The graph of f(x) is shown below.
If f(x) and its inverse function, f¹(x), are both plotted on the same coordinate plane, where is their point of intersection?
A. (0,6)
B. (1,4)
C. (2,2)
D(3,0)
Answers
The intersection would be at the point (2, 2).
This is because, graphically, the plots of f(x) and its inverse are reflections of one another across the line y = x, and (2, 2) lies on this line.
Put another way, we have f(2) = 2 = f⁻¹(2), so both f(x) and f⁻¹(x) intersect when x = 2.
Put yet another (longer) way, we can find the equation for f(x): it's a line that passes through (0, 6) and (3, 0), so it has slope -6/3 = -2. Then using the point-slope formula,
y - 6 = -2 (x - 0) ⇒ y = f(x) = -2x + 6
By definition of function inverse, we have
f(f⁻¹(x)) = x
so that with the given definition of f(x), we get
f(f⁻¹(x)) = -2 f⁻¹(x) + 6 = x
-2 f⁻¹(x) = x - 6
f⁻¹(x) = -x/2 + 3
Then we solve for x such that f(x) = f⁻¹(x). We would find x = 2 as before.
Related Questions
how to find the turning point of a polynomial function?
Answers
the turning point(s) of a polynomial function by using below steps
To find the turning point of a polynomial function, follow these steps:
1. Determine the degree of the polynomial. The turning point will occur in a polynomial of odd degree (1, 3, 5, etc.) or at most one turning point in a polynomial of even degree (2, 4, 6, etc.).
2. Write the polynomial function in the form f(x) = axⁿ + bxⁿ⁻¹ + ... + cx + d, where n represents the degree of the polynomial and a, b, c, d, etc., are coefficients.
3. Find the derivative of the polynomial function, f'(x), by differentiating each term of the function with respect to x. This will give you a new function that represents the slope of the original polynomial function at any given point.
4. Set f'(x) equal to zero and solve for x to find the x-coordinate(s) of the turning point(s). These are the values where the slope of the polynomial function is zero, indicating a potential turning point.
5. Substitute the x-coordinate(s) obtained in step 4 into the original polynomial function, f(x), to find the corresponding y-coordinate(s) of the turning point(s).
6. The turning point(s) of the polynomial function is given by the coordinates (x, y), where x is the x-coordinate(s) found in step 4 and y is the y-coordinate(s) found in step 5.
By following these steps, you can find the turning point(s) of a polynomial function.
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The blood test for determining coagulation activity defects is called the Prothrombin Time (PT) test.
The blood test for determining coagulation activity defects is called the Prothrombin Time (PT) test. This test measures the time it takes for blood to clot and is used to assess the functioning of the clotting factors in the blood. It is commonly used to evaluate the extrinsic pathway of the coagulation cascade, which involves factors outside of the blood vessels.
The PT test is an important diagnostic tool in hematology and is used to diagnose or monitor conditions that affect blood clotting, such as bleeding disorders or the effectiveness of anticoagulant medications. By measuring the PT, healthcare professionals can determine if there are any abnormalities in the coagulation process and make appropriate treatment decisions.
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William purchase a new car the total price for he will pay for the car including interest in 17,880 if he splits his car payment over 60 months how much will he pay each month
Answers
Answer:
The Amount amount he pays each month is 298
Step-by-step explanation:
Given:
Total amount of new car (including interest) = 17,880
Payment is splited over 60 months i.e time = 60 months
Required:
How much will be paid each month
To find the amount to be paid each month use the formula:
Monthly payment = Total amount / time
\( = \frac{17880}{60} = 298 \)
Therefore, the amount William pays each month is 298
List all the factors of 45 from least to greatest. Enter your answer below using a comma to separate each number
Answers
Answer:
So, the factors of 45 are 1, 3, 5, 9, 15, and 45.
Step-by-step explanation:
Edward buys 6 yards of fabric for $15. How much money does it cost per
yard?
Answers
Answer:
$2.5
Step-by-step explanation:
15 divided by 6 because its asking to split into groups equally
Answer:2.5
Step-by-step explanation:
(1 point) the epa wants to test a randomly selected sample of n water specimens and estimate the mean daily rate of pollution produced by a mining operation. if the epa wants a 90% confidence interval with a bound of error of 0.5 milligram per liter (mg/l), how many water specimens are required in the sample? assume prior knowledge indicates that pollution readings in water samples taken during a day have been approximately normally distributed with a standard deviation of 5.4 (mg/l).
Answers
The number of water specimen is 304.
What is standard deviation?
The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
What is margin of error?
The margin of Error is a statistical expression that is used to determine the percentage point by which the result arrived will differ from the value of the entire population, and it is calculated by dividing the standard deviation of the population by the sample size and lastly multiplying the resultant with the critical factor.
Given,
margin of error = 0.5
Standard deviation = 5.4
To find the total water specimens.
Margin of Error = Z * ơ / √n
For two-sided confidence interva
p' = 1-α/2
α = 1- 0.90
= 0.1
p' = 1-0.1/2
p' = 0.95
The critical z value for cumulative probability of 0.95 is 1.64.
Margin of error = 1.64(5.4/\(\sqrt{n}\))
0.5 = 1.64(5.4/\(\sqrt{n}\))
n = 304
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5 and 9 are the example of ____ number
Answers
Answer:
Step-by-step explanation:
complex numbers , real numbers , rational numbers , natural numbers , whole numbers
it rained on a hot summer afternoon and a puddle formed. after several hours, the puddle was gone. identify and describe the two processes made the puddle form and then disappear?
Answers
The two processes that caused the puddle to form and then disappear were evaporation and infiltration.
Evaporation is the process in which liquid water turns into vapor and rises into the atmosphere. It occurs when the air around the puddle is warmer than the liquid, causing the water molecules to move faster and spread out. This allows the water to evaporate into a gas. The rate of evaporation is proportional to the water surface area and the difference in temperature between the air and the water.
Infiltration is the process in which water is absorbed into the ground. It occurs when the water in the puddle is drawn into the soil due to gravity and capillary action. This process is influenced by the soil type, the amount of water, and the soil's porosity. The rate of infiltration is proportional to the soil's permeability, which is a measure of how quickly water can move through the soil.
The combination of evaporation and infiltration caused the puddle to form and then disappear. As the water evaporated, the puddle shrank until it was gone. Simultaneously, the water that remained was absorbed into the ground until all of the puddle was gone.
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Where are the correct answers to this geometry question?
Answers
1. Property
This is an example of the transitive property of equality.2. Definition
This is the definition of a right angle.3. Property
This is an exmaple of the division propety of equality.4. Definition
This is the definition of a midpoint.5. Property
This is an example of the symmetric property of equality.Let me know if you have any questions, thanks!
How do you calculate SAM and SOM?
Answers
To calculate SAM and SOM, you need to follow the following steps:
1. SAM (Simple Arithmetic Mean): SAM is calculated by adding up all the values in a set of data and then dividing that sum by the number of values in the dataset.
Formula: SAM = (x1 + x2 + ... + xn)/n
Where x1, x2, ..., xn are the values in the dataset and n is the number of values in the dataset.
Example: If you have a dataset with the values 2, 4, 6, 8, 10, then the SAM would be (2+4+6+8+10)/5 = 30/5 = 6
2. SOM (Simple Geometric Mean): SOM is calculated by multiplying all the values in a set of data and then taking the nth root of that product, where n is the number of values in the dataset.
Formula: SOM = (x1 * x2 * ... * xn)^(1/n)
Where x1, x2, ..., xn are the values in the dataset and n is the number of values in the dataset.
Example: If you have a dataset with the values 2, 4, 6, 8, 10, then the SOM would be (2*4*6*8*10)^(1/5) = 3840^(1/5) = 5.16
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Evaluate each expression if a = 4, b = 6, and c = 2.
Answers
Answer:
26
Step-by-step explanation:
ab+c
plug in #s
4(6)+2
start to solve
24+2
26
Gladys deposited $150 into her savings account that has a 4.25% simple interest rate. How much interest will she earn in 12 months?
Answers
Answer:
6.38 in 12 months
Step-by-step explanation:
Find the most general antiderivative of f(u)=u2−6u4+9u. Note: Any arbitrary constants used must be an upper-case " C ". F(u)= Find the particular antiderivative that satisfies the following conditions: dxdy=6x−2+2x−1−7;y(1)=4 y=
Answers
The most general antiderivative of the function \( f(u) = u^2 - 6u^4 + 9u \) is \( F(u) = \frac{1}{3}u^3 - \frac{6}{5}u^5 + \frac{9}{2}u^2 + C \), where \( C \) represents an arbitrary constant. Thus, the particular antiderivative that satisfies the given conditions is \( -6x^{-1} + 2\ln|x| - 7x + 15 \).
To find the most general antiderivative of \( f(u) = u^2 - 6u^4 + 9u \), we can integrate each term separately. The antiderivative of \( u^2 \) is \( \frac{1}{3}u^3 \), the antiderivative of \( -6u^4 \) is \( -\frac{6}{5}u^5 \), and the antiderivative of \( 9u \) is \( \frac{9}{2}u^2 \). Adding these antiderivatives together with an arbitrary constant \( C \) gives us \( F(u) = \frac{1}{3}u^3 - \frac{6}{5}u^5 + \frac{9}{2}u^2 + C \).
To find the particular antiderivative that satisfies \( \frac{dy}{dx} = 6x^{-2} + 2x^{-1} - 7 \) and \( y(1) = 4 \), we integrate the given derivative function with respect to \( x \). The antiderivative of \( 6x^{-2} + 2x^{-1} - 7 \) is \( -6x^{-1} + 2\ln|x| - 7x + D \), where \( D \) is another arbitrary constant.
Then, applying the initial condition \( y(1) = 4 \) gives us \( -6(1)^{-1} + 2\ln|1| - 7(1) + D = 4 \). Simplifying this equation gives \( -6 + 2\ln(1) - 7 + D = 4 \), and solving for \( D \) gives \( D = 15 \). Thus, the particular antiderivative that satisfies the given conditions is \( -6x^{-1} + 2\ln|x| - 7x + 15 \).
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The box plots show the average speeds, in miles per hour, for the race cars in two different races. average speeds of cars in race a 2 box plots. the number line goes from 120 to 170. for race a, the whiskers range from 120 to 170, and the box ranges from 143 to 165. a line divides the box at 153. for race b, the whiskers range from 125 to 165, and the box ranges from 140 to 150. a line divides the box at 145. average speeds of cars in race b which correctly describes the consistency of the speeds of the cars in the two races? the speeds in race a are likely to be near 170 mph and the speeds in race b are likely to be near to 165 mph. the speeds in race a are likely to be near 153 mph and the speeds in race b are likely to be near to 145 mph. the speeds in race a are likely to be near 120 mph and the speeds in race b are likely to be near to 125 mph. the speeds in race a are likely to be near 145 mph and the speeds in race b are likely to be near to 153 mph.
Answers
"The speeds in race a are likely to be near 145 mph and the speeds in race b are likely to be near to 153 mph" correctly describes the consistency of the speeds of the cars in the two races.
Based on the given information, the box plot for race A has a larger range of speeds (from 120 to 170 mph) compared to the range of speeds in race B (from 125 to 165 mph). The box plot for race A also has a larger interquartile range (from 143 to 165 mph) compared to the interquartile range in race B (from 140 to 150 mph). However, the median speed in race A (153 mph) is lower than the median speed in race B (145 mph).
Therefore, it is not accurate to say that the speeds in race A are likely to be near 170 mph and the speeds in race B are likely to be near 165 mph. Likewise, it is not accurate to say that the speeds in race A are likely to be near 120 mph and the speeds in race B are likely to be near 125 mph.
The correct answer is that the speeds in race A are likely to be near 145 mph and the speeds in race B are likely to be near 153 mph. This is because the medians of the two box plots are relatively close to each other, and the box plot for race B has a smaller range and interquartile range, indicating greater consistency in the speeds of the cars in that race compared to race A.
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Ira can use the greatest common factor to rewrite 75+30 as
(5+
).
Answers
Answer:
Step-by-step explanation:
15(5+2) is the Answer
The greatest common factor to rewrite 75+30 as 15(5+2)
What is GCD?Greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
An expression is a combination of numbers, variables and operators.
The given expression is 75+30.
By using distributive law we can find this.
Let us find factors of 75 and 30.
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 30 are 1, 3, 5, 9, 15, 45
Their GCF is 15.
To get 75, we will multiply 15 by 5.
To get 30, we will multiply 15 by 2.
By using distributive property
75+30 can be splitted to factors as
15(5+2)
Hence the greatest common factor to rewrite 75+30 as 15(5+2)
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what is the perimeter of square abcd? units units 28 units 37 units
Answers
The perimeter of square ABCD is 28 units.
The perimeter of a square is the sum of all its sides. In this case, we need to find the perimeter of square ABCD.
The question provides two possible answers: 28 units and 37 units. However, we can only choose one correct answer. To determine the correct answer, let's think step by step.
A square has all four sides equal in length. Therefore, if we know the length of one side, we can find the perimeter.
If the perimeter of the square is 28 units, that would mean each side is 28/4 = 7 units long. However, if the perimeter is 37 units, that would mean each side is 37/4 = 9.25 units long.
Since a side length of 9.25 units is not a whole number, it is unlikely to be the correct answer. Hence, the perimeter of square ABCD is most likely 28 units.
In conclusion, the perimeter of square ABCD is 28 units.
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55cm as a fraction of 225 cm in its simplest form
Answers
Answer:
\(\frac{11}{45}\)
Step-by-step explanation:
\(\frac{55}{225}\) ( divide numerator and denominator by 5 )
= \(\frac{11}{45}\) ← in simplest form
a fraction is in simplest form when no other number but 1 divides into the numerator and denominator.
Which statement is true about the sum of two rational numbers? It can always be written as a fraction. It can never be written as a fraction. It can always be written as a repeating decimal. It can never be written a terminating decimal. ?
Answers
Answer:
It can always be written as a fraction.
Step-by-step explanation:
The importance of this question is to differentiate rational and irrational numbers.
Rational numbers can be written as a ratio, hence a fraction, or a repeating or terminating decimal.
Irrational numbers cannot be written as a ratio and will not have a terminating or repeating decimal.
So the first statement is true since the sum of two rational numbers will be rational.
The second statement is false since the sum of two rational numbers can absolutely be represented by a fractional ratio.
The third statement is false since the sum of two rational numbers is not always a repeating decimal.
The fourth statement is false since the sum of two rational numbers could be written as a terminating decimal.
Cheers.
I agree with the other person's response. The sum is always rational (it can always be written as a fraction of integers)
----------------
Here's a proof:
Let x and y be two rational numbers. This means
x = a/b
y = c/d
where a,b,c,d are integers. The denominators b and d cannot be 0.
----------------
Let's add x and y, then simplify
x+y = (a/b) + (c/d)
x+y = (ad/bd) + (bc/bd)
x+y = (ad+bc)/(bd)
This last expression is in the form p/q
p = ad+bc is an integer
q = bd is also an integer
we have a ratio or fraction of integers, therefore x+y is also rational
Please help me with this ASAP!!
Find the probability that a randomly selected point within the circle falls in the white area.
Round to the nearest tenth of a percent.
r=4cm
Answers
Probability that a randomly selected point falls in the white area is; 84.1%
How to find the probability?The formula for area of a circle is;
A = πr²
where r is radius.
Thus;
A_circle = π * 4² = 50.265 cm²
Now, formula for area of triangle is;
A_tria = ¹/₂ * base * height
A_tria = ¹/₂ * 4 * 4 = 8 cm²
Thus;
Area of white portion = 50.265 cm² - 8 cm²
Area of white portion = 42.265 cm²
Thus;
Probability that a randomly selected point falls in the white area is;
P(White area) = 42.265/50.265 = 0.8408
= 84.1%
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FILL IN THE BLANK. Two events are said to be ________ if they can not occur at the same time.Two events are said to be _______ if the occurrence of one does not influence the probability of occurrence for the other.
Answers
Complete statement : Two events are said to be mutually exclusive if they can not occur at the same time. Two events are said to be Independent if the occurrence of one does not influence the probability of occurrence for the other.
What are Independent events?
Independent events are events for which the occurrence (or non-occurrence) of one event does not affect the probability of the other event occurring.
Two events are said to be mutually exclusive (or disjoint) if they cannot occur at the same time. In other words, if one event occurs, the other event cannot occur simultaneously.
For example, if we toss a coin, the events "getting a heads" and "getting a tails" are mutually exclusive. If we get a heads, we cannot get a tails at the same time.
Two events are said to be independent if the occurrence of one event does not influence the probability of occurrence of the other event. In other words, the probability of both events occurring together is equal to the product of their individual probabilities.
For example, if we roll a dice twice, the events "getting a 2 on the first roll" and "getting a 4 on the second roll" are independent. The probability of getting a 2 on the first roll is 1/6, and the probability of getting a 4 on the second roll is also 1/6. The probability of getting a 2 on the first roll and a 4 on the second roll is (1/6) x (1/6) = 1/36.
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3.74 = 0.4n + 2.5
What value of n makes the equation TRUE?
Answers
3.74 = 0.4n + 2.5
3.74 - 2.5 = 0.4n
1.24 = 0.4n
n = 3.1
So the value of n which makes the statement true is 3.1
Hope this helps :)
The value of n for the equation to be true is n = 3,1
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be A , 3.74 = 0.4n + 2.5
Now ,
3.74 = 0.4n + 2.5
Subtracting 2.5 on both sides of the equation , we get
0.4n = 3.74 - 2.5
0.4n = 1.24
Divide by 0.4 on both sides of the equation , we get
n = 3.1
Therefore , n = 3.1
Hence , the value of n for the equation to be true is n = 3.1
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Briefly explain the process of starch gelatinisation. In your answer name 5 common staple foods that are high in starch.
Answers
Starch gelatinisation is a critical cooking process that is used to make many starchy foods, including rice, pasta, and potatoes.
Gelatinization is the process of breaking down the intermolecular bonds of starch molecules in the presence of water and heat, resulting in the formation of a thickened mass. It is a vital cooking process in making starchy foods such as rice and pasta. The water molecules activate the hydrogen bonds between the starch molecules, which, upon heating, cause the starch granules to absorb water, swell and burst, releasing the mixture’s starch molecules. When heated further, the starch molecules rearrange themselves and begin to recombine with each other, resulting in a gelatinized matrix that contributes to the texture of the finished product. During this process, the starch granules absorb water and swell up, eventually bursting, and allowing the starch molecules to interact with the water. Once this happens, the mixture thickens, resulting in a gel-like substance that contributes to the texture of the finished product.
Starch gelatinisation is a fundamental cooking process that is used to make starchy foods such as rice and pasta. It is a simple process that involves heating the starch in the presence of water. When this happens, the water molecules activate the hydrogen bonds between the starch molecules, which, upon heating, cause the starch granules to absorb water, swell and burst, releasing the mixture’s starch molecules. The starch molecules then begin to recombine with each other, resulting in a gelatinized matrix that contributes to the texture of the finished product. There are numerous common staple foods that are high in starch, including rice, potatoes, wheat, maize, and cassava. Rice is the most commonly consumed starchy food globally, with over half of the world's population consuming it daily. Other starchy staples include potatoes, which are a staple in many cultures worldwide, and wheat, which is used in a wide range of foods, including bread, pasta, and cereal. Maize is also a significant source of starch and is commonly used to make cornmeal, tortillas, and other maize-based foods. Finally, cassava is a root vegetable that is a significant source of starch and is commonly consumed in Africa and South America.
In conclusion, starch gelatinisation is a critical cooking process that is used to make many starchy foods, including rice, pasta, and potatoes. The process involves heating the starch in the presence of water, which causes the starch granules to absorb water, swell, and burst, releasing the mixture's starch molecules. The starch molecules then recombine with each other, resulting in a gelatinized matrix that contributes to the texture of the finished product. Finally, there are numerous common staple foods that are high in starch, including rice, potatoes, wheat, maize, and cassava.
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In the figure, a∥b and m∠3 = 34°.
What is the m∠7?
Enter your answer in the box. |__|
Answers
Therefore, In the figure, a∥b angle m∠7 = 34° .
What is angle ?An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common terminus, and are referred to as the sides of the angle. Angles of two rays lie in the plane containing the rays. Angles can also result from the intersection of two planes. Dihedral angles are the name given to them.
Here,
Given that a and b are parallel lines,
∠3 and ∠7 are corresponding angles and congruent
m∠3 = 34°
thus ,m∠7 =m∠3 = 34°
so, m∠7 = 34°
Therefore, In the figure, a∥b m∠7 = 34° .
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8n+6 which wil be the nearest number in the sequence to 100
Answers
The number 102 in the sequence 8n + 6 is the nearest to 100.
To find the nearest number in the sequence 8n + 6 to 100, we need to determine the value of n that gives us a number closest to 100.
Let's start by setting up an equation:
8n + 6 = 100
To solve for n, we can subtract 6 from both sides of the equation:
8n = 100 - 6
8n = 94
Now, divide both sides of the equation by 8:
n = 94 / 8
n = 11.75
Since n represents a position in the sequence, it must be an integer. Therefore, we need to round 11.75 to the nearest whole number.
The nearest whole number to 11.75 is 12.
So, the nearest number in the sequence 8n + 6 to 100 is when n = 12.
Plugging n = 12 back into the equation:
8(12) + 6 = 96 + 6 = 102
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Which fraction below is equivalent to 7/8?
A.) 50/56
B.)63/72
C.) 49/64
D.) 15/16
Answers
Answer:
C
Step-by-step explanation:
just simplied them
a triangle has a side length of 5.4 and 7 x x=
Answers
Answer:
D. 8.8
Step-by-step explanation:
As the pythagorean theorem.
A² + B² = C²,
5.4 × 5.4 + 7 × 7 = C²,
29.16 + 49 = C²,
78.16 = C²,
8.8 ≈ C
Which of the following situations is a relationship that shows correlation but NOT causation?
A.
A child’s shoe size gets larger and his t-shirt size gets larger.
B.
The more sips you have taken from a cup of water, the less water there is in the cup.
C.
The amount of time you spend picking blueberries, the more blueberries you have in your basket.
D.
A student runs home from school every day. The student discovers that the faster she runs, the sooner she gets home from school.
Answers
The number seventeen and seven thousand in decimal form is
Answers
Answer:
17.00 and 17,000.00
this is your answer to ur question
If a student scored an 82, use your line of best fit to predict how many hours the student
watched TV.
O 0.97 hours
O 2.16 hours
0 3.25 hours
O 7.39 hours
Answers
Answer:
2.16
Step-by-step explanation:
I took the quiz
three expressions equivalent to 4^10
Answers
Answer:
4^10 = 1,048,576
A, C, E
Step-by-step explanation:
A= 1,048,576
B= 10,000
C= 1,048,576
D= 16,384
E= 1,048,576
An expression is defined as a set of numbers, variables, and mathematical operations. The expressions are A, C, and E.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression that is equivalent to 4¹⁰ is,
(4⁵)²4²⁰/4¹⁰(4²4³)²Hence, the expressions are A, C, and E.
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please, someone, help me I need an answer now, please
Answers
Answer:
y=10x+20
Step-by-step explanation:
first find the slope by counting or using the formula. the slope is 10. next determine the y intercept by looking for the y value when x is 0. The y intercept is 20. the y intercept is b and slope is m, Substitute those values into the formula y=mx+b
Answer:
1/20
Step-by-step explanation: