What is the completely factored form of this expression?
162 - 50x^4

We need to show that for vectors x, y, and z in C^n and complex scalars a and ß, the inner product (z, ax + By) is equal to a(z, x) + ß(z, y).

To prove the given equation, we will use the properties of the inner product and scalar multiplication.
First, let's expand the left-hand side of the equation:
(z, ax + By)
Using the linearity property of the inner product, we can distribute the inner product over addition:
(z, ax) + (z, By)
Next, we apply the scalar multiplication property of the inner product to each term:
a(z, x) + ß(z, y)
Now, we can see that the left-hand side (z, ax + By) is equal to the right-hand side a(z, x) + ß(z, y), proving the equation.
In summary, by utilizing the linearity and scalar multiplication properties of the inner product, we showed that (z, ax + By) is equal to a(z, x) + ß(z, y). This demonstrates the relationship between the inner product of vectors and scalar multiplication, verifying the given equation.

Learn more about complex scalars here
https://brainly.com/question/29666268



#SPJ11

Answer:

71 and 73

Step-by-step explanation:

hope this helps!

Answer:

X2+8X+6=0

We add all the numbers together, and all the variables

X^2+8X+6=0

a = 1; b = 8; c = +6;

Δ = b2-4ac

Δ = 82-4·1·6

Δ = 40

The delta value is higher than zero, so the equation has two solutions

We use following formulas to calculate our solutions:

X1=−b−Δ√2aX2=−b+Δ√2a

The end solution:

Δ−−√=40−−√=4∗10−−−−−√=4√∗10−−√=210−−√

X1=−b−Δ√2a=−(8)−210√2∗1=−8−210√2

X2=−b+Δ√2a=−(8)+210√2∗1=−8+210√2

Step-by-step explanation:

Answer:

x = -4 ± √10

Step-by-step explanation:

Step 1: Write quadratic

x² + 8x + 6 = 0

Step 2: Solve for x

Answer: A

Step-by-step explanation:

Answer:

2 8  +  1 2

Step-by-step explanation:

baku you left me alone in the comments without saying anything... :(

Quantitative literacy can be used in a clinical setting to assess the patient's health status, determine the patient's progress, and make informed decisions.

Medical professionals must be competent in quantitative literacy to ensure that patients receive the best possible care. To ensure that patients receive the best possible care, quantitative literacy must be used. Quantitative literacy is critical in a clinical setting because of its ability to provide accurate information, facilitate decision-making, and improve patient outcomes.Quantitative literacy may be used in a clinical setting in a variety of ways. Some examples of how quantitative literacy may be used in a clinical setting include:Calculating dosages: When calculating dosages, quantitative literacy is critical to ensuring that the correct amount of medication is given to the patient. This is particularly important for medications that have a narrow therapeutic window, such as insulin or digoxin.Converting temperatures: Quantitative literacy is essential when converting temperatures from Celsius to Fahrenheit or vice versa. This is important when monitoring patient's body temperature for signs of fever or hypothermia.Calculating infusion rates: When administering intravenous fluids, quantitative literacy is essential to ensure that the correct infusion rate is used. This is important because fluids that are infused too quickly can cause fluid overload, while fluids that are infused too slowly may not provide adequate hydration

.Math Problem:

Convert 50°C to Fahrenheit

To convert Celsius to Fahrenheit, you use the following formula:

F = (C x 1.8) + 32

Substitute 50 for C in the formula:

F = (50 x 1.8) + 32F = 90 + 32F = 122°F

Therefore, 50°C is equal to 122°F.

In conclusion, quantitative literacy is critical to ensure that patients receive the best possible care. In the medical field, nurses, doctors, and other healthcare professionals must have excellent quantitative skills to interpret and use numerical data. They must understand how to calculate medication dosages, infusion rates, and vital signs accurately. They must also be able to interpret lab results, which are typically presented numerically. Without quantitative literacy, healthcare professionals would not be able to provide adequate care to their patients.

To know more about Quantitative literacy visit:

brainly.com/question/32490674

#SPJ11

The terminal point of the angle is located 3.5 cm to the right and 3.5 cm above the circle's center.

To determine the position of the terminal point of the angle, we need to consider its measurement in radians, the direction of the initial ray, and the properties of a circle with a radius of 3.5 cm.

Given that the angle measures 2.3 radians, we know that it spans 2.3 times the radius of the circle. Since the radius is 3.5 cm, the arc length of the angle is 2.3 * 3.5 = 8.05 cm.

Now, let's analyze the direction of the initial ray. The 3-o'clock direction is to the right on a standard clock face. In a circle, the positive x-axis is typically considered to be the 3-o'clock direction. Therefore, the initial ray of the angle is pointing directly to the right.

Since the terminal point of the angle lies on the circumference of the circle, we can determine its position relative to the circle's center using polar coordinates. The terminal point is located at a radial distance from the center, which is equal to the radius of the circle.

Hence, the terminal point is situated 3.5 cm to the right of the circle's center, as it lies on the positive x-axis.

Additionally, the terminal point is located on the circumference of the circle, so it is also 3.5 cm above the circle's center. Since the circle is centered at the angle's vertex, the vertical displacement of the terminal point is equal to the radius of the circle.

Therefore, the terminal point of the angle is located 3.5 cm to the right and 3.5 cm above the circle's center.

For more question on angle visit:

https://brainly.com/question/31615777

#SPJ8

a logical argument that is presented in graphical form using boxes and arrows is called a flowchart proof

hope it helps ^-^

Answer:

my g get a fraction calculator

Step-by-step explanation:

3.7 or 3 7/10

Because you need to make these mixed numbers into improper fractions.

Multiply the denominator by the whole number

5 × 8 = 40

Step 2

Add the answer from Step 1 to the numerator

40 + 4 = 44

Step 3

Write answer from Step 2 over the denominator

44/5

=445

We are given the expression 6x - 5 + √x - 1 and need to evaluate it for two different values of x: (a) x = 9 and (b) x = 1.

For x = 9:

We substitute x = 9 into the expression: 6(9) - 5 + √(9) - 1.

Simplifying, we have: 54 - 5 + 3 - 1.

Combining like terms, we get: 51 + 2.

The expression evaluates to 53 when x = 9.

For x = 1:

We substitute x = 1 into the expression: 6(1) - 5 + √(1) - 1.

Simplifying, we have: 6 - 5 + 1 - 1.

Combining like terms, we get: 1 + 0.

The expression evaluates to 1 when x = 1.

Learn more about   expression here:

https://brainly.com/question/15994491

#SPJ11

Answer:

f(n) is the function f-1(n) is the inverse of that function , basically the x and y switch places

Step-by-step explanation:

Answer:

20 cm

Step-by-step explanation:

We can use ratios to solve

We know x = 7 since they are of equal length

x          x+7

----- = -------

10         y

7          7+7

----- = -------

10         y

Using cross products

7y = 14*10

7y = 140

Divide by 7

7y/7 = 140/7

y = 20

Answer:

Option A

Step-by-step explanation:

7x - y = 7

x + 2y = 6

Subtract 2y from both sides;

x = -2y + 6

Lets substitute x;

7(-2y + 6) - y = 7

Distribute;

-14y + 42 - y = 7

-15y + 42 = 7

Subtract 42 from both sides;

-15y  = -35

Divide both sides by -15

y = [tex]\frac{35}{15}=\frac{7}{3} = 2\frac{1}{3}[/tex]

Lets substitute y;

x + 2([tex]\frac{7}{3}[/tex]) = 6

x + [tex]\frac{14}{3}[/tex] = 6

Subtract [tex]\frac{14}{3}[/tex] from both sides;

x = [tex]-\frac{14}{3} +6=-\frac{14}{3}+\frac{6}{1}=\frac{-14+18}{3} =\frac{4}{3}=1\frac{1}{3}[/tex]

Answer:

there are 4 different types of tranformations. these include translation, rotation, reflection, and dilation. in the function f(x)=(x−3)2+5 there are 3 transformations. these include a horizontal shift of 3 to the left, vertical shift of 5 up, and it is reflected over the x axis.

Step-by-step explanation:

Answer:

he gained over all

Step-by-step explanation:

if he earns $8 than loses $4 we would use this equation. 8-4 to find out that he still has $4.

Answer:

B.

Step-by-step explanation:

When the number is positive and not inside the parentheses it means it gets translated up.

Answer: x=50

Step-by-step explanation:

(3x+5)+(x-25)=180

Answer:

answer is c hope it helps

Answer: a

Step-by-step explanation:

To find a matrix B that satisfies B² = A, we first need to find the matrix P that diagonalizes A, where D is the diagonal matrix with the eigenvalues of A. The matrix B = [[12, -2], [4, 6]] satisfies B² = A.

Given that the eigenvalues of A are λ = 4 and λ = 9, we can find the corresponding eigenvectors. By constructing the matrix P with the eigenvectors as columns and using the inverse of P, we obtain A = PDP⁻¹. Then, to find a matrix B such that B² = A, we can take the square root of each eigenvalue in D and construct a new diagonal matrix E. Finally, we can find B by multiplying P and E.

To diagonalize the matrix A, we find the eigenvectors corresponding to each eigenvalue. For λ = 4, we solve the equation (A - 4I)x = 0, where I is the identity matrix. The solution gives us the eigenvector [3, 1]⁺. Similarly, for λ = 9, we solve (A - 9I)x = 0, and obtain the eigenvector [-1, 3]⁺.

Next, we construct the matrix P by taking the eigenvectors as columns: P = [[3, -1], [1, 3]]. To diagonalize A, we also need the inverse of P, which can be found as P⁻¹ = (1/10)[3, 1; -1, 3].

Now, we can express A as A = PDP⁻¹, where D is the diagonal matrix with the eigenvalues: D = [[4, 0], [0, 9]].

To find B such that B² = A, we take the square root of each eigenvalue in D. We obtain E = [[2, 0], [0, 3]]. Finally, we find B by multiplying P and E: B = PEP⁻¹.

Therefore, the matrix B = [[12, -2], [4, 6]] satisfies B² = A.

Learn more about matrix here:

https://brainly.com/question/28180105

#SPJ11

Answer:

1. n = -3+2√ 11/7, n = (-) 3+2√ 11/7

2. x=-3+√ 5/2, x= -3-√ 5/2

Step-by-step explanation:

(-) means that it applys to both the numerator and denominator.

Using Delta y = f'(x) Delta x to find a decimal approximation of the radical expression, we get the value found using Delta y f' (x) Delta x is 124.176.

The Delta y = f’(x) Delta x is the linear approximation formula used in calculus to estimate the value of an unknown function based on its derivative at a particular point.

In order to solve the problem using Delta y = f’(x) Delta x, we first have to rewrite the radical expression in terms of a function.

Let the function f(x) = sqrt(x) represent the radical expression.

Then, we will find the value of f'(x) by differentiating the function f(x) using the Power Rule of differentiation.

f(x) = sqrt(x) f'(x) = 1/2x^(-1/2)

Next, we will substitute the given value of x in the function f(x) and f’(x) to solve for Delta y = f'(x) Delta x.

Given, x = 124

Delta x = 2 Δy = f’(x) Δx = 1/2 * 124^(-1/2) * 2 = 0.1762

Hence, the decimal approximation of the radical expression is 124.176.

Learn more about decimal approximation visit:

brainly.com/question/30591123

#SPJ11

The value of Exponents are:

1. √[tex]x^{36}y^{16[/tex]= x¹⁸y⁸

2. √[tex]x^{100}y^{16[/tex]= x⁵⁰y⁸

3. √300 y⁹ = 10y⁴√ 3y

1. √[tex]x^{36}y^{16[/tex]

Now, we can write [tex]x^{36[/tex] and [tex]y^{16[/tex] as

[tex]x^{36[/tex] = (x¹⁸)²

and, y¹⁶= (y⁸)²

So, √[tex]x^{36}y^{16[/tex]

= √(x¹⁸)²(y⁸)²

= x¹⁸y⁸

2. √[tex]x^{100}y^{16[/tex]

Now, we can write [tex]x^{100[/tex] and [tex]y^{16[/tex] as

[tex]x^{100[/tex] = (x⁵⁰)²

and, y¹⁶= (y⁸)²

So, √[tex]x^{36}y^{16[/tex]

= √(x⁵⁰)²(y⁸)²

= x⁵⁰y⁸

3. √300 y⁹

Now, we can write y⁹ as

y⁹ = y x (y⁴)²

and, 300 = 2 x 2 x 3 x 5 x 5

So, √300 y⁹

= √2 x 2 x 3 x 5 x 5 x y x (y⁴)²

= 10y⁴√ 3y

Learn more about Exponent and power here:

https://brainly.com/question/28515493

#SPJ2

Answer:

C)10

Step-by-step explanation:

-4(-5)-10

＝20-10

=10

Please mark as brainliest!!

by inverse operations

the area of any quadrilateral can be determined by multiplying the length of its base by its height.

Since we know the shape here is square,we know that all sides are of equal length.From this we can work backwords by taking the square root of the area to find the length of one side

In order for a set of numbers to represent three sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem. Only option C represents three sides of a triangle.

Now let's check each option to see which one satisfies the triangle inequality theorem:

a. 5, 3, and 2

The sum of 5 and 3 is 8, which is greater than 2. The sum of 5 and 2 is 7, which is also greater than 3. The sum of 3 and 2 is 5, which is not greater than 5. Therefore, this set of numbers does not represents three sides of a triangle.

b. 9, 5, and 15

The sum of 9 and 5 is 14, which is less than 15. Therefore, this set of numbers does not represent three sides of a triangle.

c. 8, 10, and 6

The sum of 8 and 10 is 18, which is greater than 6. The sum of 8 and 6 is 14, which is also greater than 10. The sum of 10 and 6 is 16, which is greater than 8. Therefore, this set of numbers represents three sides of a triangle.

d. 4, 6, and 10

The sum of 4 and 6 is 10, which is less than 10. Therefore, this set of numbers does not represent three sides of a triangle. Therefore, only option C represents three sides of a triangle.

For more questions on triangle

https://brainly.com/question/28470545

#SPJ8

We may utilize Vieta's formulas to determine the value of k in the polynomial q(x) = x2 - 5x + 5k, where the sum and product of its zeros are equal.

What is Polynomial?

Let and serve as symbols for the polynomial's zeros. According to Vieta's formulas, the product of the zeros is equal to 5k, and the total of the zeros is provided by + = -(-5)/1 = 5.

Given that the sum and product of the zeros are equal, we have α + β = α * β. Substituting the known values, we get:

5 = 5k

This equation can now be solved to determine the value of k:

5/5 = k

k = 1

Therefore, k equals 1 when the sum and product of the zeros of the polynomial q(x) = x² - 5x + 5k  are equal.

Read more about Polynomial here brainly.com/question/1496352

#SPJ1

Given parameters:

 Rate;

          2 cans of paint for 7 dollars

Number of cans of paints  = 9 cans

Unknown:

Cost of 9 cans of paints = ?

This is rate - work problem. So therefore, we can simply solve them;

   Since;

              2 cans of paint  costs 7 dollars

              9 cans of paint will now cost [tex]\frac{9 cans x 7 dollars}{2 cans}[/tex]   = $31.5

The cost of 9 cans of paint is  $31.5

Answer:

see explanation

Step-by-step explanation:

(a)

OC = OB ( both radii of the circle )

Thus Δ BOC is isosceles with congruent base angles.

∠ BOC = ∠ BCO = 50°

(b)

∠ ACB = 90° ( angle in a semicircle ), then

∠ ACO = 90° - 50° = 40°

OA = OC ( both radii of the circle )

Thus Δ ACO is isosceles with congruent base angles.

∠ BAC = ∠ ACO = 40°

We can use a programming language, Microsoft Excel, or an online random number generator to generate six random numbers between 1 and 650.

To generate six random numbers between 1 and 650, we can make use of several technology formats. Here, we will discuss three methods: using a programming language, using Microsoft Excel, and using an online random number generator. Let's discuss each of these methods in detail below.

Using a programming language: Programming languages such as Python, Java, and C++ can be used to generate random numbers. For example, using Python, we can write the following code to generate six random numbers between 1 and 650:import random for i in range(6): print(random. randint(1, 650))This code will generate six random numbers between 1 and 650 and print them to the console. We can modify the range and the upper limit of the randint function to generate more or fewer numbers or to generate numbers within a different range.

Using Microsoft Excel: Microsoft Excel has a built-in function called RANDBETWEEN that generates random numbers. To generate six random numbers between 1 and 650 in Excel, we can enter the following formula in a cell :=RANDBETWEEN (1, 650)We can copy and paste this formula into five other cells to generate a total of six random numbers. We can also use the RAND function instead of RANDBETWEEN to generate decimal numbers within a range. Using an online random number generator:

There are several online tools and websites that allow us to generate random numbers. One such tool is the Random Number Generator by Math Goodies. To generate six random numbers between 1 and 650 using this tool, we can enter 1 and 650 in the Min and Max fields and then enter 6 in the Quantity field.

We can then click the Generate button to generate the numbers.

In conclusion, we can use a programming language, Microsoft Excel, or an online random number generator to generate six random numbers between 1 and 650.

For more questions on Microsoft .

https://brainly.com/question/17177102

#SPJ8