Directions: For the following systems, determine whether or not the ordered triple (1, -1, -2) is a solution to the equations below.

1. 3x – 3y – z = 2

2. 2x – 3y + z = -3

3. x + y + z = -2

4. x + 2y – z = 0

5. 5x – y – 5z = 16

6. 4x + 5y – 6z = -13

Answer:

4 over 9

Step-by-step explanation:

4 over 7 = 0.571428571

2 over 5 = 0.4

7 over 8 = 0.875

4 over 9 = 0.444444444444444

Answer:

4/7 and 4/9

Step-by-step explanation:

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

Learn more about percentage on:

brainly.com/question/843074

#SPJ1

Step-by-step explanation:

Slope 1/2    point    5,1  

  in point slope form would be

    (y-1) = 1/2 (x-5)

Answer:

(2,1)

Step-by-step explanation:

This is the answer by substitution.

change 2x+y=5 to y=5-2x

5x-2(5-2x)=8

x = 2

y=5-2(2)

y = 1

(x,y) = (2,1)

You're welcome!!!

The requried matrix after transformation of \(R_2 < > R_3\) is:
\(\left[\begin{array}{ccc}-6&1&-8\\2&9&7\\-7&5&2\\2&-8&8\end{array}\right]\).

The given matrix,
\(\left[\begin{array}{ccc}-6&1&-8\\-7&5&2\\2&9&7\\2&-8&8\end{array}\right]\)

Matrix operations are mathematical operations performed on matrices, which are rectangular arrays of numbers.

Apply operation \(R_2 < > R_3\)

\(\left[\begin{array}{ccc}-6&1&-8\\2&9&7\\-7&5&2\\2&-8&8\end{array}\right]\)

Thus, the requried matrix after transformation of \(R_2 < > R_3\) is \(\left[\begin{array}{ccc}-6&1&-8\\2&9&7\\-7&5&2\\2&-8&8\end{array}\right]\).

Learn more about matrix here:

https://brainly.com/question/29132693

#SPJ1

Answer:

They are critical ecosystem service providers for the sustenance of humanity.The soil system is a dynamic ecosystem that has inputs, outputs, storages and flows. The quality of soil influences the primary productivity of an area..

Step-by-step explanation:

mark me the Brainliest pls

The students need to sell 25 tickets to reach their fundraising goal. This solution ensures that they will have a total of 42 tickets, including the initial 17 they had.

A group of students is organizing a fundraiser and they want to sell a certain number of tickets to reach their goal. The equation "? + 17 = 42" or "17 + ? = 42" can represent the number of tickets they need to sell. In this context, the variable "?" represents the unknown number of tickets.

To solve the problem, we need to find the value of "?" that satisfies the equation. By subtracting 17 from both sides of the equation "? + 17 = 42," we can determine that "?" is equal to 25.

Similarly, by subtracting 17 from both sides of the equation "17 + ? = 42," we also find that "?" equals 25.

We get:? = 42 - 17? = 25So, the solution of ? + 17 = 42 is ? = 25.17 + ? = 42Subtract 17 from both sides to isolate the variable. We get:? = 42 - 17? = 25So, the solution of 17 + ? = 42 is ? = 25.

For more such questions on fundraising,click on

https://brainly.com/question/2595198

#SPJ8

Part A :

Yes, the statement is true that  P( A and B ) = 0 .

Given,

Event A and Event B are mutually exclusive.

Thus P ( A and B ) = 0

Part B:

A and B are mutually exclusive events if they do not occur at the same time.

This means that A and B do not share any common outcomes and

P(A and B) = 0.

Part C:

Let,

The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.

A and B do not have any numbers in common so P(A and B) = 0.

Hence, A and B are mutually exclusive.

Learn more about Probability,

https://brainly.com/question/29492440

#SPJ1

Answer:

Area = 324ft²

Perimeter = 72ft

Step-by-step explanation:

Area of a square = length²

Area of a square = (18ft)² = 324ft²

Perimeter of a square = 4*length

Perimeter of a square = 4ft*18 = 72ft

Answer:2^1 × 3^2 × 13^1

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

You can easily graph this in desmos for a visual understanding.

The slope of a line is received by (y2-y1)/(x2-x1). Assuming that Days is X and the cost is Y, we get (160-90)/(4-2), and it makes 70/2, which equates out to 35. Because the prices become more and more expensive, the slope is positive 35.

Answer:

22.5 cm3

Step-by-step explanation: i took thy test

The volume of the rectangular prism is 22.5 cm³

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid.

Given here A right rectangular prism has a length of 10 centimeters, a width of 2.5 centimeters and a height of 0.9 centimeters.

Now we know the volume of the rectangular prism is given by

The volume of a rectangular prism = Length x Width x Height cubic units.

∴ V= 10×2.5×0.9

     = 22.5 cm³

Hence, the volume of the rectangular prism is 22.5 cm³

Learn more about the volume of the prism here:

https://brainly.com/question/16565638

#SPJ2

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

The expected value is the sum of the products of the probability of each outcome and the payout for that outcome:

Probability of winning:

Payout for winning:

Probability of not winning:

Payout for not winning:

Therefore:

Answer:

The expected value of a single ticket is -$0.9

The population in 10 years is equal to 3656 people.

We have given that

if a town with a population of 3000 grows by 2% per year,

We have to determine how large will the population be in 10 years.

A discrete group of people, animals, or things that can be identified by at least one common characteristic for the purposes of data collection and analysis.

To gather information about a large population, data is usually gathered from a sample.

3000 x 1.02^10 = 3656.98..

= 3656 people

To learn more about the population visit:

https://brainly.com/question/25630111

#SPJ2

The probability that the random sample of 100 male students has a mean gpa greater than 3. 42 is 0.9452.

A statistic known as the standard deviation is used to describe how volatile or dispersed a group of numerical values is. While a big standard deviation denotes that the values are scattered across a wider range, a low standard deviation indicates that the values tend to be close to the set mean.

From the given information, a scores random sample of 100 male students is selected and the GPA for each student is calculated which follows approximately normal with a mean of 3.5 and standard deviation of 0.5. That is,

µ = 3. 5 and σ = 0. 5

and the random sample of 100 male students has a mean GPA 3.42 is considered.

The z-score value is,

Z=( 3.42-3.5)/ (0.5/√100)

Z= -0.08/0.05

Z=-1.6

The value of z-score is obtained by taking the difference of x and µ. Then the resulting value is divided with the standard deviation by sample size.

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is obtained below:

The required probability is,

P(X>3.42)=P(z>-1.6)

= 1- P(Z≤-1.6)

From the “standard normal table”, the area to the left of Z=-1.6 is 0.0548.

P(X>3.42)= 1- P(Z≤-1.6)

=1-0.0548

=0.9452

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is 0.9452.

To learn more about standard deviation from the given link

https://brainly.com/question/475676

#SPJ1

Answer:

lcm of 3,6,9 is 18

Answer:

Step-by-step explanation:

The vertex form of a quadratic function is given by the equation f(x) = a(x - h)² + k, where (h, k) is the coordinates of the vertex of the parabola, and a is a constant coefficient.

To find the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7, we can first use the formula for the x-coordinate of the vertex of a quadratic function, which is given by h = -b / 2a. In this case, the quadratic function is f(x) = x² + 8x + 7, so b = 8 and a = 1. Plugging these values into the formula, we get:

h = -8 / 2(1) = -4

Therefore, the value of h is -4.

Next, we can use the formula for the y-coordinate of the vertex of a quadratic function, which is given by k = f(h) = a(h - h)² + k. In this case, we know that the value of h is -4, and we can plug this value into the original quadratic function to get the value of k:

k = f(-4) = (-4)² + 8(-4) + 7 = 16 - 32 + 7 = -9

Therefore, the value of k is -9.

Finally, we can use the equation f(x) = a(x - h)² + k to find the value of a. Since we know that the coordinates of the vertex are (-4, -9) and the equation of the quadratic function is f(x) = x² + 8x + 7, we can plug these values into the equation to solve for a:

f(x) = a(x - h)² + k

x² + 8x + 7 = a(x - (-4))² + (-9)

We can then distribute the squared term and simplify the equation to get:

x² + 8x + 7 = a(x² - 8x + 16) + (-9)

x² + 8x + 7 = a(x²) - 8a(x) + 16a + (-9)

We can then collect like terms to get:

x² + 8x + 7 = a(x²) - 8ax + 16a - 9

Comparing the coefficients of the x², x, and constant terms on both sides of the equation, we can see that a = 1.

Therefore, the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7 are a = 1, h = -4, and k = -9.

a) A × B is the Cartesian product of A and B, given by the set

A × B = {(a, b) | a ∈ A and b ∈ B}

Then for A = {4, 6, 8} and {4, 5, 6}, we have the product

A × B = {(4, 4), (4, 5), (4, 6), (6, 4), (6, 5), (6, 6), (8, 4), (8, 5), (8, 6)}

b) The power set of a set X is the set containing all subsets of X. I'm not sure what you're asking to find the power set of, though. Hopefully it's not of A × B, since that would contain 2⁹ = 512 elements...

Instead I'll assume you mean a simpler set, such as A ∩ B. The intersection of A and B is

A ∩ B = {4, 6, 8} ∩ {4, 5, 6} = {4, 6}

and has only 2 elements, so its power set has 2² = 4 elements (much more manageable!) and is the set

Pow(A ∩ B) = {{}, {4}, {6}, {4, 6}}

Answer:

57+x = 45

The sum means your adding numbers. it says the sum of 57 and a number x. That means you are adding 57 and the number x. which is written as 57+x. It says after that "is 45" so the sum or answer is 45.

You can also solve for x.. if you want to, the answer would be x=-12.

because.. 57+-12 = 45

Step-by-step explanation:

Step-by-step explanation:

the answer is 177.75 lb; 178.25 lb

Answer:

I believe the question is asking what it was before it was rounded to 178.

Your answer is 177.5lb

Step-by-step explanation:

A half pound is 0.5lb. After 5 or 0.5 you always round up. So rounding 177.5lb to the nearest half pound would be 178lb. Hope this helps!

Answer:

The answer is C. 60-6m.

Answer:

50(5π + 6) cm²

Step-by-step explanation:

TSA of figure = 1/2 of TSA(Cylinder) + Area of rectangle

= 1/2 of 2πr(h+r) + 20*15

= πr(h+r) + 300

= 10π(15+10) + 300

= 250π + 300 cm²

or 50(5π + 6) cm²

Answer:

31.42

Step-by-step explanation:

Answer: $0.576

Step-by-step explanation:

The total amount in prizes is $1800.

For there to be 60% profit, the total cost of the tickets need to be \(1800(1.6)=\$ 2880\).

Thus, each ticket must sell for \(\frac{2880}{5000}=\$ 0.576\)

Answer:

To make x the subject of the formula, we can isolate x by subtracting 1 from both sides of the equation:

x + 1 = 4y

x + 1 - 1 = 4y - 1

x = 4y - 1

So x is equal to 4y minus 1.

Answer:

\(x = 4y - 1\)

Step-by-step explanation:

Currently x is on the left side of the equal sign and is being added to 1. x has to be isolated and be by itself on one side of the equal sign in order to be made the subject of the formula. Therefore the 1 needs to be moved to the other side of the equal sign:

             \(x = 4y - 1\)

Answer:

\(6 + 5 = 11 + 3 = 14 + 2 = 16\)

\(6 \div 5 \div 3 \div 2 = 0.2\)

\( 6 \times 5 \times 3 \times 2 = 180\)

Step-by-step explanation:

If its addition add them, multiplication multiply them, division divided them.

Answer:

Step-by-step explanation:

i need help sorry no answer got u

Answer: To factor the expression -14 - (-8) completely using the distributive law, we need to simplify it first.

Remember that when we subtract a negative number, it is equivalent to adding the positive number. Therefore, -(-8) is the same as +8.

So the expression becomes:

-14 + 8

To factor it further using the distributive law, we can rewrite the addition as multiplication by distributing the -14 to both terms:

(-14) + (8) = -14 * 1 + (-14) * 8

This can be simplified as:

-14 + 8 = -14 * 1 + (-14) * 8 = -14 + (-112)

Finally, we can add the two negative numbers to get the result:

-14 + (-112) = -126

Therefore, the expression -14 - (-8) factors completely as -126.

For the diagonal, d, to be at least 41.5 inches, the possible length, width, and height for the box are 20 inches, 20 inches, and  27 inches respectively.

The length, width, and height of the cuboid can be found using the 3D Pythagorean theorem, which states that in a three-dimensional right triangle, the square of the length of the hypotenuse (the longest side, or the diagonal of the cuboid) is equal to the sum of the squares of the other two sides.

We are given that the diagonal of the cuboid, d, is at least 41.5 inches. We can use the 3D Pythagorean theorem to find the possible values of l, w, and h that would satisfy this condition.

Let l be the length of the cuboid, w be the width, and h be the height. Then we have the equation:

d² = l² + w² + h²

Substituting the given value for d and rearranging the terms gives us:

l² + w² + h² ≤ 41.5²

We can find the possible values of l, w, and h by finding the integer values that satisfy this inequality.

For example, one solution is l = 20, w = 20, and h = 27, which gives us a diagonal of 41.50 inches. This corresponds to answer choice B: (20 inches, 20 inches, 27 inches).

Learn more about Pythagoras's theorem here:

brainly.com/question/343682

#SPJ1