All categories

4 years ago

Solve the equation 0.5 (14a + 46) = -11a - 42 + 5a

Mathematics

2 answers:

Nata [24]4 years ago

7 0

Answer:

a = - 5

Step-by-step explanation:

Given

0.5(14a + 46) = - 11a - 42 + 5a ← distribute left side

7a + 23 = - 6a - 42 ( add 6a to both sides )

13a + 23 = - 42 ( subtract 23 from both sides )

13a = - 65 ( divide both sides by 13 )

a = - 5

MrRa [10]4 years ago

3 0

Answer: a=(-5)

Steps:

You might be interested in

Which is the product of 15 and 5/12 ?

zysi [14]

Answer:

6 1/4

Step-by-step explanation:

15 x 5/12 = 15 x 5/12 = 75/12

75/12= 6 3/12 = 6 1/4

4 0

3 years ago

What is ⅓ + ⅒? please

Molodets [167]

Answer:13 over 30

13/30 or 0.433

Step-by-step explanation:

5 0

3 years ago

Enter an equation in slope-intercept form for the line that passes through (0, 0) and is parallel to the line described by y = −

GREYUIT [131]

Answer:

Step-by-step explanation:

7 0

3 years ago

Analyzing a Graph In Exercise, analyze and sketch the graph of the function. Lable any relative extrema, points of inflection, a

Sladkaya [172]

Answer:

$y=(\ln{x})^2$

point of extremity: (1,0)

vertical asymptote: along the y-axis (x = 0)

point of inflection: (e,1)

Solution:

Although all these points can be directly observed from the graph below, but these are the analytical solutions if you're curious!

1) Extreme point can be found by differentiating 'y' once and equating to zero. solving for x:

$\dfrac{dy}{dx}=\dfrac{dy}{dx}((\ln{x})^2)$

$\dfrac{dy}{dx}=2\ln{x}\left(\dfrac{1}{x}\right)$

substitute dy/dx = 0, and solve for x

$0=2\ln{x}\left(\dfrac{1}{x}\right)$

$0=2\ln{x}$

$x=e^0$

$x=1$

use this value of x back in y, to find the y-coordinate of the extreme point

$y=(\ln{1})^2$

$y=0$

The extreme point = (1,0)

2) Differentiate y twice to find the inflection point.

$\dfrac{dy}{dx}=2\ln{x}\left(\dfrac{1}{x}\right)$

$\dfrac{d^2y}{dx^2}=2\ln{x}\left(-\dfrac{1}{x^2}\right)+\left(\dfrac{1}{x}\right)\left(\dfrac{2}{x}\right)$

$\dfrac{d^2y}{dx^2}=\dfrac{2}{x^2}\left(-\ln{x}+1}\right)$

substitute d2y/dx2 = 0, and solve for x

$0=\dfrac{2}{x^2}\left(-\ln{x}+1}\right)$

$0=-\ln{x}+1$

$\ln{x}=1$

$x = e$

use this value of x back in y, to find the y-coordinate of the inflection point

$y=(\ln{e})^2$

$y=1$

The extreme point = (e,1)

6 0

4 years ago

yesterday, Jack drove 40 1/2 miles. he used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallons

Amanda [17]

From the information we have, Jack drove 401/2 miles and used a total of 1 1/4 gallons of gasoline.

We need to find out how many miles he travelled per each gallon.

40 1/2 miles can be written as 40.5 miles

1 1/4 gallons can be written as 1.25 gallons.

So now we form an equation.

40.5 = 1.25

x = 1

Where x is the number of miles per gallon

We cross multiply the equation

40.5 * 1 = 1.25 * x

40.5 = 1.25x

40.5 / 1.25 = x

32.4 = x

x = 32 .4

So the unit rate for miles per gallons is 32.4 miles per gallon

3 0

3 years ago