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const2013 [10]
3 years ago
6

Factor the following quadratic equation;

d="TexFormula1" title="12 {x}^{2} + 22x - 14" alt="12 {x}^{2} + 22x - 14" align="absmiddle" class="latex-formula">

Mathematics
1 answer:
Bogdan [553]3 years ago
5 0

Answer:

2(3x + 7)(2x - 1)

Step-by-step explanation:

You can see it a little easier if you take out a common factor of 2

2(6x^2 + 11x - 7)

The 6 leaves you with a lot of factors, the 7 does not. It only has 2 factors.

Let 6 factor into 2 and 3 and the 7 into 7 and 1

2(3x - 1 )(2x + 7)

Now remove the brackets.

2(6x^2 + 21x - 2x - 7) This obviously does not work but we'll combine like terms anyway.

2(6x^2 + 19x - 7)

So we'll try it again

2(3x + 7)(2x - 1)

2(6x^2 + 14x - 3x - 7)    Looks like we have it.

2(6x^2 + 11x - 7)

So the right factors are

2(3x + 7)(2x - 1)

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Please help I am so confused
Ede4ka [16]

The total cost when 881 minutes is used is $477.50.

<h3>What are the equation that model the question?</h3>

a + 480b = 277 equation 1

a + 990b = 532 equation 2

Where:

  • a = flat fee
  • b = variable fee

<h3>What is the flat fee and the variable fee?</h3>

Subtract equation 1 from equation 2

510b = 255

b = 255 / 510

b = $0.50

In order to determine the flat fee, substitute for b in equation 1

a + 480(0.5) = 277

a + 240 = 277

a = 277 - 240

a = $37

<h3>What is the total cost when 881 minutes is used?</h3>

Total cost = flat fee + (variable cost x number of minutes spoken)

$37 + (881 x 0.5) = $477.50

To learn more about simultaneous equations, please check: brainly.com/question/25875552

#SPJ1

7 0
1 year ago
Find the distance between (-3, -11) and (8, -42)
Marianna [84]

Answer:

32.8937 units

Step-by-step explanation:

So, we can imagine this as a right triangle with a length of 11 (THe change of the X's) and the height being 31 (Change of the Y's)

Then we use pythagorean therom to find the hypotenuse (the length)

11^2 + 31^2 = c^2

121+961 = C^2

1082 = c^2

32.8937units

3 0
2 years ago
How add with the same denominator ?
Amiraneli [1.4K]

Answer:

you just add the top numbers and then if its over the denominator you simplify

Step-by-step explanation:

7/9 + 4/9

10/9

1-1/9

7 0
2 years ago
Someone please help I will give BRAINLIST I’m exhausted
Aliun [14]

Answer:

4x - 4

Step-by-step explanation:

Add up all common numbers and then subtract from the total amount.

Hope it helps :))

6 0
3 years ago
HELPPPP<br> please help me answer this question-
erik [133]

Answer:

\displaystyle   GH  =  2 \sqrt{30}

\displaystyle FH = 2 \sqrt{10}

\displaystyle m \angle G =  {30}^{ \circ}

Step-by-step explanation:

<h3>QUESTION-2:</h3>

we are given a right angle triangle

it's a 30-60-90 triangle of which FH is the shortest side

remember that,in case of 30-60-90 triangle the the longest side is twice as much as the shortest side thus

our equation is

\displaystyle 2FH=4\sqrt{10}

divide both sides by 2

\displaystyle\frac{2FH}{2}= \frac{ 4 \sqrt{10} }{2}

\displaystyle FH =2 \sqrt{10}

<h3>Question-1:</h3>

in order to figure out GH we can use Trigonometry because the given triangle is a right angle triangle

as we want to figure out GH we'll use sin function

remember that,

\displaystyle  \sin( \theta)  =  \frac{opp}{hypo}

let our opp, hypo and \theta be GH, 4√10 and 60° respectively

thus substitute:

\displaystyle  \sin(  {60}^{ \circ} )  =  \frac{GH}{4 \sqrt{10} }

recall unit circle:

\displaystyle   \frac{ \sqrt{3} }{2}   =  \frac{GH}{4 \sqrt{10} }

cross multiplication:

\displaystyle   2 GH  =  4 \sqrt{10}  \times  \sqrt{3}

simplify multiplication:

\displaystyle   2 GH  =  4 \sqrt{30}

divide both sides by 2:

\displaystyle   GH  =  2 \sqrt{30}

<h3>QUESTION-3:</h3>

Recall that, the sum of the interior angles of a triangle is 180°

therefore,

\displaystyle m \angle G +  {60}^{ \circ}  + {90}^{ \circ}  =  {180}^{ \circ}

simplify addition:

\displaystyle m \angle G +  {150}^{ \circ}  =  {180}^{ \circ}

cancel 150° from both sides

\displaystyle m \angle G =  {30}^{ \circ}

6 0
3 years ago
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