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2 years ago

Solve: 9x - 2(4x + 5) = 2x - (4 - x) - 12 A 16 B 9 C 3 D 13

Mathematics

1 answer:

Margarita [4]2 years ago

7 0

Step-by-step explanation:

4x+2x+x+9x=16x

16x=2+5+4=11

x=11

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Two variables are correlated with r = 0.44.

butalik [34]

It's moderate positive because when the number is closer to zero the weaker it is and the closer to one its stronger so since 0.44 is in more in the middle it moderate and since there is no negative sign which is - then it moderate positive. Btw I took the test and it was right.

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2 years ago

Mickey said that 45.7654 rounded to the nearest thousandth is 45.765 and Nicole said that it was 45.766. Who is correct and why?

Nesterboy [21]

Answer:

Mickey

Step-by-step explanation:

Mickey is correct because if you look at the number 45.7654 whenever you round to the nearest thousandth it'll be 45.765

5 is the thousandth place so look to the right. If the number to the right is greater than 5 it'll round to 47.766 but since it's a four ti rounds down.

8 0

2 years ago

Read 2 more answers

Solve 5y'' + 3y' – 2y = 0, y(0) = 0, y'(0) = 2.8 y(t) = 0 Preview

mario62 [17]

Answer: The required solution is

$y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$5y^{\prime\prime}+3y^\prime-2y=0,~~~~~~~y(0)=0,~~y^\prime(0)=2.8~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$5m^2e^{mt}+3me^{mt}-2e^{mt}=0\\\\\Rightarrow (5m^2+3y-2)e^{mt}=0\\\\\Rightarrow 5m^2+3m-2=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow 5m^2+5m-2m-2=0\\\\\Rightarrow 5m(m+1)-2(m+1)=0\\\\\Rightarrow (m+1)(5m-1)=0\\\\\Rightarrow m+1=0,~~~~~5m-1=0\\\\\Rightarrow m=-1,~\dfrac{1}{5}.$

So, the general solution of the given equation is

$y(t)=Ae^{-t}+Be^{\frac{1}{5}t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-Ae^{-t}+\dfrac{B}{5}e^{\frac{1}{5}t}.$

According to the given conditions, we have

$y(0)=0\\\\\Rightarrow A+B=0\\\\\Rightarrow B=-A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

and

$y^\prime(0)=2.8\\\\\Rightarrow -A+\dfrac{B}{5}=2.8\\\\\Rightarrow -5A+B=14\\\\\Rightarrow -5A-A=14~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Uisng equation (ii)}]\\\\\Rightarrow -6A=14\\\\\Rightarrow A=-\dfrac{14}{6}\\\\\Rightarrow A=-\dfrac{7}{3}.$

From equation (ii), we get

$B=\dfrac{7}{3}.$

Thus, the required solution is

$y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.$

7 0

2 years ago

Implicit differentiation of 1/x +1/y=5 y(4)= 4/19<br> y'(4)=?

Aneli [31]

$\frac{1}{x} +\frac{1}{y} = 5\\\\x^{-1}+y^{-1}=5\\$

Above, I changed the fraction form of x and y into exponential form so it is easier to see the differentiation. Now, we can differentiate:

$-1x^{-2}+-1y^{-2}\frac{dy}{dx}=5\\\\\frac{-1}{x^2}-\frac{1}{y^2}\frac{dy}{dx}=5\\\\-\frac{1}{y^2}\frac{dy}{dx}=5+\frac{1}{x^2}\\\\\frac{dy}{dx}=-5y^2-\frac{y^2}{x^2}$

Now that we have dy/dx, we can plug in the x, which is 4, and the y, which is 4/19. We know these values of x and y because your question stated y(4) = 4/19.

$\frac{dy}{dx}=-5(\frac{4}{19})^2-\frac{(\frac{4}{19})^2}{(4)^2}\\\\\frac{dy}{dx}=-5(\frac{16}{361})-\frac{(\frac{16}{361})}{16}\\\\\frac{dy}{dx}=\frac{-80}{361}-\frac{1}{361}\\\\\frac{dy}{dx}=\frac{-81}{361}$

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3 years ago

Carol opened 20 different bags of the same kind of candy and recorded the colors and their frequencies, as shown in the table.

Alina [70]

It is 14% as you add up all of the numbers and divide 10 by that number and finally multiply by 100 for a percent

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2 years ago

Read 2 more answers

Solve:​ ​9x - 2(4x + 5) = 2x - (4 - x) - 12 A 16 B 9 C 3 D 13

Solve: 9x - 2(4x + 5) = 2x - (4 - x) - 12 A 16 B 9 C 3 D 13