All categories

3 years ago

5(8x-3)+4(-6x-4) Distribute then simplify

Mathematics

2 answers:

alexandr1967 [171]3 years ago

6 0

40x - 15 - 24x - 16

16x - 1

Nikitich [7]3 years ago

5 0

Answer:

16x - 31

Step-by-step explanation:

Write the full equation:

5(8x - 3) +4(-6x - 4)

Distribute:

40x - 15 - 24x - 16

Combine Like Terms:

16x - 15 - 16

Your answer is:

16x - 31

You might be interested in

Find the 60th term of the arithmetic sequence 4,-1,-6-

kobusy [5.1K]

Answer:

-291

Step-by-step explanation:

The common difference is -5

So the 60th term of the arithmetic sequence is

4+(60-1)×-5

=4+59×-5

=4+-295

=-291

8 0

3 years ago

Problem 4: Solve the initial value problem

pishuonlain [190]

Separate the variables:

$y' = \dfrac{dy}{dx} = (y+1)(y-2) \implies \dfrac1{(y+1)(y-2)} \, dy = dx$

Separate the left side into partial fractions. We want coefficients a and b such that

$\dfrac1{(y+1)(y-2)} = \dfrac a{y+1} + \dfrac b{y-2}$

$\implies \dfrac1{(y+1)(y-2)} = \dfrac{a(y-2)+b(y+1)}{(y+1)(y-2)}$

$\implies 1 = a(y-2)+b(y+1)$

$\implies 1 = (a+b)y - 2a+b$

$\implies \begin{cases}a+b=0\\-2a+b=1\end{cases} \implies a = -\dfrac13 \text{ and } b = \dfrac13$

So we have

$\dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = dx$

Integrating both sides yields

$\displaystyle \int \dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = \int dx$

$\dfrac13 \left(\ln|y-2| - \ln|y+1|\right) = x + C$

$\dfrac13 \ln\left|\dfrac{y-2}{y+1}\right| = x + C$

$\ln\left|\dfrac{y-2}{y+1}\right| = 3x + C$

$\dfrac{y-2}{y+1} = e^{3x + C}$

$\dfrac{y-2}{y+1} = Ce^{3x}$

With the initial condition y(0) = 1, we find

$\dfrac{1-2}{1+1} = Ce^{0} \implies C = -\dfrac12$

so that the particular solution is

$\boxed{\dfrac{y-2}{y+1} = -\dfrac12 e^{3x}}$

It's not too hard to solve explicitly for y; notice that

$\dfrac{y-2}{y+1} = \dfrac{(y+1)-3}{y+1} = 1-\dfrac3{y+1}$

Then

$1 - \dfrac3{y+1} = -\dfrac12 e^{3x}$

$\dfrac3{y+1} = 1 + \dfrac12 e^{3x}$

$\dfrac{y+1}3 = \dfrac1{1+\frac12 e^{3x}} = \dfrac2{2+e^{3x}}$

$y+1 = \dfrac6{2+e^{3x}}$

$y = \dfrac6{2+e^{3x}} - 1$

$\boxed{y = \dfrac{4-e^{3x}}{2+e^{3x}}}$

7 0

2 years ago

Write a numerical expression with exponents to describe the sum of 3x3x3x3 and 36

grandymaker [24]

Answer:

3^3 and 36^1

Step-by-step explanation:

3x3x3x3 is multiplying that 4 times so it is to the power of 4

36 is just once so it is to the power of one

4 0

3 years ago

Read 2 more answers

Two lines intersect. Find the value of b and c.<br> bº<br> 42°

yaroslaw [1]

Answer:

b=42 degrees

c= 138 degrees

Step-by-step explanation:

B and the 42 degrees shown are congruent angles so therefore both are 42 degrees

To find C: We know that combining the 42 degrees and Angle C would form a flat angle or 180 degree angle, so therefore

subtract 180 with 42 to get Angle C

180-42= 138

4 0

3 years ago

Read 2 more answers

If MNO ~XYZ,then what corresponding parts are congruent

GuDViN [60]

MX
NY
OZ are congruent

7 0

3 years ago