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2 years ago

Factor by grouping.

2 answers:

6 0

1.)b
2.)c
3.)a
1.)work
(3dt-21d)+(35-5t)
=3d(t-7)+5 (7-t)
=3d(t-7)-5(-7+t)
=3d(t-7)-5(t-7)
=(t-7)(3d-5)

2.) work
vp+12v+8p+96
=(vp+12)+(8p+96)
=v(p+12)+8(p+12)
=(p+12)(v+8)

hram777 [196]2 years ago

4 0

The correct answers are A C and B

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3x + 12 = -6x - 9 and

Marianna [84]

Answer:

1. x = - 7/3 = - 2 1/3

2. x = -2

Step-by-step explanation:

Hi there !

3x + 12 = - 6x - 9

3x + 6x = - 12 - 9

9x = - 21

x = - 21⁽³/9

x = - 7/3

x = - 2 1/3

12x + 20 = 2x

12x - 2x = - 20

10x = - 20

x = - 20/10

x = - 2

Good luck !

5 0

2 years ago

At what point does the curve have maximum curvature? Y = 4ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as

MAXImum [283]

Answer-

At $x= \frac{1}{2304e^4-16e^2}$ the curve has maximum curvature.

Solution-

The formula for curvature =

$K(x)=\frac{{y}''}{(1+({y}')^2)^{\frac{3}{2}}}$

Here,

$y=4e^{x}$

Then,

${y}' = 4e^{x} \ and \ {y}''=4e^{x}$

Putting the values,

$K(x)=\frac{{4e^{x}}}{(1+(4e^{x})^2)^{\frac{3}{2}}} = \frac{{4e^{x}}}{(1+16e^{2x})^{\frac{3}{2}}}$

Now, in order to get the max curvature value, we have to calculate the first derivative of this function and then to get where its value is max, we have to equate it to 0.

${k}'(x) = \frac{(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})}{(1+16e^{2x} )^{2}}$

Now, equating this to 0

$(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x}) =0$

$\Rightarrow (1+16e^{2x})^{\frac{3}{2}}-(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})$

$\Rightarrow (1+16e^{2x})^{\frac{3}{2}}=(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})$

$\Rightarrow (1+16e^{2x})^{\frac{1}{2}}=48e^{2x}$

$\Rightarrow (1+16e^{2x})}=48^2e^{2x}=2304e^{2x}$

$\Rightarrow 2304e^{2x}-16e^{2x}-1=0$

Solving this eq,

we get $x= \frac{1}{2304e^4-16e^2}$

∴ At $x= \frac{1}{2304e^4-16e^2}$ the curvature is maximum.

6 0

2 years ago

Please answer both questions and show all work.

sammy [17]

(1) 6 1/3 = 76/12
2 3/4 = 33/12
___________+
109/12
divide and get 9 1/12
-----------------------------------
(2)3 1/2 = 43/12
5 1/2 = 66/12
*from first answer* 109/12
add and you get 218/12
divide and get the answer 18 1/6
Hope this helps you!

3 0

2 years ago

The length of a rectangle is stored in a double variable named length, the width in one named width. write an expression whose v

Mila [183]

sqrt(pow(length, 2) + pow(width, 2))

7 0

2 years ago

True or False ?

Gnoma [55]

True the answer is true babes :)

4 0

3 years ago