The relation between logarithmic function and exponential function is they both are inverse of each other.
As given in the question,
Relation between logarithmic function and exponential function is given by:
Logarithmic function is inverse of the exponential function.Logarithmic function is represented by x = logₐ⁰ y.Exponential function is represented by y = aˣ .We can replace 'a' by 'e'.In exponential function a⁵ × a⁷ = a⁵ ⁺ ⁷.In logarithmic function log ( 5 × 7 ) = log 5 + log 7.Therefore, relation between the logarithmic function and the exponential function is that both are inverse of each other.
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Write the following equation in slope-intercept form.
X=-y--y-3 vertical line, there is no y-intercept and the slope is undefined.
What is the correct solution?X+y= −3
(x + y) + (−y) = −3+ ( − y)
X+y-y=-3-y
X=-y-3
Using the slope formula, calculate the slope.
To find the y-intercept (b), use the slope and one of the points.
Once you have the values for m and b, you can enter them into the slope-intercept form of a line (y = mx + b) to derive the line’s equation.
No, so its slope can't be negative. What number is neither positive nor negative? Zero! This relationship always holds: a slope of zero means that the line is horizontal, and a horizontal line means you'll get a slope of zero.
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What are the solutions of quadratic inequality X² 3x 2 ≤ 0?
The solutions of this quadratic inequality are x ≤ -2 and x ≥ 1.
Step 1: Factor the quadratic expression on the left side of the inequality.
X² - 3x + 2 = 0
Step 2: Set the factors equal to zero and solve for x.
(x - 2)(x - 1) = 0
Step 3: Solve the individual equations.
x - 2 = 0
x - 1 = 0
Step 4: Set up the solutions in terms of x.
x ≤ -2
x ≥ 1
The quadratic inequality X² 3x 2 ≤ 0 can be solved by factoring the expression on the left side of the inequality. Setting the factors equal to zero and solving for x will give us the solutions for x. The solutions are x ≤ -2 and x ≥ 1, which can be read as 'x is less than or equal to -2' and 'x is greater than or equal to 1'. In other words, any value of x that is less than or equal to -2 or greater than or equal to 1 will satisfy the inequality.
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it takes an older pump 4 times as long to drain a certain pool as it does a newer pump. working together, it takes the two pumps 5 hours to drain the pool. how long will it take the newer pump to drain the pool working alone?
The newer pump will take 6.25 hours to drain the pool working alone
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
According to the data we can state:
x = time new pump to drain the pool alone
4x = time older pump
Together they drain the pool in 5 hours, therefore:
1/x + 1/4x = 1/5
Multiply everything by x:
1 + 1/4 = 1/5 x
(4+1)/4 = 1/5x
5/4 = 1/5x
5/4 * 5 = x
25/4 = x
x = 6.25 hours
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What is the average speed of the car if it covers 100 km in 2 hours?
The average speed of the car is 50 km/hour.
To find the average speed of a car, you can use the formula:
Speed = Distance / Time
In this case, the distance is 100 km and the time is 2 hours. So, to find the average speed of the car:
Speed = 100 km / 2 hours = 50 km/hour
So the average speed of the car is 50 km/hour.
In mathematics, distance refers to the measurement of the difference between two points in a space or a geometric figure. It can be represented by a numerical value, and is often used to determine the shortest path between two points. The most common distance formula used in Euclidean geometry is the distance between two points (x1, y1) and (x2, y2) is the square root of ((x2 - x1)^2 + (y2 - y1)^2). This is known as the Euclidean distance.
Therefore, the average speed of the car is 50 km/hour.
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Give a pair of alternate interior angles, a pair of corresponding angles, and a pair of alternate exterior angles.
A pair of alternate interior angles is - ∠3 and ∠5
A pair of corresponding angles is - ∠1 and ∠5
A pair of alternate exterior angles is - ∠1 and ∠7
What are parallel lines?
Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible.
Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.
When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles.
So, ∠3 and ∠5, and ∠4 and ∠6, are alternate interior angles.
According to the definition of corresponding angles, when two parallel lines are intersected by a transversal, the angles that are in the same relative position at each intersection are referred to as being corresponding angles to one another.
So, ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, and ∠4 and ∠8 are corresponding angles.
Alternate exterior angles are created when two or more lines are intersected by a transversal. These angles are formed on the outer side of the transversal on the different sides.
So, ∠1 and ∠7, ∠2 and ∠8 are alternate exterior angles.
Therefore, the alternate interior angles, corresponding angles and alternate exterior angles are ∠3 and ∠5, ∠1 and ∠5, and ∠1 and ∠7 respectively.
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If 23+37=60 does 23+37+9=60+97
Answer:
No, they not equal
Step-by-step explanation:
23+37+9=60+97
It not equal
69 ≠ 157
When multiplying two variables how is using the distributive property similar to using a table?
When multiplying a number by a sum, you can apply the distributive property of multiplication over addition. Say you want to multiply 3 by the sum of 10 plus 2, for instance: 3(10 + 2) =? This attribute allows you to add the integers and then multiply the result by three.
What exactly is the mathematical distributive property of multiplication?The distributive property of multiplication is used when multiplying each integer by the sum of two or more addends. The subtraction and addition of two or more numbers are both subject to the distributive property of multiplication.
What steps make up the distributive property?Boost the equation's size. Divide (multiply) the initial number in each set, the outer number in each set, the inner number in each set, and the last number in each set. Join similar phrases. If necessary, simplify the equation after solving it.
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1. Marcus graphed the function f(x) = 4(x - 1)³-3. His
partner, Natalia, graphed the function G(x)=1/4 squared 3√x+3+1
Which of the following is NOT a true statement about the
functions?
A. The functions f(x) and 9(x) are not inverse
functions because their graphs are not
reflected across the line y=x.
B. The functions f(x) and g(x) are not inverse
functions because their x- and y-values are not inversed.
C. The functions f(x) and g(x) are not inverse functions because their graphs do not intersect.
D. The functions f(x) and G(x) are not inverse functions because the composition of the
functions does not equal x.
The functions f(x) and 9(x) are not inverse functions because their graphs are not reflected across the line y=x. is not true.
How do you determine whether a graph lacks an inverse function?F does not have an inverse if any horizontal line crosses the graph of f more than once. F has an inverse if there are no horizontal lines that cross the graph of f more than once.The effects of the original function are effectively reversed by an inverse function. Inverse f(x) will state to remove 1 and then divide by 2 if f(x) states to multiply by 2 and then add 1. F(x) and its inverse function will be reflections over the line y = x if you wish to visualise this graphically.The functions f(x) and 9(x) are not inverse functions because their graphs are not reflected across the line y=x. is not true.To learn more about inverse functions refer to:
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help???? please need quick answer
Answer:
ang tanga mo naman para di malaman ang sagot
dragon selects three positive real numbers with sum 100, uniformly at random. he asks cat to copy them down, but cat gets lazy and rounds them all to the nearest tenth during transcription. find the probability the three new numbers still sum to 100.
The probability that the three new numbers still sum to 100 is 0.9.
The three positive real numbers that sum to 100 can be any combination of numbers that add up to 100. If we round them to the nearest tenth, we will lose some precision, and it is possible that the new numbers will not sum up to 100.
We can think of this problem in two steps: first, we pick any three positive real numbers that add up to 100, then we round them to the nearest tenth.
The total number of possible sets of three positive real numbers that add up to 100 is infinite, but we are only interested in the sets that will round to 100 after the transcription.
To find the probability of this happening, we can think of the rounding as a rounding error. There is a probability of 0.05 that the rounding error will make the sum greater than 100 and a probability of 0.05 that the rounding error will make the sum less than 100.
So the probability that the three new numbers still sum to 100 = 100-0.05-0.05 = 0.9
Therefore, the probability that the three new numbers still sum to 100 is 0.9.
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(pt. 2)
If angle M measures 45 degrees, m
The triangles are congruent if two pairs of comparable angles and a pair of sides that aren't included are both identical.
What is meant by congruent triangle?Angle measurements and side lengths are identical for congruent triangles. These are the criteria for triangle congruence: "Side-Side-Side" SAS (Side-Angle-Side)
If the five conditions for congruence are met, two triangles are congruent. These are right angle-hypotenuse-side (RAHS), side-side-side (SSS), angle-side-angle (ASA), angle-angle-side (AAS), and side-angle-side (SSS) (RHS).
Triangles are said to be congruent if two sets of corresponding angles and the pair of included sides are also so. The triangles are congruent if two pairs of comparable angles and a pair of sides that aren't included are both identical.
You would need at least one pair of comparable sides that are likewise congruent to demonstrate the congruence of two triangles with three congruent, corresponding angles. Then, you might demonstrate congruence using the ASA or AAS congruence theorems or rigid transformations.
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Absolutely value equation
-3|p|=12
27. a parallelogram has three of its vertices at (-1, 0), (2, 4) and (2, -4). what is the positive difference between the greatest possible perimeter and the least possible perimeter of the parallelogram?
The greatest possible perimeter 26 the least possible perimeter of the parallelogram 20
[ -1 + 2 , 0 + 4 ] - [ 2 , -4 ] = [ [ 1 , 4] - [2 , - 4 ] = ( -1, 8 )
The perimeter of this parallelogram =
2 [ sqrt [ (-1-2)^2 + (8-4)^2] + 8 ] =
2 [ sqrt [ 9 + 16 ] + 8 ] =
2 [ 5 + 8 ] =
26
Another possible point is
[ 2 + 2, 4 - 4] - [-1,0] = [ 4, 0] - [ -1,0] = (5,0)
The perimeter of this parallelogram =
2 [ sqrt [ (5-2)^2 + (0 - 4)^2] + sqrt [ (2- -1)^2 + (4 - 0)^2) ] ] =
2 [ sqrt (3^2 + 4*2) + sqrt (3^2 + 4^2) ] =
2 sqrt (25) + sqrt (25) ] =
2 [ 5 + 5 ] = 20
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How do you determine whether the given ordered pair XY is a solution of linear inequality in two variables?
To determine if an ordered pair (X,Y) is a solution to a linear inequality in two variables, substitute the values for X and Y into the inequality and check if the inequality holds true.
To determine whether an ordered pair (X,Y) is a solution of a linear inequality in two variables, we must first understand what a linear inequality is. A linear inequality is an equation with two variables (X and Y) that is either greater than or less than an expression. To determine if an ordered pair is a solution to a linear inequality, we must substitute the values for X and Y into the inequality and check if the inequality holds true. If the inequality is true, then the ordered pair is a solution. If the inequality is false, then the ordered pair is not a solution. For example, if we have an inequality of 2X + Y > 5 and the ordered pair (3,1), we can substitute the values for X and Y into the inequality (2(3) + 1 > 5). Since this inequality holds true, the ordered pair (3,1) is a solution
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Is it negative 1 or minus 1?
Both "negative 1" and "minus 1" refer to the same value, which is -1. They both indicate that a value is less than zero.
"Negative 1" and "minus 1" are ways to represent the value of -1 in mathematics. In general, a negative number is any number that is less than zero. For example, -1, -2, -3, etc. are all negative numbers.
When we use the word "minus" in front of a number, it indicates that we want to subtract that number from a given value. For example, if we say "5 minus 2," we mean 5 - 2 = 3. Similarly, when we say "minus 1," it means we want to subtract 1 from a given value.
So, "negative 1" and "minus 1" are both ways to indicate the value of -1, which is less than zero.
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A juice shop made 24 L. of lemonade and put 3/4 of it in a juice dispenser.
The rest of the lemonade was poured into bottles that hold 3/8 L. each. How
many bottles of lemonade did the shop fill?
18 bottles of lemonade did the shop fill
How to calculate liters?1,000 milliliters (mL) in 1 liter (L). So, to convert milliliters to liters, you would divide the number of milliliters by 1,000. 100 centiliters (cL) in 1 liter. So, to convert centiliters to liters, you would divide the number of centiliters by 100.To learn how to calculate round water tank capacity in liters, we should take three dimensions into consideration. Those three dimensions are length, breadth, and height. Let length be L, Breadth be B, and Height be H. Therefore, the total volume of tank in liters will be 240 x 28.31 = 6794.4 liter.A litre is a cubic decimetre, which is the volume of a cube 10 centimetres × 10 centimetres × 10 centimetres (1 L ≡ 1 dm3 ≡ 1000 cm3). Hence 1 L ≡ 0.001 m3 ≡ 1000 cm3; and 1 m3 (i.e. a cubic metre, which is the SI unit for volume) is exactly 1000 LTo learn more about liters refers to:
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a ladder is leaning against the side of a house so that the distance on the ground between the base of the ladder and the house is 7 feet. if the length of the ladder is 15 feet, then what is the angle at which the ladder is leaning?
The angle at which the ladder is leaning according to the base and length of the ladder is 62°.
The angle formed between ladder and house is right angled triangle. Thus, the trigonometric formula to be used for calculation is -
cos theta = base ÷ hypotenuse
Keeping the values in formula to find the value of theta which represents angle of leaning of ladder
cos theta = 7/15
Performing division on Right Hand Side of the equation to find the value of theta
cos theta = 0.47
theta = [tex] { \cos }^{ - 1} [/tex] 0.47
theta = 61.97
Thus, the angle is 61.97 or 62°.
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What is Factorise 3x+12
Answer:
3 (x + 4)
Step-by-step explanation:
3x = 3 × x
12 = 3 × 4
3x + 12
Take 3 common,
3 (x + 4)
Hence, factorised.
Hello help please thank you!
The value of the composite function are as follows:
(f - g)(x) = 2x² - x - 1
(f + g) = 2x² + x + 1
(f .g)(-2) = 2
How to solve composite functions?A composite function is a function that depends on another function. In other words, a composite function is a function that is within another function.
Therefore, let's solve the function as follows:
f(x) = 2x²
g(x) = x + 1
Therefore,
(f - g)(x) = f(x) - g(x) = 2x² - (x + 1) = 2x² - x - 1
(f + g) = f(x) + g(x) = 2x² + (x + 1) = 2x² + x + 1
(f .g)(-2) = f(g(-2))
g(-2) = -2 + 1 = -1
Hence,
(f .g)(-2) = 2(-1)² = 2
Therefore,
(f - g)(x) = 2x² - x - 1
(f + g) = 2x² + x + 1
(f .g)(-2) = 2
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I need help please!!!
Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.
How to evaluate the functions?The function f(x) = 6x - 3A) f (0)
Substituting the value of x = 0
f (0) = 6(0) -3
= 0 - 3
= -3
B) f (2)
Substituting the value of x =2
f (2) = 6(2) -3
= 12 - 3
= 9
C) f (-2)
Substituting the value of x = -2
f (2) = 6(-2) -3
= -12 - 3
= -15
D) f (1)
Substituting the value of x =1
f (1) = 6(1) -3
= 6 - 3
= 3
E ) f (-3)
Substituting the value of x =2
f (2) = 6(-3) -3
= -18 - 3
= -21
In mathematics, a function is an expression, rule, or law that establishes the relationship between two variables (the dependent variable). A polynomial function is exemplified by the formula for a circle's area.Because of how versatile they are—they can pretty much be used to approximate any connection involving real numbers—polynomial functions have been studied from the beginning of time. The largest power of the independent variable is how polynomial functions are identified.To learn more about functions, refer:
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the national fire incident reporting service stated that, among residential fires, 73% are in family homes, 20% are in apartments, and 7% are in other types of dwellings. if fourteen residential fires are independently reported on a single day, what is the probability that six are in family homes, four are in an apartment, and four are in another type of dwelling? (round your answer to four decimal places.)
A truck that can carry no more than 6900lb is being used to transport refrigerators and upright pianos. Each refrigerator weighs 300 lb and each piano weighs 525 lb. Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry. Will 12 refrigerators and 9 pianos overload the truck? Explain. Question content area bottom Part 1 Let x be the number of refrigerators in the truck and y be the number of pianos in the truck. Write an inequality to show how many refrigerators and how many pianos the truck could carry.
Answer: Hi
We can use the information given to set up the inequality:
Weight of refrigerators + weight of pianos <= 6900 (since the truck can carry no more than 6900 lb)
We can use the weight of each item to write the inequality in terms of x (number of refrigerators) and y (number of pianos):
300x + 525y <= 6900
To graph the inequality, we can use the x and y values as coordinates and plot them on a coordinate plane. The line representing the inequality would be a boundary line, with all the points that satisfy the inequality on one side of the line, and all the points that do not satisfy the inequality on the other side of the line.
To check if 12 refrigerators and 9 pianos will overload the truck, we can substitute these values into the inequality:
300(12) + 525(9) = 3900 + 4725 = 8625
Since 8625 is greater than 6900, which is the maximum weight the truck can carry, 12 refrigerators and 9 pianos would overload the truck.Step-by-step explanation:
To sum up, the inequality 300x + 525y <= 6900 represents the weight that the truck can carry. The points that satisfy the inequality (such as (4, 6) or (10, 3)) would represent a combination of refrigerators and pianos that the truck can carry, while the points that do not satisfy the inequality (such as (12, 9)) would represent a combination that overloads the truck.
9.081 divided by 18 pls help
Answer:
0.5045
Step-by-step explanation:
9.081 ÷ 18
a hotel offers a reward program based on the number of nights stayed. the function f(x) represents the number of free nights earned as a function of x, the number of nights stayed. f(x)
A customer earns 1 free night per 10 nights stayed.
A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.
f(x)=x/10
When we put x=10, we get f(1)=10/10=1
Here f(1) represents the number of free nights earned by the customer is 1 per 10 nights stayed.
When we put x=20, we get f(2)=20/10=2
Here f(2) represents the number of free nights earned by the customer is 2 per 20 nights stayed.
When we put x=30, we get f(3)=30/10=3
Here f(3) represents the number of free nights earned by the customer is 3 per 30 nights stayed.
When we put x=40, we get f(4)=40/10=4
Here f(4) represents the number of free nights earned by the customer is 4 per 40 nights stayed.
Then, the pattern permits you to conclude that a customer earns 1 free night for every 10 nights stayed.
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find and interpret the marginal frequences
What is the following quotient?
2-√8
----------
4+√12
thats the best way i could think to make a fraction lol sorry its messy :/
The quotient for the given expression [tex]\frac{2-\sqrt{8} }{4+\sqrt{12} }[/tex] is , 1/4
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
The expression, [tex]\frac{2-\sqrt{8} }{4+\sqrt{12} }[/tex]
⇒ [tex]\frac{2-\sqrt{8} }{4+\sqrt{12} }[/tex]
⇒ [tex]\frac{2-2\sqrt{2} }{4+2\sqrt{3} }[/tex]
by rationalization of of denominator
⇒ [tex]\frac{2-2\sqrt{2} }{16-12 } \frac{4-2\sqrt{3}}{}}[/tex]
⇒ [tex]\frac{2-\sqrt{3}-2\sqrt{2}+\sqrt{6} }{16-12 }[/tex]
⇒ [tex]\frac{2-\sqrt{3}-2\sqrt{2}+\sqrt{6} }{ 4 }[/tex]
Hence, the quotient is 1/4
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11f + 14g = 13
11f + 10g = 25
Answer:
f = 5
g = -3
Step-by-step explanation:
11f + 14g = 13 Q1
11f + 10g = 25 Q2
Q1 - Q2 =
4g = -12
g = -3
put it back in the equation
11f + 10g = 25
11f + 10 (-3) = 25
11f + -30 = 25
11f = 55
f = 5
Answer:
f = 5 , g = - 3
Step-by-step explanation:
11f + 14g = 13 → (1)
11f + 10g = 25 → (2)
subtract (2) from (1) term by term to eliminate f
(11f - 11f) + (14g - 10g) = 13 - 25
0 + 4g = - 12
4g = - 12 ( divide both sides by 4 )
g = - 3
substitute g = - 3 into either of the 2 equations and solve for f
substituting into (1)
11f + 14(- 3) = 13
11f - 42 = 13 ( add 42 to both sides )
11f = 55 ( divide both sides by 11 )
f = 5
solution is f = 5 , g = - 3
***WILL GIVE BRAINLIEST*** Determine whether each relation is a function. Find the domain and range.
A function is a relation in which each element of the domain is paired with exactly one element of the range.
Determine whether each relation is a function. Find the domain and range?
(-2,2) (0,0) (2,-2)
This is a function because it is a many to one relation(-2 map to 2,0 map to 0,2 map to -2
Domain( -2,0,2)
Range(-2,2)
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The absolute value inequality equation |2x – 1| > 3 will have what type of solution set? Question 6 options: A) Intersection B) Union C) All real numbers D) No solution
The absolute value of the inequality |2x -1| >3 will have a union type of solution set.
How do we solve the absolute value of an inequality equation?By using the absolute rule that states:
An inequality equation's absolute value can be solved.
If |u| > a, a > 0, then u < - a or u > awhere the "or" functionality symbolizes the union between the solution sets.
Given that:
|2x - 1| > 3
Applying the absolute rule, we have:
2x - 1 < - 3 or 2x - 1 > 3
2x < -4 or 2x > 4
x < -4/2 or x > 4/2
x< -1 or x > 2
This denotes the union of between the solution sets.
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a 12 cm cube is built from small cubes, each 2 cm on an edge. write a ratio that compares the edge lengths of the large and small cubes.
The ratio of the edge lengths of the large and small cubes is 6:1
The ratio that compares the edge lengths of the large and small cubes is the ratio of the length of the edge of the large cube to the length of the edge of the small cube.
The edge length of the large cube is 12 cm and the edge length of the small cube is 2 cm. To find the ratio, we divide the length of the large cube by the length of the small cube.
So the ratio of the edge length of the large cube to the small cube is:
12cm/2cm = 6
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