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jarptica [38.1K]
3 years ago
12

Which function has a range of y<3? y=3(2) y=2(3) O y=-(2)* +3 O y= (2)* - 3

Mathematics
1 answer:
VARVARA [1.3K]3 years ago
7 0

option C is correct.

<u>Step-by-step explanation:</u>

If a function is defined as

f(x)=a^x where, a>0, then the range of the function is greater than 0.

a^x>0               .... (1)

Option A: Using inequity (1),

2^x>0

Multiply both side by 3.

3(2^x)>0

The range of first function is y>0. Therefore option A is incorrect.

Option B: Using inequity (1),

3^x>0

Multiply both side by 2.

2(3^x)>0

The range of second function is y>0. Therefore option B is incorrect.

Option C: Using inequity (1),

2^x>0

Multiply both side by -1.

-2^x

Add 3 on both the sides.

-2^x+3

y

The range of first function is y<3. Therefore option C is correct.

Option D: Using inequity (1),

2^x>0

Subtract 3 from both the sides.

2^x-3>-3

y>-3

The range of second function is y>-3. Therefore option D is incorrect.

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20% of 57 is what number ?<br> The proportion is ?
Elanso [62]

Answer:

11.4

20/100 = x/57

Step-by-step explanation:

It is perhaps simplest just to translate the given English sentence into a mathematical sentence.

... 20% ... ... of ... 57 ... is ... what number

... 20/100 ... × ... 57 .... = ... what number . . . . . . . . translation to math sentence

... 11.4 = what number . . . . . . . . carry out the multiplication

_____

If you're asked to write this as a proportion, you can write it like this:

\dfrac{20}{100}=\dfrac{\text{what number}}{57}

You can solve this proportion by multiplying by 57 (the denominator under "what number"). Doing so gives you the same arithmetic sentence as shown above.

6 0
3 years ago
A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region. Be sur
Finger [1]

Answer:

The area of the triangle should be: [(1 + 5 + 4) × 11]/2= 55 (ft²)

The area of the rectangle should be: 5 × 2 = 10 (ft²)

The area of the shaded region is: 55 - 10 = 45 (ft²)

7 0
3 years ago
What is the answer for 8x+3=4x?
AysviL [449]

Answer:

x = -3/4

Step-by-step explanation:

<u>Step 1:  Identify the equation</u>

8x + 3 = 4x

<u>Step 2:  Move x's to one side and number to the other side</u>

8x + 3 - 4x - 3 = 4x - 4x - 3

4x = -3

<u>Step 3:  Make x by itself</u>

4x / 4 = -3 / 4

x = -3/4

Answer:  x = -3/4

7 0
3 years ago
A basketball and a pump cost $31. If the basketball costs 3 times as much as the pump how much does each item cost?
postnew [5]
3 times 7.75 = 23.25 + 7.75 = 31.00
so the basketball is $23.25 and the pump is $7.75
4 0
3 years ago
100 points!!!!!!!
creativ13 [48]

Answer:

The minimum unit cost is equal to $15,339

Step-by-step explanation:

Let

x ----> the number of engines

C ---> the cost in dollars to make each airplane engine

we have

C(x)=0.5x^{2} -100x+20,339

This is a vertical parabola open upward (the leading coefficient is positive)

The vertex represent the minimum of the parabola

The minimum unit cost is equal to the y-coordinate of the vertex

Convert the quadratic equation into vertex form

Factor 0.5

C(x)=0.5(x^{2} -200x)+20,339

Complete the square. Remember to balance the equation by adding the same constants to each side

C(x)=0.5(x^{2} -200x+100^2)+20,339-5,000

C(x)=0.5(x^{2} -200x+10,000)+15,339

Rewrite as perfect squares

C(x)=0.5(x-100)^{2}+15,339 ----> equation into vertex form

The vertex is the point (100,15,339)

The y-coordinate of the vertex is 15,339

therefore

The minimum unit cost is equal to $15,339

4 0
3 years ago
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