The function y = 5x demonstrates exponential growth.
What do we exactly mean by Exponential Function?An exponential function is indicated when the input variable x appears as an exponent in the formula f(x) = ax.Both the exponential function and the value of x have an effect on the exponential curve.The exponential function is a fundamental mathematical function with the following formula:
f(x) = aˣ
Where a>0 and a does not equal to 1.x can be any genuine number.If the value of the variable is negative, the function for (-1<x<1) is undefined.Here,
The variable is "x".The base of the function, "a," is a constant.An exponential curve may increase or decrease depending on the exponential function.If a quantity regularly increases or decreases by a predetermined percentage, it should have either exponential growth or exponential decay.So,
Given function: y = 5x
If we put x = 1 as follows:
y = 5×1y = 5Then, if we put x = 2 as follows:
y = 5×2y = 10We see that 10 > 5.
So, when x increases, y also increases.Therefore, the function y = 5x demonstrates exponential growth.
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Find the inverse of each function. Is the inverse a function?
y=5 x+7
The inverse of the function y=5x+7 is y = (x-7)/5.
What exactly is an inverse variation?An inverse variation relationship is one in which one variable increases while the other decreases.When two numbers, say X and Y, are related in such a way that increasing X causes a decrease in Y and vice versa, this is known as indirect or inverse variation.So,
All we have to do to find the inverse of an equation is switch the variables x and y.
x = 5y + 7Now, solve for y as follows:
5y = x - 7y = (x-7)/5Therefore, the inverse of the function y=5x+7 is y = (x-7)/5.
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Write a variable expression to model real world situation.
A suit costs $65. Represent the cost of n suits.
Leah is deciding between two truck rental companies. Company A charges an initial fee of $60 for the rental plus $1.50 per mile driven. Company B charges an initial fee of $30 for the rental plus $2.50 per mile driven. Let AA represent the amount Company A would charge if Leah drives xx miles, and let BB represent the amount Company B would charge if Leah drives xx miles. Write an equation for each situation, in terms of x,x, and determine the number miles driven, x,x, that would make the cost of each company the same.
The number of miles driven that would make the cost of each company the same is 30 miles.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of miles.
For company A:
total cost = 1.5x + 60
For company B:
Total cost = 2.5x + 30
If each company charges the same amount of money:
1.5x + 60 = 2.5x + 30
x = 30 miles
The number of miles driven that would make the cost of each company the same is 30 miles.
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Melissa is making bookmarks from a piece of ribbon that is 12 inches long.Each bookmark is 4 inches long. She drew this picture to see how many bookmarks she could make from a ribbon. What did she do wrong?
Where Melissa went wrong was that she should have divided it into 3 pieces that were 4 in. long.
How to Solve Algebra Word Problems?
We are given;
Length of Ribbon = 12 inches
Length of each bookmark = 4 inches
Now, since she is making bookmarks from the 12 inches length of ribbon, from online sources it is seen that she divided into 4 parts of 4 inches each.
Thus, where Melissa went wrong was that she should have divided it into 3 pieces that were 4 in. long.
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ABCD is a trapezium.
AB = P
AD = q
DC: AB= 3:2
D
a
A
Р
B
C
a) Write vector DC in terms of p.
E
b) Work out vector BC in terms of p and q.
Give your answer in its simplest form.
Answer:
a) 2/3p
b) q + 1/2p
Step-by-step explanation:
In the right triangle shown, m\angle J = 60^\circm∠J=60
∘
m, angle, J, equals, 60, degrees and JL = 6\sqrt{3}JL=6
3
J, L, equals, 6, square root of, 3, end square root.
The length of JK = 3√3
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.
Given:
angle = 60
JL = 6√3
JK= x
Now, using trigonometry
cos [tex]\theta[/tex] = B/ H
cos 60 = x/ 6√3
1/2= x/ 6√3
x= 6√3/2
x= 3√3
Hence, the length of JK = 3√3
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9. Suppose the shipping company were packing balls with a diameter of
2 inches instead of cubes. Would the large box hold more balls or
fewer balls than boxes? Explain your answer.
Larger boxes may hold more or fewer balls than smaller ones. The answer to this question must be a sphere because they have the lowest volume value.
What exactly do you mean by volume?Volume is the quantity of three-dimensional space occupied by a liquid, solid, or gas.. Although there are many different units that can be used to indicate volume, the most common ones are liters, cubic meters, gallons, milliliters, teaspoons, and ounces.
According to the information provided,
One should calculate the volumes of the figures to find out if the larger box will carry more cubes or spheres, and the result that yields the smaller value must be the solution.
Volume of cube = (edge)³ = (2 in)³
= 8 in³
Volume of sphere = (4πr³)/3
where r is the radius and is equal to half of the length of the sides. Substituting,
Volume of sphere = (4π)(1 in)³ / 3 = 4.19 in³
Since spheres give the smaller value for volume, the answer to this item would have to be SPHERE.
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Please help me out please please please
Answer:
26s-45
Step-by-step explanation:
This is according to a app that tells you the answer to the problem and this is right the app is always right i use it all the time
25446 round to 1sf i need to know
For a science project, a student plants seeds of 2 different varieties of corn plants.
The table displays the heights, in inches, of each of the corn plants after 8 weeks.
variety A 46 46 47 48 49 49 50 6 48 49
variety B 48 46 45 47 46 48 49 47 48 48
The median height of the corn plants of variety A is 48 inches. Interpret the
value of the median in the situation.
value of the median in the situation = 49
Solution :
Median :
A Median is defined as the middle value in a given set of numbers or data. In Mathematics, there are three different measures, which are used to find the average value for a given set of numbers. They are mean, median, and mode. These three measures are called the measures of central tendency. The average value of the given data is given by mean. The middle value of the given data is defined by a median. The repeated value of the given data is defined by mode.
Mean :
The mean is estimated by dividing the sum of all the numbers by the count of the numbers.
Median Formula
Based on the definition, the formula to find the median of the dataset is given by:
If the given number of observations/data is odd, then the formula to calculate the median is:
Median = {(n+1)/2}th term
If the given number of observations is even, then the formula to find the median is given by:
Median = [(n/2)th term + {(n/2)+1}th term]/2
Where,
“n” is the number of observations.
Count of variety A = 10
Median = [(n/2)th term + {(n/2)+1}th term]/2
Median = [(10/2)th term + {(10/2)+1}th term]/2
Median = [5th term + {6th term}]/2
Median = [49 + 49]/2
Median = [98]/2
Median = 98/2 = 49
value of the median in the situation = 49
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I am F years old.My brother is B years older.
What is the sum of our ages?
What will be the sum of our ages in 3 years?
What was the difference of our ages 3 years ago?
Step-by-step explanation:
The sum of ypur ages is
=F+B
in three years your ages will both grow by 3
= (F+3)+(B+3)
For the difference of ages we know tha B is older than F
=B-F
Each pair of values is from an inverse variation. Find the missing value. (4,6),(x, 3)
The missing value of the inverse variation is 8
What is inverse variation ?The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity.
Let say if x and y are two values and k is a constant value, then
According to inverse variation
k = xy or y = k/x
In the given question,
Take the order pair (4,6)
As it is an inverse variation, we can substitute it
y=k/x
6=k/4
K=24
Now find the inverse variation equation
Y=k/x
Also, k=24
Solve this equation for the second pair (x,3)
As, y=24/x
x = 24/3 = 8
Therefore, missing value is 8
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GEOMETRY HONORS
Answer Options:
Valid: Law of Detachment
Valid: Law of Syllogism
No Valid Conclusions
All questions(17-21) must be answered, thank you all so muchhh
PLEASE ANSWER ASAP
16. Valid
Reason: congruency can be represented by the symbol ≅ hence the statement still reads <1 and <2 are congruent.
17. Invalid
Reason: A rectangle also has four right angles, It is only a square when all the sides are equal.
18. Valid
Reason: congruency can be represented by the symbol ≅ hence the statement still reads <JKM and <MKL are congruent.
19. Valid
Reason: The conclusion of the battery dying is in support with the premise given which is, leaving the light on when the car is off.
20.Valid
Reason: The conclusion, Dante obtained a part time job is in line with the premise that obtaining a pert time job, is a way to afford a car payment
21. Valid
Reason: The premise which has that selling 75% of the prom tickets will make the prom hold at country club is fulfilled, hence the prom will be held at the country club
What are valid arguments?An argument is valid when the premises or conditions of the argument are all true. When the conclusion supports the premises then conclusion is valid.
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The highest temperature ever recorded in chicago was 105F and the lowest was -27F use absolute values to find the difference between the highest and the lowest temperatures
ΔT= 313.5k-240.3k = 73.2k.
Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).
One unit increase in the Kelvin scale is the same as a one-degree increase in the Celsius scale. The only difference between these two scales is zero points of the thermometer.
ΔT= highest T° in k - lowest T° in k
40.5°c+273= 313.5k
-32.7°c+273= 240.3k
therefore the difference will be 73.2k
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help me with this !! please
Answer: do i remember how to do this... no
Step-by-step explanation:
While you are waiting for your tennis partner to show up, you drop your tennis ball from 5 feet. Its rebound was approximately 35 inches on the first bounce and 21.5 inches on the second. What exponential function would be a good model for the bouncing ball?
The exponential function that would be a good model for the bouncing ball is [ 60 * [tex]0.6^{x}[/tex]] .
Given : height = 5 feet
rebound on first bounce = 35 inches
rebound on second bounce = 21.5 inches
To find : exponential function that would be a good model for the bouncing ball
Calculation :
at x = 0
ht. = 5 feet = 60 inches
at x = 1
ht. = 35 inches
at x = 2
ht. = 21.5 inches
( 21. 5 / 35 ) * 100 = 60 % approx.
Since , the ht. rebounded is about 60% of the previous ht. rebounded , the exponential function that would be used would be of the form y = a * ( [tex]b^{x}[/tex] ) .
Therefore , the exponential function that would be a good model for the bouncing ball is [ 60 * [tex]0.6^{x}[/tex]] .
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Which of the following will result in a rational number? select all that apply. A, 1 sqare root of 4/ + 5/12 B. 1 square root of 9/7 + 7/15 C. square root of 2 - 5/7 D. square root of 2/7 ÷ 5/7
Answer:
A. & B.
Step-by-step explanation:
Square root of 4 is 2, and the square root of 9 is 3. These are rational, and adding fractions keeps them rational.
But the square root of 2 is irrational, and subtracting or dividing will not make them rational.
Hope this helps! :)
Solve. Check for extraneous solutions. 5-2 √x=3
No extraneous solution.
We have to find the extraneous solution to the equation:
5 - 2[tex]\sqrt{x}[/tex] = 3
Now we have to find the value of x.
2[tex]\sqrt{x}[/tex] = 2
[tex]\sqrt{x}[/tex] = 1
x = 1
Now we have to put the value of x in the equation
5 - 2[tex]\sqrt{1}[/tex] = 3
5 - 2 = 3
3 = 3
Therefore we get no extraneous solution to the equation. x = 1 is the solution of the equation.
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What is the actual number of kilometers that is represented by 4 centimeters on the map?
The actual distance that is represented by 4 centimeters on the map is 16 kilometers
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that the scale used on the map is:
1 cm = 4 km
Hence, for 4 cm represented on the map:
Actual distance = 4 cm * 4 km per 1 cm = 16 km
The actual distance that is represented by 4 centimeters on the map is 16 kilometers
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George jumps off a tire swing into a circular pond causing circles of waves. One of the waves travels at a rate of 16 ft/sec.
b. The area of the circle depends on the radius. Write an equation to represent this relationship.
The equation representing the relationship between the area of the circle and the radius is given by A = π ( r + 16 )².
Area of a circle is that the region lined or fence like inside its boundary. it's measured in square units.Any geometrical form has its own space. This space is that the region that occupies the form in an exceedingly two-dimensional plane.
We are given that:
Waves travels at a rate of 16 feet / second.
Now, let the radius of circle be r.
Now, we know that the area of a circle is given by:
A = π r²
Now, radius increases by 16 feet every second.
So, the equation of the area will become:
A = π ( r + 16 )²
Therefore, the equation representing the relationship between the area of the circle and the radius is given by A = π ( r + 16 )².
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evaluating functions f(4)+9
0. How many numbers of small boxes of dimensions 2cm x 2cm x 2cm are needed to fill a box of length 20cm, breadth 10cm and height 5cm. Find it.
Answer:
125 small boxes
Step-by-step explanation:
[tex]n = { \tt{ \frac{volume \: of \: big \: box}{volume \: of \: small \: boxes} }} \\ \\ { \tt{n = \frac{(20 \times 10 \times 5)}{(2 \times 2 \times 2)} }} \\ \\ { \tt{n = \frac{5 \times 5 \times 5}{1} }} \\ \\ { \tt{n = 5 {}^{3} }} \\ \\ { \tt{n = 125}}[/tex]
The first one-mile speed record was made by Henry Ford in 1904 when he drove the mile in 39.40 s (sec onds). This time was 33.62 s slower than the record achieved in 1970. What was the record time in 1970?
Answer:
The record time that was achieved in 1970 was 5.78 seconds.
Step-by-step explanation:
It is given that the first one-mile speed record was made by Henry Ford in 1904 when he drove the mile in 39.40 seconds.
It is further stated that this time was 33.62 s slower than the record achieved in 1970.
Now, let us consider the first statement;
Henry Ford covered one mile in time (1904) = 39.40 sec
Now, let us consider the second statement given;
Time taken by Henry Ford (1940) was slower than the time someone else achieved in one miles by = 33.62 sec
So, to calculate the time taken in 1970;
=> 39.40 - 33.62 sec
=> 5.78 sec
Therefore, the record time that was achieved in 1970 was 5.78 seconds.
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Find the greatest integer that is less than the value of the logarithm. Use your calculator to check your answers.
log 0.08
We need to know about logarithm to solve this problem. The greatest integer that is less than log 0.08 is -2.
Logarithm is the exponent which is raised to a base to get a certain number. There are a few rules of logarithm, log a + log b can be written as log ab, log a- log b can be written as log a/b, when the number for which the logarithm is calculated is raised to a power, then the power can be directly multiplied to the log itself. Logarithms when written as log has a base of 10 and the logarithm of a number same as its base is always 1, log of 1 is zero.
log 0.08= log 8/100= log 8- log 100 = [tex]log 2^{3} -log 10^{2}[/tex]
=3 log2 -2log10=3x0.30-2=0.9-2=-1.1
Therefore the greatest integer that is less than the value of log 0.08 is -2.
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137+6y=-y^2-x^2-24x in standard form
The standard form representation of the equation of a circle as given obviously in the task content is; (x + 12)² + (y + 3)² = 4².
What is the standard from representation of the equation of the circle as given in the task content?It follows from the task content that the standard form representation of the equation of the circle as given in the task content is to be determined.
The given equation is;
137+6y=-y²-x²-24x
By rearrangement, we have;
x² + 24x + y² + 6y + 137 = 0.
Therefore by the use of completing the square method; we have;
(x + 12)² - 144 + (y + 3)² - 9 + 137 = 0.
Hence, the correct standard form representation of the equation is;
(x + 12)² + (y + 3)² = 16
(x + 12)² + (y + 3)² = 4²
Ultimately, the standard form representation of the equation of a circle as given obviously in the task content is; (x + 12)² + (y + 3)² = 4².
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Rewrite (−4)2/7 in radical form.
Answer:
[tex](-4)\x^{\frac{2}{7} } =\sqrt[7]{(-4)^{2} }[/tex]
Step-by-step explanation:
Hope this helps
Dakota Shilah works for Arizona Bath Company as a repairman. He earns $12. 00 for each fiberglass bathroom sink and $59 for each fiberglass tub enclosure he repairs. Last week he repaired a total of 23 items. Dakota’s pay for the week was $652. How many of each type of repair did he make?
Solving a system of equations we can see that he repaired 15 of the fiberglass bathroom sinks and 8 of the fiberglass tub enclosures
How many of each type of repair did he make?Let's define the two variables:
x = number of fiberglass bathrooms repaired.
y = number of fiberglass tub enclosures repaired.
Then we can write the system of equations:
x + y = 23
x*$12 + y*$59 = $652
Isolating x on the first one, we get:
x = 23 - y
Replacing that in the other equation:
(23 - y)*$12 + y*$59 = $652
23*$12 + y*($59 - $12) = $652
23*$12 + y*$47 = $652
y = ($652 - 23*$12)/$47 = 8
Then:
x = 23 - y = 23 - 8 = 15
So, he repaired 15 of the fiberglass bathroom sinks and 8 of the fiberglass tub enclosures
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Based off of that photo I have to find out how many degrees P is. Pls help!!
Answer:
it is 104
Step-by-step explanation:
you have to complete 360 degrees for shape so
89-167=256 and 256-360=104
House prices increased 13% between 1994 and 1996. How much would a house be worth
in 1996, if it cost £134,500 in 1994?
About 2o of the population of the world lives in South America.
1
if about
35 of the population of the world lives in Brazil, what
fraction of the population of South America lives in Brazil?
Answer:
Step-by-step explanation:
I am assuming you mean 20% of the world's population lives in South America.
That is 1/5.
1 /35 of world's population live in Brazil so the fraction of Brazilians in South America
= 1/35 / 1/5
= 5/35
= 1/7