Christie has $200 in her bank account. Every month, she deposits $20 into her account.
The equation of the line that models the amount of money, y, in her account x months from now is y =

it displays the computed sum and product of the diagonal elements.

Here's a MATLAB code to find the sum and product of the diagonal elements of a given matrix `A`, as well as an example execution for `A = ones(5)`:

```matlab

% Define the matrix A

A = ones(5);

% Get the size of the matrix

[n, ~] = size(A);

% Initialize variables for sum and product

diagonal_sum = 0;

diagonal_product = 1;

% Calculate the sum and product of diagonal elements

for i = 1:n

   diagonal_sum = diagonal_sum + A(i, i);

   diagonal_product = diagonal_product * A(i, i);

end

% Display the results

disp("Sum of diagonal elements: " + diagonal_sum);

disp("Product of diagonal elements: " + diagonal_product);

```

Example execution for `A = ones(5)`:

```

Sum of diagonal elements: 5

Product of diagonal elements: 1

```

In this example, `A = ones(5)` creates a 5x5 matrix filled with ones. The code then iterates over the diagonal elements (i.e., elements where the row index equals the column index) and accumulates the sum and product. Finally, it displays the computed sum and product of the diagonal elements.

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Answer: When P = 1, D = 55 So I Think The Ratio Is 1:55

Answer:

Step-by-step explanation:

The imaginary number 'i' is equal to the square root of -1. If you were to square the square root, they both cancel and you get -1.

\(21i^2=21(\sqrt{-1} )^2=21(-1)=-21\)

Answer:

2x...................

λ₀ is an eigenvalue of BA with eigenvector w.  Therefore, if λ₀ is an eigenvalue of AB, it is also an eigenvalue of BA. ii.since I + AB is invertible, x cannot be a nonzero vector that satisfies (I + AB)x = 0. Therefore, x must be the zero vector.

(i) Let λ₀ be an eigenvalue of the matrixAB. We want to show that λ₀ is also an eigenvalue of BA.

Suppose v is the corresponding eigenvector of AB, i.e., ABv = λ₀v.

Now, let's multiply both sides of the equation by A on the left:

A(ABv) = A(λ₀v)

(AA)Bv = λ₀(Av)

Since AA is the matrix A², we can rewrite the equation as:

A²Bv = λ₀(Av)

We know that Av is a vector, so let's call it u for simplicity:

A²Bv = λ₀u

Now, multiply both sides of the equation by B on the right:

A²BvB = λ₀uB

A²(BvB) = λ₀(Bu)

Since BvB is a matrix and Bu is a vector, we can rewrite the equation as:

(A²B)(vB) = λ₀(Bu)

Let's define w = vB, which is a vector. Now the equation becomes:

(A²B)w = λ₀(Bu)

We can see that λ₀ is an eigenvalue of BA with eigenvector w.

Therefore, if λ₀ is an eigenvalue of AB, it is also an eigenvalue of BA.

(ii) Let I + AB be invertible. We want to show that In + BA is also invertible, where In is the identity matrix of size n x n.

Suppose (I + AB)x = 0, where x is a nonzero vector.

We can rewrite the equation as:

Ix + ABx = 0

x + ABx = 0

Now, let's multiply both sides of the equation by B on the right:

(Bx) + (AB)(Bx) = 0

We know that AB is a matrix and Bx is a vector, so let's call Bx as y for simplicity:

y + ABy = 0

Multiplying both sides of the equation by A on the left:

Ay + A(ABy) = 0

Expanding the expression A(ABy):

Ay + (AA)(By) = 0

Ay + A²(By) = 0

We can see that A²(By) is a matrix and Ay is a vector, so let's call A²(By) as z for simplicity:

Ay + z = 0

Now, we have Ay + z = 0 and y + ABy = 0. Adding these two equations together, we get:

(Ay + z) + (y + ABy) = 0

Ay + ABy + z + y = 0

(Ay + ABy) + (y + z) = 0

Factoring out A:

A(y + By) + (y + z) = 0

We know that (y + By) is a vector, so let's call it w for simplicity:

Aw + (y + z) = 0

We can see that (y + z) is a vector, so let's call it v for simplicity:Aw + v = 0

We have shown that if x is a nonzero vector satisfying (I + AB)x = 0, then there exists a vector w such that Aw + v = 0.

However, since I + AB is invertible, x cannot be a nonzero vector that satisfies (I + AB)x = 0. Therefore, x must be the zero vector.

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Answer:

y = -3/4x + 5/4

Step-by-step explanation:

Points: (7, -4) and ( -1, 2)

Slope:

m=(y2-y1)/(x2-x1)

m=(2+4)/(-1-7)

m=6/(-8)

m= -3/4

Slope-intercept:

y - y1 = m(x - x1)

y + 4 = -3/4(x - 7)

y + 4 = -3/4x + 21/4

y = -3/4x + 5/4

Answer:

y = -3/4x + 5/4

Step-by-step explanation:

Hope this helps

Answer:

Explanation: Over the summer, Nancy exercised daily, and her weight went 145 pounds to 132 pounds. we need to find the percent change:

Change in weight is:

Change is percent is:

The distance between two points in a plane is the length of the line segment connecting them. The formula d=((x2 - x1)2 + (y2 - y1)2) is frequently used to determine the separation between two points.

The length of the line segment bridging two locations in a plane is known as the distance between them. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points. This equation can be used to determine the separation between any two locations on an x-y plane or coordinate plane.

The length of the line segment is the distance between two points. Congruent segments are those that share the same length. By using a ruler to draw a line, we may determine how far apart two points are.

x,y = (-8,0) (-8,0)

or

x/y = -8/0

If there was an association between L and K, we would use x,y = 8,0.

Since the query reads "between point K and point L," the x,y relationship becomes "-8,0."

Therefore, the answer is -8,0.

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Rational Numbers:  Any number that can be expressed as a fraction or ratio that may contain repeating decimals, or terminating decimals.

Irrational Numbers:  Any number that cannot be expressed as a fraction or ratio that has non-repeating non-terminating decimals.

With this information, sort the given values into one of each of these categories.

Cheers.

The only statement that must be based on the quadrilateral properties is; Option B: Base angles of quadrilateral Z are congruent

Some of the properties of a quadrilateral are;

1) They have four vertices.

2) They have four sides.

3) The sum of all interior angles is 360°.

4) They have two diagonals.

5) A quadrilateral can be regular or irregular.

Now, from the description of Quadrilaterals T and Z, we can say that;

- The base angles of quadrilateral T are not congruent since at least one pair of parallel side is congruent.

- Base angles of quadrilateral z are congruent since opposite sides are congruent.

- Consecutive angles of quadrilateral Z are not congruent

- Opposite angles of quadrilateral T are not supplementary.

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Answer:

what is the questions

Step-by-step explanation:

12. i) By walking the 20 kilometers in the charity walk, Vreni raised $250 at a unit rate of $12.50 per kilometer.

12. ii) The total money raised by all participants in the charity walk was $3,100, using proportions.

12. iii) The percentage increase on the previous year's total is 26.53%.

Part B:

11. i) Based on a ratio of 3:2 of road and footpath distance, the road distance covered 12 kilometers.

11. ii) Using the distance, time, and speed formula, Vreni took 7 hours and 12 minutes to walk the 20 kilometers.

11. iii) Vreni's average speed is 2.78 km/h.

11. iv) Vreni finished the charity walk at 16:07.

Part C: The scale of the map to the total distance covered by Vreni was 1: 4 or a scale factor of 25%.

The ratio is the quotient of a value compared to another.

Ratios are proportionate values, which are equated to each other.

The average speed and scale factor show the ratios of one value and the whole.

12) Charity Walk and Vreni:

The total distance walked = 20 kilometers

The unit rate of raising money per kilometer = $12.50

i) The total amount raised = $250 ($12.50 x 20)

Money raised in 12. 1 = 5/52 of the total money raised

ii) The total money raised in the charity walk = $3,100 ($250 ÷ 5/52)

iii) The total amount raised in the previous year = $2,450

The total amount raised in the current year = $3,100

Difference between current and previous year = $650 ($3,100 - $2,450)

Percentage increase on the previous year's total = 26.53% ($650/$2,450 x 100)

11b) Ratio of road and footpath walk = 3:2

The sum of ratios = 5

Road distance = 3/5 x 20 = 12 kilometers

Footpath distance = 2/5 x 20 = 8 kilometers

Vreni's walking speed along the road = 3 km/h

Road distance = 12 kilometers

Time to walk the road = 4 hours (12/3)

Vreni's walking speed along the footpath = 2.5 km/h

Footpath distance = 8 kilometers

Time to walk the footpath = 3.2 hours or 3 hours and 12 minutes (8/2.5) or 192 minutes (8/2.5 x 60)

Total time spent by Vreni = 7 hours and 12 minutes (4 hr + 3 hr + 12 min)

Vreni's average speed = Distance/Time

= 20 km/7.2 hrs

= 2.78 km/h

Starting time = 08:55

Total hours = 7 hours and 12 minutes

Finishing time = 16:07 (08:55 + 7 hrs + 12 min)

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Answer:

35.6 feets

Step-by-step explanation:

To obtain tree height :

(Height of stick / shadow of stick = height of tree / shadow of tree)

Height of stick = 2 feets

Shadow of stick = 0.8 feets

Shadow of tree = 14.24 feets

Height of tree = h

(2 / 0.8 = h /14.24)

Cross multiply

0.8h = 14.24 * 2

0.8h = 28.48

h = 28.48 / 0.8

h = 35.6 feets

On solving the provided question, we can say that the equation, we have is \(t^2 +5t +6.\)

Two assertions in a mathematical equation are joined by the equal sign (=), which stands for equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The connection between the two sentences on either side of a letter is explained by a mathematical formula. Typically, there is only one variable, which also serves as the symbol. In this case, 2x4=2.

the equation, we have is V = P/I

\(V = \frac{t^3 +9t^2 +26t +24}{t + 4}\)

on dividing

the answer will be \(x^3+9x^2+26x +24=t^2 + 5t + 6\)

x = -4

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Solution

Step 1

A)The domain refers to all real values of x for which the function is defined. The values of x for which the function is undefined are not a part of the domain. If you are given the equation then you can find the domain of that function by solving/ factorizing the denominator of the equation to find the zero(s) of the equation in the denominator. These values gotten are the values of x that will make the function undefined and hence are not part of the domain. Every other real value of x apart from these zero(s) obtained is part of the domain.

B)

Step 1

Factorize the denominator of the equation to find the zeroes of the equation

Step 2

Find the required factors to replace 13x and is equal to -90x²

Step3

Replace 13x with these factors

Step 4

Factorize the equation and find the values of x

Hence, the domain of the function is all real values of x except -3 and 5/6

For spinning the spinner one time A could be {1, 2, 3} or, A = {1, 2, 3, 4} is possible.

The set is mathematical model for a collectionof different things;a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables or even other sets.

The given spinner is divided into 8 equal sized sections, so the possible set can be written as-

S = {1, 2, 3, 4, 5, 6, 7, 8}

Now the possible subsets can be-

Even numbers = {1,3,5,7}

Odd numbers = {2,4,6,8}

Any number or group from 1 to 8, inclusive

Hence for spinner the spinner for one time, suppose A be the possible set. Then,

    A could be {1, 2, 3}.

or, A = {1, 2, 3, 4}.

where A is the subset of S.

Hence, For spinning the spinner one time A could be {1, 2, 3} or, A = {1, 2, 3, 4} is possible.

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Answer:

y=7miles

Step-by-step explanation:

The total perimeter is 21 miles and we know two sides of the triangle are 7 miles, or 14 miles together.

We need to know the one other side of the triangle, so we can subtract the 14 miles we know from the total 21 miles.

21-14=7miles

Answer:

y=7 mi

Step-by-step explanation:

If you know that each side of this triangle is 7 and they are each side is the same length, you can make an educated guess  that the answer is 7. If you need An easier method 7x3=21. a triangle has 3 sides so your answer would be 7

The measure of the angle ∠CFE is 330°.

Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc.

Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).

The angle ∠CFE is calculated as:-

∠CFE = 360 - ∠CEF

∠CFE = 360 - 30

∠CFE = 330

Hence, the angle ∠CFE is 330°.

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The probability of randomly selecting two animals and both of them being Labrador Retrievers is approximately 0.2647.

To calculate the probability of choosing two Labrador Retrievers out of all the animals, we need to determine the total number of possible pairs of animals and the number of pairs that consist of two Labrador Retrievers.

The total number of animals in the shelter is 3 Siamese cats + 3 German Shepherds + 9 Labrador Retrievers + 2 mixed-breed dogs = 17 animals.

To calculate the number of ways to choose 2 animals out of 17, we use the combination formula:

\(C(n, k) = n! / (k! * (n-k)!)\)

where n is the total number of animals (17) and k is the number of animals we want to choose (2).

C(17, 2) = 17! / (2! * (17-2)!)

         = 17! / (2! * 15!)

         = (17 * 16) / (2 * 1)

         = 136.

So, there are 136 possible pairs of animals.

Now, let's determine the number of pairs that consist of two Labrador Retrievers. We have 9 Labrador Retrievers in total, so we need to choose 2 out of the 9.

C(9, 2) = 9! / (2! * (9-2)!)

        = 9! / (2! * 7!)

        = (9 * 8) / (2 * 1)

        = 36.

Therefore, there are 36 pairs of Labrador Retrievers.

The probability of choosing two Labrador Retrievers out of all the animals is given by:

P(both labs) = (number of pairs of Labrador Retrievers) / (total number of pairs of animals)

            = 36 / 136

            = 0.2647 (rounded to four decimal places).

So, the probability of randomly selecting two animals and both of them being Labrador Retrievers is approximately 0.2647.

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Answer:

well if you would divide 74.85 by 45% you would  33.6825.

and also i am the same guy that you answered a question from bioligy i got 3 more questions plaese answer them if you can.ty:)

Answer:

$33

Step-by-step explanation:

Given :

45%

$74.85

45% of 74.85 is

Answer = $33

Answer:it’s 15

Step-by-step explanation:because think about it if it was 12 it wouldn’t be 60% it would be 70%

Answer:

Well done

Step-by-step explanation:

Zoomed in

The rational function ƒ(x) that represents the average price per minute x years after 1998 is given by ƒ(x) = g(x) / h(x), where g(x) = -0.27x³ + 1.40x² + 1.05x + 39.4 and h(x) = -8.25x³ + 53.1x² - 7.82x + 138.

To calculate the average price per minute x years after 1998, we need to find the ratio between the average monthly bill (g(x)) and the average number of minutes used (h(x)). Therefore, the rational function ƒ(x) is defined as ƒ(x) = g(x) / h(x).

Given that g(x) = -0.27x³ + 1.40x² + 1.05x + 39.4 and h(x) = -8.25x³ + 53.1x² - 7.82x + 138, we can substitute these expressions into the rational function to obtain the final formula: ƒ(x) = (-0.27x³ + 1.40x² + 1.05x + 39.4) / (-8.25x³ + 53.1x² - 7.82x + 138).

This rational function represents the average price per minute x years after 1998 based on the given average monthly bill and average number of minutes used by U.S. mobile phone users. By plugging in different values for x, you can evaluate the function and obtain the corresponding average price per minute for each year.

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Answer:

2.25 feet, 45 inches, and 6 yards

Step-by-step explanation:

first, convert all to the same unit of measurement

I will use inches

45 inches = 45 inches

6 yards, 1 yard = 3 feet so 6 yards are equal to 18 feet and 1 foot is equal to 12 inches so 12*18 is 216 inches so 6 yards = 216 inches

Next 1 foot equals 12 inches so 2.25 * 12 = 27 so 2.25 feet = 27 inches.

Now let's look at the complete conversion

45 inches

6 yards = 216 inches

2.25 feet = 27 inches

looking at the inches we can see that 27 is the least then 45 then 216 therefore

2.25 feet < 45 inches <  6 yards so the order is

2.25 feet, 45 inches, and 6 yards

Therefore, y is equal to 12 2/5 and n is equal to 2 2/5 in the equation.

An equation is a mathematical statement that shows that two expressions are equal. An equation is typically written with an equal sign (=) between two expressions. Equations can involve various mathematical operations, such as addition, subtraction, multiplication, division, exponents, and logarithms. Solving an equation typically involves performing mathematical operations on both sides of the equation to isolate the variable (the unknown value) and find its value.

Here,

To solve for y in the equation 2y + 8 1/5 = 33, we can follow these steps:

Subtract 8 1/5 from both sides of the equation:

2y = 33 - 8 1/5

2y = 24 4/5

Divide both sides of the equation by 2:

y = (24 4/5) / 2

y = 12 2/5

Therefore, y is equal to 12 2/5.

To solve for n in the equation 2n + 4 1/5 = 9, we can follow these steps:

Subtract 4 1/5 from both sides of the equation:

2n = 9 - 4 1/5

2n = 4 4/5

Divide both sides of the equation by 2:

n = (4 4/5) / 2

n = 2 2/5

Therefore, n is equal to 2 2/5.

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Answer:

The volume of shipping crate is 32 unit cubes.

Step-by-step explanation:

Given that:

Length of the crate = 4 units

Width of the crate = 2 units

Height of the crate = 4 units

Volume of shipping crate = Length * Width * Height

Volume of the crate = 4 * 2 * 4

Volume of crate = 32 unit cubes.

Hence,

The volume of shipping crate is 32 unit cubes.

Answer:

32 units

Step-by-step explanation:

Answer:

60 ft is the Perimeter.

Step-by-step explanation:

Answer:

60 ft.

Step-by-step explanation:

1. These being the side lengths, just add them.

15ft + 21ft + 24ft = 60ft

2. Answer is 60ft.

Answer:

Answer is 690 every month

Step-by-step explanation:

The total cost is $23,500

Scholarship:8200$

2nd scholarship:7400$

Grandparents: 1000$

23,500-8,200-7400-1000=6900÷10=690

He will have to save up 690 every month for 10 months