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3 years ago

Plsss help quick three question

Mathematics

1 answer:

yKpoI14uk [10]3 years ago

7 0

Answer:

1) A

2) min; min; max; max

3) y = x² + 5x - 3

Step-by-step explanation:

f(x) = x² + 2(x)(5) + 5² - 5² + 24

f(x) = (x + 5)² - 25 + 24

f(x) = (x + 5)² - 1

In ax² + bx + c,

if a > 0, it's a min

if a < 0, it's a max

y = ax² + bx + c

Using (0,-3)

-3 = a(0)² + b(0) + c

c = -3

y = ax² + bx - 3

Using (1,3)

3 = a + b - 3

a + b = 6

Using (-1,-7)

-7 = a(-1)² + b(-1) - 3

-7 + 3 = a - b

a - b = -4

b = a + 4

a + (a + 4) = 6

2a = 2

a = 1

b = 5

y = x² + 5x - 3

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find the angle between the vectors. (first find the exact expression and then approximate to the nearest degree. ) a=[1,2,-2]. B

SashulF [63]

Answer:

$\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190$

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately $\theta \approx 48$

Step-by-step explanation:

For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

a=[1,2,-2], b=[4,0,-3,]

The dot product on this case is:

$a b= (1)*(4) + (2)*(0)+ (-2)*(-3)=10$

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

$|a|= \sqrt{(1)^2 +(2)^2 +(-2)^2}=\sqrt{9} =3$

$|b| =\sqrt{(4)^2 +(0)^2 +(-3)^2}=\sqrt{25}= 5$

And finally we can calculate the angle between the vectors like this:

$cos \theta = \frac{ab}{|a| |b|}$

And the angle is given by:

$\theta = cos^{-1} (\frac{ab}{|a| |b|})$

If we replace we got:

$\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190$

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately $\theta \approx 48$

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2 years ago

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3 years ago

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Problem:

andreyandreev [35.5K]

5(n-4)=(4n-12)

First: Distribute 5 into n and -4.
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Second: Subtract 4n from both sides to eliminate the variable from the right side of the equation.

(5n-20)=(4n-12)

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Next: Add 20 to both sides to eliminate the constant from the left side of the equation.

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