Claire and Richard are both artists. Claire uses the polynomial 50x^2+250 to decide how much to charge. Richard uses the polynomial 49x^2+350 to charge how much to charge for his painting. In each polynomial x is the height of the paintings feet. To the nearest tenth what height will both Claire and Richard charge for the same amount for a painting?

The height of the painting has to be 10 feet for both Claire and Richard to charge the same amount.

Step-by-step explanation:

The polynomial expression representing the charge for Claire's paintings is:

C = 50x² + 250

The polynomial expression representing the charge for Richard's paintings is:

R = 49x² + 350

Here x represents the height of the paintings feet.

Now compute the value of x such that both Claire and Richard charge the same amount as follows:

C = R

50x² + 250 = 49x² + 350

50x² - 49x² = 350 - 250

x² = 100

x = 100

Thus, the height of the painting has to be 10 feet for both Claire and Richard to charge the same amount.

since the airplane is moving with constant speed then the distance travelled can be calculated by x=u*t

in km/h would be:

x=640*3.5=2.240 km

in m/s would be:

u=640 km/h= 640.000 m/h =640.000/ 3600 m/s =177.8 m/s

t= 3.5 h= 3.5 * 3600 s=12.600 s

then x=u*t= 177.8*12.600= 2.240.280 m

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form