Determine how many points the parabola has in common with the x-axis and whether it's vertex lies above, on, or below the x-axis.

Answers

Answer 1

Answer:

Points "in common with the x-axis" are also known as the roots of the quadratic equation $x^2-12x+12=0$ . You can apply the quadratic root formula to determine the roots, and also to determine how many such roots there are. With a quadratic (whose graph is a parabola), there can be maximum of 2 roots. But under certain circumstances, there may be only one or no such root.

The root formula for a generic quadratic $ax^2+bx+c$ is as follows:

$x_(1,2)=(-b\pm√(b^2-4ac))/(2a)$

The expression $b^2-4ac$ under the square root is called the determinant. It is called so because it determines the number of real roots. If the determinant value is > 0, there will be 2 roots (and so the parabola will cross the x-axis in 2 points), if its value is =0, there will be only a single root (the the parabola will touch the x-axis in exactly one point), and, finally, if its value is < 0, the quadratic has no real root (andthe parabola will not have any x-intercepts).

So, let's take a look:

$b^2-4ac= (-12)^2-4\cdot 1\cdot12=96$

This means the parabola will intercept the x-axis at 2 points, two real roots.

Since the coefficient of the quadratic term is positive (a=1), the parabola is oriented "open-up." But since we already know the parabola intercepts in two points, the fact that it is open-up implies now that the vertex must lie below the x-axis (otherwise it could not intercept it).

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12 eggs cost 2.04 .how much would 18 eggs cost

Answers

To find this we need to find the unit rate for each egg. To find the unit rate we need to divide $2.04 by 12. $2.04 divided by 12 equals $0.17. Now multiply 18 by $0.17 to find the price for 18 eggs. 18* 0.17 = 3.06
So the answer is $3.06

$2.04 \ 12 =.17 which means each egg costs $0.17
.17x18= 3.06 which is your answer

When solving the equation 2/3 b 5 = 7, you should first ? from both sides. Then you should multiply both sides by the ? of ?. Your answer will be ? .

Answers

Depends on the question...

If your question is 2/3b + 5 = 7, then follow this one
$(2)/(3)b + 5 = 7\n\n\sf You~ first~subtract~ 5 ~on ~both~ sides\n\nThen ~you~multiply~by~(3)/(2)~on~both~sides.\n\n So...\n\n (2)/(3)b + 5 - 5 = 7 - 5\n\n(2)/(3)b = 2\n\n(2)/(3)b * (3)/(2) = 2 * (3)/(2)\n\nb = 3$
Your final answer will be b = 3

If your question is 2/3b - 5 = 7, then follow this one
$(2)/(3)b - 5 = 7\n\n\sf You~ first~add~ 5 ~on ~both~ sides\n\nThen ~you~multiply~by~(3)/(2)~on~both~sides.\n\n So...\n\n (2)/(3)b - 5 + 5 = 7+5 \n\n(2)/(3)b = 12\n\n(2)/(3)b * (3)/(2) = 12 * (3)/(2)\n\nb =18$
Your final answer will be b = 18

marcus can buy 0.3 pound of sliced meat from a deli for $3.15 how much will 0.7 pound of sliced meat cost?

Answers

Answer: The required cost of 0.7 pounds of sliced meat is $7.35.

Step-by-step explanation: Given that Marcus can buy 0.3 pound of sliced meat from a deli for $3.15.

We are to find the cost of 0.7 pound of sliced meat.

We will be using the UNITARY method to solve the problem.

We have

the cost of 0.3 pound of sliced meat = $3.15.

So, the cost of 1 pound of sliced meat will be

$(3.15)/(0.3)=(31.5)/(3)=\$10.5.$

Therefore, the cost of 0.7 pound of sliced meat is

$10.5*0.7=1.05*7=\$7.35.$

Thus, the required cost of 0.7 pounds of sliced meat is $7.35.

$22.05 because $3.15 times 0.7 is= 22.05

Six grape fruit cost $5.34. How much does one grape fruit cost????

Answers

In order to figure this out, we can set up a proportion and simplify using cross multiplication.

$(units_1)/(cost _(1) ) =(units_2)/(cost _(2) ) \n \n (6)/(5.34) = (1)/(x) \n \n 6*x=5.34*1 \n \n 6x=5.34 \n \n x=0.89$

One grapefruit costs 89 cents.

You divide 5.53 by 6
And you'll get
.89cents

Charlie's hot tub holds 9,216 liters. If he wanted to fill his hot tub using a 9-liter bucket, how many full buckets would he have to use?

Answers

Answer:

1024

Step-by-step explanation:

9216/9=1024

3 pineapples, 2 cabbages and 6 bananas cost a total of $27.2 pineapples, 3 cabbages and 4 bananas cost a total of $23.
4 pineapples, 1 cabbage and 8 bananas cost a total of $31.
Find the costs of:
-one pineapple -one cabbage -one banana
*Please show your work step by step*

Answers

3p + 2c + 6b = 27
2p + 3c + 4b = 23
4p + 1c + 8b = 31
===============
take any 2 equations and eliminate a variable

3p + 2c + 6b = 27
4p + 1c + 8b = 31....multiply by -2
---------------------
3p + 2c + 6b = 27
-8p - 2c - 16b = - 62 (result of multiplying by -2)
--------------------add
-5p - 10b = - 35

Now take one equation, and the other equation that u have not used already, and eliminate the same variable.

4p + 1c + 8b = 31.....multiply by -3
2p + 3c + 4b = 23
---------------------
-12p - 3c - 24b = - 93 (result of multiplying by -3)
2p + 3c + 4b = 23
----------------------add
-10p - 20b = - 70

now take ur 2 equations that u eliminated the c in, and eliminate another variable

-5p - 10b = -35......multiply by -2
-10p - 20b = -70
---------------------
10p + 20b = 70 (result of multiplying by -2)
-10p - 20b = -70
-------------------add
0 = 0

when u get a result such as 0 = 0....this means there is infinite solutions to this problem

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