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3 years ago

Describe the nature of the roots for the equation 49x2– 28x +4 = 0

Mathematics

1 answer:

Zepler [3.9K]3 years ago

6 0

Answer:

The roots of the equation is real and repeated

Step-by-step explanation:

Here, we want to describe the nature of the roots of the given quadratic equation

To get the nature of the roots, we find the discriminant of the equation

The discriminant is;

b^2 - 4ac

In this case, b = -28 , a = 49 and c = 4

The discriminant is thus;

-28^2 - 4(49)(4)

= 784 - 784 = 0

Since the discriminant is zero, this means that the quadratic equation has real roots which are the same

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Rzqust [24]

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See attachment below.
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3 years ago

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quester [9]

Answer:

A: (2,-4) B: (2,-1) C: (5,-1) D: (5,-2)

Reflected over x-axis:

A: (2,4) B: (2,1) C: (5,1) D: (5,2)

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A: (4,-5)

dilated by 3

rotated 180 about the origin-

(-4,5)

Step-by-step explanation:

Your finding the transformations for only A

7 0

3 years ago

Read 2 more answers

Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.

FromTheMoon [43]

Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:

$\rho = \sqrt{x^{2}+y^{2}+z^{2}}$

$\phi = cos^{-1}\frac{z}{\rho}$

For angle θ:

If x > 0 and y > 0: $\theta = tan^{-1}\frac{y}{x}$ ;

If x < 0: $\theta = \pi + tan^{-1}\frac{y}{x}$ ;
If x > 0 and y < 0: $\theta = 2\pi + tan^{-1}\frac{y}{x}$ ;

Calculating:

a) (4,2,-4)

$\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}$ = 6

$\phi = cos^{-1}(\frac{-4}{6})$

$\phi = cos^{-1}(\frac{-2}{3})$

For θ, choose 1st option:

$\theta = tan^{-1}(\frac{2}{4})$

$\theta = tan^{-1}(\frac{1}{2})$

b) (0,8,15)

$\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}$ = 17

$\phi = cos^{-1}(\frac{15}{17})$

$\theta = tan^{-1}\frac{y}{x}$

The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = $\frac{\pi}{2}$

c) (√2,1,1)

$\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}$ = 2

$\phi = cos^{-1}(\frac{1}{2})$

$\phi$ = $\frac{\pi}{3}$

$\theta = tan^{-1}\frac{1}{\sqrt{2} }$

d) (−2√3,−2,3)

$\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}$ = 5

$\phi = cos^{-1}(\frac{3}{5})$

Since x < 0, use 2nd option:

$\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }$

$\theta = \pi + \frac{\pi}{6}$

$\theta = \frac{7\pi}{6}$

Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:

$r=\sqrt{x^{2}+y^{2}}$

Angle θ is the same as spherical coordinate;

z = z

Calculating:

a) (4,2,-4)

$r=\sqrt{4^{2}+2^{2}}$ = $\sqrt{20}$

$\theta = tan^{-1}\frac{1}{2}$

z = -4

b) (0, 8, 15)

$r=\sqrt{0^{2}+8^{2}}$ = 8

$\theta = \frac{\pi}{2}$

z = 15

c) (√2,1,1)

$r=\sqrt{(\sqrt{2} )^{2}+1^{2}}$ = $\sqrt{3}$

$\theta = \frac{\pi}{3}$

z = 1

d) (−2√3,−2,3)

$r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}$ = 4

$\theta = \frac{7\pi}{6}$

z = 3

5 0

3 years ago

The length of a rectangular garden is represented by 3x-4 and the width is represented by 2x-5. Which of the following represent

lisabon 2012 [21]

Well area of a rectangle is given by the equation

a = L x W

Since they give us the expression for length and width we can find the expression for the area...

a = (3x - 4) x (2x - 5) or simply
a = (3x -4)(2x - 5)

Now we multiply

6x^2 - 15x - 8x + 20 =
6x^2 - 23x + 20

Your answer is C.

8 0

3 years ago

Help Asap 20 points!! And Brainlist!!!

Alenkasestr [34]

Answer: 2(5c - 1x)

Step-by-step explanation: It's asking you to take out the greatest common factor (GCF).

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3 years ago