Given: rectangle MNPQ ~ rectangle RSTU

- find the perimeter of rectangle RSTU
- find the area of rectangle RSTU

(i) Each of u, v, and w are vectors in Rⁿ, so they each have size n × 1 (i.e. n rows and 1 column). So u and v both have size n × 1, while wᵀ has size 1 × n.

M is an n × n matrix, so the matrix A has been partitioned into the blocks

\(A=\begin{pmatrix}M_{n\times n}&\mathbf u_{n\times 1}\\\mathbf w^\top_{1\times n}&\alpha\end{pmatrix}\)

where α is a scalar with size 1 × 1. So A has size (n + 1) × (n + 1).

(ii) Multiplying both sides (on the left is the only sensible way) by the given matrix gives

\(\begin{pmatrix}M^{-1}&\mathbf 0\\-\mathbf w^\top M^{-1}&1\end{pmatrix}\begin{pmatrix}M&\mathbf u\\\mathbf w^\top&\alpha\end{pmatrix}\begin{pmatrix}\mathbf x\\x_{n+1}\end{pmatrix}=\begin{pmatrix}M^{-1}&\mathbf 0\\-\mathbf w^\top M^{-1}&1\end{pmatrix}\begin{pmatrix}\mathbf v\\v_{n+1}\end{pmatrix}\)

\(\begin{pmatrix}M^{-1}M&M^{-1}\mathbf u\\-\mathbf w^\top M^{-1}M+\mathbf w^\top&-\mathbf w^\top M^{-1}\mathbf u+\alpha\end{pmatrix}\begin{pmatrix}\mathbf x\\x_{n+1}\end{pmatrix}=\begin{pmatrix}M^{-1}&\mathbf 0\\-\mathbf w^\top M^{-1}&1\end{pmatrix}\begin{pmatrix}\mathbf v\\v_{n+1}\end{pmatrix}\)

and of course M ⁻¹ M = I (the identity matrix), so

-wᵀ M ⁻¹ M  + wᵀ = -wᵀ + wᵀ = 0ᵀ (the zero vector transposed)

(iii) Simplifying the system further gives

\(\begin{pmatrix}I&M^{-1}\mathbf u\\\mathbf 0^\top&-\mathbf w^\top M^{-1}\mathbf u+\alpha\end{pmatrix}\begin{pmatrix}\mathbf x\\x_{n+1}\end{pmatrix}=\begin{pmatrix}M^{-1}&\mathbf 0\\-\mathbf w^\top M^{-1}&1\end{pmatrix}\begin{pmatrix}\mathbf v\\v_{n+1}\end{pmatrix}\)

\(\begin{pmatrix}\mathbf x+x_{n+1}M^{-1}\mathbf u\\(\alpha-\mathbf w^\top M^{-1}\mathbf u)x_{n+1}\end{pmatrix}=\begin{pmatrix}M^{-1}\mathbf v\\-\mathbf w^\top M^{-1}\mathbf v+v_{n+1}\end{pmatrix}\)

So now, setting y = M ⁻¹u and z = M ⁻¹ v gives

\(\begin{pmatrix}\mathbf x+x_{n+1}\mathbf y\\(\alpha-\mathbf w^\top\mathbf y)x_{n+1}\end{pmatrix}=\begin{pmatrix}\mathbf z\\-\mathbf w^\top \mathbf z+v_{n+1}\end{pmatrix}\)

Given that α - wᵀy ≠ 0, it follows that

\(x_{n+1}=\dfrac{v_{n+1}-\mathbf w^\top\mathbf z}{\alpha-\mathbf w^\top\mathbf y}\)

(iv) Combining the result from (iii) with the first row gives

\(\mathbf x+x_{n+1}\mathbf y=\mathbf z\)

\(\mathbf x=\mathbf z-x_{n+1}\mathbf y\)

\(\mathbf x=\mathbf z-\dfrac{v_{n+1}-\mathbf w^\top\mathbf z}{\alpha-\mathbf w^\top\mathbf y}\mathbf y\)

EXPLANATION:

Given;

We are given the step by step procedure to find the height of a triangle.

Required;

We are required to determine if the step by step solution is true or false.

Solution/Explanation;

When finding the height of a triangle, we may use the Pythagoras theorem or we may use trigonometric ratios for right angled triangles.

Note that the Pythagoras' theorem is also used only for right angled triangles and one of the three sides will be the height of the triangle.

When required to calculate the the height of a triangle given a line perpendicular to the base (that is, at a 90 degree angle with the base), and passing through the vertex opposite the base, the triangle can be effectively split into two parts along the perpendicular and the perpendicular line will then become the height. Also depending on the amount of information available, we may use the Pythagoras' theorem (if the other two sides are given). Alternatively we may use the trigonometric ratios if one other side and one of the angles is given.

Therefore,

ANSWER:

FALSE

Answer:

73.5

Step-by-step explanation:

7100 km = 4411.735 miles 1 minute = 60 secs 4411.735/60 = 73.5 miles/sec.

Answer:

\(\huge\boxed{\mathrm{Range = 1.05}}\)

Step-by-step explanation:

Given Data:

2.45 , 3.50 , 2.89 , 2.99

Arrange it in ascending order.

2.45 , 2.89 , 2.99 , 3.50

Range = Highest No - Lowest No.

Range = 3.50 - 2.45

Range = 1.05

Answer:

Range=largest value-smallest value

Range=2.99-2.45

Range=0.54

Step-by-step explanation:

hope it is helpful for you

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Answer:

Step-by-step explanation:

I'll be using the quadratic equation

Answer:

he values of F(x) between x=1 and x=3 are 1, 4, and 9.

Step-by-step explanation:

To find the value of F(x) between x=1 and x=3, we need to substitute the values of x into the given function F(x) = x^2 and evaluate the function at each value. This gives us:

F(1) = 1^2 = 1

F(2) = 2^2 = 4

F(3) = 3^2 = 9

Therefore, the values of F(x) between x=1 and x=3 are 1, 4, and 9.

The statements that will be true about parallelogram ABCD are: A, B, D, and E.

Properties of a Parallelogram -

Diagonals of a parallelogram bisect each other into congruent segments.

Opposite angles and sides of a parallelogram are always congruent.

Alternate interior angles are always congruent in measure.

Thus, the following would be true of parallelogram ABCD:

AP ≅ CP (congruent segment's of a bisected diagonal)

BC ≅ AD (congruent opposite sides)

∠CAD ≅ ∠ACB (congruent angles)

∠BPC ≅ ∠APD (congruent angles)

Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.

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Answer:

15

Step-by-step explanation:

50-35

=15

sorry if wrong

hope helpful..

Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

The approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Total of 22 is more than 4500 is equivalent to average of 22 is more than \($\frac{4500}{22}\)=204.545

\($$\begin{aligned}P(\bar{x} > 204.545) & =1-P(\bar{x} < 204.545) \\& =1-P\left(\frac{\bar{x}-\mu}{\sigma / \sqrt{u}} < \frac{204.545-195}{35 / \sqrt{22}}\right) \\& =1-P(z < 1.2792) \\\end{aligned}$$\)

                        = 1 - 0.8997

                        = 0.1003

                        = 10.03%

Therefore, the approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

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Answer:

\(\huge \boxed{{x\geq -3, \ x \neq 2}}\)

Step-by-step explanation:

The function is given,

\(\displaystyle f(x)=\frac{\sqrt{x+3 }}{(x+8)(x-2)}\)

The domain of a function are all possible values of x.

There are restrictions for the value of x.

The denominator of the function cannot equal 0, if 0 is the divisor then the fraction would be undefined.

\(x+8\neq 0\)

Subtract 8 from both parts.

\(x\neq -8\)

\(x-2\neq 0\)

Add 2 on both parts.

\(x\neq 2\)

The square root of x + 3 cannot be a negative number, because the square root of a negative number is undefined. x + 3 has to equal to 0 or be greater than 0.

\(x+3\geq 0\)

Subtract 3 from both parts.

\(x\geq -3\)

The domain of the function is \(x\geq -3\), \(x\neq 2\).

The domain of the given function will be x ≥ -3 and x ≠ 2.

The entire range of independent input variables that can exist is referred to as a function's domain or,

The set of all x-values that can be used to make the function "work" and produce actual y-values is referred to as the domain.

As per the data given in the question,

The given expression of function is,

f(x) = \(\sqrt{\frac{x+3}{(x-8)(x-2)} }\)

The fraction would indeed be undefined if the base of the function were equal to zero, which is not allowed.

x + 8 ≠ 0

x ≠ -8

And, x - 2 ≠ 0

x ≠ 2

Since the square root of a negative number is undefined, x+3 cannot have a negative square root. x+3 must be bigger than zero or identical to zero.

So,

x + 3 ≥ 0

x ≥ -3

So, the domain of the function will be x ≥ -3 and x ≠ 2.

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Step-by-step explanation:

40 ÷ 3

13•333333333333333333

Answer:

Step-by-step explanation:

      $20 / 5 kg = $4 / kg

$2.50 / 0.5 kg = $5 / kg

the big bag is a better deal

Answer:

To one decimal place,

y = 16.3 m

Step-by-step explanation:

Using SOHCAHTOA,

In this case we need to use CAH,

WE know the angle = 25 and the hypotenuse H = 18,

so,

y = adjacent

\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)

Answer: 16.3 in.

Step-by-step explanation:

use SOH CAH TOA

cos x = adj/hyp

cos 25  = y/18

18 cos 25  = y

y= 16.3

The equation that shows the relation between the number of hours worked and tickets sold is t = 23h (fourth option)

Examining the table, it can be seen that the number of tickets sold increases by 23 for every hour that Gwen works.

Tickets sold when Gwen works for 2 hours = 23 x 2 = 46

Tickets sold when Gwen works for 2 hours = 23 x 3 = 69

Because the tickets sold increase by a constant number, the equation would be modelled as a linear function.

Linear equations have the form : a + bx

Ticket sold = (number of hours x ticket sold in the first hour)

t = 23h

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Answer:

The population of interest is all the students at the University, to find their parking times.

Step-by-step explanation:

Sampling

This is a common statistics practice, when we want to study something from a population, we find a sample of this population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.

Here, the population of interest is all New York state residents.

An administrator inconspicuously followed 250 students and carefully recorded their parking times.

Sample of 250 students at the University.

So the population of interest is all the students at the University, to find their parking times.

Answer:

Step-by-step explanation:

B because after having the star and the circle comes the square.

Answer:

Her answer should have been x=17/34

Step-by-step explanation:

There are 152 red pens and 190 blue pens in Max's drawer, given that there are a total of 342 pens altogether.

Let's solve the problem step by step:

Identify the given information:

The ratio of red pens to blue pens is 4 to 5.

There are a total of 342 pens in the drawer.

Set up the ratio equation:

Let's assume the number of red pens is 4x, and the number of blue pens is 5x.

Here, 'x' is a scaling factor that allows us to find the actual number of pens.

We can write the equation as: 4x + 5x = 342.

Simplify and solve the equation:

Combining like terms, we have 9x = 342.

Divide both sides of the equation by 9 to solve for 'x':

x = 342 / 9 = 38.

Calculate the number of red pens and blue pens:

Now that we have the value of 'x', we can find the number of red and blue pens:

Number of red pens: 4x = 4 × 38 = 152.

Number of blue pens: 5x = 5 × 38 = 190.

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Answer:

Y= 20x + 35

Step-by-step explanation: I have the same test.

Answer:

-6

Step-by-step explanation:

if they were both positive numbers, it would be 6. But when you multiply a negative by a positive, the answer is negative.

Answer:

-6

Step-by-step explanation:

When you multiply a positive number by another positive number, you will always get a positive number as your answer. Same thing for negative. If you multiply a negative by a negative, you will always get a positive. However, when you multiply a negative by a positive, you will always get a negative number.

Since you know this, you can multiply 2 by 3, which is 6. Because 2 is negative and 3 is positive, you know that the answer must be negative. Therefore, you add the negative symbol to 6, giving you -6.

I hope this isn't too confusing. Please let me know if you have any more questions. Good luck!

Answer:

C   x² - 2x - 1 = 3

Step-by-step explanation:

x² - 2x - 1 = 3

x² - 2x - 4 = 0

a = 1

b = -2

c = -4

x = (-b ±√(b² - 4ac)) / 2a

Answer:

-1+\(\sqrt{x} 5\)

Step-by-step explanation:

Answer:

16.7 cm

Step-by-step explanation:

Area of a triangle = ½*base*height

Area of the shaded region = area of triangle = 100.2 cm³

base = w

height = 12 cm

Plug in the value into the equation:

½*w*12 = 100.2

6w = 100.2

w = 100.2/6

w = 16.7 cm

Answer:

The answer is D. Green; The experimental probability is 22.7%, and the theoretical probability is 15%.

Answer:

I would think regions II, IV, and VI

Step-by-step explanation:

In the venn diagram, there are are three circles. In which they are overlapping, while some areas are overlapped by all three, there are three areas where only two of the circles overlap.

*I hope this helps you somewhat ^^*