MATHEMATICS HIGH SCHOOL

Which equation has exactly one solution?A. 4x^(2) - 12x - 9 = 0
B. 4x^(2) + 12x + 9 = 0
C. 4x^(2) - 6x - 9 = 0
C. 4x^(2) + 6x + 9 = 0

(Please show how you get the answer)

Answers

Answer 1
Answer:

The equation 4x² + 12x + 9 = 0 has exactly one solution. The correct answer would be an option (C).

What is a quadratic function?

The quadratic function is defined as a function containing the highest power of a variable is two.

The solutions to a quadratic equation are found using the quadratic formula, which is:

x = (-b ± √(b² - 4ac)) / 2a

As per option (C),

4x² + 12x + 9 = 0

Compare the given function to the standard quadratic function f(x) = ax² + b x + c.

We get a = 4, b = 12, and c = 9.

The discriminant of the equation,

b² - 4ac = (12)² - 4×4(9) = 144 - 144 = 0

Since the discriminant is zero, this means the equation has only one solution.

Therefore, the equation 4x² + 12x + 9 = 0 has exactly one solution.

Hence, the correct answer would be option (C).

Learn more about the quadratic function here:

brainly.com/question/14083225

#SPJ2
Answer 2
Answer: I would answer this by using the quadratic formula to figure out which equation only has one solution.
quadratic formula: (-b(+or-)√(b^2-(4ac)))/2a.
You find that the equation 4x²+12x+9=0 only has the root of x=-1.5.

Since the solution is where the parabola crosses the x-axis, you can also figure out which equation has only one solution by whether or not the axis of symmetry lands is a solution or not.  If the axis of symmetry is a solution, the function only has one solution (that being the vertex).  If the axis of symmetry is not a solution, the function has to have either two or no roots.  You can find the axis of symmetry by using the equation x=-b/2a.  Using that equation you can find that the equation 4x²+12x+9 has the axis of symmetry being at x=-1.5 which means that the vertex is (-1.5,0).  Since the equation 4x²+12x+9 has its vertex at (-1.5,0) and the vertex is the lowest or highest point of the function, that function only has one x-intercept meaning it only has 1 solution.  

I hope this helps.  Let me know in the comments if anything is unclear.

Related Questions

Reggie ate 31 raisins. Which correctly describes 31 as a prime or a composite number and tells the number of factor pairs 31 has? You're choices are: A-31 is a prime number because it has 0 factor pairs. B-31 is a prime because it has 1 factor pair. C-31 is a composite number because it has 1 factor pair. D-31 is a composite number because it has 2 factor pairs.
The cost of a basket containing apples is $48. Let x represent the number of apples in the basket. Which expression represents the cost of each apple in dollars?
Choosing a 4-letter password using only 5 letters that may each be used more than once.
What is the volume of the figure below if a = 4.2 units, b = 5.7 units, and c = 3 units?a 129.78 cubic unitsb 141.75 cubic unitsc 407.484 cubic unitsd 177.66 cubic units
What is the simplified base for the function f(x) = 2(3√27(2x)?2 3 9 18

Whats the vertex of this question​

Answers

Put a picture up So we can see what you’re talking about

Assuming that there are 10 digits used as telephone number and the area code is a fixed 3 digit number. How many numbers could be created?

Answers

Well 10 minus 3 equals 7 so 7 numbers can be created.

Given that cos42° is simpler to 0.743, What is the sine of the complementary angle?

Answers

The cos of an angle and the sine of its complement are the same number.
Spend a couple of minutes looking at a right triangle, and reviewing the definitions of sin and cos, and you'll see why.
cos(42)=sin(90-42)

So in this case:

cos(42)=sin(48)

As:

A complementary angle is either of two angles whose sum is 90 degrees. {Source: Google}

I ONLY HAVE 5 MIN TO TURN THIS IN PLS HELP!!!!!!!!!!!!!!!!!!!!!!Combine like terms.
-2+6y^3-2y^3+7-7+6x^2-2x^2

Answers

The answer is -2 + 4y^3 + 4x^2

Answer:

4y^3 + 4x^2 -2

(work included in image)

Edgar Anderson earns $300 a week plus a 15% commission only on sales he makes after his first $1000 in sales. If Mr. Anderson’s sales for one week are $2,500, what is his gross pay for that week?

Answers

Answer:

$525

Step-by-step explanation:

Edgar Anderson earns in a week = $300

He also earns commission on the sales he makes after his first $1,000 = 15%

Mr. Anderson's sales for one week are = $2,500

His commission is on his sale = 2,500 - 1,000 = 1,500

He earns commission = 15% of 1,500

                                     = 0.15 × 1,500

                                     = $225

His gross pay for that week = $225 + $300 = $525

Mr. Anderson's gross pay for that week is $525.
His gross pay would be $525.00

2500-1000=1500
1500 x .15 = 225.00
225+300= $525.00

Multiply. Write your answer in simplest form.

5/7 x 7/10

Answers

5/7 × 7/10 = 35 / 70 = 1/2
Other Questions
How to find the circumfrance of a circle
For the function f(x) = 2(8)^x evaluate f(2)
Calculate 5!.A. 5 B. 120 C. 51 D. 60
Last year Mr. John Q. Public received an inheritance. He paid $20\%$ in federal taxes on the inheritance, and paid $10\%$ of what he had left in state taxes. He paid a total of $\$10{,}500$ for both taxes. How many dollars was the inheritance?