What is the range of the function

The answers are :

a) The average price of a new home (y) is given by a linear equation which is y = -800x + 294000.

b) The average price of a new home in year 2014 will be $286000.

What is the point slope form of a line ?

Point slope form is used to represent a straight line using its slope and a point on the line.

a)

We know that the two point -slope form of a line is given by :

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex])

where : m is slope and represented by

m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]

As per the questions hint is that two points that is (-2 , 11) and (1 , -4).

These points can be represented by :

([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (0 , 294000)

([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (7 , 288400)

So : the slope will be :

m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]

m = [tex]\frac{288400-294000}{7 - 0}[/tex]

m = -5600 / 7

m = -800

So , the point -slope form of line will be :

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex])

y - 294000 = -800 ( x - 0)

y - 294000 = - 800 x

or

y = -800x + 294000

So , the average price of a new home (y) is given by a linear equation which is  :

y = -800x + 294000

b)

As per the question y is the average price of a new home in year x and is given by :

y = -800x + 294000

It is given that x = 0 meant year 2004. So , for year 2014 value of x will be x =10.

Substituting this value to get the value of y or average price of a new home in year 2014 , we get :

y = -800x + 294000

y = - 800 × 10 + 294000

y  = -8000 + 294000

or

y = $ 286000

Therefore  , the answers are :

a) The average price of a new home (y) is given by a linear equation which is y = -800x + 294000.

b) The average price of a new home in year 2014 will be $286000.

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An arithmetic sequence has the form:

where d is the common difference.

For this sequence the common difference is 3 and the first term is:

Plugging this values in the general expression we have:

Therefore the sequence is:

Now, from this expression we can determine the value of the zeroth term:

Hence the zeroth term is:

Problem

M(5,-10) is rotated 270 degrees what is M’?

Solution

For this case we need to remember that is we have any point A =(x,y) when we apply a transformation fo 270° then the new coordinates would be:

M' = (x,-y)

And for this case if we apply this transformation we got:

M'= (5, -(-10))= (5,10)

The value of x is -9.

Here the equation is :

14 - 2(x + 8) = 5x -( 3x - 34)

We have to prove that x = -9.

From the above-given equation, we have to find the value of x.

So by evaluating the equation we have:

14 -2(x +8) = 5x - (3x - 34)

= 14 - 2x - 16 = 5x - 3x + 34

= -2 -2x = 2x + 34

= 4x = -34 - 2

= 4x = -36

=x = -9

Therefore the value of the above-given equation x = -9.

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To determine wether a variable is a basic variable or not in a simplex tableu we have to look for the variables which have a one in a column and all the other values are zero, the variables that fullfil this condition are the basic ones.

Looking at the tableu we notice that the basis variables are: x2, s5 and Z. Now that we know that, we look at each row where the number one appear and put all the other variables equal to zero, with this in mind we conclude that:

The line that passes through the given point may be stated as

y - y1 = m(x - x1)

where (x1, y1) and (x2, y2) = (-6,5) and (6,-7)

m = (y2 - y1)/(x2 - x1)

= (-7 - 5)/(6 - -6)

= -12/12

= -1

Hence the equation of the line that passes through the given points is

(y - 5) = -1(x - -6)

y - 5 = - x - 6

y = -x - 6 + 5

y = -x - 1

Answer:

8, 10, 12

Step-by-step explanation:

x+x+2+x+4=30

3x+6=30

3x=30-6

3x=24

x=8

The roofer should work 5 2/3 hours of overtime.

Given:

Earnings for regular hours = $22 per hour

Earnings for overtime = $30 per hour

Time spent on regular hours = 40 hours

Total amount to be earned = $1050

To find:

The number of hours worked overtime

let the number of hours worked overtime = h

Earnings for regular hours (number of hours) + Earnings for overtime (number of hours) = 1050

Answer:

Explanation:

Here, we want to calculate the CPI for the cost of the suit

To do this,we use the weighted average method

What we will do here is to divide the past price by the current price and convert the value to a percentage

Mathematically, we have this as:

Substituting the values, we have:

Work Shown:

33 & 1/3% = 0.3333... the '3's go on forever

0.3333*88.50 = 29.49705 which rounds to 29.50

Answer: A. $29.50 is the correct answer.

SOLUTION:

a. The parametric equations that represent the balls motion is;

Inserting the values;

Simplifying, we have;

b. The graph of the parametric equation is given below;

Answer:

x = -1 and y = 9

Explanation:

Given the below system of equations;

To solve by using the elimination method, the 1st step is to multiply the 1st equation by 8 and the 2nd equation by 2, we'll have;

The 2nd will be to subtract the 4th equation from the 3rd equation and solve for y;

The 3rd step is to substitute y = 9 into the 1st equation and solve for x;

Considering the definition of an equation and the way to solve it, if 3 years ago I was 2/3 as old as I will be 8 years from now, I am 25 years old.

An equation is the equality existing between two algebraic expressions connected through the equals sign. One or more unknown values appear in it, in addition to certain known data.

Solving an equation is determining the value or values of the unknowns that transform the equation into an identity. To solve an equation, keep in mind:

Being "x" the my age today, and knowing that 3 years ago I was 2/3 as old as I will be 8 years from now, the equation in this case is:

x -3= 2/3×(x +8)

Solving:

x -3= 2/3x +2/3×8

x -3= 2/3x +16/3

x - 2/3x= 16/3 + 3

1/3x= 25/3

x= 25/3 ÷ 1/3

x= 25

Finally, I am 25 years old.

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The number 17.4 is 200 percent of 8.7

The statement is given as

"what percent of 8.7 is 17.4"

From the above statement, we have the following parameters

Dividend = 17.4

Divisor  = 8.7

The percentage is then calculated as

Percentage = Dividend/Divisor  x 100%

Substitute the known values in the above equation

So, we have

Percentage = 17.4/8.7 x 100%

Evaluate the quotient

Percentage = 2 x 100%

Evaluate the product

Percentage = 200%

Hence, the percentage is 200%

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The area of the figure = Area of the Triangle + Area of the semi-circle

Area of the Triangle = 1/2 x b x h

Base = 6 feet

Height = 8 feet

Area of the Triangle = 1/2 x 6 x 8 = 48/2 = 24 feet^2

Area of the circle = pi x r ^2 radius = 8/2 = 4 ft

= 3.14 x 4 x 4

= 50.24 feet^2

Total area = 24 + 50.24 = 74. 24 feet ^2

Answer:

Explanation:

Here, we want to get the unit price per pound

From the question, the brand sells for $3.15 per 10 ounces

Mathematically, 1 ounce is 0.0625 pound

Thus $3.15 is the price for 0.625 pounds (10 * 0.0625 pounds)

if $3.15 is for 0.625 pounds

$x will be for 1 pound

Mathematically:

To find the area of a circle, we use the formula for area

A = pi r^2 where r is the radius

We are given the diameter

d = 2r

8 = 2r

Solving for r

8/2 =r

4= r

A = pi (4)^2

A = 16 pi

Answer:

11

a

+

5

Step-by-step explanation: you're welcome. Brainlyest?

In a right triangle, the largest side is called the hypotenuse. Furthermore, from the Pythagorean Theorem, the following relation is satisfied:

To find if those measures correspond to a right triangle, verify if it satisfies the Pythagorean Theorem:

Then:

Therefore, the sides of lengths 1.25 in, 1 in and 0.75 in are indeed the sides of a right triangle.

ANSWER

C. x² - x ≥ 6

EXPLANATION

Let's analyze the solution set graphed first. We can see that the values -2 and 3 are included in the set, and all values below -2 and above 3. So, the solution set is (-∞, 2] U [3, ∞).

To find which inequality satisfies this solution set we have to solve them. To do so, we will be using the quadratic formula:

A. To solve this one, first, add x to both sides,

Now, apply the quadratic formula to find the zeros. For this inequality, a = -1, b = 1, and c = 6

But in this case, the solution set is [-2, 3] - note that for any value outside this interval the inequality is false.

B. Similarly, apply the quadratic formula for a = -3, b = 3, c = 18,

Again, the solution set is [-2, 3] since for any value outside the interval the inequality is not true.

C. Subtract 6 from both sides,

Apply the quadratic formula, with a = 1, b = -1, and c = -6,

In this case, if we take any value between -2 and 3, for example 1,

We can see that the inequality is false, while if we take a value greater than 3 or less than -2, for example, -5,

We can see that the inequality is true.

Hence, we can conclude that inequality C satisfies the solution set graphed.

The best interpretation of the confidence interval is given by:

We are 99% sure that the true mean amount of propionic acid in all 800 mg pills of the new medication is between 3.2 mg and 6.5 mg.

The x% confidence interval means that it is x% likely that the population parameter(mean/proportion/standard deviation) is between the bounds a and b of the confidence interval

The bounds of the confidence interval are given by the estimate plus/minus the margin of error.

In this problem, the bounds of the problem are already given, as follows:

The variable of interest is given by:

Mean amount of propionic acid in all 800 mg pills of the new medication

The level of confidence is of 99%, hence, considering the variable and the bounds, the interpretation of the interval is:

We are 99% sure that the true mean amount of propionic acid in all 800 mg pills of the new medication is between 3.2 mg and 6.5 mg.

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Answer: short line: 30 miles, ling leg: 224 miles

Step-by-step explanation:

Intro:
We will be using Pythagoras theorm, which states, if we have a 90 degree triangle which has 3 side as H, B and P defined as Hypotenuse, Base and Perpendicular, then H² = B² + P²
In your case, we know that hypotenuse is 226.

We also know that (A + B)² = A² + B² + 2AB

Given:
H = 226

B - P = 194

Solution:
B = 194 + P
So
(226)² = (194 + P)² + P²

51076 = (194)² + P² + (2 x 194 x P) + P²

51076 = 37636 + 2P² + 388P

51076 - 37636 = 2P² + 388P
13440 = 2P² + 388P

6720 = P² + 194P

P² + 194P - 6720 = 0
P² - 30P + 224P - 6720 = 0
P(P - 30) + 224(P - 30) = 0
(P - 30) x (P + 224) = 0
P = 30 or -224
As miles cannot be negative, we will choose answer as 30 miles.

Now we have H = 226 and P = 30
Using Pythagoras theorm:
(226)² = (30)² + B²
51076 = 900 + B²
50176 = B²

B = 224 miles.

So the missing miles are 224 miles and 30 miles

the slope for this line is 2

The slope or gradient of a line is a number  that describe both the direction and the steepness of the line. the steepness of a line is defined as the slope (or gradient). The slope is the ratio of vertical distance to the horizontal distance between any two points on a line. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).The greater the value of the slope, the "steeper" the slope is, and vice versa. So the smallest value of the absolute value of these slopes is 1/2.

So, A.T.Q:-

  The formula of slopet intercept is  Y2 -Y1 /X2-X1

  From the question:

              slope = -1-1/0-1

              slope = 2

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Let p be: John goes to the beach

Let q be: He will go surfing.

Then in symbolic form, the argument becomes:

p ⇒ q

p

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

∴ q

An argument is valid if the conjuction of the premises implies the conclusion.

p | q | p ⇒ q | (p ⇒ q) ∧ p | [(p ⇒ q) ∧ p] ⇒ q

---------------------------------------------------------------------\

F | F | T | F | T

F | T | T | F | T

T | F | F | F | T

T | T | T | T | T

The table above shows that the argument is a tautology.

Hence, the argument is valid

Solution

For this case we can model the number of fishes with the following equation:

And for this case we want to find the value for t =12 and replacing we got:

And then the number of fishes after 12 years would be 7600

so then they catched 182400

The error in the subtraction of the given fraction is that the LCM was not used before subtraction of numerators and as such if correctly answered the final fraction is; -15/4

We are given the subtraction of fraction expression as;

3/4 - 9/2

Now, the first step in this subtraction is to find the L.C.M of both denominators.

Factors of 2 ; 1, 2

Factors of 4; 1, 2, 4

Thus, the L.C.M of both denominators is; 2 * 2 = 4

Now, the next step is to divide the LCM by the denominator and multiply by the numerator while retaining the LCM as common denominator to get;

[(3 * 4/4) - (9 * 4/2)]/4

= (3 - 18)/4

= -15/4

The method used in the question to subtract the fraction did not take into account finding the LCM.

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