What is the first step in silving this equation?
3n - 4 = -2 + 2n

If the given equations are true, then the value of x + z is 6.

Simultaneous equations or systems of equations are two or more equations in algebra that must be solved jointly. The number of equations must match the number of unknowns for a system to have a singular solution.

Consider the equations are true,

4x + 2y + 8z = 30                                                                    ------------(1)

3x + 2y + 7z = 24                                                                    ------------(2)

Now,

By subtracting equation (2) from equation (1) we get:

eq(1) - eq(2)

4x + 2y + 8z - ( 3x + 2y + 7z ) = 30 -24

4x + 2y + 8z - 3x - 2y - 7z = 6

( 4x - 3x ) + ( 2y - 2y ) + ( 8z - 7z ) = 6

x + 0 + z = 6

x + z =6

Therefore, assuming the equations to be true the value of x + z is equal to 6.

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Answer:

A

Step-by-step explanation:

If im wrong please correct me.

Answer:

A- y > 0

Step-by-step explanation:

That's what I got!  I am on my Cumulative Exam!     :)

i) Selling price of 20 lemons is ₹12.

ii) The profit is ₹2.

iii) The profit percentage is 20%.

i) Jaya bought 20 lemons for ₹10, which means the cost of one lemon is 10/20 = ₹0.50.

If she sells 5 lemons for ₹3, the selling price of one lemon is 3/5 = ₹0.60.

Therefore, the selling price of 20 lemons is 20 x ₹0.60 = ₹12.

ii) The cost price of 20 lemons is ₹10, and the selling price is ₹12.

So, the profit is ₹12 - ₹10 = ₹2.

iii) The profit percentage is calculated as (Profit/Cost price) x 100%.

In this case, the profit is ₹2 and the cost price is ₹10.

So, the profit percentage is (2/10) x 100% = 20%. Therefore, Jaya made a profit of 20% by selling lemons.

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There are 12 identical marbles in a bag, and Suzy is going to select 9 marbles from the bag at random.

The problem asks how many possible outcomes there are.

To begin with, we need to understand the concept of combinations. A combination is a way to select a subset of objects from a larger set, without regard to the order of the objects. For example, if we have four marbles (A, B, C, and D), there are six possible combinations of two marbles: AB, AC, AD, BC, BD, and CD.

In this problem, we have 12 marbles and we are choosing 9 of them. To find the total number of combinations, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we are choosing, and ! represents factorial (i.e. multiplying a number by all the positive integers less than it).

So, plugging in our numbers:

12C9 = 12! / 9!(12-9)! = 12! / 9!3! = (121110) / (321) = 220

Therefore, there are 220 possible outcomes if Suzy selects 9 marbles at random from a bag containing 12 identical marbles.

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The Wronskian of the given vector functions is -42e^(6t).

The Wronskian is a determinant of a matrix composed of the given vector functions and their derivatives. For the given functions, the matrix and its determinant are calculated as follows:

| 2e^t -e^(2t) e^(3t) |

| 1e^t 3e^(2t) -5e^(3t) |

| 0e^t 5e^(2t) 0e^(3t) |

Det = 2e^t * 3e^(2t) * 0e^(3t) + (-1e^(2t)) * 5e^(2t) * 2e^(t) + 1e^(3t) * 1e^(2t) * 1e^(t)

- (0e^(3t)) * 3e^(2t) * 1e^(t) - (-1e^(2t)) * 0e^(t) * 1e^(3t) - 2e^(t) * 5e^(2t) * 1e^(3t)

Simplifying the above expression, we get:

Det = -42e^(6t)

Therefore, the Wronskian of the given vector functions is -42e^(6t).

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The Wronskian of the given vector functions is 30e^(4t) - 12e^(5t).

To find the Wronskian of the given vector functions, we need to first arrange the functions as columns of a matrix and then take the determinant of the resulting matrix. That is:

W = | x1 x2 x3 |

| 2e^t -e^(2t) e^(3t) |

| e^t 6e^(2t) -15e^(3t)|

| 0 10e^(2t) 0 |

Expanding the determinant along the first row, we get:

W = 2e^t |-e^(2t) e^(3t)|

| 6e^(2t) -15e^(3t)|

+ e^t |10e^(2t) 0 |

| 0 0 |

W = 2e^t(-e^(2t)(-15e^(3t)) - e^(3t)(6e^(2t))) + e^t(10e^(2t)(0))

W = 30e^(4t) - 12e^(5t)

Therefore, the Wronskian of the given vector functions is 30e^(4t) - 12e^(5t).

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The expression for the rectangular prism's base area is 11x² + 7x + 5.

Given;

The volume of rectangular prism = 33x³ + 43x² + 29x + 10

The height of the prism = 3x + 2

We know that, the area of the prism = length * breadth

where as, volume = length * breadth * height

So, area = volume / height

Using synthetic division, dividing volume by height, we get;

3x+2  ) 33x³ + 43x² + 29x + 10 ( 11x² + 7x + 5

            33x3 + 22x2

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

                        21x² + 29x

                        21x² + 14x

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

                                  15x + 10

                                   15x + 10

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

                                       x

Quotient is 11x² + 7x + 5 which is equal to expression for the area of the base of the rectangular prism.

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The vendor sold 172 sodas and 58 hotdogs at the hockey game.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

let, the number of soda cans be 'x' and the number of hot dogs be 'y'.

So, From the given information x = 3y and the vendor sold a total of 232.

Therefore, x + y = 232.

3y + y = 232.

4y = 232.

y = 232/4.

y = 58.

So, He sold 58 hot dogs and 3×58 = 172 soda cans.

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Answer:

60%

Step-by-step explanation:

3 divided by 5 is 0.6

Multiply this by 100 to get the percent and you will end ups with 60%

Hopes this helps please mark brainliest

Answer:x - number of minutes;

f ( x ) - the distance from the finish line.

  x :        0     2      4      6

f ( x ) :    3      2      1     0

f ( x ) = 3 - x/2

Answer: B ) f ( x ) = -1/2 x + 3

Step-by-step explanation:

Answer:

f(x) = (1/2)X

Step-by-step explanation:

speed = distance / time

distance = speed x time

3 = (1/2) X

X = 3/(0.5) = 6min

let distance = F(X)

f(x) = (1/2)X

Answer:

2, 800

Step-by-step explanation:

(3 x 1000) - (2 x 100)

3,000 - (2 x 100)

3,000 - 200

2, 800

The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.

Let's assume John has 'x' amount of  money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'

So,

p = x - 80x/100                (equation 1)

q = y - 75y/100                (equation 2)

According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.

p = q

x- 80x/100 = y - 75y/100

x - 0.8x = y - 0.75y

0.2x = 0.25y

x =  0.25y/0.2

x/y = 0.25/0.2

x/y = 25/20

x/y = 5/4

Hence, the ratio of John's money to Peter's money is 5/4.

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The initial number of dice rolled = 1000

What is exponential modeling?

Based on an equation like where Y = deterioration, T = time, and A and B = parameters to be calculated by the regression approach based on historical data, the exponential model represents the degradation failure process.

Here,

Linear models are used when a phenomenon is changing at a constant rate whereas exponential models are used when a phenomenon is changing in a way that is quick at first, then more slowly, or slow at first and then more quickly. This is the defining characteristic of the exponential model.

(a)

dice(n) = 1000 × (−0.138629436ln)........... (1)

The initial number of dice rolled when n=0

Putting n=0 in (1),

dice(0) = 1000e(0) = 1000

Hence, the initial number of dice rolled = 1000

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Answer:

The population density is 7592 people per square mile

Step-by-step explanation:

The population density of los Angeles here refers to the number of people present by square miles

Mathematically, to find this population density, what we need to do is to divide the total population that we have by the area of Los angeles

The population here is 4,000,000 while the area is 503 square miles

The population density is thus ;

4,000,000/503 = 7592.29 which is approximately 7592 people per square mile

Answer:

5.4

Step-by-step explanation:

using pythagoras theorem

a²+b²=c²

5²+2²=c²

c²= 25+4

c²=29

\( \sqrt{c ^{2} } = \sqrt{29} \)

c=5.4

Answer:

x = 16

Step-by-step explanation:

If 3.75x would equal to 60, then x would equal to 60/3.75, which would be 16

Hope this helps!

Answer:

x = 100 , x = 3

Step-by-step explanation:

(a)

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × 3 = 540°

sum the angles and equate to 540

x + x + 125 + 125 + 90 = 540 , that is

2x + 340 = 540 ( subtract 340 from both sides )

2x = 200 ( divide both sides by 2 )

x = 100

(b)

the 2 given angles are alternate exterior angles and are congruent , then

6x + 18 = 2x + 30 ( subtract 2x from both sides )

4x + 18 = 30 ( subtract 18 from both sides )

4x = 12 ( divide both sides by 4 )

x = 3

Given that:

- On the first day the school sold 5 senior citizen tickets and 3 student tickets for a total of $92.

- On the second day the school took in $72 by selling 3 senior citizen tickets and 3 student tickets.

Let be "x" the price (in dollars) of a senior citizen and "y" the price (in dollars) of a student ticket.

Using the data provided in the exercise, you can set up this System of Equations:

You can solve it using the Elimination Method:

1. Multiply the first equation by -1.

2. Add the equations.

Then:

3. Solve for "x":

4. Substitute the value of "x" into one of the original equations and solve for "y":

Hence, the answer is:

- Price of a senior citizen ticket:

- Price of a student ticket:

Answer:

the two consecutive negative integers are -2 and -1.

Step-by-step explanation:

Represent these negative integers by m and n.

Then (because the integers are consecutive) n = m + 1, and m^2 = n + 5.

Substituting m + 1 for n in the second equation, we get:

m^2 = m + 1 + 5, or

m^2 - m - 6 = 0

This factors into (m - 3)(m + 2) = 0.  The only negative root is -2.  

Thus, the two consecutive negative integers are -2 and -1.

Check:  Is the  square of the first five more than the second?

Is (-2)^2 = -1 + 5?  YES

The integers aer -2 and -1.

The surface area of the box, in square feet, that Zoe decorates is 430.35 square feet

To determine the surface area from the net of the box, we simply calculate the area of each shape.

From the given figure, we have the following shapes and dimensions:

The area is then calculated using:

Area = Areas of the rectangle + Area of the triangle

So, we have:

Area = 15 * 12 + 13.89 * 15 + 0.5 * 12 * 7

Evaluate the sum of products

Area = 430.35

Hence, the surface area of the box, in square feet, that Zoe decorates is 430.35 square feet

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Answer:577.35 square feet

Step-by-step explanation:

‍♀️

Answer:

12

Step-by-step explanation:

3×4=12

three multiply by four is equal to 12.

===========================================================

Explanation:

The given statement is claiming something like \(P(X < 2)\) produces a different result compared to \(P(X \le 2)\). The subtle difference of course is the "or equal to".

When talking about continuous random variables, the two values are the same. Why? Because probability of selecting *exactly* X = 2 is going to be zero. Think of a very very thin strip of height P(X = 2) and the width is approaching zero. The width is doing this because we're trying to pinpoint X = 2 itself. As you can see, this skinny rectangle will have its area approach 0. Ultimately, whether we compute \(P(X < 2)\) or \(P(X \le 2)\), it doesn't matter. They both produce the same result.

If you are a visual learner, consider the standard normal distribution. Now consider the task if shading to the left of z = 2. This area describes both probabiltiies mentioned above.

If X is a continuous random variable, then \(P(X < 2) = P(X \le 2)\) and we can change the "2" to any number we want to have the same outcome.

Therefore, the original claim is false.

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

Extra info:

Now if X was discrete (say from the binomial distribution), then the two probabilities would be different. This is because

\(P(X < 2) = P(0) + P(1)\\\\P(X \le 2) = P(0) + P(1) + P(2)\\\\P(X < 2) \ne P(X \le 2) \ \text{only if X is discrete}\)

We can see in this case that the second line has P(2) while the first one does not.

So the original claim would be true if we changed "continuous" to "discrete".

Although part of your question is missing, you might be referring to this full question: On a map, the scale is inches/miles = 1/75. Going from home to the first destination is 1.5 inches, and then from there to the next destination is 2.25 inches. How many miles were travelled?

281.25 miles were travelled.

The distances travelled in inches need to be added.

1.5inches + 2.25inches = 3.75 inches

Let y be the number of miles. Thus, the proportion for the given situation is,

1/75 = 3.75/y

In the next step, it needs to be cross-multiplied,

1×y = 3.75×75

Thus,

y = 281.25

So, 281.25 miles were travelled.

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Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer:

True if the question means a compass and straight edge.

Step-by-step explanation:

Its quite easy to split a line into any number of parts. This can be done by a scaling operation.

Answer:

True

Step-by-step explanation:

Yes, if the question means a compass and straight edge. Its quite easy to split a line into any number of parts. This can be done by a scaling operation.

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The city covers an area of 80.38 square kilometers.

To calculate the number of square kilometers in 31.2 square miles, we need to use the given conversion factor 1 mile = 1.61 km. We can do this by multiplying the number of square miles by the square of the conversion factor.

Hence, the number of square kilometers in 31.2 mi² is calculated as follows:

1 mi² = 1.61² km² (square both sides to convert square miles to square kilometers)1 mi² = 2.5921 km² (square of 1.61)

Now, we can calculate the area in square kilometers by multiplying the number of square miles by the area conversion factor:

31.2 mi² × 2.5921 km²/mi² = 80.38 km²

Therefore, the city covers an area of 80.38 square kilometers.

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Answer: 30%

Step-by-step explanation: Solution for 6300 is what percent of 21000: 6300:21000*100 = (6300*100):21000 = 630000:21000 = 30. Now we have: 6300 is what percent of 21000 = 30.

if we take 21000(origin amount) to be the 100%, what's 6300 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 21000 & 100\\ 6300& x \end{array} \implies \cfrac{21000}{6300}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{10}{3} ~~=~~ \cfrac{100}{x}\implies 10x=300\implies x=\cfrac{300}{10}\implies x=30\)

Answer:

no

Step-by-step explanation:

3:2 is equal to 18:12 not 17

The ranking of resistors would be, R1 < R3 < R2

The larger the time constant T = RC,  the more time it takes for the capacitor to discharge.

So the more the resistance the more time it takes for the capacitor to discharge.

In the figure, the one with R2 will take the longest time for Vc to be zero. Then R3 will take less time than R2 and R1 will take smallest time to discharge. So R2 is largest followed by R3 and R1 is smalllest.

So the ranking would be, R1 < R3 < R2

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The slope and y-intercept of each line are:

13. slope = 1/2; y-intercept: 0.

14. slope = 3; y-intercept: 0.

15. slope = -2/5; y-intercept = 0.

16. slope = -1; y-intercept = 1.

17. slope = -2/3; y-intercept = -4.

18. slope = 1; y-intercept = 0.

19. 7/9

20. 3/5

The slope and y-intercept of a line can be determine from the given equation of a line in slope-intercept form, y = mx + b, where:

13. y = 1/2x,

The slope = 1/2

The y-intercept of the equation is: 0.

14. y = 3x,

The slope = 3

The y-intercept of the equation is: 0.

15. y = -2/5x,

The slope = -2/5

The y-intercept of the equation is: 0.

16. y = -x + 1

The slope = -1

The y-intercept of the equation is: 1.

17. y = -2/3x - 4,

The slope = -2/3

The y-intercept of the equation is: -4.

18. y = x,

The slope = 1

The y-intercept of the equation is: 0.

19. Slope = change in y / change in x = (18 - 11)/(19 - 10)

Slope = 7/9

20. Slope = change in y / change in x = (2 -(-1))/(9 - 4)

Slope = 3/5

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