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2 years ago

Determine the number of real solutions for the equation: 6x^2+8x=7

Mathematics

1 answer:

densk [106]2 years ago

7 0

Answer:

Step-by-step explanation:

You could factor this to find out how many real roots you have, but it's easier to use the rule of the discriminate. The discriminate comes from the quadratic formula:

$b^2-4ac$

Plug in the numbers from the quadratic and see what the value of it is. If the:

discriminate < 0, you have 2 imaginary roots

discriminate = 0, you have 1 real root, multiplicity 2 and

discriminate > 0, you have 2 real roots

Our b is 8, our a is 6 and our c is -7 (remember you have to set the polynomial equal to 0 to do this).

$8^2-4(6)(-7)=232$

Because 232 is > 0, we have 2 real roots.

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Can you guys help me with this?

Ghella [55]

F(x)=2x^2-x-6
Factoring:
f(x)=2(2x^2-x-6)/2=(2^2x^2-2x-12)/2=[(2x)^2-(2x)-12]/2
f(x)=(2x-4)(2x+3)/2=(2x/2-4/2)(2x+3)→f(x)=(x-2)(2x+3)

g(x)=x^2-4
Factoring
g(x)=[sqrt(x^2)-sqrt(4)][sqrt(x^2)+sqrt(4)]
g(x)=(x-2)(x+2)

f(x)/g(x)=[(x-2)(2x+3)] / [(x-2)(x+2)
Simplifying:
f(x)/g(x)=(2x+3)/(x+2)

Answer: Third Option (2x+3)/(x+2)

7 0

3 years ago

An adventure race is 9.75 mi long. The race is divided into equal sections. Each section is 0.75 mi long. The race organizer nee

alexandr402 [8]

Step-by-step explanation:

9.75/.75 = 13

which means the race is divided into 13 equal section according to the question in which each section is 0.75 m long.

as 4 volunteers are needed in each section

so keeping this in mind 13×4 = 52

therefore, 52 volunteers race organizer need.

hope this answer helps you dear! take care

7 0

2 years ago

The following prism is made up of 27 identical

lutik1710 [3]

The greatest possible surface area of the prism is 78 square units, it is obtained by removing center cube on each side of the prism.

Step-by-step explanation:

The given is,

Prism is made up of 27 identical cubes

Step:1

Ref attachment,

Let, surface area of one of cube = 1 square units

Surface area of given prism,

In the given diagram it have 9 cube sides in each side of prism.

1 surface prism = 9 surface of cube

Surface area of given prism = 6 × Surface of prism

= 6 × 9

= 54 square units

Step:2 Check for alternative's

For removing one cube on the edge of prism,

1 surface of prim = 9 surfaces of cube

Surface area after removing cube on each side,

= 6 × 11 = 66 square units

For removing cube on corner of prism,

1 surface of prim = 9 surfaces of cube

Surface area after removing cube on corner,

= 6 × 9 = 54 square units

For removing center cube on each side,

1 surface of prim = 13 surfaces of cube

Surface area after removing cube on corer on the prism,

= 6 × 13 = 78 square units

Surface area after removing corner cube on prism = 78 square units

Result:

The greatest possible surface area of the prism is 78 square units, it is obtained by removing center cube on each side of the prism.

4 0

3 years ago

Using this equation for Wien’s Law (λ = 2898/T), the wavelength most emitted by the Sun (T = 6000K) is approximately: a. 48.3 µm

Paladinen [302]

<h2>Option C is the correct answer.</h2>

Step-by-step explanation:

By Wien’s Law we have

$\lambda =\frac{2898}{T}$

where λ is in μm and T is in K

Given that

T = 6000 K

Substituting

$\lambda =\frac{2898}{6000}=0.483\mu m$

Option C is the correct answer.

5 0

2 years ago

I NEED HELP!!!!

sp2606 [1]

Answer:

About 50% percent

Step-by-step explanation:

20 is 50 percent of 40, so 21 is about 50 percent (52.5 %)

~theLocoCoco

3 0

2 years ago

Read 2 more answers