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3 years ago

What else would need to be congruent to show that ABC=DEFbySSS

Mathematics

1 answer:

leva [86]3 years ago

6 0

Answer:

Side AB would need to be congruent to side DE, side BC would need to be congruent to side EF, and side CA would need to be congruent to side FD.

Step-by-step explanation:

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One-third of a number, n, minus 7 ALGEBRAIC EXPRESSION ASAP ASAP ASAP

Darya [45]

Answer:

$\frac{n}{3} - 7$

Step-by-step explanation:

The comma is important here, otherwise "one third of a number n minus 7" is

$\frac{n - 7}{3}$

4 0

3 years ago

I don’t understand please help me

-Dominant- [34]

Answer:

(1). 15

Step-by-step explanation:

The time it takes to travel the whole path will be 20 times the time it takes to travel 1/20 of the path.

20 × (3/4) s = 60/4 s = 15 s

It will take 15 seconds to travel the entire path.

5 0

3 years ago

Which of the following is not a subset of {1, 2, 3}? {0} {1, 2, 3} Ø

Butoxors [25]

Answer:

{0}

Step-by-step explanation:

{0} is not because 0 is not an element of set {1, 2, 3}

The null set is a subset of every set, so Ø is.

A set is a subset of itself.

6 0

3 years ago

In a recipe, for every 3/4 cup of flour, 1/3 cup of sugar is needed. How many cups of sugar are needed for 1 cup of flour? (Leav

sashaice [31]

Answer:

1/9 cup of sugar for every 1/4 cup of flour

Step-by-step explanation: Turn the 1/3 into 3/9 and I'm sure you can figure it out from there.

8 0

3 years ago

We would like to use the power series method to find the general solution to the differential equation d 2y dx2 − 4x dy dx + 12y

Feliz [49]

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

$\dfrac{\mathrm dy}{\mathrm dx}=\displaystyle\sum_{n\ge1}na_nx^{n-1}\implies4x\dfrac{\mathrm dy}{\mathrm dx}=4\sum_{n\ge1}na_nx^n=4\sum_{n\ge0}na_nx^n$

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}=\sum_{n\ge0}(n+2)(n+1)a_{n+2}x^n$

Substituting into the ODE

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-4x\dfrac{\mathrm dy}{\mathrm dx}+12y=0$

gives

$\displaystyle\sum_{n\ge0}\bigg((n+2)(n+1)a_{n+2}-4na_n+12a_n\bigg)x^n=0$

so that the coefficients of the series are given according to

$\begin{cases}a_0=y(0)\\a_1=y'(0)\\a_{n+2}=\dfrac{4(n-3)a_n}{(n+2)(n+1)}&\text{for }n\ge0\end{cases}$

We can shift the index in the recursive part of this definition to get

$a_n=\dfrac{4(n-5)a_{n-2}}{n(n-1)}$

for $n\ge2$ . There's dependency between coefficients that are 2 indices apart, so we can consider 2 cases:

If $n=2k$ , where $k\ge0$ is an integer, then

$k=0\implies n=0\implies a_0=a_0$

but since $y(0)=0$ , we have $a_0=0$ and $a_{2k}=0$ for all $k\ge0$ .

If $n=2k+1$ , then

$k=0\implies n=1\implies a_1=a_1$

$k=1\implies n=3\implies a_3=\dfrac{4(-2)a_1}{3\cdot2}=-\dfrac43a_1$

$k=2\implies n=5\implies a_5=0$

and so $a_{2k+1}=0$ for all $k\ge2$ . If $y'(0)=1$ , we then have $a_1=1$ and $a_3=-\dfrac43$ .

So the ODE has solution

$y(x)=\displaystyle\sum_{k\ge0}(a_{2k}x^{2k}+a_{2k+1}x^{2k+1})\implies\boxed{y(x)=x-\dfrac43x^3}$

8 0

3 years ago