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Thepotemich [5.8K]
3 years ago
7

System of equations 5x+y=7 20x+2=y

Mathematics
1 answer:
KIM [24]3 years ago
7 0
Dependent

The general form for a pair of linear equations in two variables x and y is
and

----- (1)
----- (2)
Comparing equations 1 and 2 with the general form of equation to write their co-efficient,

Compare the ratio,

If , then the pair of linear equations has exactly one solution.
So, it said to be consistent.
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adelina 88 [10]

In order to determine the vertex of the given functions, consider that the general form of a quadrati function is:

y = ax² + bx + c

The value of x for the vertex is given by:

x = -b/2a

The value for y, based on the previous values of x, is the y value of the vertex. Use the previous expression to find the vertices:

1. y = x² + 8x - 6

x = -8/2(1) = -4

y(-4) = (-4)² + 8(-4) - 6 = 16 - 32 - 6 = -22

Hence, the vertex is (-4,-22)

2. y = -4x² - 24x - 5

x = -(-24)/2(-4) = -6

y(-6) = -4(-6)² - 24(-6) - 6 = -144 + 144 - 6 = -6

Hence, the vertex is (-6,-6)

3. y = 2x² - 3x + 7

x = -(-3)/2(2) = 3/4 = 0.75

y(3/4) = 2(3/4)² - 3(3/4) + 7 = 18/16 - 9/4 + 7 =5.875

Hence, the vertex is (0.75 , 5.875)

4. y = -x² + 5x - 6

x = -5/2(-1) = 5/2 = 2.5

y(5/2) = -(5/2)² + 5(5/2) - 6 = 0.25

Hence, the vertex is (2.5 , 0.25)

5. y = 1/2 x² + 6x - 5

x = - 6/(2(1/2)) = -6

y(-6) = 1/2 (-6)² + 6(-6) - 5 = -23

Hence, the vertex is (-6 , -23)

6. y = 4x² + 7

x = -0/2(4) = 0

y(0) = 4(0) + 7 = 7

Hence, the vertex is (0 , 7)

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Answer:

a = 6\sqrt 3,\:\:b =12,\:\:c=6\sqrt 2

Step-by-step explanation:

by \: 30 \degree - 60 \degree - 90 \degree \: theorem \\  \\ 6 =  \frac{1}{2} b\\  \\ 6 \times 2 = b \\  \\ 12 = b \\  \\ \huge\red {\boxed {b= 12}} \\  \\ a =  \frac{ \sqrt{3} }{2} b \\  \\ a =  \frac{ \sqrt{3} }{2}  \times 12 \\  \\ \huge\purple {\boxed {a = 6 \sqrt{3}}} \\  \\ c =  \frac{1}{ \sqrt{2} } b \\  \\ c =  \frac{1}{ \sqrt{2} }  \times 12 \\  \\ c =  \frac{ \sqrt{2} }{2}  \times 12 \\  \\ \huge\orange {\boxed {c = 6 \sqrt{2}}} \\  \\

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Answer and Explanation:

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u = v = 164√2 / √2 = 164

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