Solve the inequality:<br> 2x - 7<-5 or 10x + 5 285

Work out the formula for the nth term of the<br>quadratic sequence:<br>5, 11, 19, 29

Sladkaya [172]

Answer:

n squared + 3n + 1

Step-by-step explanation:

5,11,19,29

Firstly look at the difference between each number. The first difference is 6 then 8 then 10 etc. After that you look at your created sequence - 6,8,10 etc. The difference is 2 each time. Then applying rules, you have to do the constant difference divided by 2 to get a coefficient of n squared. So in this case it's n squared because 2/2 = 1 so you don't have to place a 1 in front of the n squared. After you create a sequence from the n squared. That would be 1,4,9 etc. Then you need to see how to get from the sequence: 1,4,9 etc to your original sequence: 5,11,19 etc. So if you calculate it you will get 4,7,10 because firstly 5-1 = 4 then 11-4 = 7 etc. The sequence 4,7,10 is a linear sequence so the constant difference is 3 each time. So to get a nth term of a linear sequence you will start off as 3n then you will substitute 1 then 2 then 3 into the 3n. Therefore that would be 3,6 etc. So if you take the first substituted term, that would be 3 as said before then you will have to see how to get from the 3 to 4 so that is just adding 1. So the nth term of this linear sequence is 3n + 1. Check if it works at the end. So the overall nth term of the quadratic sequence is n squared as said before + 3n + 1.

8 0

2 years ago

If 48% of the students in a certain college are female and there are 1440 female students, what is the total number of students

Andrews [41]

Answer:

3000 students

Step-by-step explanation:

If 48% of the students are female, and there are 1440 female students, we can set up a percentage proportion, assuming x is the total amount of students.

$\frac{1440}{x} = \frac{48}{100}$

We can use the cross products property to find the value of x.

$1440\cdot100=144000\\\\144000\div48=3000$

Hope this helped!

5 0

3 years ago

The dimensions of a wading pool shaped like a rectangular prism are shown below. What is the volume of the pool?

sergey [27]

Answer:

i believe its b

Step-by-step explanation:

5 0

2 years ago

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A cylinder has a 12-inch diameter and is 15 inches tall. It is filled to the top with water. A 6-inch-diameter ball is placed wi

Tems11 [23]

The volume of the cylinder is the space occupied by the cylinder. The volume of the water in the cylinder is 1583.36266 in³.

<h3>What is the volume of a cylinder?</h3>

The volume of the cylinder is the space occupied by the cylinder. It is calculated with the help of the formula,

$\text{Volume of the cyllinder}= \pi r^2h$

As it is given that the diameter of the cylinder is 12 inches while the height of the cylinder is 15 inches, also, it has a ball of the diameter of 6 inches placed inside the cylinder, therefore, the volume of the water that is inside the cylinder is the difference in the volume of the cylinder and the volume of the spherical ball.

$\text{Volume of the cyllinder}= \pi r^2h = \dfrac{\pi}{4}d^2 h$

Substitute the values,

$\begin{aligned}\text{Volume of the cyllinder}&= \dfrac{\pi}{4}d^2 h\\& = \dfrac{\pi}{4} \times (12^2) \times 15\\ &=1696.46\rm\ in^3\end{aligned}$

Now, the volume of the ball is equal to the volume of the sphere therefore, the volume of the ball can be written as,

$\text{Volume of the sphere} = \dfrac{4}{3}\pi r^3$

$= \dfrac{4}{3}\pi r^3\\\\= \dfrac{4}{3}\times \pi \times (3^3)\\\\= 113.097\rm\ in^3$

Further, the volume of the water that is inside the cylinder can be written as,

The volume of water = Volume of the cylinder - Volume of the sphere

= 1696.46 - 113.097

= 1583.36266 in³

Hence, the volume of the water in the cylinder is 1583.36266 in³.

Learn more about Volume of the Cylinder:

brainly.com/question/1780981

5 0

1 year ago

The area of a square is 64n^36 square units. what is the side length of one side of the square

sesenic [268]

Area = (side length)^2

Here,
64n^36 = s^2. Take the sqrt of both sides, obtaining 8n^18 = s. This is the principal square root. We use this positive quantity because the measure of side length must be positive.

8 0

3 years ago

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Solve the inequality: 2x - 7<-5 or 10x + 5 285