PLEASE HELP NEED URGENTLY

Graph the equation y = x2 + 8x + 12 on the accompanying set of axes. You must

UkoKoshka [18]

Answer:

Step-by-step explanation:

Roots: set y = x^2 + 8x + 12 = 0 and solve for x: x + 6 = 0, so x = -6 is one root. The other is x = -2. The corresponding points are (-6, 0) and (-2, 0).

y-intercept: Let x = 0. Then y = 12. The y-intercept is (0, 12).

Axis of symmetry: x = -b / (2a) => x = -8/(2*1) = -4: x = -4

Vertex y-value: evaluate y at x = - 4: (-4)^2 + 8(-4) + 12 = -4: (-4, -4)

Arbitrarily chosen x value: x = 1 => 1^2 + 8(1) + 12 = 21: (1, 21)

The five points are: (-6, 0) and (-2, 0), (0, 12), (-4, -4), (1, 21). The vertex is (-4, -4). The parabolic graph opens UP.

8 0

3 years ago

Can anyone help with my geometry work ?

sasho [114]

Answer:

what should we do ,...?

Step-by-step explanation:

please write your questions!

6 0

3 years ago

(3c to the 5th power d 1/2)3

Alik [6]

To simplify the expression it would be $\frac{27c15d3}{8}$

5 0

3 years ago

The boxplot below shows salaries for CPAs and Actuaries in a town. 30 40 50 60 70 80 90 100 Salary (thousands of $) Actuary CPA

MA_775_DIABLO [31]

Answer: 75%

Step-by-step explanation:

In order to answer this question, we have to know the meaning of a box plot. Boxplots are especially useful in statistical analysis and gives us a meaningful range of values. A box plot consists of 2 shapes, which are the box part and the extended lines. The short sides of the box and the vertical line in the middle of the box represent a certain percentage of the values. The vertical line in the boxplot is the median of your dataset. For example, according to the shape given in the question, the median value for CPA's is 50 and this is closer to the left side of the box. This means that the first half ogf the dataset (when ranked from the smallest to the greatest) is closer to each other. The sides of the box represent the values at the 25% and 75% of the values respectfully.

For example, if we have 100 values, we rank them in order and the 25th value corresponds to the left side of the boxplot (named first quartile), 50th value (which is also the median) corresponds the vertical line in the box and and the 75the value corresponds to the right side of the box (named third quartile).

The extended arms are calculated as accordingly: IQR=(3rd quartile value-1st quartile value). Left extended arm is first quartile-1.5*IQR and right extended arm is third quartile+1.5*IQR. However, this information is not directly related to this question.

Now, this question should seem simpler. The median salary of CPA is 50 and this is equal to left side of the Actuary boxplot, which corresponds to the 25% of actuaries. As a result, CPA median salary is less than 75% of the Actuaries (100%-25%).

3 0

3 years ago

A rectangle is twice as long as it is wide and has the same perimeter as a square whose area is 36 square feet larger than that

Korvikt [17]

Answer:

rectangle: 12 ft × 24 ft
square: 18 ft square

Step-by-step explanation:

You want the dimensions of a rectangle and square such that they have the same perimeter, but the square has an area of 36 more square feet. The rectangle is twice as long as wide.

<h3>Setup</h3>

Let x represent the side length of the square. Then its area is x², and the area of the rectangle is (x² -36).

This area is the product of length and width. The expression factors as ...

rectangle area = x² -36 = (x +6)(x -6)

<h3>Solution</h3>

If we assume these factors are the dimensions of the rectangle, then the longer dimension is twice the shorter one:

(x +6) = 2(x -6)

18 = x . . . . . . . . . add 12-x to both sides

This is the side length of the square. The rectangle dimensions are ...

x+6 = 18+6 = 24 . . . . feet long

x -6 = 18 -6 = 12 . . . . feet wide

The rectangle is 12 feet wide and 24 feet long. The square is 18 feet on a side.

__

<em>Additional comment</em>

The perimeter in each case is 4x = 2((x+6) +(x -6)) = 72 ft.

The area of the rectangle is (12 ft)(24 ft) = 288 ft². The area of the square is (18 ft)² = 324 ft², a value that is 36 ft² more than the rectangle area.

<em>Alternate solution</em>

Using x for the width of the rectangle, the length is 2x and its area is x(2x) = 2x². The perimeter is 2(x +2x) = 6x, so the side length of the square is (6x)/4 = 3/2x and its area is (3/2x)² = 9/4x².

The difference is 36 square feet, so we have ...

9/4x² -2x² = 36 = x²/4 ⇒ x = √(36·4) = 6·2 = 12 . . . . width of rectangle

8 0

1 year ago