Express tan(pi/4-x) in its simplest form. Show work.

Answer:

I believe the answer is; The median is 4.5 inches.

let me know if this is right for you! :)

Step-by-step explanation:

The slope of a line in the form "y = mx + b" is given by the coefficient "m" of the x term.

For the first equation, x - 2y = -1/2, we can rearrange the terms to get y = (1/2)x - 1/2. The coefficient of the x term is 1/2, so the slope of the line is 1/2.

For the second equation, -4x - 8y = 2, we can rearrange the terms to get y = -(1/2)x - 1/4. The coefficient of the x term is -1/2, so the slope of the line is -1/2.

Answer:

The answer would be D because hundredth would be 2 numbers behind the decimal which would leave C&D but the zero behind C would just round the number to .7 so the answer is D

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation which can be used to find the amount of time Hiroshi spends on his math homework is 1/4(x + 30 + 60) = x

According to the question,

Let total time Hiroshi spent on his homework be "y"

Total time spent on history homework = 30 minutes

Total time spent on English homework = 60 minutes

It is given that the time spent on math homework is x

and Also that One fourth of his total homework time is spent on math

=> x = 1/4y

=> 4x = y ----------(1)

Also , Sum of time taken in different homework will be equal total time y

=> 30 + 60 + x = y --------(2)

Substituting the values of x from equation (1) in equation (2)

=> 30 + 60 + x = 4x

divide by 4

=> 1/4(x + 30 + 60) = x is equation

=> x + 30 + 60 = 4x

=> 3x = 90

=> x = 90/3

=> x = 30 minutes

Total time taken in doing homework is 120 minutes

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Let S be the subspace of P3 consisting of all polynomials p(x) such that p(0) = 0 and let T be the subspace of all polynomials q(x) such that q(1) = 0.

a) The two vectors are linearly independent and span S which means {x, \(x^{2}\)} forms a basis for S.

b) The two vectors are linearly independent and span T which means \({(x -1),(x - 1)^2}\)forms a basis for T.

c) The vector is linearly independent and spans S∩T which means {x(x−1)} forms a basis for S ∩ T.

We have the information from the question:

Let S be the subspace of \(P_3\) consisting of all polynomials p(x).

We have:

p(0) = 0 and let T be the subspace of all polynomials q(x) such that q(1) = 0.

a) S is all polynomials of the form p(x) = \(ax^2 + bx\) where a, b are

real numbers.

p(0) = \(a(0)^2 + b(0)\) = 0 for all a, b.

I propose that {x, \(x^{2}\)} forms a basis for S.

We must show that:

The vectors x and \(x^{2}\) are linearly independent and span S.

To show they are linearly independent we must show that:

\(\alpha _1(x^2) + \alpha _2(x) = 0(x^2) + 0(x)\)

Only has the solution :

\(\alpha _1=\alpha _2=0\)

Upon grouping the terms we find:

\(\alpha _1=0\\\\\alpha _2=0\)

Thus the two vectors are clearly linearly independent.

Now to show that the two vectors span S we must show that any element

in S which I will represent by p(x) = ax^2 + bx can be written as:

\(\alpha _1(x^2) + \alpha _2(x) = ax^2 + bx\)

where, \(\alpha _1,\alpha _2\) are scalar  vectors.

Upon grouping the terms we find that:

\(\alpha _1=a\\\\\alpha _2=b\)

With this solution we have:

\(\alpha _1(x^2) + \alpha _2(x) = ax^2 + bx\)

which means the two vectors span S.

Thus, the two vectors are linearly independent and span S which means {x, \(x^{2}\)} forms a basis for S.

b)T is all polynomials of the form :

\(q(x) = a(x - 1)(bx + c) =abx^2 + acx - abx - ca = ab(x^2) + (ac - ab)x - ac\)where a, b, c are real numbers.

This is because q(1) = a(1 − 1)(b + c) = 0 for all a, b, c.

Let s = ab and t = ac.

Now we have that T is all polynomials of the form

\(q(x) = sx^2 + (t - s)x - t\)

\({(x - 1),(x - 1)^2}\)forms a basis for S.

In order to confirm this we must show that the vectors x − 1 and \((x - 1)^2\)are linearly independent and span S.

To show they are linearly independent we must show that:

\(\alpha _1((x -1)^2) + \alpha _2(x - 1) = 0(x - 1)(0(x) + 0)\)

only has the solution α1 = α2 = 0

Upon grouping the terms we find:

\(\alpha _1=0\\\\\alpha _2=0\)

Thus the two vectors are clearly linearly independent.

Now to show that the two vectors span T we must show that any element

in T which I will represent by \(q(x) = sx^2 + (t - s)x - t\) can be written as:

\(\alpha _1((x - 1)^2) + \alpha _2(x - 1) = sx^2 + (t - s)x - t\)

Where, \(\alpha _1,\alpha _2\) are scalars.

Upon grouping the terms we find that:

\(\alpha _1=s\\\\\alpha _2=s+t\)

With this solution we have:

\(sx^2 + (t - s)x - t = sx^2 + (t - s)x - t\)

which means the two vectors span T

Thus, the two vectors are linearly independent and span T which means \({(x -1),(x - 1)^2}\)forms a basis for T.

c)  S∩T is all polynomials of the form \(c(x) = a(x-1)(bx) = abx^2-abx\)

where a, b are real numbers.

This is because \(c(0) = a(0 - 1)^2\)

(b(0)) = 0 and

c(1) =\(a(1 - 1)^2\)

(b(1)) = 0 for all a, b.

Let ab = t

This means S∩T is all polynomials of the form \(c(x) = tx^2-tx = tx(x-1).\)

I propose that {x(x − 1)} forms a basis for S ∩ T.

Now, we must show that the vector x(x − 1) is linearly independent and spans S ∩ T.

To show it is linearly independent we must show that:

\(\alpha _1\)(x(x − 1)) = 0(x(x − 1))

only has the solution \(\alpha _1\) = 0.

Upon grouping the terms we find:

\(\alpha _1\) = 0

Thus the two vectors are clearly linearly independent.

Now to show that the vector spans S ∩ T we must show that any element

in S ∩ T which I will represent by c(x) = tx(x − 1) can be written as:

\(\alpha _1\)(x(x − 1)) = tx(x − 1).

where \(\alpha _1\) is a scalar.

Upon grouping the terms we find that:

\(\alpha _1\) = t

With this solution we have:

tx(x − 1) = tx(x − 1)

which means the vector spans S ∩ T.

Thus, the vector is linearly independent and spans S∩T which means {x(x−1)} forms a basis for S ∩ T.

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Answer:

The answer is "(1, -12)"

Step-by-step explanation:

In the given question some information is missing, that is the attachment of the graph, which can be attached as follows:

In the attached figure file, the quadrilateral ABCD vertices are (-3, 4), (3,4),(1,-2), and (-5,-2)

To find the coordinates of the D' the translation of (x, y) = (x + 6, y-10)

where point D=(-5, -2),

\(\to x=x+6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to y=y-10\\\\\to x=-5+6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to y=-2-10 \\\\\to x=1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \to y=-12\)

So, the coordinates of D' is (1,-12).

Answer:

y=-x

Step-by-step explanation:

Answer: 0

Step-by-step explanation: Uh I really don't know how to explain this one

Answer:

the last one

Step-by-step explanation:

its the last one because 1x3 is 3 so you need one with a 3, then 4x2 is 8 and theres half a side so its the last answer with half 3/4 on one side

Answer:

10

\(\frac{3*2}{5 * 2} = \frac{6}{10}\)

\(\frac{1*1}{10*1} = \frac{1}{10}\)

________________________________________________________

With that information, the correct answer is option C, 10

________________________________________________________

We learned how to find the least common denominator of fractions whose parameters are not the same.

Questions related to this topic? Ask me in the comments box.

The winner got a total of 42 votes.

This can be defined as a number or ratio expressed as a fraction of 100. It is usually calculated by parts/whole × 100.

In this scenario, Jane was the winner as she got a higher percentage of votes. To calculate the exact number of vote we have to do the following:

70%/100% × 60 = 42 votes.

Therefore, the total number votes the winner got is 42.

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The 100 km difference between the two cities takes two trains to pass each other in 5 hours.

The relationship between speed, distance, and time is described using the formula of speed, distance and time.

That is speed = distance/time.

The velocity of an object in relation to another observer is referred to as the relative speed.

Given:

A train departs from city A and moves toward city B at a constant speed of 60 km/h and time taken is 8 hours.

At the same time, a second train departs city B and heads toward city A at a constant speed of 40 km/h.

The relative speed of first train with respect to the second train                                  = 60-40

= 20 km/h

It is given that the two cities A and B are located 100 kilometers apart from one another.

So, distance between both cities = 100 km

By using the speed formula,

Speed = Distance/Time

Time = Distance/Speed

Time = 100/20

∴ Time = 5 hours

Consequently, it takes 5 hours for the two trains to pass one another with 100 km distance between two cities.

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If p ≠ q in M, then ρ(p, q) > 0, we have established that the intrinsic distance ρ is a metric on M.

(a) To prove that a normal ε-neighborhood of p in M consists of all points q in M such that ρ(p, q) < ε, we need to show that every point q within this neighborhood satisfies the condition ρ(p, q) < ε, and vice versa.

Let N(p, ε) denote the normal ε-neighborhood of p in M. By definition, N(p, ε) is the set of all points q in M such that ρ(p, q) < ε.

To prove that every point q in N(p, ε) satisfies ρ(p, q) < ε, we assume q is an arbitrary point in N(p, ε). By definition, ρ(p, q) < ε. Thus, this condition holds for every point q in N(p, ε).

Now, let's prove the converse: that every point q satisfying ρ(p, q) < ε is within N(p, ε). Assume q is a point in M such that ρ(p, q) < ε. By definition, q is within the ε-neighborhood of p. Therefore, q is in N(p, ε).

Since we have shown that every point q in N(p, ε) satisfies ρ(p, q) < ε and every point q satisfying ρ(p, q) < ε is within N(p, ε), we can conclude that a normal ε-neighborhood of p in M consists of all points q in M such that ρ(p, q) < ε.

(b) To prove that if p ≠ q in M, then ρ(p, q) > 0, we assume p and q are distinct points in M. By the definition of the intrinsic distance function ρ, we know that ρ(p, q) represents the infimum of the lengths of all paths connecting p and q. Since p and q are distinct points, there exists at least one path between them.

Let's assume, for contradiction, that ρ(p, q) = 0. This would mean that the infimum of the lengths of all paths connecting p and q is zero. However, a path with zero length implies that p and q coincide, which contradicts our assumption that p ≠ q. Therefore, ρ(p, q) cannot be zero.

Since we have shown that if p ≠ q in M, then ρ(p, q) > 0, we have established that the intrinsic distance ρ is a metric on M.

By proving both (a) and (b), we have completed the proof that the intrinsic distance ρ is a metric on M.

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Answer:

30

Step-by-step explanation:

there's a few different ways of solving this:

3/4 = 0.75

0.75 * 40

30

divide 40 by 4 and then multiply by 3

40/4

10

10 * 3

30

\(\frac{3}{4} *\frac{40}{1}\)

the 4 and 40 cancel out

\(\frac{3}{1}* \frac{10}{1}\)

3 * 10 = 30

\(\frac{30}{1}\) = 30

The ordered pair (3, 3) satisfies both equations simultaneously, and hence it is the solution to the system of equations represented by the Graph.

The system of equations represented by the graph is 2x - 3y = 9 and -x + 4y = 12.

The graph contains two lines that intersect at a point, which is the solution to the system of equations.What is a System of Equations?A system of equations is a set of two or more equations that are to be solved simultaneously. These equations have the same variables.

If the system has two equations, it is called a system of two linear equations in two variables. The variables represent two unknown quantities, and the equations represent the relationships between them.Graphical Representation of a System of EquationsThe graphical representation of a system of equations is done by plotting the lines that are represented by the equations on the same coordinate plane.

If the two lines intersect at a point, then that point is the solution to the system of equations.The solution to the system of equations is the ordered pair that satisfies both equations simultaneously. This means that if we substitute the values of the ordered pair into both equations, the equations will be true.

The Solution to the System of Equations represented by the GraphThe graph of the system of equations given in the question contains two lines that intersect at a point. The point of intersection is (3, 3).

Therefore, the solution to the system of equations is (3, 3).Now we can verify that the ordered pair (3, 3) is the solution to both equations. When we substitute x = 3 and y = 3 in the first equation, we get:2x - 3y = 9 ⇒ 2(3) - 3(3) = 9 ⇒ 6 - 9 = -3This equation is true. Now we can substitute x = 3 and y = 3 in the second equation, we get:-x + 4y = 12 ⇒ -(3) + 4(3) = 12 ⇒ -3 + 12 = 9

This equation is also true.

Therefore, the ordered pair (3, 3) satisfies both equations simultaneously, and hence it is the solution to the system of equations represented by the graph.

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Given that F is a continuous function and ∫[0 to 81] f(x) dx = 8, therefore the value of the integral ∫[0 to 9] xf(x²) dx is 4/81.

Let's begin by substituting u = x² into the integral ∫[0 to 9] xf(x²) dx. This substitution allows us to express the integral in terms of u instead of x. To determine the new limits of integration, we substitute the original limits of integration into the equation u = x². When x = 0, u = 0, and when x = 9, u = 9² = 81. Therefore, the new integral becomes ∫[0 to 81] (1/2) f(u) du.

We know that ∫[0 to 81] f(x) dx = 8, which implies that ∫[0 to 81] (1/81) f(x) dx = (1/81) * 8 = 8/81. Now, in the substituted integral, we have (1/2) multiplied by f(u) and du as the differential. To find the value of this integral, we need to evaluate ∫[0 to 81] (1/2) f(u) du.

Since we have the value of ∫[0 to 81] f(x) dx = 8, we can substitute it into the integral to obtain (1/2) * 8/81. Simplifying this expression, we find the value of ∫[0 to 9] xf(x²) dx = 4/81.

Therefore, the value of the integral ∫[0 to 9] xf(x²) dx is 4/81.

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Answer:

5832

Step-by-step explanation:

54+27=81x72=5832

Even though dividing a fraction by a whole number might be challenging, it is simple to achieve with a few steps. By placing the full number above 1, you must first divide it into a fraction. After that, multiply the fraction you are dividing by the inverted version of the fraction. Lastly, simplify the response as much as possible.

For instance, to multiply 3/4 by 2:

Put 2 over 1, making it 2/1, to make it a fraction.

To get 1/2, invert 2/1.

To get 3/8, multiply 3/4 by 1/2.

Divide the numerator and denominator by 3 to get 1/4, which is the simplest representation of the fraction 3/8.

Hence, 1/4 is equivalent to 3/4 when divided by 2.

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The classroom had 24 glue bottles.

We have,

If the ratio of glue sticks to glue bottles is 7 : 4, we can express this as 7/4.

We can set up a proportion to solve for the number of glue bottles:

7/4 = 42/x

where x is the number of glue bottles. To solve for x, we can cross-multiply:

7x = 4 x 42

7x = 168

x = 24

Therefore,

The classroom had 24 glue bottles.

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Answer:

Step-by-step explanation:

H = 2x+6          - the hight

3H = 3(2x+6)      - triple the hight

3H-5 = 3(2x+6) - 5    -  five less than triple the height

Area of triangle:  A = 0.5BH

B = 3(2x+6)-5 = 6x + 18 - 5 = 6x + 13

H = 2x+6

So:

    A = 0.5(2x+6)(6x+13) = (x+6)(6x+13) = 6x² + 13x + 36x + 78

    A = 6x² + 49x + 78

Answer:

the perimeter is 5s + 14

Step-by-step explanation:

the perimeter will be the sum of the 4 sides, in our case,

(s+8) + (s + 3) + s + 3) + 2s = perimeter

so, s +8 + s +3 + s + 3 + 2s = P

s + s + s + 2s + 8 + 3 + 3 = 5s + 14 = perimeter

Answer:

An accountant

Step-by-step explanation:

Hope this helps, I don't have an explanation.

Considering the information given, we have that:

The range is the estimate plus minus the margin of error.

We have that:

Then:

We apply the amounts of 48.8% and 51.2% to the number of adults, hence:

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Answer:

5.83 = CD

Step-by-step explanation:

We can use the pythagorean theorem to solve

The legs are the x and y distances

x = (1- -4) = 5 units and y = 3 units

a^2+ b^2 = c^2

5^2 + 3^2 = c^2

25+9 = c^2

34 = c^2

Taking the square root of each side

sqrt(34) = c  which is the distance from C to D

5.830951895 = CD

5.83 = CD

Answer:

C. 5.83

Step-by-step explanation:

This is the correct answer I took the exam

Answer:

  A.  60 ft·lb

Step-by-step explanation:

You want the work done lifting a 15-lb flower pot to a height of 4 ft.

Work is the product of force and distance. When the pot is raised 4 ft, the work done is ...

  W = F·d

  W = (15 lb)(4 ft) = 60 ft·lb

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The probability that the second ball is striped, given that the first ball is not striped, is 5/29.

To find the probability, we need to calculate the favorable outcomes (the number of ways the event can occur) and the total number of possible outcomes.

Given that the first ball is not striped, there are a total of 15 white balls and 10 black balls remaining in the bag. So, the total number of possible outcomes for the second ball is 15 + 10 = 25.

Out of the remaining balls, there are still 5 striped balls. Therefore, the number of favorable outcomes (striped balls) is 5.

Thus, the probability of selecting a striped ball as the second ball, given that the first ball is not striped, is 5/25, which simplifies to 1/5 or 0.1724 (rounded to four decimal places).

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Given that ,

The sweater shack is offering 20% discount,

and the regular price is $ 15 .00,

so, the discount given would be

⇢ $ 15 x 20/100

⇢$ 15 x 0.2

⇢$ 3

⇢Regular price - Discount price

⇢$15 - $(20/100 x 15)

⇢$15 - $3

⇢$12

Given that,

20% out of 30 students scored an A in previous math test,

so ,the number of students who got an A in the test

⇢ 30 x 20/100

⇢30 x 0.2

⇢6

Hence ,6 students secured an A grade in last math test

Given that,

The Jean junction is selling the jeans at the discount rate of 15% of the regular price which is $25.00,

so, the discount is

⇢$25.00 x $ ( 15/100 )

⇢$25.00 x $ 0.15

⇢$3.75

⇢ $25.00 - $25.00 x $ ( 15/100 )

⇢$25.00- $25.00 x $ 0.15

⇢$25.00 -$3.75

⇢$21.25