Determine the Domain and Range of each graph, then decide if the graph is exponential growth or decay.
Answers
The required,
1. figure 1, domain and range are (0, ∞) and {25000, 0}, the graph shows the exponential decay.
2. figure 2, domain and range are (-∞, ∞) and {0, ∞}, the graph shows the exponential growth.
The function which is in format f(x) =aˣ where, a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
As mentioned in the question, the graph of two exponential functions are given, we have to determine the domain and range of both function and justify which graph shows the exponential growth and decay.
1.
A general exponential equation is given as,
y = aˣ
Graph 1, the graph shows the exponential decay because the value of the function is getting decreasing for the domain 0 to ∞. For this domain, the value of the function starts from point A which is at 25000 and ends at point B where y = 0, so the range is {25000, 0}.
Similarly,
Graph 2 shows exponential growth,
Domain and range are (-∞, ∞) and (0, ∞).
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Related Questions
Brian has 64 flowers for a big party decoration. In addition, he is considering buying flower arrangements that have 18 flowers each. All of the arrangements cost the same. Brian can buy up to 5 arrangements given the amount of money he has. Let x represents the number of flower arrangements Brian buys. Write a function rule to describe how many flowers Brian will have based on the number of arrangements he buys. Find a reasonable range for the function.
Answers
The function which can which can define the number of flowers in the arrangement is f(x) = 64 + 18x. The domain is found to be [ 0 , 5 ] and the range is [ 64 , 154 ].
Let the number of flowers which is to be calculated be x,
now we know that she already have 64 flowers and that each arrangement will have 18 flowers.
Therefore, the number of flowers can be given by the function , f(x) = 64 + 18x.
Now , we know that the maximum number of flowers which she can buy externally is 5 , which means the domain becomes [0,5] .
To find the range we will put the value of domain in the given function.
when x = 0 ,
f(0) = 64
when x = 5,
f(5) = 154
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A dumpster is shaped like a rectangular prism. It has a width of 8 feet, a height of 5 feet, and a volume of 880 cubic feet. What is the length of the dumpster
Answers
V=l•w•h, where V is volume, l is length, w is width, and h is height.
So, we can input the known values into the formula and solve for the unknown values since we already have the volume.
(880)=l•(8)•(5)
Simplify:
880=l•40
l•40 = 40l
880=40l
Solve for l:
Divide both sides by 40:
880/40=l
22=l
Apply the symmetric property:
l=22
Now, let’s plug the length back into the volume formula and check that it is correct:
880=(22)•8•5
880=880
So, our answer is correct.
Answer: the length is 22 feet.
Graph the solution to this inequality on the number line.
1/3x-3<-1 5/6
Help please asap
Answers
Turn left and continue past the finish line after starting at 3.5 on the number line. Simply plot x=3 1/2 on a number line.
what is inequality ?A relationship between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. Different inequalities are employed to contrast values of all sizes. By changing the two sides until only the variables are left, one can solve many straightforward inequalities. But a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.
given
the inequality for x 1/3 x - 3 -1 5/6 must first be resolved.
2 plus 3 on both sides
Simply multiply both sides of 1/3x by 3x31/2,
and then graph x31/2 on a number line.
Turn left and continue past the finish line after starting at 3.5 on the number line. Simply plot x=3 1/2 on a number line.
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solve the inequality and explain how
thank you :)
Answers
Answer:
the answer is A
[tex]x + 7 > 3[/tex]
1/4 gallon of paint costs $8. 99. What is the unit price of one gallon of paint?
Answers
The unit price of one gallon of paint is going to be $35.96.
We can use the unitary method to solve this problem. The unitary method is a technique used for solving a problem by first finding the value of a single unit, and finding the necessary value by multiplying the single unit value.
In this question, it is given that 1/4 gallon of paint costs $8.99 so for 1 gallon we will have to multiply both the paint amount and the money which buys it to 4 which will conclude that 1 gallon costs $8.99 × 4 is equal to $35.96. So, 1 gallon of paint will cost $35.96.
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Before taking his last test in a class, the arithmetic mean of Brian's test scores is 91. He has determined that if he scores 98 on his last test, the arithmetic mean of all his test scores will be exactly 92. How many tests, including the last test, does Brian take for this class
Answers
On solving the provided question, we can say that the mean that 6 tests including the last test brian took.
What is mean?A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate: Divide by how many digits there are after adding up all the digits. the total divided by the count.
(91n + 98) / (n + 1) = 92
91n + 98 = 92(n + 1)
91n + 98 = 92n + 92
98 = n + 92
6 = n
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How do you find the x-intercept and vertex of a quadratic function?
Answers
We can find the x-intercept by writing the equation in intercept form which is also known as factored form, y= (x-p) (x-q) where p, q are the x-intercepts.
To find the vertex of the quadratic function we can write the function in standard form , the vertex is located at the point where y=f (x).
A function which has a degree of two is known as a quadratic function.
Example, 3x² + 2 , here the maximum degree is 2 , hence the given function is quadratic. The general form of a quadratic equation is given as ,
f(x) = ax2 + bx + c .
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How do you find the sides of a 45 45 90 triangle when given the hypotenuse?
Answers
The value of the legs of the triangle would be hypotenuse/√2 and trignometric angle are 45 degree
You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).
That is perpendicular=hypotenuse/√2
Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)
That is base=hypotenuse/√2
Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.
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carman has saved 80% of the money she needs to buy a new video game. if she saved$36 how much does the video game cost
Answers
Carman buy the video game in the cost of $45.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
Carman has saved 80% of the money she needs to buy a new video game.
And, she saved the cost $36.
Let total cost of the video game = x
So, We can formulate;
⇒ 80% of x = $36
⇒ 80/100 × x = 36
⇒ 8x = 360
⇒ x = $45
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How are the quantities in the problem related? What steps are needed to solve the problem?
Answers
O(-, -28] is the formula for resolving the inequality +4 = 0. Inequality is the state of having a connection between two expressions or values that is not equal to them.
What is inequality?A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.
A disparity is presented to us.
[tex]y+4\leq 0[/tex]
The answer to the inequality must be discovered.
For each side of the inequality, deduct 4
y +4 - 4 ≤ 0 - 4
y ≤ -4
y ∈ ( - ∞ , - 4 ]
As a result, the solution set for the given inequality is provided by y (- , - 4].
O(-, -28] is the formula for resolving the inequality +4 = 0. Inequality is the state of having a connection between two expressions or values that is not equal to them.
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. The length of one line segment is 9cm and the length of a parallel line segment is 3cm. What scale factor would you need to use to map the first line segment onto the second line
semgment?
O 9/3=3
O 9x3=27
O 3/9=0.33
O 9/9=1
Answers
Scale factor required to map the first line segment onto second line segment is 3/9=0.33
What is scale factor?The scale factor is the ratio of the length of the image to the length of the pre-image.
In this case, we're looking for the that would map the first line segment (length 9cm) onto the second line segment (length 3cm).
To find the scale factor, we can divide the length of the image by the length of the pre-image:
scale factor = length of image / length of pre-image
In this case:
[tex]ScaleFactor=\frac{Length Of Image}{Length Of Pre-image}[/tex]
[tex]scale factor = 3cm / 9cm = 1/3=0.033[/tex]
So the scale factor to map the first line segment onto the second line segment is 1/3.
It means the 1st line is 3 times longer than the second one.
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What is the solution to this system of linear equations x − 3y − 2x 3y 16?
Answers
solution of the linear equation is x = (2a - 16)/ 3 and y = - (a+16)/ 9
What is linear equation?An algebraic expression that shows a relationship between two variables that have only first order term. One of the main criteria for linear equation is that we get a straight line when plot this equation in a coordinate system.
.
What is the solution of the system of linear equation?we are given, two linear equations x - a -3y = 0
and a - 2x -3y - 16 =0
from the first equation, x = a + 3y
we put the value of x in the second equation, a - 2(a +3y) - 3y -16= 0
a - 2a - 6y - 3y -16 = 0
- a - 9y -16 =0
- (a + 16) = 9y
y = - (a+16) / 9
now we put the value of y in the equation, x = a + 3y
get, x = a+ 3 [ - (a+16)] / 9
x = a + [ - (a+16)] / 3
x = (3a - a -16) / 3
x = (2a - 16)/ 3
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Jack spends a total of $16.50 on one bag of popcorn and three drinks.
Jill spends a total of $29.75 for two bags of popcorn and five drinks.
Write a system of equations. Determine and state the price of a bag of popcorn and the price of a drink, to the nearest cent.
Answers
Answer:
Sure! Here's a system of equations we can set up to represent this situation:
Let x be the price of a bag of popcorn and y be the price of a drink.
Then we can set up the following system of equations:
x + 3y = 16.50 (equation for Jack's purchases)
2x + 5y = 29.75 (equation for Jill's purchases)
To solve this system of equations, we can use the substitution method.
First, we can solve for x in equation 1:
x = 16.50 - 3y
Then, we can substitute this expression for x into equation 2:
2(16.50 - 3y) + 5y = 29.75
Simplifying this equation, we get:
33 - 6y + 5y = 29.75
Combining like terms, we get:
33 - y = 29.75
Subtracting 29.75 from both sides, we get:
33 - 29.75 - y = -y
Simplifying, we get:
3.25 - y = 0
Subtracting 3.25 from both sides, we get:
-y = -3.25
Dividing both sides by -1, we get:
y = 3.25
So, the price of a drink is $3.25.
Now we can substitute this value for y back into equation 1 to solve for x:
x + 3(3.25) = 16.50
Simplifying, we get:
x + 9.75 = 16.50
Subtracting 9.75 from both sides, we get:
x = 6.75
So, the price of a bag of popcorn is $6.75.
To the nearest cent, the price of a bag of popcorn is $6.75 and the price of a drink is $3.25.
Step-by-step explanation:
What are the 3 types of translations in math?
Answers
The perimeter of a rectangle is 84 cm. the length is 3 cm shorter than the width. find the length and width of the rectangle.
Answers
Taking into account the definition of a system of linear equations, the length and width of the rectangle is 22.5 cm and 19.5 cm respectively.
System of linear equationsSystems of linear equations are groupings of first degree equations with the same unknowns, of which a common solution must be found.
In the systems of equations, the values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.
Number of sodas and hot dogs soldIn this case, a system of linear equations must be proposed taking into account that:
"x" is the length of the rectangle."y" is the width of the rectangle.You know:
The perimeter of a rectangle is 84 cm. The perimeter of a flat geometric figure is called the length of its contour. It is obtained as a result of the sum of the sides of a flat geometric figureThe length is 3 cm shorter than the width.The system of equations to be solved is
2x + 2y= 84
x= y + 3
The substitution method is a way to solve systems of equations. To use the substitution method, you choose an equation and find an expression for one of the variables in terms of the other variable. Then substitute that expression for the variable in the other equation.
In this case, substituting the second equation in the first one you get:
2×(y+3) + 2y= 84
Solving:
2y+ 2×3 + 2y= 84
2y+ 6 + 2y= 84
2y + 2y= 84 - 6
4y= 78
y= 78÷4
y= 19.5
Replacing this value in the second equation, you get:
x= 19.5 + 3
x= 22.5
Finally, the length of the rectangle is 22.5 cm and the width of the rectangle is 19.5 cm.
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Given f(x) = −x² – 8x, find ƒ(−3)
Answers
Answer:
15
Step-by-step explanation:
To find f(-3), substitute x with (-3)
f(x) = -x² - 8x
f(-3) = - (-3)² - 8*(-3)
= - (9) + 24
= - 9 + 24
= 15
Answer:
15
Step-by-step explanation:
f ( x ) = - x² - 8x
Accordingly, to find the value of f ( -3 ) you have to replace x with ( - 3 ).
f ( -3 ) = - (-3)² - 8 × -3
f ( -3 ) = - 9 + 24
f ( -3 ) = 15
What is the sign of 4.3•(-3.2)•0?
Answers
Answer:
no sign (not positive or negative)
Step-by-step explanation:
The value of the expression
4.3 ⋅ (-3.2) ⋅ 0
is 0, as the value of any number multiplied by zero is 0.
The number zero is neither positive or negative; hence there is no sign.
what is 2/3(x+7)-18x+4/5 simplifyed
Answers
2x + 14
———- -18x+4/5
3
So you do the lcm of 3&5 = 15
The 4/5 dived 15 that is 5 divided by 15 is three that’s how we got three here the arrow is what I am showing you where the three is ^
5(2x+14-279x+3 (4
10x+70-270x+ 12
10 -270x + 70 + 12
= -260x+82 ( final answer)
The number of dragons of Westeros rose by a shocking 15% this year if there were 300 dragons this year how many are there this year
Answers
If the number of dragons in Westeros rose by a shocking 15% this year if there were 300 dragons in the previous year, then there will be a total of 345 dragons in this year.
The percentage increase in the number of dragons in Westeros rose = 15%
The total number of dragons in Westeros rose in previous year = 300
So, for calculating the total number of dragons in Westeros rose in this year we will first find the value of 15% of 300 and then add it to 300.
So, finding the value of 15% of 300
As we know, for removing the percentage sign we will divide the given number by 100
So, the value of 15% of 100 = (15/100)*300 = 45
So, the value of the total number of dragons in Westeros rose in this year will be 300+45 = 345
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The correct question may be like:
If the number of dragons in Westeros rose by a shocking 15% this year if there were 300 dragons in the previous year, then what will be a total of dragons in this year?
Given this unit circle, what is
the value of x?
(x,-√2)
X =
(1,0)
[?]
Enter
Answers
Answer:
x = - √2/2
Step-by-step explanation:
We know that x = rcosθ and y = rsinθ. The unit circle always have radius of 1 unit. Therefore, r = 1 as defined. Hence:
x = cosθ, y = sinθ
x = cosθ, θ = arcsin(y)
x = cos{arcsin(-√2/2)}
Find the measurement or θ that makes sinθ = -√2/2 and that is π + π/4 = 5π/4.
x = cos(5π/4)
And cos(5π/4) = - √2/2 as well. Hence, x = - √2/2.
Write the equation in standard form with integer coefficients. 0.5x - 2y - 0.75 = 0, y = - 3 x - 5
Answers
Answer:
50x - 200y = 75
3x + y = -5
Step-by-step explanation:
Standard form of a line
Ax + By = C
0.5x +-2y -0.75 Multiply through by 100
50x - 200 - 75 = 0 Add 75 to both sides
50x - 200y = 75
y = -3x - 5 Add 3x to both sides
3x + y = -5
Why is commutative property of addition important?
Answers
When adding multi-digit numbers, it's a good idea to employ the commutative property. However, counting up becomes simpler if pupils are aware that they can change the order of the addends and begin adding with the larger number FIRST.
What does the addition's commutative property mean?According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Here, a and b may be fractions, decimals, whole numbers, or even integers.
For instance, 1+2=2+1 and 2x3=3x2.
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what is 1/5 of 52 1/2
Answers
Answer: 10.5
Step-by-step explanation:
Answer:
Step-by-step explanation:
c
Input the correct values into the point-slope
formula.
y - [?] = [](x - [ ])
A. 3
A line is parallel to y = 3x - 2 and
intersects the point (3, 5).
C. -2
B. 5
D. 1/3
Answers
Answer:
B
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x - 2 ← is in slope- intercept form
with slope m = 3
• Parallel lines have equal slopes
then slope of parallel line is 3
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = 3 and (a, b ) = (3, 5 ) , then
y - 5 = 3(x - 3) ← equation of parallel line in point- slope form
PLEASE HELP!!! WILL MARK ANSWER BRAINLIEST!!!!!!! The manager of a hardware store took a random sample of 4.5 pounds of nails from a delivery of 350 pounds of nails. The manager found that 0.3 pounds of nails in the sample were defective. They were either bent, the heads were damaged, or they had been clipped too short during manufacture. How many pounds of defective nails should the manager expect the 350-pound delivery to contain? Round your answer to the nearest tenth of a pound.
Answers
The manager should expect the defective nails of 350-pound delivery to contain 23.3 pounds .
How to find defective rate?The defect rate is a measurement of the proportion of production units that are flawed or useless relative to a certain number of units. Businesses use this assessment to assess the quality of their products and how they affect their bottom line. Although lower rates are desired, no industry has a set acceptable fault rate. Therefore, businesses must choose their goal defect rate.
Defect rate is crucial because it enables firms to calculate the proportion of output units that fail quality checks. This assists the firms in identifying any issues with quality control or manufacturing and estimating the cost of each fault. To estimate the profitability of a product, businesses can also compare failure rates among comparable or dissimilar products.
In ever 4.5 pounds of nail defective nails are = 0.3 pounds
In ever 1 pounds of nail defective nails are = 0.3/4.5 pounds
In ever 350 pounds of nail defective nails are = (0.3/4.5)*350 pounds
⇒ the defective nails in 350 pounds of nails= 105/4.5
⇒ the defective nails in 350 pounds of nails= 23.3 pounds
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Which is not a polynomial a 4x2 2x 1 by 3 YC x3 1 D y2 5y 1?
Answers
2) y+ 3÷y is the equation that is not a polynomial. Using addition, subtraction, multiplication, and division of numbers .
what is polynomial ?Using just the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables, a polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients. Using addition, subtraction, multiplication, and division of numbers, a polynomial is an equation that combines variables, constants, and exponents (No division operation by a variable).
given
An algebraic mathematical equation known as a polynomial might have two components. coefficients and parameters
You can combine the solutions to these algebraic equations to achieve the result.
It follows the general formula as follows:
a + a1 + a+ …
2)y+ 3y is the equation that deviates from the formula above.
So, 2)y+ 3y is the equation that is not a polynomial.
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Elena made two batches of food to put in a bird feeder. She uses 1/8 cups of cracked corn, 3/4 cups of sunflower seeds, and 1/4 of dried cranberries for each batch. What is the best estimate of the total amount of bird food she made?
Answers
Elena made 2 batches of bird food, each with 1/8 cup cracked corn, 3/4 cups sunflower seeds, and 1/4 cup dried cranberries, for a total of 1.75 cups of bird food.
Elena made two batches of bird food using a combination of cracked corn, sunflower seeds, and dried cranberries. Each batch uses 1/8 cup of cracked corn, 3/4 cup of sunflower seeds, and 1/4 cup of dried cranberries.
To find the total amount of bird food she made, we need to add the ingredients of the two batches together.
Since she made two batches and each batch contains 1/8 cup of cracked corn + 3/4 cup of sunflower seeds + 1/4 of dried cranberries, the total amount of bird food is 2 × (1/8+3/4+1/4) = 2 × (7/8) = 7/4 = 1.75 cups.
This is the best estimate of the total amount of bird food made by Elena. It's important to note that this estimate is based on the assumption that the proportion of ingredients in each batch is the same, and that the ingredients are measured accurately.
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By some estimates, about 30% of all males have a particular defect related to their eyes. How would you assign random numbers to conduct a simulation based on this
statistic?
Answers
Answer:
related to their eyes. How would you assign random numbers to conduct a simulation based on this
-(4-7)
How do you do this?
I got -4+7
(Is that right)
Answers
-(4-7)
= -4+7
=3
The result of the operation is 3.
You are adding 7 to -4, so you would start with -4 and count up 7 steps which gives you 3 as a result.
In mathematical notation, the plus sign (+) indicates addition and the minus sign (-) indicate subtraction. In this case you have -4+7 so it's -4 plus 7.
What does the slope of a log-log graph represent?
Answers
The Slope of log - log graph represents the power of the relationship, and a straight line which indicates that there exists a definite power relationship .
What is Logarithm ?
The Logarithm is defined as power to which a number must be raised to get some other number .
A log-log plot is the plot in which both the x-axis and y-axis use a log scale.
The plot of logarithms of variables helps in extracting the information about the power relationship. The case of freely falling object is used to illustrate a log - log plot.
A plot of the logarithm of freefall distance as a function of logarithm of time gives a straight line of slope 2.
Therefore , The slope of log-log plot gives the power of relationship, and a straight line indicating that a definite power relationship exists.
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