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3 years ago

Determine if the sequence is algebraic or geometric, and find the common difference or ratio. x 1 2 3 4 f(x) 81 72 63 54

Mathematics

1 answer:

sergeinik [125]3 years ago

6 0

Answer:

The given sequence is Algebraic (Arithmetic) with common difference is -9.

Step-by-step explanation:

The given sequence is Arithmetic Sequence.

Arithmetic Sequence is a sequence in which every two neighbor digits have equal distances.

Geometric Sequence is the sequence in which every digit is the same multiplier of its previous digit.

The given sequence is: 81, 72, 63, 54,...

Here, First term(a) = 81, Second term(b) = 72

Common difference (d) = b - a = 72 - 81 = -9

Hence, Common difference is -9.

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For what values of a is the value of the binomial 2a−1 smaller than the value of the binomial 7−1.2a by 7?

Nimfa-mama [501]

ANSWER

$a = \frac{5}{16}$

EXPLANATION

We want to find the value of a for which the binomial, 2a-1 is smaller than the value of the binomial 7-1.2a by 7.

This means that, when we subtract 2a-1 from 7-1.2a, we should get 7.

$7 - 1.2a - (2a - 1) = 7$

Expand:

$7 - 1.2a - 2a + 1= 7$

Group similar terms:

$- 1.2a - 2a = 7 - 7 - 1$

$- 3.2a = - 1$

Divide both sides by -3.2,

$a = \frac{ - 1}{ - 3.2}$

$a = \frac{5}{16}$

7 0

3 years ago

The volume of a sphere can be described by the following formula, where V = volume and r = radius of the sphere.

Anika [276]

Option C: $r = \sqrt[3]{\frac{3V}{4\pi} }$ is the right answer

Step-by-step explanation:

Given formula for volume of a sphere is:

$V = \frac{4}{3}\pi r^3$

We have to make r the subject of the formula

Multiplying equation by 3/4

$\frac{3}{4}V = \frac{4}{3} * \frac{3}{4} \pi r^3\\\frac{3}{4}V = \pi r^3$

Dividing both sides by pi

$\frac{3}{4\pi}V =\frac{ \pi r^3}{\pi}\\\frac{3V}{4\pi} = r^3$

Taking cube root on both sides

$\sqrt[3]{\frac{3V}{4\pi} } = \sqrt[3]{r^3} \\ r = \sqrt[3]{\frac{3V}{4\pi} }$

Hence,

Option C: $r = \sqrt[3]{\frac{3V}{4\pi} }$ is the right answer

Keywords: Volume, Sphere

Learn more about volume at:

#LearnwithBrainly

5 0

3 years ago

Each cube in this rectangular prism is 1 cm3. What is the volume of the rectangular prism? A. 9 cm3 B. 20 cm3 C. 40 cm3 D. 48 cm

snow_tiger [21]

Did this test its c. 40

7 0

3 years ago

Read 2 more answers

In a class there are 15 students. 8 of them like playing soccer, 6 of them like swimming, and 2 like both and swimming and playi

xenn [34]

Answer:

6+8-2=12, 15-12=3 answer=3

5 0

3 years ago

two business partners, Ellen and Bob, invested money in their business at a ratio of 3 to 7. Bob invested the greater amount. th

Shtirlitz [24]

Answer:

Ellen invested $60 and Bob invested $140

Step-by-step explanation:

let the two amounts invested by 3x and 7x

(notice 3x : 7x = 3 : 7 )

then 3x + 7x = 200

10x = 200

x = 20

then 3x = 3(20) = 60

and 7x = 7(20) = 140

60+140=200

7 0

3 years ago