Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k.

k = ______

Can you explain how to figure this out?

The expression 12x+15x-11x can be combined using the associative property of addition.

The expression 12x+15x-11x can be combined by using the associative property of addition.

Therefore, the simplified expression is 16x. The associative property of addition allows us to group the terms in any order and still get the same result.

Final answer:

The expression 12x + 15x - 11x can be simplified due to the associative property of addition, enabling terms to be grouped and combined to yield a simplified form of 16x. The correct option is not provided in the choices, but would be the associative property, not listed in the student's options.

Explanation:

The expression 12x + 15x - 11x can be simplified by combining like terms, which is possible because of the associative property of addition. This property allows us to group numbers in an addition expression in any way we choose without changing the result.

Therefore, using the associative property, we can group and combine the terms with 'x' to get (12x + 15x) - 11x, which simplifies to 27x - 11x, and then further to 16x.

The correct answer to the question is Option A: associative property of addition, though it is important to note that this option was not listed in the initial question provided. The commutative property allows us to change the order of the terms without changing the result, but does not directly apply to the combination of like terms.

Nevertheless, both the associative and commutative properties are used when combining like terms in algebra.

the answer to this question is 19!

Final answer:

In the context of congruent polygons, side EF of polygon CDEF is congruent to side PQ of polygon MNPQ due to the corresponding order of sides in congruent figures.

Explanation:

The question refers to congruent figures in geometry, specifically congruent polygons. If polygons are congruent, all corresponding sides and angles are congruent as well. Therefore, if CDEF ≅ MNPQ, then side EF must be congruent to the side of polygon MNPQ that corresponds to EF in the order of letters given. Following the order, side EF corresponds to side PQ.

Answer:  About 2 times.

Step-by-step explanation:

Given : In 2010, the national debt of the United States was about 14 trillion dollars.

We know that 1 trillion [tex]=1,000,000,000,000= 10^{12}[/tex]

then, In 2010, the national debt of the United States was about [tex]14\times10^{12}[/tex]

dollars.

In 2003 it was about [tex]7\times10^{12}[/tex] dollars.

Now, the number of times the national debt was larger in 2010 than 2003 :-

[tex]\dfrac{ 14\times10^{12}}{7\times10^{12}}\\\\=\dfrac{14}{7}\times10^{12-12}\\\\=2\times10^0=2[/tex]

Hence, national debt was about 2 times larger in 2010 than 2003 .

Answer: 15x3y

Step-by-step explanation:

We rewrite the expressions by using factorisation method of their primes. This will give:

60x4y7= 2×2×3×5×x×x3×y×y6

45x5y5= 3×3×5×x×x4×y×y4

75x3y= 3×5×5×x×x2×y

Common factors= 3 × 5 × x3 × y

= 15x3y

Answer:

its B

Step-by-step explanation:

The value of variable y in y - 3.5 = -2.1 is 1.4 .

Given , equation : y-3.5=-2.1

To get the value of y isolate the variable y.

y - 3.5 = -2.1

Combine like terms,

Take -3.5 from LHS to RHS . The sign will be changed from negative to positive.

y = 3.5 - 2.1

y = 1.4

Therefore the value of y that will satisfy the equation is 1.4 .

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x = total number of students

equation is:

 (3/4)x = 1464

 to solve for x divide both sides by 3/4

x = 1464 / 3/4 = 1952

 x = 1952

 there are 1952 total students

To solve the inequality -3 < 2x + 1 < 7 for the number x, subtract 1 from all parts and then divide by 2. The solution is the range of numbers greater than -2 and less than 3.

The problem statement here results in an inequality that can be expressed algebraically. If 'x' represents the unknown number, we can write the inequality as -3 < 2x + 1 < 7.

To solve for 'x', we will isolate the variable on one side by following the rules of inequalities similar to solving equations.

First, subtract 1 from all parts of the inequality to get the pure inequality without a constant.

-4 < 2x < 6

Now, divide all parts of the inequality by 2, which yields:

-2 < x < 3

All numbers greater than -2 and less than 3 satisfy the original problem statement. Therefore, the range of numbers that solve the inequality is from -2 to just below 3.

Answer:

$7,632 would have been contributed to the 401(k) plan after 2 years.

Step-by-step explanation:

A technical writer makes salary per year = $45,000

She contributing 8% of her salary to her 401(k) plan = 8% of 45,000

0.08 × 45,000 = $3,600

Her employer matches 6% of her contributions = 6% of 3,600

= 0.06 × 3,600 = $216.00

Total contribution for one year = 3,600 + 216.00 = $3,816

After 2 years = 3,816 × 2 = $7,632.00

$7,632 would have been contributed to the 401(k) plan after 2 years.

x = hours 25 per hour = 25x

y = total

 so y = 25x +140

Answer: y = 140+25x

Step-by-step explanation:

Since According to the question, Luigi initally charged $140.

And, per hour he charged an additional amount $25 for each contract with the city.

Here, x represents the number of hours worked on a project.

Thus the additional amount after x hours = 25x

So, the total amount he charged in x hours= 140+ 25x

And, according to the question y represents the above change.

Thus, we get a function for the given situtaion

which is , y= 140+ 25x , where x is number of hours and y is total amount charged.

Answer:

The equation can be used to determine the total number of guests is 13.50g + 540 = 1512  and the total number of guest are 72 .

Step-by-step explanation:

As given

Mrs. Howard is hosting a catered dinner party to celebrate her daughter's graduation.

The catering company she plans to use charges $13.50 per plate of food and an additional fee of $540 to cover linens and tableware.

The total bill for the catering services is $1,512.

Total number of guests, g .

Than the equation becomes

1512 = 540 + 13.50 g

1512 - 540 = 13.50 g

972 = 13.50 g

[tex]g = \frac{972}{13.50}[/tex]

g = 72

Therefore the equation can be used to determine the total number of guests is 13.50g + 540 = 1512  and the total number of guest are 72 .

The expression so it forms a perfect square trinomial is 14x.

We have given that,

The expression so it forms a perfect-square trinomial.

We have to determine the  x² +___ x + 49.

A divisor of an integer n also called a factor of n, is an integer m that may be multiplied by some integer to produce n.

In this case, one also says that n is a multiple of m.

(x + 7)(x + 7)

x^2 + 14x + 49

The expression so it forms a perfect square trinomial is 14x.

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Answer:

a.

Step-by-step explanation:

|x+2|>16

x+2>16 or x+2<-16

So, tecnically a and b are incorrect, but if you change the "and" to "or" the correct would be a.

Final answer:

Using the law of detachment, if it is sunny on Tuesday and there is a habit of going outside in nice weather, one can conclude that they will go outside on Tuesday.

Explanation:

The law of detachment is a concept in logic used to form conclusions given a conditional statement and its hypothesis being true. For instance, in the scenario provided:

If it is sunny on Tuesday (hypothesis).

I will always go outside if the weather is nice (conditional statement).

By applying the law of detachment, we can conclude that:

I will go outside on Tuesday (conclusion).

This logical reasoning assumes that a 'nice' weather includes a sunny day. Hence, if it is indeed sunny on Tuesday, the condition for going outside is met.

No plane contains these points, as we can see on the image, point J does not belong to any of the shown planes.

A plane contains a point if the point lies on the plane. For example, here you can see that plane X contains the points K and N.

But, if you look at the image, no plane contains the point J, then there is no plane that contains the 3 points J, K, and N, so the correct option is 0.

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Answer:

3 blocks due west

Step-by-step explanation:

The solution to the system of equations  are (1, 3) and (-5, -3)

Given the following functions

Y=x^2+5x-3

Y-x=2; y = x + 2

Equating both outputs will give

x^2+5x-3 = x + 2

x^2+5x-3 - x - 2 = 0

x^2 + 4x - 5 = 0

Factorize the equation

x^2 + 5x - x - 5=0

x(x+5) - 1(x+5) = 0

(x-1)(x+5) = 0

x = 1 and -5

Recall that y = x + 2

y = 3 and -3

Hence the solution to the system of equations  are (1, 3) and (-5, -3)

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The solution to a linear quadratic system of equations can be found by substitifying one equation into the other and solving. In this case, the solutions are (1,3) and (-5,-3).

To find the solution of a linear quadratic system of equations, you need to substitute one equation into the other. In this case, for the equations [tex]Y = x^2 + 5x - 3[/tex] and [tex]Y - x = 2[/tex], you would first isolate Y in the linear equation, resulting in [tex]Y = x+2.[/tex]

Then, you substitute (x + 2) for Y in the quadratic equation, leading to [tex]x + 2 = x^2 + 5x - 3.[/tex]

Next, rearrange the equation to get it in the standard quadratic form: 0 = [tex]x^2 + 5x - x - 3 - 2.[/tex] Simplifying this results in the equation [tex]0 = x^2 + 4x - 5.[/tex]

Finally, solve this equation by factoring or using quadratic formula, which gives the solutions as x = 1, -5. Substituting both 1 and -5 into the equation Y = x + 2 gives the corresponding y-values, Y = 3 and -3. Therefore, the solutions to the system of equations are (1,3) and (-5,-3).

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