Use an algebraic method (substitution or elimination) to solve the system of equations. Show your work.

PLEASE HELP!!!!

4X − 2Y = 16

2X + 3Y = 32

The factor of 18 is 1,2,3,6,9,18,-1,-2,-3,-6,-9,-18 if we want we can take negative factor also .

Due to its even composite nature, the number 18 has extra variables besides 1 and 18. As a result, the components of 18 are 1, 2, 3, 6, 9, and 18, and their opposites are -1, -2-3,-6,-9,-18  

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Factors can be found using either division or multiplication. Rules of divisibility can also be applied.

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Answer:

[tex]16x^2-24x+9[/tex]

Step-by-step explanation:

To find (c circle d)(x), we need to first find d(c(x)) and then simplify.

First, we need to find c(x) and substitute it into d(x), as follows:

d(c(x)) = d(4x - 2) = (4x - 2)^2 + 5(4x - 2)

Expanding the square and simplifying, we get:

d(c(x)) = 16x^2 - 24x + 9

Now, we have (c circle d)(x) = d(c(x)) = 16x^2 - 24x + 9.

Answer:

Equation: 1,152.00 = 21.80x + 16.60y

21.80x + 16.60y = 1,152.00

x = 52 days

y = 69 days

This money will buy 121 days of food for Jasmine and Siri.

about 2.1134 us quarts

the parabola has an equation of y = (-1/8)x² + (1/2)x - 1/2, its vertex is at (2, 0), and it opens to the left with a focus at (0, -2) and a directrix at x=2.

Since the directrix of the parabola is a vertical line x=2, the axis of the parabola is horizontal, and its vertex is the point of intersection between the axis and the directrix, which is (2, 0). The focus is located at (0, -2), which is two units below the vertex, so the distance between the focus and the vertex is |p| = 2, where p is the distance between the vertex and the directrix. Since the directrix is to the right of the vertex, the parabola opens to the left. Therefore, its equation can be written in the form:

(x - h)² = -4p(y - k)

where (h, k) is the vertex. Plugging in the values we have, we get:

(x - 2)² = -8(y - 0)

Simplifying, we get:

x² - 4x + 4 = -8y or

y = (-1/8)x² + (1/2)x - 1/2

Therefore, the parabola has an equation of y = (-1/8)x² + (1/2)x - 1/2, its vertex is at (2, 0), and it opens to the left with a focus at (0, -2) and a directrix at x=2.

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The quadratic function will be x²+ 2x,Carolina will need to have at least 272 square feet available in her yard.

A quadratic function is a polynomial function of degree two, which means it is a function that can be expressed as an equation with the second-degree degree of the highest exponent of the unknown variable. It is typically expressed as ax² + bx + c, where a, b and c are constants, and x is an unknown variable. Quadratic functions can be used to model many real-world situations, such as the height of a projectile in motion or the area of a circle.

a. The area of the pool and the deck can be represented by a quadratic function, A = f(x) = x² + 2x, where x is the width of the pool in feet.

b. For the 16-ft wide pool, the area of the pool and the deck will be A = f(16) = 16² + 2(16) = 272 ft². Therefore, Carolina will need to have at least 272 square feet available in her yard.

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Answer:

Therefore, the unknown number is 5.

Step-by-step explanation:

We can translate "Eight times the difference of a number and six is negative eight" into an algebraic equation as given below,

8(x - 6)

= -8                (where x is the unknown number we are trying to find)

The expression "the difference of a number and six" means x - 6. So, "eight times the difference of a number and six" means 8(x - 6).

The equation states that the product of 8 and the difference of the number x and 6 is equal to -8.

To solve for x, we can simplify the equation,

8(x - 6) = -8

8x - 48 = -8

8x = 40

x = 5

Therefore, the unknown number is 5.

Answer:

  65 cm

Step-by-step explanation:

You want the perimeter of the shape that results from removing a 60° sector from a circle.

The curved edge of the shape is 5/6 of the circumference of the circle.

  5/6C = 5/6(2πr) = 5/6·2·π·(9 cm) = 15π cm ≈ 47 cm

Each straight edge of the shape has a length equal to the radius. Then the straight edges have a total length of ...

  2r = 2(9 cm) = 18 cm

The perimeter of the shape is the sum of the length of its curved edge and the lengths of the straight edges:

  P = 47 cm + 18 cm = 65 cm

The perimeter is about 65 cm.

__

Additional comment

A total circle is 360°, so 1/6 of the circle is 60°. The size of a sector of a circle can be described by the angle measure of its central angle. Here, that means the removed portion is a 60° sector.

It is not possible to get 8 aces from a standard 52 cards deck. The indicated degree of likelihood as a probability value is 0 (Zero).

The procedure for probability states that the possibility of an occurrence occurring, or P(E), equals the proportion of the number of favorable outcomes to the number of total outcomes.

Mathematically,

Possibility (E) = favorable outcomes/total outcomes.

We know that there are four aces in total in a 52-card deck.

Therefore the probability of getting 8 aces can be expressed by using the factorial of the number. This can result in a decrease of numbers by multiplying the previous number, this is called the factorial of a number.

P(8A) = 7/52 × 6/51 × 5/50 × 4/49 × 3/48 × 2/47 × 1/46 × 0/45

P(8A) = 0

The probability of getting is zero.

Therefore, it is not possible to get 8 aces from a standard 52 cards deck.

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Yes, mathematical phrases can be considered as polynomials. Because the mathematical sentences conform to the definition of polynomial.  

A polynomial is a mathematical expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

Mathematical phrases, such as:

"3x^2 + 2x - 5" or "2y^3 - 4y + 1"

Are examples of polynomials because they only involve the operations of addition, subtraction, multiplication, and non-negative integer exponents. Therefore, mathematical phrases can be considered as polynomials.

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Answer:1st and 3rd

Step-by-step explanation:

Answer: (-4, -2) and (-13, 0)

Used a calculator

Answer:

Factoring a polynomial means breaking it down into simpler parts that can be multiplied together to get the original polynomial. To factor a polynomial completely, we want to find all of its factors, including any that are in the form of a constant, a variable, or a combination of both.

Let's take a look at how to factor two of the given polynomials.

x^5 - x^3

We can factor out the greatest common factor (GCF) of x^3 to get:

x^5 - x^3 = x^3(x^2 - 1)

Now, we have a difference of squares, which we can factor using the formula:

a^2 - b^2 = (a + b)(a - b)

In this case, a = x and b = 1, so we get:

x^5 - x^3 = x^3(x + 1)(x - 1)

Therefore, the polynomial x^5 - x^3 can be completely factored as x^3(x + 1)(x - 1).

3x^2 - 75

We can factor out the GCF of 3 to get:

3x^2 - 75 = 3(x^2 - 25)

Now, we have a difference of squares, which we can factor as:

a^2 - b^2 = (a + b)(a - b)

In this case, a = x and b = 5, so we get:

3x^2 - 75 = 3(x + 5)(x - 5)

Therefore, the polynomial 3x^2 - 75 can be completely factored as 3(x + 5)(x - 5).

In general, to factor a polynomial completely, we should first look for any common factors that can be factored out using the GCF. Then, we can look for special patterns, such as differences of squares, sums or differences of cubes, or quadratic trinomials that can be factored using the quadratic formula or by factoring the sum or difference of two perfect squares. Finally, we can use trial and error or other methods to find any remaining factors that are not immediately obvious.

If you could label my answer brainliest, that would be awesome!

- Dante

In mathematics, the term "orthogonal" refers to a relationship between two objects where they are perpendicular or at right angles to each other.

More generally, it refers to a relationship where two objects are independent or uncorrelated with each other. For example, in Euclidean geometry, two lines are orthogonal if they meet at a right angle. In linear algebra, two vectors are said to be orthogonal if their dot product (also known as inner product) is zero. Similarly, in statistics, two variables are said to be orthogonal if they have a correlation coefficient of zero, indicating that they are uncorrelated.

The term "orthogonal" is also used in various other fields, such as signal processing, computer science, and quantum mechanics, with similar meanings of independence, uncorrelatedness, or perpendicularity.

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Answer:

There are 1440 minutes in 24 hours.

Step-by-step explanation:

24 x 60 = 1440

Hope this helped. Have a good day!

A liter is a metric unit of volume, while a milliliter (ml) is a subunit of a liter. There are 1,000 milliliters in one liter.

This means that to convert liters to milliliters, you can multiply the number of liters by 1,000. Conversely, to convert milliliters to liters, you would divide the number of milliliters by 1,000.

For example, if you have 2.5 liters of water, you can convert this to milliliters by multiplying 2.5 by 1,000, which gives you 2,500 milliliters. This conversion is commonly used in fields such as chemistry and medicine, where small amounts of liquids are measured in milliliters.

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The value of phone B is [tex]\omega = 840[/tex].

Any equation with a maximum degree of 1 is said to be linear. In a linear equation, no variable has an exponent bigger than 1, thus. There is always a straight line on the graph of a linear equation.

Given that each term in a linear equation has an exponent of 1, graphing an algebraic equation always yields a straight line.  For this reason, it is referred to as a "linear equation." There are both one-variable and two-variable linear equations.

[tex]v= 1000[/tex]

[tex](\frac{4}{5})^d[/tex] is the value of phone A and

[tex]\omega = 840[/tex] is the value of phone B.

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Complete Question;

For each cell phone, write an equation that relates the value of the phone in dollars to the years since release, t. Use v for the value of Phone A and w for the value of Phone B.

Answer:

x=-10, PR=10.

Step-by-step explanation:

(x+15)/(x+20)=1/2 => 2(x+15)=x+20 => x=-10. PR=20-10=10.

51 centimetres equal to 20.08 inches.

In the International System of Units( SI), the current replication of the metric system, a centimetre (symbol cm) is a unit of length.

The symbol of inch is 'in'.

As one inch was exactly equal to 25.4 millimetres.

1 in equal to 2.54 cm

So, 1 cm equals [tex]\frac{1}{2.54}[/tex]  inch

Here we want to convert 51 cm to inches.

For the conversation of cm into the inches multiply the cm value by 0.3937 or  [tex]\frac{1}{2.54}[/tex]

We can write as:

51 cm = 51 × [tex]\frac{1}{2.54}[/tex] inches.

51 cm = 20.08  inches (rounded to two decimal places)

Therefore, 51 cm is equivalent to 20.08 inches.

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value of given expression = 48

The order of operations is a rule that specifies the correct steps for evaluating mathematical expressions. We can remember the order with PEMDAS -

Parentheses, exponents, multiplication and division (left to right), addition and subtraction (left to right).  

Given expression,

9 - 4 ÷ (2 + 2) + 2³ . 5

By PEMDAS rule

First solving parentheses

= 9 - 4 ÷ 4 + 2³ . 5

then solving exponent

= 9 - 4 ÷ 4 + 8 . 5

Now solving multiplication

= 9 - 4 ÷ 4 + 40

Now solving division

= 9 - 1 + 40

Now solving addition

= 49 - 1

Now solving subtraction

= 48

Hence, 48 is the value of the expression.

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Therefore , the solution of the given problem of inequality comes out to be Paul can drive at most 208 more miles before he will have to refill the tank.

A connection or collection of variables without the equal sign is a mathematical inequality. Equilibrium is typically followed by equity. Inequality happens when two values are not equal. Differences exist between equality and inequality. It was decided to utilize the most factors symbol because the quantities are not identical or equivalent (). Any discrepancy, regardless of how small or large, can be used to compare values.

Here,

Let x be the number of miles Paul can drive before he will have to refill the tank.

Since Paul's car can go at most 375 miles on one tank of gas, and he has already driven 167 miles, we can write the inequality:

x ≤ 375 - 167

Simplifying, we get:

x ≤ 208

Therefore, Paul can drive at most 208 more miles before he will have to refill the tank.

Interpretation: If Paul drives more than 208 miles, he will not have enough gas to complete the journey and will need to refill the tank.

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The value of x in the two congruent triangles is 3.9 and length CB is 53.9.

The value of x can be determined by applying the principle of congruent theorem.

The congruent theorem states that, if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other.

( 11x + 11 ) / 77 = 21 / 30

11x + 11 = 53.9

11x = 53.9 - 11

11x = 42.9

x = 42.9 / 11

x = 3.9 units

The length of CB = ( 11 x 3.9 ) + 11 = 53.9

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The option that is not available to Jacob is: He can purchase the computer now using his debit card, even though he does not have enough money in his bank account to cover the cost.

Using a debit card requires that there are sufficient funds in the linked bank account to cover the transaction. If there is not enough money available, the transaction will be declined. Therefore, Jacob cannot purchase the computer using his debit card unless he has enough funds in his account. The other options, including saving up to purchase the computer with cash, using a credit card, or putting more money in his bank account to use his debit card at a later date, are all valid options for Jacob.

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The domain of the given function in the graph will be x ≤ -1.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, a function as we can see in the graph,

Since The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values.

The y-axis on a graph represents the possible output values or range.

thus, in the given graph the domain of the function will be All real values smaller than -1.

therefore, the domain of the given function in the graph will be x ≤-1.

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At the end of 18 years, there will be a total of $5,890.37 in the account.  

Compound interest is a powerful financial tool that can help you grow your money over time.

In the case of the $1,800 deposited into an account earning 6% interest compounded weekly, the total amount in the account at the end of 18 years can be calculated as follows:

Let P be the principal balance, r be the interest rate, n be the number of times the interest is compounded per year, and x be the number of years. Using the compound interest formula, we can calculate the amount in the account at the end of 18 years:

A = P(1 + (r/n))ⁿˣ

A = 1800 * (1 + (0.06/52))⁵²ˣ¹⁸

A = 5,890.37

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Answer:

height = 21.8 ft from ground

Step-by-step explanation:

see photo for explanation.

The surface area of a cylinder can be calculated using the following formula: Surface Area = 2πr2 + 2πrh, where r is the radius and h is the height of the cylinder.

In this case, Jenny is looking to store her soup in a cylindrical container and completely cover it in aluminium foil. This means the surface area of the container will be equal to the surface area of the cylinder plus the surface area of the foil. So, if the radius of the cylinder is r and the height is h, the surface area of the container is:

Surface Area = 2πr² + 2πrh  
Surface Area of Foil = 2πr² + 2πrh + 2r²π

Substituting in the given value for pi, we get Surface Area = 6.28r² + 6.28rh + 2r²π.

Therefore, the surface area of the container is equal to 6.28r² + 6.28rh + 2r²π, where r is the radius and h is the height of the cylinder.

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The percentage change in the population of fish at Roe River42 from 2000 to 2016 is 33.72%.

The percentage change refers to the increase or decrease in the population of fish between 2000 and 2016 computed as a percentage or rate.

To determine the percentage change, the difference is divided by the original value and multiplied by 100.

The total fish population in 2000 at Roe River42 = 5,730

The decrease in the population in 2016 = 1,932

The percentage change = 33.72% (1,932/5,730 x 100)

Thus, we can conclude that the fish population decreased by 33.72% from 2000 to 2016.

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The solution to the system of inequalities is:

x ≥ -3.8 and

x ≤ 3

This can also be expressed as

-3.8 ≤ x ≤ 3

solving the first inequality:

-2x - 3x ≤ 19

Combining like terms, we get:

-5x ≤ 19

Dividing both sides by -5 :

x ≥ -3.8

So we have found that x is greater than or equal to -3.8.

From the second inequality:

-8x ≥ -24

Dividing both sides by -8:

x ≤ 3

So we have found that x is less than or equal to 3.

Therefore, the solution to the system of inequalities is:

-3.8 ≤ x ≤ 3

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Answer:

22.86

multiple 3.54 to 9

Therefore , the solution of the given problem of expression comes out to be the simplified expression is 8n³ + 6n - 20.

There is a requirement for mathematical operations as addition, multiplication, and division. When combined, they produce the following: A mathematical operator, some data, and an expression. A statement of fact contains values, parameters, and mathematical operations including additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.

Here,

Given :

2n² + 4n + 4

    x 4n - 5

    -----------

    8n³ - 10n² + 16n² - 20n + 16n - 20

    -----------

    8n³ + 6n - 20

Thus, the simplified expression is 8n³ + 6n - 20.

Therefore , the solution of the given problem of expression comes out to be the simplified expression is 8n³ + 6n - 20.

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