Which statement about the value of x is true?

What is the answer for this question?

drek231 [11]

Answer: B

Step-by-step explanation:

(-3, -1) and (4, 5) are the points given

Slope formula: $\frac{Y2-Y1}{X2-X1}$

$\frac{5--1}{4--3} = \frac{5+1}{4+3} \\$

$\frac{5+1}{4+3} = \frac{6}{7}$

8 0

3 years ago

Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isot

Andrews [41]

Answer:

The approximate difference in the half-lives of the isotopes is 66 days.

Step-by-step explanation:

The decay of an isotope is represented by the following differential equation:

$\frac{dm}{dt} = -\frac{t}{\tau}$

Where:

$m$ - Current mass of the isotope, measured in kilograms.

$t$ - Time, measured in days.

$\tau$ - Time constant, measured in days.

The solution of the differential equation is:

$m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$

Where $m_{o}$ is the initial mass of the isotope, measure in kilograms.

Now, the time constant is cleared:

$\ln \frac{m(t)}{m_{o}} = -\frac{t}{\tau}$

$\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }$

The half-life of a isotope ( $t_{1/2}$ ) as a function of time constant is:

$t_{1/2} = \tau \cdot \ln2$

$t_{1/2} = -\left(\frac{t}{\ln\frac{m(t)}{m_{o}} }\right) \cdot \ln 2$

The half-life difference between isotope B and isotope A is:

$\Delta t_{1/2} = \left| -\left(\frac{t_{A}}{\ln \frac{m_{A}(t)}{m_{o,A}} } \right)\cdot \ln 2+\left(\frac{t_{B}}{\ln \frac{m_{B}(t)}{m_{o,B}} } \right)\cdot \ln 2\right|$

If $\frac{m_{A}(t)}{m_{o,A}} = \frac{m_{B}(t)}{m_{o,B}} = 0.9$ , $t_{A} = 33\,days$ and $t_{B} = 43\,days$ , the difference in the half-lives of the isotopes is:

$\Delta t_{1/2} = \left|-\left(\frac{33\,days}{\ln 0.90} \right)\cdot \ln 2 + \left(\frac{43\,days}{\ln 0.90} \right)\cdot \ln 2\right|$

$\Delta t_{1/2} \approx 65.788\,days$

The approximate difference in the half-lives of the isotopes is 66 days.

4 0

3 years ago

Read 2 more answers

Find the distance between (-4,6) and (3,-7)

Natali5045456 [20]

Answer:

4-6 is 2 and 3-7 is 4

Step-by-step explanation:

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8 0

3 years ago

Mathwiz wya?? pic below i need help asap

n200080 [17]

Answer:

Step-by-step explanation:

First, you gotta work out the hypotenuse of ABC, which is AC.

To do that, you need to figure out the scale factor between the two right-angled triangles. You can do that for this question because this is a similar shapes question.

12.5/5 = 2.5

The scale factor length between the two triangles is 2.5.

You can use 2.5 now to work out AC, so AC would be 13 x 2.5, which gives 32.5.

Now that you've got the hypotenuse and BC of ABC, you can use Pythagoras's theorem to work out the length of AB

Pythagoras's theorem = $a^2 + b^2 = c^2$

a = BC = 12.5

b = AB = we need to work this out

c = AC (the hypotenuse we just worked out) = 32.5

$12.5^2 + b^2 = 32.5^2$ Let's both simplify and rearrange this at the same time so that we have our b on one side.

$b^{2}$ = 1056.25 - 156.25

b = $\sqrt{(1056.25 - 156.25)}$

b = $\sqrt{900}$

b = AB = 30 We've found b or AB, now we can work out the perimeter of ABC.

Perimeter of ABC = AB + BC + AC

= 30 + 12.5 + 32.5

= 75 Here's the perimeter for ABC.

8 0

2 years ago

What is the simplified value of the exponential expression 64 1/4

katrin [286]

$\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} 
\qquad \qquad
\sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\
-------------------------------\\\\
64^{\frac{1}{4}}\qquad \boxed{64=2^6}\qquad (2^6)^{\frac{1}{4}}\implies 2^{6\cdot \frac{1}{4}}\implies 2^{\frac{6}{4}}\implies 2^{\frac{3}{2}}
\\\\\\
\sqrt[2]{2^3}\implies \sqrt{2^{2+1}}\implies \sqrt{2^2\cdot 2^1}\implies 2\sqrt{2}$

3 0

3 years ago