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nikitadnepr [17]
2 years ago
15

3k - 14 = 3(k – 5) +1 one solution, no solution, or infinite solution ​

Mathematics
1 answer:
Nana76 [90]2 years ago
3 0
Always true so it would be so THEYRE interval notation. I believe it’s infinite solution
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Find the x- and y- intercepts of parabola y=5x^2-16x+10
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Y-INTERCEPT

y = 5x^2 - 16x + 10

The y-intercept is where the equation/curve/parabola cosses the y-axis.

The y-axis is where x = 0. (The x-axis is where y = 0)

To find the y-intercept:

\text{y-axis} \rightarrow \text{x = 0} \rightarrow y = 5(0)^2 -16(0) + 10 = 10

The y-intercept must be at (0, 10)

X-INTERCEPT (ROOTS/SOLUTIONS)

y = 5x^2 - 16x + 10\\\text{make it equal 0}\\y = 0\\\therefore 5x^2 - 16x + 10 = 0

We need to use the quadratic formula

The quadratic formula helps us find what values of x make the equation = 0

Quadratic formula: x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

x=\frac{-(-16) + \sqrt{(-16)^2-4(5)(10)}}{2(5)}\\\\x = \frac{16 + \sqrt{256-200}}{10}\\x = \frac{16 + \sqrt{56}}{10}\\x = \frac{16 + 2\sqrt{14}}{10}\\x = \frac{8 + \sqrt{14}}{5}\\\\\\x=\frac{-(-16) - \sqrt{(-16)^2-4(5)(10)}}{2(5)}\\\text{doing the same thing...}\\\text{end up with...}\\x = \frac{8 - \sqrt{14}}{5}\\

The x-intercepts are at:

(\frac{8 + \sqrt{14}}{5}, 0)\\(\frac{8 - \sqrt{14}}{5}, 0)

5 0
2 years ago
PLEASE HELP ME ASAP!!
Dmitry_Shevchenko [17]
13 cm+ 13 cm= 26 cm, 26 cm is the answer to Part B.
3 0
3 years ago
Please helppp!!<br> I have to find the slope of the blue line that is in the graph!!
Travka [436]
Slope = 4/5 because the formula for slope is rise/run. count the x and y units point one and point two are away from each other.
5 0
2 years ago
Does anybody know how to do time with exponential decay
My name is Ann [436]
<span>From the message you sent me:

when you breathe normally, about 12 % of the air of your lungs is replaced with each breath. how much of the original 500 ml remains after 50 breaths

If you think of number of breaths that you take as a time measurement, you can model the amount of air from the first breath you take left in your lungs with the recursive function

b_n=0.12\times b_{n-1}

Why does this work? Initially, you start with 500 mL of air that you breathe in, so b_1=500\text{ mL}. After the second breath, you have 12% of the original air left in your lungs, or b_2=0.12\timesb_1=0.12\times500=60\text{ mL}. After the third breath, you have b_3=0.12\timesb_2=0.12\times60=7.2\text{ mL}, and so on.

You can find the amount of original air left in your lungs after n breaths by solving for b_n explicitly. This isn't too hard:

b_n=0.12b_{n-1}=0.12(0.12b_{n-2})=0.12^2b_{n-2}=0.12(0.12b_{n-3})=0.12^3b_{n-3}=\cdots

and so on. The pattern is such that you arrive at

b_n=0.12^{n-1}b_1

and so the amount of air remaining after 50 breaths is

b_{50}=0.12^{50-1}b_1=0.12^{49}\times500\approx3.7918\times10^{-43}

which is a very small number close to zero.</span>
5 0
3 years ago
Consider the sequence 8, 14, 20, 26, . . .. (a) What is the next term in the sequence? 2.2 Exercises 98 (b) Find a formula for t
omeli [17]

Answer:

Step-by-step explanation:

Each term of the given arithmetic sequence is 6 more than the previous one.  Thus, the next term is 26+6, or 32.

a(n) = 8 + 6(n-1)

3 0
3 years ago
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