Y-3x=-4<br> 2x+y=11<br> Solve each system of equations by using a table

find the coordinates of the vertex of the following parabola algebraically. write your answer as an (x,y) point..y=x²+9

Alexandra [31]

Explanation:

using the parabola formula:

y = a(x-h)² + k²

vertex = (h, k)

We are given a parebola equation of: y = x²+9

comparing both equations to get the vertex:

y = y

a = 1

(x-h)² = x²

x² = (x + 0)²

(x-h)² = (x + 0)²

h = 0

+k = +9

k = 9

The vertex of the parabola as (x, y): (0, 9)

3 0

1 year ago

Solve ln 2 + ln x = 5. Round to the nearest thousandth, if possible.

azamat

Answer:

The value of x nearest to thousandths is, 74.207

Step-by-step explanation:

Solve : $\ln 2 + \ln x = 5$

$\ln$ represents the logarithmic function with base e.

Using logarithmic properties:

$\ln (mn) = \ln m + \ln n$

$\ln x = a$ , then $x = e^a$

$\ln 2 + \ln x = 5$

Apply the logarithmic properties; we have

$\ln 2x = 5$

then;

$2x = e^5$

or

$2x=148.41315910258$

Divide both sides by 2 we get;

$x = 74.2065796$

Therefore, the value of x nearest to thousandths is, 74.207

3 0

2 years ago

(I|HEEEEELP)At the city museum, child admission is

lapo4ka [179]

LIKE 15.SOMETHING IDK M8 SORRY

5 0

3 years ago

The plan for the Thorne’s backyard play area, shaped like a trapezoid, is shown. The area of the play area is 286.56 square feet

lorasvet [3.4K]

The length of material needed for the border is the perimeter of the backyard play area

<h3>How to calculate the length of material needed </h3>

The area of the play area is given as:

$Area = 286.56$

The area of a trapezoid is calculated using:

$Area = 0.5 * (L1 + L2) * H$

Where L1 and L2, are the parallel sides of the trapezoid and H represents the height.

The given parameter is not enough to solve the length of material needed.

So, we make use of the following assumed values.

Assume that the parallel sides are: 25 feet and 31 feet long, respectively.

While the other sides are 10.2 feet and 8.2 feet

The length of material needed would be the sum of the above lengths.

So, we have:

$Length = 25 + 31 + 10.2 + 8.2$

$Length = 74.4$

Using the assumed values, the length of material needed for the border is 74.4 feet

Y-3x=-4 2x+y=11 Solve each system of equations by using a table