Find two consecutive positive odd integers such that three times the sum of the largest number plus 22 is equal to the product of both numbers. ​

The evaluation of the rational algebraic expression  are presented as follows;

1.  [tex]\dfrac{1}{3} +\dfrac{2}{5} = \dfrac{11}{15}[/tex]

2. [tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{x^2 + 2\cdot x \cdot y + y^2}{x \cdot y}[/tex]

3. [tex]\dfrac{3 \cdot x + 1}{x^2+2\cdot x +1} +\dfrac{5}{2\cdot x + 8} =\dfrac{11\cdot x^2 +36\cdot x +13}{2\cdot x^3 + 12\cdot x^2 + 18\cdot x+ 8}[/tex]

A rational algebraic expression is an algebraic expression that consists of a quotient and divisor that consists of variables and numbers.

1. [tex]\dfrac{1}{3} + \dfrac{2}{5}[/tex]

[tex]\dfrac{1}{3} + \dfrac{2}{5} = \dfrac{5\times 1 + 2 \times 3}{3\times 5} =\dfrac{5 + 6}{15}[/tex]

[tex]\dfrac{5 + 6}{15} = \dfrac{11}{15}[/tex]

Therefore, we get;

[tex]\dfrac{1}{3} +\dfrac{2}{5} = \dfrac{11}{15}[/tex]

2. [tex]\dfrac{x + y}{x} + \dfrac{x + y}{y}[/tex]

[tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{y\times (x + y) + x\times (x+ y)}{x\cdot y}[/tex]

[tex]\dfrac{y\times (x + y) + x\times (x+ y)}{x\cdot y}= \dfrac{x^2+ 2\cdot y \cdot x +y^2 }{x \cdot y}[/tex]

Therefore;

[tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{x^2+ 2\cdot y \cdot x +y^2 }{x \cdot y}[/tex]

3. [tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8}[/tex]

[tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8} = \dfrac{(3 \cdot x + 1) \times (2\cdot x + 8) + 5 \times (x^2 + 2\cdot x + 1) }{(x^2 + 2\cdot x + 1) \times (2\cdot x + 8)}[/tex]

[tex]\dfrac{(3 \cdot x + 1) \times (2\cdot x + 8) + 5 \times (x^2 + 2\cdot x + 1) }{(x^2 + 2\cdot x + 1) \times (2\cdot x + 8)} = \dfrac{11\cdot x^2+ 36\cdot x+ 13}{2\cdot x^3 + 12\cdot x^2+18\cdot x+ 8}[/tex]

[tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8}=\dfrac{11\cdot x^2+ 36\cdot x+ 13}{2\cdot x^3 + 12\cdot x^2+18\cdot x+ 8}[/tex]

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Considering the proportional relationship graphed, it is found that:

A. The constant is of 20.

B. A pair on the graph is given as follows: C. ) (45, 900); the machine caps 900 bottles in 45 seconds.

A proportional relationship is a linear function with intercept zero in which the output variable y is given by the multiplication of the input variable x and the constant k, as follows:

y = kx.

Considering point (15, 300) on the graph presented, the constant is calculated as follows:

300 = 15k

15k = 300

k = 300/15

k = 20.

The input and the output are given as follows:

Hence option C is the correct option for item 2.

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Answer:

Step-by-step explanation:

(2 1/2) : (1/4) = 10/1 =10

The equation of the line that passes through the points (6,2) and (7,1) is y = -x+8

The points are

(6,2) and (7,1)

The slope of the line is the change in y coordinate with respect to the change in x coordinate of the function.

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the value in the equation

The slope of the line = (1-2) / (7-6)

= -1/1

=-1

The point slope form is

[tex](y-y_1)=m(x-x_1)[/tex]

Choose one point and substitute the values in the equation

y-2 = -1(x-6)

y-2 = -x+6

Move the 2 to right hand side of the equation

y = -x+6+2

y = -x+8

Hence, the equation of the line that passes through the points (6,2) and (7,1) is y = -x+8

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The solution to the system of equations will be;

⇒ (2, 0)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The first equation is,

y = - 2x + 4

And, A line goes through (0, 4) and (2, 0).

Now,

For the second linear equation;

The coordinates are,

(-4, -3) (0, -1) , (2, 0) , (6, 2)

Hence, The equation of line passes through the points (-4, -3) and (0, -1).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - (-3)) / (0 - (-4))

m = 2 / 4

m = 1/2

Thus, The equation of line with slope 1/2 is,

⇒ y - (-3)= 1/2 (x - (-4))

⇒ y + 3 = 1/2 (x + 4)

⇒ y = 1/2x + 2 - 3

⇒ y = 1/2x - 1

Now, We find the value of system of equations;

y = - 2x + 4

y = 1/2x - 1

Solve both above equation, we get;

1/2x - 1 = - 2x + 4

1/2x + 2x = 4 + 1

5/2x = 5

x = 2

And, y = 1/2 (2) - 1 = 0

Thus, The solution to the system of equations will be;

⇒ (2, 0)

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Answer:

A

Step-by-step explanation:

Answer:

27/31

Step-by-step explanation:

Answer:

-44

Step-by-step explanation:

-2|6 * -3 - 4|

-2|-18-4|

-2|-22|

-2 * 22

-44

Answer:

1-10.

Step-by-step explanation:

Answer:

For x² + kx + 16/9 to be a perfect square, k should be equal to 8/3

Step-by-step explanation:

If x² + kx + 16/9 is a perfect square then it must satisfy the formula of (a + b)² i.e. equal to a² + 2ab + b².

So, first we will form a equal that looks similar to the formula:

[tex] \rm \implies {x}^{2} + kx + \dfrac{4 \times 4}{3 \times 3} \\ \\ \rm \implies {x}^{2} + kx + { \bigg( \dfrac{4}{3} } \bigg)^{2} [/tex]

Now by comparing we get,

[tex] \rm \implies k \cancel{x} = 2 \times \cancel{x}\times \frac{4}{3} \\ \\ \rm \implies k = \dfrac{8}{3} [/tex]

Using a translation, the graph of the function f(x) = x² + 3 is given by the image at the end of the answer.

Among the many transformations that a function or a figure can undergo is a translation, and other examples are reflections, rotations and dilation.

The difference of a translation from these other transformations is that the only thing that changes for the function is the position. The inclination, orientation and length all remains constant.

The four possible types of a translation are given as follows:

The parent function in this problem is given as follows:

f(x) = x².

Which has the U format of a parabola and a vertex at the origin (3,3).

The translated function is given as follows:

g(x) = x² + 3.

The addition by 3 means that the function was translated up 3 units, as shown in the image given at the end of the answer.

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A person must have a score of 126.26 to qualify Mensa.

it is given that,

Mean [tex](\mu) = 100,[/tex]

Standard deviation [tex](\sigma) = 15[/tex].

A person must score in the upper 4% of the population,

100% - 4% = 96% = 0.96

P(X < Xo) = 96% = 0.96

P(X < 1.7507) = 0.96          ....................................using the Normal distribution table,

Or, when the Invnorm function is used, Invnorm(0.96) = 1.7507

Therefore, The required value of X is,

[tex]Z = \frac{(X - \mu )}{ \sigma }[/tex]

1.7507 = (X - 100) / 15

X - 100 = 26.26

X = 100 + 26.26

X = 126.26

thus, the score a person must have to qualify Mensa is 126.26.

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In 27 minutes, Daquin completed 30% of his schoolwork. He must therefore finish another 70% of her homework.

We must multiply both sides of the equation by 3 to see how long it takes Daquin to finish 10% of the homework. It takes her 9 minutes.

We simply need to multiply our time estimate by seven to determine how long it will take her to complete the remaining 70% of her homework.

9 minutes are required for 10% of the homework.

63 minutes are required to complete 70% of the homework.

% finished equals 30%

Duration: 27 minutes

70% of the homework is still to be done.

Time required for the remaining task is 70/30 divided by 27 is equal to 63 minutes.

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Answer: What do those numbers mean

Step-by-step explanation:

Answer: [tex]g(2n)=4n^2 -8n[/tex]

Step-by-step explanation:

Substituting [tex]2n[/tex] for [tex]x[/tex],

[tex]g(2n)=(2n)^2 -4(2n)\\\\g(2n)=4n^2 -8n[/tex]

The function rule in slope-intercept form is y = -4x - 2

Mathematically, the slope-intercept form of a straight line can be calculated by using this equation:

y = mx + c

Where:

From the graph of this line, we have the following data points:

Point (x, y) = (-1, 2)

Point (x, y) = (0, -2)

In Mathematics, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (-2 - 2)/(1 - 0)

Slope, m = -4/-1

Slope, m = -4

Note: The y-intercept occurs at the point where the x-value is equal to zero (0).

Now, we can write the function rule for this line in slope-intercept form as follows:

y = mx + c

y = -4x - 2

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Sherry needs to invest 2000$ in mutual fund and 13200$ in bond to earn 548$ at the end of the year.

A percentage is just one of the many ways that a number, ratio, or fraction can be expressed. It is a number or ratio expressed as a fraction of 100.

Given:

Sherry has 15200$ to invest in mutual funds and in bonds.

Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year.

Here we need to find how much does she need to invest in each type of account if she wants to earn 548 at the end of the first year.

Here we have total amount = 15200$

So, let us consider x be the amount invested in mutual funds, then the amount invested in bonds will be 15200 - x.

It can be written in the following matrix

[x     15200-x ]

We know that the total amount earned at the end of the year is 548.

So, it can be written as

amount invested x percentage = final amount

[tex]\left[\begin{array}{cc}x&15200-x\\\\\end{array}\right][/tex]*[tex]\left[\begin{array}{ccc}1/100\\4/100\\\end{array}\right][/tex] = 548

We can simply it as

[x*1/100 + (15200 - x)*4/100] = 548

⇒ x/100 + 60800/100 - 4x/100 = 548

⇒ x + 60800 - 4x = 54800

⇒ -3x = 54800 - 60800

⇒ -3x = -6000

⇒ x = 2000

⇒ 15200 - 2000 = 13200

Therefore, Sherry invests 2000$ in mutual funds and 13200$ in bond to earn 548 at the end of the year.

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No, The scatter plot does not show a linear association

A graph is way of presenting data used by several disciplines.

There are many types of graphs and scatter plot is one of them.

scatter plot can be defined as set of dots plotted on a horizontal and vertical axis.

scatter plots can demonstrate the degree of connection, if any, between the values of observed quantities or events, they are crucial in statistics

The scatter plot does not show a straight line graph or a linear function. tracing the line shows a inverted shape of "s" which is not associated with linear functions.

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The length and width of a rectangle that maximises the enclosed area are 162.5 yards. The maximum area is 26,406.25 square yards.

In the given question we have to find the maximum area of the rectangular area.

A farmer with 650 meters of fencing wants to enclose a rectangle plot that border on a river.

As we know that the perimeter of rectangle

P= 2(l+b)

Let length of the rectangle is x yards and width is y yards.

So the equation should be

2(x+y) = 650

Divide by 2 on both side we get

x+y = 325................(1)

From the area of rectangle is

A = xy

From the equation the value of y is 325-x.

Now putting the value of y

A = x(325-x)

A = 325x-x^2

On differentiating

dA/dx = 325-2x

Putting dA/dx=0

325-2x=0

Subtract 325 on both side we get

-2x= -325

Divide by -2 on both side we get

x = 162.5 yards

Now putting the value of x in the y=325-x

y=325-162.5

y=162.5 yards

So the maximum area is

A= 162.5*162.5

A= 26,406.25 square yards

Hence, the length and width of a rectangle that maximises the enclosed area are 162.5 yards. 26,406.25 square yards is the maximum area.

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Answer:

Step-by-step explanation:
Here is an example:
Use this step by step explanation in your equation to help you find the answer.
For polynomial 2x2 - 3x5 + 5x6.

We observe that the above polynomial has three terms. Here the first term is 2x2, the second term is -3x5 and the third term is 5x6.

Now we will determine the exponent of each term.

(i) the exponent of the first term 2x2 = 2

(ii) the exponent of the second term 3x5 = 5

(iii) the exponent of the third term 5x6 = 6

Since, the greatest exponent is 6, the degree of 2x2 - 3x5 + 5x6 is also 6.

Therefore, the degree of the polynomial 2x2 - 3x5 + 5x6 = 6.

The show is 1 hour 4 minutes long.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Ben watched 3/8 of his television show.

There are still 40 minutes left.

let the show be x long.

So, 3/8x + 40 = x

x- 3/8x= 40

5x/8 = 40

x= 320/5

x= 64 minutes

x= 1 hour 4 minutes

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The events “blonde hair” and “brown eyes” are not independent.

What are independent events?

The term "independent events" refers to those whose occurrence is not reliant on another event.

When two events A and B are independent then the intersection of the two events is equal to zero. i.e. They do not have any element in common.

But from the given table we can see that the intersection of the events of  "blonde hair" and "brown eyes" exists.

Therefore, the events "blonde hair" and "brown eyes" are not independent.

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Answer:

The red symbol drawn over ∠2 and ∠3 indicates that the two angles total 90°. Therefore:

[tex]m\angle{2}+m\angle{3}=90^{\circ}[/tex]

Dimensions of the area enclosed is 800 * 800 and the maximum area = 6,40,000 square yards.

Given:

Liana has 3200 yards of fencing to enclose a rectangular area.

Let l and b be the length and width.

we know that:

perimeter of rectangle = 2(l+b)

2l + 2b = 3200

l+b = 1600

b = 1600 - l

Area of rectangle A = lb

= l*1600-l

= 1600 l - l^2

Apply derivative:

dA/dl = 1600 - 2l

1600 - 2l = 0

1600 = 2l

l = 1600/2

l = 800

l+b = 1600

b = 1600 - 800

= 800

Area = 800*800

= 6,40,000

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The frequency of data value 1 that is 10 will be 6 as "Dividing each frequency by the total number of data values gives the relative frequency. So multiplying the relative frequency by the total number of data values gives the frequency."

The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event. The relative frequency is calculated by dividing each frequency by the total number of data values. Therefore, the frequency is calculated by multiplying the relative frequency by the total number of data values.

Here,

Value                                           Relative frequency

10                                                  0.15

20                                                 0.30      

30                                                 0.45

40                                                 0.10

data 1 value=10

Dividing each frequency by the total number of data values gives the relative frequency.

So, multiplying the relative frequency by the total number of data values gives the frequency.

40*0.15=6

Since "multiplying the relative frequency by the total number of data values gives the frequency," the frequency of the data value 1 that is 10 will be 6.

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Answer:

24

Step-by-step explanation:

Start by finding the unit price. Unit price is the term for finding the price of one unit of an item, often used in word problems. We find this by dividing the cost of an item after a certain amount is sold, by that amount.

[tex]96/8 = \$12[/tex]

Now, we know the unit price is 12. Divide the end value of everything you sold by the unit price, 12.

[tex]288/12 = 24[/tex]

Therefore, you sold 24 candles.

Hope this helps!

The volume of prism with 1 layer=16 inch³; The volume of prism with 3 layer=48 inch³;The volume of prism with 5 layer=80 inch³;The volume of prism with 7 layer=112 inch³.

The total amount of space an object occupies in three dimensions is indicated by its volume. The term "capacity" describes something's ability to hold, absorb, or receive by an object .

Here,

Since each layer is of 1 inch.

So the volume of first prism,

=4*4*1

=16 inch³

When there is 3 layer, so the height is 3 inch,

=4*4*3

=48 inch³

When there is 5 layer, so the height is 5 inch,

=4*4*5

=80 inch³

When there is 7 layer, so the height is 7 inch,

=4*4*7

=112 inch³

The volume of a prism with one layer is equal to 16 inch³; with three layers, it is 48 inch³; with five layers, it is 80 inch³; and with seven layers, it is 112 inch³.

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Answer:

-1/3

Step-by-step explanation:

m = y2-y1/x2-x1                     formula for slope

m = 7-9/8-2                          Plug in the numbers

m = -2/6                                Subtract 7-9 and 8-2

m = -1/3                                 Simplify

Answer:A - 200

B - 1 Class Ring and 796 yearbooks

C - No, they would come up short 2800 dollars

Step-by-step explanation:

Without decimal, 4 canisters need to buy for making 5 meatloafs for party or if answer in decimal values needed then it is 3.333 canisters.

From the provided data, we have

number of meatloafs = 5

Here we have need the cup measurements the number of meatloafs made per recipe and the net weight of canister.

net weight of the contents of 1 canister = 15 ounces

1 cup = 8 ounces

1.25 cups = 10 ounces

10 ounces of breadcrumbs makes 1 meatoafs.

but we made 5 meatloafs so, for 5 meatloaf needed breadcrumbs = 5×10

= 50

If we consider 4 canisters then

15ounces × 4 canisters = 60 ounces which are 10 more than the needed ( > 50 ounces.

and if we are consider 3 canisters then

15 ounces × 3 canisters = 45 ounces which is not enough.

So, we need 4 canisters of breadcrumbs and we will have 2/3 of a canister left over.

approximately 3.333 is a value of needed canisters in decimals values. If decimal values are not need ,i.e, whole are canisters are not partial then 4 canisters is right .

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Complete question:

you're planning on making 5 meatloafs for a party. you go to the store to buy breadcrumbs, and see they are sold by the canister. how many canisters do you need to buy?

First, determine what information you need to answer this question, then click here to display that info (along with other info).

How much breadcrumbs does the recipe call for? It calls for 1 1/4 cups of breadcrumbs. How many meatloafs does the recipe make? It makes 1 meatloaf.

How many servings does that recipe make? It says it serves 10.

How big is the canister? It is cylindrical, 3.5 inches across and 7 inches tall.

What is the net weight of the contents of 1 canister? 15 ounces.

How much does a canister cost? $2.39

How much does a cup of breadcrumbs weigh? I'm not sure, but maybe something from the nutritional label will help.