MATHEMATICS HIGH SCHOOL

Solve 3x2 + 12x = 3.

Answers

Answer 1

Answer:

Answer:

The solutions to the quadratic equation are: $x=-2+√(5),\:x=-2-√(5)$

Step-by-step explanation:

To solve the quadratic equation $3x^2+12x=3$ you must:

Subtract 3 from both sides and simplify

$3x^2+12x-3=3-3\n\n3x^2+12x-3=0$

For a quadratic equation of the form $ax^2+bx+c=0$ the solutions are

$x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)$

$\mathrm{For\:}\quad a=3,\:b=12,\:c=-3$

$x=(-12+√(12^2-4\cdot \:3\left(-3\right)))/(2\cdot \:3)=(-12+√(180))/(2\cdot \:3)=(-12+6√(5))/(6)=(6\left(-2+√(5)\right))/(6)=-2+√(5)$

$x=(-12-√(12^2-4\cdot \:3\left(-3\right)))/(2\cdot \:3)=(-12-√(180))/(2\cdot \:3)=(-12-6√(5))/(6)=-(6\left(2+√(5)\right))/(6)=-2-√(5)$

The solutions to the quadratic equation are:

$x=-2+√(5),\:x=-2-√(5)$

Answer 2

Answer: $3 x^(2) + 12x = 3$
$3 x^(2) + 12x - 3 = 0$
Using the quadratic formula
$x = \frac{-b (+ or -) \sqrt{b^(2 - 4ac) } }{2a}$
$x = \frac{-12 + \sqrt{12^(2 - 4(3)(-3)) } }{2(3)}$ OR $x = \frac{-12 - \sqrt{12^(2 - 4(3)(-3)) } }{2(3)}$
$x = (-12 + √(180) )/(6)$ OR $x = (-12 - √(180) )/(6)$
∴ x = 0.236 and x = -4.236

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Rewrite 5/2 as a mixed number.
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Using only the values given in the table for the function f(x) = –x3 + 4x + 3, what is the largest interval of x-values where the function is increasing?

What are the factor pairs of 23?

Answers

it is a prime, it doesn't have, the only (I don't know if your system counts 1,23 as factors but there are no others)

HELP PLEZ!!!!!!!!!!!Which equations are true for the values of x, y, and z? Select three options.

X° + 65° = 180°
x° = z°
y° = 65°
x° = 65°
x° + y° + z° = 115°

Answers

Answer:

a, b, and c

Step-by-step explanation:

a. x°+65°=180°

b. x°=z°

c. y°=65°

d. x°=65°

e. x°+y°+x°=115°

x = 115°

y = 65°

z = 115°

There are 4 kings, 4 queens, 4 jacks, and 4 aces, corresponding to these suits. Kings, queens, and jacks are called face cards. If you are not familiar with what these cards look like, below is an image: You shuffle the deck, draw out a card at random, and note whether the card is a face card (either a king, queen, or jack) or not. You then put the card back, shuffle the deck, and draw again. You repeat this process a few more times, for a total of 17 trials. What is the expected number of face cards drawn? Round your answer to two (2) decimal places.

Answers

The expected number of face cards drawn in 17 trials with a number rounded to two is 3.92.

In each trial, the probability of drawing a face card is 3/13, since there are 12 face cards in a standard deck of 52 cards. The expected value of a random variable is the average of the values of each outcome. In this case, the outcome is either drawing a face card or not drawing a face card.

The value of drawing a face card is 1 since it is a success. The value of not drawing a face card is 0 since it is a failure. So, the expected number of face cards drawn in 17 trials is 3.92, calculated by the number of face cards drawn in 17 trials as 17 * (3/13) = 3.92.

Learn more about the probability at

brainly.com/question/31634956

A 15-foot pole is leaning against a tree. The bottom of the pole is 8 feet away from the bottom of the tree. Approximately how high up the tree does the top of the pole reach?

A.
17.0 feet

B.
12.7 feet

C.
7.0 feet

D.
1.9 feet

Answers

Answer: Actually the answer is 12.7 I took the quiz

Step-by-step explanation:

It would be C. 7.0 feet

You are going on a 1,940-mile trip, and your car gets about 28 miles per gallon. Gas prices along your route average $2.95 per gallon. Calculate the cost of thetrip. Round final answer to the nearest cent.

Answers

Answer: $204.39

Reason

The number of gallons used is estimated to be approximately: distance/mpg = 1940/28 = 69.2857 gallons.

Each gallon costs $2.95, so the total cost is 69.2857*2.95 = 204.392815 which rounds to 204.39

A long distance telephone company advertised the rates of 5 minutes for 85¢ and 10 minutes for $1.10.Use a linear equation to find the cost of a 25 minute phone call.

Answers

Let x represent the number of minutes and y the cost. Then
y - 0.85 = (1.10 - 0.85)/(10 - 5) (x - 5)
y - 0.85 = 0.25/5 (x - 5) = 1/20 (x - 5) = 1/20 x - 1/4
y = 0.05x - 0.25 + 0.85 = 0.05x + 0.6
y = 0.05x + 0.6

The cost of 25 minutes = 0.05(25) + 0.6 = 1.25 + 0.6 = $1.85

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