Question 12 (1 point) Find T(v) using the following properties assuming T is a linear transformation. T:P, → Pz; T(22) = x3, T(x + 1) = 0, T(x - 1) = x; ; v=x2 +2

Answer:

Step-by-step explanation:

Answer:

A) Down and to the right.

Step-by-step explanation:

Hope it helps! :)

There are 214 distinct paths from (-1,2,0) to (1,3,7) in Euclidean three-space.

We can approach this problem using a combinatorial approach.

Let's say that there are a total of n moves from the starting point (-1,2,0) to the ending point (1,3,7). Then, the number of H moves is nh, the number of V moves is nv, and the number of A moves is na, where nh + nv + na = n.

The starting point (-1,2,0) is (1,1,7) moves away from the ending point in the x, y, and z directions, respectively. Therefore, we have the following constraints:

   nh ≥ 1 (to move from x = -1 to x = 1)

   nv ≥ 1 (to move from y = 2 to y = 3)

   na ≥ 7 (to move from z = 0 to z = 7)

The number of distinct paths from (-1,2,0) to (1,3,7) is simply the number of ways to choose nh, nv, and na moves from n total moves such that the constraints are satisfied. This is equivalent to finding the number of solutions to the equation nh + nv + na = n subject to the constraints.

Using the stars and bars technique, the number of solutions can be calculated as:

C(n - 1, 2) = C(n - 1, n - 3) = C(n - 1, na - 1)

where C(n, k) is the binomial coefficient representing the number of ways to choose k items from a set of n items.

Since na ≥ 7, we can start by setting na = 7 and then increasing it by one to see if there are additional solutions. For na = 7, n = 7 + nh + nv. Therefore, n >= 8 and n <= 14. The number of solutions for each value of n can be calculated using the formula above, and the total number of solutions can be obtained by summing up the results for each value of n.

For example, when n = 8, there are C(7, 2) = 21 solutions, when n = 9, there are C(8, 2) = 28 solutions, and so on. The final answer is the sum of all the solutions, which is:

21 + 28 + 35 + 35 + 28 + 21 + 13 + 6 = 214

Therefore, there are 214 distinct paths from (-1,2,0) to (1,3,7) in the Euclidean three-space.

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In pounds and ounces, 96 kg equals 216 lb, 1 oz.

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4min/hr jon can paddle in the water.

consider the velocity formula:

velocity = distance/time

The given information is:

Distance downstream = 5 miles

Distance upstream = 6 miles

Trip time = 3 hours

Time downstream = (5 / 5+6)(3) = 15/11 hours

Time upstream = (6 / 5+6)(3) = 18/11 hours

velocity downstream = 5 / 15/11 = 11/3mi/hr + 1mi/hr

velocity upstream = 6 / 18/11 = 11/3mi/hr - 1mi/hr

average velocity = 11/3 or 3.6667 or 4 mi/hr

This question can also be calculated in another way:

velocity = distance/time

time = distance/velocity

x + 1 for downstream because it is on current and x - 1 for upstream because it is against the current.

3hours = (5 / x + 1) + (6 / x - 1)

3(x + 1)(x - 1) = 5(x - 1) + 6(x + 1)

3x^2 - 3x + 3x - 3 = 5x - 5 + 6x + 6

3x^2 - 3 = 11x + 1

3x^2 - 11x - 4 = 0

using a quadratic equation, we can find the roots of the equation:

The roots are = 4, -1/3

since there is no negative velocity, x = 4 mi/h

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In the experiment, the subject whose behavior is being assessed are observational units. The observational unit in this instance is Harley (Dog).

We will first investigate if canines can comprehend both non-human and human gestures in this investigation. The dogs were placed around 2.5 meters apart from the experimenter so that the researchers could test this. Two glasses were placed one on either side of the experimenter.

A gesture would be made at one of the cups by either the experimenter (pointing, bowing, or staring) or by a non-human object (a mechanical arm pointing, a doll pointing, or a stuffed animal looking). After then, the scientists would observe whether the dog would approach the cup that was pointed out. Six dogs were put to the test. We'll focus on one of the dogs who participated in both of his trial sets.

The four-year-old mixed breed dog was given the name Harley. Each of the ten trials in a set consisted of one gesture and one pair of cups. In order to see if Harley would approach a particular cup, the experimenter bowed toward it during one round of experiments.

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This statement is TRUE. When we are doing a problem, we could use these questions " what is the equation asking you do? what is your plan to solve?" as the part of starting solving the problem in math about equation matter.

In mathematics, an equation is an equation statement that contains one or more variables. Solving equations consists of determining which variable values makes an equality true. The variable is also called "unknown" and the value of an "unknown" that satisfies the equation is called the equation solution. There are two types of equations: identity and conditional equations. True identity for all variable values. The conditional equation is true only for certain variable values.

An equation is a mathematical statement in the form of a symbol which states that two things are exactly the same. Equations are written with an equal sign (=), as follows:

x + 3 = 5, which states that value x = 2.

2x + 3 = 5, which states that the value x = 1.

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The diameter of the middle shelf is solved using similar triangle to get

The middle shelf is in the mid segment hence Using the concept of similar triangle the proportions are as follows

The proportions

1 / 2 = x / 15

cross multiplying

15 = 2x

rearranging the equation

2v = 15

isolating x by dividing through by 2

2v / 2 = 15 / 2

x = 7 1/2

x = 7.5

The diameter of the middle shelf is equal to x which is calculated to be 7.5

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The expression 2x² + 8x - 8 represents a polynomial.

An expression represents a polynomial when these following conditions are satisfied:

The exponents for this problem are given as follows:

2, 1 and 0.

(as the constant term has an exponent of zero).

Which are both integer and non-negative, hence the expression 2x² + 8x - 8 in fact represents a polynomial.

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Answer:

Juan can fill 4 mugs.

Step-by-step explanation:

Take the total amount of hot chocolate and divide by the amount each mug will hold.

1/2 ÷ 1/8

Copy dot flip.

1/2 * 8/1

8/2

4

Juan can fill 4 mugs.

Answer:

4 mugs

Step-by-step explanation:

If each mug holds 1/8 of a quart, and Juan has 1/2 of a quart of hot chocolate, then he can fill:

[tex]\sf:\implies{1/2 ÷ 1/8 = 4 \: mugs.}[/tex]

So, Juan will be able to fill 4 mugs.

Answer:

[tex]5\cdot \sqrt{5}\cdot \sqrt[3]{x^4}\cdot y\cdot z^2[/tex] = [tex]5\cdot \sqrt{5}\cdot x\sqrt[3]{x}\cdot y\cdot z^2[/tex]

Step-by-step explanation:

Let's take the individual terms and convert them to radical form

[tex]5^{\frac{3}{2}} = (5^3)}^{\frac{1}{2}} = 125^{\frac{1}{2}[/tex]

A term raised to the power 1/2 is nothing but the square root of that term

[tex]125^{\frac{1}{2}} = \sqrt{125} = \sqrt{25\cdot 5} = \sqrt{25} \sqrt{5} = 5 \sqrt{5}[/tex]

[tex]x^{\frac{4}{3}} = (x^4)^{\frac{1}{3}} = \sqrt[3]{x^4}[/tex]  since any term raised to 1/3 is the cube root of that term

We can simplify this further by noting [tex]x^4 = x^3 \cdot x[/tex]'

So [tex]\sqrt[3]{x^4} = \sqrt[3]{x^3} x = x\sqrt[3]{x}[/tex]

The other exponents are integers

Putting them all together we get

[tex]5^{\frac{3}{2} }x^{\frac{4}{3}}yz^2 = 5\cdot \sqrt{5}\cdot x\sqrt[3]{x}\cdot y\cdot z^2[/tex]

For all the points slope is constant. Hence they all lie on a certain line, then the m = -2.

Given that,

x              y

-5            0

-1            -8

1             -12

4            -18

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Then,

Points are,  ( - 5,0 ) , ( -1,-8), (1,-12) , (4,-18)

Points are,  ( - 5,0 ) , ( -1,-8)

Slope m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

m = [tex]\frac{-8-0}{-1-(-5)}[/tex]

m = [tex]\frac{-8}{-1+5}[/tex]

m = [tex]\frac{-8}{4}[/tex]

m = -2

Points are,  ( -1,-8 ) , ( 1,-12),

m = [tex]\frac{-12-(-8)}{1-(-1)}[/tex]

m = [tex]\frac{-12+8}{1+1}[/tex]

m = [tex]\frac{-4}{2}[/tex]

m = -2

Points are,  ( 1,-12 ) , ( 4,-18),

m = [tex]\frac{-18-(-12)}{4-1}[/tex]

m = [tex]\frac{-18+12}{3}[/tex]

m = -6/3

m = -2

Then, m = -2

Therefore,

For all the points slope is constant. Hence they all lie on a certain line, then the m = -2.

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For all the points slope is constant. Hence they all lie on a certain line, then the m = -2.

Given that,

x              y

-5            0

-1            -8

1             -12

4            -18

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Then,

Points are,  ( - 5,0 ) , ( -1,-8), (1,-12) , (4,-18)

Points are,  ( - 5,0 ) , ( -1,-8)

Slope

m = -2

Points are,  ( -1,-8 ) , ( 1,-12),

m = -2

Points are,  ( 1,-12 ) , ( 4,-18),

m = -6/3

m = -2

Therefore,

For all the points slope is constant. Hence they all lie on a certain line, then the m = -2.

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Cost of 9 miles ride = $19.25

Cost of m miles ride = $3.50 + $1.75m

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Taxi charges $3.50 for pickup and $1.75 per mile.

Total charges can be expressed as

y = $3.50 + $1.75m

where m is the  number of miles

For 9 miles

cost y = $3.50 + $1.75×9

          = $3.50 + $15.75

          = $19.25

Hence, $19.25 will cost for 9 miles ride

For m miles ride will cost $3.50 + $1.75m.

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The ∆GHI is an isosceles triangle and have the base angles m∠H and m∠G equal to 74° and the angle I is equal to 32°.

An isosceles triangle have the measure of its base angles to be equal, and the sum of the interior angles sum up to 180°.

Given that sides IG ≅ HI, then the triangle ∆GHI has two sides with similar length and base angles so;

angles m∠H and m∠G are the base angles and m∠G = 74°

m∠I = 180° - (74 + 74)° {sum of interior angles of a triangle}

m∠I = 32°

Therefore, the ∆GHI is an isosceles triangle and have the base angles m∠H and m∠G equal to 74° and the angle I is equal to 32°.

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If A is a m × n matrix, with columns a1, . . . , an, and if b is in R

m,

then the matrix equation

Ax = b

has the same solution set as the vector equation

x1a1 + x2a2 + · · · + xnan = b

which, in turn, has the same solution set as the system of linear

equations whose augmented matrix is

a1 a2 · · · an b.

The equation Ax = b is consistent if−2b1 + b3 = 0.

(equation of a plane in R3)

x1a1 + x2a3 + x3a3 = b

if and only if b3 − 2b1 = 0.

Columns of A span a plane

in R3 through 0

Instead, if any b in R3

(not just those lying on a particular line or

in a plane) can be expressed as a linear combination of the

columns of A, then we say that the columns of A span R3

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Answer:

The formula for the area of a circle is given by Pi * r^2, where r is the radius of the circle. If the area of the circle is 100 Pi, we can solve for the radius:

100 Pi = Pi * r^2

r^2 = 100

r = 10

The formula for the circumference of a circle is given by 2 * Pi * r. Substituting the value of r = 10, we get:

C = 2 * Pi * r = 2 * Pi * 10 = 20 * Pi

So, the circumference of the circle is 20 Pi.

The shaded region in the graph represents the possible solution sets to the inequality.

Given is the inequality -

x² + 15 ≥ 23

The given inequality is -

x² + 15 ≥ 23

Refer to the graph attached.

The shaded region represents the possible solution sets to the inequality above.

Therefore, the shaded region in the graph represents the possible solution sets to the inequality.

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The expected value for the card that Dan selects is 2.5, as it is the average of the probabilities of selecting each card.

The expected value for the card that Dan selects is calculated by taking the sum of the product of each card and its respective probability. The probability distribution for the deck of four cards is as follows: Card 1 has a probability of 0.25, card 2 has a probability of 0.4, card 3 has a probability of 0.2, and card 4 has a probability of 0.15. To calculate the expected value, we first multiply each card number by its respective probability and then add each product together. This gives us 0.25 x 1 = 0.25, 0.4 x 2 = 0.8, 0.2 x 3 = 0.6, and 0.15 x 4 = 0.6. Adding all of these together gives us a total of 2.5, which is the expected value for the card that Dan selects.

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Answer:

Step-by-step explanation:

To find the time it takes for the car to travel 950 m, we need to find the time it takes for each segment and add them up. Let's call the travel time for the first quarter t1, and the travel time for the remaining 3 quarters t2.

a) Travel time:

For the first quarter (0 m to 237.5 m), the equation for the velocity can be found using the kinematic equation:

v = v0 + at

where v0 is the initial velocity (0 m/s), a is the acceleration (+5.40 m/s^2), and t is t1.

So,

t1 = (v - v0) / a = (0 - 0) / 5.40 = 0

For the next 3 quarters (237.5 m to 950 m), the equation for the velocity can be found using the kinematic equation:

v^2 = v0^2 + 2ad

where d is the displacement (950 m - 237.5 m = 712.5 m), and a is the acceleration (-1.80 m/s^2).

So,

t2 = sqrt((2ad + v0^2) / a) = sqrt((2 * -1.80 * 712.5 + 0^2) / -1.80) = sqrt(1286.25 / -1.80) = sqrt(709.03) = 26.6 s

Adding t1 and t2 gives the total travel time:

t = t1 + t2 = 0 + 26.6 = 26.6 s

b) Maximum speed:

To find the maximum speed, we need to find the velocity at the halfway point (475 m) by using the kinematic equation:

v = v0 + at

where v0 is the initial velocity (0 m/s), a is the acceleration (+5.40 m/s^2), and t is t1.

So,

v = 0 + 5.40 * (475 / 237.5) = 4.96 m/s

The maximum speed is 4.96 m/s.

sorry for making it so long.

Answer:

(f - h) (-4) = 26.

Step-by-step explanation:

First, find the value of f(-4):

f(x) = x² + 4

f(-4) = (-4)² + 4 = 16 + 4 = 20

Next, find the value of h(-4):

h(x) = x-2

h(-4) = -4 - 2 = -6

Finally, subtract h(-4) from f(-4) to find (f - h) (-4):

(f - h) (-4) = f(-4) - h(-4) = 20 - (-6) = 20 + 6 = 26

So (f - h) (-4) = 26.

Answer:

10q + 5

Step-by-step explanation:

6q+7-2+4q

=10q+5

:]

Hope this helps

The graph does not represent a function, as it has vertically aligned points.

A relation represents a function when each input value is mapped to a single output value.

On the function graph, a vertical line through the graph of the function would cross the graph twice for x > -4, meaning that there are inputs is mapped to two outputs, hence the relation is not a function.

This means that the correct option is given by option B.

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The distance between two points A (3, 2) and B (9, 7) is [tex]\sqrt{61}[/tex] units.

The midpoint between a celestial body's greatest and smallest separations from its primary.

The metre is the SI unit for distance (m). Long distances can be measured in kilometres, whereas little distances can be gauged in millimetres (cm) (km).

For instance, you might measure the distance in centimetres between the bottom and top of a piece of paper and the kilometres between your home and school.

You are a long way from anything in space or time if you are far away from it, cannot see it, or cannot recall it.

I need to keep my mum at a distance if I want to manage.

Distance between P and Q if two points are given P([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and Q([tex]x_{2}[/tex], [tex]y_{2}[/tex]) , PQ = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Given:

A (3,2) and B (9,7) are the two points in a plane. We have to find the distance between A and B. Here, [tex]x_{1}[/tex] = 3, [tex]x_{2}[/tex] = 9, [tex]y_{1}[/tex] = 2 and [tex]y_{2}[/tex] = 7.

AB = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

AB = [tex]\sqrt{(9 - 3)^2 + (7 - 2)^2}[/tex]

AB = [tex]\sqrt{(6)^2 + (5)^2}[/tex]

AB = [tex]\sqrt{36 + 25}[/tex]

AB = [tex]\sqrt{61}[/tex] units.

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The sum of a quadratic trinomial with the same variable is twice the individual and the difference will be zero.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We know a quadratic equation is of the form ax² + bx + c.

The sum will be,

(ax² + bx + c) + (ax² + bx + c).

= 2ax² + 2bx + 2c.

= 2(ax² + bx + c).

The difference will be,

ax² + bx + c - (ax² + bx + c).

= 0.

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The truth values of a compound statement are displayed in a truth table for all feasible combinations of the truth values of its component propositions.

A truth table is a graph that shows the truth value of one or more compound propositions for any two compound propositions that can have the same truth value. It is used to judge whether a logical argument is sound. A truth table is made up of rows and columns, each row having the truth value of the compound proposition for the specified set of truth values, and each column containing the truth value of the individual proposition. The propositions that make up the compound proposition must first be identified, and all potential combinations of truth values for each of those propositions must then be listed in order to produce a truth table. The truth value of the compound proposition can then be calculated for each combination. Applying reasoning to the provided combination will do this. The truth value of the compound proposition will then be shown in the truth table for each combination of truth values. This can assist in determining the viability of a given logical argument.

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The equation to find the number of overtime hours worked on the second day is 19.5x = 87.75.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Earning of Lynette for one hour when she works overtime = $19.50

She worked overtime twice this week.

One day she worked 3 hours of overtime.

Earning on first day = 3 × $19.50 = $58.50

Total earnings for overtime = $146.25

Earnings on second day = $146.25 - $58.50 = $87.75

Let x be the number of hours worked overtime.

19.5x = 87.75

x = 4.5

Hence the required equation is 19.5x = 87.75.

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Answer:

(z + 6)(z + 4)

Step-by-step explanation:

z² + 10z + 24

consider the factors of the constant term (+ 24) which sum to give the coefficient of the z- term (+ 10)

the factors are + 6 and + 4 , since

6 × 4 = + 24 and 6 + 4 = + 10 , then

z² + 10z + 24 = (z + 6)(z + 4) ← in factored form

The length of x to the nearest 10th of an inch is 7.1 inches.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

We have law of sine of triangle, which states that,

sin X / x = sin Y / y = sin Z / z

where X, Y and Z are three angles of a triangle and x, y and z are the sides opposite to X, Y and Z respectively.

Using this,

Sin V / v = Sin W / w = Sin X / x

Given that, m ∠V = 76° and m ∠W = 44°

m ∠V + m ∠W + m ∠X = 180°

76° + 44° + m ∠X = 180°

m ∠X = 180° - ( 76° + 44° )

m ∠X = 60°

Also, given that, v = 7.9 inches

Sin V / v = Sin X / x

sin (76°) / 7.9 = sin (60°) / x

x = [sin (60°) × 7.9] / sin (76°)

x = [0.866 × 7.9] / 0.970

x = 7.051 ≈ 7.1

Hence the length of the x is 7.1 inches to the nearest 10th of an inch.

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The lattice point of the inverse is (3, 0).

To find the lattice points of the inverse of the function f(x), we need to find the points where both x and y are integers.

To find the inverse of the function, we switch the x and y values, then solve for y:

y = log2(-x + 3) - 4

x = log2(-y + 3) - 4

y = 3 - 2^(x + 4)

For x and y to be integers, both 2^x and - 2^(x + 4) must be integers.

This occurs when y is a positive integer and y <= 2, since 2^y becomes larger than 3 for y > 2.

Thus, the only lattice point of the inverse is (3, 0).

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The linear equation of Johnny's charges is C(x) = 10 + 7.5x

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

Initial charge = $10

Hourly rate = $7.50

Let the number of hours be x and the total cost be C(x)

So, we have the following representation

C(x) = Initial charge + Hourly rate * x

Substitute the known values in the above equation, so, we have the following representation

C(x) = 10 + 7.5x

Hence, the function is C(x) = 10 + 7.5x

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Complete question

Johnny charges $10 plus $7.50 per hour to mow lawns.

Determine the linear equation