Answer:
The value of <em>c</em> is 
.
Step-by-step explanation:
The perfect square of the difference between two numbers is:
The expression provided is:
The expression is a perfect square of the difference between two numbers.
One of the number is <em>x</em> and the other is √<em>c</em>.
Use the above relation to compute the value of <em>c</em> as follows:
![x^{2}-15x+c=(x-\sqrt{c})^{2}\\\\x^{2}-15x+c=x^{2}-2\cdot x\cdot\sqrt{c}+c\\\\15x=2\cdot x\cdot\sqrt{c}\\\\15=2\cdot\sqrt{c}\\\\\sqrt{c}=\frac{15}{2}\\\\c=[\frac{15}{2}]^{2}\\\\c=\frac{225}{4}](https://tex.z-dn.net/?f=x%5E%7B2%7D-15x%2Bc%3D%28x-%5Csqrt%7Bc%7D%29%5E%7B2%7D%5C%5C%5C%5Cx%5E%7B2%7D-15x%2Bc%3Dx%5E%7B2%7D-2%5Ccdot%20x%5Ccdot%5Csqrt%7Bc%7D%2Bc%5C%5C%5C%5C15x%3D2%5Ccdot%20x%5Ccdot%5Csqrt%7Bc%7D%5C%5C%5C%5C15%3D2%5Ccdot%5Csqrt%7Bc%7D%5C%5C%5C%5C%5Csqrt%7Bc%7D%3D%5Cfrac%7B15%7D%7B2%7D%5C%5C%5C%5Cc%3D%5B%5Cfrac%7B15%7D%7B2%7D%5D%5E%7B2%7D%5C%5C%5C%5Cc%3D%5Cfrac%7B225%7D%7B4%7D)
Thus, the value of <em>c</em> is .
31.
There's a pattern, +1, +2,+3,+4 ect.
Step-by-step explanation:
Note: I used the identity
for the last step.
PS. I love proving trigonometric identities!
Answer:
3+13i
Step-by-step explanation:
(10+10i)+(-7+3i)
Combine the real parts
10+-7 = 3
And the imaginary parts
10i +3i = 13i
Combine them to make the complex number
3+13i
Answer:
(3, - 1 )
Step-by-step explanation:
Given the 2 equations
3x + y = 8 → (1)
7x - 4y = 25 → (2)
Multiplying (1) by 4 and adding to (2) will eliminate the y- term
12x + 4y = 32 → (3)
Add (2) and (3) term by term to eliminate y
19x + 0 = 57
19x = 57 ( divide both sides by 19 )
x = 3
Substitute x = 3 into either of the 2 equations and solve for y
Substituting into (1)
3(3) + y = 8
9 + y = 8 ( subtract 9 from both sides )
y = - 1
solution is (3, - 1 )
