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The sum of 4 consecutive integers is 254. What is the value of the greatest integer?

Let

x -----> the first integeer

x+1 ----> second integer

x+2----> third integer

x+3 ----> fourth integer

we have that

x+(x+1)+(x+2)+(x+3)=254

solve for x

4x+6=254

4x=254-6

4x=248

x=62

therefore

the greatest integer is x+3

so

62+3=65

Recall that the slope-intercept form of the line equation is of the form y=mx+b, where m is the slope and b is the y-intercept.

To transform the equation 10=-2y-x into the slope-intercept form we should apply algebraic operations so we isolate the y on one side of the equation.

Let's add x on both sides, we get

Now, lets divide by -2 on both sides, we get

we see that this now has the slope-intercept form, where the slope is m=(-1/2) and b=-5

7. The unit cost for a piece of fabric is $4.99 per yard including tax. You have $30 to spend on material. How many whole feet of material can you buy?

we know that

1 yard --------> cost $4.99

so

x yards ------> $30

Applying proportion or rule of three

x=30/4,99

x=6.01 yd

answer 6 yards

Answer:

10 (duh)

Step-by-step explanation:

A rational number can be said to be a number that is expressed as a quotient of s fraction. The denominator of a rational number must be a non-zero number.

You can simply say a rational number is any number that can be written as a fraction.

To find the number when added to 5 produces a rational number, we have:

A. 5.38516480...

This number has infinite decimal so it is an irrational number

B. 10

10 + 5 = 15

This is not a rational number

C. 0

0 + 5 = 5

This is not a rational number

D. 0.22

0.22 + 5 = 5.22

This is a rational number because it can be written as a fraction

Therefore, the number that produces a rational number when added to 5 is 0.22

ANSWER:

D. 0.22

The value of x for the ordered pair (x,0) is 0. B is the correct option.

What is ordered pair?

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

Given function is

y = 200 tan x.

Given ordered pair is (x,0).

The value of y for the given ordered pair is 0.

The value of tangent function is increasing with increase the value of degree.

The value of tangent at 0 degree is 0 that is tan 0 = 0.

If we multiply a number with zero it returns 0.

The possible value of x is 0.

Hence option B is the correct option.

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The boxplot that shows points that Dwight scored in each game has a minimum value of 1 point and a maximum value of 20 points.

The box plot that shows the points that Ron scored in each game, has a minimum value of 4, and a maximum value of 18 points.

The values below the minimum point and above the maximum point of the data set can be considered "outliers", i.e. atypical observations, and the probability if them being observed is very low.

Ron's box plot goes from 4 to 18 points, it is very unlikely for him to score less than 3 points or above 18, both scores would be considered "outliers" for him.

But, Dwigth's box plot goes from 1 to 20, which means that "scoring less than 3 on a game" or "scoring more than 18 on a game" are more possible situations for him.

So Dwight is more likely to score more than 18 points on a game and he is also more likely to have a very bad game and score less than 3 points.

Let's begin by listing out the information given to us:

Old Price = $54

New Price = $74

The percentage change is given by:

EXPLANATION :

From the problem, we have two events :

Event A : rolling an even number {2, 4, 6}

Event B : rolling a number greater than four {5, 6}

1. Union of A and B is the combination of Event A and B

Since there's a common element, 6, we will take this as one only.

That will be {2, 4, 5, 6}

2. Intersection of A and B is the common element between the two events.

So that is {6}

3. Complement of A is the set of elements that is NOT present in Event A.

Since a cube has 6 sides, the elements are {1, 2, 3, 4, 5, 6}

The complement of A will be {1, 3, 5}

4. Event B, from the data we have from above, B will have {5, 6}

There is no mistake in Chase solving steps.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.

We have a equation :

(1/3)(g - 3) = 3

We can write -

(1/3)(g - 3) = 3

We can write -

g - 3 = 3 x 3

g - 3 = 9

g = 12

Therefore, there is no mistake in Chase solving steps.

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Given equation:

Let's solve the question to identify the type of solution.

Using factorization method:

The solution is thus

Hence, there is one solution and it is real.

Answer: 1 real (Option B)

Answer:

A. as x→∞, y→∞ as x→−∞, y→−∞

Explanation:

Given the function:

In order to determine the end behavior of f(x), we use the leading coefficient test.

When using the Leading coefficient test, the following rule applies:

• When the ,degree is odd and the leading coefficient is positive,, the graph falls to the left and rises to the right.

• When the ,degree is odd and the leading coefficient is negative,, the graph rises to the left and falls to the right.

• When the ,degree is even and the leading coefficient is positive,, the graph rises to the left and right.

• When the ,degree is even and the leading coefficient is negative,, the graph falls to the left and right.

From the function, f(x):

• The degree of the polynomial = 3 (Odd)

• The leading coefficient is 2 (Positive)

Thus, using the 1st rule of the 4 given above, we have that as x→∞, y→∞ as x→−∞, y→−∞.

The correct option is A.

a)

Given:

The equation is,

The objective is to sketch the graph of the equation.

Since, the highest degree of the equation is 1, it could be a straight line. The general equation of straight line is,

Here, m represents the slope of the equation and c represents the y intercept. Then comparing the both equations,

Substitute, y = 0 in the given equation.

Thus, at y = 0, the value of x = 5.

Using the coordinates (5,0) and y intercept c = 7, the graph will be,

Hence, the required graph is obtained,

From the information given, the entrance to a state park costs $5 per vehicle, plus $2 per person in the vehicle. Given that 4 people entered the one vehicle, the amount that would be paid for the vehicle is $5. Sinec it is $2 per person, the amount for 4 persons would be 2 * 4 = 8

Thus, the total cost would be

5 + 8 = $13

aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2 is the solution of aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1

Recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms

aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1

Homogenous case,

aₙ -2aₙ₋₁ + aₙ₋₂ with characteristic t²-2t-1=0

t=1

aₙ=C₁.(1-√2)ⁿ+C₂.(1+√2)ⁿ

Special case, Since non homogenous part is 2n+1

Let aₙ=pn+q, then

aₙ -aₙ₋₁ + aₙ₋₂=2n+1

pn+q-2(p(n-1)+q)-p(n-2)-q=2n+1

-2pn+qp-2q=2n+1

p=-1 and q=4p-1/2=-5/2

Combine both cases, aₙ = C₁(1-√2)ⁿ+C₂((1+√2)ⁿ-n-5/2

Substitute a₁=7 and a₂=19

a₁ = C₁(1-√2)+C₂((1+√2)-1-5/2

a₁ = C₁(1-√2)+C₂((1+√2)-7/2=7

(C₁+C₂)+(C₂-C₁)√2)=21/2..(1)

a₂ = C₁(1-√2)²+C₂((1+√2)²-2-5/2

= C₁(1-√2)²+C₂((1+√2)²-9/2=19

3(C₁+C₂)+2(C₂-C₁)√2)=97/2..(2)

By solving 1 and 2 we get

C₁=1/2(5/2-4√2)

C2=1/2(5/2+4√2)

aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2

Hence, aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2 is the solution of aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1

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Write a function with vertical asymptote x=4, horizontal asymptote y=1, y intercept at (0,2).

A possible function can be express as:

Let's prove that this function fulfils our conditions. Let's start with the y-intercept, we know that this happens when x=0, then we have:

Hence the y-intercept is at (0,2).

Now, we know that a rational function has horizontal asymptote y=b if:

Let's find these limits:

and:

This means that we have a horizontal asymptote y=1 as we wanted.

Now, a rational function has vertical asymptote at x=a if:

to determine the value of a we need to look where the function is not defined, that is, the values which make the denominator zero, in this case we have:

Then we need to find the limits:

Now, if we approach the value x=4 from the left we notice that as x gets closer to 4 the function gets bigger and bigger, for example:

if we follow this procedure, we conclude that:

Similarly, if we approach x=4 from the right the function gets smaller and smaller, for example:

Then we can conclude that:

Hence, we conclude that the function we proposed has a vertical asymptote x=4 like we wanted.

the properties we gave can be seen in the following graph:

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following expression:

We simplify as follows:

In the question, we are given that 6 garbage trucks can collect the trash of 36 homes in a day. We can find how many trucks are needed to collect in 180 houses below.

Explanation

Answer: 30 trucks

The domain of a function is the set of values where the function is defined (values of x where y is defined).

The range of a function are the values of the function where is defined (values of y).

For the given function:

Domain: values of n {6,-8, 4, 2}

Range: values of k(n)

n= 6

n=-8

n=4

n=2

Then, the range is: {-16, 26, -10, -4}

Question:

Use the graph to write a linear function that relates y to x

Solution:

To find the linear function that relates y and x in the above graph, we have to know that a linear function is given by the following formula:

where m is the slope of the line and b is the y-coordinate of the y-intercept (when x = 0). Now, notice that in this case, when x = 0 then y= 2, thus we can conclude that b = 2 and:

On the other hand, by definition, the slope of the line is given by:

where (X1,Y1) and (X2, Y2) are any two points on the line. Take for example:

(X1,Y1) = (0,2)

(X2,Y2) = (6,10)

then, replacing this data in the equation of the slope, we obtain:

then, using the slope obtained above, we can conclude that the equation of the linear function is:

The meaning of;

In algebra, when there is an unknown number it is generally represented by a letter (such as x,y,z etc.)

The letters x in x/4 represents an unkown number.

So, x/4 represent the unknown number x divided by 4.

For example; if x=20, then;

The value of x is 50 for which line l is parallel to line m and the angles are equal by the properties of parallel lines that is vertically opposite angles are equal.

Two lines (in the same plane) are said to be parallel if they never collide, regardless matter how far they are extended on either side. Parallel lines travel parallel to each other, like train tracks. Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. Parallel lines can be found in everyday life, such as zebra crossings, notepad lines, and railway tracks.

Here,

Since l ⇵ m,

Vertically opposite angles are equal by the properties of parallel lines.

2x-5=95

2x=100

x=50

The value of x is 50, which means that line l is parallel to line m and the angles are equal according to the property of parallel lines, which states that vertically opposing angles are equal.

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ANSWER

EXPLANATION

First we have to find the partial products by multiplying each term of the first polynomial by each term of the second polynomial:

Now the second term of the second polynomial:

And now we just have to add these partial products:

Answer: 80

Step-by-step explanation:

= 72/90

= 72/0.9

= 80

For point A, you just have to replace t by a in the given function, like this

For point B, you just have to replace t by a+2 in the given function, like this

You have to determine the solution of the equation system by looking at the graph.

For any equation system there are three possible scenarions, that the system has "no solution", that the system has "infinite solutions" and that the system has "one solution"

Looking at the graph you can determine which situation if:

- both lines are parallel, they never meet, which indicates that the system has no solution.

- both lines are superimposed, i.e. they seem as if there is only one line, the system has infinite solutions.

- both lines cross at one point, this indicates that the system has only one solution and the solution will be the point where the lines intersect.

In the given graph, the lines cross at one point, which means that the system has one solution. To determine said solution you have to read the x and y coordinates of the point in the grid.

The lines meet at x=4 and y=2, which means that the solution of this system is a

we have

solve for d

therefore