Answer:
The answer is 13x
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
![48 \geqslant 6 - 7a \\ 48 - 6 \geqslant - 7a \\ 42 \geqslant - 7a \\ a \geqslant \frac{ 42}{ -7} \\ a \geqslant - 6](https://tex.z-dn.net/?f=48%20%5Cgeqslant%206%20-%207a%20%5C%5C%2048%20-%206%20%5Cgeqslant%20%20-%207a%20%5C%5C%2042%20%5Cgeqslant%20%20-%207a%20%5C%5C%20a%20%20%5Cgeqslant%20%20%20%5Cfrac%7B%2042%7D%7B%20-7%7D%20%20%5C%5C%20a%20%5Cgeqslant%20%20-%206)
Hope this helps..
A)
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) Q&({{ 0}}\quad ,&{{ 2}})\quad % (c,d) P&({{ 0.5}}\quad ,&{{ 0}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0AQ%26%28%7B%7B%200%7D%7D%5Cquad%20%2C%26%7B%7B%202%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0AP%26%28%7B%7B%200.5%7D%7D%5Cquad%20%2C%26%7B%7B%200%7D%7D%29%0A%5Cend%7Barray%7D%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D)
![\bf QP=\sqrt{(0.5-0)^2+(0-2)^2}\implies QP=\sqrt{0.5^2+2^2} \\\\\\ QP=\sqrt{\left( \frac{1}{2} \right)^2+4}\implies QP=\sqrt{ \frac{1^2}{2^2}+4}\implies QP=\sqrt{\frac{1}{4}+4} \\\\\\ QP=\sqrt{\frac{17}{4}}\implies QP=\cfrac{\sqrt{17}}{\sqrt{4}}\implies QP=\cfrac{\sqrt{17}}{2}](https://tex.z-dn.net/?f=%5Cbf%20QP%3D%5Csqrt%7B%280.5-0%29%5E2%2B%280-2%29%5E2%7D%5Cimplies%20QP%3D%5Csqrt%7B0.5%5E2%2B2%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AQP%3D%5Csqrt%7B%5Cleft%28%20%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%5E2%2B4%7D%5Cimplies%20QP%3D%5Csqrt%7B%20%5Cfrac%7B1%5E2%7D%7B2%5E2%7D%2B4%7D%5Cimplies%20QP%3D%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7D%2B4%7D%0A%5C%5C%5C%5C%5C%5C%0AQP%3D%5Csqrt%7B%5Cfrac%7B17%7D%7B4%7D%7D%5Cimplies%20QP%3D%5Ccfrac%7B%5Csqrt%7B17%7D%7D%7B%5Csqrt%7B4%7D%7D%5Cimplies%20QP%3D%5Ccfrac%7B%5Csqrt%7B17%7D%7D%7B2%7D)
b)
since QR=QP, that means that QO is an angle bisector, and thus the segments it makes at the bottom of RO and OP, are also equal, thus RO=OP
thus, since the point P is 0.5 units away from the 0, point R is also 0.5 units away from 0 as well, however, is on the negative side, thus R (-0.5, 0)
c)
what's the equation of a line that passes through the points (-0.5, 0) and (0,2)?
![\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) Q&({{ 0}}\quad ,&{{ 2}})\quad % (c,d) R&({{ -0.5}}\quad ,&{{ 0}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{0-2}{-0.5-0}\implies \cfrac{-2}{-0.5}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%20%28a%2Cb%29%0AQ%26%28%7B%7B%200%7D%7D%5Cquad%20%2C%26%7B%7B%202%7D%7D%29%5Cquad%20%0A%25%20%20%20%28c%2Cd%29%0AR%26%28%7B%7B%20-0.5%7D%7D%5Cquad%20%2C%26%7B%7B%200%7D%7D%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0A%25%20slope%20%20%3D%20m%0Aslope%20%3D%20%7B%7B%20m%7D%7D%3D%20%5Ccfrac%7Brise%7D%7Brun%7D%20%5Cimplies%20%0A%5Ccfrac%7B%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%7D%7B%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%7D%5Cimplies%20%5Ccfrac%7B0-2%7D%7B-0.5-0%7D%5Cimplies%20%5Ccfrac%7B-2%7D%7B-0.5%7D)
![\bold{\huge{\pink{\underline{ Solution }}}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Chuge%7B%5Cpink%7B%5Cunderline%7B%20Solution%20%7D%7D%7D%7D)
<u>We </u><u>have </u><u>given </u><u>in </u><u>the </u><u>question </u><u>that</u><u>, </u>
- <u>The </u><u>sum </u><u>of </u><u>2</u><u> </u><u>numbers </u><u>is </u><u>equal </u><u>to </u><u>1</u><u>1</u><u> </u>
- <u>The </u><u>difference </u><u>between </u><u>two </u><u>numbers </u><u>is </u><u>1</u><u>9</u><u> </u><u>.</u>
![\bold{\underline{ To \: Find }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cunderline%7B%20To%20%5C%3A%20Find%20%7D%7D)
- <u>We </u><u>have </u><u>to </u><u>find </u><u>the </u><u>value </u><u>of </u><u>x </u><u>and </u><u>y</u><u>. </u>
![\bold{\underline{ Let's \: Begin }}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cunderline%7B%20Let%27s%20%5C%3A%20Begin%20%7D%7D)
Let the two numbers be x and y
<u>According </u><u>to </u><u>the </u><u>question</u><u>, </u>
![\sf{ x + y = 11......eq(1) }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%2B%20y%20%3D%2011......eq%281%29%20%7D)
![\sf{ x - y = 19......eq(2) }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20-%20y%20%3D%2019......eq%282%29%20%7D)
<u>Solving </u><u>eq(</u><u> </u><u>1</u><u> </u><u>)</u><u> </u><u>we </u><u>get </u><u>:</u><u>-</u><u> </u>
![\sf{ x + y = 11 }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%2B%20y%20%3D%2011%20%20%7D)
![\sf{ x = 11 - y ......eq(3 ) }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%3D%2011%20-%20y%20......eq%283%20%29%20%7D)
<u>Subsituting </u><u>eq(</u><u>3</u><u> </u><u>)</u><u> </u><u>in </u><u>eq</u><u>(</u><u>2</u><u>)</u><u> </u><u>:</u><u>-</u>
![\sf{ x - y = 19 }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20-%20y%20%3D%2019%20%7D)
![\sf{ ( 11 - y) - y = 19 }](https://tex.z-dn.net/?f=%5Csf%7B%20%28%2011%20-%20y%29%20-%20y%20%3D%2019%20%7D)
![\sf{ 11 - y - y = 19 }](https://tex.z-dn.net/?f=%5Csf%7B%2011%20-%20y%20-%20y%20%3D%2019%20%7D)
![\sf{ 11 - 2y = 19 }](https://tex.z-dn.net/?f=%5Csf%7B%20%2011%20-%202y%20%3D%2019%20%7D)
![\sf{ - 2y = 19 - 11 }](https://tex.z-dn.net/?f=%5Csf%7B%20-%202y%20%3D%2019%20-%2011%20%20%7D)
![\sf{ - 2y = 8}](https://tex.z-dn.net/?f=%5Csf%7B%20-%202y%20%3D%208%7D)
![\sf{ y = 8/(-2) }](https://tex.z-dn.net/?f=%5Csf%7B%20y%20%3D%208%2F%28-2%29%20%7D)
![\sf{ y = - 4 }](https://tex.z-dn.net/?f=%5Csf%7B%20y%20%3D%20-%204%20%7D)
![\sf{\red{Thus ,\: the\: value\: of \: y = -4}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cred%7BThus%20%2C%5C%3A%20the%5C%3A%20value%5C%3A%20of%20%5C%3A%20y%20%3D%20-4%7D%7D)
<u>Now</u><u>, </u><u> </u><u>Subsitute </u><u>the </u><u>value </u><u>of </u><u>y </u><u>in </u><u>eq(</u><u> </u><u>3</u><u> </u><u>)</u><u> </u><u>:</u><u>-</u>
![\sf{ x = 11 - y }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%3D%2011%20-%20y%20%20%7D)
![\sf{ x = 11 - (-4 ) }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%3D%2011%20-%20%28-4%20%29%20%20%7D)
![\sf{ x = 11 + 4 }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%3D%2011%20%2B%204%20%20%7D)
![\sf{ x = 15 }](https://tex.z-dn.net/?f=%5Csf%7B%20x%20%3D%2015%20%7D)
Hence, The value of x and y are 15 and (-4) .