Find The Rate Of Change Y=x4 +5 (2024)

Mathematics High School

Answers

Answer 1

The rate of change, y=−√x−4 +5, is expressed as 1/5−2i/5 .The square root of a number is the number itself.

what is a square root ?

A number can be obtained by multiplying the square root by itself. Square root is represented by the symbol sqrt, which stands for square root of, end square root. The reverse of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number can be found by looking for a number that, when squared, yields the original value. If 'a' is the square root of 'b,' then a a = b.

given

Use the average rate of change formula to substitute.

(√1)−(√−4) / (1)−(−4)

Condense the phrase.

1/5−2i/5

The rate of change, y=−√x−4 +5, is expressed as 1/5−2i/5 .The square root of a number is the number itself.

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Related Questions

Start with a circle whose equation is (x-a)^2 + (y-b)^2=r. Dilate that circle by a scale factor of 1/r with center of dilation (a,b). What does this transformation demonstrate

Answers

The dilation of the circle with a scale factor 1/r and center at (a,b) will transform the circle into a point at (a,b).

A dilation is a transformation that results in an image with the same shape as the original but a different size. • An enlargement is a dilation that produces a larger image. • A reduction is a dilation that produces a smaller image.

To solve this we will use the transformation formula for a dilation with center (a,b) and scale factor

k, (x,y) --> (a + k(x-a), b + k(y-b)).

Substituting in our values, we get

(x,y) --> (a + (1/r)(x-a), b + (1/r)(y-b)).

Setting this equal to (a,b), we get

(a + (1/r)(x-a) = a, b + (1/r)(y-b) = b).

Solving for x and y gives x = a and y = b. Therefore, the dilation of the circle with a scale factor of 1/r and center at (a,b) will transform the circle into a point at (a,b).

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What is the length of the short side of one of the 30 60 90 triangles?

Answers

Remembering the ratio of 1: 3: 2 and understanding that the smallest side length is always opposite the shortest angle (30°) and the longest side length is always opposing the greatest angle (90°) can help you recall the 30-60-90 triangle principles.

According to the 30-60-90 triangle theorem, the hypotenuse is twice as long as the shorter leg. Additionally, the sides of this particular triangle have a ratio of 1:2: [tex]\sqrt{3}[/tex].

A 30-60-90 triangle can have three sides, and if you only know one, you can use shortcuts to discover the other two. The three scenarios you encounter when performing these computations are as follows:

You are aware of the short leg (the side across from the 30-degree angle). To find the hypotenuse, multiply the length by two. The long leg can be calculated by multiplying the short side by the square root of 3.You are aware of the hypotenuse. To get the short side, divide the hypotenuse by two. To determine the long leg, multiply this response by the square root of 3.You are aware of the long leg (the side across from the 60-degree angle). To determine the short side, divide this side by the square root of 3. To find the hypotenuse, multiply that amount by two.

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PLEASE HELP ASAP. I WILL GIVE BRAINLIEST!!!

Which of the following is not an expression

A. 7 - 5x
B. 2 + 3x = 8
C. x/2 + 1
D. 2x + 6

Answers

B because it’s the only one with an equal sign

Answer:

B) 2 + 3x = 8

Step-by-step explanation:

Option B is not an expression as expressions do not have equal signs.

David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour,
but realizes that he will be 1 hour late if he continues at this speed. He increases his speed by 15
miles per hour for the rest of the way to the airport and arrives 30 minutes early. How many miles
is the airport from his home?
(A) 140 (B) 175 (C) 210 (D) 245 (E) 280

Answers

If David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. The number of miles that is the airport from his home is 210.

How to find the distance?

Let d represent the distance that is needed to travel 1 hour

1 hour late decreased to 0.5 hours early = 1.5

Hence,

d/50 + 1.5 = d/35

Simplify

7d + 525 =10d

Collect like terms

525 = 10d - 7d

525 = 3d

Divide both side by 3d

d = 525/3

d = 175

Total number of miles :

Total number of miles = 175 + 35

Total number of miles = 210

Therefore we can conclude that the correct option is C.

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The value of x is -1/4 Order these expressions from least to greatest:
X
1-x
x-1
-1÷x

Answers

Answer:

Step-by-step explanation:

-1 divided by x

1 - x

X - 1

In altitude BH and angle bisector AL intersect at point M. Given m∠HML = 100° and m∠MLC = 110°. Find angles of △ABC

Answers

The angles of triangle ABC are 60 degrees when altitude BH and bisector AL intersect at point M.

What is equilateral triangle?

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides.

Given that:

[tex]\angle HML = 100 \\\\\angle MLC = 110[/tex]

Since, BH is the altitude [tex]\angle MHC= 90[/tex].

The total angle of a quadrilateral is 360, hence:

100 + 110 + 90 + C = 360

C = 60 degrees.

Now consider triangle BHC:

The sum of angle of a triangle is 180, hence:

90 + 60 + B = 180

B = 30

Since the half angle B = 30, the entire [tex]\angle ABC = 60[/tex].

Consider triangle ABC:

Using sum of triangles, we have:

[tex]\angle A + \angle B + \angle C = 180\\\\\angle A + 60 + 60 = 180 \\\\\angle A = 60[/tex]

Hence the measure of angles of triangle ABC is 60 degrees.

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How do you draw a line segment equal to a given segment?

Answers

draw a line from the starting point of the segment to the endpoint using the same angle and length.

1. Place a ruler or straightedge on the given segment and draw a line along the length of the ruler.

2. Use a compass to create a line segment equal to the given segment. Set the compass to the length of the given segment, place the point of the compass on one end of the segment, and draw an arc to the other end of the segment.

3. Use a protractor to measure the angle and length of the given segment. Then, draw a line from the starting point of the segment to the endpoint using the same angle and length.

The answer explains three methods for drawing a line segment equal to a given segment: using a ruler or straightedge, using a compass, and using a protractor.

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What is the vector equivalent to the directed line segment from the point?

Answers

The vector equivalent to the directed line segment from the point (x1, y1) to the point (x2, y2) is the vector <x2-x1, y2-y1>.

The vector of a directed line segment is the difference between the two endpoints of the line segment. In this case, the endpoints are the points (x1, y1) and (x2, y2). Therefore, the vector of the directed line segment is equal to the vector <x2-x1, y2-y1>.

The vector equivalent of a directed line segment from the point (x1, y1) to the point (x2, y2) is the vector with initial point (x1, y1) and terminal point (x2, y2). This vector is equal to the vector form <x2-x1, y2-y1>, which describes the displacement from the initial point to the terminal point. This vector can also be written in component form, meaning the magnitude of the vector in the x-direction is x2-x1, and the magnitude of the vector in the y-direction is y2-y1.

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What are the real roots of the equation x2 3 x1 3 − 2?

Answers

The real roots of the equation x^(2/3) + x^(1/3) - 2 = 0 are 1 and -8.

The equation x^(2/3) + x^(1/3) - 2 = 0 does not have any real roots. Since the exponents are not integers, x^(2/3) and x^(1/3) are not defined for negative values of x, and so the equation has no solutions for real values of x.

But,

Let y = x^(1/3)

The equation x^(2/3) + x^(1/3) - 2 = 0 will become y² + y - 2 = 0.

Solving for the roots of this equation,

y² + y - 2 = 0

(y + 2)(y - 1) = 0

y = -2 ; y = 1

Substitute the value of y and solve for x.

y = x^(1/3)

-2 = x^(1/3) ; 1 = x^(1/3)

x = -8 ; x = 1

Therefore, the real roots of the equation is 1 and -8.

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What is the angle of turn clockwise from South East to North?

N

A 45°

B 135°

C 225°

D 315°

Answers

The angle of a turn clockwise from South East to North is Option B 135°.

When determining the angle of turn, it is important to consider the direction of rotation (in this case, clockwise) and the starting and ending points (in this case, South East to North).

If we imagine the compass as a clock, with North at the 12 o'clock position, South at the 6 o'clock position, East at the 3 o'clock position, and West at the 9 o'clock position. Then South East would be at the 4:30 position and the North would be at the 12 o'clock position. To rotate from 4:30 (South East) to 12 o'clock (North) in a clockwise direction, we would have to rotate 135 degrees. Thus, the angle of a turn clockwise from South East to North is 135 degrees.

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How do you draw a logarithmic graph?

Answers

Choose the range of values for the x-axis and the y-axis , Plot the points on the graph, using the logarithmic formula , Connect the points with a smooth curve and Label the axes and add any other details you want to include.

1. Choose the range of values for the x-axis and the y-axis. Select the minimum and maximum values for both the x-axis and the y-axis.

2. Plot the points on the graph, using the logarithmic formula. Use the formula log(x) = y to calculate the points that should be plotted on the graph. For example, if the x-axis range is from 1 to 10, and the y-axis range is from 0 to 10, then the first point would be (1,0).

3. Connect the points with a smooth curve. Once all the points have been plotted, use a ruler or a graphing calculator to connect them with a smooth curve.

4. Label the axes and add any other details you want to include. Use a ruler or a graphing calculator to label the axes and add any other details you want to include, such as a title, a legend, or a grid.

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Determine the vertical distance and the horizontal distance of point P and point Q. (a) P=4m Q=6m.​

Answers

if you dog like something

What i the cartoonit' purpoe in thi cartoon?

to convince people that fungal band are dangerou for beetle
to convince people that beetle are damaging to tree
to make people laugh at a play on word
to make people believe that longhorn beetle hate fungi

Answers

The cartoonist's purpose of the given cartoon is C: "to make people laugh at a play on the words".

Though the cartoon in the picture is designed based on the concept that fungal bands are an effective way of the biological control of Asian longhorn beetles, the core purpose of the cartoonist in designing this cartoon is to portray the idea in a comical way, indicating how these fungi actually form a music band called 'the fun guy' and they remove the beetles by playing their music, that awful racket as the beetle says.

Thus, the cartoonist's purpose of this cartoon is to make people laugh at a play on the words.

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-35PTS- what theorem can be used to prove these triangles are congruent

Answers

Answer:

Neither

----------------------------

We see two sides and one angle marked as congruent on both triangles.

The congruent angle is not included.

It means we can neither state it is ASA nor SAA as both of these require two congruent angles.

The mean length of 10 childrens' index finger is 6.8cm.
The mean length of 7 adults' index finger is 12.8cm.
What is the mean length (rounded to 2 DP) of these 17 people's index finger?

Answers

Answer:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

What is the coefficient of x³?

Answers

Let x equal the x³-1 coefficient. Thus, x=1 is the coefficient of the given function.

Coefficient definition.

A number or symbol that multiplies another number or symbol is referred to as a "coefficient" (used as a mathematical variable).

Give a co-efficient example in writing.

A coefficient is a result of multiplying an amount by a variable. 6z, for instance, is short for six times z. 6 is a coefficient since z is a variable. The coefficient is one for variables that don't have a value.

Let x equal the x³-1 coefficient. Thus, x=1 is the coefficient of the given function.

The expression's coefficient is the term multiplied by x³. Since x³ is not a word, the answer is 1.

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The full question should be:

What is the coefficient form of X³ 2 *?

15) 3x2 - x - 10 When this trinomial is factored completely, one of its factors is A) x 2 B) x - 5 C) 3x 5 D) 3x - 2

Answers

When the trinomial 3x² - x - 10 is factored completely, one of its factors is 3x+5.

Solving the given trinomial 3x² - x - 10.

=>3x² - 6x+5x - 10

=>3x(x-2)+5(x-2)

=>(3x+5)(x-2)

The two factors of the given trinomial 3x² - x - 10 is (3x+5) and (x-2), but according to the given options, the correct answer is option C - 3x+5.

Thus, When the trinomial 3x² - x - 10 is factored completely, one of its factors is 3x+5.

Complete question: 3x² - x - 10

When this trinomial is factored completely, one of its factors is

A) x + 2

B) x - 5

C) 3x + 5

D) 3x - 2

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solve 2+n=0(mod6)
solve2+(3+n)=1 (mod6)

Answers

Solving the modular arithmetic will result to

2 + n = 0 (mod 6): n = -22 + (3 + n) = 1 (mod 6): n = -4

What is modular arithmetic?

The term modular arithmetic is the arithmetic that works with whole numbers in a such that, following division by a modulus, all numbers are replaced by their remainders.

Solving the modular arithmetic: 2 + n = 0 (mod 6)

2 + n = 0 (mod 6)

n = -2

Solving the modular arithmetic: 2 + (3 + n) = 1 (mod 6):

2 + (3 + n) = 1 (mod 6)

5 + n = 1 (mod 6)

n = 1 - 5

n = -4

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Ellie bought snacks for her team's practice. She bought a bag of oranges for

$2. 66 and a 5-pack of juice bottles. The total cost before tax was $7. 46. Write

and solve an equation which can be used to determine j, how much each

bottle of juice costs?

Answers

The linear equation for jj is ($7.46 - $2.66) / 5 and the cost of each bottle of juice is $0.96.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The first step to take in order to determine jj, is to determine the total cost of the 5-pack of juice bottles.

Cost of the 5-pack of juice bottles = Total cost before tax - cost of the bag of oranges

Cost of the 5-pack of juice bottles = $7.46 - $2.66 = $4.80

The second step is to determine the cost of each bottle of juice

The cost of each bottle of juice = Cost of the 5-pack of juice bottles / total number of bottles

$4.80 / 5

= $0.96

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“Theresa’s Transportation” rental car company charges $30 to rent a car and $0.60 per mile for each rental. “Pete’s propulsions” rental car company charges $20 to rent a car and $0.85 per mile. After how many miles will it be more expensive to rent from Pete’s Propulsions than Theresa’s Transportation

Answers

On solving the provided question, we got to know that he fraction can bake 200/57 loaves or 3 29/57 loafs.

what is fraction?

Mathematically speaking, fractions are represented by integers that indicate a portion of a whole. In the same way that a whole can be any quantity, value, or object, a fraction can be a portion or subset of any quantity of a whole. As an example, let's try to comprehend this idea. The pizza in the picture below is cut into 8 equally sized pieces. The chosen slice of pizza might now be expressed as 1/8 if we wanted to. This indicates that we are talking about one of eight equally sized sections. It denotes a ratio of 1/8. Reading options include: One-eighth, or

1 by 8

13 1/3 divided by 3 4/5

Let's first convert these mixed numbers to incorrect fractions.

13 1/3 = 13(3) + 1 = 39 + 1 = 40/3

3 4/5 = 3(5) + 4= 19/5

Now that we have divided 40/3 by 19/5, we can just switch the operation to multiplication and flip the second fraction because we know how to divide fractions.

40/3 x 5/19 = 200/57

he can bake 200/57 loaves or 3 29/57 loafs.

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What are the values for the coefficients and constant term of 0 2 3x² 5x?

Answers

The coefficient of the expression 3x² is the number 3 and constant term is 20

What are the coefficients?

The coefficients are the numbers on the left side or before each variable.

What is an algebraic expression?

Is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

If the expression of a single term is:. 3x²

Then the only coefficient will be the number that is placed before it and it is:

Number 3

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PLEASE HELPP
mia has 3 bags the number of toys in each bag is 6, 8 and x what is the number of toys in the third bag if the average number of toys in the three bags is 6?

a. 3

b.6

c.4

d.8

Answers

Answer:

b

Step-by-step explanation:

i think b because it makes more sense than a or c

The answer here is b here’s hii

Which functions have an axis of symmetry of x = –2? Check all that apply.

f(x) = x2 + 4x + 3
f(x) = x2 – 4x – 5
f(x) = x2 + 6x + 2
f(x) = –2x2 – 8x + 1
f(x) = –2x2 + 8x – 2

Answers

The quadratic functions that have an axis of symmetry at x = -2 are given as follows:

f(x) = x² + 4x + 3.f(x) = -2x² - 8x + 1.

How to obtain the axis of symmetry of a quadratic function?

The standard definition of a quadratic function is given by the rule presented as follows:

y = ax² + bx + c, in which a is different of zero.

The axis of symmetry is given by the x-coordinate of the vertex, hence it's equation is defined as follows:

x = -b/2a.

Meaning that the correct options are given by the first and by the fourth options in this problem.

For the first function, we have that:

a = 1, b = 4.

Hence the axis of symmetry is obtained as follows:

x = -4/2 = -2.

For the fourth function, we have that:

a = -2, b = -8.

Hence:

x = -8/4 = -2.

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Seth built a wooden step stool out of two rectangular prisms and two cubes. Before fastening the components together, he stained each component to give it its final color.

To completely stain the bottom rectangular prism, Seth had to cover

square inches of wood. For one of the cubes to be completely stained, he had to cover

square inches of wood. To completely stain the top rectangular prism, he had to cover

square inches of wood.

Once the stool was fastened together, he applied a coat of sealant to all exposed surfaces of the stool, including the bottom, to cover a total of

square inches.

Answers

To complete stain the bottom rectangular prism, he needs to cover 624 square inches.

What is surface area?

A solid object's surface area is a measurement of the overall space that the object's surface takes up.

Given that:

Bottom rectangular prism:

Length = 22 in

Width = 8 in

Height = 6 in

The surface area of the rectangular prism is:

SA = 2( lh + wh + lw)

SA = 2((22)(6) + (8)(6) + (22)(6))

SA= 624 square inches.

To complete stain the bottom rectangular prism, he needs to cover 624 square inches.

Square:

Side = 4 in

The surface area of the cube is:

[tex]SA = 6a^2[/tex]

[tex]SA = 6 (4)^2\\\\SA= 96[/tex]square inches.

To completely stain two squares, he needs to cover 96 * 2 = 196 square inches.

Top rectangular prism:

Length = 18 in

Width = 5 in

Height = 2 in

The surface area of the rectangular prism is:

SA = 2( lh + wh + lw)

SA = 2((18)(2) + (5)(2) + (18)(5))

SA = 136 square inches

Hence to completely stain top rectangular prism, he needs to cover 136 square inches.

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3 Write an equation for each function, where x is the
number of months and y is the amount owed.
Mr. Allen's plan:
Mr. Jessup's plan:
rriculum Associates, LLC Copying is not permitted.
In
-L-
ODPPY LINAL

Answers

The y-intercept represents the loan amount initially. And the rate of change of the function will be negative The equation of Mr. Allen's plan will be y = - 80x + 560 and Mr. Jessup's plan will be y = - 40x + 400.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the graph, the y-intercept of the line represents the value of the loan initially.

From the graph, the slope of both lines is negative, then the rate of change of the function will be negative.

Let 'x' be the number of months and 'y' be the amount owed.

The two points are (0, 560) and (1, 480). Then the equation of the line is given as,

(y - 560) = [(560 - 480) / (0 - 1)](x - 0)

y - 560 = - 80x

y = - 80x + 560

And the equation of the line for Mr. Jessup's plan will be given as,

y = - 40x + 400

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What are the factors of the expression x² 4x 3?

Answers

The factors of the expression x² 4x 3 are (x + 3)(x − 3).

What is factor?

Factor is a number that can be multiplied to produce another number. Factors are used to find the greatest common factor (GCF) and least common multiple (LCM) of two or more numbers. Factors are also used in equations to find solutions and in algebra to solve polynomials. Factors are also important in computing, since they are used to identify prime numbers and prime factorisation.

This is determined by using the factoring technique called factoring by grouping.

First, the expression is written in two groups: x2 and 4x 3. Then, each group must be factored. For the first group, the factors are x and x, since any number multiplied by itself results in the number itself. For the second group, the factors are 4 and 3, since 4 multiplied by 3 equals 12.

Next, the two factors of each group must be multiplied together. The product of x and 4 is 4x, and the product of x and 3 is 3x. The product of 4 and 3 is 12.

Finally, the two groups of factors are combined to form the final expression: (x + 3)(x − 3).

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These tables correspond to inputs and outputs. Which of these input and output tables could represent a function rule, and which ones could not? ​

Answers

Table A is a function.

Table B is not a function.

Table C is a function.

Table D is not a function.

What is a function?

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

We know a relation is a function if it is one-to-one or many-to-one.

But a relation is not a function if it is one to many.

Table A is a function and it is a many-to-one function.

Table B is not a function as input 1 leads to two different outputs 1, - 1.

Table C is a function and it is a one-to-many function.

Table D is not a function as one input leads to 3 different outputs.

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The ratio of the sides of a triangle is 3:5:6. If the perimeter of the triangle is 154 feet, what are the side lengths?

Answers

The side length of the triangle are

33 feet55 feet66 feet

How to find the side length of the triangle

A triangle with given ratio of sides as 3 : 5 : 6 and a perimeter of 154 feet is calculated from the formula of perimeter which is

= a + b + c

where

a, b, and c are the dimensions of the side length of the triangle:

Using the values given in the problem we have

let the ratio be a multiple of x such that

154 = 3x + 5x + 6x

154 = 14x

x = 11

a = 3 * 11 = 33 feet

b = 5 * 11 = 55 feet

c = 6 * 11= 66 feet

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Luc is investigating dilations of scale factor 2 of the line y = -4x +3. He claims that for some centers of dilation, the line will remain the same. Which centers of dilation could be used to support Luc's claim? Select ALL that apply. ​

Answers

Luc is correct in stating that the line will remain the same with certain dilation centers, such as the origin (0, 0) and the point (3, -4). These centers of dilation will cause a scale factor of 2, but the line will remain the same.

To check if Luc is correct, we can calculate the points of the dilation with scale factor 2.

For the origin (0, 0):

Point A: (x, y) = (0, 3)

Point B: (x, y) = (-4, -3)

Dilated Point A: (x, y) = (0, 6)

Dilated Point B: (x, y) = (-8, -6)

Equation of the dilated line: y = -4x + 6

This shows that the line is dilated with scale factor 2, but is the same line.

For the point (3, -4):

Point A: (x, y) = (3, -1)

Point B: (x, y) = (-1, -7)

Dilated Point A: (x, y) = (6, -2)

Dilated Point B: (x, y) = (-2, -14)

Equation of the dilated line: y = -4x + 3

This shows that the line is dilated with scale factor 2, but is the same line.

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Simplify: [tex]\frac{32a^2bc^3}{20abc}[/tex]

Answers

The fractions is simplified to 8ac²/ 5

What is a fraction?

A fraction can be described as the part of a whole element, number or variable.

There are different types of fractions, which includes;

Improper fractionsProper fractionsMixed fractionsComplex fractionsSimple fractions

Examples of improper fractions; 5/3, 7/5

Examples of proper fractions; 3/4, 5/6

Examples of mixed fractions; 3 1/2, 4 5/6

Examples of simple fractions; 1/2 , 1/ 4

From the information given, we have that;

[tex]\frac{32a^2bc^3}{20abc}[/tex]

This is simplified to;

32 × a × a × b × c × c × c/ 20 × a × b × c

Divide the common terms

8ac²/ 5

Hence, the fractions is 8ac²/ 5

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Find The Rate Of Change Y=x4 +5 (2024)

FAQs

How do I find the rate change? ›

Rate of change problems can generally be approached using the formula R = D/T, or rate of change equals the distance traveled divided by the time it takes to do so. Depending on the context involved in the problem, the change in distance can be replaced with a different variable, such as the change in value or price.

What is the rate of change of y 5x 4? ›

Rate of change of the equation y = 5x + 4 can be obtained by differentiating it with respect to x. Hence, rate of change of y = 5x + 4 is 5.

What is the rate of change of y 2x? ›

What is the average rate of change of y = 2x? The average rate of change of y = 2x is 2. Since it is a linear function, the average rate of change is just the function's slope. In this case, for every change in the x-coordinate, the y-coordinate will double it.

What is the rate of change of the function y =- 7 4x 2? ›

Expert-Verified Answer

The requried rate of change of the function y = -7/4x - 2 is -7/4.

How to calculate rate of change of y? ›

To find the average rate of change, we divide the change in y (output) by the change in x (input). And visually, all we are doing is calculating the slope of the secant line passing between two points.

How to find the rate? ›

To find a rate in math, divide the value of the dependent variable by the value of the independent variable. Then, reduce the fraction if possible.

What's the slope of y=5x+4? ›

The slope of y = 5x - 4 is 5.

Thus, it is in slope-intercept form. When the equation of a line is in slope-intercept form, we know that the slope of the line is equal to m, the coefficient of x. In y = 5x - 4, the coefficient of x is 5. Thus, the slope of the line, y = 5x - 4, is 5.

What is the rate of change function in math? ›

The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.

What is rate of change in math slope? ›

The rate of change for a line is the slope, the rise over run, or the change in over the change in. The slope can be calculated from two points in a table or from the slope triangle in a graph.

What is the rate of change of y 2x 4? ›

In the equation y = 2x + 4, the coefficient of x, which is 2, represents the slope of the line and therefore the rate of change. Hence, the rate of change of y = 2x + 4 is 2.

What is the rate of change of the function y =- 5 2x 1? ›

Expert-Verified Answer

The rate of change or slope of the function y = -5/2x - 1 is -5/2. This indicates a decrease in 'y' of 2.5 for each unit increase in 'x'.

What is the rate of change of the function y =- 2x + 2? ›

Final answer: The rate of change in the function y = -2x - 2 is -2, which represents the slope of the graph of the function. It provides the relationship between changes in x and y.

How do I solve for rate of change? ›

The average rate of change represents a measurement that can provide insight into a variety of applications. From finance and accounting to engineering applications, you can calculate the average rate of change using the simple algebraic formula: (y1 - y2) / (x1 - x2).

What is the rate of change of the function y = 3 4x + 2? ›

Final answer:

The rate of change of the function y = 3/4x - 2 is 3/4.

What is the formula for the rate of change 7th grade? ›

Let y represent the dependent variable and x represent the independent variable, then the formula for the rate of change is ( y 2 − y 1 ) / ( x 2 − x 1 ) .

How do you calculate price rate of change? ›

✅ The price rate of change (ROC) indicator is a technical analysis tool used to measure the percentage change between the most recent price and an earlier price. (Source: Investopedia) ✅ The formula for calculating ROC is [(Current Price - Price n periods ago) / Price n periods ago)] x 100. (Source: TradingView)

How do you calculate the price change rate? ›

How Do I Calculate Percent Change? If you are tracking a price increase, use the formula: (New Price - Old Price) ÷ Old Price, and then multiply that number by 100. Conversely, if the price decreased, use the formula (Old Price - New Price) ÷ Old Price and multiply that number by 100.

How do you find the percent rate of change? ›

To find the percent change, you first subtract the earlier index value from the later one, then divide that difference by the earlier index value, and finally multiply the result by 100.

How do I calculate the rate of increase? ›

How to Calculate Percent Increase. To the find the percent increase, first subtract the initial value from the final value. Then take the difference and divide it by the initial value. Finally, multiply this number by 100% to convert the number to a percentage.

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