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viktelen [127]
3 years ago
11

Can someone please explain how to do this.

Mathematics
1 answer:
lutik1710 [3]3 years ago
4 0
Set the to equal:

x^2 - 4x+4 = 2x-4
 solve for X

subtract 2x from each side:
x^2 -6x + 4 = -4

subtract 4 from each side:

x^2 -6x = -8

add 8 to both sides:

x^2 -6x +8 = 0

factor the polynomial:

x = 4 and x = 2

using the line equation replace x with 2 and 4 and solve for y

y = 2(2) - 4 = 0
y = 2(4)-4 = 4

so the 2 points the line  crosses the curve is (2,0) and (4,4)

using those 2 points you can calculate the length:
 distance = sqrt((x2-x1)^2 +(y2-y1)^2

distance = sqrt( (4-2)^2 + (4-0)^2)

distance = sqrt (2^2 + 4^2)
 distance = sqrt (4+16)
= sqrt 20 
= 2 sqrt(5)  EXACT LENGTH


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52 and 48 if you take away 2 from 50 then,add it to the other 50 52+48
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Which logarithmic equation is equivalent to the exponential equation below?<br><br> 7^x=21
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Log base 7 (21)=x
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7 0
3 years ago
Read 2 more answers
Find x?<br> In 3x - In(x - 4) = ln(2x - 1) +ln3
earnstyle [38]

Answer:

x = \displaystyle \frac{5 + \sqrt{17}}{2}.

Step-by-step explanation:

Because 3\, x is found in the input to a logarithm function in the original equation, it must be true that 3\, x > 0. Therefore, x > 0.

Similarly, because (x - 4) and (2\, x - 1) are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, x > 4.

Let a and b represent two positive numbers (that is: a > 0 and b > 0.) The following are two properties of logarithm:

\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right).

\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right).

Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}

Right-hand side of this equation:

\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right).

Equate these two expressions:

\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}.

The natural logarithm function \ln is one-to-one for all positive inputs. Therefore, for the equality \begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned} to hold, the two inputs to the logarithm function have to be equal and positive. That is:

\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1).

Simplify and solve this equation for x:

x^2 - 5\, x + 2 = 0.

There are two real (but not rational) solutions to this quadratic equation: \displaystyle \frac{5 + \sqrt{17}}{2} and \displaystyle \frac{5 - \sqrt{17}}{2}.

However, the second solution, \displaystyle \frac{5 - \sqrt{17}}{2}, is not suitable. The reason is that if x = \displaystyle \frac{5 - \sqrt{17}}{2}, then (x - 4), one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.

The only solution that satisfies the requirements would be \displaystyle \frac{5 + \sqrt{17}}{2}.

Therefore, x = \displaystyle \frac{5 + \sqrt{17}}{2}.

7 0
3 years ago
Solve.<br><br> 10 · w = 90<br><br> w = ______
Ratling [72]

Answer:

80

Step-by-step explanation:

10- w = 90

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w = 80

5 0
3 years ago
Read 2 more answers
A company has a fleet of 200 vehicles. On average, 50 vehicles per year experience property damage. What is the probability that
ICE Princess25 [194]

Answer:

The probability is \frac{1}{4} or 25%

Step-by-step explanation:

The question states the total number of vehicles, as well as the number of damaged vehicles on a yearly basis. If 50 vehicles in every 200 vehicles per year are damaged, then we can obtain:

Probability of a damaged vehicle in any given year = \frac{Number of Damaged Vehicles}{Total Number of Vehicles}

= \frac{50}{200} = \frac{1}{4} or 25%

4 0
3 years ago
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