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4 years ago

Which of the sequences is an arithmetic sequence?

Mathematics

2 answers:

Dennis_Churaev [7]4 years ago

7 0

Answer:

B. -3, -10, -17, -24, -31

Step-by-step explanation:

An Arithmetic sequence is defined as a set of numbers with a common difference. In answer choice B, it is seen that the difference between each number is seven.

A is incorrect as one to eight has a difference of seven, while the other numbers have a difference of eight.

C is incorrect as it skips the number 12 between 9 and 15, thus breaking the sequence.

D is incorrect as the numbers jump from positive to negative, thus not having a common difference.

Hope this helps!

11111nata11111 [884]4 years ago

7 0

Answer: “B”

Step-by-step explanation: An arithmetic sequence is a pattern where the same number is repeatedly added or subtracted. “B” would be the correct answer because each time, we have a common difference of -7 because we subtract 7 each time to get to our next term. We could also write this in recursive description as followed.

Starting at -3, subtract 7 to get to the next term.

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Please help with these math questions part 2

NikAS [45]

5).
and
6).
The volume of a sphere is

   (4/3) (pi) (radius)³ .

In #5, the 'pi' is already there next to the answer window.
You just have to come up with the (4/3)(radius³).

Remember that the radius = 1/2 of the diameter.

7). The volume of a cylinder is

   (pi) (radius²) (height) .

Divide the juice in the container by the volume of one can,
to get the number of cans he can fill.

8). The volume of a cone is

   (1/3) (pi) (radius of the round bottom)² (height) .

He starts with a small cone, he then adds clay to it to make it higher.
The question is: How much clay does he ADD to the short one,
to make the bigger one ?

Use the formula to find the volume of the short one.
Use the formula again to find the volume of the bigger one.
Then SUBTRACT the smaller volume from the bigger volume.
THAT's how much clay he has to ADD.

Notice that the new built-up cone has the same radius
but more height than the first cone.
_______________________________________

Don't worry if you don't understand this.

The answer will be this number:

(1/3) (pi) (radius²) (height of the big one minus height of the small one).

6 0

3 years ago

What properties can be used to solve 7y-15=-29. Identity property of multiplication,addition property of equality ,distributive

Sveta_85 [38]

Answer:

Addition Property of Equality.

Inverse property of multiplication.

Step-by-step explanation:

Given the equation:

$7y-15=-29$

First of all, let us use Addition Property of Equality.

According to the property, if we add a number on both sides of an equality, there is no change in the equality.

In other words, the equality will be same if we add the same number on Left Hand Side and Right Hand Side of the equality.

First of all, let us add 15 on both sides of the equality:

$7y-15+15=-29+15\\\Rightarrow 7y=-14$

Now, let us Inverse property of multiplication.

i.e. Multiplication of a number with its inverse is equal to 1.

$a\times \frac{1}{a} = 1$

So, let us multiply the given equation with $\frac{1}7$

$7y \times \dfrac{1}{7}=-14 \times \dfrac{1}{7}\\\Rightarrow 1y =-2\\\Rightarrow y=-2$

The properties used are:

Addition Property of Equality.

Inverse property of multiplication.

7 0

3 years ago

Find the possibility of rolling even numbers three times, using a six-side die number from 1 to 6

seraphim [82]

Answer:

$\frac{1}{8}$

Step-by-step explanation:

Number of sides of die = 6

Number of sides with even numbers = 3

P( rolling an even number 1 time) = $\frac{3}{6}$ = $\frac{1}{2}$

P(rolling even number 3 times) = $\frac{1}{2}$ x $\frac{1}{2}$ x $\frac{1}{2}$ = $\frac{1}{8}$

5 0

3 years ago

A gym membership at one gym costs $10 every month plus a one-time membership fee of $15, and a gym membership at another gym cos

Minchanka [31]

Answer: Let us assume that the number of months after which

the gym memberships will cost the same = x

Then

15 + 10x = 40 + 4x

10x - 4x = 40 - 15

6x = 25

x = 25/6

= 4 1/6

So the membership fee of both the gyms will become same after 4 1/6 months. You can also consider that as after 5 months the membership fees of both the gyms will become same. I hope the procedure is not very complicated for you to understand.

Step-by-step explanation: Hope this helps!!

6 0

3 years ago

What is the y-intercept of the line perpendicular to the line y = 4/3x + 1 that includes the point (4, 1)?

Alexeev081 [22]

$\bf y=\stackrel{\downarrow }{\cfrac{4}{3}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill$

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{4}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{3}{4}}\qquad \stackrel{negative~reciprocal}{-\cfrac{3}{4}}}$

so then, we know this line has a slope of -3/4 and runs through (4 , 1)

$\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{1})~\hspace{10em} slope = m\implies -\cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=-\cfrac{3}{4}(x-4)\implies y-1=-\cfrac{3}{4}x+3$

$\bf y=-\cfrac{3}{4}x\stackrel{\downarrow }{+4}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}~\hfill \stackrel{\textit{y-intercept}}{(0,4)}$

3 0

3 years ago