-matrices-Determine the dimensions of each product. If it is undefined, state it. a.b. c.

The two options that could result from combining two linear functions with addition are "16x – 12" and "17x – 12". The r to your question is:

To combine two linear functions with addition, you simply add the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with addition, you add the coefficients of x and the constant terms. So, 3x + 4 + 2x - 5 becomes (3 + 2)x + (4 - 5) = 5x - 1.

To combine two linear functions with multiplication, you multiply the coefficients of the same variables. For example, if you have the functions 3x + 4 and 2x - 5, when you combine them with multiplication, you multiply the coefficients of x and the constant terms. So, (3x + 4)(2x - 5) becomes

(3 * 2)x^2 + (3 * -5)x + (4 * 2x) + (4 * -5)

= 6x^2 - 15x + 8x - 20

= 6x^2 - 7x - 20.

To know more about functions visit:

https://brainly.com/question/31062578

#SPJ11

The exact values of sin(2x), cos(2x), and tan(2x) without solving for x are: a) sin(2x) = 2sin(x)cos(x). b) cos(2x) = cos^2(x) - sin^2(x). c) tan(2x) = 2tan(x) / (1 - tan^2(x))

(a) To find the exact value of sin(2x), we can use the double angle formula for sine:

sin(2x) = 2sin(x)cos(x)

Therefore, the exact value of sin(2x) is 2sin(x)cos(x).

(b) To find the exact value of cos(2x), we can use the double angle formula for cosine:

cos(2x) = cos^2(x) - sin^2(x)

Therefore, the exact value of cos(2x) is cos^2(x) - sin^2(x).

(c) To find the exact value of tan(2x), we can use the double angle formula for tangent:

tan(2x) = 2tan(x) / (1 - tan^2(x))

Therefore, the exact value of tan(2x) is 2tan(x) / (1 - tan^2(x)).

The exact values of sin(2x), cos(2x), and tan(2x) without solving for x are:

a) sin(2x) = 2sin(x)cos(x)

b) cos(2x) = cos^2(x) - sin^2(x)

c) tan(2x) = 2tan(x) / (1 - tan^2(x))

These formulas allow us to express the values of sin(2x), cos(2x), and tan(2x) in terms of the values of sin(x) and cos(x) without explicitly solving for x.

To know more about cos, visit;

https://brainly.com/question/28165016

#SPJ11

Answer:

C = 22cm

Step-by-step explanation:

If the radius equals to 11, then the diameter is 22 since the diameter is double of radius. They told us to use π, so the answer is 22π.

The equation represent to determine the \(x^n\) number in a sequence is this function f(  x+1) = 5/2 f(x). This is the equation used to determine the xth number in a sequence.

Here, these values are given,

f(x) = 3/2 [5/2] x-1 [ After putting the values of f(x)}

So,here from this ,the equation will become ,

f(x+1) = 3/2 [ 5/2] x+1-1

f(x+1) = 3/2 [5/2] x

Here, 5/2 f(x)= 5/2×3/2 [5/2] x-1

5/2 f(x) = 3/2 [5/2] x-1+1

5/2 f(x) = 3/2 [5/2] x

So, f(x+1) =[ 5/2]f (x)

So, this will be the equation for this function .

Learn more about function here:

https://brainly.com/question/12431044

#SPJ4

\(f(x) = (3/2)^(5/2)^(x - 1)\) this function can be used to calculate the xth number in the sequence for any given value of x.

f(x) is the function that will generate the xth number in the sequence.

The function is written as:

\(f(x) = (3/2)^(5/2)^(x - 1)\)

This can be read as:

Take 3/2 (three halves) to the power of 5/2 (five halves) to the power of x minus 1.

This will generate the xth number in the sequence.

The function f(x) is used to determine the xth number in a sequence. It is written as: f(x) = \((3/2)^(5/2)^(x - 1)\). This means that we take the number 3/2 (three halves) and raise it to the power of 5/2 (five halves) and then to the power of x minus 1. This will generate the xth number in the sequence, where x is the position in the sequence. For instance, if x is 5, then the fifth number in the sequence will be generated using the function f(x). Therefore, this function can be used to calculate the xth number in the sequence for any given value of x.

learn more about function here

https://brainly.com/question/12431044

#SPJ4

Answer:

solution,

\(mass = volume \times density \\ \: \: \: \: \: \: \: \: = 2.4 \: \frac{g}{ {cm}^{3} } \times 13.4 \: {cm}^{3} \\ \: \: \: \: \: \: \: \: = 2.4 \times 13.4 \: \: grams \\ \: \: \: \: \: \: \: \: \: \: = 32.16 \: \: grams \)

Hope this helps...

Good luck on your assignment..

To complete the square, we need to add and subtract (b/2)^2 inside the brackets, where b is the coefficient of x. In this case, b = -2, so (b/2)^2 = 1. We add and subtract 1 inside the brackets. the vertex of the parabola is \((1, 6)\).

the quadratic function  \(f(x) = -5x^2 + 10x + 1\)  into vertex form:

Step 1: Factor out the coefficient of x^2:

\(f(x) = -5(x^2 - 2x) + 1\)

Step 2: Complete the square for the expression inside the parentheses:

\(f(x) = -5(x^2 - 2x + 1) + 5 + 1\)

Step 3: Simplify:

\(f(x) = -5(x - 1)^2 + 6\)

Step 4: Verify that the quadratic function is now in vertex form:

\(f(x) = a(x - h)^2 + k, where a = -5, h = 1, and k = 6.\)

Therefore, the vertex of the parabola is \((1, 6)\) .

Learn more about quadratic here:

https://brainly.com/question/18958913

#SPJ1

The difference in elevation between the height of mountain and height of valley measuring from sea level is equal to 6594 feet.

Since it is given that the height of mountain from the sea level is 6874 feet and the height of valley is 280 feet. Therefore to calculate the difference in elevation, the heights will be subtracted from one another to get a value which will show the elevation. Since both the heights are measured from the sea level which is taken as constant, so no extra calculations will be needed.

Elevation difference = Height of mountain - height of valley

Elevation difference = 6874 - 280 = 6594 feet

Learn more about elevation difference at:

brainly.com/question/2536394

#SPJ4

Answer:

1.8m per minute

Step-by-step explanation:

Answer:

\(\frac{1.8 \ m}{1 \ min}\) ; (1.8 meters per minute)

Step-by-step explanation:

Use dimensional analysis to solve this problem.

The proper units of conversion are given in parentheses on this question: 100 cm = 1 m.

Start with the given value, 3 centimeters/1 second.

Convert this rate to meters/minute by multiplying 3 cm/1 sec by 1 m/100 cm.

The top and bottom units should cancel out, so that's how you know to put the cm units on the bottom to cancel out with the 3 cm on the top.

Multiply the fractions together. The "cm" units cancel out.

Now you want to make the bottom units = minutes. There are 60 seconds in 1 minute, so you can use \(\frac{60 \ sec}{1 \ min}\) to multiply with \(\frac{3\ m}{100 \ sec}\).

The "seconds" unit cancels out, so you are left with meters on the top and minutes on the bottom. Multiply the fractions together.

We want the rate to be meters per minute (1), so completely simplify this fraction and divide the fraction by (100/100), so the denominator is 1 min.

Answer:

31/21

Step-by-step explanation:

17/21+2/3

First step is to get both denominators equal so 3 should be multiplied by 7 to get 21 and 2 should also be multiplied by 7,

This leaves 17/21+14/21 which equals to 31/21

Answer:

Step-by-step explanation:

What you want to do is find a common denominator of this equation. You can actually use 21 as that denominator because 7×3=21.

You'll keep the 17/21 for your first value, and for the second...

multiply each side of 2/3 by 7/7. That will end up being 14/21.

Finally, you will add those two values up and get 31/21 or 1 10/21.

Answer:

side angle side theorem

Step-by-step explanation:

======================================================

Explanation:

To find the inverse, we swap x and y, then solve for y.

y = 2x-3

x = 2y-3

x+3 = 2y

2y = x+3

y = (x+3)/2

y = x/2 + 3/2

y = (1/2)x + 3/2

This shows the original function y = 2x-3 leads to the inverse y = (1/2)x+3/2, and vice versa.

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

Another approach:

Since we're given a list of multiple choice answers, we can rule out the non-answers.

Plug x = 0 into the first equation of choice A. It leads to y = 2

That output 2 is then plugged into the second equation for choice A. It leads to y = 13/2. We do not get the original input 0, which shows that the equations in choice A do not undo one another. They aren't inverses of each other.

This allows us to rule out choice A. Choices B and C are similar stories.

Notice that plugging x = 0 into the first equation of choice D leads to the output y = -3. Then plug this as the input into y = (1/2)x+3/2 and you should get y = 0 to get us back where we started. This partially helps confirm we have a pair of functions that are inverses of each other. I'll let you try other values.

Answer:

Step-by-step explanation:

Algorithm for deriving the formula of the inverse function

Step 1. In the formula for the original function, replace the notation of the argument and the value:

Step 2. From the resulting formula, express y(x).

Step 3. Take into account the constraints on the area of definition and the area of values of the original and/or inverse functions.

\(\displaystyle\\ y=\frac{1}{2}x+2\\\\ 1.\ x=\frac{1}{2}y+2\\ \Rightarrow\ x-2=\frac{1}{2}y \\2.\ Multiply\ both\ parts\ of\ the\ equation\ by\ 2:\\\\2(x-2)=y\\\\2x-4=y\\Thus,\\y=2x-4\neq 3x+\frac{1}{2} \\Answer:\ no\\\\2.\ y=5(x-2)\\\\1.\ x=5(y-2)\\\\2.\ Divide\ both\ parts\ of\ the\ equation \ by\ 5:\\\\\frac{x}{5} =y-2\\\\\Rightarrow\ \frac{x}{5}+2=y \\Thus,\\\\y=\frac{x}{5}+2 \neq \frac{1}{5}(x+2)\\ Answer:\ no\)

\(y=2x-3\\1.\ x=2y-3\\\\2,\ x+3=2x\\\\Divide\ both\ parts\ of\ the \ equation\ by \ 2:\\\\\frac{1}{2}(x+3)=y\\\\ Thus,\\\\y=\frac{1}{2}x+\frac{3}{2} \equiv\frac{1}{2}x+\frac{3}{2} \\\\Answer:\ yes\)

The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

for such more question on measure of arc

https://brainly.com/question/25716982

#SPJ8

Answer: 1. Slope equals 3/4 or 0.75,  2. Slope equals -5/2 or -2.5

Step-by-step explanation:

1. Subtract y coordinates 4 and -2 to get 6. Then subtract x coordinates 4 and -4 to get 8, so that is equal to 6/8. Then simplify to get 3/4 or 0.75

2. Subtract y coordinates 10 and -5 to get -15. Then subtract x coordinates 0 and -6 to get 6, so that is equal to-15/6. Then simplify to get -5/2 or -2.5.

the length of the steel beam is approximately 31.4 meters to the nearest meter.

The length of the steel beam is equal to the circumference of the semi-circle formed by bending the beam into the shape of an arch.

The formula for the circumference of a circle is:

C = πd

Where C is the circumference, π is the value of pi, and d is the diameter of the circle.

Since the arch is a semi-circle, the diameter is equal to the span of the arch, which is 20m. So we can calculate the circumference of the arch as follows:

C = πd/2

= 3.14 x 20m / 2

= 31.4m

Therefore, The steel beam measures, to the nearest meter, 31.4 meters in length.

To learn more about circumference click here

brainly.com/question/28757341

#SPJ4

Complete Question

An arch of a bridge is made by bending a steel beam into the shape of a semi circle, if the span (diameter) of the arch in 20m, use the value 3.14 for pi to find the length of the steel beam to the nearest meter.

The division of the number 21.9 by 4.37 will be 5.01.

Division is an arithmetic operation in mathematics that involves splitting a quantity or a value into equal parts.

The number or quantity being divided is called the dividend, while the number or quantity by which the dividend is divided is called the divisor. The result of division is called the quotient.

Given that there are two numbers 21.9 and 4.37.

When we divide 21.9 by 4.37, we get:

21.9 ÷ 4.37 = 5.01

Therefore, when 21.9 is divided by 4.37 we will get a result equal to 5.01.

To know more about division follow

https://brainly.com/question/28119824

#SPJ9

The new price per pound of cat food will be $13.9.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that last week a customer paid $65.60 for 4 pounds of cat food this week she has a coupon for $2.50 off per pound.

The price will be calculated as below:-

$65.60 price ⇒ 4 pounds

1 pound ⇒ 65.60 / 4

1 pound ⇒ 16.4

Discounted price = 16.4 - 2.50 = $13.9

Therefore, the new price per pound of cat food will be $13.9.

To know more about an expression follow

https://brainly.com/question/625174

#SPJ1

We need to first find the probability of P(A) and P(B). These are found by dividing the frequency they appear by the number of surveyed classmates.

We can now calculate the probabilities the problem asks for. When we need to calculate the probability of two events happening at the same time, we express it as P(A and B). In this cases we need to multiply the individual probabilities, in this case we need to multiply P(A) to P(B). Since they're fractions we need to multiply the numerator of one by the numerator of the other, while we multiply the denominator of one to the denominator of the other.

We now need to find the value of the probability of P(A or B). In cases where the two events are independent, that means that they are mutually exclusive, if one happens the other won't, we need to sum the individual probabilities. This case is mutually exclusive, if the classmate has 4 credit cards in his wallet he won't have 1, therefore we can sum the probabilities. Since they are fractions with the same denominator we can simply mantain the denominator and sum the numerators.

Since the events are mutually exclusive we don't need to subtract the probability of both happening at the same time.

Answer:

C

Step-by-step explanation:

\((a^{-2}*8^{7})^2 = a^{-2*2}*8^{7*2} = a^{-4}*8^{14}\)

The equation that correctly applies the distributive property of multiplication is C. ​(0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2)​.

The distributive property of multiplication indicates that a mathematical expression in the form of a(b + c) can also be expressed to be equal to ab + ac.

When doing multiplication operations involving addition or subtraction, the distributive property can be used because it yields the same solution.

(0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2) = 0.5⋅(0.5+0.3+0.2)​

= 0.5 x 0.5 + 0.5 x 0.3 + 0.5 x 0.2

Learn more about the distributive property at brainly.com/question/4077386

#SPJ1

These limitations are represented by the inequalities x 500 + 2y and 35x + 50y > 225002.

How do equations work?

An equation is an expression that shows the relationship between two or more numbers and variables. Numerical constants, symbolic names, mathematical operators, functions, and conditional expressions are all examples of components that can be included in expressions.

If x stands for the quantity of product A and y for the quantity of product B, then:

x ≤ 500 + 2y (1) (1)

Also:

35x + 50y > 22500² (2) (2)

These limitations are represented by the inequalities x 500 + 2y and 35x + 50y > 225002.

To know more about equations, click the below link

brainly.com/question/2972832

#SPJ4

True. If matrix A is an n × n matrix with linearly independent eigenvectors v1, v2, ..., vn, then the n × n matrix P = [v1 v2 ... vn] forms a matrix of eigenvectors. In other words, the columns of matrix P are the eigenvectors of matrix A.

1. When a matrix A has linearly independent eigenvectors v1, v2, ..., vn, it means that each eigenvector corresponds to a distinct eigenvalue. The eigenvectors span the entire vector space of dimension n.

2. The matrix P = [v1 v2 ... vn] is constructed by arranging the eigenvectors v1, v2, ..., vn as columns. Since the eigenvectors are linearly independent, the matrix P formed by these columns is invertible.

3. When we multiply matrix P by its inverse P^(-1), we obtain the identity matrix I. This implies that P^(-1) exists and is the inverse of P.

4. Now, let's consider the equation A * P = P * D, where D is a diagonal matrix that contains the eigenvalues corresponding to the eigenvectors v1, v2, ..., vn along its diagonal.

5. Multiplying both sides of the equation by P^(-1) from the left, we get P^(-1) * A * P = P^(-1) * P * D, which simplifies to P^(-1) * A * P = D.

6. Since P^(-1) exists, we can rewrite the equation as A = P * D * P^(-1). This equation shows that matrix A can be diagonalized using the matrix P formed by the eigenvectors and its inverse P^(-1).

7. Therefore, matrix P = [v1 v2 ... vn] is indeed an n × n matrix consisting of linearly independent eigenvectors of matrix A.

learn more about linearly independent eigenvectors here: brainly.com/question/32355061

#SPJ11

We can model the number of successful corner kicks in a game as a binomial distribution with parameters n = 15 and p = 0.08.

a) The probability of scoring on 2 out of 15 corner kicks is:

P(X = 2) = (15 choose 2) * 0.08^2 * 0.92^13 = 0.256

Therefore, the chances of scoring on 2 out of 15 corner kicks is 0.256 or 25.6%.

b) For the entire season, the number of successful corner kicks can be modeled as a binomial distribution with parameters n = 200 and p = 0.08.

We want to find P(X > 22). We can use the complement rule and find P(X ≤ 22) and subtract it from 1.

P(X ≤ 22) = Σ(i=0 to 22) [(200 choose i) * 0.08^i * 0.92^(200-i)] ≈ 0.985

P(X > 22) = 1 - P(X ≤ 22) ≈ 0.015

Therefore, the chance of scoring more than 22 times in 200 corner kicks is approximately 0.015 or 1.5%.

To know more about binomial distribution refer here:

https://brainly.com/question/7863139

SPJ11

Answer:68.57                                                                                                                      

Step-by-step explanation:                                                                                                                                          

If the last number is less than 5 (1,2,3,4) no round is needed.

If the last number is greater than 4 (5,6,7,8,9) round up and add 1.

I think that is how you do it (try it first) then ask parents

Answer:

A.

- Line 1 - Dead Sea

- Line 2 - Lake Assal

- Line 3 - Laguna del Carbon

- Line 4 - Death Valley

B.

Lake because it is closer to zero on a number line than Death Valley

C.

-8 < -282 < 0

Hope This Helps! And so sorry it tool me so long to answer!

Answer:

Christmas! I get to go to Maine and Indiana and have four christmas's. Also, I get do a lot of fun stuff.

By using Stoke's theorem ∬ S [ (∇ × v) ⋅ n ] dσ  is  6π. So, option e is the correct answer.

To apply Stoke's theorem and evaluate the surface integral, we need to calculate the curl of vector field v(x, y, z) and then find its dot product with the unit normal vector n.

Let's start by finding the curl of v(x, y, z):

∇ × v =

| i j k |

| ∂/∂x ∂/∂y ∂/∂z |

| 3z² 3x -4y³|

Applying the determinant expansion along the top row, we have:

∇ × v = (∂/∂y)(-4y³) - (∂/∂z)(3x) i

+ (∂/∂z)(3z²) - (∂/∂x)(-4y³) j

+ (∂/∂x)(3x) - (∂/∂y)(3z²) k

Simplifying, we get:

∇ × v = -12y² i + 3z² j + 3 k

Now, we need to find the dot product of ∇ × v with the unit normal vector n. Since the upper half of the unit sphere has positive z-component, the unit normal vector for this surface is n = (0, 0, 1).

Therefore, the dot product (∇ × v) ⋅ n simplifies to:

(-12y² i + 3z² j + 3 k) ⋅ (0, 0, 1)= 3

Now, we can evaluate the surface integral using Stoke's theorem:

∬ S [ (∇ × v) ⋅ n ] dσ = ∬ S (3) dσ

Since the surface S is the upper half of the unit sphere, the area element dσ can be written as dσ = r² sinθ dθ dφ, where r = 1 is the radius of the unit sphere, θ ranges from 0 to π/2, and φ ranges from 0 to 2π.

Therefore, the surface integral becomes:

∬ S (3) dσ = ∫∫ (3) r² sinθ dθ dφ

= 3 ∫[0 to 2π] ∫[0 to π/2] (1)² sinθ dθ dφ

= 3 ∫[0 to 2π] [-cosθ] [0 to π/2] dφ

= 3 ∫[0 to 2π] 1 dφ

= 3 (2π)

= 6π

Hence, the correct answer is e) 6π.

To know more about Stoke's theorem:

https://brainly.com/question/28381095

#SPJ11

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

For more questions on expected value

https://brainly.com/question/14723169

#SPJ8

Answer:

enjooooooooooooyyyyyyyyyyy