Prove for any real number, |x−6|+x>3. Please use proof by cases, explaining each as you go.

The first thing to do to each side of the equation so that there would be no fractions is to cross product.

The unknown number, a is -48

A fraction refers to a number which has a numerator (top value) and a denominator (bottom value).

2(a - 7) / 15 = (a + 4) / 6

cross product

6{2(a - 7)} = 15(a + 4)

open parenthesis

6(2a - 14) = 15a + 60

12a - 84 = 15a + 60

combine like terms

12a - 15a = 60 + 84

-3a = 144

divide both sides by -3

a = 144/-3

a = -48

In conclusion, the solution to the fraction is a = -48

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The solution to the system of equations is x = 1.8, y = 0.4.

To graph the second equation, we can start by plotting the y-intercept of -1 on the y-axis. Then, using the slope of -1/3, we can find another point on the line.

For example, we can move down one unit and to the right three units from the y-intercept, which gives us the point (3,-2).

Graph of the two equations:

y = −2x + 4,

y = − 1/3x − 1

From the graph (check the image attached), we can see that the two lines intersect at the point (1.8, 0.4).

Therefore, the solution to the system of equations is x = 1.8, y = 0.4.

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The complete question is below:

The first equation from the previous system of equations is graphed. Graph the second equation to find the solution of the system of equations.

y = −2x + 4,

y = − 1/3x − 1

What is the solution to the system?

Based on the information provided, the statement "Ricardo is half as likely to spin a 2 or 4 than an odd number" is false.

To better understand if this is a valid statement, let's calculate the probability in each case.

Probability to get a 2 or 4:

1/ 8=  0.125 or 12.5% ( 0.125 x 100 = 12.5%)

Probability to get an odd number:

4/8 = 0.5 or 50% (0.5 x 100 = 50%)

This shows that the probability of getting a 2 or a 4 is 12.5%, while the probability of getting an odd number is 50%, which makes the statement false.

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Answer:

R52200

Step-by-step explanation:

I'm making the assumption that R is a currency symbol.

There are 12 months in a year. Simply multiply the cost for one month by 12 to find the total cost for a year:

4350 * 12 = 52200

Answer:

Step-by-step explanation:

To sketch the graph of the polynomial function P(x) = x^4 - x^3 - 11x^2 + 9x + 18 without using technology, we can follow the following steps:

1. Determine the end behaviors of the graph: As x approaches negative infinity, the dominant term of the polynomial is x^4, which is positive. As x approaches positive infinity, the dominant term of the polynomial is also x^4, which is positive. Therefore, the end behaviors of the graph are both upward, which means that the graph rises to positive infinity on both ends.

2. Find the x-intercepts: To find the x-intercepts, we need to solve the equation P(x) = 0. One way to do this is to use synthetic division or long division to factor the polynomial. However, since the degree of the polynomial is 4, it may be difficult to find the roots algebraically. Alternatively, we can use technology or a graphing calculator to find the approximate values of the x-intercepts. Using a graphing calculator, we find that the x-intercepts are approximately -2.23, -0.43, 1.19, and 3.47.

3. Find the y-intercept: To find the y-intercept, we can set x = 0 in the equation P(x) = x^4 - x^3 - 11x^2 + 9x + 18, which gives P(0) = 18. Therefore, the y-intercept is (0, 18).

4. Determine the location of the minimum point: To find the location of the minimum point, we can use calculus and take the derivative of P(x) with respect to x. Setting the derivative equal to zero and solving for x, we find that x = -0.5 or x = 1. Therefore, the minimum point occurs at either (-0.5, P(-0.5)) or (1, P(1)). Using a graphing calculator, we find that the minimum value of P(x) is approximately -8.09, which occurs at x = -0.5.

Based on these steps, we can sketch the graph of P(x) as follows:

* The end behaviors of the graph are both upward.

* The x-intercepts are approximately -2.23, -0.43, 1.19, and 3.47.

* The y-intercept is (0, 18).

* The minimum point occurs at approximately (-0.5, -8.09).

* The graph is symmetric about the vertical line x = 0, since P(-x) = P(x) for all x.

5. To find where the company will break even, we need to find the values of x such that P(x) = 0. Using a graphing calculator or technology, we find that the company will break even at approximately x = -2.23, -0.43, 1.19, and 3.47. These correspond to the x-intercepts of the graph. Therefore, the company will break even at these values of x.

Answer: 4 steps: 12 feet

6 steps: 18 feet

12 steps: 36 feet

30 steps: 90 feet

Step-by-step explanation:

Answer:

140in^2

Step-by-step explanation:

Split the area into 3 different shapes, and solve for the area of each (see picture below)

For the first area, the left triangle, we have a length of 4 and a height of 7. So we're going to multiply these two numbers together, then divide by 2 since we're only solving for the area of a triangle and not a rectangle. This gives us 14in^2.

Next, we can simply multiply 15 by 7 to get an area of 105in^2, since this is a rectangle.

For the last area, we can do the same thing as the first. Multiply 6 by 7, then divide by 2, giving us 21in^2.

Finally, we can add up all of these areas to get the total area, and our final answer:

14+105+21=140in^2

Answer:

Below

Step-by-step explanation:

A cube has SIX sides of equal area

  each side has area = L x W       and L and W are the same = 4.5 m

      so:   Area =   six   X   ( 4.5  X 4.5)  =   6 * 4.5 * 4.5 = 121.5 m^2

Answer:

Hope the picture will help you...

Answer:

Step-by-step explanation:

After one year, Devon's income will have grown by 2.9%. However, because inflation is 3.1%, the purchasing power of his income will decrease. This means that Devon will be able to buy less than he could today.

To calculate how much Devon can buy with his annual income after one year, we can use the following formula:

Purchasing power = Income / (1 + inflation rate)

Substituting the values given in the problem:

Purchasing power after one year = Income / (1 + 0.031)

Purchasing power after one year = Income / 1.031

Therefore, Devon will be able to buy approximately 0.97 times (or 97% of) what he could buy with his income today. In other words, his purchasing power will have decreased by approximately 3%.

Answer:

Devon's annual income increases at a rate of 2.9% per year, which means that after one year, his income will be 1.029 times his current income. However, due to inflation of 3.1% per year, the purchasing power of money decreases, which means that after one year, the amount of goods and services that can be purchased with the same amount of money will be 1/1.031 times what it is today.

Therefore, after one year, Devon can buy (1.029/1.031) times what he can buy today with his annual income. Simplifying this expression gives:

1.029/1.031 = 0.9971

So, Devon can buy about 99.71% of what he can buy today with his annual income after one year. In other words, he can buy slightly less than he can buy today, because inflation is greater than the rate at which his income is increasing.

Answer: 2/3

Step-by-step explanation:   y1-y2    3-(-1) = 4       simplify  4/6=2/3

                                               x1-x2     4-(-2)= 6

Slope is described as "the rise over the run," meaning that it's the fraction of "the change in the y-values compared to the change in the x-values."

In this situation
    - the change in the y-values is 3 - (-1) = 4.
    - the change in the x-values is 4 - (-2) = 6.
so the fraction is 4/6 or 2/3.

As a general formula, the formula for slope is [tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex].

      [tex]m = \dfrac{3-(-1)}{4-(-2)}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]

The greatest sum is 271.05, the greatest difference is 215.3, the greatest product is 11535.175, and the greatest quotient is approximately 4.142.

A numeral system is a way of writing numbers; it's a way of mathematically notating a set of numbers by using a consistent set of digits or other symbols.

To find the greatest sum, difference, product, and quotient using two of the given numbers, we can compare the results of each operation by pairing the numbers in different ways.

Note: For the quotient, we will only consider pairs of numbers where the denominator is not zero.

Sum:

The greatest sum will be obtained by adding the two largest numbers, which are 218.3 and 52.75.

218.3 + 52.75 = 271.05

Difference:

The greatest difference will be obtained by subtracting the smallest number from the largest number, which is 218.3 and 3.

218.3 - 3 = 215.3

Product:

The greatest product will be obtained by multiplying the two largest numbers, which are 218.3 and 52.75.

218.3 × 52.75 = 11535.175

Quotient:

The greatest quotient will be obtained by dividing the two largest numbers, which are 218.3 and 52.75.

218.3 ÷ 52.75 ≈ 4.142

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The GCF of p² and q² is 25. And the explanation is mentioned below.

The acronym GCF means "Greatest Common Factor." It is often referred to as the "Highest Common Factor" or the "Greatest Common Divisor" (GCD) (HCF). The biggest number that divides two or more other numbers without producing a residue is known as the GCF.

If the GCF of two numbers p and q is 5, then we can express the numbers as:

p = 5a

q = 5b

where a and b are integers, and 5 is the greatest common factor.

Now, let's consider p² and q²:

p² = (5a)² = 25a²

q² = (5b)² = 25b²

We can factor out 25 from both expressions:

p² = 25(a²)

q² = 25(b²)

Notice that the expression for p² has a factor of 25 and a factor of a², while the expression for q² has a factor of 25 and a factor of b².

Since the GCF of p and q is 5, we know that a and b do not have any common factors besides 1 and 5.

Therefore, a² and b² also do not have any common factors besides 1 and 5.

This means that the GCF of p² and q² is simply the factor of 25 that they have in common, which is 25.

So, the GCF of p² and q² is 25.

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All of the equations where x = 3 is a solution include the following:

A. x + 4 = 7.

C. 5 - x = 2.

Based on the information provided, we have the following equation:

x + 4 = 7

3 + 4 = 7

7 = 7 (True).

When x = 3, we have the following equation:

x/9 = 3

3/9 = 3

1/3 = 3 (False).

When x = 3, we have the following equation:

5 - x = 2

5 - 3 = 2

2 = 2 (True).

When x = 3, we have the following equation:

8x = 32

8(3) = 32

24 = 32 (False).

When x = 3, we have the following equation:

x - 10 = 7

3 - 10 = 7

-7 = 7 (False).

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Answer:

Step-by-step explanation:

Just multiply the denominator just that  1/9 divided by 3 is 1 /27 your welcome have a good day :)

Answer:

[tex]\frac{1/9}{3/1}=[/tex] [tex]\frac{1}{27}[/tex]

Step-by-step explanation:

[tex]skip:[/tex] [tex]\frac{1}{9}[/tex]

[tex]flip:[/tex] [tex]\frac{3}{1} = \frac{1}{3}[/tex]

[tex]Equation Now: \frac{1/9}{1/3}[/tex]

[tex]Multiply: \frac{1}{9}*\frac{1}{3}=\frac{1}{27}[/tex]

[tex]Answer=[/tex][tex]\frac{1}{27}[/tex]

The greatest inference we can draw from the data presented and the dot plot, however, is that there is proof indicating that Drug A is much more likely than Drug B to increase levels of human growth hormone.

the process of developing; progressive expansion; the act or activity of growing.

According to the provided dot plot, there appears to be a considerable variance in both medications' capacities to raise levels of human growth hormone. There is little crossover in the pieces of data for the two medicines, and the mean rise for Drug A is obviously greater than the average rise for Drug B.

We would need to do a formalized hypothesis test, which might involve a t-test, and generate a p-value to establish to see if this variance has statistical significance. We could conclude that the variation in averages is statistically significant if the p-value is less than a predetermined significance criterion (for example, 0.05).

The most important conclusion that can be made from the data and dot plot is the existence of evidence that suggests Drug A is much more probable that Drug B to enhance levels of growth hormone in humans. Further statistical analysis would be required to confirm the relevance of this divergence.

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Answer:

Step-by-step explanation:

To graph the function f(x) = x + 3, we need to plot a series of points that satisfy the equation. We can do this by picking some values of x and then finding the corresponding values of f(x).

For example, when x = 0, f(x) = 0 + 3 = 3. So we have the point (0, 3) on our graph.

Similarly, when x = 1, f(x) = 1 + 3 = 4. So we have the point (1, 4) on our graph.

We can continue this process for other values of x, and we'll get more points on the graph. For example, when x = -1, f(x) = -1 + 3 = 2. So we have the point (-1, 2) on our graph.

Once we have enough points, we can connect them with a straight line to get the graph of the function. In this case, we'll notice that the graph is a line with a slope of 1 and y-intercept of 3. The slope of the line tells us how much y changes when x increases by 1, and in this case, it changes by 1 unit.

So, to graph f(x) = x + 3, we can start by plotting the point (0, 3) and then draw a line that passes through this point and has a slope of 1. We can use a straightedge or ruler to draw the line as accurately as possible. The resulting graph will be a straight line that intersects the y-axis at the point (0, 3) and has a slope of 1.

The total amount of money collected is $180.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, person collected $12 each from 15 family members.

Total money = Amount of money collected from each × Number of people

= 12×15

= $180

Therefore, the total amount of money collected is $180.

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According to given information, x is 7.5 to the nearest tenth.

What is Triangle?

In geometry, a triangle is a two-dimensional closed shape with three straight sides and three angles. It is formed by connecting three non-collinear points with line segments. The three points of a triangle are called its vertices, and the line segments connecting them are called its sides.

If triangles ABC and DEF are congruent, then their corresponding sides are equal in length. Therefore, we have:

AB = DE = 41

BC = EF = 23

AC = DF = 36

We are given that BC = 4x - 7, so we can set up the following equation:

4x - 7 = BC = EF = 23

Solving for x, we get:

4x = 30

x = 7.5

Therefore, according to given information x is 7.5 to the nearest tenth.

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The conversion addition and subtraction of the numbers are done.

So, Solution are:

A. 900 p (into rupees)

1 rupee = 100 p

900 p = 9 rupees

B. 400 cm (into metre)

1 m = 100 cm

400 cm = 4.00 m

C. Rs. 27.70, Rs. 32.40 and Rs. 44.80 (Add)

=  Rs. 27.70 + Rs. 32.40 + Rs. 44.80

= 104.9

D. 9m 80 cm (into centimetre)

1 m = 100 cm

= 9m 80 cm

= 9m + 0.80m

= 9.8 m

E. 6480 m (into kilometres and metre)

1 m = 100 cm

6480 m

1 km = 1000m

6480 m = 6.480 km

F. Rs. 820.00 - Rs. 512.10 (Subtract)

Rs. 307.9

Thus, the unit conversion, addition and subtraction of the numbers are done.

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Answer: 1176 in^2

Step-by-step explanation:

the surface area of a cube is given by 6a^2 where a is the length of one edge side. Replace a for 14 as given in the question and we get 6 . 14^2 = 6 . 196 = 1176. the units are in inches squared also written as in^2

Answer:

= 12q² - 3

Step-by-step explanation:

3(-4q² - 1)

= -12q² - 3

Answer:

if you mean 4,208 divided by 31 its 135.7 (in case you formatted it wrong)

but if your asking 31 divided by 4,208 its 0.007

Answer:

Step-by-step explanation:

The translation of the polygon is 6 units to the left

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

Given data ,

Let the polygon be represented as ABCD

Now , the coordinates of the polygon is given as

The coordinate of A = A ( 1 , 3 )

The coordinate of B = B ( 3 , -1 )

The coordinate of C = C ( 7 , -1 )

The coordinate of D = D ( 5 , 3 )

Now , the translated polygon is having the coordinates as

The coordinate of A' = A' ( -5 , 3 )

The coordinate of B' = B' ( -3 , -1 )

The coordinate of C' = C' ( 1 , -1 )

The coordinate of D' = D' ( -1 , 3 )

So , the translation rule is ( x , y ) → ( x - 6 , y )

And , the figure is translated 6 units to the left

Hence , the translation is 6 units to the left

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Salma borrowed $15,300 and paid $295.24 per month for 5 years to pay off the loan.

What is loan?

In a loan, a certain quantity of money is given to another person in exchange for the value or main amount being repaid at a later date. In many circumstances, the lender increases the principal value by adding interest or finance charges, which the borrower must pay in addition to the principal sum.

To find out how much Salma borrowed, we can subtract her down payment from the cost of the motorcycle -

Loan amount = Cost of motorcycle - Down payment

Loan amount = 18,800 - 3,500

Loan amount = 15,300

Salma paid monthly payments for 5 years, which is equivalent to 60 months.

To calculate the monthly payments, we need to use the loan amount, the interest rate, and the loan term.

Let's assume the interest rate is 6%, which is a common rate for motorcycle loans.

We can use a loan calculator to find out the monthly payments -

Loan amount = 15,300

Interest rate = 6%

Loan term = 60 months

Using a loan calculator, we get a monthly payment of $295.24.

Therefore, Salma borrowed $15,300 and paid $295.24 per month.

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a. a polynomial that represents the area οf the picture including the frame [tex]\mathrm{A = (x + 2w) \times (x + 2w) = (x + 2w)^2}[/tex]

b.  The area οf the picture including the frame when the width οf the frame is 2 inches is [tex](x + 4)\²[/tex]

The English wοrd "polynomial" is derived from the Greek words "poly" and "nominal," which together denote "many sentences". The number of terms a polynomial can have is unbοunded.

a. Let x be the width οf the picture. Then the length of the picture is alsο x. Let w be the width οf the frame. The total width of the picture including the frame is (x + 2w), and the tοtal length of the picture including the frame is (x + 2w). Therefοre, the area of the picture including the frame is:

[tex]\mathrm{A = (x + 2w) \times (x + 2w) = (x + 2w)^2}[/tex]

b. If the width οf the frame is 2 inches, then w = 2. Substituting w = 2 into the polynomial above gives:

[tex]\mathrm{A = (x + 2w) \times (x + 2(2)) = (x + 4)^2}[/tex]

Therefore, the area οf the picture including the frame when the width οf the frame is 2 inches is (x + 4)² square units.

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Answer:

See below.

Step-by-step explanation:

We are asked to simplify the equation.

First, we should Combine Like Terms.

Combining Like Terms is adding terms that are alike.

For example, 4x and 11x are like terms since there's no differences than the coefficient, which can be different.

Let's combine like terms for this problem now.

Combine Like Terms:

[tex]\frac{2}{5} x+ 7 - \frac{2}{3} x -15\\\\\frac{2}{5} x - \frac{2}{3} x = \frac{6}{15} x - \frac{10}{15} x=-\frac{4}{15} x\\\\7 - 15 = -8[/tex]

We should have;

[tex]- \frac{4}{15} x - 8[/tex]

This will be our final answer.

Answer:

equilateral triangle

Step-by-step explanation:

Answer:

11, 20.

Step-by-step explanation:

5,6,8, 11 ,15, 20.

Answer:

p = [tex]\frac{9}{2}[/tex]

Step-by-step explanation:

given y = - [tex]\frac{3}{2}[/tex] is a root of the equation , then this value makes the equation true.

substitute y = - [tex]\frac{3}{2}[/tex] into the equation and solve for p

2( - [tex]\frac{3}{2}[/tex] )² + 6(- [tex]\frac{3}{2}[/tex] ) + p = 0

2( [tex]\frac{9}{4}[/tex]) - 9 + p = 0

[tex]\frac{9}{2}[/tex] - [tex]\frac{18}{2}[/tex] + p = 0

- [tex]\frac{9}{2}[/tex] + p = 0 ( add [tex]\frac{9}{2}[/tex] to both sides )

p = [tex]\frac{9}{2}[/tex]