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3 years ago

20 POINTS PLEASE HELP

Mathematics

2 answers:

Karolina [17]3 years ago

8 0

Answer:

a) -3

Step-by-step explanation:

Zero of a function is the x-value where y = 0

x² + 2x - 3 = 0

x² + 3x - x - 3 = 0

x(x + 3) - (x + 3) = 0

(x - 1)(x + 3) = 0

x = 1, -3

quester [9]3 years ago

7 0

Answer:

Step-by-step explanation:

Essentially, if we plug in any of the given choices into the function and we get 0, then that's our answer.

A) (-3)^2 + 2 * (-3) - 3 = 9 - 6 - 3 = 0 - correct

B) (-1)^2 + 2 * (-1) - 3 = 1 - 2 - 3 = -4 - incorrect

C) 0^2 + 2 * 0 - 3 = -3 - incorrect

D) 2^2 + 2 * 2 - 3 = 4 + 4 - 3 = 5 - incorrect

So, the answer is A.

The alternative, more "formal" way of doing this problem is to factor the quadratic: x^2 + 2x - 3 = (x + 3)(x - 1) = 0

Then set each of these equal to 0: x + 3 = 0 and x - 1 = 0

We get the values of x = -3 and x = 1. Only -3 is one of the answer choices, so A is correct.

Hope this helps!

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A motorboat travels 165 kilometers in 3 hours going upstream and 510 kilometers in 6 hours going downstream. What is the rate of

nikitadnepr [17]

<h3>Rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr</h3><h3>Solution:</h3>

Given that,

A motorboat travels 165 kilometers in 3 hours going upstream and 510 kilometers in 6 hours going downstream

Therefore,

Upstream distance = 165 km

Upstream time = 3 hours

<h3>Find upstream speed:</h3>

$speed = \frac{distance}{time}\\\\speed = \frac{165}{3}\\\\speed = 55$

Thus upstream speed is 55 km per hour

Downstream distance = 510 km

Downstream time = 6 hours

<h3>Find downstream speed:</h3>

$speed = \frac{510}{6}\\\\speed = 85$

Thus downstream speed is 85 km per hour

If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then

Speed downstream = u + v km/hr

Speed upstream = u - v km/hr

Therefore,

u + v = 85 ----- eqn 1

u - v = 55 ----- eqn 2

Solve both

Add them

u + v + u - v = 85 + 55

2u = 140

u = 70

Substitute u = 70 in eqn 1

70 + v = 85

v = 85 - 70

v = 15

Thus rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr

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3 years ago

What is the elapsed time between 1:35 and 6:00?

castortr0y [4]

The Answer Is D (4hrs 25min)
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4% of 73 is what ?????

kumpel [21]

4% of 73 will be 2.92.
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3 years ago

Find cos(2*ABC) 100POINTS

juin [17]

Answer:

$-\dfrac{7}{25}$

Step-by-step explanation:

Trigonometric Identities

$\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B$

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Using the trig ratio formulas for cosine and sine:

$\cos(\angle ABC)=\dfrac{3}{5}$

$\sin(\angle ABC)=\dfrac{4}{5}$

Therefore, using the trig identities and ratios:

$\begin{aligned}\implies \cos(2 \cdot \angle ABC) & = \cos(\angle ABC + \angle ABC)\\\\& = \cos (\angle ABC) \cos (\angle ABC) - \sin(\angle ABC) \sin (\angle ABC)\\\\& = \cos^2(\angle ABC)-\sin^2(\angle ABC)\\\\& = \left(\dfrac{3}{5}\right)^2-\left(\dfrac{4}{5}\right)^2\\\\& = \dfrac{3^2}{5^2}-\dfrac{4^2}{5^2}\\\\& = \dfrac{9}{25}-\dfrac{16}{25}\\\\& = \dfrac{9-16}{25}\\\\& = -\dfrac{7}{25} \end{aligned}$

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Which statements are true about the solution 2 < x - 7 and its graph? Check all that apply.

Mashutka [201]

Answer:

O x >9

The arrow points left

Step-by-step explanation:

Explanation:-

Given 2 < x-7

adding '7' on both sides, we get

⇒ 2 + 7 < x -7 +7

⇒ 9 < x

⇒ x>9

Given inequality 2 < x -7

The arrow points left

Final answer:-

solution is x >9

The arrow points left

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