Use the elimination method to solve the following system of equations.

2x - y + z = -3
2x + 2y + 3z = 2
3x - 3y - z = -4

To solve the equation, let’s translate the given information into an algebraic equation. The solution to the equation is x = -18.

To solve the equation, let’s translate the given information into an algebraic equation. Let the number be represented by 'x'. The quotient of the number and 3 is x/3. The problem states that four less than the quotient of a number and 3 is -10, so we can write the equation as:

x/3 - 4 = -10

To solve for x, we can start by adding 4 to both sides:

x/3 = -6

Next, we can multiply both sides of the equation by 3 to isolate x:

x = -18

Therefore, the solution to the equation is x = -18.

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Answer:

Area function : [tex]A(x)=12x-x^2[/tex]

Domain: (0,6)

The area of rectangle is maximum at x=6. The area of a rectangle is maximum if it is a square.

Step-by-step explanation:

It is given that the length of wire is 24 inches. It is to be cut into four pieces to form a rectangle.

Let x be the length of shortest side.

Perimeter of a rectangle is

Perimeter = 2( Shortest side + longest side).

[tex]24 = 2( x + \text{longest side})[/tex]

[tex]12 = x + \text{longest side}[/tex]

[tex]12 - x = \text{longest side}[/tex]

So, length of longest side is (12-x) inches.

Area of a rectangle is

[tex]A=length \times width[/tex]

Area function is

[tex]A(x)=x(12-x)[/tex]

The area of rectangle and dimensions of a rectangle can not be a negative.

[tex]A(x)>0[/tex]

[tex]x(12-x)>0[/tex]

It means,

[tex]x>0[/tex]

[tex]12-x>0\Rightarrow 12>x[/tex]

One side is less that the other side.

[tex]x<12-x[/tex]

[tex]2x<12[/tex]

[tex]x<6[/tex]

It means the domain of the function is (0,6).

The simplified form of the area function is

[tex]A(x)=12x-x^2[/tex]

Differentiate with respect to x.

[tex]A'(x)=12-2x[/tex]

[tex]A'(x)=0[/tex]

[tex]12-2x=0[/tex]

[tex]x=6[/tex]

Differentiate A'(x) with respect to x.

[tex]A''(x)=-2<0[/tex]

Therefore the area of rectangle is maximum at x=6.

[tex](12-x)=12-6=6[/tex]

It means the area of a rectangle is maximum if it is a square.

There are 8 quarters and 14 dimes.

Let there are x quarters.

and y dimes.

Also as we know,

1 quarter= 0.25 dollar

Hence, x quarter= $ 0.25x

and 1 dime= $ 0.10

Hence,  y dimes= $ 0.10y

This means that:

                 0.25x+0.10y=3.40

Also, in non-decimal form it could be written as:

                  25x+10y=340

This means that:

                       x+y=22

Now on solving it graphically we see what is the point of intersection of the two lines or system of linear equations.

We get the point of intersection as: (8,14)

i.e. x=8 and y=14

Hence, there are 8 quarters.

and 14 dimes.

Answer:

This is a square inscribed in a circle.

Step-by-step explanation:

Answer:

I took the test its 1

Step-by-step explanation:

The population density for a country with a population of 307.5 million and an area of 3.79 million square miles is approximately 81.14 people per square mile. This figure is calculated by dividing the population by the area and is rounded to the nearest hundredth.

To calculate the population density of a country for 2009, when the population was reported to be 307.5 million and the total area was 3.79 million square miles, you must divide the population by the total area. The formula for population density is:

Population Density = Population / Area

In this case, the calculation would be:

Population Density = 307,500,000 people / 3,790,000 square miles

When you do the math, you get:

Population Density ≈ 81.14 people per square mile

This result has been rounded to the nearest hundredth as requested. Comparing this with other countries' population densities, such as those of South Asian countries, can provide a remarkable insight into how population distribution and globalization impact living conditions and resource availability.

The population density of a country with a population of more than 307.5 million and an area of 3.79 million square miles, in 2009, was approximately 81.14 people per square mile after rounding to the nearest hundredth.

To calculate the population density of a country for the year 2009 when the population was more than 307.5 million and the total area was 3.79 million square miles, we use the following formula:

Population Density = Population / Area

Now, let's substitute the given values:

Population Density = 307.5 million people / 3.79 million square miles

To proceed with the calculation, we need to convert the population into a number without the word 'million' since 'million' is also part of the area's units. Therefore, 307.5 million people become 307,500,000 people and 3.79 million square miles become 3,790,000 square miles.

Population Density = 307,500,000 people / 3,790,000 square miles

After doing the division, we get:

Population Density ≈ 81.14 people per square mile (rounded to the nearest hundredth)

Therefore, the population density for that country in 2009 was approximately 81.14 people per square mile.

The expected winnings for this game is calculated by multiplying the value of each possible outcome by their probability, providing an overall expected value of $1.33. This indicates that over a long period of repeated games, the average winnings per game would be $1.33.

In this question, we're dealing with calculating the expected value in a game of probability. The game involves rolling a dice with outcomes ranging from 1 to 6 and the associated payoffs for roll outcomes of 4, 5, and 6 are $1, $2, and $5 respectively.

We calculate the expected winnings (value) for a single round of the game by multiplying all possible outcomes by their respective probabilities, then summing these products. In this case, symbols represent the payout (in $) and P represents the probability of each outcome.

Adding up these expected outcomes gives us our overall expected winnings: $0.83 + $0.33 + $0.17 + $0.00 = $1.33 per game

If you play this game repeatedly, over the long term, you'd expect to win around $1.33 on average each game. Note that the exact winnings in a single instance of the game could be $0, $1, $2, or $5, and this value simply provides an average expected outcome over time.

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Final answer:

The dimensions of each corral should be 40 meters by 10 meters.

Explanation:

To find the dimensions of the rectangular corrals, we can set up an equation using the perimeter and area of the enclosed space. Let's call the length of one corral x and the width y. The perimeter of the two corrals is 2x + 2y, which equals 100 meters. The area of the enclosed space is xy, which equals 350 square meters.

Using these equations, we can solve for x and y. Rearranging the perimeter equation, we get x = 50 - y. Substituting this into the area equation, we have (50 - y)y = 350.

Simplifying the equation, we get y^2 - 50y + 350 = 0. This is a quadratic equation that can be factored as (y - 35)(y - 10) = 0. Therefore, the possible values for y are 35 and 10.

Since we are looking for positive values for the dimensions, we choose the values y = 10 and x = 50 - y = 50 - 10 = 40. Therefore, the dimensions of each corral should be 40 meters by 10 meters.

To find the dimensions of the rectangular corrals, we can set up a system of equations. By solving the system of equations, we find that the dimensions of the rectangular corrals can be either 25 meters by 14 meters or 7 meters by 50 meters to obtain a total area of 350 square meters.

To find the dimensions of the rectangular corrals, we can set up a system of equations. Let x represent the width of one corral and y represent the length. Since the rancher wants to enclose a total of 350 square meters, we have the equation xy = 350. The perimeter of each corral is 2x + y, so the total amount of fencing used would be 4x + 2y.

Given that the total fencing available is 100 meters, we can set up the equation 4x + 2y = 100. Now we can solve the system of equations:

By substituting the value of y from the first equation into the second equation, we can solve for x. After finding the value of x, we can substitute it back into the first equation to find the corresponding value of y. The solutions will give us the dimensions of the rectangular corrals.

Let's solve the system of equations:

The solutions for x are x = 25 and x = 7. Plugging these values back into the equation xy = 350, we find that the corresponding values for y are y = 14 and y = 50, respectively. Therefore, the dimensions of the rectangular corrals can be either 25 meters by 14 meters or 7 meters by 50 meters to obtain a total area of 350 square meters.

Answer:

1. 30%

2.46%

Step-by-step explanation:

The probability of Kayla not drawing a yellow or a green bead is  30 %. The probability of Kayla drawing a red or a green bead is  46 %.

Correct for plato! :)

Both B & E; They are both using -225 which represents debt

The expression that shows the given statement will be equal to -225(3). Hence, options B and E are correct.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Gena's food cart business last year = $225 in debt = -225

The dept has tripled this year.

Then, the equation according to the statement will be,

(-225) × 3

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Answer:

First question, x= 10^10.

Second question is 10!. or 362880

Step-by-step explanation:

First Question:

Simple logx has a base of 10, i.e log10 x,

the question will be 10 = log10 x,

when taking the base "10" from the right side to the left, the number on the left side becomes the power of the base, in this case 10 from the right will be base and 10 from the left will power and log will vanish.

x=10^10.

Another example with different numbers

Y=logx if Y= 12, What is x?

The base is ten when not given,so:

12=logx

10^12=x

Second Question;

simple multiplication just multiply the numbers.

10! is pronounced as 10 factorial,

5! will be 5x4x3x2x1=120

The interest earned on a deposit of $1,295 at a 7% annual rate for 180 days is approximately $44.70.

To compute the amount of interest earned we can use the simple interest formula:

Interest = Principal × Rate × Time

Since simple interest does not complicate by itself, and the time is less than a year, we'll adjust the time and rate accordingly.

First, we express the annual interest rate as a decimal by dividing the percentage by 100:

Rate = 7% / 100 = 0.07

Next, we convert the time period of 180 days into years, considering there are 365 days in a year:

Time = 180 days / 365 days/year = 0.49315 years (approximately)

Now, let's plug the values into the simple interest formula:

Interest = $1,295 × 0.07 × 0.49315

Calculating the interest:

Interest = $44.70

the answer on APEX is 6

Final answer:

The expected value of the game to the player is $3.68. If played 1000 times, the player would expect to lose $320.

Explanation:

Expected value for the game:

Expected Loss in 1000 Games:

Therefore, you can expect to lose an average of $210.50 if you play this game 1000 times.

Answer:

two side measures are the same

all angle measures less than 90°

two angle measures are the same

Step-by-step explanation:

The three true statements about an acute isosceles triangle are:

- Two side measures are the same:

- All angle measures are less than 90°:

- Two angle measures are the same:

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

About an acute isosceles triangle are:

- Two side measures are the same:

In an isosceles triangle, two sides have the same length.

In an acute isosceles triangle, all angles are acute, which means they are less than 90°.

Therefore, the two sides that are the same length must be the two sides opposite the acute angles.

- All angle measures are less than 90°:

An acute triangle is a triangle in which all angles are less than 90°.

Since an acute isosceles triangle has two equal acute angles, all three angles in the triangle are less than 90°.

- Two angle measures are the same:

An isosceles triangle is a triangle in which two sides have the same length. In an acute isosceles triangle, the two sides that have the same length are opposite the two equal acute angles.

Therefore, the two angles opposite those sides must also have the same measure.

Thus,

The three true statements about an acute isosceles triangle are:

- Two side measures are the same:

- All angle measures are less than 90°:

- Two angle measures are the same:

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Answer:

option (d) is correct.

[tex]f(x+1) = 2x^2+4x+5[/tex]

Step-by-step explanation:

Given : [tex]f(x) = 2x^2 + 3[/tex]

We have to choose out of given option which represent f(x + 1)

Consider the given function [tex]f(x) = 2x^2 + 3[/tex]

Since we have to find f( x + 1 ) , replace x by x + 1 in the given function f(x) , we have,

[tex]f(x+1) = 2(x+1)^2+3[/tex]

Using algebraic identity, [tex](a+b)^2=a^2+b^2+2ab[/tex] , we have,

[tex]f(x+1) = 2(x^2+1+2x)+3[/tex]

Simplify the expression by multiplying 2 with each term in bracket, we have,

[tex]f(x+1) = 2x^2+2+4x+ 3[/tex]

Simplify , we have,

[tex]f(x+1) = 2x^2+4x+5[/tex]

Thus, option (d) is correct.