Answers
d) \(\frac{48y^{10} }{x^{9} }\) is the answer to your question
Exponents:
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64.In this case, the exponent is 4 and the base is 6. This can be understood as 4 increased to the power of 6.The symbol used for representing the exponent is ^. This symbol (^) is called a carrot. For example, 4 raised to 2 can be written as 4^2 or 42. Thus, 4^2 = 4 × 4 = 16Adding exponents while maintaining the same base is the rule for multiplying like bases.exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.To know more about Exponents:
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Related Questions
x is a normally distributed random variable with a mean of 22 and a standard deviation of 5. the probability that x is between 17 and 27 is
Answers
To find the probability that x is between 17 and 27, we need to standardize the values using the standard normal distribution, with a mean of 0 and a standard deviation of 1.
First, we standardize 17 and 27 as follows:
z = (x - μ) / σ
For x = 17:
z = (17 - 22) / 5 = -1
For x = 27:
z = (27 - 22) / 5 = 1
We can then look up the area under the standard normal distribution curve between z = -1 and z = 1 using a standard normal distribution table or a calculator. The area between these values represents the probability that x is between 17 and 27.
Using a standard normal distribution table, we find that the area between z = -1 and z = 1 is approximately 0.6827.
Therefore, the probability that x is between 17 and 27 is approximately 0.6827.
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16a² − 25?? please help
Answers
Answer:
(4a - 5)(4a + 5)
Step-by-step explanation:
Assuming you require to factor the expression
Given
16a² - 25 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
16a² - 25
= (4a)² - 5²
= (4a - 5)(4a + 5) ← in factored form
Answer100 POINTS! (50 split up) PLSSSSSTO GIVE BRAINLIEST AND FIVE STARS AND A THANKS! 6TH GRADE SCIENCE! i used all my points for this!
You measure the mass of an apple using a balance.
The cost, c, of supplies for school depends
on other factors. list at least two
independent variables that could affect
the cost of school supplies.
Answers
Social researchers treat gender identity, ethnicity, race, income, and education as independent variables because they are all significant subject factors.
What is an example of an independent variable?
It is an independent variable that doesn't alter as a result of the other variables you're attempting to assess. An independent variable could be something like a person's age.
Other elements (such as what they consume, how much they attend school, and how much television they watch) won't alter a person's age.
What distinguishes a variable from a dependent one?
The cause is the independent variable. The other factors in your study have no bearing on its value. Effect is the dependent variable.
Changes in the independent variable affect how much it is worth. Characteristics called variables can have various values.
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Use the distributive property to remove the parentheses.
-4(p - 212) = 44
Solve for the remaining two step equation.
I need this very quickly
Answers
Answer:
P = 201.
Step-by-step explanation:
In mathematics, distributivity is a property of binary operations in which the multiplication is distributed, dividing the same multiplier by the different multipliers to obtain the result.
Thus, to solve the equation -4 (P - 212) = 44 the following calculation must be performed:
-4 (P - 212) = 44
(-4 x P) - (-4 x 212) = 44
-4P - (-848) = 44
-4P + 848 = 44
-4P = 44 - 848
-4P = -804
P = -804 / -4
P = 201
The average of four different positive integers is 9. What is the greatest value for one of the integers?
Answers
From the given information; Let the unknown different positive integers be (a, b, c and d).
An integer is a set of element that are infinite and numeric in nature, these numbers do not contain fractions.
Suppose we make an assumption that (a) should be the greatest value of this integer.
Then, the other three positive integers (b, c and d) can be 1, 2 and 3 respectively in order to make (a) the greatest value of the integer.
Therefore, the average of this integers = 9
Mathematically;
\(\mathbf{\dfrac{(a+b+c+d)}{4} =9}\)
\(\mathbf{\dfrac{(a+1+2+3)}{4} =9}\)
\(\mathbf{\dfrac{(6+a)}{4} =9}\)
By cross multiplying;
6+a = 9 × 4
6+a = 36
a = 36 - 6
a = 30
Therefore, we can conclude that from the average of four positive integers which is equal to 9, the greatest value for one of the selected integers is equal to 30.
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The greatest value for one of the four positive integers is 30.
To find the largest positive integer, you have to minimize the other three positive integers.
The least three different positive integers available = 1, 2, 3let the largest positive integer = ythe sum of the four different positive integers = 1 + 2 + 3 + y = 6 + yFind the average of the four positive integers and equate it to the given value of the average.
\(\frac{6 + y}{4} = 9\\\\6+ y = 36\\\\y = 36-6\\\\y = 30\)
Thus, the greatest value for one of the positive integers is 30
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Is the coordinates of a point are 3 and 4?
Answers
The coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25)
The coordinates of point A = (-5, -4),
The coordinates of the point B = (-3, 3)
Let the point at the distance 3/4 from A to B = P
The coordinates of point 3/4 from A to B = P
At the x-coordinate, the distance from B to A is = -3-(-5) = 2 units.
At the y-coordinate, the distance from B to A is = 3-(-4) = 7 units.
Hence, the coordinates of P = (-5 + (3/4×(x-coordinate), -4 + 3/4×(y-coordinate)
P = (-5 + (3/4×(2), -4 + 3/4×(7))
P = (-3.5, 1.25)
Hence, the coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25).
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The complete question is -
What are the coordinates of the point 3/4 of the way from A to B?
somebody help pls
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Answers
Answer:
As it is a right angle triangle, you can find a by Pythagoras Theorem.
\( {a}^{2} + {51}^{2} = {60}^{2} \\ a = \sqrt{( {60}^{2} - {51}^{2} )} \\ a = 31.63 \: yd\)
Miram is studying a type of plant that grows at a constant rate. Every month, she visits two of these plants and measures their heights. She made this table:Week
1
11
2
22
3
33
Plant A's height (
cm
cmstart text, c, m, end text)
22
2222
24
2424
26
2626
Plant B's height (
cm
cmstart text, c, m, end text)
26
2626
28
2828
30
3030
Miram wants an equation she can use to find Plant A's height in centimeters (
a
aa) given Plant B's height in centimeters (
b
bb).
Answers
An equation she can use to find Plant A's height in centimeters is a = b - 4
What is an equation?
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
Here, we have
Given: Miram is studying a type of plant that grows at a constant rate. Every month, she visits two of these plants and measures their heights.
Let's use the table to think about the difference between Plant A's height and Plant B's height. That will help us write an equation we can use to find Plant A's height from Plant B's height.
plant A's height is always 4 cm less the plant B's so we can write an equation to find plant A's height in terms of plant B's.
Hence, An equation she can use to find Plant A's height in centimeters is a = b - 4
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Susan runs 22 km in 2 hours and 45 minutes. What is her average speed in km an hour? Explain your answer please!
Answers
Answer:
22km= 2 hours and 45 mins
To find speed: Distance/Time
22/2.75 = 8
Your answer 8km/h
Step-by-step explanation: When finding speed, the formula is always distance divided by time. 45 minutes of 60 minutes is 3/4 of an hour, and 3/4 is 0.75 is decimal. So you add the 2 + .75, and you'll get 2.75. After you convert the time, you begin dividing and you'll get your answer!
the rationale underlying the use of projective personality tests, such as the rorschach test and the thematic apperception test, is that they
Answers
The rationale underlying the use of projective personality tests, such as the Rorschach test and the thematic apperception test, is that they reveal the subjects' personalities by eliciting responses to vague, ambiguous stimuli.
The rationale underlying the use of projective personality tests, such as the Rorschach test and the Thematic Apperception Test, is that they can reveal a person's unconscious thoughts, feelings, and motivations. These tests use vague and ambiguous stimuli, such as inkblots or pictures, and ask the person to describe what they see or make up a story about the stimuli. The person's responses are believed to reflect their underlying personality traits and psychological conflicts.
The theory is that when faced with ambiguous stimuli, people project their own thoughts, feelings, and motivations onto the stimuli, revealing their unconscious processes.
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Each marble bag sold by Dlane's Marble Company contains 2 purple marbles for every 3 green marbles. If a bag has 12 purple marbles, how many green marbles does it contain? how many green marbles does it contain
Answers
Given statement solution is :-The bag contains 18 green marbles.
If each bag sold by Dlane's Marble Company contains 2 purple marbles for every 3 green marbles, we can set up a ratio to find the number of green marbles in the bag.
The ratio of purple marbles to green marbles is 2:3.
We know that the bag has 12 purple marbles. Let's set up a proportion using this information:
2/3 = 12/x
To solve for x, we can cross-multiply:
2x = 3 * 12
2x = 36
Dividing both sides of the equation by 2, we get:
x = 36/2
x = 18
Therefore, the bag contains 18 green marbles.
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1. Fernando is using a garden hose to fill his backyard pool at a rate of 10 gallons per minute. The pool already contains 9000 gallons of water. The capacity of the pool is 12,000 gallons. a. Define the independent and dependent variables. b. Define the unit rate of change. 2. Use double number lines to solve each equation. a. 2(x + 1) = 10 b. −(x − 5) = 0 3. Solve for each unknown. a. 1.6 = x 2.8 7 b. 2 = 0.4 d4 5
Answers
The independent variable is the time in minutes.
The dependent variable is the capacity (volume) of the pool.
The unit rate of change is equal to 10.
The solution to each equation is shown on the number line below.
The solutions to each equations 1.6/2.8 = x/7 and 2/d = 0.4/5 are 4 and 25 respectively.
What is an independent variable?In Mathematics, an independent variable can be defined as the variable that is being manipulated by an experimenter, scientist, or a researcher. This ultimately implies that, an independent variable is always considered as the cause in an experiment and it is represented by the x-axis value on a graph.
In this context, we can reasonably infer and logically deduce that time measured in minutes represent the independent variable while the capacity (volume) of the pool represent the dependent variable.
Next, we would solve the equation algebraically;
1.6/2.8 = x/7
2.8x = 11.2
x = 11.2/2.8
x = 4.
2/d = 0.4/5
0.4d = 10
d = 10/0.4
d = 25.
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Which of the following products is negative?
Select all that apply.
A. (–4)(–9)
B. (–4)(9)
C. (6)(6)
D. (–6)(–6)
E. (6)(–6)
Answers
e. -36
the trick is, when you’re multiplying two numbers together, if both of them are negative, then it will equal a positive. but, if only one of the numbers is a negative, and the other is positive, then it would equal a negative. and obviously two positives equal a positive. hope this helps!
Answer:
b and e
Step-by-step explanation:
trust '
Which ratio is also equal to StartFraction R T Over R X EndFraction and StartFraction R S Over R Y End Fraction?
Answers
Answer:
ST/XY
Step-by-step explanation:
(RT/RX)/(RS/RY)= ST/XY
if the shapes are equal and the same then the ratio are equal
if RT is corresponds to RX and RS is corresponds to RY then TS corresponds to TS
you need to add lines, segments, and angles to create your ultimate circle. you need to incorporate specific theorems. Each problem must ask for a missing measure(an arc measure, segment length or angle measure. Provide information that someone would need to solve at the top of the puzzle could include angle measures, arc measures, tangent lines, parallel ect. You must list which problem number is used for each listed theorem show all work.
Answers
Some information that someone might use to solve problems related to a circle design is the Tangent Arc theorem.
What is the tangent arc theorem?The tangent arc theorem states that if an angle is formed by two secants, one secant, one tangent, or two tangents, and also intersects in a space outside of the circle, then the value obtained will be equal to the difference of the values of the intercepted arcs divided by one and a half.
Also, note that angles outside a circle are those whose vertex or arc is pointed outwards and their sides are either secants or tangents. With this information, it will be possible to solve problems related to tangent lines and arc measures.
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write and equation that would create the graph of the line
Answers
we have two points (x, y): (0,1) and (1,3)
We can use the point-slope form
(y - y1) = m (x -x1)
The slope = m= (y2-y1)/ (x2-x1)
or
The slope-intercept form.
y = mx + b
m= (y2-y1)/ (x2-x1)
y-intercept is (0, b)
__________________________
Using The slope-intercept form,
y = mx + b
b = 1
point (0,1)
Replacing
y = mx + 1
finding the slope
point 1 (0, 1), x1= 0; y1= 1
point 2 (1, 3); x2= 1; y2= 3
m= (y2-y1)/ (x2-x1)
Replacing
m= ( 3- 2)/ (1 - 0) = 2/1 = 2
___________________
Replacing the slope
y = 2x + 1
__________________
Answer
y = 2x + 1
If B = 0 in a linear equation of the form Ax + By = C, then which statement is also true? A. The graph of this equation is a horizontal line. B. The graph of this equation is a vertical line. C. The graph of this equation is a slanted line. D. The graph of this equation can be any straight line.
Answers
Answer:
A) Its horizontal lineStep-by-step explanation:
Ax + By = C
so Ax + (0)y = C
a= c /x
its horizontal
Answer:
c
Step-by-step explanation:
the ratio of cats to dog at the animal shelter is 4:5 if there are 20 cats.
A group of animals arrive at the shelter and the ratio of cats to dogs becomes 5:3.
work out the smallest number of new animals that could have arrived at the shelter
Answers
Answer: 25 cats and 15 dogs
Step-by-step explanation:
If the ratio of cats to dogs is 4:5 and the amount of cats is 20, you can evenly distribute this product by multiplying 5 on each side, meaning there would be 20 cats and 25 dogs.
For the group of animals that has just arrived, the amount of cats went up by 1.25% and the amount of dogs went down by 1.67%. To figure out the new total of animals, you are going to have to divide or multiply both sides of the ratio depending if they increased or decreased.
So in the ratio 5:3, you would multiply 20 and 1.25 to get 25, and divide 25 and 1.67 to get 15. Your final answer should be 25:15
If c is a positive number, how many solutions does √x = c have? Explain.
Answers
Answer:
varied
square root of number never result negative number
Step-by-step explanation:
There will only be one real solution.
If \(x\) is a real number, the square root function \(\sqrt x\) will only have real solutions when \(x\ge0\).
For \(x<0\), we get imaginary solutions.
Also, when \(\sqrt x> 0\), \(x>0\)
In other words, when the square root of \(x\) is a positive real number, \(x\) will be a unique positive number.
We can see this when trying to solve the equation given in the question
So, the equation
\(\sqrt x=c\)
where \(c>0\), when solved, will give
\(\sqrt x=c\\(\sqrt x)^2=c^2\\x=c^2\)
We will have a unique solution because squaring a positive real number gives a single result.
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B=x-3/x-1
- rút gọn P=A.B
Answers
A
Steliên hợp p-by-step explanaliên hợp ion:
for 3x + 2 = x - 2 does x = 0?
Answers
Answer:
No
Step-by-step explanation:
Solve for x.
You want to isolate all the variables (x) to one side.
3x+2=x-2
-3x -3x
2=-2x-2
+2 +2
4=-2x
x=-2
-2\(\neq\)0
Answer:
no, x = -2Step-by-step explanation:
for 3x + 2 = x - 2
does x = 0?
3x + 2 = x - 2
2x +2 = -2
2x = -4
x = -4 : 2
x = -2
--------------------------
check
3 * (-2) + 2 = -2 - 2
-4= -4
the answer is good
In the diagram below, the measure of angle 3 is 140, what is the measure of angle 5 ?
I need help with question number 2.
Help me please !
Answers
Answer:
2
Step-by-step explanation:
Angles 3 and 5 are alternate interior angles because they are inside the lines and are on opposite sides of the transversal.
This means they are equal to one another, so 2 is correct because they are alternate interior and angle 5 will be 140 degrees.
Maureen bought a new car worth $26,525 one year ago. She knows that her car's value will depreciate each year. She uses an online calculator to find that her car is worth $24,403 today. Write an exponential equation in the form y = a(b) that can model the value, y, of Maureen's car x years after purchase. Use whole numbers, decimals, or simplified fractions for the values of a and b.
Answers
The equation to model the value of Maureen's car x years after purchase can be written in the form of y = a(b)^x , where y is the value of the car, x is the number of years after purchase, and a and b are constants.
Using the information given, we can find the values of a and b.
We know that the value of the car one year after purchase is $24,403.
So, we can substitute this value into the equation:
24403 = a(b)^1
We also know that the car's original value is $26,525
So we can substitute this value into the equation:
26525 = a
Now we can use these two equations to find the value of b
24403 = 26525 (b)^1
b = 24403 / 26525
b = 0.9153
So the final equation is:
y = 26525 (0.9153)^x
where y is the value of the car, x is the number of years after purchase, and a = 26525 and b = 0.9153
(1.5x10^13)^2 in standard form
Answers
The standard form of the number \((1.5*10^(13))^2\) is 2.25×\(10^(26)\) .
What is standard form of a number ?
An equation, an expression, or a set of integers can all be written in standard form using the standard form approach. It is possible to express a number in a way that adheres to certain standards by writing it in its standard form. Standard form refers to any number between 1.0 and 10.0 that may be expressed as a decimal number and multiplied by a power of 10. The term "standard form" in this context refers to the act of condensing a particularly big expanded form of a number.
Here given is ,
=> \((1.5*10^(13))^2\)
=> \(1.5^2\) × \(10^(13)^2\)
=> 2.25×\(10^(26)\)
Therefore standard form of the number is 2.25×\(10^(26)\).
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graph the function g(x)=10*(3/5)^t
Answers
Answer:
Hope this helps you.
Step-by-step explanation:
I plugged in x for t, but it is the same graph.
Shonda wants to rewrite 24+924+9using the greatest common factor and the distributive property.Complete the statements below.CLEAR CHECKThe greatest common factor of 2424and 99is .Shonda can use the greatest common factor to rewrite 24+924+9as (8+(8+)).
Answers
Shonda can rewrite the expression as 24 + 9 =3(8+3)
First we find out the greatest common factor of 24 and 9.
since 24=3×8 and
9=3×3,
Here 3 is a factor of both 24 and 9
So the expression using the distributive property can be written as
24+9= 3×8 + 3×3
Take 3 common, we get
= 3(8 + 3)
As 24 + 9 = 33
and 3(8+3)=3(11)= 33
Both the expressions are equivalent.
Therefore, Shonda can rewrite the expression as 24 + 9 =3(8+3)
Answer:
24 + 9 =3(8+3)
Step-by-step explanation:
Find the antiderivative F(x) of the function f(x) (Use C for the constant of the antiderivative:) f(x) = 2 csc(x) cot(*) sec(x) tan(x) F(x)
Answers
the antiderivative of the function f(x) = 2 csc(x) cot(x) sec(x) tan(x) is F(x) = 2x + C.
To find the antiderivative F(x) of the function f(x) = 2 csc(x) cot(x) sec(x) tan(x), we can simplify the expression and integrate each term individually.
We know that csc(x) = 1/sin(x), cot(x) = 1/tan(x), sec(x) = 1/cos(x), and tan(x) = sin(x)/cos(x).
Substituting these values into the expression:
f(x) = 2 * (1/sin(x)) * (1/tan(x)) * (1/cos(x)) * (sin(x)/cos(x))
= 2 * (1/sin(x)) * (1/(sin(x)/cos(x))) * (sin(x)/cos(x)) * (sin(x)/cos(x))
= 2 * (1/sin(x)) * (cos(x)/sin(x)) * (sin(x)/cos(x)) * (sin(x)/cos(x))
= 2 * 1
= 2
The antiderivative of a constant function is simply the constant multiplied by x. Therefore:
F(x) = 2x + C
where C represents the constant of the antiderivative.
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Ahmed is making a sandwich. He has the following ingredients: 2 types of bread (white and wheat), 2 types of cheese (Cheddar and Swiss), 3 types of meat (Chicken, Beef, and Turkey).How many different types of sandwiches can Ahmed make if he has to use 1 bread, 1 cheese and 1 meat? Hint: Draw a tree diagram. *
12
1
3
20
Answers
Prove that if f : R^n → R^m is continuous, then ||f(x)|| is continuous on Rn.(Note: Let x = (x1, . . . , xn) ∈ Rn. We define the euclidean norm by ||x|| = √Σni=1 xi2 )(Note- Use exercise: Prove that ||·|| is a continuous function on Rm.)(Elementary Real Analysis 11.7.11)
Answers
To prove that ||f(x)|| is continuous on Rn given that f : R^n → R^m is continuous, we can use the fact that ||·|| is a continuous function on R^m. This is the definition of convergence, so we have shown that ||f(x1)||, ||f(x2)||, ..., ||f(xn)|| converges to ||f(x)||, which means that ||f(x)|| is continuous on Rn.
Let x1, x2, ..., xn be a sequence in Rn that converges to a point x in Rn. We want to show that the sequence ||f(x1)||, ||f(x2)||, ..., ||f(xn)|| converges to ||f(x)||.
Since f is continuous, we know that for any ε > 0, there exists a δ > 0 such that if ||x-y|| < δ, then ||f(x) - f(y)|| < ε.
Let ε > 0 be given. We want to find a δ > 0 such that if ||x-y|| < δ, then ||f(x)-f(y)|| < ε.
Using the triangle inequality, we have
||f(x) - f(y)|| = ||f(x) - f(x) + f(y) - f(x)|| ≤ ||f(x) - f(x)|| + ||f(y) - f(x)||
= ||f(y) - f(x)||
Since x1, x2, ..., xn converge to x, we know that there exists some N such that for all n ≥ N, ||xn - x|| < δ.
Therefore, for all n ≥ N, we have
||f(xn) - f(x)|| ≤ ||f(xn) - f(x)|| + ||f(x) - f(x)||
= ||f(xn) - f(x)|| + 0
< ε
Thus, we have shown that for any ε > 0, there exists an N such that for all n ≥ N, ||f(xn) - f(x)|| < ε. This is the definition of convergence, so we have shown that ||f(x1)||, ||f(x2)||, ..., ||f(xn)|| converges to ||f(x)||, which means that ||f(x)|| is continuous on Rn.
To prove that if f : R^n → R^m is continuous, then ||f(x)|| is continuous on R^n, we will follow these steps:
1. Recall the definition of continuity for a function: A function is continuous at a point x₀ if for every ε > 0, there exists δ > 0 such that for all x with ||x - x₀|| < δ, we have ||f(x) - f(x₀)|| < ε.
2. Since we know that ||·|| is a continuous function on R^m (given in the exercise), we can say that for every ε > 0, there exists δ > 0 such that for all y, z in R^m with ||y - z|| < δ, we have ||||y|| - ||z|||| < ε.
3. Now, we want to show that ||f(x)|| is continuous on R^n. Let x₀ be any point in R^n, and let ε > 0 be given.
4. Since f is continuous, there exists δ > 0 such that for all x in R^n with ||x - x₀|| < δ, we have ||f(x) - f(x₀)|| < ε.
5. Let x be any point in R^n such that ||x - x₀|| < δ. Then, by the continuity of f, we have ||f(x) - f(x₀)|| < ε.
6. Now, apply the continuity of ||·|| on R^m. Since ||f(x) - f(x₀)|| < ε, there exists a δ > 0 such that for all y, z in R^m with ||y - z|| < δ, we have ||||y|| - ||z|||| < ε.
7. Let y = f(x) and z = f(x₀). Then ||y - z|| = ||f(x) - f(x₀)|| < ε, and so ||||f(x)|| - ||f(x₀)|||| < ε.
8. This shows that for every ε > 0, there exists a δ > 0 such that for all x in R^n with ||x - x₀|| < δ, we have ||||f(x)|| - ||f(x₀)|||| < ε.
9. Thus, ||f(x)|| is continuous on R^n, as required.
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Consider the parabola y = 4x - x2. Find the slope of the tangent line to the parabola at the point (1, 3). Find an equation of the tangent line in part (a).
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The given parabolic equation is y = 4x - x² and the point is (1, 3). We are to determine the slope of the tangent line at (1, 3) and then obtain an equation of the tangent line. we must first calculate the derivative of the given equation.
We can do this by using the power rule of differentiation. The derivative of x² is 2x. So the derivative of y = 4x - x² is dy/dx = 4 - 2x.Since we want to find the slope of the tangent line at (1, 3), we need to substitute x = 1 into the equation we just obtained. dy/dx = 4 - 2x = 4 - 2(1) = 2. Therefore, the slope of the tangent line at (1, 3) is 2.We can now write the equation of the tangent line. We know the slope of the tangent line, m = 2, and we know the point (1, 3).
We can use the point-slope form of the equation of a line to obtain the equation of the tangent line. The point-slope form of the equation of a line is given as: y - y₁ = m(x - x₁)where m is the slope, (x₁, y₁) is a point on the line.Substituting in the values we have, we get:y - 3 = 2(x - 1)We can expand this equation to obtain the slope-intercept form of the equation of the tangent line:y = 2x + 1Therefore, the equation of the tangent line to the parabola y = 4x - x² at the point (1, 3) is y = 2x + 1.
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