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3 years ago

What is the first step in solving the quadratic equation x2 = 9/16

2 answers:

8 0

The equation is $\displaystyle{ x^2= \frac{9}{16}$ . We can rewrite the equation as:

$\displaystyle{ x^2= (\frac{3}{4})^2$ .

Our next step here is to take the square root of both sides, remembering that $\sqrt{x^2}=|x|$ .

Thus, we have $\displaystyle{ |x|= \frac{3}{4}$ . Our final step is solving the absolute value equation, which yields:

$\displaystyle{ x= \frac{3}{4}$ or $\displaystyle{ x= -\frac{3}{4}$ .

Solution set: { $-\frac{3}{4}, \frac{3}{4}$ }

icang [17]3 years ago

4 0

Answer:

x² = (9/16)

The first step is to take square root of both sides.

√x² = √(9/16)

x = 3/4

Answer: take the square root of both sides of the equation

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You are given the parametric equations x=2cos(θ),y=sin(2θ). (a) List all of the points (x,y) where the tangent line is horizonta

vladimir1956 [14]

Answer:

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

Step-by-step explanation:

The slope of the tangent line at a point of the curve is:

$m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

$m = -\frac{\cos 2\theta}{\sin \theta}$

The tangent line is horizontal when $m = 0$ . Then:

$\cos 2\theta = 0$

$2\theta = \cos^{-1}0$

$\theta = \frac{1}{2}\cdot \cos^{-1} 0$

$\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)$ , for all $i \in \mathbb{N}_{O}$

$\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}$ , for all $i \in \mathbb{N}_{O}$

The first four solutions are:

x: $\sqrt{2}$ $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$

y: 1 -1 1 -1

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

6 0

3 years ago

Write the expression that appears under the radical symbol in the quadratic formula. what is the quality called? what can it be

ira [324]

This expression is called the Discriminant, also shown as Δ.
It is equal to b² - 4ac. This is a very important part of the quadratic formula as it determines whether x will have two values, one repeated value or no real values. Here are a few examples.

a) x² - 2x - 1. a is equal to 1 since 1x² = x². b = -2, c = -1
The discriminant will be (-2)² - 4×1×-1 = 4 + 4 = 8.
Since Δ > 0, there are two x values. Graphed, the parabola sinks below the x axis.

b) x². a = 1, b = 0 (0x = 0), c = 0
The discriminant will be 0² - 4×1×0 = 0 - 0 = 0.
Since Δ = 0, there is only one x value. Graphed, the parabola touches the x axis at only one point.

c) x² + 1. a = 1, c = 1.
The discriminant will be 0² - 4×1×1 = 0 - 4 = -4
Since Δ < 0, there are no real x values. Graphed, the parabola floats above the x axis.

Hope this helps!

8 0

3 years ago

B is two-fifth of c

notka56 [123]

Answer:

8a:15b:6c

a:b:c = 8:15:6

7 0

3 years ago

In the xy-plane above, o is the center of the circle, and the measure of

Marina86 [1]

N the xy-plane above, O is the center of the cirlce. In the xy-plane above, O is the center of the cirlce, and the measure of angle AOB is pie/a radians

7 0

3 years ago

I don’t know what to do

sergey [27]

20% of 15 is 12$, and tax is 5% so it comes out to 12.60$
The answer is B

4 0

3 years ago

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