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kirza4 [7]
2 years ago
13

What is the range of the function y=-x² +1? A) y≤ -1 B) y²-1 C) y≤ 1 D) y≥ 1

Mathematics
1 answer:
MakcuM [25]2 years ago
8 0

Answer:

Option (C)

Step-by-step explanation:

The minimum value of x² is 0, and the maximum value is unbounded, so therefore, the maximum value of -x² is 0, and the minimum value is unbounded.

So, this means that adding 1 to this, the range matches with option C.

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Q. Ross and Chandler go to Taco Land and order sodas for a total of $3.50.
ICE Princess25 [194]

Answer:1.75t + 3.50 ≤ 20

Step-by-step explanation:hope this helps :)

6 0
3 years ago
Using the side of a building as one side and fencing for the other three sides, a rectangular garden will be constructed. Given
scZoUnD [109]

Answer:

The dimensions that would create the garden of maximum area are 30 feet and 15 feet

The maximum area is 450 feet²

Step-by-step explanation:

The garden is fencing for three sides only, That means the length of the fencing is equal to the sum of the length of the three sides

Assume that garden is y feet long and x feet wide and the fencing will cover on side of y feet and two sides of x feet

∵ The sum of the length of the 3 sides = y + x + x

∴ The sum of the length of the 3 sides = y + 2x

- The length of the fencing is equal to the sum of the sides

∵ The fencing is 60 feet

- Equate y + 2x by 60

∴ y + 2x = 60

- Find y in terms of x by subtracting 2x from both sides

∴ y = 60 - 2x

<em>To find the dimensions which make the maximum area, find the area of the garden, then substitute y by x, and differentiate it with respect to x, then equate the differentiation by 0 to find the value of x, and substitute this value in the equation of y to find y and in the equation of the area to find the maximum area</em>

∵ The formula of the area of a rectangle is A = l × w

∵ l = y and w = x

∴ A = x y

- Substitute the value of y above in A

∵ A = x(60 - 2x)

- Multiply bracket by x

∴ A = 60x - 2x²

Now differentiate x with respect to x

∵ A' = 60(1) - 2(2)x

∴ A' = 60 - 4x

- Equate A' by 0 to find x

∴ 0 = 60 - 4x

- Add 4x to both sides

∴ 4x = 60

- Divide both sides by 4

∴ x = 15

- Substitute the value of x in the equation of y to find it

∵ y = 60 - 2(15)

∴ y = 30

The dimensions that would create the garden of maximum area are 30 feet and 15 feet

To find the maximum area substitute x by 15 in the equation of the area

∵ A = 60(15) - 2(15)²

∴ A = 900 - 450

∴ A = 450

The maximum area is 450 feet²

5 0
3 years ago
K/8+7=19<br> solve for k
Slav-nsk [51]

Hello.

k / 8 + 7 = 19, The value of k is 96.

6 0
3 years ago
Read 2 more answers
I need help with this
Aleksandr [31]

Answer:

3. m∠1 = 106° ~ this is because ∠1 and ∠2 together make a straight line and are therefore supplementary, meaning added together, they equal 180° (so I did 180° - 74° = 106°)

4. m∠3 = 74° ~ again, it is supplementary to ∠1. It is also equal to ∠2

5. m∠8 = 114° ~ angles opposite of each other (like 1 and 4) are equal (as we know from question 4). From there, we can use the corresponding angle theorem, so we know 4 and 8 are congruent. (also you can just know 1 and 8 are congruent by using the opposite exterior angles theorem)

6. m∠6 = 124° ~ using same-side interior angle theorem, they are supplementary angles (or the corresponding angles theorem mentioned above, make 4 congruent to 8, and 8 is supplementary to 6)

7. m∠7 = 96° ~ using same side exterior angle theorem, these angles are supplementary

8. m∠2 = 64° ~ again, same side exterior angle theorem

4 0
2 years ago
If a is an integer, when is a/b always equal to an integer?
White raven [17]
A must be equal to b or be a multiple of b or -b in order to be an integer

example   5/5 is an integer (1)
                60/5 is an integer (12) because 60 is a multiple of 5
                -30/5  is an integer (-6) because -30 is a multiple of -5
4 0
3 years ago
Read 2 more answers
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