Which equation is equivalent to the statement?

Answer:

  see attached

Step-by-step explanation:

Given a partially-filled circle pattern, you want to place the remaining numbers so the sum in each circle is 21.

There are seven (7) circles, and nine (9) unknown values. This means there are a couple of "free choice" values that cannot be found directly. Our approach is to limit the number of possibilities we must examine.

We note that if we multiply the sum (21) by the number of circles, that product includes the "single cover" circle shapes once, and each of the overlapping "double cover" areas twice. There are three unknown "single cover" values, and six unknown "double cover" values. If we represent the sums of these by "s" and "d" respectively then we have ...

  (10 +11 +6 +4 +s) +2(d +5) = 7×21

  41 +d +2s = 147 . . . simplify

  d +2s = 106 . . . . . . subtract 41

The total of all of the unplaced numbers is ...

  (2 +12 +7 +14 +1 +8 +9 +3 +13) = s +d

  69 = s +d

Now, we have two equations in s and d:

Subtracting the second from the first gives ...

  (d +2s) -(d +s) = (106) -(69)

  s = 32

The sum s is the sum of 'a', 'b', and 'c' as marked in the attachment. There is only one set of unplaced numbers that has a total of 32: {7, 12, 13}.

Using these numbers means that the set of allowed values for the "double cover" areas is {1, 2, 3, 8, 9, 14}.

Working clockwise from the space marked 'c' in the attachment, the "double cover" oblong spaces must have the values ...

As we noted above, {a, b, c} is some permutation of {7, 12, 13}. This means the value (a-c) will be one of ±1, ±5, ±6.

If (a-c) = ±6, then 6 -(a-c) = {0, 12}. Neither value is allowed: 0 is not on the list, and 12 is already used.

If (a-c) = ±5, then we would have ...

  for (a-c) = -5, 6 -(a-c) = 11, not an allowed value (already used).

  for (a-c) = 5, all of the values 6-5=1, 9+5=14, and 8-5=3 are allowed. This case corresponds to {a, b, c} = {12, 13, 7}.

If (a-c) = ±1, then we would have 6 -(±1) = {5, 7}. Neither value is allowed.

The only allowed choice for {a, b. c} is {12, 13, 7}. Using c=7 and (a-c)=5, the "double cover" values clockwise from 'c' are ...

When all of the values are filled in the diagram it looks like the attachment.

__

Additional comment

As you might imagine, there was a bit of thrashing around before this method of solution presented itself. The system of 7 equations in 9 unknowns cannot be solved directly, and we know of no way to include the requirement that the solution set must include each number of the given set, used only once.

Fortunately, the method we tried here proved to find a solution in fairly straightforward fashion.

Answer:

Maysa forgot to subtract from the hundredths place

3.5= 3.50

3.50

-2.46

1. 04

Step-by-step explanation:

a + b = 16

a = 16 - b

45a + 30b = 585 | divide both sides by 15

3a + 2b = 39

now we are using the first in the second equation :

3(16 - b) + 2b = 39

48 - 3b + 2b = 39

48 - b = 39

48 = 39 + b

9 = b

he sold 9 pairs of type b socks.

FYI :

a = 16 - b = 16 - 9 = 7

Answer:

0.9 Litres or 900 ml

Step-by-step explanation:

First we will find out the total volume of Sunflower oil he has.

Sunflower Oil bought = 6 cana x 3 litre = 18 litres

Now we divide this 18 litres into 20 parts to find out the volume of sunflower oil per bottle:

[tex] \frac{18}{20} \\ = \frac{9}{10} \\ = 0.9litres \: or \: 900ml[/tex]

By taking the quotient between the two volumes in ounces, we conclude that you will need about 8 cans to fill the bottle. So the correct option is C.

We know that the 2-liter bottle holds (67 + 3/5) ounces of water, and each one of the cans holds a volume of 8 ounces.

To see how many cans we need to fill the bottle, we need to take the quotient between the two volumes (using ounces in both cases, obviously), we will get:

Q = (67 + 3/5)/8 = 8.45

So you need 8.45 cans to completely fill the 2 liter bottle, then we can see that the correct option will be C, 8 cans, as that is the best estimation.

We conclude that you need about 8 cans to fill the bottle.

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Answer:

The Fibonacci sequence is a series of numbers in which each number is the sum of the two that precede it. Starting at 0 and 1, the sequence looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on forever. The Fibonacci sequence can be described using a mathematical equation: Xn+2= Xn+1 + Xn.

Step-by-step explanation:

If the linear equation [(x + 117) = 150°], then the value of (x + 47) will be 80.

As per question statement, we are provided with a linear equation, as  

[(x + 117) = 150°].

We are required to calculate the value of (x + 47) using the above mentioned equation.

To solve this question, we will find out the value of "x" from the equation

[(x + 117) = 150°] and then, add 47 to the value of x to obtain our desired answer, i.e.,

[tex][(x + 117) = 150]\\or, x=(150-117)\\or,x=33\\or, (x + 47)=(33+47)\\or, (x + 47)=80[/tex]

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A spreadsheet expression=IF(A1<40000,(21%*I21),(26%*A1))

The "IF" function should be used in the spreadsheet expression. The "IF" function returns a value based on the criteria specified in the spreadsheet formula. This, like other spreadsheet functions, begins with =.In response to the question,

Cell A1 contains the value to be inspected. If A1 is smaller than $40000 (written as A140000), the spreadsheet performs the following function: (21%*I21). otherwise (which may be understood as A1 higher than or equal to $40000 in this example), calculate the following command as indicated above; (26%*A1).

The command is finished with the last parenthesis.

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Answer:

2x + 5y = 20

Step-by-step explanation:

[tex]y = - \frac{2}{5} x + 4[/tex]

[tex] - 5y = 2x - 20[/tex]

[tex] - 2x - 5y = - 20[/tex]

[tex]2x + 5y = 20[/tex]

The product of 9 and Jenny's age 15 is 135.

So, let the missing value be 'x'.

Then,

Therefore, the product of 9 and 15 is 135.

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The types of angle can ABC be are (a) Acute (b) Right and (c) Obtuse

The statement is given as:

BX bisects ABC to form two congruent acute angles

The above statement means that the smallest type of angle, the angle ABC can be is an acute angle

Also, when a right angle is divided into 2 (or bisected), the resulting angles are acute angles.

Lastly, when an obtuse angle is bisected, the resulting angles are acute angles.

Hence, the types of angle can ABC be are (a) Acute (b) Right and (c) Obtuse

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The price of of 1 pound of almond is given as  2.2/0.65

A line is defined as the shortest distance between two points. Given the coordinate (0.65, 2.2)

This shows that 0.65 pound of almond costs $2.2. For the cost of one pounds of almond;

Unit price = 2.2/0.65

Unit price = $3.38

This shows that the price of of 1 pound of almond is given as  2.2/0.65

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The bookstore pays the publisher $27 for each book thus making a profit of 30%.

The profit is defined as the difference between the sell price and the cost price.

The sell price is defined as the price at which an object is sold.

The cost price is defined as the price at which an object is bought.

When the sell price is greater than the cost price profit is made by the seller.

Let the cost price (price paid to publisher) be x dollars.

Therefore when sold at a profit of 30% then

profit= 30%of x=0.3x dollars

Now the sell price = cost price +profit

∴Sell price= x+0.3x=1.3x

But the sell price is given as $35.10

So we can equate the two terms to get a linear equation in x.

∴1.3x=35.10

or, x=35.10÷1.3

or, x=27

Therefore the cost price is $27.

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The equation that describes the graphed function is  [y = f(-x + 4)].

As per the question statement, we are provided with the information about a function f(x) which is equal to square root of "x", and a reference graph diagram.

We are supposed to determine the equation from the given four options that describes the graphed function.

To solve this question, we will use the trial and error method, using the options to determine out correct answer.

First of all, from the graph, we can see that the graph cuts the x-axis at

(4, 0) and y-axis at (0, 2). Now, since [y = f(x)], our equation must be equal to 0 when (x = 4) is substituted, and 2 when (x = 0).

Considering option (A), [tex]y=f[(-x)+4]=\sqrt{[(-x)+4]}[/tex], and substituting

(x = 4), we get,

[tex]y=\sqrt{[(-4)+4]}\\or, y=\sqrt{(4-4)}\\ or,y=\sqrt{0}\\ or,y=0[/tex]

While substituting (x = 0), we get,

[tex]y=\sqrt{[(-0)+4]}\\or, y=\sqrt{(4-0)}\\ or,y=\sqrt{4}\\ or,y=2[/tex]

Hence, option (A) satisfies at the points of (4, 0) and (0, 2).

Similarly, if we substitute and check on the other three options, we will see that for (x = 4), (y ≠ 0) and for (x = 0), (y ≠ 2).

Therefore, if [f(x) = (√x)], then the equation that describes the graphed function is [y = f(-x + 4)].

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Answer:

10/9

Step-by-step explanation:

Answer:

y = 9x + 7

Step-by-step explanation:

Line is parallel to y = 9x + 4 and passes through the point (-1, -2)

m = slope

the slope of the line is the same for both lines, m = 9

the equation of the parallel line is y = 9x + a

-2 = (9) * (-1) + a

a = 7

y = 9x + 7

The scale factor of the dilation is -5

The points are given as

Point = (3, -5)

Image = (-15, 25)

The scale factor of the dilation is calculated using

Scale = Image/Point

So, we have

Scale = (-15, 25)/(3, -5)

Evaluate

Scale = -5

Hence, the scale factor of the dilation is -5

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The linear cost function is C(x) = 15x + 3250 and the cost function in marginal cost: $15; 150 items cost $5500 to produce is $ 5500 .

Let C(x) is that the total value, and x is that the range of things.

The slope "m" is named the cost and "b" is named the charge.

The value of m is $15 and the price of "x" is 150.

Total cost of 150 items are $5500

Substitute all the values within the equation (1) , we get

   5500 = 15 (150) + b

    5500 = 2250 + b

    3250 = b

Hence , linear cost function is given by C(x) = 15x + 3250

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According to the information, it can be inferred that in the room worth 3,000, the break-even point would be 25 students enrolled. On the other hand, in the room of 200, the break-even point would be 7 students enrolled.

The break-even point is an economic term to refer to the moment when a company's income covers its fixed and variable expenses, that is, when you manage to sell the same amount you spend, you neither win nor lose, you have reached the break-even point.

Thus, calculating the break-even point is essential for companies to assess their profitability, since in this way it is possible to know how much they need to sell to generate profit. Knowing this value, even before starting a new project, allows you to know how financially interesting your business idea is.

To calculate the break-even point, we must take into account the expenses that the students will have to offer their service:

According to the above, the expenses in case A, with room 1 would be:

On the other hand, the expenses in case B with room 2 would be:

So, we know that in case A the expenses are going to be 3,750 and in case B the expenses are going to be 950. To find the break-even point for each case, we must divide this value by the price at which they are going to sell the item. course to students. However, it should be clarified that it must be divided by 150 because 50 will be used to pay for each student's handouts.

3,750 ÷ 150 = 25

950 ÷ 150 = 6.33 = 7

According to the above, the break-even point for case A would be 25 students. Additionally, in case B the balance point would be 6.33 students who are close to 7.

To conclude, it can be stated that the best option would be to take room 2 because they will have fewer expenses and will have to sell fewer units of their course to reach the break-even point.

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Answer:

x=

Step-by-step explanation:

Given the midpoint formula: ([tex]\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}[/tex]),the Segment Addition Postulate, and the line attached, find x, HK, HJ, KJ

1st step is in the picture.

doing the first step gives us [tex]x + 9[/tex]

Since k is the midpoint, both sides of the midpoint are the same length

so we can use the equation [tex]3x - 10 = x+9[/tex]

subtract x from both sides: [tex]3x-10-x=x+9-x[/tex]

[tex]2x-10=9[/tex]

[tex]2x-10+10=9+10[/tex]

[tex]2x=19[/tex]

[tex]2x/2=19/2[/tex]

[tex]x=9.5[/tex]

Now that we know x, we can substitute to find HK, HJ, and KJ

[tex]HK = 3(9.5)-10[/tex]

[tex]HJ = 4(9.5)+19[/tex]

[tex]KJ = x +9[/tex]

[tex]HK = 28.5 -10\\HJ = 38+19\\\\KJ = 9.5 + 9\\HK = 18.5\\HJ=57\\KJ = 18.5\\[/tex]

Our HK and KJ answer is correct because they are the same, and the midpoint of HK and KJ is point K.

Answer:

The answer would be A.

Step-by-step explanation:

You can eliminate b because 15/5=3 copies but 5/5 would be 1 not 15. You can eliminate d because 15/3=5 copies but 5/3 would not equal 1. You can eliminate c because 15/15=1 but 5/15 does not equal 3.

Answer:

the smallest even whole number which is divided by 3 is 6

The final balance in the account is $9,620

Here we need to write an addition. The amounts that the company receive will be positive amounts, while the amount that the company pays will be represented by negative amounts, then:

Now we can add these values, assuming that the initial balance is $0.

$0 + $4,790 + $5,480 - $1,050 - $1,150+ $1,550 = $9,620

This is the balance, they still have a debt of $4,790 and $1,650, but the amount of money that they have in the account is $9,620

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Answer:

y [tex]\geq[/tex] 4x - 6

Step-by-step explanation:

1. Find the slope using the slope formula (rise over run)

2. Use the slope and one of the points to solve for the y-intercept (b)

3. Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{ 5}(x-\stackrel{x_1}{0})\implies y=5x+8[/tex]

Maria’s net pay is $2,025.82.

The net pay is the gross pay minus mandatory and voluntary deductions, like taxes, insurance, and other expenses.

The net pay represents the amount of money the income earner receives.

The net pay is also known as the take-home.

Monthly salary = $2,750

FICA withholding = 15%

Social security tax withholding = 7.2%

Medicate tax withholding = 1.37%

Health Insurance Premium = $76 per month

Total withholding = 23.57%

= $648.18 (2,750 x 23.57%)

Total deductions and withholding = $724.18 ($76 + $648.18)

Net pay = $2,025.82 ($2,750 - $724.18)

Thus, Maria's net pay after the withholdings and deductions is $2,025.82.

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If a naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet then 145 is the position of the submarine relative to the surface of the ocean now.

What is Mathematical function ?

Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.

If a naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet. we need to find the position of the submarine relative to the surface of the ocean now.

The submarine initial position= 310 feet.

To pass above an underwater mountain, or seamount, it rose = 165 feet.

The position of submarine is

310-165

=145 feet.

Therefore  the position of the submarine relative to the surface of the ocean now is 145 feet.

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