What transformation is described by the notation (x, y) to (x, -y)?

If using the method of completing the square to solve the quadratic equation x2 + 3x - 17 = 0, which number would have to be add

MatroZZZ [7]

Answer:

Step-by-step explanation:

To solve using completing square, we need to write the equation as x2+3x=17.

The next step is to add a number such that the square can be completed. The number must be equal to (b/2a)^2, so here it will be (3/2)^2 = 9/4

The equation then becomes x2+3x+(9/4)=17+(9/4).

Solving it further will get you the final answer

8 0

2 years ago

Please help with this one question that I've been stuck on!!! In a random sample of 74 homeowners in a city, 22 homeowners said

Arturiano [62]

Anders Celsius (Swedish pronunciation: [ˌanːdəʂ ˈsɛlːsiɵs], 27 November 1701 – 25 April 1744) was a Swedish astronomer, physicist and mathematician. He was professor of astronomy at Uppsala University from 1730 to 1744, but traveled from 1732 to 1735 visiting notable observatories in Germany, Italy and France. He founded the Uppsala Astronomical Observatory in 1741, and in 1742 proposed (an inverted form of) the Centigrade temperature scale which was later renamed Celsius in his honor.

Romeo and Juliet is a tragedy written by William Shakespeare early in his career about two young Italian star-crossed lovers whose deaths ultimately reconcile their feuding families. It was among Shakespeare's most popular plays during his lifetime and, along with Hamlet, is one of his most frequently performed plays.

6 0

3 years ago

Suppose the radius of a circle is 3 units what is the circumference

HACTEHA [7]

Answer:

$6\pi$ or approximately $18.85$ units

Step-by-step explanation:

The formula for finding the circumference of a circle is $C=2\pi r$ , where $C$ = circumference and $r$ = radius. In this case, $r=3$ , so after plugging that into $C=2\pi r$ , we get:

$C=2\pi r\\ = 2*\pi *3\\=6\pi$

Since $\pi$ is approximately $3.1415$ , $6\pi =6*3.1415=18.849$ , which rounds to $18.85$ . Therefore, the circumference of the circle is $6\pi$ , or approximately $18.85$ units. Hope this helps!

8 0

3 years ago

Which statement is true?

natka813 [3]

Every square is a rectangle because it is a quadrilateral with all four angles right angles.

7 0

3 years ago

This is due today i would appreciate it a lot if smn could help me with it :/

Vesnalui [34]

Answer:

Conclusion:

The rate of change of function 1 = 3

The rate of change of function 2 = 5/3

Hence, function 1 has a greater rate of change

The initial Value of function 1 = y = 2

The initial Value of function 2 = y = 3

Hence, function 2 has a greater initial value.

Step-by-step explanation:

Function 1)

Determining rate of change for function 1:

x 1 2 3 4

y 5 8 11 14

Finding the rate of change or slope using the formula

Rate of change = m = [y₂-y₁] / [x₂-x₁]

Taking any two points, let say (1, 5) and (2, 8)

Rate of change = m = [8-5] / [2-1]

= 3/1

= 3

Therefor, the rate of change of function 1 = m = 3

using point-slope form to determine the function equation

y-y₁ = m (x-x₁)

where m is the rate of change or slope

substititng m = 3 and the point (1, 5)

y - 5 = 3(x - 1)

y - 5 = 3x-3

y = 3x-3+5

y = 3x + 2

Thus, equation of function 1 will be:

y = 3x + 2

Determining Initial Value for Function 1:

substituting x = 0 in the equation to determine the initial value

y = 3(0)+2

y = 0+2

y = 2

Therefore, the initial Value of function 1 will be: y = 2

Function 2)

Determining the rate of change for function 2:

Given the function 2

$y\:=\:\frac{5}{3}x+3$

comparing with the slope-intercept form of a linear function

y = mx+b where m is the rate of change

so the rate of change of function 2 = m = 5/3

Determining Initial Value for Function 2:

substituting x = 0 in the equation to determine the initial value

$y\:=\:\frac{5}{3}x+3$

$y\:=\:\frac{5}{3}\left(0\right)+3$

$y = 0+3$

$y = 3$

Therefore, the initial Value of function 2 will be: y = 3

Conclusion:

The rate of change of function 1 = 3

The rate of change of function 2 = 5/3

Hence, function 1 has a greater rate of change

The initial Value of function 1 = y = 2

The initial Value of function 2 = y = 3

Hence, function 2 has a greater initial value.

8 0

3 years ago