9514 1404 393
Answer:
- c = 2
- segments 10, 8, 6 (top down)
Step-by-step explanation:
The sum of top and bottom bases is twice the midsegment.
(c² +6) +(c² +2) = 2(4c)
2c² -8c +8 = 0 . . . . . . . . . subtract 8c
2(c -2)² = 0 . . . . . . . . factor
c = 2 . . . . . . the value that makes the binomial be zero
The value of c is 2; the segment lengths (top-down) are 10, 8, 6.
Answer: 818.4
Step-by-step explanation:
Using the area of a sector formula, we get the area of the entire sector is 
.
Using the formula 
, we get the area of the triangle is 
.
So, the area of the shaded sector is 
Answer:
A = 58
B = 112
Step-by-step explanation:
A + B = 180 Supplementary angles
B = 2A - 24 Given
Substitute for B in the first equation
A + 2A - 24 = 180
3A - 24 = 180 Add 24 to both sides
3A = 180 + 24 Combine the right
3A = 204 Divide both sides by 3
A = 204/3
A = 68
B = 2A - 24
B = 2*68 - 24
B = 136 - 24
B = 112
Answer:
$201.99
Step-by-step explanation:
Given that:
Amount held on Monday = $61.72
Amount withdrawn on Tuesday = $57.00
Amount deposited on Thursday = $197.27
Final balance :
Amount held on Monday - Amount withdrawn on Tuesday + Amount deposited on Thursday
$61.72 - $57.00 + $197.27 = $201.99
Hence, final balance = $201.99
Answer:
The extraneous solution is 4.
Step-by-step explanation:
First, let us calculate the value of 'x' without squaring both side of the expression. This is illustrated below:
-5 = 3x - 7
Collect like terms
-5 + 7 = 3x
2 = 3x
Divide both side by 3
x = 2/3.
Now, let us calculate the value of 'x' by squaring both side of the expression. This is illustrated below:
(-5)^2 = (3x - 7)^2
25 = (3x - 7)(3x - 7)
25 = 9x^2 - 21x - 21x + 49
9x^2 - 42x + 49 - 25 = 0
9x^2 - 42x + 24 = 0
Solving by factorisation:
Multiply the first term i.e 9x^2 and 3rd term i.e 24 together. The result is 216x^2.
Next, we shall obtain two factors of 216x^2 such that when we add them together, it will give the 2nd term i.e -42x in the equation. These factors are: -6x and -36x
Now we can write the above equation as:
9x^2 - 42x + 24 = 0
9x^2 - 6x - 36x + 24 = 0
3x(3x - 2) - 12(3x - 2) = 0
(3x - 12)(3x - 2) = 0
3x - 12 = 0 or 3x - 2 = 0
3x = 12 or 3x = 2
x = 12/3 or x = 2/3
x = 4 or 2/3.
We can see that when we solve the question without squaring both side, the value of x is 2/3. But when we solve by squaring both side, the value of x are 4 and 2/3.
Therefore, the extraneous solution to the question is 4.
