Use cramers rule to solve the system below

2x -3y = -8
4x + 3y = -34

A) Let A be to coefficient matrix, fill in matrix a below


b) Find the determinant of matrix A.


C) Let Matrix X be the matrix used to solve for the x variable. Write this matrix below

D) find the determinant of matrix X


E) Let Matrix Y be the matrix used to solve for the 'y' variable. Write this matrix below:


F) find the determinant of matrix y

G) write your solution to the system above as a coordinate

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

It is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known. It is also used to determine if a triangle is a right-angled triangle or not, by checking if the lengths of the sides satisfy the theorem.

The Pythagorean Theorem has many practical applications, such as in construction, engineering, and physics. For example, it can be used to calculate the distance between two points in a two-dimensional plane, the height of a building or tower, or the force required to move an object up a ramp at a given angle.

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Answer:

2/6

Step-by-step explanation:

15 isn't a decimal number

11/25=0.44 not recurring (not repeating)

3/20=0.15 not recurring (not repeating)

2/6=0.333333 recurring

so the answer is D

Answer:

12 packages of water

5 packages of cheese sticks

Step-by-step explanation:

The LCM (least common multiple) of 5 and 12 is 60.

w = # of pkgs of water

c = # of pkgs of cheese sticks

5w = 12c = 60

w = 60/5 = 12

c = 60/12 = 5

The graph of the line passing through the points (-1, 0) and (-5, 0) is attached.

Given are two points we need to find the equation of line passing through them,

We know that the equation of a line passing through two points, (x₁, y₁) and (x₂, y₂) is,

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Here, (x₁, y₁) and (x₂, y₂) are (-1, 0) and (-5, 0).

So,

y-0 = 0-0 / -5+1 (x+1)

y = 0

Hence, the equation of the line is y = 0.

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The total cost paid on the condominium is $468,046.80.

The total cost means total expenditure incurred to produce some type of output.  The total cost is calculated as follows:

The total number of monthly payments is:

= 30 years x 12 months/year

= 360 months

The total amount paid towards mortgage is:

= 360 x $1175.13

= $423,046.80

The total cost of the condominium will be:

= Down payment + Total amount paid towards mortgage

= $45,000  + $423,046.80

= $468,046.80.

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Answer: D

Step-by-step explanation:

To determine which month had a higher z-score for sales on the 15th, we need to calculate the z-scores for each month's sales.

For July:

z-score = (x - μ) / σ

where x is the sales on the 15th, μ is the mean daily sales for July, and σ is the standard deviation of daily sales for July.

Plugging in the values, we get:

z-score for July = (315 - 270) / 30 = 1.5

For August:

z-score = (x - μ) / σ

where x is the sales on the 15th, μ is the mean daily sales for August, and σ is the standard deviation of daily sales for August.

Plugging in the values, we get:

z-score for August = (300 - 250) / 25 = 2

Since the z-score for August is higher than the z-score for July, August had a higher z-score for sales on the 15th.

The value of the z-score for August's sales on the 15th was 2.

The fraction model we are given can be represented by the expression: 7/1 ÷ 1/2

From the fraction model given, we can see that each of the shaded parts represents a half of the model parts.

Thus, we have in total:

(1/2) * 7 = 3¹/₂

This means the 7 parts shaded is being divided by 1/2

Therefore, we can easily conclude that the equation to represent a fraction model is expressed by the algebra form:

7/1 ÷ 1/2

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The requried inverse function is [tex]f^{-1}(y) = (y + 3)/2[/tex].

To find the inverse of y = 2x - 3, we need to solve for x in terms of y.

Starting with y = 2x - 3:

Add 3 to both sides: y + 3 = 2x

Divide both sides by 2: (y + 3)/2 = x

Therefore, the inverse of y = 2x - 3 is:

x = (y + 3)/2

We can also express this as:

[tex]f^{-1}(y) = (y + 3)/2[/tex]

Thus, the inverse function is [tex]f^{-1}(y) = (y + 3)/2[/tex]

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The best answer to the given question is B.

When a variable "varies inversely as y," it means that as y increases, the variable decreases, and vice versa. This relationship is expressed mathematically as:

variable = k/y

where k is a constant.

When a variable "varies directly as y," it means that as y increases, the variable also increases, and vice versa. This relationship is expressed mathematically as:

variable = k*y

where k is a constant.

Option (a) does not provide any information about the relationship between variables. Option (c) and (d) provide incomplete information as they do not specify the variable that varies with y. Option (b) correctly explains the two types of relationships between variables and their mathematical expressions.

Option B is the best answer.

Answer:

Find the angle bisectors and draw them.

The point where they meet is the center of the circle.

Make a circle which goes through the point where the angle bisector and sides meet.

Step-by-step explanation:

The percentage of the data values are between 110 and 170 = 37.5%

We know that in the box plot, the first quartile is nothing but 25% from smallest to largest of data values.

The second quartile is nothing but between 25.1% and 50% (i.e., till median)

The third quartile: 51% to 75% (above the median)

And the fourth quartile: 25% of largest numbers.

In the attached box plot, we can observe that between two numbers on the number line there are 5 equal parts.

So, each unit length measures 10 units.

Also, the median of the data = 110

We need to find the percentage of the data values are between 110 and 170.

i.e., the percentage of the data values are in the third quartile.

The range of this box plot is: 190 - 30 = 160

The data values are between 110 and 170 = 60

Using percentage formula,

P = (60/160) × 100

P = 37.5%

This is the required percentage.

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Find the complete question below.

Assuming that a fair coin was tossed twice, the probability that exactly one of the tosses is a head and the other toss is a tail is 1/2.

The probability of a certain event happening is the number of ways that event can occur, divided by the total number of possible outcomes. In this case, we are interested in finding the probability that exactly one of the two coin tosses results in a head and the other results in a tail.

There are two possible outcomes that satisfy this condition: HT and TH. Since the coin is fair, each of these outcomes has a probability of 1/4. Therefore, the total probability of getting exactly one head and one tail is:

P(HT or TH) = P(HT) + P(TH) = 1/4 + 1/4 = 1/2

In other words, there is a 50-50 chance of getting exactly one head and one tail when a fair coin is tossed twice.

To see why this is the case, we can think of each toss as an independent event with two possible outcomes (head or tail). There are four possible outcomes when we toss a coin twice, and two of these outcomes satisfy the condition of exactly one head and one tail. Therefore, the probability of getting exactly one head and one tail is 2/4, which simplifies to 1/2.

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Answer:

Let x be the number of bottles of water that Yui buys, and let y be the number of sports drinks she buys.

Since Yui buys a total of 6 bottles of water and sports drinks, we know that:

x + y = 6

We also know that each bottle of water costs $1.50 and each sports drink costs $2.50, and that Yui spends a total of $10. Therefore, we can write another equation based on the total cost:

1.5x + 2.5y = 10

We now have a system of two equations with two variables:

x + y = 6

1.5x + 2.5y = 10

To solve for x and y, we can use substitution. Rearranging the first equation, we get:

x = 6 - y

Substituting this expression for x into the second equation, we get:

1.5(6 - y) + 2.5y = 10

Expanding and simplifying, we get:

9 - 1.5y + 2.5y = 10

Combining like terms, we get:

y = 2

Substituting this value of y back into the equation x + y = 6, we get:

x + 2 = 6

Solving for x, we get:

x = 4

Therefore, Yui buys 4 bottles of water and 2 sports drinks.

Answer: $1856

Step-by-step explanation: 88 x 58 = 5104. 5104/2.75= 1856

Kathy worked 9.14 hours for Job A and 18.86 hours for job B to make 186.10

Assuming hours of work for job A is x while that of job B is y

According to the given information, Kathy works a total of 28 hours per week

x + y = 28

Job A pays $6.10 per hour, and Job B pays $6.80 per hour, to make $184.10, we have the equation below

6.10x + 6.80y = 184

x + y = 28

6.10x + 6.80y = 184

solving simultaneously using calculator

x = job A = 9.143 = 9.14 (to 2 decimal places)

y = job B = 18.857 = 18.86 to 2 decimal places))

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Answer:

C. complementary

Michel-Eugène Chevreul discovered that placing complementary colors next to each other can create the greatest contrast and vibrancy in color perception. This is because complementary colors are located opposite each other on the color wheel and, when placed side by side, they enhance each other and create a strong visual impact. For example, placing yellow next to violet or blue next to orange can create a dynamic and eye-catching effect. In contrast, placing tertiary colors (colors made by mixing primary and secondary colors) or arbitrary colors next to each other may not create as much contrast or visual interest. Overall, understanding color theory and the relationships between different colors can be helpful for creating visually appealing designs, artworks, or other color-based projects.

Answer:

c. Cournot oligopoly (20 firms):

The optimal per unit price for a Cournot oligopoly with 20 firms is $485.10.

Step-by-step explanation:

Answer:

y = 1

Step-by-step explanation:

the absolute value function always gives a positive result , that is

| - a | = | a | = a

then

y = | 3 - x | ← substitute x = 4

y = | 3 - 4 | = | - 1 | = | 1 | = 1

Answer:

To the nearest mile, Tony and Jim are 9 miles apart.

To visualize this, imagine a right triangle where Jim's starting point is at the right angle. Tony travels 5 miles due south, which is the adjacent side of the triangle. Jim travels 6 miles north east, which is the hypotenuse of the triangle. The opposite side of the triangle is the distance between Tony and Jim.

Using the Pythagorean theorem, we can find the length of the opposite side:

opposite side = sqrt(hypotenuse^2 - adjacent side^2)

opposite side = sqrt(6^2 - 5^2)

opposite side = sqrt(11)

To the nearest mile, the distance between Tony and Jim is 9 miles.

Answer:

Step-by-step explanation:

5 is greater than 0.004

Answer: 5 is greater

Step-by-step explanation:

(7.5, -9) is the final value after reflection and dilation.

To reflect a vector across the line y=x, we switch the x and y coordinates. Therefore, the reflection of (6,-5) across the line y=x is (-5,6).

To dilate a vector by a scale of -1.5, we multiply the vector by -1.5. Therefore, the resulting vector is (-5,6) multiplied by -1.5, which gives us:

(-5,6) * (-1.5) = (7.5, -9)

So the final result after the reflection and dilation is (7.5, -9).

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Answer:522

Step-by-step explanation:

cut the shape on top to make a triangle and rectangle so then it would be 25x18=450 then for the triangle it would be 18x8=72 450+72=522

If the determinant of the matrix formed by the coordinates of the three points is zero, then they are collinear

Given data ,

To show that three points lie on the same line using coordinate geometry, we need to check if they satisfy the equation of a line.

Let the coordinates of the three points be (x1, y1), (x2, y2), and (x3, y3).

To check if these three points are collinear, we can calculate the slope of the line passing through the first two points using the formula

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

Then, we can check if the slope of the line passing through the second and third points is equal to the slope we calculated above. If they are equal, then all three points lie on the same line

m' = (y3 - y2) / (x3 - x2)

If m = m', then the three points are collinear

Alternatively, we can use the determinant method to check if the three points lie on the same line. If the determinant of the matrix formed by the coordinates of the three points is zero, then they are collinear

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The graph that represents the function f(x) = -2sin(x) +37 is graph D

The graph of the function f(x) = -2sin(x) +37 is a sinusoidal wave with an amplitude of 2 and a vertical shift of 37. The negative sign in front of the sine function indicates that the wave is inverted or reflected about the x-axis.

In this graph, the maximum value of the function is 39 (when x = 0) and the minimum value is 35 (when x = π).

In conclusion, the graph that represents the function f(x) = -2sin(x) +37 is graph D

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1. intrest earned per year $116.25

2. total after 20 years $3,825

116x20= $2325

$1500+ 2325=3825

When the planes are at the same altitude after 48 seconds, they will be at an altitude of 4014 feet.

Let's assume that after t seconds, Plan A will be at an altitude of A and Plan B will be at an altitude of B. We want to find the value of t when A = B.

We can use the following equations to model the altitude of each plane after t seconds:

A = 2172 + 35.25t

B = 80.5t

We can set A equal to B and solve for t:

2172 + 35.25t = 80.5t

Subtracting 35.25t from both sides, we get:

2172 = 45.25t

Dividing both sides by 45.25, we get:

t = 48 seconds (rounded to the nearest second)

Therefore, the planes will be at the same altitude after 48 seconds.

To find the altitude they will be at, we can substitute t = 48 into either of the altitude equations. Let's use the equation for Plan A:

A = 2172 + 35.25t

A = 2172 + 35.25(48)

A = 4014 feet

Correct Question :

An air traffic controller is tracking two planes. To start, Plan A is at an altitude of 2172 feet and Plan B is just taking off. Plan A is gaining altitude at 35.25 feet per second and Plan B is gainnig altitude at 80.5 feet per second.

How many seconds will pass before the planes are at the same altitude?

What will their altitude be when they're at the same altitude?

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Answer:

The sum of the interior angles of a 10-sided polygon is 1,440 degrees.

To find the sum of the interior angles of any polygon, you can use the formula:

sum of interior angles = (n - 2) x 180 degrees

where n is the number of sides of the polygon.

So, for a 10-sided polygon, we have:

sum of interior angles = (10 - 2) x 180 degrees

sum of interior angles = 8 x 180 degrees

sum of interior angles = 1,440 degrees

Therefore, the sum of the interior angles of the 10-sided polygon on the left is 1,440 degrees.

Answer:

1440 degrees

Step-by-step explanation:

Credit to the the first person who answered. :)

Answer:

Step-by-step explanation:

-11°

The symmetric property of congruence is Option C) If AB ≅ CD, then CD ≅ AB.

The symmetric property of congruence states that if one segment is congruent to another segment, then the second segment is also congruent to the first.

Therefore, the correct answer is C) If AB ≅ CD , then CD ≅ AB.

This statement shows that if segment AB is congruent to segment CD, then segment CD is also congruent to segment AB, which satisfies the definition of the symmetric property of congruence.

Answer choices A) and D) do not represent the symmetric property of congruence, as they simply state that a segment is congruent to itself or to another segment without reversing the order of the comparison.

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