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2 years ago

Please help I will give brainliest

Mathematics

1 answer:

pentagon [3]2 years ago

7 0

The option that represents the answers for 6, 8, 10, and 14 is the second option- 31, 41, 51, 71

<h3>Sequence and Series </h3>

From the question, we are to determine the option that represents the answer for pictures 6, 8, 10, and 14

In the given diagram,

The first picture requires 6 matches

The 2nd picture requires additional 5 matches

the 3rd picture requires additional 5 matches

and so on

That is

1 → 6

2 → 6 + 5 = 11

3 → 11 + 5 = 16

4 → 16 + 5 = 21

5 → 21 + 5 = 26

6 → 26 + 5 = 31

7 → 31 + 5 = 36

8 → 36 + 5 = 41

9 → 41 + 5 = 46

10 → 46 + 5 = 51

11 → 51 + 5 = 56

12 → 56 + 5 = 61

13 → 61 + 5 = 66

14 → 66 + 5 = 71

Hence, the option that represents the answers for 6, 8, 10, and 14 is the second option- 31, 41, 51, 71

Learn more on Sequence and Series here: brainly.com/question/10321751

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You might be interested in

The larger of two numbers is twice the smaller . If the sum is 54 find the numbers

Rom4ik [11]

So there are 2 numbers

pretend the smaller number is x, so the larger number must be 2x because it's twice as large

so 2x+x equals 54

simplifies to 3x=54

x= 18

the smaller number is 18 and the larger one is 36 (because 36 is 18 x 2)

6 0

3 years ago

What is the distribution property of 4 times 37

hjlf

Answer:

4(30 +7) = 120 +28 = 148

Step-by-step explanation:

When applying the distributive property to integers, we usually break them apart according to place value. That is not the only way it can be done.

4×37 = 4(30 +7) = 4·30 +4·7 = 120 +28 = 148

___

You can also break apart 37 other ways:

4×37 = 4(35 +2) = 4·35 +4·2 = 140 +8 = 148

4×37 = 4(40 -3) = 4·40 -4·3 = 160 -12 = 148

Or, you can break apart 4:

37×4 = 37(2 +2) = 37·2 +37·2 = 74 +74 = 148

_____

The distributive property is usually written in generic form as ...

a(b+c) = ab +ac

Then you may want to stop after the first couple of steps:

4(30 +7) = 4·30 +4·7

We can't tell if you're suppose to evaluate the expression or not. Check your reference materials for an example of this kind of problem.

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cint%20t%5E2%2B1%20%5C%20dt" id="TexFormula1" title="\frac{d}{dx} \

Kisachek [45]

Answer:

$\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} \ = \ 2x^5-8x^2+2x-2$

Step-by-step explanation:

$\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} = \ ?$

We can use Part I of the Fundamental Theorem of Calculus:

$\displaystyle\frac{d}{dx} \int\limits^x_a \text{f(t) dt = f(x)}$

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

$\displaystyle\int\limits^b_a \text{f(t) dt} + \int\limits^c_b \text{f(t) dt} = \int\limits^c_a \text{f(t) dt}$

We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

$\displaystyle \frac{d}{dx} \int\limits^0_{2x} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}$

We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

$\displaystyle\int\limits^b_a \text{f(t) dt}\ = -\int\limits^a_b \text{f(t) dt}$

We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

$\displaystyle \frac{d}{dx} -\int\limits^{2x}_{0} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}$

Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

$\displaystyle \frac{d}{dx} \int\limits^u_a \text{f(t) dt} = \text{f(u)} \cdot \frac{d}{dx} [u]$
where u represents any function other than a variable

For the first term, replace $\text{t}$ with $2x$ , and apply the chain rule to the function. Do the same for the second term; replace

$\displaystyle-[(2x)^2+1] \cdot (2) \ + \ [(x^2)^2 + 1] \cdot (2x)$

Simplify the expression by distributing $2$ and $2x$ inside their respective parentheses.

$[-(8x^2 +2)] + (2x^5 + 2x)$
$-8x^2 -2 + 2x^5 + 2x$

Rearrange the terms to be in order from the highest degree to the lowest degree.

$\displaystyle2x^5-8x^2+2x-2$

This is the derivative of the given integral, and thus the solution to the problem.

6 0

3 years ago

Evaluate 144 to the power of one half

Alborosie

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-------------------------------\\\\
144^{\frac{1}{2}}\implies \sqrt[2]{144^1}\implies \sqrt{144}\implies 12$

6 0

3 years ago

Read 2 more answers

Are lines e and f parallel? Show your work.

SashulF [63]

Answer:

last two both should be = 180

Step-by-step explanation:

5 0

3 years ago