use a scalar projection to show that the distance from a point p1sx1, y1d to the line ax 1 by 1 c − 0 is

Answer:

A 21/4

Step-by-step explanation:

When forming a perfect square trinomial you need to "complete the square".

All of the steps to completing the square when solving an equation:

1.  The leading coefficient must be 1.  

2.  Divide b by 2.

3.  Square (b/2)

4.  Add (b/2)^2 to both sides to keep the polynomial balanced.

5.  You can now write the perfect square trinomial and solve.

x^2 - 3x  

-3/2

(-3/2)^2 = 9/4 = 2 1/4

with 4 df.

The correct answer is d. Two-sample t test with 9 df.

Volume of refrigerator ---> cubic feet

Distance a person can run in 10 minutes ---> mile

The surface area of a tissue box ---> square inches

The perimeter of a baseball field ---> meters

The surface area of the moon ---> square kilometers

The volume of a large lake ---> cubic kilometers

The lenght of macaroni noodle ---> centimeter

The area of a bed sheet ----> square feet

Answer:3 and 1/4 is closer to 3 and 3/5 is closer to 4

Step-by-step explanation:  one is closer on the number scale then the other

This equation shows that the flow rate, f, is directly proportional to the time, t, with a constant rate of change of 1200 liters per minute.

To write the equation (y = mx) for the scenario of water flow through a firefighter hose, where the flow rate, f, is 1200 liters per minute, we need to assign variables to the terms in the equation.

In the equation y = mx, y represents the dependent variable, m represents the slope or rate of change, and x represents the independent variable.

In this scenario, the flow rate of water, f, is the dependent variable, and it depends on the time, t. So we can assign y = f and x = t.

The given flow rate is 1200 liters per minute, so we can write the equation as:

f = 1200t

This equation shows that the flow rate, f, is directly proportional to the time, t, with a constant rate of change of 1200 liters per minute.

To know more about variables visit:

https://brainly.com/question/15078630

#SPJ11

Answer:

Step-by-step explanation:

Divide and find:

Correct choice is C

The correct statements are:

The mean serves as a metric of central tendency widely known as the arithmetic average. This statistical measure is obtained by aggregating a collection of values and subsequently dividing the sum by the total count of values present within the dataset.

It is a prevalent tool employed in statistical analysis, providing insights into the typical magnitude that can be expected from the dataset's values.

Learn about mean here https://brainly.com/question/1136789

#SPJ1

Step-by-step explanation:

given

In a circle

Area of circle (A) = 225π

Let r be the radius of the circle then

we know

A = πr²

225π = πr²

r²= 225

r = 15 units

Answer: Just took the test the guy above me is correct correct

Step-by-step explanation:

Answer:

(2,-1)

Step-by-step explanation:

I took the test

For T to be a normal operator on a finite-dimensional complex inner product space V,

(a) If Tⁿ is the zero map, then T is the zero map.

(b) U commutes with T if and only if U commutes with each eigenprojection of T.

(c) There exists a normal U such that U² = T.

(d) T is invertible if and only if lambda_j is nonzero for all eigenvalues λ_j of T.

(e) T is a projection if and only if lambda_j is either 0 or 1 for all eigenvalues λ_j of T.

(f) T = -T* if and only if each eigenvalue of T is imaginary.

(a) If Tⁿ = 0 for some n ∈ ℕ, then the characteristic polynomial of T is p_T(x) = xⁿ. But by the spectral decomposition, the characteristic polynomial of T is given by p_T(x) = (x - λ₁)(d₁) × ... × (x - λ_k)(d_k), where λ₁, ..., λ_k are the distinct eigenvalues of T and d₁, ..., d_k are the dimensions of the corresponding eigenspaces. Since T is normal, the eigenspaces are orthogonal and hence the dimensions add up to the dimension of V. Thus we must have n = dim(V), which implies that T is the zero map.

(b) Let U be a linear operator on V that commutes with T. By the spectral decomposition, we can write T = λ₁P₁ + ... + λ_kP_k, where P₁, ..., P_k are orthogonal projections onto the eigenspaces of T. Since U commutes with T, we have U(P_i(v)) = P_i(U(v)) for any eigenvector v of T. It follows that U commutes with each P_i. Conversely, suppose U commutes with each P_i. Then we have U(T(v)) = U(λ_i P_i(v)) = λ_i U(P_i(v)) = λ_i P_i(U(v)) = T(U(v)) for any eigenvector v of T. Since the eigenvectors span V, this implies that U commutes with T.

(c) Let T = λ₁P₁ + ... + λ_kP_k be the spectral decomposition of T. Define U = λ₁(1/2)P₁ + ... + λ_k(1/2)P_k. Since T is normal, the eigenspaces are orthogonal and hence the projections P₁, ..., P_k are also orthogonal. It follows that U is also an orthogonal operator, and hence a normal operator. Moreover, we have U² = λ₁P₁ + ... + λ_kP_k = T.

(d) By the spectral theorem for normal operators, we can write T = λ₁P₁ + ... + λ_kP_k, where λ₁, ..., λ_k are the distinct eigenvalues of T and P₁, ..., P_k are orthogonal projections onto the corresponding eigenspaces. Moreover, we have T⁻¹ = λ₁⁻¹P₁ + ... + λ_k⁻¹P_k if all the eigenvalues are nonzero. Indeed, if all the eigenvalues are nonzero, then T is invertible and hence bijective. It follows that each eigenspace has a dimension at most 1, and hence T has a unique decomposition into a sum of orthogonal projections onto its eigenspaces. It is then easy to check that T⁻¹ has the desired decomposition. Conversely, suppose that T⁻¹ has the desired decomposition. Then we have T(T⁻¹(v)) = v for any v ∈ V. It follows that each eigenspace has dimension at most 1, and hence T is bijective, and hence invertible.

(e) By the spectral theorem for normal operators, we can write T = λ₁P₁ + ... + λ_kP_k, where λ₁, ..., λ_k are the distinct eigenvalues of T and P₁, ..., P_k are orthogonal projections onto the corresponding eigenspaces. It follows that T is a projection if and only if T² = T, which is equivalent to the condition that λ_i ∈ {0, 1} for all i.

(f) By the spectral theorem for normal operators, we can write T = λ_1 P_1 + ... + λ_k P_k, where λ_1, ..., lambda_k are the distinct eigenvalues of T and P_1, ..., P_k are the orthogonal projections onto the corresponding eigenspaces. Note that T is self-adjoint if and only if T = T*, or equivalently, λ_j is real for all j. On the other hand, T = -T* if and only if λ_j = -λ_j × for all j, or equivalently, lambda_j is imaginary for all j. Thus, T = -T* if and only if each λ_j is imaginary, as desired.

Learn more about the finite-dimensional complex at

https://brainly.com/question/30531953

#SPJ4

The equivalent pairs are y - x and x - y, y/x and x/y, and y + x + z and y + (x + z).

The pairs of expressions that are equivalent are:

  (The order of subtraction does not affect the result)

  (Division is commutative, so the order of operands does not affect the result)

  (Addition is associative, so the grouping of terms does not affect the result)

The pairs of expressions that are not equivalent are:

  (The order of multiplication affects the result)

  (In the second expression, y is squared in the denominator, which is not the same as y being divided by x in the first expression)

  (Adding y and x cannot yield a result of 0)

Therefore, the equivalent pairs of expression are y - x and x - y, y/x and x/y, and y + x + z and y + (x + z).

Learn more about equivalence of pairs of expressions

brainly.com/question/29001991

#SPJ11

Answer:

i know this is really late but it's B

Step-by-step explanation:

Answer:B

Step-by-step explanation:

trust meh

Answer:

  26, 11, 4, 5, 14

Step-by-step explanation:

To find the value of the function, replace the variable with the number and do the arithmetic.

  f(-2) = 4(-2)² -3(-2) +4 = 16 +6 +4 = 26

For doing repetitive calculations, it is convenient to write the formula into a calculator or spreadsheet and let it work from the list of values. That is what we did in the attached. It shows a table of x and f(x) for the values of x you are interested in.

The function values are ...

_____

Additional comment

For evaluating polynomials, either by hand or machine, it is often convenient to rewrite the polynomial in Horner Form. The total number of math operations tends to be reduced. When doing this by hand, the arithmetic tends to be easier.

  f(x) = (4x -3)x +4

That is, the powers of x accumulate as each layer in parentheses is multiplied by x and the next coefficient added to the result.

Using this form, ...

  f(-1) = (4(-1) -3)(-1) +4

  f(-1) = (-7)(-1) +4 = 11

Answer:

C.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Just take the 1.25 x 4 months, then multiply that by the 2500 to get your answer of 12,500 people.

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Answer:

a = 27

b = 38

c = 19

Step-by-step explanation:

a + b + c = 84

b = 2c

a = 8+c

8+c +2c+c = 84

4c + 8 = 84

4c = 76

c = 19

b = 2(19) = 38

a = 8 + 19  = 27

The probability that three of out nine cars need new brakes is 0.294  

Combination:

The combination is the process of selecting items from a group of objects where the order of objects does not matter. In simple words, we can say that it is a combination of n things in r times without repetition.

The formula for the combination of 'a' things from the set of n things without replacement is given

Here from the given problem,

Number of automobiles = 25

Number of automobiles that need new tune-ups = 15  

Number of automobiles that need new brakes = 10

Number of automobiles chosen at time = 9  

From above formula

The number of ways of selecting 9 cars from 25 cars

²⁵C₉ = 25!/9!(25 - 9)!

= 25!/9!(16)!  

= 2,042,975

The number of ways that can be chosen as 3 out of 9 cars that need breaks

Choosing 3 cars that need breaks from 10 cars = ¹⁰C₃

= 10!/3!(10 - 3)!  

= 10!/3!(7)!

= 120

Choosing the remaining 6 cars from the 15 groups of cars that need new tune-ups =  ¹⁵C₆

=  15!/6!(15 - 6)!  

=  15!/6!(6)!    

= 5,005

From above calculations

The number of ways that can be chosen as 3 out of 9 cars that need new  breaks  = 120 × 5,005

= 600600

As we know that

Probability of event = No of favorable outcomes / total outcomes  

The probability that three of them need new brakes

= 600600/2042975

= 0.294  

Learn more about Combinations at

brainly.com/question/28720645

#SPJ4

The correct designations for the signs of Δ.h, Δ.s, and Δ.g for this reaction are Δ.h < 0, Δ.s > 0, and Δ.g < 0.

The dissolution of ammonium nitrate in water is an exothermic process, meaning that it releases heat to the surroundings. Therefore, Δ.h is negative. The dissolution also increases the disorder of the system, or entropy, which is positive for Δ.s. Finally, Δ.g, the Gibbs free energy change, can be calculated using the equation

where T is the temperature in Kelvin. Since Δ.h is negative and Δ.s is positive, Δ.g will be negative at room temperature, indicating that the reaction is spontaneous.

To calculate Δ.h for the dissolution of ammonium nitrate, we can use the equation Δ.h = q/m, where q is the heat absorbed or released by the system, and m is the mass of the solute. In this case, the temperature change was 5.0°C, or 5.0 K, and the solution contained 80.0 g of ammonium nitrate. The heat released by the system can be calculated using the equation q = mcΔT, where c is the specific heat capacity of water (4.18 J/g°C). Therefore,

The negative sign indicates that heat was released by the system, as expected for an exothermic process. Dividing q by m gives us Δ.h:

Since Δ.h is negative and Δ.s is positive, we can conclude that Δ.g is negative and the reaction is spontaneous.

Learn more about ammonium nitrate

https://brainly.com/question/28866036

#SPJ4

Step-by-step explanation:

just as the graph shows.

no trick or hidden meaning or whatever.

#1

0 seconds to 5 seconds.

0 meters to 3 meters.

traveled 3-0 = 3 meters in 5-0=5 seconds

#2

0 seconds to 8 seconds.

0 meters to 5 meters.

traveled 5-0=5 meters in 8-0=8 seconds.

The ratio of the sides of the given similar triangles is: C. 4/12 = 5/15 = 1/3.

The corresponding sides of similar triangles have ratios that are equal to each other.

The corresponding sides and their ratios are:

4/12 = 1/3

5/15 = 1/3

Therefore, the ratio of their sides in its lowest term is:

C. 4/12 = 5/15 = 1/3

Learn more about the similar triangles on:

https://brainly.com/question/2644832

#SPJ1

a least squares linear trend line is just a simple regression line with the years recoded  then it is a true statement

The simple linear regression model is;

y = mx + c

Where,

y = dependent variable

m is the slope

x is the independent variable

c is the y- intercept

The long-term trend only Least-Squares Regression Model also follows the same format except y becomes Yt and x becomes t.

The long-term trend only Least-Squares Regression Model is therefore the same as a simple linear regression only with different variable terms.

learn more about of square here

https://brainly.com/question/19595237

#SPJ4

Answer:

2x - y = -5

Step-by-step explanation:

do the math equation in the calculator and you will get the right answer

Answer:

y = -2x + 6

Step-by-step explanation:

The equation is,

→ 6x + 3y = 18

Then the value of y will be,

→ 6x + 3y = 18

→ 3y = -6x + 18

→ y = (-6x + 18)/3

→ [ y = -2x + 6 ]

Hence, value of y is -2x + 6.

There are 216 possible ways for the numbers to become a multiple of 5 when a fair die is tossed 4 times.

The four-digit integer will be in the range of 1000-9999 and can only be a multiple of 5 if the number ends in either a 0 or 5.
There are 6^4 or 1296 ways to form a four-digit integer with the numbers that appear on top of a fair die after it is tossed 4 times. However, for the number to be a multiple of 5, the last digit must be either 0 or 5.

Since a fair die does not have a 0, the last digit can only be 5. Therefore, there are 6^3 or 216 ways for the first three digits to be arranged, and only 1 way for the last digit to be a 5.

So, the total number of ways for the numbers to become a multiple of 5 is 216 * 1 = 216.

Know more about multiple here:

https://brainly.com/question/96515

#SPJ11

\($$z = \frac{x-\mu}{\sigma}\) \frac{8-10}{4}

= -0.5$$ Now, we can find the area to the left of

z = -0.5, which is 0.3085. Therefore, the probability of the given area is 0.3085.

A normal probability table shows the areas to the left of z-values. So, we must understand that to find the area to the right of a negative z-score, we need to add 0.5 to the area associated with the corresponding positive z-score. Also, to find the area to the left of a positive z-score, we must subtract 0.5 from the area associated with the corresponding negative z-score.

Let's calculate the following using the provided normal probability table and illustrate your answers with graphs: a. P(-0.5 < Z < 1.2) = Using the standard normal table, the area associated with z = -0.5 is 0.3085, and the area associated with z = 1.2 is 0.3849. We need to find the probability that -0.5 < z < 1.2, that is, the area to the right of z = -0.5 and to the left of z = 1.2.

To know more about probability visit:-

https://brainly.com/question/31828911

#SPJ11

Answer:
Melissa's old job gave her 17.20 dollars.

Step-by-step explanation:

Why? Because if you 10.80 x 2 - 3.80 hr less, you get 17.80

Answer:

(-1373)

Step-by-step explanation:

a = 1st term = -13

Common difference = d = 2nd term - 1st term

                            d = -33 - (-13) = -33 + 13

                             d = -20

n = 69

nth term = a + (n-1)d

69th term = (-13) + 68 * (-20)

                 = -13 - 1360

                =  - 1373

Answer:

When Miranda works 5 hours instead of 4, her pay goes up by

 $56.00 - 44.80 = $11.20

That is, Miranda is paid $11.20 for each hour she works.

The slope of Tyler's graph indicates he is paid $9.00 for each hour he works. Miranda's pay per hour is $11.20 - 9.00 = $2.20 more than Tyler's.

Miranda earns $2.20 more per hour than Tyler

Step-by-step explanation:

Congratulations!!!!

Answer:

Congratulations! Hope that she can drive around now!