streets that form a square block. The length of each side of the block is 221 m. Find the area of the square defined by this city block.

The domain of the function f(x)= -long(5-x)+b is Dom(f) = [– ∞,  5]., range is all real numbers except for x = 5.

IF function is the process or state of instruction that text inputs performance is specific task and produce an output functional key components of programming language allowing the quarter to create complex commands with simple instruction for example a function can be used to add two numbers together or to generate a random number function can also be combined to create more complex sequence of instruction.

The range of this function is all real numbers as the long function will never return a negative value. The value of b determines the exact range of the function, as it shifts the graph up or down.

The formula is: f(x) = - log(5 - x) + b.

Limitation for the f domain:

5 – x > 0

x < 5

Hence, f's domain is

Dom(f) = {x ∈ R:  x < 5}

Alternatively by notating intervals,

Dom(f) = [– ∞, 5].

Secondly, we wish to demonstrate that there is always an x Dom(f) for any given y R.

y = f(x) (x)

Once we've demonstrated that, we can say that f's operating range is R. (all real numbers).

How to find x in an equation:

\(y = f(x)\\y = - log(5 - x) + b\\y - b = - log(5 - x) (5 - x)\\-(y - b) = log(5 - x) (5 - x)\\b - y = log(5 - x) (5 - x)\\5 - x = 10^{(b - y) (b - y)}\\x = 5 - 10^{(b - y) (b - y)}\\\)

Because y is not constrained, the range of f is R. (all real numbers).

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The given subset satisfies all three conditions of a subspace, we can conclude that it is a subspace of ℙ2.

To prove this, we need to show that the set satisfies the three conditions of a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.

Let p(t) and q(t) be two polynomials of the form \(p(t) = at²\)and \(q(t) = bt²\), where a and b are real numbers. Then, the sum of these two polynomials is:

\(p(t) + q(t) = at² + bt²\)

\(= (a+b)t²\)

Since a+b is a real number, the sum of p(t) and q(t) is still of the form at² and thus belongs to the given set. Therefore, the set is closed under addition.

Now, let p(t) be a polynomial of the form \(p(t) = at²\) and c be a real number. Then, the scalar multiple of p(t) by c is:

\(c p(t) = c(at²) = (ca)t²\)

Since ca is a real number, the scalar multiple of p(t) by c is still of the form at² and thus belongs to the given set. Therefore, the set is closed under scalar multiplication.

Finally, the zero vector is the polynomial of the form \(p(t) = 0t² = 0\), which clearly belongs to the given set. Therefore, the set contains the zero vector.

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Step-by-step explanation:

the smallest :13

the largest :75

Answer:

smallest :13

largest :75

Answer:

x= -3 and y= 0

Step-by-step explanation:

5x+2y=-15

2x-2y=-6    

7x        =-21

x= -3

Putting value of x in equation 1  

5(-3) +2y=-15

-15+2y= -15

2y= 0

y= 0

This can be solved with the help of matrices

In matrix form the above equations can be written in the form

\(\left[\begin{array}{ccc}5&2\\2&-2\/\end{array}\right]\)  \(\left[\begin{array}{ccc}x\\y\\\end{array}\right]\)  = \(\left[\begin{array}{ccc}-15\\-6\\\end{array}\right]\)

Let

\(\left[\begin{array}{ccc}5&2\\2&-2\/\end{array}\right]\) = A  \(\left[\begin{array}{ccc}x\\y\\\end{array}\right]\)  = X  and  \(\left[\begin{array}{ccc}-15\\-6\\\end{array}\right]\)= B

Then AX= B

or X= A⁻¹ B

where  A⁻¹= adj A/ ║A║   where mod A≠ 0

adj A=  \(\left[\begin{array}{ccc}-2&-2\\-2&5\/\end{array}\right]\)

║A║= ( 5*-2- 2*2)= -10-4= -14≠0

X= A⁻¹ B

 \(\left[\begin{array}{ccc}x\\y\\\end{array}\right]\)    =- 1/14  \(\left[\begin{array}{ccc}-2&-2\\-2&5\/\end{array}\right]\)   \(\left[\begin{array}{ccc}-15\\-6\\\end{array}\right]\)

 \(\left[\begin{array}{ccc}x\\y\\\end{array}\right]\)    =- 1/14     \(\left[\begin{array}{ccc}-2*-15&+ -2*-6\\-2*-15&+ 5*-6\\\end{array}\right]\)

 \(\left[\begin{array}{ccc}x\\y\\\end{array}\right]\)  =- 1/14 \(\left[\begin{array}{ccc} 30&+12\\30&+-30\\\end{array}\right]\)

 \(\left[\begin{array}{ccc}x\\y\\\end{array}\right]\)  =- 1/14 \(\left[\begin{array}{ccc}42\\0\\\end{array}\right]\)

\(\left[\begin{array}{ccc}x\\y\\\end{array}\right]\)  = \(\left[\begin{array}{ccc}-42/14\\0/-14\\\end{array}\right]\)

\(\left[\begin{array}{ccc}x\\y\\\end{array}\right]\)  = \(\left[\begin{array}{ccc}-3\\0\\\end{array}\right]\)

From here x= -3 and y= 0

Solution Set = [(-3,0)]

Step-by-step explanation:

7.083, 7.2,and 7.21

This should be the answer

Answer:

60 and 70°

Step-by-step explanation:

the angle sum of a quadrilateral is 360

200°+30°+6x+7x=360°

13x=130°

x=10°

1st angle: 10°×6=60°

2nd angle: 10°×7=70°

Answer:

-The increase in dollars is $1598

-The amount in her account at the end of last year was $8398.

Step-by-step explanation:

To find the increase, you have to multiply the initial amount for the percentage increase:

6800*23.5%=1598

Now, to find the amount in her account at the end of last year, you have to add the initial amount plus the increase in dollars:

6800+1598=8398

According to this, the amount in her account at the end of last year was $8398.

Answer:

b = 8.485

c = 23.995 ≈ 24

Step-by-step explanation:
Part b:

\(\sqrt{(10-4)^2+(9-3)^2}\)

√(36 + 36)

= 8.485

Part c:

Base = \(\sqrt{(6-2)^2+(1-5)^2}\)

Base = 5.656

Area = Base x Height x 0.5

Area = 5.656 x 8.485 x 0.5

Area = 23.995 ≈ 24

Answer:

A. 25 cubic meters

Explanation:

The volume of a cone is obtained using the formula below:

Substitute the given values:

The correct choice is A.

Answer: it's 72 (B)

Step-by-step explanation: that's what I put. It was correct

To determine the force t2 needed to pull the rope over the two fixed drums, we must first consider the forces acting on the rope. The force t1 applied at point A will create a tension force along the length of the rope, and this tension force will be transferred to point B. At point B, the tension force will need to overcome the frictional forces acting on the drums in order to move the rope.

The frictional forces acting on the drums are caused by the angles of contact and the coefficients of static friction. The angles of contact are the angles formed by the rope and the drums, and the coefficients of static friction are the values that represent the resistance of the surfaces to sliding against each other. The greater the angle of contact and the higher the coefficient of static friction, the greater the frictional force acting on the rope.

To determine the force t2 needed to overcome these frictional forces, we can use the following equation:

t2 = t1 * e^μθ

Where μ is the coefficient of static friction and θ is the angle of contact. We can plug in the values given in the problem to get:

t2 = t1 * e^(0.3 * 120°) ≈ 1.54t1

Therefore, the force t2 needed to pull the rope over the two fixed drums is approximately 1.54 times the force t1 applied at point A.

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Answer/Step-by-step explanation:

Square all three numbers. If the largest number squared is equal to the sum of the squares of the other two, then the numbers form a Pythagorean triple.

or

Since a Pythagorean triple is three positive integers a, b, and c such that (a^2)+(b^2)=(c^2), first take the sum of the squares of the two legs and make an estimate. For example, 3, 4, and 5 is a Pythagorean triple since 9+16=25

either one works

The DMM buys the stock from the floor broker who wants to sell; and then immediately sells that stock for $.01 more to the floor broker who wants to buy. This is an example of scalping or trading ahead.

Designated Market Maker (DMM) on the New York Stock Exchange (NYSE), the DMM has certain obligations and responsibilities to maintain fair and orderly markets for the stocks they oversee. They are expected to provide liquidity by facilitating trades and maintaining an orderly market.

However, in the scenario you provided, the DMM takes advantage of the situation by executing a trade with a floor broker who wants to sell ABC stock and immediately selling it to another floor broker who wants to buy at a slightly higher price. By doing so, the DMM profits from the price difference, earning an extra $.01 per share.

This practice goes against the principles of fair and orderly markets, as the DMM is essentially prioritizing their own profit over providing fair execution prices for buyers and sellers. It can be considered unethical and may be subject to regulatory scrutiny or penalties, as it undermines the integrity and fairness of the market.

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The domain refers to all the values that can be entered into a relation or function (input). The set of all initial elements in ordered pairs constitutes the domain (x-coordinates). The set of all second items in ordered pairs is the range (y-coordinates). The range only consists of the elements "used" by the relation or function.

The domain (what goes in) of a straightforward function like f(x) = x2 can be limited to counting numbers 1, 2, 3, etc., and

The range will then be set to 1, 4, 9, etc. Another function, g(x) = x2, may have an integer domain of..., -3, -2, -1, 0... 1, 2, 3, and its range is..., 1, 4, 9,...

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Answer:

x>24

Step-by-step explanation:

−2x+7< −41

−2x+7−7< −41−7

−2x< −48

−2x /−2  <  −48 /−2

x>24

The vector in the direction is [1/sqrt(46), 3/sqrt(46), 2/sqrt(46), 0]

A unit vector in the direction of u is u/|u| where |u| is the magnitude of u.

To find the magnitude of u, we use the formula:

|u| = sqrt(1^2 + 6^2 + 3^2 + 0^2) = sqrt(46)

So, a unit vector in the direction of u is:

u/|u| = [1/sqrt(46), 6/sqrt(46), 3/sqrt(46), 0/sqrt(46)]

Simplifying the vector, we get:

[1/sqrt(46), 3/sqrt(46), 2/sqrt(46), 0]

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Answer:

The answer will be listed below.

Step-by-step explanation:

I don't see any options, but to find a line with a slope of zero, the line must be straight either vertically or horizontally.

A vertical line has a slope of zero.

Answer:

16) x = 32 degrees

17) x = 22 degrees

Answer:

Slope Intercept

Step-by-step explanation:

The value of the expression of the percentage as the friend details is; 0.04888....... and as such the friend is not correct

Percentages are usually calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:

Percentage = (value / total value) * 100%

Now, we are given the number 4.8% with 8 having a bar over it.

A bar over a number is called  vinculum  and it means that the number is being repeated indefinitely after a decimal point.

This tells us that our given number can now be expressed as;

4.888.....%

This is because from the definition of  vinculum , 8 is repeated indefinitely. Thus, this can be simplified as;

4.888...../100 = 0.04888.......

Thus, the friend is not correct in conclusion.

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Answer:

Here you go sorry.

Step-by-step explanation:

Question 1.

y = 4x - 8 has a slope of 4. Since parallel lines have equal slopes, the slope of your new line will also be 4.

Now, you have a point (3,9) and a slope 4. Use the Point-Slope Form for the equation of a line.

y - y1 = m(x - x1)

y - 9 = 4(x - 3)

y - 9 = 4x - 12

y = 4x - 3

Question 2.

Since it is parallel, it must have the same slope.

y = (1/2)x + b

Find b from the given point.

4 = (1/2)(2) + b

b = 3

y = (1/2)x + 3

9514 1404 393

Answer:

  ∠4 = 145°

  ∠5 = ∠6 = 35°

Step-by-step explanation:

Angles 5 and 35° are corresponding angles, so are congruent.

Angles 5 and 6 are vertical angles, so are congruent.

Angles 4 and 35° are a linear pair, so are supplementary.

  ∠4 = 180° -35°

  ∠4 = 145°

  ∠5 = ∠6 = 35°

173 would be dividable by at least one prime number less than or equal to 173 13.2 if it weren't a prime number. Since 173 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know it is a prime number.

173 is a prime number.

Prime factorization: 173 is prime.

The exponent of prime number 173 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 173 has exactly 2 factors.

Factors of 173: 1, 173

Factor pairs: 173 = 1 x 173

173 has no square factors that allow its square root to be simplified. √173 ≈ 13.1529

If 173 were not a prime number, then it would be divisible by at least one prime number less than or equal to √173 ≈ 13.2. We know that 173 is a prime number since it cannot be divided by 2, 3, 5, 7, 11, or 13 in an equal amount.

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Answer:

6.1 * 10^-3

Step-by-step explanation:

This is because 10^-3 = 0.001 so 0.0061=6.1 * 10^-3

Answer:

6,100,000,000

Step-by-step explanation:

0.0061 x 10^12 =6,100,000,000

Answer:

Wrong values are plotted in the question statement graph.

Please find correct graph.

Step-by-step explanation:

Given that:

\(y =x+3\) and \(-1<x<5\)

i.e. we can put a value of x in the equation which is greater than -1 and lesser than 5.

OR

we can say, the points where x = -1 and x = 5 will not be included in the graph (they will be shown as hollow circle).

Now, let us put the values one by one:

x = -1, y = -1 + 3 =2

x = 0, y = 0 + 3 = 3

x = 1, y = 1 + 3 = 4

x = 2, y = 2 + 3 = 5

x = 3, y = 3 + 3 = 6

x = 4, y = 4 + 3 = 7

x = 5, y = 5 + 3 = 8

Therefore, the table of values become:

\(\begin{center}\begin{tabular}{ c c } x & y\\ -1 & 2\\ 0 & 3 \\ 1 & 4 \\ 2 & 5 \\ 3 & 6 \\ 4 & 7 \\5 & 8\\\end{tabular}\end{center}\)

Points (-1, 2) and (5, 8) will not be included in the graph.

Please find attached corrected graph.

To find the equation of the tangent line to the function f(x) at x = 0, we need to find the derivative of f(x) and evaluate it at x = 0.

Given that f(x) = (e - 3)(x³ + 2x - 1), we can find the derivative f'(x) using the power rule and the product rule of differentiation.

f'(x) = (e - 3)(3x² + 2) + (x³ + 2x - 1)(0)

      = (e - 3)(3x² + 2)

To find the equation of the tangent line at x = 0, we evaluate f'(x) at x = 0:

f'(0) = (e - 3)(3(0)² + 2)

     = (e - 3)(0 + 2)

     = (e - 3)(2)

     = 2(e - 3)

The slope of the tangent line at x = 0 is given by f'(0), which is 2(e - 3).

To determine the equation of the tangent line, we need the slope and a point on the line. Since we are looking for the tangent line at x = 0, we know that the point (0, f(0)) is on the line.

Plugging x = 0 into f(x), we find:

f(0) = (e - 3)(0³ + 2(0) - 1)

    = (e - 3)(0 - 1)

    = -(e - 3)

Therefore, the point on the tangent line is \((0, -(e - 3))\).

Using the slope-intercept form of a line (y = mx + b), where m is the slope and b is the y-intercept, we can write the equation of the tangent line:

y = 2(e - 3)x + -(e - 3)

  = 2(e - 3)x - (e - 3)

  = (2e - 6)x - (e - 3)

Hence, the equation of the tangent line to the function f(x) at x = 0 is (2e - 6)x - (e - 3).

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Answer:

28

Step-by-step explanation:

700 x 4% = 700 x 0.04 = 28