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3 years ago

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Mathematics

1 answer:

Crazy boy [7]3 years ago

7 0

Answer:

Each point (or pair in a proportional relationship) must share the same difference

Step-by-step explanation:

The graph of a proportional relation is a straight line through the origin. Such a line has the same ratio of y/x everywhere.

A relation in which the difference is constant will be a straight line, but it won't be through the origin. Such a relation is not proportional.

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Find the first term and the common ratio <br>third term =6 and seventh term= 96

mamaluj [8]

Answer:

First term a₁ = 3/2 and common ratio r = 2

Step-by-step explanation:

We need to find the first term and common ratio while we are given third term = 6 and seventh term = 96

Since common ratio is required so, the sequence is geometric sequence

The formula used is: $a_n= a_1r^{n-1}$

We are given: third term = 6 i,e

$a_3=a_1r(3-1)\\6=a_1r^2----eq(1)$

Seventh term = 96

$a_7=a_1r(7-1)\\96=a_1r^6----eq(2)$

Dividing eq(2) and eq(3)

$\frac{96}{6}=\frac{a_1r^6}{a1r2}\\16=\frac{r^6}{r^2}\\16=r^{6-2}\\=> r^4=16\\Taking \ fourth \ root\\ r=2,-2,2i,-2i\\ \ We \ will \ consider \ only \ positive \ value \ of \ r \ i.e \ \textbf{ r= 2}$

So, Common Ratio r = 2

Finding First term using eq(1)

$a_3=a_1r^2\\6=a_1(2)^2\\6=a_1(4)\\a_1= \frac{6}{4}\\a_1= \frac{3}{2}$

So, First term a₁ = 3/2 and common ratio r = 2

6 0

3 years ago

Analyze the diagram below and complete the instructions to follow.<br><br> Find a, b and c

Feliz [49]

Answer/Step-by-step explanation:

✔️Using trigonometric ratio, find b:

Reference angle = 45

opposite = 8

Hypotenuse = b

Thus,

Sin(45) = 8/b

b = 8/sin(45)

b = 8/(1/√2) (sin 45 = 1/√2)

b = 8 × √2/1

b = 8√2

✔️Find a using trigonometric ratio:

Reference angle = 60°

Hypotenuse = b = 8√2

Adjacent = a

Therefore,

Cos(60) = a/8√2

8√2*cos(60) = a

8√2*½ = a

4√2 = a

a = 4√2

✔️Find c using Pythagorean Theorem:

c² = b² - a²

c² = (8√2)² - (4√2)²

c² = 128 - 32

c² = 96

c = √96

c = √(16*6)

c = 4√6

5 0

3 years ago

Which of the following is the quotient of the rational expressions shown here? x/x-1 / 1/x 1.

WINSTONCH [101]

The quotient of the rational expressions is $\rm \dfrac{x^2-x}{x-1}$ .

<h3>Given that</h3>

Rational Expression; $\rm \dfrac{x}{x-1}$ ÷ $\rm \dfrac{1}{x+1}$

<h3>We have to determine</h3>

Which of the following is the quotient of the rational expressions shown here?

<h3>According to the question</h3>

Rational Expression; $\rm \dfrac{x}{x-1}$ ÷ $\rm \dfrac{1}{x+1}$

Then,

The quotient of the rational expressions is,

$\rm \dfrac{x}{x-1}$ ÷ $\rm \dfrac{1}{x+1}$

$\rm =\dfrac{x}{x-1} \times \dfrac{x+1}{1}\\
\\ =\dfrac{x(x-1)}{x\times 1}\\
\\
=\dfrac{x^2-x}{x-1}$

Hence, The quotient of the rational expressions is $\rm \dfrac{x^2-x}{x-1}$ .

To know more about Division click the link given below.

brainly.com/question/26163188

7 0

3 years ago

Which of the follwing regular polygons can make a tessellation?

Elodia [21]

I think it's square and hexagon.

6 0

3 years ago

A pool table supply company is making a cardboard box to package new cubes of pool cue chalk. Each cube of chalk is 1 cubic inch

rosijanka [135]

Answer:

Step-by-step explanation:

they all require the same amount of card board because if you take all of the numbers times eachother they all come out as 16 Take a bottle arranged with tubes, as in the middle one shown in the figure on page 87.

8 0

3 years ago