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2 years ago

83 Tee (CsT Sequences and Functions

Mathematics

1 answer:

NISA [10]2 years ago

3 0

Answer:

The common difference is same = d = -9

Therefore, the data represent a linear function.

Step-by-step explanation:

Given the table

x y

1 4

2 -5

3 -14

4 -23

5 -32

Finding the common difference between all the adjacent terms of y-values

d = -5 - 4 = -6,

d = -14 - (-5) = -14+5 = -9

d = -23 - (-14) = -23 + 14 = -9

d = -32 - (-23) = -32 + 23 = -9

It is clear that the common difference between all the adjacent terms is same.

Thus,

d = -9

We know that when y varies directly with x, the function is a linear function.

Here, it is clear that each x value varies 1 unit, and each y value varies -9 units.

i.e. The common difference is same = d = -9

Therefore, the data represent a linear function.

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What is the equation, in slope-intercept form, of the line that contains the points (3, -4) and (5 -6)

Alika [10]

Answer:

y = -x - 7

Step-by-step explanation:

As we move from the point (3, -4) to the point (5, -6), x increases by 2 and y decreases by 2. Thus, the slope of this line is m = rise / run = -2/2, or -1.

Starting with the general slope-intercept form of the equation of a straight line, we get y = mx + b => y = -1x + b.

Subbing -4 for y and 3 for x, we get

-4 = -1(3) + b, which yields b = -1

Thus, the desired equation is

y = -x - 1

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3 years ago

With some functions, the value of the

Romashka-Z-Leto [24]

Answer and explanation:

This is an example of negative correlation/inverse relationship between two variables. A negative correlation between two variables, independent and dependent variable, occurs when increase in one variable is associated with decrease in the other. In other words, the two variables tend to go in opposite direction.

The independent variable is the variable that causes a change in the dependent variable. For example, an increase in the independent variable in an inverse relationship will bring about a decrease in the dependent variable.

A good real world example is the increase in inflation and the decrease in purchasing power of money.

An equation for this could be

Y=-0.2(x)

Where y is dependent variable purchasing power and x is independent variable inflation

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3 years ago

To find the area of a triangle, you can use the expression b × h ÷ 2, where b is the base of the triangle and h is its height. W

kobusy [5.1K]

Answer:

Step-by-step explanation:

Since the formula is b × h ÷ 2, just plug in the numbers from the question

b × h ÷ 2

2 × 8 ÷ 2 = 8

Hope this helps

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2 years ago

What is 1,000 minus 500

Vinil7 [7]

1,000 - 500 = 500

Hope this Helps!!

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3 years ago

8-35. Use your knowledge of polygons to answer the questions below, if possible.

Nataliya [291]

Answer:

(a)I. 13 Sides II. 7 Sides

(b) 4 Sides, Square

(c)x=52 degrees

(d)x=107 degrees

(e)1620 degrees

Step-by-step explanation:

(a)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

I. If the Interior angle is $1980^0$

Then:

$(n-2)180^0=1980^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=11\\$Add 2 to both sides of the equation\\n-2+2=11+2\\n=13$

The polygon has 13 sides.

II. If the Interior angle is $900^0$

Then:

$(n-2)180^0=900^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=5\\$Add 2 to both sides of the equation\\n-2+2=5+2\\n=7$

The polygon has 7 sides.

(b)The sum of the exterior angle of a polygon is 360 degrees,

Each exterior angle of a n-sided regular polygon is: $\frac{360^0}{n}$

If the exterior angle of a regular polygon is 90°

Then:

$90\°=\frac{360^0}{n}\\ 90n=360\\n=4$

The regular polygon has 4 sides and it is called a Square.

(c)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

Each Interior angle of a regular n-sided polygon is: $\frac{(n-2)180^0}{n}$

For a pentagon, n=5

Then:

$\frac{(5-2)180^0}{5}=2x+4\\108=2x+4\\108-4=2x\\104=2x\\x=52^0$

(d)The sum of the exterior angle of a polygon is 360 degrees.

If four of the exterior angles of a pentagon are 57, 74, 56, and 66.

Let the fifth angle=x

Then:

$57+74+56+66+x=360^0\\253+x=360\\x=107^0$

(e)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

In an 11-gon., n=11

Therefore, the sum of the interior angle=(11-2)180= $1620^0$

The sum of the interior angle does not change either in a regular or irregular polygon.

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3 years ago