Anna invented a robot. The robot's name is David. David can go a maximum speed of 4 mph. At that rate, how long would it take David to go 9 miles?​

Given:

89.3%

To convert into decimal:

Hence, the answer is 0.893.

The equation for the circle in the graph is (x + 3)² + (y - 1)² = 16

The general equation for a circle whose center is at (a, b) and has a radius R is:

(x - a)² + (y - b)² = R²

We can see that the center of the circle is at (-3, 1), and the radius of the circle is the distance between the center and any of the edges, which is 4 units, then the equation for the circle in the graph is:

(x + 3)² + (y - 1)² = 4²

(x + 3)² + (y - 1)² = 16

That is the equation for the graph.

Learn more about circles at:

https://brainly.com/question/1559324

#SPJ1

T is a linear transformation, we need to verify two properties: additivity and scalar multiplication. Additivity: Let A and B be matrices in M_3(R). We have to show that T(A + B) = T(A) + T(B).

  T(A + B) = (A + B) - (A + B)^T = A + B - (A^T + B^T) = (A - A^T) + (B - B^T) = T(A) + T(B).

Scalar Multiplication: Let A be a matrix in M_3(R) and k be a scalar. We need to show that T(kA) = kT(A).
   T(kA) = kA - (kA)^T = kA - (kA^T) = k(A - A^T) = kT(A).

Next, we describe Ker(T) and Im(T) and find bases for these spaces.

Ker(T): It is the set of matrices A in M_3(R) such that T(A) = A - A^T = 0.
To find the basis of Ker(T), we solve the homogeneous system T(A) = 0.
The equation A - A^T = 0 can be rewritten as A = A^T.
This represents the set of symmetric matrices. A basis for Ker(T) is the set of all 3x3 symmetric matrices.

Im(T): It is the set of matrices B in M_3(R) such that there exists A in M_3(R) with T(A) = B.
To find the basis of Im(T), we find the column space of T(A).
The column space of T(A) is the same as the column space of A.
A basis for Im(T) is the set of all 3x3 matrices.

Ker(T) and Im(T) are equivalent to Nul(A) and Col(A) respectively because the standard matrix A of T represents the linear transformation T.
The kernel of a linear transformation T is the same as the null space of its standard matrix A. Therefore, Ker(T) = Nul(A).
Similarly, the image of a linear transformation T is the same as the column space of its standard matrix A. Hence, Im(T) = Col(A).

In summary, Ker(T) is the set of symmetric matrices and the basis for Ker(T) is the set of all 3x3 symmetric matrices. Im(T) is the set of all 3x3 matrices and the basis for Im(T) is the set of all 3x3 matrices. Ker(T) is equivalent to Nul(A) and Im(T) is equivalent to Col(A).

To know more about transformation visit:

https://brainly.com/question/11709244

#SPJ11

Ker(T) is the same as Nul(A) because they both represent the vectors that map to zero, and Im(T) is the same as Col(A) because they both represent the vectors that can be obtained by applying the transformation or forming linear combinations of the columns of A.

a)

i. To show that T is a linear transformation, we need to demonstrate that it preserves vector addition and scalar multiplication. Let's consider two matrices A and B in M_3(R) and a scalar c:

T(A + B) = (A + B) - (A + B)^T         [Definition of T]

        = A + B - (A^T + B^T)         [Expanding the transpose]

        = A - A^T + B - B^T             [Rearranging terms]

        = T(A) + T(B)                    [Definition of T]

T(cA) = cA - (cA)^T                     [Definition of T]

      = cA - cA^T                         [Properties of transposition]

      = c(A - A^T)                         [Distributive property]

      = cT(A)                               [Definition of T]

Therefore, T preserves vector addition and scalar multiplication, making it a linear transformation.

ii. To describe Ker(T) and Im(T), we need to find the null space and column space of the matrix representation of T. Let's calculate these spaces:

Ker(T) = {A ∈ M_3(R) | T(A) = 0} = {A ∈ M_3(R) | A - A^T = 0}

      = {A ∈ M_3(R) | A = A^T}           [Transpose of A is zero]

      = Sym_3(R)                              [Set of symmetric matrices in M_3(R)]

Im(T) = {T(A) | A ∈ M_3(R)}

      = {A - A^T | A ∈ M_3(R)}

      = {B ∈ M_3(R) | B = -B^T}             [B is skew-symmetric]

      = Skew_3(R)                               [Set of skew-symmetric matrices in M_3(R)]

Bases for Ker(T) and Im(T) are the bases for Sym_3(R) and Skew_3(R), respectively.

b) Let T: R^n → R^m be a linear transformation with a standard matrix A. The kernel of T, Ker(T), represents the set of vectors in R^n that map to the zero vector in R^m. It is equivalent to the null space of matrix A, denoted Nul(A). This is because the standard matrix A represents the transformation T, and the null space of A captures all vectors that satisfy Ax = 0, where x is a column vector in R^n.

Similarly, the image of T, Im(T), represents the set of all vectors in R^m that can be obtained by applying T to vectors in R^n. It is equivalent to the column space of matrix A, denoted Col(A). This is because the column space of A consists of all linear combinations of the columns of A, which corresponds to the image of the linear transformation T.

Learn more about vectors

https://brainly.com/question/28028700

#SPJ11

The correct answer is x = 2

(x + 1 < 4) ∩ (x-8>-7)

Make x the subject in each case:

(x<4-1)(x>-7+8)

        (x<3)∩(x>1)

If x<3, then x could be 2, 1, -1, etc.

If x>1, then x could be 2, 3, 4, etc.

Thus (x<3)∩(x>1) = 2

More on inequalities can be found here: https://brainly.com/question/24853349

#SPJ1

Answer:

x = 2

Step-by-step explanation:

Hello!

We are looking at the intersection of two sets, or common values found between two sets of data.

We can solve for x on each side and find any common values between.

As you can see, the intersection occurs at the common values. The only value that is common between the two sets is 2.

Therefore, the intersection of these sets is 2.

To graph the equation y = 1x / 2 + (-5), you will need to plot several points that satisfy the equation and then connect them with a line.

To do this, you can pick a few values of x, substitute them into the equation to find the corresponding values of y, and then plot these points on the coordinate plane.

For example, if you choose x = -2, the corresponding value of y is (-2) * (1 / 2) + (-5) = -5.5. If you choose x = 0, the corresponding value of y is (0) * (1 / 2) + (-5) = -5. And if you choose x = 2, the corresponding value of y is (2) * (1 / 2) + (-5) = -4.

You can then plot these points on the coordinate plane and connect them with a line to graph the equation.

Im really sorry that I was unable to provide a picture.  I hope this helped!

Answer:

Graph the line using the slope and y-intercept, or two points.

Slope:

1/2

y-intercept: (0,−5)

x   y

0 −5

2 −4

Step-by-step explanation:

The expression that can be added to both sides of the given quadratic equation to change it to a perfect square trinomial is \(\frac{b^2}{4a^2}\) .

The standard form of perfect square trinomial is given as:

\(ax^2 + bx + c\)

here,

a = coefficient of x² .

b = coefficient of x.

c = constant .

Given the quadratic equation:

\(x^2 + \dfrac{b}{a}x\ +\ ?= -\dfrac{c}{a}\ +\ ?\)

The above equation is needed to be changed to a perfect square trinomial.

To change the quadratic equation into the perfect square, the squared of half the value of the coefficient of degree one variable can be added to both sides of the equation.

Therefore, the term to be that is needed to be added to the given quadratic equation is \(\frac{b^2}{4a^2}\) .

Now, the quadratic equation can be written as:

\(x^{2} + \frac{b}{a} x + \frac{ b^{2}}{4a^{2}} = \frac{-c}{a} + \frac{ b^{2}}{4a^{2}}\)

Therefore, \(\dfrac{b^2}{4a^2}\) should be added to both sides to convert it into the perfect polynomial.

Learn more about quadratic polynomial, here:

https://brainly.com/question/30098550

#SPJ12

The given question is incomplete. Probably the complete question is:

When deriving the quadratic formula by completing the square what expression can be added to both sides of the given equation to create a perfect square trinomial?

\(x^2 + \dfrac{b}{a}x\ +\ ?= -\dfrac{c}{a}\ +\ ?\)

The resulting expression we can see that the value of a and b are 3 and zxy respectively

Given the following expression

4x^2y/3z x a/b = 4x/z^2

In order to determine the value of a and b, we will divide 4x^2y/3z by 4x/z^2 as shown;

a/b =  4x/z^2 ÷ 4x^2y/3z

a/b = 4x/z^2 * 3z/4x^2y

a/b = 1/z * 3/xy

Simplify

a/b = 3/zxy

Hence from the resulting expression we can see that the value of a and b are 3 and zxy respectively

Learn more on indices here; https://brainly.com/question/10339517

#SPJ1

The given expression r^2 - 2r + 1 can be factored as (r-1)^2.

So the answer is D. (r-1)(r-1).

To factor the given expression r^2 - 2r + 1, we can look for two factors that when multiplied together give us the original expression.

We can use the method of perfect square trinomials here because the first and last terms are perfect squares (r^2 and 1, respectively), and the middle term is twice the product of their square roots (-2r = -2*sqrt(r^2)*sqrt(1)).

The formula for a perfect square trinomial of the form (a+b)^2 is a^2 + 2ab + b^2. In this case, we have a=r and b=1, so:

(r+1)^2 = r^2 + 2r + 1

Comparing this to the original expression, we see that it differs only in the sign of the middle term. To get the same sign as in the original expression, we can use:

(r-1)^2 = r^2 - 2r + 1

Therefore, the given expression r^2 - 2r + 1 can be factored as (r-1)^2, which is equivalent to (r-1)(r-1).

Hence, the answer is D. (r-1)(r-1).

Learn more about expression from

brainly.com/question/1859113

#SPJ11

Answer:

It is 4y = -3x + 9

Step-by-step explanation:

\(3x + 5y - 4 = 0 \\ 5y = - 3x + 4 \\ y = - \frac{3}{4} x + 4\)

since it is parallel, its slope, m is -¾

\(2x - 3y - 6 = 0 \\ - 3y = - 2x + 6 \\ y = \frac{2}{3} x - 2\)

at x-intercept, y is zero

\(2 = \frac{2}{3} x \\ x = 3\)

therefore

\(y = mx + c \\ 0 = ( - \frac{3}{4} \times 3) + c \\ c = \frac{9}{4} \)

equation is

\(y = - \frac{3}{4} x + \frac{9}{4} \\ \\ 4y = - 3x + 9\)

Compound interest formula

where

• A: final amount, in dollars

• P: principal, in dollars

• r: interest rate, as a decimal

• n: number of times interest is compounded per year

• t: time, in years

Substituting with P = $20,000, r = 0.05 (=5/100), n = 4 (quarterly means that the interest is compounded 4 times per year), and t = 3/4 years, we get:

Answer:

225 cm³

Step-by-step explanation:

Volume of a prism = base area × height

The volume of this prism

\( = 5 \times 5 \times 9\)

\( = 225\)

Answer:

225 cu cm ^3

Step-by-step explanation:

can i be brainliest?

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

Equation A

Equation B

let us consider x as the number of stools and y be the number of recliners

therefore, total seats \(\leq\) 50

= x + y \(\leq\) 50

then, owner wants a least 20 of the seats to  be stools

x \(\geq\) 20

the rest are the number of recliners.

the equation of inequality is x + y \(\leq\) 50

x + y =50

if x = 0 and y = 50

if y = 0 and x = 50

therefore the joining points are (0, 50) and ( 50, 0) in the coordinate plan

0+0 \(\leq\) 50

then the shaded region will contain the origin

Graphing of x \(\geq\) 20

shading the region left side x = 20

Hence, number of materials can never be negative.

therefore,

x \(\geq\) 0 and y \(\geq\) 0

To learn more about Inequality,

https://brainly.com/question/24372553

#SPJ4

Hello!

If six friends went to a movie and spent $9 per each ticket and also purchased a small bag of popcorn each with them spending a total of $82.50, the cost of each small bag of popcorn costs $4.75.

Step-by-step explanation:

\(6\) × \(9=54\)

\(82.50-54=28.50\)

\(28.50\) ÷ \(6=4.75\)

Hope this helps!

Answer:

answer is B

Step-by-step explanation:

Volume of the sphere is 2.304\(\pi\) unit³ or 7234.56 unit³.

A sphere is a three dimensional solid shape. It is a set of points that are all at the same distance r from a common point. The distance r is the radius and the common point is the centre of the sphere.

Here,

The radius of the sphere is given by,

r = 12 units

The equation for volume of a sphere with radius r is given by,

V = 4/3 \(\pi\)r³

So, the volume of the sphere is,

V = 4/3 x \(\pi\) x 12³

V = 2.304 \(\pi\)

V = 7234.56 unit³

Hence,

Volume of the sphere is 2.304\(\pi\) unit³ or 7234.56 unit³.

To learn more about sphere, click:

https://brainly.com/question/12390313

#SPJ7

The observed z value is 1. Therefore, the given option that falls under the criteria of the correct answer is Option C.

To find the observed z value we have to use the principles to create a formula.

The formula for finding the value of z is

z = ( x - μ)/(σ/√n)

here,

x = sample mean

μ = population mean

σ = standard deviation of the population

n = sample size

for the given question the values are

x = 50

μ = 45

σ = 5

n = 1

staging the values in the formula

z = (50-45)/(5/√1)

z = 1

The observed z value is 1. Therefore, the given option that falls under the criteria of the correct answer is Option C.

To learn more about z value ,

https://brainly.com/question/25638875

#SPJ4

a)  E(\(x_i\)) = θ, \(x_i\) is an unbiased estimator of θ. b) "θ29," which is unclear and does not represent a valid estimator.

(a) To determine whether \(x_i\) is an unbiased estimator of θ, we need to check if the expected value of \(x_i\) is equal to θ. The expected value of a Bernoulli distribution with parameter θ is given by E(\(x_i\)) = θ.

Thus, if E(\(x_i\)) = θ, \(x_i\) is an unbiased estimator of θ.

(b) To assess whether an estimator is unbiased, we need to examine its expected value. However, you provided the notation "θ29," which is unclear and does not represent a valid estimator.

You can learn more about Unbiased estimators at

brainly.com/question/29646467

#SPJ4

To show that the projection maps π₁: X × Y → X and π₂: X × Y → Y are open maps, we need to demonstrate that for every open set U in X × Y, the sets π₁(U) and π₂(U) are open in X and Y, respectively.

Let U be an open set in X × Y. We can write U as the union of open sets U = U₁ × U₂, where U₁ is an open set in X and U₂ is an open set in Y. Since U is open, every point (x, y) in U has an open neighborhood contained within U.

Now, consider the image of U under the projection map π₁: X × Y → X. The set π₁(U) is the collection of all x-coordinates of the points in U. For any point x' in π₁(U), there exists a point (x', y') in U. Since U is open, there exists an open neighborhood N = N₁ × N₂ of (x', y') contained within U. The projection of N onto the x-coordinate, N₁, is an open neighborhood of x' contained within π₁(U). Therefore, π₁(U) is open in X.

Similarly, for the projection map π₂: X × Y → Y, we can show that π₂(U) is open in Y. For any point y' in π₂(U), there exists a point (x', y') in U. By a similar argument as above, there exists an open neighborhood N = N₁ × N₂ of (x', y') contained within U. The projection of N onto the y-coordinate, N₂, is an open neighborhood of y' contained within π₂(U). Therefore, π₂(U) is open in Y.

Since this holds for an arbitrary open set U in X × Y, we have shown that the projection maps π₁: X × Y → X and π₂: X × Y → Y are open maps.

Learn more about Sets here -: brainly.com/question/25369230

#SPJ11

Answer:

x=1/4

Step-by-step explanation:

Solve for x

by simplifying both sides of the equation, then isolating the variable.

x=12

Step-by-step explanation: i think its right

Artifacts are physical or digital objects which can be used to prove points.

Ultimately, determining the reliability of the source of information is essential to understanding the reliability of answer choices.

When assessing the reliability of a group of answer choices, it is important to consider the source of the information. This can be done by analyzing the origin of the information and its credibility.

Examples and illustrations are useful forms of evidence that can be used to support an argument. Statistics are numerical data that can be used to demonstrate the validity of a point.

Artifacts are physical or digital objects which can be used to prove a point. By evaluating the source of the information, and considering examples, illustrations, statistics, and artifacts, one can assess the reliability of a group of answer choices.

To know more about Artifacts click on below link:

https://brainly.com/question/17362933#

#SPJ11

Answer:

6720 Kuna

Step-by-step explanation:

multiply the rate for one dollar by the amount of money your are converting

6.72 x 1000 = 6720

Answer:

how this was solve like this 37

Step-by-step explanation:

12

Answer:

X = 63 + 86 = 149 (because interior angle = interior opposite angles

Step-by-step explanation:

Hope this help

Answer:

so the bigger number is 20

Step-by-step explanation:

you would divide 3 into 60

Answer:

A

Step-by-step explanation:

Trust me

Answer: the Answer is A

Step-by-step explanation: I used a graphing calculator

Answer:

D.

Step-by-step explanation:

The easiest way to tell is a relation is a function is to look at every x. A function cannot have two x's that are the same.

A. There are two x's with the value of 10.

B. There are two x's with the value of 20.

C. If you wrote this in ordered pairs, there would be two x's with the value 2.

D. Every x is different, so the answer is D.

Hope this helps! Have a great day c:

To solve this problem, we need to use the Law of Cosines. The law states that given any triangle ABC:

Then;

Since we want to find the measure of angle x, we can use:

c = 175 mi

a = 200 mi

b = 50 mi

C = x

Now, by the Law of Cosines:

And solve:

To the nearest whole number, x = 54°

The equation of the parabola opening upward with a focus at and a directrix  is  f(x) = 1/32(x - 9)² + 19

Therefore option A  is correct.

Our objective is to find the equation of the parabola opening upward with a focus at (9, 19) and a directrix of y = -19

The standard form of the equation of a parabola with a vertical axis is:

4p(y - k) = (x - h)²

(h, k) = (9, 0)  we know this because the focus lies on the x-axis and the directrix is a horizontal line.

The distance between the vertex and the focus = 19.

4 * 19(y - 0) = (x - 9)²

76y = (x - 9)²

y = 1/76(x - 9)²

Comparing this equation to the options provided, we see that the likely answer is: A. f(x) = 1/32(x - 9)² + 19

Learn more about vertex  at:

https://brainly.com/question/21191648

#SPJ1