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charle [14.2K]
3 years ago
8

Determine the nth term for each of the following sequences:16,15,14,13,12,..

Mathematics
1 answer:
Vladimir79 [104]3 years ago
7 0
F(n) = 1st term - common difference (n - 1)

The operation is subtraction because the sequence is decreasing.

n = number of the term you are looking for
1st term = 1st number in the sequence, in this case, 16
common difference = difference between one number to the next

f(n) = 16 - 1(n-1)

Assuming we are looking for the 5th term.
f(5) = 16 - 1(5-1)
       = 16 - 1(4)
       = 16 - 4
       = 12     * as you can see, 12 is the 5th term of the sequence.

If you are looking for the equivalent of the nth term, simply substitute n by the number you are looking for and solve the equation.
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To make four cakes, Dena used 6 cups of sugar. Using the same recipe, how much sugar does she need to make one cake?​
Fantom [35]
1.5 cups per cup. cups/cake
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5 0
3 years ago
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Find the sine of Write your answer in simplified, rationalized form. Do not round.<br> Please help!!!!!
erma4kov [3.2K]

Answer:

Sin (E) = √74/(2√23)

Step-by-step explanation:

Reference Angle = E

Hypotenuse = 2√23

Adjacent = 3√2

Opposite = DC = √(2√23)² - (3√2)²) = √(4*23 - 9*2) = √(92 - 18) = √74 (pythagorean theorem)

Recall SOHCAHTOA.

Thus,

Sin (E) = opp/hyp

Sin (E) = √74/(2√23)

6 0
3 years ago
The legs of a right triangle have the following measurements: 5 and 10 inches. What is the length of the hypotenuse??
RideAnS [48]

Answer:

5\sqrt{5}

Step-by-step explanation:

1. 5^2 + 10^2 = c^2

2.125 = c^2

3. c=5\sqrt{5}

7 0
3 years ago
Order the following numbers from least to greatest.
zaharov [31]

Answer:

-5.5  -\sqrt{20}  \sqrt4  \frac{22}{7}  4.5

Step-by-step explanation:

Given:

The numbers to order from least to greatest is given as:

-5.5, 4.5, 22/7,\sqrt4,-\sqrt{20}

In order to compare these numbers, we have to convert them in same form.

Let us simplify each number in decimal form.

-5.5 = -5.5\\\\4.5=4.5\\\\\frac{22}{7}=3.14\\\\\sqrt4=2\\\\-\sqrt{20}=-\sqrt{5\times 2^2}=-2\sqrt5=-4.47

So, the least number is one which has the largest value with a negative sign.

Here, -5.5 is the least number.

The next smallest number is -4.47. So, -\sqrt{20}

The next smallest number is 2. So, \sqrt4

The next smallest number is 3.14. So, \frac{22}{7}

The greatest number is 4.5.

Therefore, the order from the least to greatest is:

-5.5 < -\sqrt{20} < \sqrt4 < \frac{22}{7} < 4.5

8 0
3 years ago
Find the sum of 10 x 2 + 7 x + 6 10x 2 +7x+6 and 6 x + 5 6x+5.
dusya [7]

The sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

<h3>Sum of expressions</h3>

Expressions are equations separated by mathematical signs. This expressions are known to contains certain unknowns

Given the following expression

10x^2 +7x+6 and 6x + 5

We are to take the sum of both expression to have:

f(x) = 10x^2 +7x+6 + 6x + 5

Collect the like terms

f(x) = 10x^2 + 7x + 6x + 6 + 5

f(x) = 10x^2 + 13x + 11

Hence the sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

Learn more on sum of functions here: brainly.com/question/11602229

#SPJ1

8 0
2 years ago
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