Use the Distributive Property to simplify the expression. 6(s-9)

Mathematics

2 answers:

telo118 [61]3 years ago

6 0

Answer:

6s - 54

Step-by-step explanation:

VARVARA [1.3K]3 years ago

4 0

Answer: 6s-54

Step-by-step explanation:

6(s-9) - [simplify]

= (6)(s + -9)

= (6)(s)+(6)(-9)

= 6s-54

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leva [86]

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3 years ago

If 3x^2 + y^2 = 7 then evaluate d^2y/dx^2 when x = 1 and y = 2. Round your answer to 2 decimal places. Use the hyphen symbol, -,

S_A_V [24]

Taking $y=y(x)$ and differentiating both sides with respect to $x$ yields

$\dfrac{\mathrm d}{\mathrm dx}\bigg[3x^2+y^2\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[7\bigg]\implies 6x+2y\dfrac{\mathrm dy}{\mathrm dx}=0$

Solving for the first derivative, we have

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x}y$

Differentiating again gives

$\dfrac{\mathrm d}{\mathrm dx}\bigg[6x+2y\dfrac{\mathrm dy}{\mathrm dx}\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[0\bigg]\implies 6+2\left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2+2y\dfrac{\mathrm d^2y}{\mathrm dx^2}=0$

Solving for the second derivative, we have

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=-\dfrac{3+\left(\frac{\mathrm dy}{\mathrm dx}\right)^2}y=-\dfrac{3+\frac{9x^2}{y^2}}y=-\dfrac{3y^2+9x^2}{y^3}$

Now, when $x=1$ and $y=2$ , we have

$\dfrac{\mathrm d^2y}{\mathrm dx^2}\bigg|_{x=1,y=2}=-\dfrac{3\cdot2^2+9\cdot1^2}{2^3}=\dfrac{21}8\approx2.63$

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3 years ago

Gregorio took two tests. Find his z-score for each test. (Remember: The number of standard deviations between a score and the me

never [62]

I found the missing parts of this question.
Test A
Gregorio’s score 62 
Mean score 80 
Standard deviation 6 

Test B 
Gregorio's score 70 
Mean score 90 
Standard deviation 10 

a. Test A: 3; Test B: 2; Test A 
c. Test A: –2; Test B: –3; Test A 
b. Test A: –3; Test B: –2; Test B 
d. Test A: –3; Test B: –2; Test A


Refer to the attachment for the formula of z score:

test A: z = (62-80)/6 = -18/6 = -3
test B: z = (70-90)/10 = -20/10 = -2

B. Test A: –3; Test B: –2; Test B