The answer is 12>x>-7
Step-by-step explanation:
it's first divided into 2 parts
1 . 15 > 2x - 9
2. 2x - 9 > -23
Then solve them individually.
let's do it,
<u>First half</u>
15 > 2x - 9
15+9 > 2x
24 > 2x
24/2 > x
12>x
<u>Second half</u>
2x-9>-23
2x>-23+9
2x>-14
x>-14/2
x>-7
<u>Joining of the two halves</u>
We have :
12>x>-7
Answer:
B
Step-by-step explanation:
For answer A it is stretching the graph of function f by a factor of 15.
For answer C and D it is changing the function itself and that is not what the question is asking.
(5,12,13) is a right triangle and can be constructed.
All the others do not satisfy the triangle inequality, i.e. the sum of two short sides must exceed the long side in order for the triangle to be constructed.
Examples:
2+11<15, so no
3+7<11, so no
4+8<15, so no
but 5+12>13 so yes, it can be constructed.
Find the area of the top, which is a circle.
Area of a circle = pi x r^2
Area = 3.14 x 1.5^2 = 7.065
Now for the volume multiply the area of the top by the height:
7.065 x 12 = 84.78 cubic inches
Round to the nearest tenth: 84.8 cubic inches
There are 5 solutions for this system.
x^2 + 4y^2 = 100 ____1
4y - x^2 = -20 ____2
Add both 1 & 2 together. x^2 gets cancelled
4y^2 + 4y = 80 (send 80 to the other side and divide by 4)
Then equation the becomes : y^2 + y -20 =0
Now factorise the equation: (y+5) (y-4) = 0
Solve for y : y = -5 and y = 4
Using the values of y to find the values of x. From equation 1:
x^2 = 100 - 4y^2 x = /100 - 4y^2 (/ means square root) Replace values of y
y = -5, x = /100 - 4(-5)^2 = /100 - 100 = 0
y = 4, x = /100 - 4(4)^2 = / 100 - 64 = /36 = -6 or 6
Thus we have 6 solutions y = -5, 4 and x = -6, 0, 6
