Answer:
Step-by-step explanation:
Both triangles in this figure are similar. Therefore, we can set up the following proportion:
.
Cross-multiply to solve:
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The amount of tax would be $67.92. the total he would pay would be $916.92
This pattern of question is always coming up. Since we can't easily guess, then let us set up simultaneous equation for the statements.
let the two numbers be x and y.
Multiply to 44. x*y = 44 ..........(a)
Add up to 12. x + y = 12 .........(b)
From (b)
y = 12 - x .......(c)
Substitute (c) into (a)
x*y = 44
x*(12 - x) = 44
12x - x² = 44
-x² + 12x = 44
-x² + 12x - 44 = 0.
Multiply both sides by -1
-1(-x² + 12x - 44) = -1*0
x² - 12x + 44 = 0.
This does not look factorizable, so let us just use quadratic formula
comparing to ax² + bx + c = 0, x² - 12x + 44 = 0, a = 1, b = -12, c = 44
x = (-b + √(b² - 4ac)) /2a or (-b - √(b² - 4ac)) /2a
x = (-(-12) + √((-12)² - 4*1*44) )/ (2*1)
x = (12 + √(144 - 176) )/ 2
x = (12 + √-32 )/ 2
√-32 = √(-1 *32) = √-1 * √32 = i * √(16 *2) = i*√16 *√2 = i*4*√2 = 4i√2
Where i is a complex number. Note the equation has two values. We shall include the second, that has negative sign before the square root.
x = (12 + √-32 )/ 2 or (12 - √-32 )/ 2
x = (12 + 4i√2 )/ 2 (12 - 4i√2 )/ 2
x = 12/2 + (4i√2)/2 12/2 - (4i√2)/2
x = 6 + 2i√2 or 6 - 2i√2
Recall equation (c):
y = 12 - x, When x = 6 + 2i√2, y = 12 - (6 + 2i√2) = 12 - 6 - 2i√2 = 6 - 2i√2
When x = 6 - 2i√2, y = 12 - (6 - 2i√2) = 12 - 6 + 2i√2 = 6 + 2i√2
x = 6 + 2i√2, y = 6 - 2i√2
x = 6 - 2i√2, y = 6 + 2i√2
Therefore the two numbers that multiply to 44 and add up to 12 are:
6 + 2i√2 and 6 - 2i√2
Answer:
Explained below.
Step-by-step explanation:
(11)
Subtract the sum of (13x - 4y + 7z) and (- 6z + 6x + 3y) from the sum of (6x - 4y - 4z) and (2x + 4y - 7z).
![[(6x - 4y - 4z) +(2x + 4y - 7z)]-[(13x - 4y + 7z) + (- 6z + 6x + 3y) ]\\=[6x-4y-4z+2x+4y-7z]-[13x-4y+7z-6z+6x+3y]\\=6x-4y-4z+2x+4y-7z-13x+4y-7z+6z-6x-3y\\=(6x+2x-13x-6x)+(4y-4y+4y-3y)-(4z+7z+7z-6z)\\=-11x+y-12z](https://tex.z-dn.net/?f=%5B%286x%20-%204y%20-%204z%29%20%2B%282x%20%2B%204y%20-%207z%29%5D-%5B%2813x%20-%204y%20%2B%207z%29%20%2B%20%28-%206z%20%2B%206x%20%2B%203y%29%20%5D%5C%5C%3D%5B6x-4y-4z%2B2x%2B4y-7z%5D-%5B13x-4y%2B7z-6z%2B6x%2B3y%5D%5C%5C%3D6x-4y-4z%2B2x%2B4y-7z-13x%2B4y-7z%2B6z-6x-3y%5C%5C%3D%286x%2B2x-13x-6x%29%2B%284y-4y%2B4y-3y%29-%284z%2B7z%2B7z-6z%29%5C%5C%3D-11x%2By-12z)
Thus, the final expression is (-11x + y - 12z).
(12)
From the sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy) subtract (-3x² + 4y² - xy + x - y + 3).
![[(x^{2} + 3y^{2} - 6xy)+(2x^{2} - y^{2} + 8xy)+(y^{2} + 8)+(x^{2} - 3xy)] - [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[x^{2} + 3y^{2} - 6xy+2x^{2} - y^{2} + 8xy+y^{2} + 8+x^{2} - 3xy]- [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[4x^{2}+3y^{2}-xy+8]-[-3x^{2} + 4y^{2} - xy + x - y + 3]\\=4x^{2}+3y^{2}-xy+8+3x^{2}-4y^{2}+xy-x+y-3\\=7x^{2}-y^{2}-x+y+5](https://tex.z-dn.net/?f=%5B%28x%5E%7B2%7D%20%2B%203y%5E%7B2%7D%20-%206xy%29%2B%282x%5E%7B2%7D%20-%20y%5E%7B2%7D%20%2B%208xy%29%2B%28y%5E%7B2%7D%20%2B%208%29%2B%28x%5E%7B2%7D%20-%203xy%29%5D%20-%20%5B-3x%5E%7B2%7D%20%2B%204y%5E%7B2%7D%20-%20xy%20%2B%20x%20-%20y%20%2B%203%5D%5C%5C%3D%5Bx%5E%7B2%7D%20%2B%203y%5E%7B2%7D%20-%206xy%2B2x%5E%7B2%7D%20-%20y%5E%7B2%7D%20%2B%208xy%2By%5E%7B2%7D%20%2B%208%2Bx%5E%7B2%7D%20-%203xy%5D-%20%5B-3x%5E%7B2%7D%20%2B%204y%5E%7B2%7D%20-%20xy%20%2B%20x%20-%20y%20%2B%203%5D%5C%5C%3D%5B4x%5E%7B2%7D%2B3y%5E%7B2%7D-xy%2B8%5D-%5B-3x%5E%7B2%7D%20%2B%204y%5E%7B2%7D%20-%20xy%20%2B%20x%20-%20y%20%2B%203%5D%5C%5C%3D4x%5E%7B2%7D%2B3y%5E%7B2%7D-xy%2B8%2B3x%5E%7B2%7D-4y%5E%7B2%7D%2Bxy-x%2By-3%5C%5C%3D7x%5E%7B2%7D-y%5E%7B2%7D-x%2By%2B5)
Thus, the final expression is (7x² - y² - x + y + 5).
(13)
What should be subtracted from (x² – xy + y² – x + y + 3) to obtain (-x²+ 3y²- 4xy + 1)?
Thus, the expression is (2x² - 2y² + 3xy - x + y + 2).
(14)
What should be added to (xy – 3yz + 4zx) to get (4xy – 3zx + 4yz + 7)?
Thus, the expression is (3xy - 7zx + 7yz + 7).
(15)
How much is (x² − 2xy + 3y²) less than (2x² − 3y² + xy)?
Thus, the expression is (x² - 6y² + 3xy).
4 because it is the only number on the x side of the table that you can get a single value for y from
