help me with these 2 questions thank you so much #17 and #18
#17: Domain: [−4,∞),{x|x≥−4}
Range: [−2,∞),{y|y≥−2}
#18 g(2)=4(2)+2
g(2)=10
f(10)=3(10)^2-2
f(10)=298
For this case we have:
Question 1:
We have the following functions:
[tex]f (x) = 2x-1\\g (x) = x ^ 2-2[/tex]
We must find (g_ {0} f) (x).
By definition of composition of fusions we have to:
[tex](g_ {0} f) (x) = g [f (x)]\\(g_ {0} f) (x) = g [2x-1]\\(g_ {0} f) (x) = (2x-1) ^ 2-2\\(g_ {0} f) (x) = 4x ^ 2-2 (2x) + 1-2\\(g_ {0} f) (x) = 4x ^ 2-4x-1[/tex]
Answer:
[tex](g_ {0} f) (x) = 4x ^ 2-4x-1[/tex]
Question 2:
For this case we have a function of the form[tex]y = f (x)[/tex], where: [tex]f (x) = \sqrt {x + 4} -2[/tex]
We must graph the given function.
By definition, the domain of the function will be given by the values for which the function is defined. The function is not defined when the root is negative, that is to say for values of "x" less than -4. Then, the domain is:
[-4, ∞)
For its part, the range is the set of values that correspond to the domain. When replacing the values from -4 to infinity we have the following range:
[-2, ∞)
Answer:
See attached image
Domain: [-4, ∞)
Range: [-2, ∞)
Question 3:
For this case we have the following functions:
[tex]f (x) = 3x ^ 2-2\\g (x) = 4x + 2[/tex]
We must find, (f + g) (x):
By definition, we have to:
[tex](f + g) (x) = f (x) + g (x)\\(f + g) (x) = 3x ^ 2-2 + (4x + 2)\\(f + g) (x) = 3x ^ 2-2 + 4x + 2\\(f + g) (x) = 3x ^ 2 + 4x[/tex]
Now, we must find [tex](f + g) (2):[/tex]
[tex](f + g) (2) = 3 (2) ^ 2 + 4 (2)\\(f + g) (2) = 3 (4) +4 (2)\\(f + g) (2) = 12 + 8\\(f + g) (2) = 20[/tex]
Answer:
[tex](f + g) (2) = 20[/tex]
NEED HELP!! 15 POINTS!!
The graphs of f(x) and g(x) are shown above:
What are the solutions to the equation f(x)=g(x)?
A) x=-1, 5.4
B) x=-3,4
C) x=-1,2
D) x=-10,12
Answer:
A
Step-by-step explanation:
Given the graphs of f(x) and g(x) then the solution to f(x) = g(x) are at the points of intersection of the 2 functions.
That is at the points with x- coordinates
x = - 1 and x ≈ 5.4 → A
The solutions to the equation f(x)=g(x) is x=-1, 5.4
WHAT IS FUNCTIONS?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Given
the graphs of f(x) and g(x) then the solution to f(x) = g(x) are at the points of intersection of the 2 functions.
That is at the points with x- coordinates
x = - 1 and x ≈ 5.4
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PLEASE HELP!!!! solve for x.
Answer: x=11.67
Step 1
Use the following equation to find x. We can use this equation because Triangle 1 (triangle within triangle ABC) and Triangle 2 (triangle ABC) are proportional and we can use the system of equations below to create and equation.
[tex]\frac{x}{9}=\frac{x+5}{12}[/tex]
Step 2
We can then use the equation below by cross multiplying the previous equation in step 1.
12x= 9x+35
Step 3
Then solve the equation to find x!
12x=9x+35
3x=35
x=11.67 (rounded to the nearest hundredth)
I got no clue how to do this.
Answer:
Step-by-step explanation:
Just to keep the computer happy by not having to figure out rounding answers that involve square roots and other problem numbers. I've chosen numbers that should work out evenly. And you should be able to draw the trapezoid.
Givens
H = 14
a = 23
b = 25
Area = 336
Formula
Area = (a + b)*h/2
Solution
Area = (23 + 25)*14/2
Area = 48 * 7
Area = 336
Note if a + b = 48 any values for a and b will work.
determine the missing number in the equation 13-2=12-?
For the equation to work, you have to have the same number on both sides of the equal sign
so to find ?, you can do:
13 - 2 = 12 - ? Simplify
11 = 12 - ? Subtract 12 on both sides
-1 = - ? Multiply -1 on both sides
1 = ?
To find the missing number in the equation 13-2=12-?, we subtract the known numbers on both sides of the equation.
Explanation:To find the missing number in the equation 13-2=12-?, we subtract the known numbers on both sides of the equation.
In the equation 13-2=12-x, we need to find the missing number x.
We can solve this equation by subtracting the known numbers on both sides.
Subtract 2 from 13 to get 11.Subtract x from 12 to get 12-x.Using the concept of simple mathematics, we found the subtraction of the given number.
So the missing number in the equation 13-2=12-x is 11.
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Which of the following expressions is equivalent to -6? 10 - (-4) 4 - 10 4 - (-10) -4 - (-10)
Answer
-4-(-10)
explain
-4+10=6
the dude above me is correct
Need Help!!!!!!!!!!!!!!!
Add by positive 3 for each of the numbers
-6+3=-3
-3+3=0
0+3= 3
3+3= 6
Answer is 6
ANSWER
The next term is 6.
EXPLANATION
The given arithmetic sequence is -6,-3,0,3,
There is a constant difference of 3.
That is,
-3--6=-3+6=3
This means that, we need to add 3 to the previous terms to get the subsequent terms.
To get the next term after 3, we add 3 to obtain 3+3=6
Therefore the next term of the sequence is 6.
How do u solve 2x less than or equal to 30
2x ≤ 30
You must isolate x. To do this divide 2 to both sides
2x/2 ≤ 30/2
x ≤ 15
x is less then or equal to 15
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer: x ≤ 15
Step-by-step explanation:
Because...
2x ≤ 30
[tex]\frac{2x}{2} \leq \frac{30}{2}[/tex]
so after dividing 30 by 2 you get 15.
* Therefor, the answer is x ≤ 15
* Hopefully this helps:) Mark me the brainliest:)!!!
How to do stem and leaf plot?
I found this, Hope this helps you.
A stem-and-leaf plot is a graphical representation of data that shows the distribution of values in a data set. It is created by writing the stem values in ascending order on the left side of the vertical line and the leaf values next to the corresponding stem value, in increasing order.
Explanation:A stem-and-leaf plot is a graphical representation of data that shows the distribution of values. It is especially useful when dealing with small to medium-sized data sets. Here are the steps to create a stem-and-leaf plot:
Write the stem values in ascending order on the left side of the vertical line.Write the leaf values next to the corresponding stem value, in increasing order.Label the plot with a title, a key, and any other necessary information.For example, if you have the following data set: 12, 15, 19, 22, 23, 28, the stem-and-leaf plot would look like this:
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How can you determine that a point lies on the perpendicular bisector of MA ¯ ¯ ¯ ¯ ¯ ¯ ¯ with endpoints M(−2, 4) and A(−6, −2)?
Answer:
You can find the perpendicular bisector of MA and then plug in the point.
Step-by-step explanation:
To find the perpendicular bisector of MA, you have to go through a 4 step process.
1. Find the midpoint of MA
2. Find the slope of MA
3. Find the perpendicular slope to the slope of MA.
4. Substitute in your midpoint into the equation and solve for the y-intercept.
Plug in your point into the equation and see if it works out.
You'll have to do the actual work yourself though!
The point which satisfy the equation of line having the slope -2/3 and point (-4,1), lies on the perpendicular bisector of MA.
What is a perpendicular bisector on a line?The perpendicular bisector on a line segment is the line which divides the line in two equal parts and intersect the line at 90 degrees.
The line segment MA has the end points as M(−2, 4) and A(−6, −2). The midpoint of this line segment is,
[tex]p=(\dfrac{-2+(-6)}{2},\dfrac{4+(-2)}{2})\\p=(\dfrac{-8}{2},\dfrac{2}{2})\\\\p=(-4,1)[/tex]
The slope of this line segment MA is,
[tex]m=\dfrac{-2-4}{-6-(-2)}\\m=\dfrac{-6}{-4}\\m=\dfrac{3}{2}[/tex]
The slope of MA is 3/2. Thus, the slope of a line segment which is perpendicular to this is -2/3.
Thus, the point which satisfy the equation of line having the slope -2/3 and point (-4,1), lies on the perpendicular bisector of MA.
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Which of the following elevations are deeper than -200 feet? Select all that apply.
-1,300 feet
sea level
300 feet
-250 feet
-400 feet
Answer:-250
Step-by-step explanation:
Angle rst is a right angle
90 degrees is a right angle
PLEASE HELP 15 POINTS
Step-by-step explanation:
The sample space is the list of possible combinations:
H1, H2, H3, H4, T1, T2, T3, T4
Combinations that include a 2 are:
H2, T2
Jerome is a co-owner of a small company and received 1/3 of the company’s profits this year. What were the company’s overall profits if Jerome made $150,000? Type an equation and solve..
Answer: $450,000
Step-by-step explanation:
Answer: $450,000
Step-by-step explanation:
We know that Jerome's earnings were from $150,000
And we know that this was 1/3 of the company's overall earnings.
Then let's call "x" to the company's general earnings
So a third multiplied by x must equal Jerome's earnings
[tex]\frac{1}{3}x=150,000[/tex]
Now we solve the equation for the variable x
[tex]x=150,000*3\\\\x= \$450,000[/tex]
Finally, the general earnings of the company were $450,000
Jack owns a small restaurant called Best Burgers. For one week, he collected sales data on the type of side order served with each type of burger purchased. Jack serves a half pound of french fries with every kind of burger. If Jack sells 180 regular hamburgers how many pounds of french fries will he serve? (round to nearest whole number)
A) 35 pounds
B) 36 pounds
C) 54 pounds
D) 72 pounds
Answer:
The answer is C) 54 pounds
Step-by-step explanation:
because im batman
Derek purchased a 2010 model sedan for $21,000. The dealership offered him a $149/month payment plan for 60 months, at the end of which the unpaid balance will be due. If the interest rate is 6%, find the balloon payment due at the end of 60 months.
Answer:
$17,930.12
Step-by-step explanation:
A suitable financial calculator can tell you the unpaid balance is $17,930.12 after 60 monthly payments of $149.
___
It seems likely the formulas and examples in your reference material will be helpful, too.
Answer: $17,930.12
Step-by-step explanation:
confirmed
–29 + 40Add or subtract.
Answer:
11
Step-by-step explanation:
We are given the following expression which we are to solve:
[tex] - 2 9 + 4 0 [/tex]
Since there are no brackets, multiplication or division signs so we will solve this from left to right starting from the negative sign.
Adding 40 to -29 or subtracting 29 from 40 is the same so we get:
[tex] - 2 9 + 4 0 = 1 1 [/tex]
What does w=11 plus negative 7
Answer:
w=4
Step-by-step explanation:
adding a negative is like subtracting so w=11-7
Answer:
w = 4
Step-by-step explanation:
w = 11 + (-7)
w = 11 - 7
w = 4
Solve.
What percent of 146 is 29.2?
% of 146 is 29.2.
Answer: 146 is 500% of 29.2
Step-by-step explanation:
100%/x%=29.2/146
(100/x)*x=(29.2/146)*x - we multiply both sides of the equation by x
100=0.2*x - we divide both sides of the equation by (0.2) to get x
100/0.2=x
500=x
x=500
now we have:
146 is 500% of 29.2
For this case we propose a rule of three:
146 ----------> 100%
29.2 ---------> x
Where the variable "x" is the percentage that represents 29.2 of 146.
[tex]x = \frac {29.2 * 100} {146}\\x = \frac {2920} {146}\\x = 20[/tex]
So, 29.2 is 20% of 146
Answer:
29.2 is 20% of 146
Complete the steps to find the difference
Answer:
3x² - 9x + 5
Step-by-step explanation:
Given
(5x² - 3x + 4) - (2x² + 6x - 1)
Distribute the first parenthesis by 1 and the second by - 1
= 5x² - 3x + 4 - 2x² - 6x + 1 ← collect like terms
= (5x² - 2x²) + (- 3x - 6x) + (4 + 1)
= 3x² - 9x + 5
You decide to throw a guacamole party at your house. You have a mixing bowl that is 12 inches in diameters if one Tostito scoop chip and hold 1.125 cubic inches, which of the following is closest to the maximum number of scoops the mixing bowl can hold.
A. 804 scoops
B. 201 scoops
C. 402 scoops
D. 18 scoops
Answer: d
Step-by-step explanation:
Write a quadratic function in the standard form who’s graph satisfies the given conditions
1. Passes through (-5,0), (1,0), and (4,0)
Answer:
This is frankly impossible.
Step-by-step explanation:
What you have given me are three x-intercepts. And it is impossible for a quadratic function to have more than two roots. However, if this was an cubic function, we could multiply (x+5)(x-1)(x-4) which results in the equation which simplifies into x^3 -21x + 20. However, this is a cubic function, not a quadratic function, so something must be wrong with this problem all together.
someone please help
h(17) = ?
i know for a fact it's not √17t
Answer:
[tex]h(17)=\sqrt{17\times17}=\boxed{17}[/tex]
Kayla scored 110 in the first game she bowled but she can’t remember her score from the second game. The average of the two scores is 116. Help Kayla figure out what her second score was
Answer:
122
Step-by-step explanation:
The average of her two scores is calculated by the sum of her two scores divided by 2.
[tex]\boxed{\text{Average}=\frac{\text{sum of data}}{\text{number of data sets}} }[/tex]
Total score= 116(2)
Total score= 232
Total score= score of 1st game +score of 2nd game
Substituting value of first score and total score:
110 +score of 2nd game= 232
Subtract 110 from both sides:
score of 2nd game
= 232 -110
= 122
Additional:
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