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Zina [86]
2 years ago
11

Find the slope of the line that passes through the points A(0, 2) and B(4, –1).

Mathematics
1 answer:
kati45 [8]2 years ago
5 0

Slope=M=y2-y1/X2-X1=

-1 -2 /4-0=

-3/4  =

-0.75

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Test the set of polynomials for linear independence. If it is linearly dependent, express one of the polynomials as a linear com
aliina [53]

Answer:

The set of polynomial  is Linearly Independent.

Step-by-step explanation:

Given - {f(x) =7 + x, g(x) = 7 +x^2, h(x)=7 - x + x^2} in P^2

To find - Test the set of polynomials for linear independence.

Definition used -

A set of n vectors of length n is linearly independent if the matrix with these vectors as columns has a non-zero determinant.

The set is dependent if the determinant is zero.

Solution -

Given that,

f(x) =7 + x,

g(x) = 7 +x^2,

h(x)=7 - x + x^2

Now,

We can also write them as

f(x) = 7 + 1.x + 0.x²

g(x) = 7 + 0.x + 1.x²

h(x) = 7 - 1.x + 1.x²

Now,

The coefficient matrix becomes

A = \left[\begin{array}{ccc}7&1&0\\7&0&1\\7&-1&1\end{array}\right]

Now,

Det(A) = 7(0 + 1) - 1(7 - 7) + 0

           = 7(1) - 1(0)

           = 7 - 0 = 7

⇒Det(A) = 7 ≠ 0

As the determinant is non- zero ,

So, The set of polynomial  is Linearly Independent.

5 0
2 years ago
1. If you wanted to make a triangle with side lengths of 3 units, 3 units, and 4
ivanzaharov [21]

Answer:

Since 4 is the largest number its the hypotenuse. The two 3s are equal so they are interchangeable so it doesn't matter where you put them. If its a right triangle the hypotenuse is opposite the right angle.

Step-by-step explanation:

7 0
3 years ago
(100+ POINTS)
horsena [70]

Answer:

1) 102.7 meters

2) 11

Step-by-step explanation:

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25x = 38

x = 1.52 s

Height = -4.9(1.52)² + 75(1.52) = 102.67904 m = 102.7 m

2) f(x) = x² + 3x - 2

f(2) = 2² + 3(2) - 2 = 8

f(6) = 6² + 3(6) - 2 = 52

Average rate of change:

(52-8)/(6-2) = 11

5 0
3 years ago
Read 2 more answers
Kayla is going on a trip. The mass of everything she is packing is 8.1 kg. She packs everything into a bag that has a mass when
Agata [3.3K]

Answer:

8.81 KG (8810 g)

Step-by-step explanation:

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8 0
2 years ago
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In A ABC, AB = 51 cm, BC = 52 cm and CA = 101 cm, then find the area of A ABC,​
liberstina [14]

Step-by-step explanation:

sorry..by any chance if my answer is incorrect

7 0
3 years ago
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