Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. Picture attached.

The slope of the line is 125.

The meaning of the slope in this context is the change in prices with respect to the change in sizes of the houses in square feet.

Using the slope intercept equation the line won't pass through (5, 650)

The graph is a relationship between the cost of a home and the size of the houses in square.

Therefore, the slope can be found as follows:

The slope is the change in y with respect to the change in x.

The slope is rise over run.

Therefore,

slope of the line(m) = y₂ - y₁ / x₂ - x₁

using (1, 125)(2, 250)

m = 250 - 125 / 2 - 1

slope = 125

The slope in this context is the change in price with respect to the change in sizes of the house.

Let's check if the line will pass through (5, 650) using slope intercept equation.

y = mx + b

where

y = 125x + 0

625 = 125(5)

Therefore, the lines won't pass through (5, 650) instead it will pass through (5, 625)

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The range of the function will be equal to [-1, 27].

Function may be defined as an expression in which for every input variable there is only one output variable. The input variable is the variable x and also called as independent variable and output variable is the y variable and is also called as dependent variable. Domain of a function may be defined as the set of values of all the input values. Range of a function may be defined as the set of values of all the output values. For the domain -5 ≤ x < 3 we have function x² + 2. So, if we put -5 as x, we get the value equal to 27. Also, for the domain 3 ≤ x < 7 we have the function x - 4 and if we put the value 3 as x, we get the value equal to -1. Now, the range will be equal to [-1. 27].

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Given:

The given problem is:

Using the identity:

Now substitute a = x and b = 3 in this identity:

Hence , the correct solution to the problem is:

Answer:

6.5

Step-by-step explanation:

19.5 divided by 3 is 6.5

if you want to double check, you can multiply 3 by 6.5 and find it is 19.5

We have the following system of functions:

The second equation gives us an expression for y. We can replace y with these expression in the first equation:

We can substract 3x from both sides:

The x is a factor of both terms on the left. Then we can rewrite this equation:

So we have that the product of two terms is equal to 0. This happens when any of them is equal to 0 so we have two equations:

From the first we have x=0 and we can add 3 to both sides of the second equation:

Then we divide both sides by 49:

So we have the two x-values of the solutions: x=0 and x=3/49. In order to find their respective y-values we can use any of the two original functions:

We have two solutions: (0,0) and (3/49,21/49). We can round the values of the second solution:

Then the solutions are (0,0) and (0.06,0.43). Then the answer is the fourth option.

Step-by-step explanation:

I assume the question is about the distance between both points.

2 points in the coordinate grid create a right-angled triangle :

their direct connection (distance) is the Hypotenuse (the baseline, it is the side opposite of the 90° angle), and the x and y coordinate differences are the legs.

so, we can use Pythagoras to get the distance.

c² = a² + b²

c being the Hypotenuse, a and b being the legs.

so,

distance² = (-9 - -7)² + (-4 - -1)² = (-9 + 7)² + (-4 + 1)² =

= (-2)² + (-3)² = 4 + 9 = 13

distance = sqrt(13) = 3.605551275...

just in case, if you needed the line equation connecting these 2 points, I would assume the slope-intersect form

y = ax + b

"a" being the slope, "b" being the y-intersect (the y-value when x = 0).

the slope is always the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

using the 2 given points

x changes by +2 (from -9 to -7).

y charges by +3 (from -4 to -1).

the slope is

+3/+2 = 3/2

and our equation looks like

y = 3x/2 + b

now we use the coordinates of 1 point, e.g. (-7, -1), to get b

-1 = 3/2 × -7 + b = -21/2 + b

-1 + 21/2 = b

-2/2 + 21/2 = b

19/2 = b

our equation is then

y = 3x/2 + 19/2

or

y = (1/2)×(3x + 19)

Solving for x :

Answer:

33

Step-by-step explanation:

3

Regular decagon.

The same decagon can be obtained by rotating the figure by 36 degrees, it is mapped onto itself every time it is rotated by 36 degrees.

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Using long division:

The correct answer is option C.

With this, we can already rule out option A.

Next, we can see a slanted dashed line, that when x = 0, y = 2. The solution set is below this line. The inequality that represnts this is:

Thus, option C is the correct one.

Solution

Step 1:

Write the systems of equations

Step 2

To find the value of y, add both equations

Let's rewrite the system as:

Using elimination:

Replace x into (2):

The amount or balance left in the bank account is $39.97.

The amount of money held in a financial institution, such as a savings or checking account, at any particular time is known as the account balance. The net amount, which includes all debits and credits, is always the account balance.

The current balance in the bank account is $120.22.

The check was issued for $80.25.

Let x be the balance left in the account.

Then,

The balance left = Initial balance in the account - The amount for which the check was issued

x = Initial balance in the account - The amount for which the check was issued

x = $120.22 - $80.25

x = $39.97

The balance left in the bank account is $39.97.

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Let's call X the number of pounds of cashews and Y the number of pounds of Brazil nuts.

Now, we want to make 33 pounds of the mixture, so:

X + Y = 33

Adittionally, every pound mixture will be sell for $5.64 per pound. It means that:

7X + 4Y = 5.64*33

7X + 4Y = 186.12

Because every pound of cashews cost $7 and every pound of Brazil nuts cost $4

Then, we can solve for X on the first equation and replace it on the second as:

So, we can solve for Y as:

Now, we can calculate X as:

Therefore, we need to use 18.04 pounds of cashews and 14.96 pounds of Brazil nuts to make a 33 pounds mixture that sells for $5.64 per pound

Answer 18.04 pounds of cashews and 14.96 pounds of Brazil nuts

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

If 3x + 2y = 72 and 2y = 3z then 3x + 3z = 72.

This is due to the property of substitution.

Option E is the correct answer.

None of the above.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

3x + 2y = 72 _____(1)

2y = 3z ______(2)

Substitute (2) in (1) we get,

3x + 3z = 72

We got 3x + 3x = 72 using the property of substitution.

Thus,

If 3x + 2y = 72 and 2y = 3z then 3x + 3z = 72.

This is due to the property of substitution.

Option E is the correct answer.

None of the above.

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Solution

- The question tells us to find the % change from $250 to $303.

- To calculate the percentage change, we use the formula given below:

- The New is $303 and the Old is $250. Thus, we can calculate the percentage change as follows:

Final Answer

The percentage change from $250 to $303 is 21.2%

The ratios 1 to 0.4 and 9 to 3.6 are proportional.

A ratio is a relationship between two objects that is expressed using numbers or amounts.

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Consider the ratio 1 to 0.4 and 9 to 3.6,

Let,

x = 1 to 0.4 = 1 : 0.4

= 1/0.4

= 10/4

= 5/2

Let, y = 9 to 3.6

y = 9 : 3.6

y = 9/3.6

y = ( 9 × 10 ) / 36

y = 10/4

y = 5/2

Therefore,

x = y

1 : 0.4 = 9 : 36

Hence, the ratios 1 to 0.4 and 9 : 3.6 are proportional.

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Using the relation between velocity, distance and time, it is found that these trains are 1049 km apart at 1:30 pm.

Velocity is given by the distance divided by the time, hence the following equation is built to model the relationship between these variables:

v = d/t.

In which:

For Train X, the time and the velocity are given as follows:

Hence the distance of train X from the station is:

dX = 144 x 3.75 = 540 km.

For Train Y, the time and the velocity are given as follows:

Hence the distance of train Y from the station is:

dY = 165 x 3.0833 = 509 km.

They travel in opposite directions, hence we add the distances of each from the station to find their distances as follows:

540 km + 509 km = 1049 km.

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The inverse of the function is 1/64x², for x≥0

What is a function?

Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the first documented treatment of the concept of function. Initially, functions expressed the idealized interaction of two changing quantities. A planet's location, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity). The realms of application of the idea of a function were substantially expanded at the conclusion of the 19th century when it was defined in terms of set theory.

The inverse of the function is given by option (D) 1/64x², for x≥0

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From the function, we can conclude:

Answer:

Zero(s) of multiplicity one: 6

Zero(s) of multiplicity two: 9

Zero(s) of multiplicity three: -6, -4

82

1) Since Tanner is going to write a number with 8 tens and 2 ones

Then we can write:

2) Tanner writes the number 82

Answer:

Step-by-step explanation: Take awa thoese and it would be 70%

We are given that the rate of growth is:

Now, recall that the growth factor is:

Therefore, the growth factor is:

Answer:

2.50 + 1.50m = c

Step-by-step explanation:

Since he pays a fee of 2.50 when he enters the taxi were going to start with:
2.50 +

Now after its 1.50 for each mile so were going to do :

2.50 + 1.50m

Since we want to find the cost the equation will be:

2.50 + 1.50m = c

EXPLANATION

Since we have 3 1/2 slices of cake, and we need to distribute a half of slice by each friend, we need to divide 3 1/2 by 2, as follows:

Therefore, since each friend gets a half slice of cake, we can affirm that each whole slice of cake can be divided into two halves.

Now, adding from half to half to obtain 3 1/2 slices of cake, give us:

1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 7 slices

So, 3 1/2 slices of cake is a total of 7 halves.

Because each friend gets half of a slice of cake, we can affirm there are 7 friends.

Answer:

See below

Step-by-step explanation:

3  +  one half     slices      each whole (3 of them ) can be cut into two halves

6  halves  + 1 half = 7 halfves

   if everyone gets a a half, there are 7 people

Answer:

[tex]2^1[/tex]

Step-by-step explanation:

Hello! So, to tackle this problem let's start off with writing out the formula as such! [tex]\frac{2^2 * 2^3}{2^4}[/tex]

To solve this, what we can do is start off by isolating [tex]\frac{2^2}{2^4}[/tex] (we can worry about [tex]2^3[/tex] later). To evaluate [tex]\frac{2^2}{2^4}[/tex], we're essentially just simplifying the fraction and reducing the exponents. In this case, we can reduce the power of 2 from both the numerator and denominator to get [tex]\frac{1}{2^2}[/tex] (this is obtained by dividing both numerator and denominator by [tex]2^2[/tex])

Once we have that, we are now essentially left with [tex]\frac{2^3}{2^2}[/tex]! From here, we can apply exponent rule, which allows us to get rid of the denominator entirely and now it becomes 2^(3-2). We can subtract the numbers to then simplify it into our answer, [tex]2^1[/tex] or in other words just 2!

In the equation f(x) = -3(2), reflected about x - axis is : f(x) = 3.2

According to the question, given that

equation f(x) = -3(2)

the equation reflected x - axis is f(x) = 3.2

Therefore, Reflected about the x-axis in the equation f(x) = -3(2) is f(x) = 3.2

The graph of the parent function is either "moved," "resized," or "reflected" by a function transformation. The three primary categories of function transformations are as follows:

- Translation

- Dilation

- Reflection

The only one of these transformations, dilation, alters the size of the original shape; the other two, however, just affect the shape's location.

By comparing the original and converted graphs, you can quickly determine which one has changed because you can tell by by glancing at the graph that it has moved up 2 units, left 3 units, etc. However, it can be challenging to graph the function transformation when a graph is provided. The next few steps make it much simpler to graph transformations. Here, the function y = f(x) is changed to y = a f(b (x + c)) + d.

Step 1: Write down some of the original curve's defining coordinates. Thus, we are aware of the previous x and y coordinates.

Step 2: Simply put "b (x + c) = old x-coordinate" and solve for x to determine the new x-coordinate of each location.

Step 3: Simply apply all outside operations (of brackets) on the old y-coordinate to determine the new y-coordinate of each point. To determine each new y-coordinate, find ay + d, where 'y' is the old y-coordinate.

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