A health store sells two different sized square granola bars. the side length of the smaller granola bar, C(x), is modeled by the function C(x)=1/4 square root x +2, where x is the area of the larger granola bar in square inches. which graph shows C(x)

If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.

The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.

Then, we have:

Av = λv

Taking transpose on both sides we have:

\(v^T A^T = \lambda v^T\)

The above equations thus relates transpose of vector and transpose of A to λ.

Now, consider a matrix:

\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)

Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.

The eigenvectors are:

\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)

Now, for transpose of A:

\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)

The eigen vectors are:

\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)

Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

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Answer:47 X=16

Step-by-step explanation:

Answer:

l = 58.5

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

112 = 2l - 5

Step 2: Isolate term l by adding 5 on both sides

117 = 2l

Step 3: Isolate l by dividing both sides by 2

117/2 = l

Step 4: Evaluate

l = 58.5

Answer:

\(\Large \boxed{l = \frac{117}{2}}\)

Step-by-step explanation:

Let the length be \(l\).

\(112 = 2 l - 5\)

Adding 5 to both sides.

\(112 +5= 2 l - 5+5\)

\(117 = 2 l\)

Dividing both sides by 2.

\(\displaystyle \frac{117}{2} = \frac{2 l}{2}\)

\(\displaystyle \frac{117}{2} = l\)

Answer:

736

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

edge2020

The measure of the other leg of the right Triangle is approximately 9.8 cm.

The measure of the other leg of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

Let's denote the length of the other leg as "x." Given that one leg measures 10 cm and the hypotenuse measures 14 cm, we can set up the equation as follows:

10^2 + x^2 = 14^2

Simplifying the equation:

100 + x^2 = 196

Subtracting 100 from both sides:

x^2 = 196 - 100

x^2 = 96

To find the value of x, we take the square root of both sides:

x = √96

x ≈ 9.8 (rounded to the nearest tenth)

Therefore, the measure of the other leg of the right triangle is 9.8 cm.

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Answer: 5.3 repeated portions or about 5 portions

Step-by-step explanation: 25 pounds = 400 ounces

400/75 = 5.3 repeated

Answer:33

Step-by-step explanation:

Hello here would be your answers:

mean: 13.6  

mediun: 15.5  

mode: 16

remember it like this

Mean is the average

Mode is the most often number

Range is when you subtract the smallest number from the largest number

Medium is the middle number when you line it up from the greatest to the least.

hope this helps!

The graph of g(x) is obtained from the graph of f(x) by the following transformations:

- A horizontal stretch by a factor of 9. This is because the graph of g(x) is 9 times wider than the graph of f(x).

- A vertical translation down by 2 units. This is because the graph of g(x) is 2 units lower than the graph of f(x).

In other words, to obtain the graph of g(x) from the graph of f(x), we stretch the graph horizontally by a factor of 9 and then translate it down by 2 units.

Here is a more detailed explanation of the transformations:

- Horizontal stretch by a factor of 9: To stretch the graph horizontally by a factor of 9, we multiply all of the x-coordinates by 9. This means that every point on the graph of f(x) will be moved 9 units to the right on the graph of g(x).

- Vertical translation down by 2 units: To translate the graph down by 2 units, we subtract 2 from all of the y-coordinates. This means that every point on the graph of f(x) will be moved 2 units down on the graph of g(x).

Answer:

The brown house has the longer driveway

Step-by-step explanation:

So we would need to convert both of these units of measurements to feet in order to compare them.

Converting yards to feet, wee need to multiply the number of yards by 3

Since the red house has a driveway of 7 yards and 9 feet, we can rewrite this to 21 feet + 9 feet, which is equivalent to 30 feet

Now comparing the two driveways, the 35 ft-long brown driveway is 5 feet longer than the 30 ft-long red driveway.

The brown house has the longer driveway

Answer:

a = (v-u)/t

Step-by-step explanation:

v = u + at

subtract u from both sides

v - u = at

divide each side by t

(v-u)/t = a

Answer:

16 deliveries

Step-by-step explanation:

238 ≤ 10d + 78

160 ≤ 10d

16 ≤ d

Thus, he needs to make at least 16 deliveries to make at least $238 in one day.  Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.

The  volume of the cube is  2744 cm³.

There are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example,  in a square all angles are 90° and all sides present the same value.

A square is a 2D figure, when the square is associated a 3D figure, the figure is called a cube. The cube presents 6 faces with length (l) , height (h) and width (w) equal. Thus, the cube presents congruent edges.

The volume is given from the formula V=a³, where a is a congruent edge.

The question gives:

Therefore,

V=a³

V=14³

V=14*14*14

V=2744 cm³

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The measurements of the figures that should be equal in order for the ratio of volumes between the volumes of the cone, sphere, and cylinder of 1:2:3 to be true is; The radius and the height

A ratio is a comparison between the magnitudes or measurements of items, expressing the number of times one item in the ratio is contained within another item in the ratio.

The formula for the volume of a cone, \(V_p\) is, \(V_p\) = (1/3)·π·r₁²·h₁

The formula for the volume of a sphere, \(V_s\), is \(V_s\) = (4/3)·π·r₂³

The formula for the volume of a cylinder, \(V_c\), is \(V_c\) = π·r₃²·h₃

The ratio of the volumes in the question is 1:2:3

Therefore; The volume of the sphere is twice the volume of the cone, and the volume of the cylinder is three times the volume of the cone, which indicates;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁...(1)

π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁...(2)

Equation (1) indicates that we have;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁

Where, h₁ = 2·r₂, we get;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·(2·r₂) = (4/3)·π·r₁²·r₂

Therefore; r₁ = r₂, and the diameter of the sphere is equal to the height of the cone

The radius of the cone is equal to the radius of the sphere

Equation (2) indicates;

π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁ = π·r₁²·h₁

Therefore;

r₃²·h₃ = r₁²·h₁

r₃ = r₁

h₃ = h₁

The radius of the cone = The radius of the cylinder

The height of the cone = The height of the cylinder

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Answer: 1. Well, for one they both have a 'radicand' and you can arrange both of them in a fraction form.

2. Graph is increasing, there's an asymptotic value, the domain is all real numbers, the range is y > 0. If you add a constant, you are shifting it vertically, which means it's y-intercept will change by the magnitude of the constant.

3. Linear functions are a straight line with one definite slope. Exponential functions are basically curves with their slopes, not constantly, but changing. As you increase your x-values, the linear functions lacks behind, and the exponential one becomes very large.

4. I really don't know how to explain this, it's kind of confusing.

5. You can use the slope formula: (y2-y1)/(x2-x1). Plug in values, you get:

(12-8)/(4-2). This can be simplified to 4/2 or just 2. That's his average rate of change: 2 balls per day.

6. An arithmetic sequence adds on a specific value every time. For example: {1, 3, 5, 7...}

A Geometric sequence increases every time by a common ratio. For example: {2, 6, 18, 54...}

6. If it's relative to time, then you have a parametric equation dealing with time. Just like that, you can see that 1 variable changes with respect to the other, and that implies parametricity.

Step-by-step explanation:

9514 1404 393

Answer:

  \(x^{a/b}=\sqrt[b]{x^a}=(\sqrt[b]{x})^a\)

Step-by-step explanation:

The denominator of the fractional exponent becomes the index of the root. The exponent numerator is left as the power of the base. The exponent can be inside or outside the radical.

  \(x^{a/b}=\sqrt[b]{x^a}=(\sqrt[b]{x})^a\)

The solution for the given inequalities is x≥15 or x≤1. Therefore, option A is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequalities are 3x + 7 ≤ 4x-8 or-2x + 3≥1.

Here, 3x + 7 ≤ 4x-8

Subtract 3x on both the sides of an inequality, we get

7 ≤ x-8

Add 8 on both the sides of an inequality, we get

15≤ x

x≥15

Here, -2x + 3≥1

Subtract 3 on both the sides of an inequality, we get

-2x≥-2

Divide -2 on both the sides of an inequality, we get

x≤1

So, x≥15 or x≤1

Therefore, option A is the correct answer.

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Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

A sample is only a small portion of the population.

Let's imagine you were interested in determining the average income for all Americans in your population.

Instead of knocking on every door in America because of time and money constraints, you decide to ask 1,000 random people. Your sample consists of these a thousand persons.

Given, A gardener wants to determine which of two brands of fertilizer is best for the plants.

And the gardener decides to conduct an experiment using 28 individual plants.

Plan A will be a biased sampling and the experiment would not yield

desired results.

Therefore, The gardener should choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

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Answer:

e

Step-by-step explanation:

The perimeter of the smaller figure among the two figures with similarity ratio of 4:3 is 18cm.

A ratio is a number that allows one quantity to be expressed as a fraction of another quantity. Two numbers in a ratio can only be compared if they have the same units. Use ratios to compare two things.  

The similarity of two similar shapes is the ratio of each pair of corresponding sides. Simply put, when two figures are found to be similar, all pairs of corresponding sides have the same proportions. 

According to the information:

Perimeter of larger figure= 24cm

Let, perimeter of smaller figure be "x"

So,

4:3 = 24/x

4/3 = 24/x

⇒x = (24 x 3)/4

⇒x = 72/4

⇒x = 18

Thus the perimeter of smaller figure is 18cm.

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The length and width of a rectangle with area 108 inches² are 18 inches and 6 inches respectively.

What is area of rectangle ?

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.

We know that the formula of area of rectangle is given by :

A = Length × Width

It is given that the area is 108 inches².

Let's assume the width be x.

Then , the length will be 3x.

Putting these values in formula , we get :

108 = 3x × x

108 = 3x²

or

x² = 108 / 3

x² = 36

x = 6 inches

So , the width is of 6 inches and length will be of :

= 3 × 6

= 18 inches

Therefore , the length and width of a rectangle with area 108 inches² are 18 inches and 6 inches respectively.

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Answer: The volume of the trunk is 1355 inches cubed.

Step-by-step explanation:

The volume of a rectangular prism is base x width x height. In the problem, the trunk is a rectangular prism, so its volume is \(12 \text{ in} \times 4 \text{ in} \times 28 \text{ in} = 1355 \text{ in}^3.\)

The machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..

A vending machine automatically pours soft drinks into cups.

The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6oz and a standard deviation of 0.4oz.

Examine figure 7.- and answer the following questions.

a) estimate the probability that the machine will overflow an 8oz cup.

Procedure:

Determine the z-score for 8

z(8) = (8-7.6)/0.4 = 0.4/0.4 = 1

P(x>8) = P(z>1) = 0.1587..

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

b) Estimate the probability that the machine will not overflow an 8oz cup.

P(z<1) = 1 - 0.1587 = 0.8413..

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

c) the machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..; Rounded down you get 134 cups

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Answer:

b. x + 4

Solution:

Student's age = x

Teacher's age = 6 + 2x

Principal's age = 10 + 3x

Difference in the age of the teacher and principal

(10 + 3x) - (6 + 2x)

= 10 + 3x - 6 - 2x

= (10 - 6) + (3x - 2x)

= 4 + x

Answer: \(300\) \(times\)

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

-3 - (-4) - (-2) + 1

-3 + 4+ 2 +1

1 +2+1

2 + 2

4

Answer:

first graph

Step-by-step explanation:

x > n

the graph will have an open circle at the value n , indicating that x cannot equal n ( note solid circle if x ≥ n )

the arrow from n will point in the right direction, indicating values of x greater than n.

the graph representing x > n is the first graph

The distance between town A and town B is 93.5 km.

Solving for  the distance between town A and town B:

Let's first convert the 42 minutes delay of the car to hours:

42 minutes = 42/60 hours

                    = 0.7 hours

Now, let's assume that the time it took for the car to travel from A to B is t hours.

The distance between A and B is the same for both the lorry and the car, so we can set up an equation:

Distance = Speed x Time

For the lorry:

Distance = 50t

For the car:

Distance = 80 (t-0.7)

We know that when the car arrived at B, the lorry had 25km left to cover. So:

50t - Distance covered by lorry = 25

50t - (50t - 25) = 25

Simplifying:

25 = 25

This equation is always true, which means our assumptions are correct.

Therefore, we can equate the two distance equations:

50t = 80(t-0.7)

50t = 80t - 56

30t = 56

t = 1.87 hours

Finally, we can use the distance equation with either the lorry or the car to find the distance between A and B:

Distance = Speed x Time

Distance = 50 x 1.87

Distance = 93.5 km

So the distance between town A and town B is 93.5 km.

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Answer:

12

Step-by-step explanation:

12 can go into all of the numbers above & is the greatest common factor of the numbers above.