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lyudmila [28]
4 years ago
7

Solve using substitution technique; -3x+y=2, 12x-4y=-8

Mathematics
1 answer:
vladimir1956 [14]4 years ago
4 0

The first equation is easier to solve for y than is the 2nd: y = 3x+2. Subst. 3x+2 for y in the second equation:


12x - 4(3x+2) = -8

Expanding, 12x =12x -8 = -8


This is always true, no matter the value of x. Thus, the solution set is "all real numbers."

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Find all the points having an x-coordinate of 4 whose distance from the point (-2,-1) is 10
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A(x_1;\ y_1);\ B(x_2;\ y_2)\\\\the\ distance\ between\ A\ and\ B:\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\A(-2;-1);\ B(4;\ y);\ d=10\\\\subtitute\\\\\sqrt{(4-(-2))^2+(y-(-1))^2}=10\\\\\sqrt{(4+2)^2+(y+1)^2}=10\\\\\sqrt{6^2+(y+1)^2}=10\\\\\sqrt{36+(y+1)^2}=10\ \ \ |square\ both\ sides\\\\36+(y+1)^2=10^2\\\\36+(y+1)^2=100\ \ \ |subtract\ 36\ from\ both\ sides\\\\(y+1)^2=64\iff y+1=-\sqrt{64}\ or\ y+1=\sqrt{64}\\\\y+1=-8\ or\ y+1=8\ \ \ \ |subtract\ 1\ from\ both\ sides\\\\y=-9\ or\ y=7

Answer:{\boxed{(4;-9)\ or\ (4;\ 7)}
4 0
3 years ago
The coefficient of x^ky^n-k in the expansion of (x+y)^n equals (nk). True or false.
AVprozaik [17]

Answer:

The correct option is;

False

Step-by-step explanation:

The coefficient of x^k·y^(n-k) is nk,   False

The kth coefficient of the binomial expansion, (x + y)ⁿ is  \dbinom{n}{k} = \dfrac{n!}{k!\cdot (n-k)!} = C(n,k)

Where;

k = r - 1

r = The term in the series

For an example the expansion of (x + y)⁵, we have;

(x + y)⁵ = x⁵ + 5·x⁴·y + 10·x³·y² + 10·x²·y³ + 5·x·y⁴ + y⁵

The third term, (k = 3) coefficient is 10 while n×k = 3×5 = 15

Therefore, the coefficient of x^k·y^(n-k) for the expansion  (x + y)ⁿ = C(n,k) not nk

7 0
3 years ago
15-3(2+6 times -3) <br> What would this simplify to?
pickupchik [31]
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8 0
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Read 2 more answers
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NeTakaya

Answer:

rachael is 35 and sarah is 32.

Step-by-step explanation:

6 0
3 years ago
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8-5=3
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7 0
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