Explain how you can determine that the following
system has one unique solution – without actually
solving the system.

2x+y = 4
2y = 6- 2x

The polygon ABCD is transformed 4 units to the left after being reflected across the x-axis.

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

Reflect the polygon ABCD across the x-axis as;

A(x, y) → A'(x, -y) (x, -y) (x, -y)

According to this rule, A's coordinates are

A(1, -5) →  A'(1, 5) (1, 5) (1, 5)

ABCD is shifted 4 units further to the left.

Now apply to the translation:

A"(x - 4, y) = A'(x, y) (x - 4, y)

A'(1, 5) → A"(1 - 4, 5) (1 - 4, 5) (1 - 4, 5)

→ A"(-3, 5) (-3, 5) (-3, 5)

Thus Polygon ABCD will eventually overlap Polygon A'B'C'D' through a series of transformations.

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Answer:

2x-8>x+9

Step-by-step explanation:

8 less than 2 times a number is greater than the sum of the same number and 9.

the last option is the correct choice

Answer:

An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.

To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.

Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is

20,18,16,14,12

In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.

Answer:

yes

Step-by-step explanation:

if you subtract 4 from both sides then m < -14

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x=5/2

Decimal Form:

x=2.5

Mixed Number Form:

x=2 1/2

Step-by-step explanation:

The number of hours that James have to work each week will be 25 hours.

The word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge.

In this case, James has a job moving lawns during the summer. Suppose the formula for calculating the number of hours he will have to work each week is five times the difference of thirty-eight and three times the difference of fifteen and four hours.

The number of hours that James have to work each week will be:

= 5(38) - 3(15 - 4)

= 5(38) - 3(11)

= 5(38 - 33)

= 5 × 5

= 25 hours

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Answer:

1320x^2y−4224x^2−3165xy+10128x+375y−1200

Step-by-step explanation:

(8x−1)(11x−25)(15y−48)

=((8x−1)(11x−25))(15y+−48)

=((8x−1)(11x−25))(15y)+((8x−1)(11x−25))(−48)

=1320x2y−3165xy+375y−4224x2+10128x−1200

=1320x^2y−4224x^2−3165xy+10128x+375y−1200

Answer:

x = 3 (I think)

Step-by-step explanation:

14x - 13 = 8x + 5 (I'm assuming the two expressions are equal)

6x - 13 = 5

6x = 18

x = 3

The simplified value of x from the equation is x = 3

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

( 14x - 13 ) = ( 8x + 5 )

Subtracting 8x on both sides , we get

( 14x - 8x ) - 13 = 5

6x - 13 = 5

Adding 13 on both sides , we get

6x = 18

Divide by 6 on both sides , we get

x = 18/6

x = 3

Hence , the equation is solved and x = 3

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Answer: what unit is this?

Step-by-step explanation:yeah I’ll need the unit to solve this question

Answer:

the solution to the system of equations is (x, y) = (3, -2).

Step-by-step explanation:

y = -2x + 4 (Equation 1)

y = x - 5 (Equation 2)

To solve for x, we can equate the right sides of the equations:

-2x + 4 = x - 5

Now, we can solve for x:

-2x - x = -5 - 4

-3x = -9

x = (-9) / (-3)

x = 3

Substituting the value of x back into Equation 2, we can solve for y:

y = 3 - 5

y = -2

7 x² + 7 y² - 28 x + 42 y - 35 = 0 /: 7

x² + y² - 4 x + 6 y - 5 = 0

( x² - 4 x + 4 ) + ( y² + 6 y + 9 ) - 4 - 9 - 5 = 0

The equation in the standard form is:

( x - 2 )² + ( y + 3 )² = 18

The center is at the point ( 2, - 3 ).

Its radius is: √18 = 3√2 units.

Answer:

A. (x - 2)^2 + (y + 3)^2 = 18.

B. (2, -3)

C. 3(2^(1/2))

Step-by-step explanation:

The equation of this circle in standard form is (x - 2)^2 + (y + 3)^2 = 18. The center of the circle is at the point (2, -3), and its radius is 3(2^(1/2)) units.

Answer:                                                                                                                there are 200 nickels in 1 kilogram of nickels

Step-by-step explanation:

For this case we must take into account the following conversion:

1Kg = 1000 g

Therefore, we can make the following rule of three:

5 grams ---------> 1 nickel

1000 grams ----> x

Clearing x we have:

x = (1000/5) * (1)

x = 200 nickels

Step-by-step explanation:

We can use the proportion. We already know

that Dixon is 6 ft tall and that his shadow is 9

ft long. Also we know that the shadow of his

sister is 6 ft long. 6: x = 9:6, or 6 / x=9/6.

After that we will cross multiply : 9 * x = 6 * 6,

9 x = 36, x = 36:9, x = 4. Answer: Ariadne

is 4 feet tall.Hope I helped! :) Cheers!

Answer:

- 1/8 im pretty sure

Step-by-step explanation:

Answer:3100

Step-by-step explanation:

If 3.1 x 10^3 is because you count the first number and then you use what is less in the power like you have 3 and u used 1 for the number 1 so you left with 2 those 2 will be zeros 3100.

I hope this helped pls put it as brainliest

Answer: 3.1 × 103

Step-by-step explanation:

Answer:

awedawedwadddddddddddddddddddddddddddddddd

Step-by-step explanation:

awedwadawaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Answer:

29

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

..........................

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.

Elimination of the parameter means to rewrite the equations in terms of only x and y. To do this, substitute t from one equation into the other equation. Here, the two equations are:x = t1/3 and y = t – 4Substitute t from the first equation into the second equation:y = (x^3) – 4Now the equation is in terms of x and y only.

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.The rectangular equation, y = (x^3) – 4 can be plotted on a graph. It is a cubic equation. The graph will look like a curve that passes through the point (0, -4) and continues to move towards infinity. The graph will be symmetric to the origin because the equation involves an odd power of x.

If the equation involved an even power of x, the graph would be symmetric to the y-axis. The graph will never touch the x-axis or y-axis, it will only approach them.In conclusion, the rectangular equation y = (x^3) – 4 is derived from the two parameter equations, x = t1/3 and y = t – 4. The graph of this equation is a cubic curve that is symmetric to the origin. The curve passes through (0, -4) and approaches the x and y-axes but never touches them.

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The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

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The equation of a quadratic function P with rational coefficients that have a zero of 3 + 7i is; P(x) = x² - 6x + 58

We are given one of the zero of the quadratic function as 3 + 7i.

The given zero of the function is a complex number and we know that when dealing with complex numbers, if the zero of the function is of the form a + bi then we can deduce that the other zero of the function will be a - bi.

This means that the other zero of our function is 3 - 7i.

Thus, the factors of the quadratic function are;

(x - (3 + 7i)) and (x - (3 - 7i))

Thus, the equation of the quadratic function is;

P(x) = (x - (3 + 7i)) × (x - (3 - 7i))

We know that i² = -1

Thus, our equation is;

P(x) = x² - 6x + 58

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To solve this, we can follow the next steps:

Then, the result of the expression is 16.

Answer:

the answer is d

Step-by-step explanation:

Answer:

20 ft

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

The main limiting issue with the domain this function is potentially picking an x-value that makes that denominator equal 0, because dividing by 0 is bad.

So, the domain will be all real numbers, except for those that make g(x)=0.

g(-1) = 0, g(-2)=0, and g(2) = 0, so -1, -2, and 2 must be excluded from the domain.

Your answer is {x ∈ ℝ| x ≠ −1, −2, 2}.

Answer:

\(\textsf{Domain}: \quad \{ x \in \mathbb{R}\;|\;x \neq -1, -2, 2\}\)

Step-by-step explanation:

Given functions:

\(\begin{cases} f(x)=x^2+6x+5\\g(x)=x^3+x^2-4x-4\end{cases}\)

Factor function f(x):

\(\begin{aligned}\implies f(x)&= x^2+6x+5\\&=x^2+x+5x+5\\&=x(x+1)+5(x+1)\\&=(x+5)(x+1)\end{aligned}\)

Factor function g(x):

\(\begin{aligned}\implies g(x)&=x^3+x^2-4x-4\\&=(x+1)(x^2-4)\\&=(x+1)(x+2)(x-2)\end{aligned}\)

Therefore the composite function is:

\(\implies \dfrac{f(x)}{g(x)}=\dfrac{(x+5)(x+1)}{(x+1)(x+2)(x-2)}\)

A rational function is undefined when the denominator equals zero.

Therefore, the given composite function is undefined when (x+1)(x+2)(x-2)=0:

The domain of a function is the set of all possible input values (x-values).

Therefore, as the composite function is undefined when x = -1, x = -2 and x = 2, the domain is: