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2 months ago

Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.

2 answers:

6 0

If x equals zero, both functions have the same value.

Therefore, the first and second choices are incorrect.

Evaluating at x = -1:
g(-1) equals 1,
h(-1) equals -1,
so the third option is correct.

The fourth option is false.

Except at zero, for all other values, g(x) is greater than h(x).

Hence, the valid statements are:

g(x) is greater than h(x) when x = -1.
For positive x values, g(x) exceeds h(x).
For negative x values, g(x) exceeds h(x).

Svet_ta [12.7K]2 months ago

5 0

Answer: g(x) > h(x) when x = -1.

For x greater than zero, g(x) is greater than h(x).

For x less than zero, g(x) is greater than h(x).

Step-by-step explanation:

Given the functions: $g(x)=x^2$ and $h(x)=-x^2$

At x = 0, $g(0)=0^2=0$ and $h(0)=-0^2=0$

. Therefore, g(0) equals h(0).

Hence, statements claiming that for all x, g(x) is always greater than h(x), or vice versa, are incorrect.

At x = -1, $g(-1)=(-1)^2=1$ and $h(-1)=-(-1)^2=-1$

So, g(x) > h(x) for x = -1............................(1)

At x = 3, $g(3)=(3)^2=9$ and $h(3)=-(3)^2=--9$

Therefore, g(x) > h(x) at x = 3........................(2)

Which disproves the statement that g(x) < h(x) for x = 3.

From points (1) and (2):

For any positive x, g(x) > h(x).

For any negative x, g(x) > h(x).

$3,000

Detailed breakdown:

This scenario is centered around compound interest, with the formula for compound interest defined as

Provided Data

A = final amount =?

P = initial principal balance = $2,500

r = interest rate = 2.1%= 0.021

t = number of time units passed= 14 years

By inserting our data into the compound interest equation, we can determine the final amount

$A= 2500(1+0.021)^1^4\\A= 2500(1.021)^1^4\\A= 2500*1.3377\\A= 3344.25\\$

Therefore, rounding to the nearest hundred gives us an account balance of $3,000

6 0

26 days ago

1. The C major key, starting with the middle C, consists of seven notes (white keys on the piano) with the following frequencies

Zina [12379]

1.) The ratio of note A compared to middle C is 440.0 / 261.6 = 1.6820 ≈ 1.6818

2.) The D note's ratio against middle C is 293.7 / 261.6 = 1.1227

3.) D# = 293.6 multiplied by 1.0595 equals 311.1

4.) The frequency ratio of G compared to C is 1: 262/392 = 1: 0.6683 ≈ 3: 2

5.) The frequency ratio of E to C is 1: 262/330 = 1: 0.7939 ≈ 5: 4

6.) The element in a musical note referred to as pitch is the frequency.

8 0

1 month ago

Read 2 more answers

At what rate would you need to invest $12000 and make $2880 after 8 years?

PIT_PIT [12445]

Answer:

$3\%$

Step-by-step explanation:

We start with the fact that

The formula for simple interest is represented by

$I=P(rt)$

where:

I denotes the Final Interest Value

P indicates the Principal amount to be invested

r specifies the interest rate

t refers to the Number of Time Periods

For this scenario, we have

$t=8\ years\\ P=\$12,000\\I=\$2,880\\r=?$

We can substitute these values into the formula mentioned above

$2,880=12,000(8r)$

Next, we solve for t

$2,880=96,000(r)$

$r=2,880/96,000$

$r=0.03$

Convert to a percentage format

$0.03*100=3\%$

4 0

1 month ago

1. Darnell reads at a constant rate

Svet_ta [12734]

Answer:

Darnell reads 1,715 words in 7 minutes.

Step by step Explanation:

1. First, determine how many words he can read in a minute by dividing 735 words by 3. The result is 245.

245

______

3)735

6 drop the 3 to form 13

-_____

1 3

12 drop the 5 to make 15

-______

1 5

___________

2. Next, since he reads 735 words over 3 minutes, multiply that by 2 to find words read in 7 minutes: 3×2=6, thus, 735+735 (735×2) equals 1,470 words.

3. Finally, add 245 to account for the last minute we calculated. Therefore, the total is 1,715 words in 7 minutes.

8 0

1 month ago