Answer:
The Answer is A, a line segment that has both endpoints on a circle.
Step-by-step explanation:
Answer:
half of the atoms of an unstable isotope to go through radioactive decay. ... amount of a sample will be left after a certain amount of time, or it can tell us how long has ... If the sample contained 510 grams, how much chromium would remain ... 5) Titanium-51 decays with a half-life of 6 minutes. ... How many grams of bismuth-.
Step-by-step explanation:
Answer:
y = -2x^2(x - 3)
Step-by-step explanation:
<em><u>Preliminary Remark</u></em>
If a cubic is tangent to the x axis at 0,0
Then the equation must be related to y = a*x^2(x - h)
<em><u>(3,0)</u></em>
If the cubic goes through the point (3,0), then the equation will become
0 = a*3^2(3 - h)
0 = 9a (3 - h)
0 = 27a - 9ah
from which h = 3
<em><u>From the second point, we get</u></em>
4 = ax^2(x - 3)
4 = a(1)^2(1 - 3)
4 = a(-2)
a = 4 / - 2
a = -2
<em><u>Answer</u></em>
y = -2x^2(x - 3)
![\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ % templates f(x)= A( Bx+ C)+ D \\\\ ~~~~y= A( Bx+ C)+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \\\\ f(x)= A sin\left( B x+ C \right)+ D \\\\ --------------------](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bfunction%20transformations%7D%0A%5C%5C%5C%5C%5C%5C%0A%25%20templates%0Af%28x%29%3D%20%20A%28%20%20Bx%2B%20%20C%29%2B%20%20D%0A%5C%5C%5C%5C%0A~~~~y%3D%20%20A%28%20%20Bx%2B%20%20C%29%2B%20%20D%0A%5C%5C%5C%5C%0Af%28x%29%3D%20%20A%5Csqrt%7B%20%20Bx%2B%20%20C%7D%2B%20%20D%0A%5C%5C%5C%5C%0Af%28x%29%3D%20%20A%28%5Cmathbb%7BR%7D%29%5E%7B%20%20Bx%2B%20%20C%7D%2B%20%20D%0A%5C%5C%5C%5C%0Af%28x%29%3D%20%20A%20sin%5Cleft%28%20B%20x%2B%20%20C%20%20%5Cright%29%2B%20%20D%0A%5C%5C%5C%5C%0A--------------------)
![\bf \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbullet%20%5Ctextit%7B%20stretches%20or%20shrinks%20horizontally%20by%20%20%7D%20%20%20A%5Ccdot%20%20%20B%5C%5C%5C%5C%0A%5Cbullet%20%5Ctextit%7B%20flips%20it%20upside-down%20if%20%7D%20%20A%5Ctextit%7B%20is%20negative%7D%5C%5C%0A~~~~~~%5Ctextit%7Breflection%20over%20the%20x-axis%7D%0A%5C%5C%5C%5C%0A%5Cbullet%20%5Ctextit%7B%20flips%20it%20sideways%20if%20%7D%20%20B%5Ctextit%7B%20is%20negative%7D)
![\bf ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~%5Ctextit%7Breflection%20over%20the%20y-axis%7D%0A%5C%5C%5C%5C%0A%5Cbullet%20%5Ctextit%7B%20horizontal%20shift%20by%20%7D%5Cfrac%7B%20%20C%7D%7B%20%20B%7D%5C%5C%0A~~~~~~if%5C%20%5Cfrac%7B%20%20C%7D%7B%20%20B%7D%5Ctextit%7B%20is%20negative%2C%20to%20the%20right%7D%5C%5C%5C%5C%0A~~~~~~if%5C%20%5Cfrac%7B%20%20C%7D%7B%20%20B%7D%5Ctextit%7B%20is%20positive%2C%20to%20the%20left%7D%5C%5C%5C%5C%0A%5Cbullet%20%5Ctextit%7B%20vertical%20shift%20by%20%7D%20%20D%5C%5C%0A~~~~~~if%5C%20%20%20D%5Ctextit%7B%20is%20negative%2C%20downwards%7D%5C%5C%5C%5C%0A~~~~~~if%5C%20%20%20D%5Ctextit%7B%20is%20positive%2C%20upwards%7D%5C%5C%5C%5C%0A%5Cbullet%20%5Ctextit%7B%20period%20of%20%7D%5Cfrac%7B2%5Cpi%20%7D%7B%20%20B%7D)
and with that template in mind,
notice from a parent function of f(x) = x³,
a derived function with f(x+5) = (x + 5)³
has a C component of 5, C = 5, which means is the as the parent, just shifted to the left by 5 units.
Answer:
![\boxed{ \bold{ \sf{ \: 1. \: \: \: \: \: 198}}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Cbold%7B%20%5Csf%7B%20%5C%3A%201.%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20198%7D%7D%7D)
![\boxed{ \bold{ \sf{2. \: \: \: \: \: - 8}}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Cbold%7B%20%5Csf%7B2.%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20-%208%7D%7D%7D)
![\boxed{ \bold{ \sf{ 3. \: \: \: \: \: \frac{64}{343} }}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Cbold%7B%20%5Csf%7B%203.%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%5Cfrac%7B64%7D%7B343%7D%20%7D%7D%7D)
Step-by-step explanation:
1. Given, u = 20 , x = 4 , y = 7 , z = 10
![\sf{ \frac{u}{z} + x {y}^{2} }](https://tex.z-dn.net/?f=%20%5Csf%7B%20%5Cfrac%7Bu%7D%7Bz%7D%20%20%2B%20x%20%7By%7D%5E%7B2%7D%20%7D)
⇒![\sf{ \frac{20}{10} + 4 \times {7}^{2} }](https://tex.z-dn.net/?f=%20%5Csf%7B%20%5Cfrac%7B20%7D%7B10%7D%20%20%2B%204%20%5Ctimes%20%20%7B7%7D%5E%7B2%7D%20%7D)
⇒![\sf{ \frac{20}{10} + 4 \times 49}](https://tex.z-dn.net/?f=%20%5Csf%7B%20%5Cfrac%7B20%7D%7B10%7D%20%20%2B%204%20%5Ctimes%2049%7D)
⇒![\sf{ \frac{20}{10} + 196}](https://tex.z-dn.net/?f=%20%5Csf%7B%20%5Cfrac%7B20%7D%7B10%7D%20%20%2B%20196%7D)
⇒![\sf{ \frac{20 + 196 \times 10}{10} }](https://tex.z-dn.net/?f=%20%5Csf%7B%20%5Cfrac%7B20%20%2B%20196%20%5Ctimes%2010%7D%7B10%7D%20%7D)
⇒![\sf{ \frac{20 + 1960}{10} }](https://tex.z-dn.net/?f=%20%5Csf%7B%20%5Cfrac%7B20%20%2B%201960%7D%7B10%7D%20%7D)
⇒![\sf{ \frac{1980}{10} }](https://tex.z-dn.net/?f=%20%5Csf%7B%20%5Cfrac%7B1980%7D%7B10%7D%20%7D)
⇒![\sf{198}](https://tex.z-dn.net/?f=%20%5Csf%7B198%7D)
2. ![\sf{4( - 2)}](https://tex.z-dn.net/?f=%20%5Csf%7B4%28%20-%202%29%7D)
Multiplying or dividing a positive integer by any negative integer gives a negative integer
= - 8
3. ![\sf{( \frac{4}{7} ) ^{3} }](https://tex.z-dn.net/?f=%20%5Csf%7B%28%20%5Cfrac%7B4%7D%7B7%7D%20%29%20%5E%7B3%7D%20%7D)
⇒![\sf{( \frac{ {4}^{3} }{ {7}^{3} } })](https://tex.z-dn.net/?f=%20%5Csf%7B%28%20%5Cfrac%7B%20%7B4%7D%5E%7B3%7D%20%7D%7B%20%7B7%7D%5E%7B3%7D%20%7D%20%7D%29)
⇒![\sf{ \frac{4 \times 4 \times 4 }{7 \times 7 \times 7}}](https://tex.z-dn.net/?f=%20%5Csf%7B%20%5Cfrac%7B4%20%5Ctimes%204%20%5Ctimes%204%20%7D%7B7%20%5Ctimes%207%20%5Ctimes%207%7D%7D%20)
⇒![\sf{ \frac{64}{343} }](https://tex.z-dn.net/?f=%20%5Csf%7B%20%5Cfrac%7B64%7D%7B343%7D%20%7D)
Hope I helped!
Best regards! :D