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2 years ago

Simplify the expression 2x+4(3y+x).

Mathematics

2 answers:

Degger [83]2 years ago

8 0

Answer:

6x + 12y

Step-by-step explanation:

2x + 4(3y + x)

Use distributive property.

4 (3y + x)

4 x 3y = 12y

4 * x = 4x

2x + 12y + 4x

Combine like terms.

2x + 4x = 6x

6x + 12y

inysia [295]2 years ago

3 0

Answer:

The answer in simplified form would be 6x+12y.

Step-by-step explanation:

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The length of line segment AG is 17 m and the line segment AD is 25 m. What is the length of line segment GD?

vladimir1956 [14]

Answer:

AG = 17 m

AD = 25 m

GD = ?

AD = AG + GD

GD = AD - AG

= 25 - 17

= 8 m

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2 years ago

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A political pollster wants to know what proportion of voters are planning to vote for the incumbent candidate in an upcoming ele

balandron [24]

Answer:

$1.\ \ np\geq 10\\\\2.\ \ n\geq 10x$

Step-by-step explanation:

-Let x be the sample size and n the population size

-The conditions for a one-sample proportion z-test are:

-The sample is randomly selected from the population.

-The sample size is greater than or equal to ten times the population size:

$n\geq 10x\\\\n=2000\\x=150\\10x=1500\\\therefore n\geq 10x$

-The expectation np is greater than or equal to 10:

$np\geq 10\\n=2000, p=0.6\\np=1200\\\\Hence, np\geq 10$

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3 years ago

If x = a cosθ and y = b sinθ , find second derivative

Olin [163]

I'm guessing the second derivative is for <em>y</em> with respect to <em>x</em>, i.e.

$\dfrac{\mathrm d^2y}{\mathrm dx^2}$

Compute the first derivative. By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

We have

$y=b\sin\theta\implies\dfrac{\mathrm dy}{\mathrm d\theta}=b\cos\theta$

$x=a\cos\theta\implies\dfrac{\mathrm dx}{\mathrm d\theta}=-a\sin\theta$

and so

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{b\cos\theta}{-a\sin\theta}=-\dfrac ba\cot\theta$

Now compute the second derivative. Notice that $\frac{\mathrm dy}{\mathrm dx}$ is a function of $\theta$ ; so denote it by $f(\theta)$ . Then

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm dx}$

By the chain rule,

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm df}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

We have

$f=-\dfrac ba\cot\theta\implies\dfrac{\mathrm df}{\mathrm d\theta}=\dfrac ba\csc^2\theta$

and so the second derivative is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\frac ba\csc^2\theta}{-a\sin\theta}=-\dfrac b{a^2}\csc^3\theta$

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3 years ago

If θ is an angle in standard position that terminates in Quadrant III such that tanθ = 5/12, then sinθ/2 = _____

babunello [35]

Answer:

sin θ/2=5√26/26=0.196

Step-by-step explanation:

θ ∈(π,3π/2)

such that

θ/2 ∈(π/2,3π/4)

As a result,

0<sin θ/2<1, and

-1<cos θ/2<0

tan θ/2=sin θ/2/cos θ/2

such that

tan θ/2<0

Let

t=tan θ/2

t<0

By the double angle identity for tangents

2 tan θ/2/1-(tanθ /2)^2 = tanθ

2t/1-t^2=5/12

24t=5 - 5t^2

Solve this quadratic equation for t :

t1=1/5 and

t2= -5

Discard t1 because t is not smaller than 0

Let s= sin θ/2

0<s<1.

By the definition of tangents.

tan θ/2= sin θ/2/ cos θ/2

Apply the Pythagorean Algorithm to express the cosine of θ/2 in terms of s. Note the cos θ/2 is expected to be smaller than zero.

cos θ/2 = -√1-(sin θ/2)^2 = - √1-s^2

Solve for s.

s/-√1-s^2 = -5

s^2=25(1-s^2)

s=√25/26 = 5√26/26

Therefore

sin θ/2=5√26/26=0.196....

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3 years ago

What is the circumference of a 18.5ft circle?

Elza [17]

Answer:

The answer is 56.57.

Step-by-step explanation:

Step by step explanation but hope this helps!

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