MATHEMATICS HIGH SCHOOL

Which graph shows the quadratic function y = 3x^2 + 12x + 10?

Answers

Answer 1

Answer:

Answer with explanation:

→The quadratic function is

y = 3 x² + 12 x + 10

$y=3(x^2+4 x+(10)/(3))\n\ny=3[(x+2)^2-4+(10)/(3)]\n\ny=3[(x+2)^2-(2)/(3)]\n\ny+2=3(x+2)^2$

→Vertex of the parabola=(-2,-2),in third Quadrant.

→Drawing the Parabola,which will open upwards ,that is along positive y axis.

→ Line, x= -2 , is the line of symmetry of Quadratic function.

As,the function is Quadratic, it has either two real root or two imaginary.

But, it has two real root, which are , x=-2.816,-1.184, because,

Discriminant >0.

D=12²-4×3×10

=144 -120

D=24

Answer 2

Answer: The graph of the function is attached.

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The number of chips of different colors in Amy's bag is shown below: 8 blue chips 9 pink chips 1 white chip Amy takes out a chip from the bag randomly without looking. She replaces the chip and then takes out another chip from the bag. What is the probability that Amy takes out a pink chip in both draws?

Answers

probability of an event happening = number of ways it can happen
total number of outcomes

Given:
blue chips = 8
pink chips = 9
white chips=1
total = 18

1st draw:
pink chip = 9/18 = 1/2

2nd draw:
pink chip = 9/18 = 1/2

Answer:

81/324

Step-by-step explanation:

9/18 * 9/18 = 81/324

What is the rate of change for the interval between 0 and 2 for the quadratic equation as f(x) = 2x2 + x – 3 represented in the table? (The table has this: Left side X and the options going down are -2, -1, 0, 1, 2. Right Side f(x) and the options going down are 3, -2, -3, 0, 7) THE ANSWER OPTIONS ARE: 1/5, 4, 5, 10

Answers

By definition the rate of change of a function is given by:
$AVR = (f(x2) - f(x1))/(x2 - x1)$
For the interval [0, 2] We have to make use of the table:
$f(0)=-3 f(2)=7$
Therefore, substituting values in the given expression we have that the average change of rate is given by:
$AVR = (7-(-3))/(2-0)$
Rewriting we have:
$AVR = (7+3)/(2-0)$
$AVR = (10)/(2)$
$AVR = 5$
Answer:
the rate of change for the interval between 0 and 2 is:
$AVR = 5$

Answer:

Step-by-step explanation:

♥☺

The rectangle is 3 3⁄4 centimeters long and 2 1⁄2 centimeters wide. What is the area of this rectangle?please help me ASAP
Ive been struggling

Answers

Answer:

The answer to your question is Area = 9 3/8

Step-by-step explanation:

Data

length = 3 3/4 cm

width = 2 1/2 cm

Process

1.- Write the equation of the Area of a rectangle

Area = length x width

2.- Convert the values to improper fractions

3 3/4 = (12 + 3)/ 4 = 15/4

2 1/2 = (4 + 1) / 2 = 5/2

3.- Substitution

Area = (15/4)(5/2)

4.- Simplification

Area = 75/8

5.- Convert to a mixed fraction

8 75

6.- Result

Area = 9 3/8

If the average of three numbers is V if one number is Z and another is y what is the remaining number ?

Answers

The remaining number, using the concept of average, is $3V-y-z$

It is given that

Average of three numbers = V

One number = z

Another number = y

What is an average?

Average is the sum of observations divided by a number of observations.

Let us take the third number x

From the question

$(x+y+z)/(3) = V$

$x+y+z = 3V\n\nx=3V-y-z$

Therefore, the remaining number is $3V-y-z$

To get more about the average visit:

brainly.com/question/6504879

The formula for an average of three numbers is (x+y+z)/3. So if V equals the average, then we find the formula
V = (x+y+z)/3
We are now looking for x. We can divide each of the variables in the parentheses by 3, making the formula
V = x/3 + y/3 + z/3
So now bring the unwanted variables to the same side as V.
V - y/3 - z/3 = x/3
Now multiply both sides by 3 to find x.
3V - y - z = x

x = 3V - y - z

You are given a standard deck of 52 cards. Three cards are chosen at random with replacement. What is the probability of choosing an ace, a spade, and a four?

Answers

Answer:

0.0288 = 2.88%

Step-by-step explanation:

First we need to know that in one standard deck of 52 cards we have 13 ace cards, 13 spade cards, and 4 four cards.

If we want a combination of ace, spade and four, we calculate the probability of each one, and then multiply them all:

The probability of getting an ace is 13/52 = 1/4

The probability of getting a spade is 13/52 = 1/4

The probability of getting a four is 4/52 = 1/13

As the order of our three cards doesn't matter, we have 3! (factorial of three) = 6 different ways of having a group of ace, spade and four, so our total probability will be multiplied by 6.

So, our probability is:

(1/4) * (1/4) * (1/13) * 6 = 6/208 = 3/104 = 0.0288 = 2.88%

Answer:

Probability = 0.23

Step-by-step explanation:

Probability of picking it choosen those at random without replacement =Pr(ace) + Pr(spade)+Pr(a four)

Probability = 4/52 + 4/52 + 4/52

Probability= 3(4/52)

Probability = 0.23

'Solve using perfect square factoring patterns.
x^2 – 12x + 36 = 4'

Answers

$x^2-12x + 36 = 4 \n \nx^2-12x + 36 - 4 =0\n \nx^2-12x + 32 =0 \n \na=1 , \ b=-12, \ c =32\n \n \Delta =b^2-4ac = (-12)^2 -4\cdot1\cdot 32 = 144-128 =16\n \nx_(1)=(-b-√(\Delta) )/(2a)=(12-√(16))/(2 )=( 12-4)/(2)=(8)/(2)= 4$

$x_(2)=(-b+√(\Delta) )/(2a)=(12+√(16))/(2 )=( 12+4)/(2)=(16)/(2)= 8$

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