Let T: R2 → R3 be the matrix transformation corresponding to A = 4 1 1 -11 2 . Find T (u) and T (V), where u = 3 Find Tycu) and TẠ(w), where u = ( 2 ) and v= [-2] and v = 2 T(u) = _____. TA(V) = _____.

Let the number missed = x

They made 6 times that amount which would be 6x

The total of missed and made is 308:

X + 6x = 308

Combine like terms

7x = 308

Divide both sides by 7

X = 44

They missed 44

Given that:

Foci: (0,3), (0,-3)

Co-vertces: (1,0), (-1,0)

The foci are on the y-axis, so the major axis is the y-axis. Thus the equation will have the form:

The foci are (0,3) and (0,-3), so

The co-vertices are (1, 0) and (-1, 0), so

The co-vertices and foci are related by the equation

Solving for the square of a.

Substituate the obtained values into the standard form of he ellipse. Hence the equation of the ellipse is

Step-by-step explanation:

\(s = 20km \\ t = 30min\)

\(v = \frac{s}{t} \\ v = \frac{2}{3} \)

\(v = 0.67\)

\(v = 0\)

Answer:

Beth made 60% of her shots.

Step-by-step explanation:

Given:

Total shots take = 10

Total goal = 6

Find:

Best describer this number.

Computation:

Converting goal numbers into percentage:

⇒ Total goal percentage = [Total goal/Total shots take]100

⇒ Total goal percentage = [6/10]100

⇒ Total goal percentage = 60%

Beth made 60% of her shots.

Answer:

6:10 is the ratio

Step-by-step explanation:

as a fraction it would be 6/10

as a decimal it would be 0.60 or 0.6

and she made 60% of her shots

The mean amount of snow per day is equal to 19 cm snow per day.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total amount of snow based on the frequency, we have;

Total amount of snow (s cm), F(x) = 5(8) + 15(10) + 25(7) + 35(2) + 45(3)

Total amount of snow (s cm), F(x) = 40 + 150 + 175 + 70 + 135

Total amount of snow (s cm), F(x) = 570

Now, we can calculate the mean amount of snow as follows;

Mean = 570/30

Mean = 19 cm snow per day.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

2sqaured + 24

Step-by-step explanation:

Assuming the track is straight, the distance at which they are apart one hour before they meet is; 30 km

We are told that a Nonstop trains leave Toronto and Montreal at the same time each day going to the other city along the main line.

Speed of Train 1 = 120 km/h

Speed of Train 2 = 90 km/h

Time spent by train 1 = 1 hour

Time spent train 2 = 1 hour

Formula for distance is;

Distance = Speed * time

If they leave the same time each day, it means that;

Distance of train 1 = 120 * 1 = 120 km

Distance of train 2 = 90 * 1 = 90 km

Thus, distance at which they will be apart before meeting each other is;

Distance apart = 120 - 90

Distance apart = 30 km

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a. All values where the pogo stick's spring will be equal to its non-compressed length are:

\($ \rm {{\theta\ =\ {\frac{4\pi}{3}}\ a n d\ {\frac{5\pi}{3}}}}\)

If the angle was doubled, that is θ became 2θ, Then  the solutions in the interval [0, 2π) are:

\($\theta\ =\ \frac{2\pi}{3}\,,\ \frac{5\pi}{6}\,,\ \frac{5\pi}{3}\,,\ \frac{11\pi}{6}$\)

In mathematics, a functiοn is a rule that assigns tο each element in a set (called the dοmain) exactly οne element in anοther set (called the range). The dοmain and range can be any sets, but they must be well-defined.

In simpler terms, a functiοn takes an input (οr multiple inputs) and prοduces an οutput. The οutput value depends οn the input value and the rule that defines the functiοn.

a)

When pogo stick's spring will be equal to its non-compressed length. the difference between their lengths will be zero.

The difference between lengths is f(θ).

\($\begin{array}{c}{{f\left(\theta\right)\,=\,0}}\\ {{f(\theta)\,=\,2\sin\theta\,+\,\sqrt{3}\,=\,0}}\end{array}$\)

\($\begin{array}{l}{{\sin\theta\ =\ {\frac{-\sqrt{5}}{2}}}}\\ {{\theta\ =\ 240^{\circ}\,{a n d\ \mathrm{300}}^{\circ}}}\\ {{\theta\ =\ {\frac{4\pi}{3}}\ a n d\ {\frac{5\pi}{3}}}}\end{array}$\)

b)

\($\begin{array}{II}{{\rm\theta\,b e c o m e s\,2\theta}}\\&\\ {{f\left(2\theta\right)\,=\,0}}&{{}}\\ {{f(2\theta)\,=\,2\mathrm{sin}2\theta\,+\,\sqrt{3}\,=0}}\\ {{\sin2\theta\,=\,\,\dfrac{-\sqrt{3}}{3}}}&{{}}\end{array}$\)

\($\begin{array}{I I}{{2\theta\:=\:240^{\circ}\:,\:300^{\circ}\:,\:600^{\circ}\:,\:660^{\circ}}}\\ {{2\theta\:=\:\:\frac{4\pi}{3}\:\:,\:\:\frac{5\pi}{3}\:,\frac{10\pi}{3}\:,\:\:\frac{11\pi}{3}}}\end{array}$\)

\($\theta\ =\ \frac{2\pi}{3}\,,\ \frac{5\pi}{6}\,,\ \frac{5\pi}{3}\,,\ \frac{11\pi}{6}$\)

In original solution,

\($\theta\ =\ \frac{4\pi}{3}\ \rm a n d\ \frac{5\pi}{3}$\)

c)

\($\begin{array}{l}{{g(\theta)\;=\;f(\theta)\;}}\\ {{1-\cos^{2}\!\theta+{\sqrt{3}}\;=\;2\sin\theta+{\sqrt{3}}}}\\ {{1-\cos^{2}\!\theta\;=\;2\sin\theta}}}\end{array}$\)

\($\sin^{2}\theta\,=\,2\sin\theta$\)

\($\begin{array}{I}{\sin^{2}\!\theta-2\sin\theta\,=\,0}\\ {\sin\theta(\sin\theta-2)\,=\,0}\end{array}$\)

\($\begin{array}{l c r}\rm{{\sin\theta\,h a v e\,v a l u e\,b e t w e e n\,-\,1\,t o\,1.}}\\ \rm{{T h e r e f{o r e\,s i n\theta\,c a n\,n e v e r\,b e\,2.}}}\\&\\ \rm{{S i n\theta}}{{=}}{{0}}\\ {{\theta\,=\,0\,\,,\,\pi}}\end{array}$\)

Therefore.

a. All values where the pogo stick's spring will be equal to its non-compressed length are:

\($ \rm {{\theta\ =\ {\frac{4\pi}{3}}\ a n d\ {\frac{5\pi}{3}}}}\)

b. If the angle was doubled, that is θ became 2θ, Then  the solutions in the interval [0, 2π) are:

\($\theta\ =\ \frac{2\pi}{3}\,,\ \frac{5\pi}{6}\,,\ \frac{5\pi}{3}\,,\ \frac{11\pi}{6}$\)

c. Sin θ have value between -1 to 1

Therefore sin θ can never be 2 i.e.

Sinθ = 0, or θ = 0, π

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The value of the x in the expression 2(1/4) = 1(2/7) ÷ x is 4/7.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2(1/4) = 1(2/7) ÷ x

2(1/4) = 9/4

1(2/7) = 9/7

Now,

9/4 = 9/7 ÷ x

9/4 = 9/7x

7x = (9 x 4)/9

x = 4/7

Thus,

The value of x is 4/7.

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Answer:

D. 4√2

Step-by-step explanation:

A triangle with 45°, 45°, and 90° is a special right triangle.

hypotenuse = √2 · leg

1. Set up the equation

8 = √2 · x

2. Divide by √2 and solve

x = \(\frac{8}{\sqrt{2} }\) · \(\frac{\sqrt{2} }{\sqrt{2}}\) = \(\frac{8\sqrt{2} }{2}\) = 4√2

The mistake he makes is by saying 3/4 + 1/4 = 4/8

The denominators stay the same when adding fractions, and the denominators must be the same value.

So instead, he should have 3/4 + 1/4 = 4/4 = 1

Overall, 5 3/4 + 2 1/4 = 5+2+1 = 8

Answer: 10

Step-by-step explanation:

first solve for x, 3x+10=4x-15

x=25

now solve both equations to find two of the angles

angle 1: 85 angle 4:85

now add the two angles and subtract them from 180, 85+85=170. 180-170=10

angle 7 is 10

Step-by-step explanation:

One out of six chance of rolling a '2'    = 1/6

one out of two chance of landing on tails    = 1/2

1/6 * 1/2 = 1/12  

answer

A. graph attached

B. yes , it is in included in the solution area for the

system

STEPS:

1.

y < 2x - 7

y > -12x+3

2.

(3, -7)

plug in

2x - 7 >  y  > -12x + 3

2(3) - 7 > -7 > -12(3) + 3

6 - 7 > -7 > -36 + 3

-1 > -7 > -33

is -1 > -7 > -33 true?

yes

so it is in included in the solution area for the

system

Answer: try internet

Step-by-step explanation:

sorry

Answer:

the answer is 97 student tickets and 15 adult tickets

Step-by-step explanation:

The first order differential equation (\(e^y\) + \(ye^{(2x)}dx\) +\(xe^{(2x)\)- 1)dy = 0 can be solved using the exact method and is \(e^{(y^2/2 + x) }(e^{y }+ ye^{(2x)}) - \sqrt{(2\pi)\phi(y)} = C\)

To use the exact method, we need to check if the equation satisfies the condition ∂M/∂y = ∂N/∂x, where M and N are the coefficients of dx and dy respectively. In this case, we have:

∂M/∂y = \(e^y\) +\(2xye^{(2x)\)

∂N/∂x = \(2xe^{(2x)\)

Since ∂M/∂y is not equal to ∂N/∂x, we need to make the equation exact. To do this, we need to find a function u(x, y) such that uMdx + uNdy = 0 is exact. We can find u(x, y) by solving the following equation:

∂(uM)/∂y = ∂(uN)/∂x

Differentiating both sides with respect to y, we get:

u∂M/∂y + \(Mu_y\) = \(u_xN_y\)+ \(Nu_x\)

Comparing coefficients of dx and dy, we get two equations:

∂u/∂x = \(Nu_x - Mu_y\)

∂u/∂y =\(Mu_x\)

Solving these equations, we get:

u(x, y) = \(e^{(y^2/2 + x)\)

Multiplying both sides of the original equation by u(x, y), we get:

\((e^{(y^2/2 + x)} (e^{y }+ ye^{(2x))}dx + (e^{(y^2/2 + x) }(xe^{(2x)} - 1))dy\) = 0

This equation is exact since ∂(uM)/∂y = ∂(uN)/∂x. We can now find the solution by integrating with respect to x and y:

\(\int(e^{(y^2/2 + x) }(e^{y} + ye^{(2x))})dx = ∫(-e^{(y^2/2 + x)} (xe^{(2x)} - 1))dy\)

Integrating the left-hand side with respect to x, we get:

\(e^{(y^2/2 + x) }(e^{y} + ye^{(2x)}) + g(y)\)

Differentiating this with respect to y and comparing with the right-hand side of the equation, we get:

\(g'(y) = -e^{y^2/2)\)

Integrating both sides, we get:

\(g(y) = -\int(e^{(y^2/2)})dy = -\sqrt{(2\pi)\phi(y)\)

where Φ(y) is the cumulative distribution function of the standard normal distribution.

Substituting g(y) into the solution for the left-hand side, we get:

\(e^{(y^2/2 + x) }(e^{y }+ ye^{(2x)}) - \sqrt{(2\pi)\phi(y)} = C\)

where C is the constant of integration. This is the general solution to the given differential equation.

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Median length of time required to review an application = (45 + 100)/2= 72.50 Hence, the correct option is A, 72.50

Given times (in minutes) that several underwriters took to review applications for similar insurance coverage are 100, 110, 42, and 45 and we need to find the median length of time required to review an application.What is the median?The median is the middle value when a data set is ordered from least to greatest.To find the median of a data set, the first step is to write the data set in order from least to greatest. In the above given dataset,Let's first order these numbers from least to greatest;42, 45, 100, 110 Now we can see the median will be between 45 and 100, so we just need to find the mean of these two numbers. the correct option is A

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The equation of the given curve is given by r2 cos(2θ) = 36.

To find the Cartesian equation of the curve, we need to convert the polar equation into its equivalent Cartesian form. This can be done by substituting x = r cos θ and y = r sin θ into the given equation, yielding:
x2cos(2θ) + y2cos(2θ) - 36 = 0
Using the identity cos(2θ) = cos2θ - sin2θ, the equation can be rewritten as:
x2(cos2θ - sin2θ) + y2(cos2θ - sin2θ) - 36 = 0
Simplifying, we get:
x2 - y2 - 36 = 0

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When $20,000 is spent on advertising, the rate of change of sales is 6.67. This means that for every additional $1,000 spent on advertising, sales will increase by approximately $6,670.To find the derivative of S(x), we will use the quotient rule:

S(x) = (600x)/(x+40)

S'(x) = [(x+40)(600) - (600x)(1)]/(x+40)^2

= (24000)/(x+40)^2

Therefore, S'(x) = 24000/(x+40)^2

Interpretation: S'(x) represents the rate of change of sales with respect to advertising expenditure. For every additional $1,000 spent on advertising, sales will increase by $1,200/(x+40)^2.

When $20,000 is spent on advertising, we have:

S'(20) = 24000/(20+40)^2

= 24000/3600

= 6.67

Interpretation: The rate of change of sales is 6.67 when $20,000 is spent on advertising.

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Answer:

x = 9

Step-by-step explanation:

2(x + 5) = 3x + 1

open the parenthesis

2x + 10 = 3x + 1

subtract 2x from both sides of the equation

2x - 2x + 10 = 3x - 2x + 1

10 = x + 1

subtract 1 from both sides of the equation

9 = x

Answer:

Step-by-step explanation:

Substitute

2x+10=3x+1

Subtract 3x to other side

-x+10=1

Subtract 10

-x=-9

divide -1 both sides

x= 9

Consequently, C"s dimensions are (-9, -2) as the function rule (-y, x) to determine the new coordinates of position C.

In mathematics, an object in space is located using coordinates. They are numerical pairs that express how a location compares to an origin or a reference point. When expressing coordinates in two dimensions, an ordered pair (x, y) is usually used, where x denotes the horizontal distance from the origin and y denotes the vertical distance from the origin. Typically, the origin is referred to as the location (0, 0), where the x and y values are both zero.

given

Act I:

The following function rule can be used to define a rotation that is 90 degrees clockwise around the origin:

(x, y) ▷ (-y, x) (-y, x)

In other words, the new y-coordinate is equivalent to the original x-coordinate and the new x-coordinate is equal to the original y-negative coordinate's value.

part two:

A: (-2, 2) ▷ (2, -2) (2, -2)

We enter the initial coordinates (-2, 2) into the function rule (-y, x) to determine point A's new coordinates:

Consequently, A"s values are (2, -2).

B: (-6, 2) ▷ (-2, -6) (-2, -6)

We enter the initial coordinates (-6, 2) into the function rule (-y, x) to determine the new coordinates of point B:

x' = -y = -2

y' = x = -6

Consequently, B"s values are (-2, -6).

C: (-2, 9) ▷ (-9, -2) (-9, -2)

We enter the initial coordinates (-2, 9) into the function rule (-y, x) to determine the new coordinates of position C:

x' = -y = -9

y' = x = -2

Consequently, C"s dimensions are (-9, -2) as the function rule (-y, x) to determine the new coordinates of position C.

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The complete question is:-   Given the triangle with vertices at A: (-2, 2) B: (-6, 2) C: (-2, 9), write the transformation rule and the coordinates of A'B'C' after a rotation of 90 degrees clockwise. Part I:

Write the function rule. There are two boxes on either side of the comma. In the first box you will enter either a + or - sign. A plus + indicates there is no sign change. A - sign indicates that there is a sign change. In the second box you will either enter xory.

(x, y)▷ type your answer...

type your answer...

Answer:i think its 115 degres

Step-by-step explanation:

Answer:

Step-by-step explanation:

if x represent a base number in the following equation what is the value of x in 3x+101x-24x=8​?

3x + 101x - 24x = 8

80x = 8

x = 1/10

-------------------------

check

3 * 1/10 + 101 * 1/10 - 24 * 1/10 = 8

8 = 8

The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = (k²x, k²y, k²

What are the real numbers?

Real numbers are a set of numbers that includes all the rational and irrational numbers. The set of real numbers is denoted by the symbol R.

We need to check if the set of all triples of real numbers with the standard vector addition, denoted by (V, +), and scalar multiplication defined by k(x, y, z) = (k²x, k²y, k²z), denoted by (V, ·), is a vector space.

First, we need to check the vector space axioms:

Closure under addition: For any vectors u = (u1, u2, u3) and v = (v1, v2, v3) in V, their sum u + v = (u1 + v1, u2+v2, u3+v3) is also in V. This is true since the standard vector addition is used.

Commutativity of addition: For any vectors u, v in V, u + v = v + u. This is true since the standard vector addition is commutative.

Associativity of addition: For any vectors u, v, w in V, u + (v + w) = (u + v) + w. This is true since the standard vector addition is associative.

Identity element of addition: There exists a vector 0 in V, called the zero vector, such that for any vector u in V, u + 0 = u. The zero vector is (0, 0, 0), and this axiom holds.

Inverse elements of addition: For any vector u in V, there exists a vector -u in V, called the additive inverse of u, such that u + (-u) = 0. This is true since the standard vector addition is used.

Closure under scalar multiplication: For any vector u in V and any scalar k, k · u = (k²u1, k²u2, k²u3) is also in V. This is true since scalar multiplication is defined as k(x, y, z) = (k²x, k²y, k²z).

Distributivity of scalar multiplication over vector addition: For any vectors u, v in V and any scalar k, k · (u + v) = k · u + k · v. This is true since scalar multiplication is defined using the standard scalar multiplication of the real numbers.

Distributivity of scalar multiplication over scalar addition: For any vector u in V and any scalars k, l, (k + l) · u = k · u + l · u.

This is true since scalar multiplication is defined using the standard scalar multiplication of the real numbers.

Associativity of scalar multiplication: For any vector u in V and any scalars k, l, (kl) · u = k · (l · u).

This is true since scalar multiplication is defined using the standard scalar multiplication of the real numbers.

The identity element of scalar multiplication:

For any vector u in V, 1 · u = u, where 1 is the multiplicative identity of the real numbers.

This is not true in this case, since 1 · (x, y, z) = (x, y, z), whereas the scalar multiplication defined in this problem is k(x, y, z) = (k²x, k²y, k²z).

Thus, the set of all triples of real numbers with the given operations is not a vector space, since it violates the identity element of scalar multiplication axiom.

Therefore, the set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = (k²x, k²y, k²).

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The amount of land the railroad companies received for each mile of track they laid varied depending on the specific circumstances and agreements.

However, a common benchmark used during the construction of railroads in the United States was the granting of land through the Homestead Act of 1862. Under this act, railroad companies were granted approximately 6,400 acres (10 square miles) of land for every mile of track laid. This land was typically located alongside the tracks and served as an incentive for the companies to expand and develop the rail network across the country.

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Answer:

Step-by-step explanation:

4x - 8 - 27 + 6x - 2x + 10 - 12x =

4x + 6x - 2x - 12x - 8 - 27 + 10 =

-4x -25