Suppose f ( x ) = 7 ( 2.5 ) x and g ( x ) = 52 ( 1.5 ) x . Solve f ( x ) = g ( x ) for x .
Answers
The value of x in when we equate the functions f(x) = g(x) is 0
FunctionsA function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
A function in mathematics is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input. A function is an equation for which any x that can be put into the equation will produce exactly one output such as y out of the equation. It is represented as; y = f(x)
Where x is an independent variable and y is a dependent variable.
In the question given;
f(x) = 7(2.5)xg(x) = 52(1.5)xf(x) = g(x)
7(2.5)x = 52(1.5)x
Solving for x
x = 0; This is because they both cancel each other out.
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Related Questions
Please answer quickly!
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Answer:
0/6 <--------------------------
write 100 in exponential notation
Answers
Answer:
10^2 AKA ten squared
Step-by-step explanation:
A number squared is that number times its self to 10 times 10 is 100
Answer:
\(1.00\) × \(10^{2}\)
I hope this helps!
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How does an object become electrically charged?
A) Though the transfer of charges from one object to another
B) Through the movement of heat from one object to another
C) Through the transfer of sound from one object to another
D) Through the movement of water from one object to another
Answers
A is the correct option:) Three ways electrons can be transferred are conduction, friction, and polarization. In each case, the total charge remains the same. This is the law of conservation of charge. Conduction occurs when there is direct contact between materials that differ in their ability to give up or accept electrons.
The volume of a cuboid is 450cm3.
The length is 10cm and the width is 15cm.
Work out the height of the cuboid.
Answers
Answer:
3cm
Step-by-step explanation:
The formula for the volume of the cuboid is \(w*l*h=volume\)
We already have the length, width, and volume, so we have to plug it in to the equation.
\(15*10*h=450\) (Just a heads up in case you didn't know: the centimeters cubed is just part of the units, so you don't need to worry about it when plugging it in to the equation.)
To solve for h:
1. Multiply 15 and 10
\(150*h=450\)
2. Divide both sides by 150
\(h = 450/150\)
h = 3
This is in centimeters, so the final answer is 3cm.
The height of a cuboid with a volume of 450cm³ with a length of 10cm and width of 15cm is 3cm.
How to calculate volume?The volume of a cuboid can be calculated using the following formula:
Volume = length × width × height
According to this question, the volume of a cuboid is 450cm³ and has a length of 10cm and the width is 15cm. The height is as follows:
450cm³ = 15cm × 10cm × h
450cm³ = 150²h
h = 450/150
h = 3
Therefore, the height of a cuboid with a volume of 450cm³ with a length of 10cm and width of 15cm is 3cm.
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The midpoint of segment AB is M(-2,2). If A is located at (-5,7) find the coordinates of the endpoint B
Answers
Answer:
B (1, -3)
Step-by-step explanation:
Step 1: Use the midpoint formula to find the coordinates of the endpoint:
Normally, we find the midpoint of a segment using the midpoint formula, which is given by:
M = (x1 + x2) / 2, (y1 + y2) / 2, where
M is the midpoint,(x1, y1) are one endpoint on the segment,and (x2, y2) are the other endpoint of the segment.Since we're solving for the coordinates of an endpoint, we can allow (-5, 7) to be our (x1, y1) point and plug in (-2, 2) for M to find (x2, y2), the coordinates of the endpoint B:
x-coordinate of B:
x-coordinate of midpoint = (x1 + x2) / 2
(-2 = (-5 + x2) / 2) * 2
(-4 = -5 + x2) + 5
1 = x2
Thus, the x-coordinate of the endpoint B is 1.
y-coordinate of B:
y-coordinate of midpoint = (y1 + y2) / 2
(2 = (7 + x2) / 2) * 2
(4 = 7 + x2) -7
-3 = y2
Thus, the y-coordinate of the endpoint B is -3.
Thus, the coordinates of the endpoint B are (1, -3).
A police officer invested $5,000 in a treasury bond paying 4.75% interest compounded quarterly. After 25 years, the value of the bond will be $16,280.08. If the police officer's investment was compounded continuously instead of four times per year, what would be the difference in the account balances after 25 years?
Answers
Answer:
114.29
Step-by-step explanation:
Count the average-case number of + operations performed by the following pseudocode segment. Assume that all possible data sets are equally likely. (Round your answer to two decimal places.) Preconditions: X = {X1, X2, X3, X4,X5} = {10, 20, 30, 40, 50, 60}, where x1 < x2 < X3 < X4 < X5. teo ir 1 while t < 101 do rtet + Xi Liri + 1
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Count the average-case number of + operations performed by the following pseudocode segment. The average-case number of + operations performed is 6.67.
The pseudocode segment is a while loop that runs from t=0 to t=101. For each iteration, it adds Xi to the value of the variable liri. Since the preconditions list X as a set of five integers (10, 20, 30, 40, 50, 60) in increasing order, the variable Xi will take on each of these values in turn. Thus, the loop will perform + operations six times (once for each value of Xi). The average-case number of + operations performed is 6.67 (6 operations in total divided by the number of iterations, i.e. 101).
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Answer plzzzzzzzzzzzzHere's a graph of a linear function. Write the equation that describes that function. Express it in slope-intercept form. Enter the correct answer.
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My teacher out the answer on the right but can you show me how he got the answer
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112 is the number with base 10
now we have to convert in base 3
firstly we divide the number by 3
so the answer is 10110
112 in base 3 will be equal to the 10110
elect all equations that represent the number of subscribers, , in terms of months since the beginning of the year (when she had 150 subscribers).
Answers
The Heflin household is laying down mulch around their garden. The following image depicts the shape and dimension of their garden and the area they want to place the mulch:
A triangular garden inside a rectangular mulch area. The garden has a base of 6 feet and a height of 5 feet, and the mulch area has a height of 9 feet and a base of 12 feet.
If the mulch costs $0.59 per square foot, determine the total cost.
Answers
Answer:
$54.87
Step-by-step explanation:
The area of the triangular garden is (1/2) x base x height = (1/2) x 6 x 5 = 15 square feet.
The area of the rectangular mulch area is base x height = 12 x 9 = 108 square feet.
The total area to be covered with mulch is 108 - 15 = 93 square feet.
The cost of the mulch is $0.59 per square foot, so the total cost is 93 x $0.59 = $54.87.
Therefore, the total cost of the mulch will be $54.87.
what is 2 4/5 divided by 7/8?
Answers
Answer: 3.2 or 16/5
Step-by-step explanation:
the mixed number would be 3 1/5
Solve for u.u + 8 = 16
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In this case the answer is very simple. .
We must apply algebraic rules to find the solution.
u + 8 = 16
u = 16 - 8
u = 8
The answer is:
u = 8
Why do you think people who are good at math are usually successful on their jobs?
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hope this helps!:)
The ratio of the corresponding linear measures of two similar cans of fruit is 4 to 7. The smaller can has a surface area of 220 square centimeters. Find the surface area of the larger can. Write your answer as a decimal or mixed number.
The surface area is
square centimeters.
Answers
The surface area of the larger can is approximately 674.375 square centimeters.
We have,
The ratio of the corresponding linear measures of two similar cans is 4 to 7.
The ratio of their surface areas will be the square of this ratio, which is (4/7)² = 16/49.
Let A be the surface area of the larger can.
(220 cm²) / A = 16/49
220 cm² x 49 = A x 16
10780 cm² = A x 16
A = 10780 cm² / 16
A = 674.375 cm²
Therefore,
The surface area of the larger can is approximately 674.375 square centimeters.
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two more than a number is less than 13
Answers
Answer:
x + 2 < 13
Step-by-step explanation:
hopefully this helps :)
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A plane leaves an airport at noon flying due south at 900 km/h. That same day, another plane is flying due east toward the
airport at 600 km/h.
If the incoming plane is 2000 km away from the airport at 4 pm, what is the rate of change of the distance between the planes?
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The rate of change of the Distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.
The rate of change of the distance between the planes, we need to determine how the distance between them changes over time.
the distance between the two planes is represented by the variable D, and time is represented by the variable t.
At noon, the southbound plane starts flying and continues for 4 hours until 4 pm. During this time, the plane covers a distance of 900 km/h * 4 hours = 3600 km due south.
Meanwhile, the eastbound plane is also traveling towards the airport. It starts from a distance of 2000 km away from the airport at 4 pm.
To find the distance between the planes at any given time, we can use the Pythagorean theorem, as the planes are moving at right angles to each other. The distance D between the planes can be calculated as:
D^2 = (2000 km)^2 + (3600 km)^2
Simplifying the equation:
D^2 = 4000000 km^2 + 12960000 km^2
D^2 = 16960000 km^2
Taking the square root of both sides:
D = sqrt(16960000) km
D = 4120 km
Now, we can find the rate of change of the distance between the planes by calculating the derivative of the distance equation with respect to time
dD/dt = 0
Since the distance between the planes is constant, the rate of change is zero.
Therefore, the rate of change of the distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.
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solve the system by elimination. need work to be shown
Answers
Answer:
x=1, y=1, z=0
Step-by-step explanation:
System of Equations
We are required to solve the system of equations by elimination:
\(\left\{\begin{matrix}-2x+2y+3z=0\qquad [1]\\-2x-y+z=-3 \qquad [2]\\2x+3y+3z=5 \qquad [3]\end{matrix}\right\)
Adding [1] and [3], and subtracting [1] and [2]:
\(\left\{\begin{matrix}5y+6z=5\qquad [4]\\3y+2z=3\qquad [5] \end{matrix}\right.\)
Multiplying [5] by -3 and adding to [4]:
\(-4y=-4\)
Solving:
\(y = -4 / (-4) = 1\)
\(y=1\)
Substituting into [5]:
\(5(1)+6z=5\)
Simplifying:
\(6z = 0\)
z=0
Substituting into [3]
\(2x+3(1)+3(0)=5\)
Operating:
\(2x+3=5\)
\(2x = 2\)
\(x = 2/2=1\)
x=1
The solution is
x=1, y=1, z=0
If f(x) = (x+1)^-1 and g(x) = x-2, what is the domain of f(x)/g(x)?
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Consider the probability that no more than 28 out of 304 students will not graduate on time. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.
a. Area to the right of 27.5
b. Area to the right of 28.5
c. Area to the left of 27.5
d. Area to the left of 28.5
e. Area between 27.5 and 28.5
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Solution :
Here the probability that exactly 28 out of 304 students will not graduate on time. That is
P (x = 28)
By using the normal approximation of binomial probability,
\($P(x=a) = P(a-1/2 \leq x \leq a+1/2)$\)
∴ \($P(x=28) = P(28-1/2 \leq x \leq 28+1/2)$\)
\($=P(27.5 \leq x \leq 28.5)$\)
That is the area between 27.5 and 28.5
Therefore, the correct option is (e). Area between 27.5 and 28.5
Corey is dropping off his dry cleaning. If Corey has 12 lbs of dark clothes and 4 lbs of whites, what is the ratio of pounds of dark clothes to pounds of white?
A. 3:1
B. 4:1
C. 6:2
D. 12:4
Answers
The ratio of pounds of dark clothes to pounds of white clothes is 3:1, which is option A
To find the ratio of pounds of dark clothes to pounds of white clothes, we need to divide the pounds of dark clothes by the pounds of white clothes.
Given that Corey has 12 lbs of dark clothes and 4 lbs of whites.
So, the ratio of pounds of dark clothes to pounds of white clothes = 12/4.
Simplifying this ratio, we get:
Ratio of pounds of dark clothes to pounds of white clothes = 3/1
Therefore, the ratio of pounds of dark clothes to pounds of white clothes is 3:1, which is option A.
This means that for every 3 pounds of dark clothes, Corey has 1 pound of white clothes. Ratios are a way to compare two quantities, and they can be expressed in different ways, such as in fraction or in the form of a colon. In this case, the ratio is 3:1, which means that for every 3 pounds of dark clothes, there is 1 pound of white clothes.
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I need the answer please
Answers
Answer:
\( \frac{x - 9}{2} = 5 \\ x - 9 = 5 \times 2 \\ x = 10 + 9 \\ x = 19\)
A zorb is a large inflated ball within a ball. The formula for the radius of a sphere with surface area A is given by \(r = \sqrt{} \frac{a}{4\pi} \)Calculate the radius of a standard zorb whose outside surface area is 21.24 sq m.
Answers
1.3 meters
Explanation
Step 1
\(\begin{gathered} \text{ } \\ \text{Area}=4\cdot\pi\cdot radius^2 \\ \text{isolate radius} \\ \frac{Area}{4\text{ }\pi}=radius^2 \\ \text{radius}=\sqrt[]{\frac{Area}{4\pi}} \end{gathered}\)Let
Area = 21.24 square meters
then, replace
\(\begin{gathered} \text{radius}=\sqrt[]{\frac{Area}{4\pi}} \\ \text{radius}=\sqrt[]{\frac{21.24}{4\pi}} \\ \text{radius}=\sqrt[]{1.69} \\ \text{radius}=1.3\text{ meters} \end{gathered}\)I hope this helps you
Calculate the APY for an account that pays 6% compounded daily.
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To calculate the APY (Annual Percentage Yield) for an account that pays 6% compounded daily, we can use the following formula:
APY = (1 + r/n)^n - 1
where r is the annual interest rate and n is the number of compounding periods per year.
In this case, r = 0.06 (6%) and n = 365 (since the interest is compounded daily). Therefore, we have:
APY = (1 + 0.06/365)^365 - 1
APY = 0.0618 or 6.18%
Therefore, the APY for an account that pays 6% compounded daily is 6.18%.
A baby is 70 days old. How many hours old is the baby?
Answers
Answer:
The answer to your question is 1680
Step-by-step explanation:
1 day is 24 hours
So to find the answer we will multiply 70 days by 24 hours which will give us 1680 hours.
I hope this helps and have a wonderful day!
Find the volume of the irregular figure. 3 cm 3 cm [?] cm 9 cm 7 cm 3 cm 3cm 12 c
No links for answers
![Find the volume of the irregular figure. 3 cm 3 cm [?] cm 9 cm 7 cm 3 cm 3cm 12 cNo links for answers](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/qs1dufOUXY9ZwfNnyCgRtVNDnThgq3eD.jpeg)
Answers
Answer:
\(144cm^{3}\)
Step-by-step explanation:
Hope this helps!
![Find the volume of the irregular figure. 3 cm 3 cm [?] cm 9 cm 7 cm 3 cm 3cm 12 cNo links for answers](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/E60e6Ig9uoyf5Pi2JD8DFnRSMvp1s8rb.png)
Could someone help me with this? Been stuck on it for a minute
Answers
Part a: Area of habitat - Area of field = Area of mowed portion.
Part b: Area of mowed portion: 4x(b - x)
Explain the term area of the square?The maximum number of unit squares forming a square is referred to as the square's area. In other terms, it is described as the area that the square occupies.For the stated question:
Part a:
The complete area is given as: Area of habitat.
The area kept for birds: Area of mowed portion
Central unmowed portion: area of field
Thus,
Area of habitat - Area of field = Area of mowed portion
Part b: Area of mowed portion: 4x(b - x)
Proof:
b² - (b - 2x)² = [b - (b - 2x)] [b + (b - 2x)]
= [b - b + 2x] [b + b - 2x]
= (2x)(2b - 2x)
= 4x(b - x)
Thus, the Area of mowed portion: 4x(b - x).
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The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
Select one:
a.
bus
b.
car
c.
subway
d.
train
Answers
Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.
How to Interpret a Box-and-whisker Plot?
In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.
The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.
Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.
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PLEASE HELP!!!!!! I WILL GIVE BRAINLIST!!!!!!!!!!!
The local elementary school is creating a new playground for the students. A basketball court will take up 1/4 of the playground. A soccer field will take up another 3/8 of the new playground. How much of the playground will remain for swings and other equipment?
A) 1/3 of the playground
B)3/8 of the playground
C)5/8 of the playground
D)2/3 of the playground
Answers
Answer:
The Answer is B
Step-by-step explanation:
1/4 = 2/8
2/8 + 3/8 = 5/8
8/8 - 5/8 = 3/8
Please help i need it
Answers
Answer:
Mei is correct because -9 is to the left of -3 on the number line.
Step-by-step explanation:
This is because -9 is LESS than -3, when you add or subtract using negative numbers, such as 7-9, you get -2. However when you subtract 7-13, you get -6. Because you subtracted a greater number from 7, your answer is -6 is LESS than -2. This is the same with inequalities, greater negative numbers will always be smaller and smaller negative numbers will always be greater.
Hope this helps!