How do I find the slope of a coordinate plane?

Consider the sequence of numbers: 3/8, 3/4, 1 /18, 1 1/2, 1 7/8

vredina [299]

Question:

Consider the sequence of numbers: $\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}$

Which statement is a description of the sequence?

(A) The sequence is recursive, where each term is 1/4 greater than its preceding term.

(B) The sequence is recursive and can be represented by the function

f(n + 1) = f(n) + 3/8 .

(C) The sequence is arithmetic, where each pair of terms has a constant difference of 3/4 .

(D) The sequence is arithmetic and can be represented by the function

f(n + 1) = f(n)3/8.

Answer:

Option B:

The sequence is recursive and can be represented by the function

$f(n + 1) = f(n) + \frac{3}{8} .$

Explanation:

A sequence of numbers are

$\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}$

Let us first change mixed fraction into improper fraction.

$\frac{3}{8}, \frac{3}{4}, \frac{9}{8}, \frac{3}{2}, \frac{15}{8}$

To find the pattern of the sequence.

To find the common difference between the sequence of numbers.

$\frac{3}{4}-\frac{3}{8}=\frac{6}{8}-\frac{3}{8}= \frac{3}{8}$

$\frac{9}{8}-\frac{3}{4}=\frac{9}{8}-\frac{6}{8}= \frac{3}{8}$

$\frac{3}{2}-\frac{9}{8}=\frac{12}{8}-\frac{9}{8}= \frac{3}{8}$

$\frac{15}{8}-\frac{3}{2}=\frac{15}{8}-\frac{12}{8}= \frac{3}{8}$

Therefore, the common difference of the sequence is 3.

That means each term is obtained by adding $\frac{3}{8}$ to the previous term.

Hence, the sequence is recursive and can be represented by the function $f(n + 1) = f(n) + \frac{3}{8} .$

3 0

3 years ago

a rectangle has a hight to width ratio of 3:4.5 Give two examples of dimensions for rectangle that could be scaled versions of t

Free_Kalibri [48]

Answer:

vb n bf dgmhumrynwtfvt

Step-by-step explanation:

vb hgetyhrtewr34y4j4htredwed5g

8 0

3 years ago

Choose one of the factors of 500x3 + 108y18

sammy [17]

Answer:

Option C

Therefore, one of the factors of $500x^3 +108y^\left (18\right )$ is $(5x+3y^6)$ .

Step-by-step explanation:

Given: $500x^3 +108y^\left (18\right )$

the common factor from $500x^3$ and $108y^\left (18\right )$ is 4.

therefore, $4\cdot \left ( 125x^3+27y^\left (18\right ) \right )$

$4\cdot \left ( (5x)^3+(3y^6)^3 \right))$

Now, use the formula for above expression: $(a^3+b^3)=(a+b)(a^2-ab+b^2)$

here, $a=5x$ and $b=3y^6$

$( (5x)^3+(3y^6)^3 \right))$ $=(5x+3y^6)(25x^2-15xy^6+9y^12)$

Therefore, we have

$500x^3 +108y^\left (18\right )$ $=4\cdot (5x+3y^6)\left (25x^2-15xy^6+9y^\left ( 12 \right ) \right )$

Therefore, one of the factors of $500x^3 +108y^\left (18\right )$ is $(5x+3y^6)$ .

7 0

3 years ago

Read 2 more answers

Need help with this if you can explain please do if not then just and answer is okay

pshichka [43]

Step-by-step explanation:

f(x) = x / (x - 7) = 1 + 7 / (x - 7).

The domain of f(x) depends whether the denominator of the rational expression is non-zero.

When (x - 7) = 0, x = 7.

Hence domain of f(x)

= All real values of x excluding 7. (C)

5 0

3 years ago

Read 2 more answers

If £23 = 500rubles, how many £ are in 616 rubles? Give your answer to 2 dp.

astraxan [27]

Answer:

28.34

Step-by-step explanation:

5 0

2 years ago