f r=9, b=5, and g=−6, what does (r+b−g)(b+g) equal?


-20


-8


8


19


20

Hello there. To solve this system of equations, we'll use the method of substitution.

Take the first equation, in which y = 2/3x + 5 and plug in this value of y in the second equation:

7x - 3(2/3x + 5) =15

Apply the FOIL

7x - 2x - 15 = 15

Sum 15 on both sides of the equation and add the values

5x = 30

Divide both sides of the equation by a factor of 5

x = 6

Now, plug in this value on the first equation:

y = 2/3 * 6 + 5

Multiply and add the values

y = 4 + 5 = 9

The solution to this system of equations is the pair (6, 9)

I hate my grandma I hope she goes to hell but lucky for her she is Christian.

Answer:

a) Plan B cost more, and $6

b) Plan B cost less according to long calls

Step-by-step explanation:

As you can see that at 175 minutes used(per month) Plan A is $14 and Plan B is $20. So Plan B cost more but the difference between then is 20 - 14 = 6. For the second question: They cost the same at 250 minutes used(per month) and Plan B since the line is flat and the price is the same for all minutes

The reasonable domain for the function is (b) x > 0

From the question, we have the following parameters that can be used in our computation:

The function f(x) = 75x + 100

Where x is the number of hours

f(x) is the total cost.

In this case, the number of hours cannot be negative or 0

This means that the values of x in the function would be x > 0

These values of x are the domain

So, the reasonable domain for the function os (b) x > 0

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The maximum amount the firm should pay for the machinery is $61,672.67

The maximum amount that the firm should pay for the machinery can be determined by calculating the present value of the cash flows expected from the new piece of machinery

Present value is the sum of the discounted cash flows from the investment

Discounted year 1 cash flow: $8000 ÷ 1.06 = 7547.17

Discounted year 2 cash flow: $8000 ÷ 1.06² = 7119.97

Discounted year 3 cash flow: $8000 ÷ 1.06³ = 6716.95

Discounted year 4 cash flow: $8000 ÷ 1.06^4 = 6,336.75

Discounted year 5 cash flow: $8000 ÷ 1.06^5 = 5,978.07

Discounted year 6 cash flow: $8000 ÷ 1.06^6 = 5,639.68

Discounted year 7 cash flow: $8000 ÷ 1.06 ^7= 5,3204.57

Discounted year 8 cash flow: $8000 ÷ 1.06^8 = 4,322.15

Discounted year 9 cash flow: $8000 ÷ 1.06^9 = 4,735.19

Discounted year 10 cash flow: $8000 ÷ 1.06^10 = 4,467.16

Discounted year 10 cash flow: $5000  ÷ 1.06^10 = 2,791.97

The sum of the discounted cash flows is $61,672.67

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Answer:

1. 18

2. 13.5

3. 3rd choice

4. 2nd choice

5. 18.6

6.3m + 8

7. 5x2 + y

i hope this work for you

Answer:

Step-by-step explanation:

To find the number of antiviral proteins injected into the person, we can set up a proportion:

2 mL contains 2.3 × 10^3 antiviral proteins

x mL contains how many antiviral proteins?

The proportion can be written as:

2 mL / 2.3 × 10^3 = x mL / (unknown number of antiviral proteins)

We can solve this proportion by cross-multiplication:

2 mL * (unknown number of antiviral proteins) = 2.3 × 10^3 antiviral proteins * x mL

x = (2.3 × 10^3 antiviral proteins * x mL) / 2 mL

Simplifying, we get:

x = 1.15 × 10^3 * x mL

Therefore, the number of antiviral proteins injected into the person is 1.15 × 10^3.

The total number of cells in the person's body is approximately 1 × 10^14. If 8% of the person's cells are infected with the virus, we can calculate the percentage of cells that can be affected by the medication:

Percentage of cells affected = (Number of infected cells / Total number of cells) * 100

Number of infected cells = 8% of 1 × 10^14 cells

Number of infected cells = (8/100) * 1 × 10^14

Number of infected cells = 8 × 10^12

Percentage of cells affected = (8 × 10^12 / 1 × 10^14) * 100

Percentage of cells affected = 8 × 10^-2 * 100

Percentage of cells affected = 8%

Therefore, the administered medication can affect 8% of the person's cells.

To find the amount of medication needed to have 1 antiviral protein for every infected cell, we can set up a proportion:

2.3 × 10^3 antiviral proteins in 2 mL

1 antiviral protein in x mL

The proportion can be written as:

2.3 × 10^3 antiviral proteins / 2 mL = 1 antiviral protein / x mL

We can solve this proportion by cross-multiplication:

(2.3 × 10^3 antiviral proteins) * x mL = 2 mL * 1 antiviral protein

x = (2 mL * 1 antiviral protein) / (2.3 × 10^3 antiviral proteins)

Simplifying, we get:

x = 0.8696 mL

Therefore, to have 1 antiviral protein for every infected cell, approximately 0.8696 mL of medication needs to be administered. This is equivalent to 0.0008696 liters.

Answer:

2.4 × 10^-2

Step-by-step explanation:

You can do a sort of "undistributive" property and factor out the 10^-2 and then add the 1.2+1.2

1.2×10^-2 + 1.2×10^-2

= 10^-2(1.2 + 1.2)

= 10^-2(2.4)

= 2.4 × 10^-2

OR you can change from scientific notation to standard and add them and change back to sci. not. See image.

According to the information, it can be inferred that the total matches that would be played in total are 160,461.

A combination is a term to refer to an arrangement of elements in no particular order. For example:

When we put together a sandwich with salami, ham and turkey. The order in which the deli meats are placed does not matter as long as they are in a sandwich. There is only one way to stack the meat on the sandwich when the order doesn't matter.

To calculate how many matches will be played in total we have to perform the following procedure:

\(= ^{567} C_{2} \\= \frac{(567)!}{2!565!} \\= \frac{567 * 566 * (565)!}{2 * (565)!} \\= 567 * 283\\= 160,461\\\\\)

As we can see after the combination, the number of games that would be played in this tournament would be 160,461.

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We can compute Amy's monthly budget for each question using division operations, as follows:

1. Amy's monthly budget for textbooks and course supplies is $100.

2. Amy's monthly budget for rent, utilities, and food is $1,422.

3. Amy's monthly budget for personal and miscellaneous costs is $251.

4. Amy's total monthly budget is $1,825.

The total monthly budget is the total budget divided by the period (nine months).

Division operations can be used to determine the individual monthly budgets for each expense class by dividing the total cost by 9.

Textbooks and Course Supplies =         $900      $100

Rent, Utilities, and Food =                   $12,798   $1,422

Personal & Miscellaneous Expense = $2,259     $251

Transportation =                                      $468       $52

Total non-tuition expenses =             $16,425  $1,825 ($16,425/9)

The number of months for the year = 9 months

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Answer:

1

Step-by-step explanation:

Using a slope triange we can see that the rise is 1 and the run is 1 and 1/1=1

The Length is 5 inches and the Breadth is 15 inches

What is Perimeter?

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.

Solution:

Perimeter of Rectangle = 2*(Length + Breadth)

According to the question

Breadth = 3*Length

Perimeter = 40

40 = 2*(Length + 3*Length)

20 = 4*Length

Length = 5 inch

Breadth = 15 inch

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Median is the Middle number

1. Sort the numbers until they are all in value order

2. Find the middle number

So the answer would be 12

Answer:

Median = 12

Step-by-step explanation:

12, 11, 14, 14, 14, 12, 7

Arranging the given data in ascending order, we find:

7, 11, 12, 12, 14, 14, 14

Here,

Number of observations (N) = 7

\( \therefore \: \frac{N + 1}{2} = \frac{7 + 1}{2} = \frac{8}{2} = 4 \\ \\ median \: = 4th \: term \\ \huge \red{ \boxed{median = 12}}\)

Answer:

Standard Deviation = 5.928

Step-by-step explanation:

a) Data:

Days  Hours spent  (Mean - Hour)²

1              5                61.356

2             7                34.024

3            11                  3.360

4           14                   1.362

5           18               26.698

6          22               84.034

6 days 77 hours,    210.834

mean

77/6 = 12.833    and 210.83/6 =  35.139

Therefore, the square root of 35.139 = 5.928

b) The standard deviation of 5.928 shows how the hours students spend outside of class on class work varies from the mean of the total hours they spend outside of class on class work.

Answer:

Step-by-step explanation:

The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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Answer:

x = 6

Step-by-step explanation:

∠ DBC + ∠ ABC = ∠ ABD , substitute values

5x - 4 + 8x - 3 = 79

13x + 1 = 79 ( subtract 1 from both sides )

13x = 78 ( divide both sides by 13 )

x = 6

The values of x, y , and z in the matrix equation is 3, 4, 0 respectively.

The solution of the matrix equation is calculated by applying Cramer's rule as shown below;

[ 1     1     -1 ]  [ 7 ]

[ 2    3     0 ] [ 18 ]

[ -5   -7    -1 ] [ -43 ]

The determinant of the matrix is calculated as follows;

[ 1     1     -1 ]  

[ 2    3     0 ]

[ -5   -7    -1 ]

Δ = 1 (-3 - 0) - 1(-2 - 0 )  - 1(-14 + 15)

Δ = -2

The x determinant of the matrix is calculated as follows;

[ 7     1     -1 ]  

[ 18    3     0 ]

[ -43   -7    -1 ]

Δx = 7 (-3 - 0) - 1 (-18 - 0 )  - 1(-126 + 129)

Δx = -6

The y determinant of the matrix is calculated as follows;

[ 1     7     -1 ]  

[ 2    18     0 ]

[ -5   -43   -1 ]

Δy = 1 (-18 - 0 )   - 7(-2 - 0 )  -1(-86 + 90)

Δy = -8

The z determinant of the matrix is calculated as follows;

[ 1     1     7 ]  

[ 2    3    18 ]

[ -5   -7   -43]

Δz = 1 (-129 + 126) - 1(-86 + 90) + 7(-14 + 15)

Δz = 0

The values of x, y , and z is calculated as;

x = Δx/Δ = -6/-2 = 3

y = Δy/Δ = -8/-2 = 4

z = Δz/Δ = 0/-2 = 0

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Answer:

18

Step-by-step explanation:

The question in algebra :

7x = 126

what is x ? :

x = 126 ÷7 (done through balancing)

x = 18  

Hoep this helped and brainliest please

Answer:

\(t=1.201\ \text{hour}\)

Step-by-step explanation:

Given that,

Distance, d = 100 mile

Velocity of the winner, v = 120.1229 mph

We know that velocity of an object is equal to distance per unit time. Let t is the time. So,

\(v=\dfrac{d}{t}\\\\t=\dfrac{d}{v}\\\\t=\dfrac{120.1229}{100 }\\\\t=1.201229\ \text{hour}\\\\\text{Round to the nearest thousandth}\\\\t=1.201\ \text{hour}\)

Hence, 1.201 hour is taken by the winner.

Answer:

A positive.

Step-by-step explanation:

Remember that there is an even amount of negatives in this situation which makes it a positive.  Two positive numbers multiplied together are still positive.

Answer:

Step-by-step explanation:

10 x 2=20 white chocolate

10+20=30 chocolates altogether

Answer:

25. -7/5 \(\leq\) x \(\leq\) 1

Step-by-step explanation:

18:

\(5-|x|\leq 2\\-|x| \leq -3\\|x|\leq 3\\x\geq -3\)or       \(x\leq 3\)

25:

\(3|5x+1|-6\geq 12\\3|5x+1|\geq 18\\|5x+1|\geq 6\\x\leq -7/5\)or               \(x\geq 1\)

\(-7/5\leq x\leq 1\)

I don't think I explained this well let me know if you need more explanation.

We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

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To find the coterminal angle for a rotation of -757°, we can add or subtract multiples of 360° until we find an angle between 0° and 360° that is coterminal with -757°.

Adding 360° multiple times:

-757° + 360° = -397° (not coterminal)

-397° + 360° = -37° (not coterminal)

-37° + 360° = 323°

Therefore, the coterminal angle for -757° is 323°.

To find the quadrant in which 323° lies, we can note that 323° is between 270° and 360°, which means it lies in the fourth quadrant.

To find the reference angle for 323°, we can subtract 360° from 323° until we get an angle between 0° and 90°:

323° - 360° = -37° (not in the correct range)

-37° + 360° = 323°

So the reference angle for 323° is 37°.

The value of n, considering the intersecting chords in the circle, is given as follows:

n = 6m.

A chord of a circle is a straight line segment that connects two points on the circle. Specifically, it is a line segment whose endpoints are on the circle. A chord is often denoted by drawing a line segment between the two endpoints, with the segment passing through the interior of the circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Considering the two intersecting chords for the circle in this problem, the value of n is obtained as follows:

5n = 15 x 2

5n = 30

n = 30/6

n = 6m.

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Step-by-step explanation:

To find the profit of the firm, we need to first determine the quantity Q that maximizes the profit, and then use that quantity to find the price and profit.

The profit function can be written as:

π(Q) = TR(Q) - TC(Q)

where TR(Q) is the total revenue function and TC(Q) is the total cost function. We can write TR(Q) as:

TR(Q) = P(Q) * Q

where P(Q) is the price function, which is given as:

P(Q) = 240 - 20Q

So, the profit function becomes:

π(Q) = (240 - 20Q) * Q - (120 + 45Q - Q^2 + 0.4Q^3)

Simplifying this expression, we get:

π(Q) = -0.4Q^3 + 24.6Q^2 - 195Q + 120

To maximize the profit, we take the derivative of the profit function with respect to Q and set it equal to zero:

π'(Q) = -1.2Q^2 + 49.2Q - 195 = 0

Solving for Q using the quadratic formula, we get:

Q = (49.2 ± sqrt(49.2^2 - 4*(-1.2)(-195))) / (2(-1.2))

Q = 21 or Q = 32.5

Since the coefficient of the Q^3 term in the profit function is negative, the profit function has a maximum at Q = 32.5. Therefore, the firm should produce and sell 32.5 units of output.

To find the price that the firm should charge, we substitute Q = 32.5 into the demand function:

P = 240 - 20Q

P = 240 - 20(32.5)

P = 160

Therefore, the firm should charge a price of $160 per unit.

To find the profit at the optimal level of output, we substitute Q = 32.5 and P = 160 into the profit function:

π(Q) = -0.4Q^3 + 24.6Q^2 - 195Q + 120

π(32.5) = -0.4(32.5)^3 + 24.6(32.5)^2 - 195(32.5) + 120

π(32.5) = $1,722.81

Therefore, the profit at the optimal level of output is $1,722.81

As, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively. So,  if a commutes with d, then it must be block diagonal.

Let's suppose that d is a diagonal matrix with repeated diagonal entries grouped contiguously, i.e.,

d = \(\begin{pmatrix} D_1 & 0 & 0 & \cdots & 0 \ 0 & D_1 & 0 & \cdots & 0 \ 0 & 0 & D_2 & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & D_k \end{pmatrix}\),

where \(D_1, D_2, \dots, D_k\) are scalars and appear with frequencies \(m_1, m_2, \dots, m_k\), respectively, so that \(m_1 + m_2 + \dots + m_k = n\), the size of the matrix.

Suppose that \(a\) is a matrix that commutes with d, i.e., ad = da.

Then, for any \(i \in {1, 2, \dots, k}\), we have

\(ad_{ii} = da_{ii}\)

Here, \(d_{ii}\) denotes the \(i$th\) diagonal entry of d, i.e., \(d_{ii} = D_i\) for \(i = 1, 2, \dots, k\). Since d is diagonal, \(d_{ij} = 0\) for \(i \neq j\), and

hence

\(ad_{ij} = da_{ij} = 0\)

for all \(i \neq j\).

Therefore, a is also diagonal, with diagonal entries \(a_{ii}\), and we have

\(a = \begin{pmatrix} a_{11} & 0 & 0 & \cdots & 0 \ 0 & a_{11} & 0 & \cdots & 0 \ 0 & 0 & a_{22} & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & a_{kk} \end{pmatrix}\)

Thus, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively.

Therefore, if a commutes with d, then it must be block diagonal.

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