Steve is creating a web page. He starts with a font of 5 9/10 points and decreases it by 1/2. He decreases it again by 6/10 points. Steve then realizes that the font is to small to read easily and increases it by 1 4/5 points. Which is the best estimate of the font's final size?

6 3/5 points

Step-by-step explanation:

Steve is creating a web page.

Step 1

He starts with a font of 5 9/10 points and decreases it by 1/2.

Hence: Current font

= 5 9/10 - 1/2

= 5 + ( 9/10 - 1/2)

Lowest common denominator

= 10

= 5 + (9 - 5/10)

= 5 + 4/10

= 5 + 2/5

= 5 2/5 points

Step 2

He decreases it again by 6/10 points.

Current fonts

= 5 2/5 - 6/10

= 5 + ( 2/5 - 6/10)

Lowest common denominator

= 10

= 5 + (4 - 6/10)

= 5 + (-2/10)

= 5 - 1/5

= 4 4/5 points

Step 3

Steve then realizes that the font is to small to read easily and increases it by 1 4/5 points.

New font

= 4 4/5 points + 1 4/5 points

Lowest common denominator = 5

= 4 + 1 + (4/5 + 4/5)

= 5+ ( 4 + 4/5)

= 5 +(8/5)

= 6 3/5 points

The best estimate of the font's final size is 6 3/5 points

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

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2