Answer:
x = 8 y = 8
Step-by-step explanation:
Multiply 2nd equation by -3 to get -6x - 3y = -72
Now 4x + 3y = 56
<u>-6x - 3y = -72</u>
-2x = -16
x = 8
Substitute x = 8 into the 2nd equation
2(8) + y = 24
16 + y = 24
y = 8
Check: Substitute the values into the 1st equation
4(8) + 3(8) = 32 + 24 = 56 So we have the correct values for x and y
The total cost would be 2.14 cents
Step-by-step explanation:
8)
describe y in terms of x
y=5+x
so now replace y with terms of x
5+x+3x=37
4x=32
x=8
y=13
9)
do the same here
x=y+1
2y+x=19
2y+y+1=19
3y=18
x=6
y=7
Answer:
Step-by-step explanation:
Whether we divide using long division or using synthetic division, the rule is the same: If, after division, there is no remainder (i. e., the remainder is zero), the divisor binomial is a factor or the associated root is indeed a root/zero/solution.
Divide 5x³+8x²-7x-6 by (x+2) using synthetic division. Use the divisor -2 (which comes from letting x+2 = 0):
--------------------------
-2 / 5 8 -7 -6
-10 4 6
------------------------------
5 -2 -3 0 Since the remainder here is 0, we know that
-2 is a root of 5x³+8x²-7x-6 and that (x+2) is
a factor of 5x³+8x²-7x-6.
Now check out the possibility that (x+1) is a factor of 5x^3 + 8x^2 - 7x - 6:
Use -1 as the divisor in synthetic division:
--------------------------
-1 / 5 8 -7 -6
-5 -3 10
------------------------------
5 3 -10 4
Since there is a non-zero remainder (4), we can conclude that (x + 1) is NOT a factor of the given polynomial expression.
Answer:
The volume of water in the vase is 
Step-by-step explanation:
A cylinder vase has a height, h, of 10 inches and its diameter of 3 inches. This means that its radius, r, is:
r = 3 / 2 = 1.5 inches
To find the volume of the water in the vase if the water raises to 9/10 of the way to the top, we first have to find the volume of the vase when it is filled with water and then, find 9/10 of that volume.
The volume of a cylinder is given as:
The volume of the vase will be:
Hence, the volume of the water in the vase when it is 9/10 filled is:
Approximating to the nearest cubic inch, the volume of water in the vase is
