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3 years ago

Which expressions are equivalent to 6a(5+d) ?

Mathematics

2 answers:

mrs_skeptik [129]3 years ago

6 0

Answer:

first, second and fourth

Step-by-step explanation:

If you use distribution,

6a(5+d) is the same as

6a(5) + 6a(d)

Multiplied = 30a + 6ad

So it's the 1st 2nd and fourth choice.

1st is stated above when multiplied out and combined.

2nd is after distribution.

4th choice is basically combination of 1 and 2 where one is combined (first term) and the second one just set up to be multiplied.

It cannot be third because you are multiplying the factors and not adding so you cannot have 11a.

It cannot be last choice because you have different types of terms that cannot be combined (one with a alone and one with ad)

goblinko [34]3 years ago

3 0

Answer:

(6a*5) + (6a*d)

30a + 6ad

30a + (6a*d)

Step-by-step explanation:

Hope you ace your test!

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HELP!!!!

Harman [31]

The lateral area is the area of everything but the base. A shortcut formula for this area is Ph. (where P is the perimeter of the base and h is the height of the prism).

So the lateral area is (3+9+9.49)x37 = 795.13 m^2 or 795 m^2

The surface area is the lateral area plus the area of the 2 bases. The base is a triangle. (area = 1/2 bh)

Since there are two identical bases, the total area of the base is just 3x9 = 27

So the surface area is 795.13 + 27 = 822.13 m^2 or 822 m^2.

3 0

3 years ago

For the differential equation 3x^2y''+2xy'+x^2y=0 show that the point x = 0 is a regular singular point (either by using the lim

Svetlanka [38]

Given an ODE of the form

$y''(x)+p(x)y'(x)+q(x)y(x)=f(x)$

a regular singular point $x=c$ is one such that $p(x)$ or $q(x)$ diverge as $x\to c$ , but the limits of $(x-c)p(x)$ and $(x-c)^2q(x)$ as $x\to c$ exist.

We have for $x\neq0$ ,

$3x^2y''+2xy'+x^2y=0\implies y''+\dfrac2{3x}y'+\dfrac13y=0$

and as $x\to0$ , we have $x\cdot\dfrac2{3x}\to\dfrac23$ and $x^2\cdot\dfrac13\to0$ , so indeed $x=0$ is a regular singular point.

We then look for a series solution about the regular singular point $x=0$ of the form

$y=\displaystyle\sum_{n\ge0}a_nx^{n+k}$

Substituting into the ODE gives

$\displaystyle3x^2\sum_{n\ge0}a_n(n+k)(n+k-1)x^{n+k-2}+2x\sum_{n\ge0}a_n(n+k)x^{n+k-1}+x^2\sum_{n\ge0}a_nx^{n+k}=0$

$\displaystyle3\sum_{n\ge2}a_n(n+k)(n+k-1)x^{n+k}+3a_1k(k+1)x^{k+1}+3a_0k(k-1)x^k$
$\displaystyle+2\sum_{n\ge2}a_n(n+k)x^{n+k}+2a_1(k+1)x^{k+1}+2a_0kx^k$
$\displaystyle+\sum_{n\ge2}a_{n-2}x^{n+k}=0$

From this we find the indicial equation to be

$(3(k-1)+2)ka_0=0\implies k=0,\,k=\dfrac13$

Taking $k=\dfrac13$ , and in the $x^{k+1}$ term above we find $a_1=0$ . So we have

$\begin{cases}a_0=1\\a_1=0\\\\a_n=-\dfrac{a_{n-2}}{n(3n+1)}&\text{for }n\ge2\end{cases}$

Since $a_1=0$ , all coefficients with an odd index will also vanish.

So the first three terms of the series expansion of this solution are

$\displaystyle\sum_{n\ge0}a_nx^{n+1/3}=a_0x^{1/3}+a_2x^{7/3}+a_4x^{13/3}$

with $a_0=1$ , $a_2=-\dfrac1{14}$ , and $a_4=\dfrac1{728}$ .

6 0

4 years ago

All natural numbers are members o f which other subsets of real numbers?

Leona [35]

All natural numbers are member of all integers.

6 0

3 years ago

PLZ HELP ASAP ILL GIVE BRAINLEST PLZ

bagirrra123 [75]

Answer:

the answer is yes

Step-by-step explanation:

k(3)=5(3)-3

k(3)=15-3

k(3)=12

12 is the answer

4 0

3 years ago

Find the value of x and y

tiny-mole [99]

x° + 2y° = 180° ⇒ 2y° = 180° - x°

x° = 60° {three sides of the same lengh, means three angles=60°}

2y° = 180° - 60°

2y° = 120°

y° = 60°

4 0

3 years ago