f (x)=2^2-7x-6 Find f (6)

Answer:

:Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded

Step-by-step explanation:

Answer:  Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded to the nearest hundreth.

Step-by-step explanation:

Answer: Plain:  the product is 24 ∠ 15° in polar form. This means that the magnitude of the product is 24 and the angle between the positive real axis and the line connecting the origin and the product is 15°, measured counterclockwise.

Step-by-step explanation: To multiply complex numbers in polar form, we multiply their magnitudes and add their angles. We can start by converting the given complex numbers from rectangular form to polar form:

6√5 - 6i = 6(√5 - i) = 12 ∠ -30°

(√3 + √3i) = √3(1 + i) = 2 ∠ 45°

where we have used the fact that ∠θ is the angle between the positive real axis and the line connecting the origin and the complex number a + bi, measured counterclockwise.

Now, we can multiply the two complex numbers in polar form:

(6√5 - 6i)(√3 + √3i) = 12 ∠ -30° * 2 ∠ 45°

= 24 ∠ 15°

Therefore, the product is 24 ∠ 15° in polar form. This means that the magnitude of the product is 24 and the angle between the positive real axis and the line connecting the origin and the product is 15°, measured counterclockwise.

To determine the quadrant of the complex plane in which the product lies, we note that the angle 15° is in the first quadrant (between 0° and 90°). Therefore, the product lies in the first quadrant of the complex plane.

Answer:

D

Step-by-step explanation:

|6y-3|+8=35

|6y-3|=35-8

|6y-3|=27

[|x-a|=b⇒x-a=± b]

6y-3=±27

1. case 1

6y-3=27

6y=27+3

6y=30

y=30/6=5

case 2.

6y-3=-27

6y=-27+3

6y=-24

y=-24/6=-4

so D

6m≤36

m≤36/6

or m≤6

and m+24≥20

m≥20-24

m≥-4

no solution as m≤-6 and m≥-4

A parametric description of the solution set of a linear system is the same as solving the system is the false statement.

If a linear system has at least one solution, only then can the solution set be stated using a parametric description. The set of ordered pairs that make up the solution to an equation with two variables is referred to as the solution set. You'll discover what a solution set is in this tutorial and witness an example. By combining two equations with two variables into one equation with one variable, we can solve a system of equations. Since there are two variables in each equation in the system, replacing a variable with an expression can help minimize the number of variables in an equation.

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The machine required at least 12 hours and 45 minutes to complete the hole on schedule.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given, a special machine is used to construction site to dig holes.

And the depth of hole must be at least \(12\frac{1}{2}\) feet at the end of day.

After 4.75 feet, digging speed slows to the rate of 3/5 feet per hour.

In order to solve the problem:

First, we convert mixed fraction to decimal form,

\(12\frac{1}{2}\) feet  = 25 / 2

               = 12.5 feet

Digging speed slows,

12.5 - 4.75 = 7.75 feet.

To find the minimum amount of the time:

Time = 7.75 feet divided by the present rate of feet per hour.

Time = 7.75 ÷ 3/5

Time = 7.75 / 0.6

Time = 12.90

Converting  12.92 to hours and minutes.

0.90 is 90 percentage of 60 minutes,

90 x 60 / 100 = 45.

Time = 12 hours and 45 minutes.

Therefore, at the end of day to slay on the time machine needs to dig at least 12 hours and 45 minutes.

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Selling price = $6.37 .

Selling price = $6.94

Selling price = $346.80

1)

Sales revenue = 6,000

Less:-Variable costs ($1.5 per unit 1,000) = 1,500

Less:- Fixed costs = (1,700)

Operating Income = 2,800

Variable costs and Fixed costs have increased.

Hence, in order to maintain the same Operating Income, the selling price should be higher than the current selling price .

Thus to maintain same operating income the selling price should be $6.37 .

2)

The computation is given below:

Sales price = ( Total sales revenue ÷ packages sold)

Total sales revenue = ( Total Cost + Operating income )

Total Cost = ( Variable Cost + Fixed cost)

Now

Variable cost = 1,000 packages × $1.90 per unit

= $1,900

Fixed cost = $1,700 × 120%

= $2040

Total cost = $1,900 + $2,040

= $3,940

Now  

Total sales revenue is

= $3,940 + $3,000

= $6,940

Now  

Sales price = $6,540 ÷ 1,000 packages

= $6.94

3)

-Fruit Computer Company has variable costs of $220 per unit and fixed costs of $32,000 per month.

- The company currently sells 500 units per month at a sales price of $300.

Net margin = $8000

- The company wants to increase its operating income by 30%.

- If the company upgrades the computer quality, the variable cost per unit will increase to $240 and the fixed costs will rise by 50%.

Thus the selling price per unit will be  $346.80 per unit.

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In the polar coordinate system, the region R corresponds to 0 ≤ r ≤ (2 - 9sin(θ))/(9cos(θ) + 9sin(θ)) and 0 ≤ θ ≤ π/2.

To evaluate the given iterated integral ∫∫R (1 - y²)/(9(x + y)) dA, where R is the region in the xy-plane bounded by the curves x = 0, y = 1, and 9(x + y) = 2, we can convert it to polar coordinates for easier computation.

In polar coordinates, we have x = rcos(θ) and y = rsin(θ), where r represents the distance from the origin and θ is the angle measured counter clockwise from the positive x-axis.

The integral becomes ∫∫R (1 - r²sin²(θ))/(9(rcos(θ) + rsin(θ))) r dr dθ. In the polar coordinate system, the region R corresponds to 0 ≤ r ≤ (2 - 9sin(θ))/(9cos(θ) + 9sin(θ)) and 0 ≤ θ ≤ π/2.

In the given integral, we substitute x and y with their respective polar coordinate representations. The numerator becomes 1 - r²sin²(θ), and the denominator becomes 9(rcos(θ) + rsin(θ)). Multiplying the numerator and denominator by r, we have (1 - r²sin²(θ))/(9(rcos(θ) + rsin(θ))) = (1 - r²sin²(θ))/(9r(cos(θ) + sin(θ))). We then rewrite the double integral as two separate integrals: the outer integral with respect to θ and the inner integral with respect to r. The limits of integration for θ are 0 to π/2, while the limits for r are determined by the curve 0 = (2 - 9sin(θ))/(9cos(θ) + 9sin(θ)).

We can simplify this curve to 2cos(θ) - 9sin(θ) = 9, which represents an ellipse in the xy-plane. The limits of r correspond to the radial distance within the ellipse for each value of θ. By evaluating the double integral using these limits, we can determine the result of the given iterated integral.

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To write the equation that represents the situatio, as y is in function of x, you multiply the rate by the number of minutes (x):

In 7.5 minutes he can type:

Answer:

8

Step-by-step explanation:

x^3

Let x=2

2^3

2*2*2

8

Answer: 9

Step-by-step explanation:

The transformation that will NOT carry the rectangle onto itself is option D: a rotation of 180 degrees about the point (5,5).

A reflection over the line y=x (option A) will swap the x-coordinates with the y-coordinates, preserving the shape of the rectangle. A reflection over the line y=-x+10 (option B) will also preserve the shape of the rectangle.

A rotation of 180 degrees about the point (6,6) (option C) will rotate the rectangle by half a turn, but it will still maintain its original shape and orientation.

However, a rotation of 180 degrees about the point (5,5) (option D) will change the position of the rectangle. The point (5,5) does not coincide with the center of the rectangle, so the rotation will not keep the rectangle intact. Therefore, option D is the correct answer.

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The correct order from least to greatest is 3/4 × 4/9, 7/7 × 4/9, 2 × 4/9, 1 2/3 × 4/9.

To order the expressions from least to greatest, we need to compare their values. Let's evaluate each expression:

7/7 × 4/9 = 1 × 4/9 = 4/9

3/4 × 4/9 = 3 × 4/36 = 12/36 = 1/3

1 2/3 × 4/9 = (5/3) × 4/9 = 20/27

2 × 4/9 = 8/9

Now, let's arrange the expressions from least to greatest:

1/3 < 4/9 < 8/9 < 20/27

Therefore, the correct order from least to greatest is:

3/4 × 4/9, 7/7 × 4/9, 2 × 4/9, 1 2/3 × 4/9

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The inverse of the function y = - 5x will be;

⇒ f ⁻¹ (x) = - x / 5

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The function is,

⇒ y = - 5x

Now,

Find the inverse function as;

The function is,

⇒ y = - 5x

Solve value for x as;

⇒ y = - 5x

⇒ x = - y / 5

Substitute x = f ⁻¹ (x) and y = x, we get;

⇒ f ⁻¹ (x) = - x / 5

Thus, The inverse of the function y = - 5x will be;

⇒ f ⁻¹ (x) = - x / 5

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Answer:

A     and      d

Step-by-step explanation:

The wind speed is 37.5 miles per hour.

We are given that;

Number of files= 750

Time=2.5 hours

Now,

Let p be the plane’s rate of speed and w be the wind speed. Then, when the plane flies against the wind, its rate is p - w. When the plane flies with the wind, its rate is p + w.

Using the formula d = rt, we can write two equations for the two trips. For the trip from Chicago to New York, we have 750 = (p - w) * 2.5. For the trip from New York to Chicago, we have 750 = (p + w) * 2.

Simplifying the equations, we get 300 = p - w and 375 = p + w.

Adding the two equations, we get 675 = 2p. Solving for p, we get p = 337.5. This means that the plane’s rate of speed is 337.5 miles per hour.

Substituting p = 337.5 into one of the equations, we get 300 = 337.5 - w. Solving for w, we get w = 37.5.

Therefore, by speed the answer will be 7.5 miles per hour.

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Answer:

Aaron was the sitter for 4 hours

Step-by-step explanation:

from the sentence my equation is 12x + 10 = 58

x represents the amount of hours

now solve

12x + 10 = 58

12x = 48

x = 4

Answer:

Aaron worked for 4 hours

Step-by-step explanation:

f(x)=12x+10

f(?)=58

58=12x+10

48=12x

4=x

If the coach was to pick the player based on the best average, the coach would choose Jessie.

If the coach is picking based on who has been the most consistent, they would pick Sam.

The average for Jessie is :

= ( 150 + 145 + 181 + 235 + 196 + 211 + 204 + 221 + 185 ) / 9

= 192 points

The average for Sam :

= ( 186 + 187 + 192 + 195 + 194 + 157 + 157 + 162 + 200 ) / 9

= 181 points

The coach would pick Jessie based on average.

For consistency, we can use the measure of variability of range. The range for Jessie is:

= 235 - 145

= 90 points

The range for Sam would be:

= 200 - 157

= 43 points

This shows that Sam is more consistent and so would be picked based on consistency.

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Answer:

The baker should add 3.75 gallon of water to 5 gallons of 70 % sugar syrup to make the 40 % syrup.

Step-by-step explanation:

The percentage concentration (\(r\)), dimensionless, is determined by the following expression:

\(r = \frac{V_{sugar}}{V_{sugar}+V_{water}}\) (1)

Where:

\(V_{sugar}\) - Volume of sugar, measured in gallons.

\(V_{water}\) - Volume of water, measured in gallons.

A 70 % sugar syrup means that there are 7 parts of sugar for each 10 parts of solution, that is, 7 parts of sugar and 3 parts of water. We need to add more water to dilute the solution to 40 %. Then, the new concentration must be equal to:

\(r' = \frac{V_{sugar}}{V_{sugar}+V_{water}+V'}\) (2)

Where \(V'\) is the addition of water needed to dilute the solution, measured in gallons.

If we now that \(V_{sugar} = 3.5\,gal\), \(V_{water} = 1.5\,gal\) and \(r' = 0.4\), then the quantity of additional water is:

\(\frac{3.5\,gal}{5\,gal+V'} = 0.4\)

\(3.5 = 0.4\cdot (5+V')\)

\(3.5 = 2+0.4\cdot V'\)

\(0.4\cdot V' = 1.5\)

\(V' = 3.75\,gal\)

The baker should add 3.75 gallon of water to 5 gallons of 70 % sugar syrup to make the 40 % syrup.

Answer:

3.75 gallons of water should be added

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

Recognize that all angles of a triangle add up to 180 degrees, so your equation would be x + 16 + x + 24 + 78 = 180.

Step 1: Combine like-terms.

2x + 118 = 180

Step 2: Subtract 118 from both sides to isolate the variable.

2x = 62

Step 3: Simplify

x = 31

Answer:

it should be linear

Step-by-step explanation:

if its linear u can draw a straight line through most of the points

Answer:

Multiplicative Identity

Step-by-step explanation:

This is what they all basically mean:

Additive Identity - addition

Associative Property - simplifying

Distributive Property - multiplying brackets, or expanding

Multiplicative Identity - multiplication

In this equation, you first expand 16(4x-1) which uses multiplication but only has one bracket meaning, you use multiplicative identity first.

Answer:

\(\displaystyle \large{\frac{11}{3} < \sqrt{17} < \sqrt{20}}\)

Step-by-step explanation:

( 1 ) 11/3

\(\displaystyle \large{\frac{11}{3}}\) can be converted to mixed fractions to \(\displaystyle \large{3\frac{2}{3}}\)

Therefore, 11/3 is at least around 3, almost 4. It could be more than 3.5 by approximation but not exactly 4.

( 2 ) √20

\(\displaystyle \large{\sqrt{20}=\sqrt{5\cdot 4}}\\\displaystyle \large{\sqrt{20}=\sqrt{5\cdot 2\cdot 2}}\\\displaystyle \large{\sqrt{20}=2\sqrt{5}}\)

We know that \(\displaystyle \large{\sqrt{4}=2}\) so \(\displaystyle \large{\sqrt{5} > \sqrt{4}}\) which means approximately, \(\displaystyle \large{\sqrt{20}}\) can be either at least 4.3 up to 4.4

( 3 ) √17

We know that \(\displaystyle \large{\sqrt{16} = 4}\) so \(\displaystyle \large{\sqrt{17}}\) can be at least 4.1 up to 4.2, but it’s obvious that the square root of 17 is less than square root of 20 since \(\displaystyle \large{\sqrt{a} > \sqrt{b}}\) for a > b

Hence, from least to greatest:

\(\displaystyle \large{\frac{11}{3} < \sqrt{17} < \sqrt{20}}\)

The given sequence is defined by an=cos(n/2). Now, we are supposed to determine if the sequence converges or diverges and if it converges, we are supposed to find the limit.

The given sequence is defined by an=cos(n/2). Now, we are supposed to determine if the sequence converges or diverges and if it converges, we are supposed to find the limit. Using the limit comparison test, the limit as n approaches infinity of cos(n/2) over 1/n is 0. As a result, the given sequence and the harmonic series have the same behavior. Thus, the series diverges. When a sequence is divergent, it does not have any limit, and the limit does not exist, which means the limit in this case is DNE.

Since it has been proven that the given sequence diverges, its limit does not exist (DNE). Therefore, the answer to the question "determine whether the sequence converges or diverges. if it converges, find the limit. (if an answer does not exist, enter dne.) an = cos(n/2)" is "The sequence diverges, and the limit is DNE."

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Answer:

A

Step-by-step explanation:

the first number in slope intercept is the slope and the second number is the y-intercept

Answer:

The answer is Choice a

Step-by-step explanation:

We have proven that if a>b and c<0, then a/c < b/c as shown below

From the question, we are to prove that if a>b and c<0, then a/c < b/c

To do this,

We will pick numbers to represent the letters a, b, and c that satisfy the given conditions

From the given information,

a > b

Let a = 6

and b = -2

Also, we have that

c<0

Let c = -1

Now, evaluate each of the expressions

Evaluating a/c

a/c = 6/-1

a/c = -6

Evaluating b/c

b/c = -2/-1

b/c = 2

-6 < 2

Thus,

a/c < b/c

Hence, we have proven that if a>b and c<0, then a/c < b/c

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Answer:

x = 4

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define

2.4x + 4.6x = 28

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

Here we see that 28 does indeed equal 28.

∴ x = 4 is a solution of the equation.

1. We can use the subset A = R as the domain of the function f.

2. The data support a well-defined function.

3.  (a) f(x) = x^2 -- The function is well-defined.

(b) g(a) = 1/a --The function is not well-defined on R.

(c) h(x) = √(x-2) + 42 -- The function is not defined for any input x less than 2, so it is not well-defined on the entire domain of R.

1. To make f(x) = 3 - 7x a well-defined function, we need to ensure that the output of the function is a real number for every input in the domain.

Since the function is defined for all real numbers x, the domain of the function can also be all real numbers.

2. The data { (1,3), (2,4), (3,2), (4,1)} support a well-defined function from (1,2,3,4) to (1,2,3,4).

For a function to be well-defined, each input in the domain must correspond to exactly one output in the range.

In this case, we can see that each input in the domain (1,2,3,4) has exactly one corresponding output in the range (1,2,3,4).

3.

(a) f(x) = x^2 is a well-defined function on the domain of all real numbers, R. For every input x, the output x^2 is a real number, so the function is well-defined.

(b) g(a) = 1/a is not a well-defined function on the domain of all real numbers, R. The function is undefined at a = 0 because division by zero is not allowed. Therefore, the function is not well-defined on R.

(c) h(x) = √(x-2) + 42 is a well-defined function on the domain x ≥ 2. For every input x greater than or equal to 2, the output √(x-2) + 42 is a real number, so the function is well-defined.

However, the function is not defined for any input x less than 2, so it is not well-defined on the entire domain of R.

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Answer:

They are similar.  Triangle abc is similar to triangle edc.

Step-by-step explanation:

To prove that triangles are similar, you must show that the 3 angles in one triangle are equal to the 3 angles in the other triangle.  We know that they both have a 50 degree angle.  We can also see that they both have a right angle.  That means that the 3rd angle must also equal 40 (180-90-50).  So by AAA the two triangles are congruent.

Triangle ABC is similar to triangle EDC.

Answer:

triangle ABC is similar to triangle DCE

Step-by-step explanation:

Reason being that angles in triangle ABC Correspond to That of triangle DCE Eg triangle ABC=CDE

Answer:1

Step-by-step explanation:

(20-14)*2/12

= 6*2/12

=1

The logarithm : \(log_{12} (7^{16} )\) ÷ \(log_{12} (7^4)\) = 4.

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