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3 years ago

Solve -8z + 3+2z = -4 - 6z + 7. Tell how many solutions there are.

Mathematics

1 answer:

Paul [167]3 years ago

3 0

Answer:

2 solutions 3 (-2 z + 1) and 3 (1 - 2 z)

Step-by-step explanation:

Left side

Simplify the following:

-8 z + 3 + 2 z

Grouping like terms, -8 z + 3 + 2 z = (2 z - 8 z) + 3:

(2 z - 8 z) + 3

2 z - 8 z = -6 z:

-6 z + 3

Factor 3 out of -6 z + 3:

Answer: 3 (-2 z + 1)

____________________________________

Right side

Simplify the following:

-6 z - 4 + 7

Grouping like terms, -6 z - 4 + 7 = (7 - 4) - 6 z:

(7 - 4) - 6 z

7 - 4 = 3:

3 - 6 z

Factor 3 out of 3 - 6 z:

Answer: 3 (1 - 2 z)

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Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = e−4x, [0, 2] Yes, it does not m

Zigmanuir [339]

Answer:

(a) Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem.

(b) $c =0.51995$

Step-by-step explanation:

Given

$f(x) = e^{-4x};\ [0,2]$

Solving (a); Does the function satisfy M.V.T on the given interval

We have:

$f(x) = e^{-4x};\ [0,2]$

The above function is an exponential function, and it is differentiable and continuous everywhere

Solving (b): The value of c

To do this, we use:

$f'(c) = \frac{f(b) - f(a)}{b - a}$

In this case:

$[a,b] = [0,2]$

So, we have:

$f'(c) = \frac{f(2) - f(0)}{2 - 0}$

$f'(c) = \frac{f(2) - f(0)}{2}$

Calculate f(2) and f(0)

$f(x) = e^{-4x}$

So:

$f(2) = e^{-4*2} = e^{-8} = 0.00033546262$

$f(0) = e^{-4*0} = e^{0} = 1$

This gives:

$f'(c) = \frac{0.00033546262 - 1}{2}$

$f'(c) = \frac{-0.99966453738}{2}$

$f'(c) = -0.4998$

Note that:

$f'(x) = (e^{-4x})'$

$f'(x) = -4e^{-4x}$

This implies that:

$f'(c) = -4e^{-4c}$

So, we have:

$f'(c) = -0.4998$

$-4e^{-4c} =-0.4998$

Divide both sides by -4

$e^{-4c} =\frac{-0.4998}{-4}$

$e^{-4c} =0.12495$

Take natural logarithm of both sides

$\ln(e^{-4c}) =\ln(0.12495)$

$\ln(e^{-4c}) =-2.0798$

Apply law of natural logarithm

$\ln(e^{ax}) =ax$

So:

$-4c =-2.0798$

Solve for c

$c =\frac{-2.0798}{-4}$

$c =0.51995$

3 0

3 years ago

Seiji and Gavin both worked hard over the summer. Together, they earned a total of $425. Gavin earned $25 more than Seiji. How m

schepotkina [342]

S + g = 425
g = s + 25
-----------------
We will use the method of substitution:
s + s + 25 = 425
2 s = 425 - 25
2 s = 400
s = 400 : 2
s = $425
g = 200 + 25
g = $225
Answer: Seiji earned $200 and Gavin earned $225.

5 0

3 years ago

The canteen made 15 liters of soup. By the afternoon they had sold

babunello [35]

Answer:

11.25 liters

Step-by-step explanation:

(3 / 4) * (15 liters)

3 0

3 years ago

Use a graphing calculator to sketch the graph of the quadratic equation, and then give the coordinates for the x-

Umnica [9.8K]

Given:

The quadratic equation is

$y=6x^2-15x+6$

To find:

The x-intercepts of the given equation.

Solution:

We have,

$y=6x^2-15x+6$

Splitting the middle term, we get

$y=6x^2-12x-3x+6$

$y=6x(x-2)-3(x-2)$

$y=(x-2)(6x-3)$

For x-intercepts, y=0.

$(x-2)(6x-3)=0$

Using zero product property, we get

$x-2=0\text{ and }6x-3=0$

$x=2\text{ and }6x=3$

$x=2\text{ and }x=\dfrac{3}{6}$

$x=2\text{ and }x=0.5$

So, the x-intercepts are (0.5,0) and (2,0).

Therefore, the correct option is a.

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3 years ago

Please help me with the problem

Arisa [49]

Nick is incorrect because he subtracted 3-1 and 3-2. The answer is 1 3/4 It is that distance because 3 2/4-1 3/4=1 3/4.

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3 years ago