A snack mix recipe calls for 2
1
4
cups of chips and
1
5
cup of dip.
Xander wants to make the same recipe using 1 cup of dip. How many cups of chips will Xander need?

The value of n(AxB) is mathematically given as

n(A x B)  = 18

Generally, It is possible to extend the formula for calculating the magnitude of a vector to any number of dimensions. For instance, the magnitude of a four-dimensional vector denoted by

a=(a1,a2,a3,a4) may be calculated using the following formula: a=a21+a22+a23+a24.

The question "how much of a quantity" is what's meant to be answered when one asks about magnitude.

For instance, the magnitude may be used to provide an explanation for why the speeds of a vehicle and a bicycle cannot be compared directly to one another. It is also possible to use it to describe the distance traveled by an item or the quantity of an object in terms of its magnitude. Both of these applications need the usage of magnitude.

n(A x B) = |A| x |B|

= 6 x 3

n(A x B)  = 18

Where

The product of these two values is the total number of ordered pairs that can be formed from the elements of A and B, which is 18.

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number of tickets for adult = 170 and number of tickets for children = 151

What is equation with two variables?

The equation that has two unknown variables and express the equality between two or more expression is called equation with two variables.

let, x denotes the number of adults went to theater.

y denotes the number of children went to theater

price of ticket for each adult = $3.50

price of tickets for each child = $2.50

if the number of total tickets = 321

x + y = 321

total cost of tickets = $3.50x + $2.50y = 972.21 dollar

we will solve the above two equations, y = 321 - x

by putting the y value in the second equation,

3.50x + 2.50 (321- x) = 972.21

3.50x + 802.5 - 2.50x = 972.21

x = 169.71

number of adults went to theater = 170

from, y = 321 -169.71

    y = 321 - 169.71

y = 151.3, y= 151

number of children went to theater = 151

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The rate of interest is given by the equation R = 3.5 %

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the rate of interest be represented as R

Now , the simple interest I = $ 175

The principal amount invested P = $ 2,500

The time period T = 2 years

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Rate of Interest = (Simple Interest x 100 ) / Principal Amount x Time Period )

Substituting the values in the equation , we get

Rate of Interest R = ( 175 x 100 ) / ( 2500 x 2 )

Rate of Interest R = 17500 / 5000

Rate of Interest R = 3.5 %

Hence , the interest rate is 3.5 %

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Answer:

y = -3

Step-by-step explanation:

The midline of a sinusoidal function is y = a where "a" is halfway between the minimum and maximum y-values of the function.

From inspection of the given graph:

Therefore, the y-value that is halfway between the minimum and maximum points is:

[tex]\implies y=\dfrac{y_2+y_1}{2}=\dfrac{-7+1}{2}=\dfrac{-6}{2}=-3[/tex]

Therefore, the equation of the midline of the given sinusoidal function is:

The amount that Cameron is paid per hour, given the number of hours he worked, is $ 18 per hour

To find the payment that Cameron got per hour, you first need to find the number of hours that he worked.

This number of hours is:

= 4 pm  - 7 am

= 1600 hrs - 0700 hours

= 9 hours

The payment per hour is therefore:

= Amount Cameron paid / Number of hours worked

= 162 / 9

= $ 18 per hour

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The rest of the question is:

How much was Cameron paid per hour worked?

Answer:

Step-by-step explanation:

y=ax²+bx+c

x=1,y=-5

-5=a+b+c   ...(1)

x=2,y=-3

-3=4a+2b+c   ...(2)

x=3,y=3

3=9a+3b+c  ...(3)

(2)-(1) gives

2=3a+b   ...(4)

(3)-(2) gives

6=5a+b   ...(5)

(5)-(4) gives

4=2a

a=4/2=2

from (4)

6=5(2)+b

b=6-10=-4

from (1)

-5=2+(-4)+c

-5=-2+c

c=-3

y=2x²-4x-3

Answer:

synthetic division method use it

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{1}}} \implies \cfrac{ -13 }{ -6 } \implies \cfrac{13 }{ 6 }[/tex]

Answer:

x+2 domain: (-infiniy, +infinity) or -infinity<x<infinity

1/x +2 domain: (-infinity, 0) and (0, infinity) or 0<x<0

If a car radiator needs a 40% antifreeze solution the radiator now holds 49% of a 30% solution. The number of  liters that should be drained and replaced with 100% antifreeze to get the desired strength is 7 liters.

Let x represent the number of liters that should be drained

So, Let solve for x

x+.30(49-x)=.40× 49

x=14.7-.30x=19.6

.7x=19.6 - 14.7

.7x=4.9

x=4.9/.7

x = 7 liters need to be drained & filled with 100% antifreeze.

Therefore the number of liters is 7 liters.

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Explanation:

First we solve for y.

x + 2y = -14

2y = -14 - x

2y = -x - 14

y = (-x - 14)/2

y = -x/2 - 14/2

y = (-1/2)x - 7

The equation is in slope intercept form y = mx+b

Parallel lines have equal slopes, but different y intercepts. This means the slope of any line parallel to this given one will have a slope of -1/2

For example, y = (-1/2)x + 10 is parallel to y = (-1/2)x - 7, since both have the same slope of -1/2 but different y intercepts.

Answer:

ln(d) = n can be rewritten in exponential form as d = e^n.

Step-by-step explanation:

The natural logarithm, denoted by ln, is the logarithm to the base e (approximately 2.718). The inverse of the natural logarithm function is the exponential function e^x. Therefore, when you take the natural logarithm of a number, you can raise e to the power of that number to get the original value.

ln(d) = n is the same as d = e^n

So, Ln(d)=n can be written as d = e^n

This is because e^n is the inverse function of Ln(d) and Ln(d)=n is the logarithm form of d = e^n

Answer:

f(8) = - 1

Step-by-step explanation:

f(8) has x = 8 which is in the interval x > 0 , then f(x) = - 1 , so

f(8) = - 1

Answer:

38[tex]\sqrt{3}[/tex]

Step-by-step explanation:

6[tex]\sqrt{5x5x3}[/tex] + 4[tex]\sqrt{2x2x3}[/tex]  We can pull out a pair of 5's and 2's

6(5) [tex]\sqrt{3}[/tex] + 4(2)[tex]\sqrt{3}[/tex]

30[tex]\sqrt{3}[/tex] + 8[tex]\sqrt{3}[/tex]

38[tex]\sqrt{3}[/tex]

Answer: (-2, 10)

Explanation:

The left endpoint is -2. The right endpoint is 10. Both endpoints are open holes, which means we don't include them as part of the green-shaded solution region. If x is a solution, then the solution can be described as [tex]-2 < x < 10[/tex] converting to interval notation [tex](-2,10)[/tex] . The curly bracket says "do not include endpoint".

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The solution of the system of equations by using substitution method is x = 1 and y = 3

The substitution method is a method for solving systems of equations. It involves solving for one variable in one of the equations and then substituting that value into the other equation to find the value of the other variable.

We have the equations 4x + 4y = 16 and y = x+2

Substitute y = x +2 into  4x + 4y = 16:

4x + 4y = 16

4x + 4(x +2) = 16

Clear the parenthesis:

4x + 4x + 8 = 16

8x + 8 = 16

8x = 16-8

8x = 8

x = 8/8

x = 1

put x = 1 into  y = x+2:

y = x+2

y = 1 + 2

y = 3

Therefore, the solution of the system of equations is x = 1 and y = 3

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Answer:

1.806 (to the nearest thousandth)

Step-by-step explanation:

1.806 (to the nearest thousandth)

The number 1.80642 would round down to 1.806

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We need to round  1.80642 to the nearest hundredth,

We can see that the 1.80642 is below 2 so it goes down, and it rounds down to 1.80642 instead of, 14.62 then that would round up to the decimal is higher than 1.

1.80642 rounded to the nearest thousandth is 1.806.

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to get the y-intercept of any equation we can simply set x = 0 and solve for "y", so let's do so

[tex]y=6\left( x-\cfrac{1}{2} \right)(x+3)\implies \stackrel{\textit{setting x = 0}}{y=6\left( 0-\cfrac{1}{2} \right)(0+3)}\implies y=6\left( -\cfrac{1}{2} \right)(3) \\\\\\ y=(-3)(3)\implies y=-9\hspace{12em} {\Large \begin{array}{llll} \stackrel{y-intercept}{(0~~,~~-9)} \end{array}}[/tex]

Answer:

Step-by-step explanation:

Distance formula is as follows.

The distance between two co-ordinates, say, (x₁ , y₁) and (x₂,y₂), is equal to

√((x₁ - x₂)² + (y₁ - y₂)²)

Just substitute the values here.

√((1 - (-7) )² + ( - 3 - 2)²)

= √((1 + 7)² + ( - 3 - 2)²)

= √(8² + -5²)

= √(65 + 25)

= √90  ≈9.5 units

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If he walks up the moving escalator at a speed of 25 meters per minute,

the person will reach the top in six minutes.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

A person standing on an escalator reaches the top in 3 minutes.

The escalator is 150 meters long.

He walks up the moving escalator at a speed of 25 meters per minute.

So, the time taken = divide 150 by 25

The time taken = 150/25

The time taken = 6 minutes.

Therefore, he will reach the top in six minutes.

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Answer:

1) The vertex is the maximum value.

2) The axis of symmetry is x = negative one-half.

3) The domain is all real numbers.    

Step-by-step explanation:

Step-by-step explanation:

the intersection of the diagonals of a parallelogram is always the middle point of either of the diagonals.

so, all we need to do is identify a diagonal and find is middle point.

a diagonal is e.g. from all the way on the left and up (-2, 5) to all the way right and down (4, 0).

the middle point between 2 points is

((x1 + x2)/2, (y1 + y2)/2)

so, here

((-2 + 4)/2, (5 + 0)/2) = (1, 2.5)

the coordinates of the intersection are (1, 2.5).

The balance sheet for McGuire Corporation as at December 31, 2021, is as follows:

McGuire Corporation

As at December 31, 2021

Current Assets:

Cash                                  $56,000

Accounts Receivable       $22,000

Inventory                          $50,000

Rent Prepaid                      $2,000

Total current assets                          $130,000

Long-term assets:

Office Equipment              $30,000

Accumulated Depreciation (3,000)  $27,000

Total assets                                      $157,000

Current Liabilities:

Accounts payable                            $30,000

Salaries Payable                                $5,000

Interest Payable                                $3,600

Total current liabilities                    $38,600

Long-term liabilities:

Notes Payable                                $40,000

Total liabilities                                $78,600

Common Stock      $50,000

Net income            $28,400          $78,400

Total liabilities and Equity           $157,000

The balance sheet is one of the financial statements where an entity or individual reports their financial position.

The financial position consists of assets, liabilities, and equity or net worth at a specific time.

Cash $56,000 ($410,000 - $354,000)

Accounts Receivable $22,000

Inventory $50,000

Rent Prepaid $2,000

Office Equipment $30,000

Accumulated Depreciation on Equipment $3,000

Accounts payable $30,000

Salaries Payable $5,000

Common Stock $50,000

Notes Payable $40,000

Interest Payable $3,600

Sales Revenue $342,000 ($320,000 + $22,000)

Cost of goods sold $200,000 ($220,000 + $30,000 - $50,000)

Salaries Expense $85,000 ($80,000 + $5,000)

Rent Expense $12,000 ($14,000 - $2,000)

Miscellaneous Expense $10,000

Interest Expense $3,600 ($40,000 x 12% x 9/12)

Depreciation Expense $3,000 ($30,000/10)

Account Titles                 Debit        Credit

Cash                             $56,000

Accounts Receivable    22,000

Inventory                       50,000

Rent Prepaid                   2,000

Office Equipment         30,000

Accumulated Depreciation:

  Office Equipment                        $3,000

Accounts payable                          30,000

Salaries Payable                              5,000

Common Stock                             50,000

Notes Payable                              40,000

Interest Payable                             3,600

Sales Revenue                           342,000

Cost of goods sold   200,000

Salaries Expense        85,000

Rent Expense              12,000

Miscellaneous Exp.     10,000

Interest Expense          3,600

Depreciation Expense 3,000

Totals                     $473,600  $473,600

Sales Revenue                                 $342,000

Cost of goods sold       $200,000

Salaries Expense            $85,000

Rent Expense                  $12,000

Miscellaneous Expense $10,000

Depreciation Expense     $3,000

Interest Expense              $3,600    $313,600

Net income                                        $28,400

Thus, before the balance sheet can be prepared, the general ledger must be summarized into an adjusted trial balance and an income statement that shows the net income.

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The prime polynomial in this problem is defined as follows:

D. 3x² + x - 6x + 3

A prime polynomial is a polynomial that cannot be reduced, that is, the polynomial cannot be factored.

The reduced forms of each polynomial are given as follows:

The first polynomial can be factored as follows:

x^4 - x² + 3x² - 3

x²(x² - 1) + 3(x² - 1)

(x² + 3)(x² - 1).

It can be factored, hence it is not prime.

The second polynomial is factored as follows:

x^4 - 3x² - x² + 3

x^4 - x² - 3x² + 3

x²(x² - 1) - 3(x² - 1)

(x² - 3)(x² - 1).

It can be factored, hence it is not prime.

The third polynomial is factored as follows:

3x² + x - 6x - 2

3x² - 6x + x - 2

3x(x - 2) + x - 2

(x - 2)(3x + 1)

It can be factored, hence it is not prime.

The fourth polynomial cannot be factored, hence it is prime.

3x² + x - 6x + 3

3x² + 6x + x + 3

3x(x + 2) + x + 3.

x + 2 and x + 3 cannot be factored.

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The number of seats of each bus is given as follows:

The number of seats of each bus is obtained applying the proportions in the context of the problem.

One bus has 3 rows of seats with 9 seats in each row, hence the number of seats of the first bus is given as follows:

3 x 9 = 27.

The other bus has four times as many seat as the first bus, hence the number of seats of the second bus is given as follows:

4 x 27 = 108.

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Answer:

[tex]\textsf{A)} \quad 5+3\sqrt{2}[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{4+\sqrt{2}}{2 -\sqrt{2}}[/tex]

To rationalise the denominator, multiply both the numerator and denominator by the conjugate of the denominator.

The conjugate of an expression is where we change the sign in the middle of the two terms.  Therefore, the conjugate of the denominator of the given expression is:

Multiply the numerator and denominator by the conjugate of the denominator:

[tex]\implies \dfrac{4+\sqrt{2}}{2 -\sqrt{2}} \cdot \dfrac{2 +\sqrt{2}}{2 +\sqrt{2}}[/tex]

Simplify:

[tex]\implies \dfrac{(4+\sqrt{2})(2 +\sqrt{2})}{(2 -\sqrt{2})(2 +\sqrt{2})}[/tex]

[tex]\implies \dfrac{8+4\sqrt{2}+2\sqrt{2}+\sqrt{2}\sqrt{2}}{4+2\sqrt{2}-2\sqrt{2}-\sqrt{2}\sqrt{2}}[/tex]

[tex]\implies \dfrac{8+6\sqrt{2}+2}{4-2}[/tex]

[tex]\implies \dfrac{10+6\sqrt{2}}{2}[/tex]

Reduce to its simplest form by dividing the numerator and the denominator by 2:

[tex]\implies 5+3\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

To find the solutions to f(x) = g(x), we need to find the values of x that make the two sides of the equation equal.The function f(x) = −|x−4| + 4 is a piecewise function. For x≤4, f(x) = −(x−4) + 4 = 4−x and for x>4, f(x) = (x−4) + 4 = x.The function g(x) = 1/2x − 4 is a linear function.When we graph these two functions in the same coordinate plane, we can see that they intersect at the point (4, 4) this point is the only solution where f(x) = g(x)so the solution of x = 4

x = 4