MATHEMATICS HIGH SCHOOL

Question: Find the x-intercepts for the parabola defined by this equation:y = 2x²
- 8x + 10
Write your answer as two ordered pairs:
(x1, y1), (×2, y2)
Separate the values with a comma.
Round, if
necessary, to the nearest hundredth.

Answers

Answer 1
Answer:

Answer:

To find the x-intercepts of the parabola defined by the equation y = 2x² - 8x + 10, you need to set y equal to zero (because x-intercepts occur when y is zero) and solve for x.

So, you have:

0 = 2x² - 8x + 10

Now, you can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 2, b = -8, and c = 10. Plug these values into the formula:

x = (-(-8) ± √((-8)² - 4 * 2 * 10)) / (2 * 2)

x = (8 ± √(64 - 80)) / 4

x = (8 ± √(-16)) / 4

Since the discriminant (the value inside the square root) is negative, there are no real solutions, which means this parabola does not have x-intercepts in the real number system.

So, there are no ordered pairs (x1, y1) and (x2, y2) for x-intercepts because there are no x-intercepts for this parabola in the real number system.

Step-by-step explanation:

Certainly, let's find the x-intercepts step by step for the equation:

y = 2x² - 8x + 10

Step 1: Set y to zero because x-intercepts occur when y equals zero:

0 = 2x² - 8x + 10

Step 2: Now, we want to solve this equation for x. We can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this formula:

a is the coefficient of the x² term (which is 2 in this case).

b is the coefficient of the x term (which is -8).

c is the constant term (which is 10).

Step 3: Plug the values of a, b, and c into the formula:

x = (-(-8) ± √((-8)² - 4 * 2 * 10)) / (2 * 2)

Step 4: Simplify the equation inside the square root:

x = (8 ± √(64 - 80)) / 4

x = (8 ± √(-16)) / 4

Step 5: Now, notice that we have a square root of a negative number (√(-16)). In the real number system, we can't take the square root of a negative number. This means there are no real solutions for x.

Step 6: Since there are no real solutions, there are no x-intercepts for this parabola in the real number system. Therefore, there are no ordered pairs (x1, y1) and (x2, y2) for x-intercepts in this case.

Related Questions

How much is 96.25 in a fraction
It is not always helpful to rewrite an equation in standard form as a first step in solving it.True/False?
For 7/20, what is an equivalent fraction with a denominator of 100?
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What is 371/2% as a fraction. simplify your answer..

Answers

(371)/(2)%
=(371)/(2) × (1)/(100) (percentage)
Because (371)/(2) ÷ 100 is the percent
and we multiply by the reciprocal of 100 which is (1)/(100)
=(371)/(200)
As a fraction it is: (371)/(200)
As a decimal it is: 1.855

A scientist begins an experiment with a culture of 5 bacteria cells. Every hour, the number of bacteria cells triples. Which equation can be used to represent the number of bacteria cells, y, as it relates to time in hours, x?a. y = 5 x
b. y = 3(5) x
c. y = 3 x
d. y = 5(3) x

Answers

The answer is c hope it helps

Which of the following represents "the difference between a number and eight is twenty-two"?8 - N = 22
N - 8 = 22
8 - 22N

Answers

Both of the first 8 - N = 22 N - 8 = 22 Represent the difference between a number and 8 is 22 as it is not mentioned that either 8 or the unknown number N is greater so both of the first two represent the difference between a number and 8 is twenty two.

Answer:

The Answer is N - 8 = 22

this is because the question ask the difference of a number and eight is twenty-two, which means a number (N) comes first before the difference ( - ) is  eight (8) is (=) twenty two (22) following this order gives the answer above in bold.

Step-by-step explanation:

Which number produces a rationale number when added to 0.5

Answers

Answer:

only 1/4 produces a rational number when added to 0.5.

Step-by-step explanation:

At a store, ice cream cones cost $1.80 and sundaes cost $3.30. One day the receipts for a total of 148 cones and sundaes were $360.90. How many cones were sold? How many sundaes?

Answers

X= cones; y= sundaes

1.80x + 3.30y = 360.90 -------(i)

x + y = 148 -----------(ii)

from (ii) y= 148-x

1.80x + 3.30(148-x) = 360.9

1.80x + 488.4 + 3.30x = 360.9

1.5x = 127.5

x  = 85 cones

What is the domain of y = cos θ?A. [-1, 1]
B. [0, infinity]
C. All real numbers
D. 2pi,

Answers

Answer:

Option C - All real numbers                                      

Step-by-step explanation:

Given : Function y=\cos \theta

To find : The domain of given function ?

Solution :

Domain is defined as the set of values for which function is defined.

We have given the function,

y=\cos \theta

We know, for any value of \theta the function  y=\cos \theta is defined.

Which means the set of all real numbers defined the given function i.e. x\in(-\infty,\infty)

Therefore, Option C is correct.

The domain of  y=\cos \theta is all real numbers.
The domain of y = cos θ is all real numbers. This is because any real number can be plugged in for θ and y will be equal to a real number. This can be shown graphically because the y = cos θ will go on infinitely both to the right and left.
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