8. Evaluate the following expression for the given value.
-3x^2-4x+4 for x=-2
A) 0



B) 4



C) 12



D) 20

Answer:

a reflection of the line segment across the line y = –x

Step-by-step explanation:

Reflecting across the line y = -x switches the x- and y-coordinates and negates both.  This will map

(-1, 4)→(4, -1)→(-4, 1) and

(4, 1)→(1, 4)→(-1, -4)

The reflection that produces an image with endpoints at (–4, 1) and (–1, –4) is a reflection of the line segment across the line y = -x.

Option D is the correct answer.

There are two ways of translation.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

The reflection of a point over the x-axis involves changing the sign of its

y-coordinate while leaving the x-coordinate unchanged.

The reflection of a point over the y-axis involves changing the sign of its

x-coordinate, while leaving the y-coordinate unchanged.

The reflection of a point over the line y = x involves swapping its x and y-coordinates.

The reflection of a point over the line y = -x involves swapping the sign of its x and y-coordinates.

To find the reflection that produces an image with endpoints at (–4, 1) and (–1, –4), we need to reflect the original line segment across a line that produces an image with the same length and orientation as the given endpoints.

One way to do this is to plot the points and draw the line segment, then draw the candidate lines of reflection and see which one produces the desired image.

Another way is to compute the midpoint of the original line segment and see which reflection takes that midpoint to the midpoint of the desired image.

Using the second method, the midpoint of the original line segment is:

= ((–1 + 4) / 2, (4 + 1) / 2)

= (1.5, 2.5)

The midpoint of the desired image is:

= ((–4 + –1) / 2, (1 + –4) / 2)

= (-2.5, -1.5)

To find the reflection that takes (1.5, 2.5) to (-2.5, -1.5), we can see that this is the reflection across the line y = -x.

Therefore,

The reflection that produces an image with endpoints at (–4, 1) and (–1, –4) is a reflection of the line segment across the line y = -x.

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Elvira spend $83 on the fifth order to keep the average within her budget.

What is Average mean?

The average mean of numbers is calculated by dividing the sum of all numbers by the total number of terms.

Given that;

Elvira finds that she has order veggie burgers four times and paid $78, $72, $87, and $90 on the orders.

And, To stay within budget, she needs to be sure her average order of veggie burgers is not more than $82.

Now, Let the fifth order to keep the average within her budget = $x

Then, By the definition of average mean we get;

= 78 + 72 + 87 + 90 + x / 5 = 82

= 327 + x = 82 × 5

= 327 + x = 410

= x = 410 - 327

= x = 83

Thus, Elvira spend $83 on the fifth order to keep the average within her budget.

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The value of x in the given equation 1/5x-2/3 y = 30 when y = 15 is given by option D. x = 200.

To find the value of x in the equation 1/5x - 2/3y = 30 when y = 15,

substitute the value of y into the equation and then solve for x.

Equation is 1/5x - 2/3y = 30

Substitute y = 15:

1/5x - 2/3(15) = 30

Now, calculate the value of 2/3(15):

2/3 × 15 = 30/3 = 10

Now, the equation becomes:

1/5x - 10 = 30

To isolate the term with x, add 10 to both sides of the equation:

1/5x = 30 + 10

1/5x = 40

Finally, to find x, multiply both sides by 5:

x = 40 × 5

x = 200

Therefore, the value of x in the equation when y = 15 is  option D. x = 200.

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Answer:

The answer would be (D) 77 coins :)

Step-by-step explanation:

the correct graph is bottom left

 the one that the 2 lines cross each other

The two lines 4x + 5y = 10 and 5x - 4y = 28 are perpendicular to each other as they have slopes that are negative reciprocals of each other.

The slope is generally defined as the rate of change of the y-axis with respect to the x-axis.

We know we can determine if two lines are parallel or perpendicular to each other by their slope.

If they are parallel they will have the same slope and if they are perpendicular they will have slopes that are negative reciprocals of each other.

Given are two lines 4x + 5y = 10 and 5x - 4y = 28.

We know the equation of a line is y = mx + b.

∴ 4x + 5y = 10 can be written as 5y = -4x + 10 Or y = -(4/5)x + 5/2.

And 5x - 4y = 28 can be written as -4y = -5x + 28 Or y = (5/4)x - 7.

Thus we can conclude that these two lines are perpendicular to each other as (-4/5) is the negative reciprocal of (5/4).

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The student's question seems to be about algebraic operations with an unclear equation, but the provided example with y = 9 + 3x demonstrates how to create a table and graph of a linear equation with a slope of 3 and y-intercept of 9.

The student's question involves performing the indicated operations with algebraic expressions that include variables and fractions. The expressions mentioned resemble an equation that could potentially be simplified or solved, but the question as written contains typos and lacks clear structure. Consequently, to provide an accurate answer, we would need the correct and complete version of the equation.

However, in similar problems, one would typically combine like terms, find a common denominator for fractions, and simplify the equation to solve for the variable. For the equation y = 9 + 3x, to create a table of values, one can choose different values of x, substitute them into the equation, and calculate the corresponding y values. Then, plotting these points on a graph would show the linear relationship represented by the equation with a slope (m) of 3 and a y-intercept (b) of 9.

The equation that represents a line perpendicular to line g is Y= 7/4x (option D).

A line that is perpendicular to line g will have a slope that is the negative reciprocal of -4/7. The negative reciprocal of a slope is found by flipping the fraction and changing the sign. The negative reciprocal of -4/7 is 7/4. Therefore, the equation that represents a line perpendicular to line g is Y= 7/4x (option D).

The rate of mr Rodriguez to complete 1 job is 1/3 while that of his assistant is 1/4.5.

So if mr Rodriguez works for 1 hour, the job left would be 2/3 of the job. So the total time needed by assistant is:

(2/3) / (1/4.5) = 3 hours

Answer:

3 hours

Answer:

Option: b is the answer.

( f(x)=(x-a)^2(x-b)^4 )

Step-by-step explanation:

Clearly from the graph of the function we could see that zero is not a root of the polynomial function hence option (a) ( f(x)=x(x-a)^3(x-b)^3 ) and option (c) (  f(x)=x(x-a)^6(x-b)^2 )are discarded.

Now we will check for option (b) and option (d)

As the graph touches the x-axis at two point i.e. a and b that means that both the roots of the polynomial equation are of even degree.

Hence, the correct option is:

option: b ( f(x)=(x-a)^2(x-b)^4 ).

It can be deduced that the option that represents the graph is B. f(x)=(x-a)²(x-b)⁴

From the graph, a and b be real numbers where a=b=0. In this case, zero is not a root of the polynomial function

When the graph touches the x-axis at two point l, it implies that means that both the roots of the polynomial equation are of even degree.

In conclusion, the correct option is B.

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The result of the expression 15 + 17 - 100 + 1000 + (-132) x 0 is 932.

Multiplication first according to the order of operations (PEMDAS/BODMAS):

(-132) x 0 = 0

Now, substitute the result back into the equation:

15 + 17 - 100 + 1000 + 0

Next, perform the addition and subtraction from left to right:

15 + 17 = 32

32 - 100 = -68

-68 + 1000 = 932

So, the final answer is 932.

Final answer:

The length of the room is calculated by dividing the area of 271.25 square feet by its width of 15.5 feet, resulting in a length of 17.5 feet.

Explanation:

To find the length of the room given its area and width, we will divide the area by the width. The formula for finding the area of a rectangle is Area = length × width. So, to find the length, we can rearrange this formula as length = Area ÷ width, which means dividing the given area by the width.

We know the area of the room is 271.25 square feet and the width is 15.5 feet. So the calculation for the length will be:

Length = 271.25 sq ft ÷ 15.5 ft

Length = 17.5 ft

Therefore, the length of the room is 17.5 feet.

width=m

length=5m

Area= l x w

Area=5m x m

Area=5m^2

(^ the exponent or power)