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2 years ago

Which is the best interpretation of the solution set for the compound inequality?

Mathematics

2 answers:

lara [203]2 years ago

4 0

The Answer is C)x>3 or x<4 but i think you switched the signs around

Fantom [35]2 years ago

4 0

Answer: The correct option is (b) $3$

Step-by-step explanation: We are given to select the best interpretation of the solution set for the following compound inequality :

$3(2x+1)>21~~\textup{or}~~4x+3$

We are to solve the inequalities separately.

We have

$3(2x+1)>21\\\\\Rightarrow 2x+1>\dfrac{21}{3}\\\\\Rightarrow 2x+1>7\\\\\Rightarrow 2x>6\\\\\Rightarrow x>\dfrac{6}{2}\\\\\Rightarrow x>3$

$4x+3$

Thus, the required solution is

$3$

Option (b) is CORRECT.

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Find the 75th term of the following arithmetic sequence.<br> 6, 11, 16, 21,

katrin [286]

Answer:

The 75th term in the sequence is 16

Step-by-step explanation:

The 75th term of a sequence can be considered as the term that is in the position at 75% along the sequence. This is assuming that the sequence has been sorted already from lowest value to highest value

In this sequence, which has 4 terms, we can find the 75th term by finding what term is at 75% (or three-quarters) along the sequence.

To find the 75th term:

Multiply the number of terms by 0.75 (or 75%/100%) :

0.75*4 terms= 3

Then, we find the value of the term that is at position 3 from the left (lowest number)

In this case, the term that is at the 3rd position from the left is 16

Thus, the 75th term in the sequence is 16

8 0

2 years ago

What type of transformation occurred in the graph for g(x)?

Galina-37 [17]

Answer:

The tranformation ocurred in the graph is b.

Step-by-step explanation:

Because it is going inner, meaning the tranformation ocurred in the graph is b.

3 0

3 years ago

Read 2 more answers

Kendra dives off a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation: ,

MAVERICK [17]

Answer:

1. 6 feet

2. 6.25 feet

3. 1 feet

4. 6 feet

Step-by-step explanation:

The equation is : $h(x)=x^2-7x+6$

1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

$h(0)=0^2-7(0)+6$

$=0-0+6$

$=6$

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

It is the minimum height which represents the depth Kendra dives into the water.

So the $x$ coordinate of the vertex is = $\frac{-b}{2a}$

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴ x coordinate = $\frac{-(-7)}{2 \times 1}$

$\frac{7}{2}=3.5$

Now substituting to find f(x),

$h(3.5)=(3.5)^2-7(3.5)+6$

= -6.25

Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ $0=x^2-7x+6$

Factorizing, we get $(x-1)(x-6)=0$

∴ $x=1 \text{ or}\ x=6$

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has $\text{two}$ x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height $h(x)=0$ . The height is the water surface level.