MATHEMATICS MIDDLE SCHOOL

Determine the smallest integer value of a for which f(x) has imaginary zeroes. Show how you foundthis answer.

Answers

Answer 1

Answer:

1 is the smallest possible integer.

Given that: $f(x)=ax^2-2x+5$ .

The discreminant of this equation is:

$b^2-4ac=(-2)^2-4a(5)=4-20a$

For imaginary zeros, we must get discreminant less than 0.

So,

$4-20a<0\n20a>4\na>(4)/(20)\na>0.2$

Next integer of 0.2 is 1.

So 1 is the smallest possible integer.

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Answer 2

Answer:

The question is incomplete, the complete question is

Determine the smallest integer value of a for which f(x) = ax² - 2x + 5 has imaginary zeroes. Show how you found this answer

Answer:

The smallest integer value of a is 1

Step-by-step explanation:

To find the zeroes of a function equate it by 0, then find the values of x which are the zeroes of the function

To find the types of the roots (zeroes) of a function f(x) = ax² + bx + c use the discriminant of the function b² - 4ac

If b² - 4ac > 0, then the function has two different real roots
If b² - 4ac = 0, then the function has one real root
If b² - 4ac < 0, then the function has no real roots (imaginary roots)

∵ f(x) = ax² - 2x = 5

- To find its zeroes equate f(x) by 0

∴ ax² - 2x + 5 = 0

∵ f(x) has imaginary zeroes

- That means the discriminant is less then zero

∴ b² - 4ac < 0

∵ a = a, b = -2 and c = 5

- Substitute them in the inequality above

∴ (-2)² - 4(a)(5) < 0

∴ 4 - 20 a < 0

- Add 20 a to both sides

∴ 4 < 20 a

- Divide both sides by 20

∴ 0.2 < a

- That means a is greater than 0.2

∴ a > 0.2

∵ You must to find the smallest integer value of a

- The first integer greater than 0.2 is 1

∴ a = 1

The smallest integer value of a is 1

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Alana and her friends decided to have a water fight on a hot summer day. They filled a bunch of water balloons and started the fight at 12:20 P.M. The water balloons lasted for 25 minutes. When all the water balloons were gone, they sprayed water with hoses for 55 minutes, until Alana's dad showed up with ice cream. What time was it when the water fight ended?

Answers

The time was it when the water fight ended is when they started the fight at 12:20 P.M. at 1:40 P.M.

To find out what time the water fight ended, you can start with the initial time when they began the water fight (12:20 P.M.) and then add the duration of the water balloon fight and the hose spraying.

Water balloons lasted for 25 minutes, and spraying water with hoses lasted for 55 minutes, so:

Total duration = 25 minutes (water balloons) + 55 minutes (hose spraying)

= 80 minutes

Now, add these 80 minutes to the starting time:

12:20 P.M. + 80 minutes = 1:40 P.M.

So, the water fight ended at 1:40 P.M.

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1:40 PM

hope this helps :)

Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 + 2x + 6? left 1 unit, up 5 units right 1 unit, up 5 units left 2 units, up 2 units right 2 units, up 2 units

Answers

Answer:

Shift left by 1 unit
Shift up by 5 units

Step-by-step explanation:

In order to answer this question first we have to convert g(x) into vertex form.

$g(x)=x^(2)+2x+6\ng(x)=x^(2)+2(x)(1)+(1)^(2)+5\ng(x)=(x+1)^(2)+5$

Now from this form we can visualize the transformations made to f(x) to get the graph of g(x).

Addition of 2 in x means that graph of f(x) = x2 is shifted 1 unit to left to get (x + 1)² .

Addition of 5 in the function value indicates that the graph is shifted 5 units up.

So the changes which have been made to f(x) in order to get g(x) are:

Shift left by 1 unit
Shift up by 5 units

Mr grant need 30 pieces of felt .he can buy them in packs of 10 or single pieces.what are the different ways mr.grant can buy the felt?

Answers

Mr Grant can buy the felt in a variety of ways. He can buy 3 packs of10 pieces, 30 single pieces, 1 pack of 10 and 20 single pieces, or 2packs of 10 and 10 single pieces. Hope that answered your question foryou!

What dose the 9 in 4.59 stand for

Answers

9 is there in hundredth place of the given decimal number.

The given decimal number is 4.59.

What are decimal numbers?

Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point.

In the given decimal number 4.59, 9 is there in hundredth place

Therefore, 9 is there in hundredth place of the given decimal number.

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In decimals the 9 in 4.59 stands for hundredths

A student walks 8 meters down the hall, realizes they forgot something from their locker andturns around and walks back 2 meters. Calculate their net displacement.