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3 years ago

Please help me with this question I will mark you as the best answer if correct

Mathematics

2 answers:

alexgriva [62]3 years ago

8 0

Answer:

Line : y = ax + b, passes (0, 3) and (2, -3)

=> b = 3

=> 2a + b = -3

=> a = -6/2 = -3

=> Slope a = -3

=> Option D is correct

Hope this helps!

vlabodo [156]3 years ago

3 0

Answer:

D is the answer

Step-by-step explanation:

Slope = rise / run

Slope = y2-y1 / x2-x1

Where coordinates are

(0,3),(2,-3)

So x1=0,y1=3 , x2=2 , y2= -3

Slope= -3-3/ 2-0

Slope = -6/2

Slope = -3

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timama [110]

Use the change-of-basis identity,

$\log_x(y) = \dfrac{\ln(y)}{\ln(x)}$

to write

$xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}$

Use the product-to-sum identity,

$\log_x(yz) = \log_x(y) + \log_x(z)$

to write

$xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}$

Redistribute the factors on the left side as

$xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}$

and simplify to

$xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)$

Now expand the right side:

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}$

Simplify and rewrite using the logarithm properties mentioned earlier.

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1$

$xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}$

$xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}$

$xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)$

$\implies \boxed{xyz = x + y + z + 2}$

(C)

6 0

2 years ago

A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound o

sertanlavr [38]

Answer:

Step-by-step explanation:

From the given information:

$R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min$

Given that the solution is pumped at a slower rate of 4gal/min

Then:

$R_{out} = \dfrac{4A}{100+(6-4)t}$

$R_{out}= \dfrac{2A}{50+t}$

The differential equation can be expressed as:

$\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)$

Integrating the linear differential equation; we have::

$\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|$

$\int_c \dfrac{2}{50 +t}dt = (50+t)^2$

multiplying above integrating factor fields; we have:

$(50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2$

$\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2$

$(50 + t)^2 A = (50 + t)^3+c$

A = (50 + t) + c(50 + t)²

Using the given conditions:

A(0) = 20

⇒ 20 = 50 + c (50)⁻²

-30 = c(50) ⁻²

c = -30 × 2500

c = -75000

A = (50+t) - 75000(50 + t)⁻²

The no. of pounds of salt in the tank after 35 minutes is:

A(35) = (50 + 35) - 75000(50 + 35)⁻²

A(35) = 85 - $\dfrac{75000}{7225}$

A(35) =69.6193 pounds

A(35) $\simeq$ 70 pounds

Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.

6 0

3 years ago

10 of 10

DedPeter [7]

Answer:

-16

Step-by-step explanation:

10 Divided by 5=2

-16 + 2 = -14

5 0

3 years ago

Read 2 more answers

Tom had $56. He bought a soda for $2 and 2 cookies for $3. Which expression correctly shows the total money Tom has left? A. $56

deff fn [24]

C ($56) - ($2) - ($3)

4 0

4 years ago

Multiply 613 by the reciprocal of −716.

Bumek [7]

Answer:

-613/716.

Step-by-step explanation:

The reciprocal of a number is basically that number upside down. to find the reciprocal of a whole number, you can just turn the number into a fraction, and put one as the numerator, and the original number as the denominator. given this information we know that the reciprocal of -716 is -1/716, so now yoj can simply cross multiply 613 by -1/716, which gives you -613/716.

5 0

3 years ago