Calculate the rate of change for each linear function. Determine which linear function has a greater rate of change.







a. Rate of change for linear function A:
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b. Rate of change for linear function B:
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Answer:

              Since you are looking for an equation to represent the pattern, the correct equation in y = mx + b form would be y = 4x - 3.

Step-by-step explanation:

              It's important to look for two things in order to write a slope-intercept form equation: the rate of change, and the beginning value.

              First thing we can start with is the rate of change, which can be found by simply selecting any two points - or in this case terms - and find the difference between term values and term number, and then divide them by each other to find the rate of change. To make things easy, we can just use terms 1 and 2. Term 1 has a term 1 value of 1 block, while term 2 has a value of 5 blocks. In order to find the rate of change, we first find the difference in term value (5 - 1 = 4 blocks), then find the difference in term numbers (2 - 1 = 1 term), and lastly divide the difference in term value by the difference in term number (4 ÷ 1 = 4 blocks per term), which is your rate of change. Note that 4 is the number of blocks each term increases by when the term number increases by 1, and not the total number of blocks in each term.

           Now that we know the rate of change, we can input it into the base equation, which will become y = 4x + b. Now we only need to find b. The simple way to solve for b would be to use a single term as reference, and plug in its term number and value into the equation and calculate b. Once again, it's easier to just use the lowest one, which would be term 1, with a term number of 1, and a term value of 1. By inserting these values, we'll get an algebraic equation to solve for b, which is 1 = 4(1) + b or 1 = 4 + b. Now, we just need a value for b that would make 4 + b equal to 1, which would be b = 1 - 4 = -3, so b would equal -3. Which means the final equation to represent this situation would be y = 4x - 3.

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Answer:

Assuming you are looking for an expression to represent the area of the rectangle, as you didn't provide any values for the length or width, the area of the rectangle is [tex]x^{2} +4x[/tex] [tex]un^{2} .[/tex]

Step-by-step explanation:

          The formula for the area of a rectangle is [tex]a=lw[/tex], where [tex]l[/tex] represents the length of the rectangle, and [tex]w[/tex] represents the width. We are given that the length of the rectangle is 4 units longer than its width, so we can set the width to be represented by the variable [tex]x[/tex], and we get that the length and width are [tex]x+4[/tex] and [tex]x[/tex] respectively. As we are trying to find the area of the rectangle, we have to multiply the length and width of the rectangle together, which then we will get that the area of the rectangle is [tex]x(x+4)=x^{2} +4x[/tex] [tex]un^2.[/tex]

          If your teacher or whatever website you're using requires a specific variable, you can just replace the [tex]x[/tex] in the expression to whatever you need.

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

  y = 6x -5

Step-by-step explanation:

You want the equation of the line through (1, 1) that is parallel to the line y = 6x -7.

The parallel line will have the same slope. In this slope-intercept form, that means the x-term is the same. The constant is chosen to make the line pass through the given point:

  y = 6x +b . . . . . . . . . . . . . . where 'b' is the new y-intercept

  b = y -6x = 1 -6·1 = -5 . . . . solve for b, use (x, y) = (1, 1)

The desired equation is ...

  y = 6x -5

The equation that shows how the number of square feet the painter can cover, y, depends on the number of gallons of paint available, x is y = 400x.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

A house painter knows that he can cover 400 square feet with a gallon of paint.

Let x be the number of gallons of paint.

Let y be the number of square feet the painter can cover.

Number of square feet the painter can cover with 1 gallon of paint = 400

Number of square feet the painter can cover with x gallon of paint = 400x

So y = 400x

Hence the required equation is y = 400x

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The probability of drawing a green marble and replacing it is 2/10 = 1/5.

Since the marble is replaced, the probability of drawing a red marble on the second draw is still 3/10.

The probability of both events occurring is the product of their individual probabilities:

1/5 * 3/10 = 3/50

So the probability of drawing a green marble, replacing it, and drawing a red marble is 3/50.

The value of the angle P is 107°

Consecutive angles, also called contiguous or adjoining angles, are angles that have a common side and the same vertex.

They are located next to each other and share a side and vertex. The sum of the consecutive angles is equal to the angle formed by the non-common sides of the angles.

Consecutive angles are also adjacent angles, which means that the other two sides are opposite rays.

Given that, a figure, we need to find the measurement of the angle P,

We know that, the consecutive angles between the parallel lines are supplementary, so,

∠M + ∠P = 180°

7x+31 + 21x-19 = 180

28x = 180-12

28x = 168

x = 6

Therefore,

∠P = 21(6)-19 = 107

Hence, the value of the angle P is 107°

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Answer:

90.00%

Step-by-step explanation:

Answer:

90% is quarters

Answer:

Could you upload the whole picture? I think I can help but I don't understand what's it's asking.

Step-by-step explanation:

..

The sum of 17.25 and 1.725, to the nearest integer, is 19.

First, let's add the two numbers together: 17.25 + 1.725 = 19.975

Next, we need to round the sum to the nearest integer. To do this, we need to look at the tenths place of the number. Since the tenths place is a nine, we need to round up to the nearest integer.

In this case, the nearest integer is 19.

To check our answer, we can add the two numbers together again using a calculator and confirm that the answer is 19.

To make sure we understand how to round to the nearest integer, let's look at another example. If we add 3.45 + 2.735, the sum is 6.185.

Looking at the hundredths place, we see that it is a five. Since five is greater than or equal to five, we need to round up to the nearest integer.

In this case, the nearest integer is 7.

To check our answer, we can add the two numbers together again using a calculator and confirm that the answer is 7.

In summary, to round a number to the nearest integer, we need to look at the tenths place. If the tenths place is greater than or equal to five, we round up to the nearest integer. If it is less than five, we round down to the nearest integer.

Therefore, the sum of 17.25 and 1.725, to the nearest integer, is 19.

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The sum of 17.25 and 1.725 is 18.975. To the nearest integer, this number is rounded up to 19.

Rounding to the nearest integer involves finding the closest whole number to a decimal or fractional number. When the decimal portion of a number is greater than or equal to 0.5, the number is rounded up to the next whole number. When the decimal portion of a number is less than 0.5, the number is rounded down to the previous whole number. In this case, the decimal portion of 18.975 is greater than 0.5, so the number is rounded up to 19.

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we are given that circle A has a secant EC and a tangent BC that intersect at point C. We are also given that mEB = 166° and mBD = 80°. Our task is to find the measure of angle ZBCD, which is formed by the intersection of secant EC and tangent BC.

To find mZBCD, we first need to find mECB. Since EC is a secant and BC is a tangent to circle A, and EC and BC intersect at C, we know that:

mECB = mBEC (because they are opposite angles formed by intersecting lines)

Also, mBEC = 180° - mEB (because BEC is a straight line)

So, mECB = 180° - mEB = 180° - 166° = 14°

Since mBD is 80°, we have:

mZBCD = mECB + mBD = 14° + 80° = 94°

So, mZBCD = 94°. This means that angle ZBCD is 94°.

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1) Vertex -  A,B,C,O,Q,F

2) Points in the interior of ∠COB - Q,F

3) Sides of ∠2 - side OC and side OA.

What is Interior angles?

Interior angles can be generated in two methods in geometry. The first occurs within a polygon, whereas the second occurs when parallel lines are cut by a transversal. Angles are classified into many sorts based on their measurements.

1) Vertex of angles would be A,B,C,O,Q,F

2) The points in the interior of ∠COB would be, Q,F

3) The sides of ∠2 would be, side OC and side OA.

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The Mean likely to be a better measure of the center of the data set.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Since Median represents the middle value of the given data when arranged in a particular order.

The measure of central tendency is the value that best describes a data set.

The measure of central tendency could be the mean, mode, and median

Recall that the best measure of central tendency is the mean

In this exercise, since the data values and the frequency of occurence, the measure of center that best describes the set of data in the table is the mean (Average).

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The equation of the line passing through (1,5) and parallel to y = 3x - 1 is   f(x) = 3x + 2

The equation of a line can be formed with the help of the slope of the line and a point on the line.

The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis.

Parallel lines have the SAME SLOPE.  Since the formula is in the form y=mx+b, the slope. m. is 3.

The line is y = 3x + b and goes through (1,5), so, let's determine b:

  5 = 3(1) + b

  2 = b

 Hence, the equation of the line is f(x) = 3x + 2

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Answer: equivalent

To determine if two expressions are equal, we can set them equal to each other and simplify if possible.

12d + 8r = 2(5d + 4r) + 4d

Expanding the right-side expression:

12d + 8r = 10d + 8r + 4d

Combining like terms:

12d + 8r = 14d + 8r

Subtracting 8r from both sides:

12d = 14d

Subtracting 12d from both sides:

0 = 2d

Dividing both sides by 2:

d = 0

So the expressions are equal if d = 0, meaning if the coefficient of the variable d is 0 in both expressions. If d is not 0, then the expressions are not equal.

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's call the height of the ladder "h" and the distance from the wall to the base of the ladder "d".

From the problem, we know that the ladder forms a 42° angle with the ground. This means that the sine of the angle is equal to the opposite side (h) over the hypotenuse (41 inches):

sin(42°) = h/41

We can solve for h by multiplying both sides by 41 and taking the sine of 42°:

h = 41 × sin(42°)

h ≈ 28.61 inches

So the top of the ladder is about 28.61 inches from the ground.

To find the distance from the wall to the base of the ladder, we can use the cosine of the angle:

cos(42°) = d/41

We can solve for d by multiplying both sides by 41 and taking the cosine of 42°:

d = 41 × cos(42°)

d ≈ 31.15 inches

So the base of the ladder is about 31.15 inches from the wall.

The missing angle measures are given as follows:

b = c = 137º.

Vertical angles are angles that are opposite by the same vertex in crossing segments, and these angles are congruent.

The vertical angles in this problem are:

b and c.

Additionally, these angles form a linear pair with the angle of 43º, meaning that they are supplementary, with a sum of their measures of 180º, hence their measures are given as follows:

b + 43º = 180º

b = 180º - 43º

b = 137º.

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Answer:

340

Step-by-step explanation:

[tex]2(5 + 3(10 + 5(12 - 3)))[/tex]

let's start with:

[tex]5(12 - 3)[/tex]

[tex](12 - 3) = 9[/tex]

[tex]5(9) = 45[/tex]

let's rewrite the question now while removing the solved brackets and substituting it with 45

[tex]2(5 + 3(10 + 45))[/tex]

[tex]3(10 + 45)[/tex]

[tex](10 + 45) = 55[/tex]

[tex]3(55) = 165[/tex]

let's rewrite the question and do the same thing as before

[tex]2(5 + 165)[/tex]

[tex]2(5 + 165)[/tex]

[tex](5 + 165) = 170[/tex]

[tex]2(170) = 340[/tex]

The equation is P(t)= 97(0.875)t, where t is the number of years since 2021 and P(t) is the population at time t.

The animal population's change through time is modelled by the function P(t) = 97(0.875)t, where P(t) is the population at time t and t is the number of years since 2021. The function is based on the assumption that the population declines by 12.5% annually. As a result, starting in 2021, the population will fall by 12.5% year. The initial population in 2021 (97) must be multiplied by 0.875t in order to determine the population at any given year t. You will receive the population at that specific year from this. For instance, 97(0.875)5 = 60.2 will be the population in 2026 if t = 5. Accordingly, the population fell from 97 to 60.2 after five years. We can track and research population changes by using this function to anticipate the animal species' population over time.

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After rewriting the expression [tex]4 ^ {( 2x -4)}[/tex] using distributive property, [tex]4^{2x} . 4^{-4}[/tex] is the equivalent expression.

In mathematics, it is acceptable to multiply, divide, add, or negate. The construction of an expression looks like this: Amount, a mathematical operator, and an expression A mathematical expression's variables can be numbers, amounts, or functions (such as addition, subtraction, multiplication or division etc.)

Contrasting concepts and language is typical practice. Any mathematical statement that rates systems, numbers, and then an arithmetic operation between them is referred to as an expression, sometimes known as a formula. For instance, the arithmetic operator + separates the word m from the terms 4m and 5 in the balanced formula, just as it does for the variable m in the phrase 4m + 5.

given

Expressions that are equivalent do the same thing even when they have distinct appearances.

Two quadratic expressions that are analogous have the same value when we use the same value for the variable.

[tex]4 ^ {( 2x -4)}[/tex]

[tex]4^{2x} . 4^{-4}[/tex]

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The construction of similar triangles are given in attached figure.

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Similar shapes are shapes whose lengths are in an equivalent ratio. Triangle ABC and triangle DEF are similar because the side lengths of both triangles are in an equivalent ratio (refer to the attachment).

Step 1: Draw a random triangle ABC

The lengths of two sides and an angle are:

AB=10

BC=6

C=90

Step 2: Draw and measure the length of DE

DE=15

Step3: Calculate the ratio

The corresponding line segment to DE is line segment AB.

So, the ratio (k) is:

k= DE/AB

k= 15/10

k=1.5

Step 4: Multiply the ratio by the other line segment in step 1

In (1), we have:

BC=6

So,

EF=k*BC

EF=1.5*6

EF=9

Step 4: Draw a circle with center F and radius EF  

The center of the circle is point F and the radius of the circle is 9 units

Step 5: Draw a ray from the center (i.e. point F) to DE

Refer to the attached image for

Triangle ABC

Triangle DEF

Circle with center F and radius 9

Ray from F to DE

Therefore, construction of similar triangles are given in attached figure.

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Answer:

Length = 5 cm

Width = 3 cm

Step-by-step explanation:

Part (a)

Length L = c

(i) Width W = c- 2 (width is 2 cm less than width)

(ii) Area of the rectangle = L x W
= c(c - 2) = c² - 2c

Part (b)
Area is given as 15 cm²

Therefore, c²- 2c = 15

Part (c)

The equation for area from part (b) is

c² - 2c = 15

Carry 15 to the left side by subtracting 15 from both sides:
c²- 2c - 15 = 15 - 15

c²- 2c - 15 = 0

This is a quadratic equation which can be solved easily by factoring

The factors of the constant 15 are 5 and 3
The constant is product of the factors is -15; so one of the numbers is negative

The sum of the numbers is the coefficient of c

Since this -2, the numbers are -5 and 3

Therefore the factorization of the equation

c² - 2c - 15 = (c + 3)(c - 5)

And since c² - 2c - 15 = 0 this means  (c + 3)(c - 5) = 0

So either c + 3 = 0 ==> c = -3 which can be rejected because length cannot be negative

This gives us
c - 5 = 0

Or c = 5

So length = 5 cm

Since width = c - 2

width = 5 - 2 = 3

Length = 5

Width = 3

According to algebra properties, the following properties are used in the resolution of a linear equation:

Step 2: compatibility with multiplication.

Step 3: existence of multiplicative inverse, associative and modulative properties and definition of multiplication.

Step 4: existence of additive inverse.

Step 5: associative and modulative properties and existence of additive inverse.

Herein we find the case of a linear equation with one variable, that must be cleared by algebra properties. First, write the entire equation:

8 · (y + 3) = - 16 / 8

Second, use compatibility with multiplication:

8 · (y + 3) / 8 = - 16 / 8

Third, apply existence of multiplicative inverse, associative and modulative properties and definition of multiplication:

y + 3 = - 2

Fourth, use existence of additive inverse:

y + 3 - 3 = - 2 - 3

Fifth, use associative and modulative properties and existence of additive inverse:

y = - 5

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The equivalent fractions for their ratios are given as follows:

Hence, due to the higher numerator, Puja Limbu had the better performance.

Equivalent fractions are fractions that have the same denominator.

The fractions for this problem are given as follows:

The common denominator is the least common multiple of 10 and 15, which is of 30, hence the equivalent fractions are given as follows:

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Answer:

440cm (to 3 s.f.)

Step-by-step explanation:

circumference= πd

= π×140

= 440cm (to 3 s.f.)

After 4 weeks the amount of coffee that Marshall will have left would be = 20 ounces.

The amount of ground coffee that Marshall bought for his office machine = 40 ounces

The quantity of coffee he uses per week in his office = 5 ounces.

Therefore for 4 weeks would be= ?

But, 1 week = 5 ounces

4 weeks = X

make X the subject of formula;

X = 5×4 = 20 ounces

The amount of ground coffee that will remain = 40-20 = 20 ounces.

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The two system of linear equation with two variables has unique solution if and only if ( a₁ / a₂ ) ≠  ( b₁ / b₂ )  ≠  ( c₁ / c₂ ).

Let us consider two linear equation with two variables 'x' and 'y'.

Number of equations are same as number of variables

⇒We have two system of linear equation that is :

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

Condition for system of linear equation has unique solution is:

( a₁ / a₂ ) ≠  ( b₁ / b₂ )  ≠  ( c₁ / c₂ )

⇒ lines intersect at one point gives unique solution.

Therefore, the linear system of equation with two variables representing it has unique solution by ( a₁ / a₂ ) ≠  ( b₁ / b₂ )  ≠  ( c₁ / c₂ ).

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B) The alpha value of the reliability coefficient is one way to establish the validity of a questionnaire.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

The alpha value of the reliability coefficient, also known as Cronbach's alpha, measures the internal consistency of a questionnaire. It indicates how well the items on the questionnaire are related to each other and form a consistent measure of the concept being assessed. A high alpha value indicates that the items on the questionnaire are measuring the same underlying concept and that the questionnaire is reliable.

Correlation between the score on the questionnaire and another measure of the same concept (Option A) and consistency by which multiple subjects are able to complete the questionnaire without error (Option D) can also provide information about the reliability of a questionnaire.

The alpha value of the reliability coefficient is one way to establish the validity of a questionnaire.

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The possible definitions of f(x) and g(x), considering the composition of the functions, are given as follows:

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

The functions for this problem are defined as follows:

As the composition of the functions is then given as follows:

[tex]h(x) = f(g(x)) = f(8x + 6) = \sqrt{8x + 6}[/tex]

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By applying the Isosceles trapezoid concept, it can be concluded that the value of CP is 1.1 units.

Isosceles trapezoid has four sides, in which the two opposite sides (bases) are parallel to each other and the other two sides are equal in length but non-parallel to each other. The diagonals of an isosceles trapezoid are congruent.

We have an isosceles trapezoid with:

Length BD = 2.8 = diagonal

Length AP = 1.7 where P is the center

Since the diagonals of an isosceles trapezoid are congruent, so BD = AC = 2.8

Meanwhile AC = AP + CP. If we substitute the value of AC and AP, we got the value of CP:

CP = AC - AP

     = 2.8 - 1.7

     = 1.1

Thus, the value of CP is 1.1 units.

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The statement that are true about the function and its graph is "The graph of the function is a parabola " , the correct option is (b) .

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

In the question ,

it is given that ,

the quadratic function is f(x) = x² – 5x + 12 .

for x = -10 ,

f(-10) = (-10)² – 5(-10) + 12

= 100 + 50 + 12

= 162

option(a) is false .

the graph of the quadratic function is shown below .

form the graph we can see that the graph is a parabola ,

and the function opens upwards ,

the graph does not contain the points (20,-8) and (0,0)

Therefore , The statement that are true about the function and its graph is "The graph of the function is a parabola " , the correct option is (b) .

The given question is incomplete , the complete question is

Consider the quadratic function f(x) = x² – 5x + 12. Which statement is true about the function and its graph?

(a) The value of f(–10) = 82

(b) The graph of the function is a parabola.

(c) The graph of the function opens down.

(d) The graph contains the point (20, –8).

(e) The graph contains the point (0, 0).

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