So x + y = 45, and 4x + 5y = 195. Get y by itself. Subtract x from both sides in the first equation to get y = 45 -x, and subtract 4x from the second equation to get 5y = 195 - 4x. Divide by 5 to both sides to get y = 39 - 4/5x. 39 - 4/5x = 45 - x. Add x to both sides to get 39 - 1/5x = 45. Subtract 39 from both sides to get -1/5x = 6. Divide by -1/5 to get x = -30, or 30. In the first equation, do 30 + y = 45. Subtract 30 from both sides to get y = 15. Check. 4(30) + 15(5) = 195, or 120 + 75 = 195.
Answer:
254 cm² (to 3 s.f.)
Step-by-step explanation:
Area of shaded region
= area of large circle -area of smaller circle

Radius of large circle= 15cm
Radius of smaller circle= 12cm
Area of shaded region
= π(15²) -π(12²)
= 225π -144π
= 81π
= 81(3.14)
= 254.34
= 254 cm² (3 s.f.)
Answer:
Step-by-step explanation:
4/12 <9/12
Answer:
(7b-8) (7b+8)
Step-by-step explanation:
49b^2 – 64
This is the difference of squares
(a^2 -c^2) = (a-c) (a+c)
a^2 = 49b^2 so a = 7b
c^2 = 64 so c = 8
(49b^2 -64) = (7b-8) (7b+8)
Answer:

Step-by-step explanation:
This is asking you to write the equation in <em>slope-intercept</em> form:

where:
- m is the slope
- b is the y-intercept
- x and y are any corresponding coordinate points (x,y)
You need to find the slope of the two given points using:

Insert the values:

The slope of the given line is -1. Insert this value into the equation:

Now insert one of the given coordinate points as x and y to solve for b:

The y-intercept is 9. Insert the value:

:Done