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3 years ago

What is the slope of the line 7, 0 and -5, 0

Mathematics

1 answer:

lutik1710 [3]3 years ago

6 0

Answer:

Slope = (Y2 -Y1) ÷ (X2 -X1)

Slope = (0 -0) / (-5, -7)

Slope = 0 / -12 = 0

The slope of the line is zero. It is perfectly horizontal.

Step-by-step explanation:

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What is the final amount if 975 is increased by 1% followed by a further 9% increase?

alexgriva [62]

975 x 1.01 = 984.75
984.75 x 1.09 = 1073.38

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3 years ago

Please see attachment

Dafna11 [192]

Answer:

a) The value of absolute minimum value = - 0.3536

b) which is attained at $x = \frac{1}{\sqrt{2} }$

Step-by-step explanation:

Step(i):-

Given function

$f(x) = \frac{-x}{2x^{2} +1}$ ...(i)

Differentiating equation (i) with respective to 'x'

$f^{l} = \frac{2x^{2} +1(-1) - (-x) (4x)}{(2x^{2}+1)^{2} }$ ...(ii)

$f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} }$

Equating Zero

$f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0$

$\frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0$

$2 x^{2}-1 = 0$

$2 x^{2} = 1$

$x^{2} = \frac{1}{2}$

$x = \frac{-1}{\sqrt{2} } , x = \frac{1}{\sqrt{2} }$

Step(ii):-

Again Differentiating equation (ii) with respective to 'x'

$f^{ll}(x) = \frac{(2x^{2} +1)^{2} (4x) - 2(2x^{2} +1) (4x)(2x^{2}-1) }{(2x^{2}+1)^{4} }$

put

$x = \frac{1}{\sqrt{2} }$

$f^{ll} (x) > 0$

The absolute minimum value at $x = \frac{1}{\sqrt{2} }$

Step(iii):-

The value of absolute minimum value

$f(x) = \frac{-x}{2x^{2} +1}$

$f(\frac{1}{\sqrt{2} } ) = \frac{-\frac{1}{\sqrt{2} } }{2(\frac{1}{\sqrt{2} } )^{2} +1}$

on calculation we get

The value of absolute minimum value = - 0.3536

Final answer:-

a) The value of absolute minimum value = - 0.3536

b) which is attained at $x = \frac{1}{\sqrt{2} }$

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3 years ago

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Roman55 [17]

Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

Find sin theta if theta is an angle in standard position and the point with coordinates (3, -4) lies on the terminal side of an

alisha [4.7K]

Answer:

$\sin \theta=-\frac{4}{5}$

Step-by-step explanation:

Given:

Angle is in standard position which means the starting ray is at the origin. The terminal side has coordinates (3, -4).

So, the 'x' value is 3 and 'y' value id -4.

Using Pythagoras Theorem, we find the hypotenuse.

Hypotenuse = $\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5$

Now, using the sine ratio for the angle, we have

$\sin \theta=\frac{Opposite}{Hypotenuse}\\\sin \theta=\frac{-4}{5}\\\sin \theta=-\frac{4}{5}$

Therefore, the value of $\sin \theta$ is $-\frac{4}{5}$ .

The value is negative as the point (3, -4) lies in the fourth quadrant and sine ratio is negative in the fourth quadrant,

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3 years ago

7. A business begins with $1,000,000 from its owners. It places $100,000 into a bank account which it wishes to maintain as a ca

joja [24]

Answer:

The amount need to borrow a owner is $100,000

Step-by-step explanation:

The total amount a owner having to start a business = $1,000,000.

He wishes to place $ 100,000 into bank account to maintain as cash reserve.

Now the amount he left with to spent in business purposes = $1,000,000 - $100,000 = $ 900,000.

He needs to purchase equipment and material of $1,000,000

But he is left with only $900,000.

So the amount he has to borrow to fulfill his business requirement is

= $1,000,000 - $900,000 = $100,000

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3 years ago