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3 years ago

If c = 4 and d = 5, find c:d. 1:5 4:5 5:4

2 answers:

8 0

Your answer is 4:5 because your question asks you to find c:d, so first you have to plug in your numbers. c = 4 and d = 5 so now you have 4:5. This is the same as the fraction 4/5, and you cannot simplify it any smaller. So, 4:5 is your answer. :)

nadya68 [22]3 years ago

5 0

The answer would be the second choice. 4:5

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Is my answer correct? 10 points + brainleist!

Liono4ka [1.6K]

Answer:

your answer is incorrect. The correct answer is $h=-13$ and $k=13$ .

Step-by-step explanation:

If a quadratic function is $f(x)=ax^2+bx+c$ and a>0, then minimum value of the function at point $\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)$ .

The given function is

$f(x)=x^2+bx+182$

Here, a=1, b=b and c=182. So.

$-\dfrac{b}{2a}=-\dfrac{b}{2(1)}=-\dfrac{b}{2}$

Put $x=-\dfrac{b}{2}$ in the given function to find the minimum value of the function.

$f(-\dfrac{b}{2})=(-\dfrac{b}{2})^2+b(-\dfrac{b}{2})+182$

We know that minimum value is 13. So,

$13=\dfrac{b^2}{4}-\dfrac{b^2}{2}+182$

$13-182=-\dfrac{b^2}{4}$

$-169=-\dfrac{b^2}{4}$

$169\times 4=b^2$

Taking square root on both sides.

$13\times 2=b$

$b=26$

The value of b is 26.

So, the given function is

$f(x)=x^2+26x+182$

Now, add and subtract square of half of coefficient of x.

$f(x)=x^2+26x+182+(13)^2-(13)^2$

$f(x)=(x^2+2(13)x+(13)^2)+182-169$

$f(x)=(x+13)^2+13$

On comparing with $f(x)=(x-h)^2+k$ , we get

$h=-13$

$k=13$

Therefore, your answer is incorrect.

8 0

3 years ago

What is the correct radical form of this expression

marshall27 [118]

Answer:

The answer is choice A and here's why

The 2/5 outer most exponent means that we can break it down into 2*(1/5). The 2 is going to apply as an exponent for the whole parenthesis group. The 1/5 indicates we have a 5th root (similar to a square root or cube root,but instead of 2 or 3, it's 5)

Step-by-step explanation:

3 0

3 years ago

Find quotient 10/6 / 1/ 24

Maru [420]

Answer:

Step-by-step explanation:

Quotient means dividing so we must divide 10/6 by 1/24.

10/6 ÷ 1/24

10/6 * 24/1 = 40 <--- Multiply by the reciprocal in order to divide.

Final Answer: 40

I hope this helps! :)

3 0

2 years ago

Determine the values of the constants r and s such that i(x, y) = x rys is an integrating factor for the given differential equa

garri49 [273]

$\underbrace{y(7xy^2+6)}_{M(x,y)}\,\mathrm dx+\underbrace{x(xy^2-1)}_{N(x,y)}\,\mathrm dy=0$

For the ODE to be exact, we require that $M_y=N_x$ , which we'll verify is not the case here.

$M_y=21xy^2+6$
$N_x=2xy^2-1$

So we distribute an integrating factor $i(x,y)$ across both sides of the ODE to get

$iM\,\mathrm dx+iN\,\mathrm dy=0$

Now for the ODE to be exact, we require $(iM)_y=(iN)_x$ , which in turn means

$i_yM+iM_y=i_xN+iN_x\implies i(M_y-N_x)=i_xN-i_yM$

Suppose $i(x,y)=x^ry^s$ . Then substituting everything into the PDE above, we have

$x^ry^s(19xy^2+7)=rx^{r-1}y^s(x^2y^2-x)-sx^ry^{s-1}(7xy^3+6y)$
$19x^{r+1}y^{s+2}+7x^ry^s=rx^{r+1}y^{s+2}-rx^ry^s-7sx^{r+1}y^{s+2}-6sx^ry^s$
$19x^{r+1}y^{s+2}+7x^ry^s=(r-7s)x^{r+1}y^{s+2}-(r+6s)x^ry^s$
$\implies\begin{cases}r-7s=19\\r+6s=-7\end{cases}\implies r=5,s=-2$

so that our integrating factor is $i(x,y)=x^5y^{-2}$ . Our ODE is now

$(7x^6y+6x^5y^{-1})\,\mathrm dx+(x^7-x^6y^{-2})\,\mathrm dy=0$

Renaming $M(x,y)$ and $N(x,y)$ to our current coefficients, we end up with partial derivatives

$M_y=7x^6-6x^5y^{-2}$
$N_x=7x^6-6x^5y^{-2}$

as desired, so our new ODE is indeed exact.

Next, we're looking for a solution of the form $\Psi(x,y)=C$ . By the chain rule, we have

$\Psi_x=7x^6y+6x^5y^{-1}\implies\Psi=x^7y+x^6y^{-1}+f(y)$

Differentiating with respect to $y$ yields

$\Psi_y=x^7-x^6y^{-2}=x^7-x^6y^{-2}+\dfrac{\mathrm df}{\mathrm dy}$
$\implies\dfrac{\mathrm df}{\mathrm dy}=0\implies f(y)=C$

Thus the solution to the ODE is

$\Psi(x,y)=x^7y+x^6y^{-1}=C$

4 0

3 years ago

7 girls audition for 12 roles in a school play. What is the probability that at least 2 of the girls audition for the same part?

Sophie [7]

Answer:

Step-by-step explanation:

This is one minus the probability that all the girls audition for different roles. The total number of ways of assigning roles to the girls is 12^7, because to each of the 7 girls, you have a choice of 12 roles.

Then if each girl is to receive a different role, then there are 12!/5! possibilities for that. If you start assigning roles to the girls, then for the first girl, there are 12 choices, but for the next you have to choose one of the 11 different ones, so 11 for the next, and then one of the 10 remaining for the next etc. etc., and this is 12*11*10*...*6 = 12!/(12-7)! =12!/5!

The probability that a random assignment of one of the 12^7 roles would happen to be one of the 12!/5! roles where each girl has a different role, is

(12!/5!)/12^7 = 12!/(12^7 5!)

Then the probability that two or more girls addition for the same part is the probability that not all the girls are assigned different roles, this is thus:

1 - 12!/(12^7 5!)

6 0

3 years ago