Answer:
The length of side AB is 5 units
Step-by-step explanation:
* Lets revise how to find the distance between two points
- If there are two points their coordinates are (x1 , y1) and (x2 , y2),
then we can find the distance between them by this rule:
d = √[(x2 - x1)² + (y2 - y1)²]
- Now lets solve the problem
∵ A = (4 , -5)
∵ B = (7 , -9)
- To find the length of AB use the rule of the distance above
- Let point A is (x1 , y1) and point B is (x2 , y2)
∵ x1 = 4 and x2 = 7
∵ y1 = -5 and y2 = -9
∴ AB = √[(7 - 4)² + (-9 - -5)²]
∴ AB = √[(3)² + (-4)²]
∴ AB = √[9 + 16] = √25 = 5
* The length of side AB is 5 units
![\sf{\bold{\green{\underline{\underline{Given}}}}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cbold%7B%5Cgreen%7B%5Cunderline%7B%5Cunderline%7BGiven%7D%7D%7D%7D%7D%20)
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<u>______________________</u>
![\sf{\bold{\green{\underline{\underline{To\:Find}}}}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cbold%7B%5Cgreen%7B%5Cunderline%7B%5Cunderline%7BTo%5C%3AFind%7D%7D%7D%7D%7D%20)
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<u>______________________</u>
![\sf{\bold{\green{\underline{\underline{Solution}}}}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cbold%7B%5Cgreen%7B%5Cunderline%7B%5Cunderline%7BSolution%7D%7D%7D%7D%7D%20)
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W = 7a + 4b
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![\sf \implies W - 4b = 7a](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20W%20-%204b%20%3D%207a%20)
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![\sf \implies \dfrac{W - 4b}{7} = a](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7BW%20-%204b%7D%7B7%7D%20%3D%20%20a%20)
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<u>Option 1 :</u>
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![\sf \bigg( a = \dfrac{W - 4b}{7} \bigg) \neq \bigg( a = \dfrac{W - 7b}{4}\bigg)](https://tex.z-dn.net/?f=%5Csf%20%5Cbigg%28%20a%20%3D%20%5Cdfrac%7BW%20-%204b%7D%7B7%7D%20%20%5Cbigg%29%20%5Cneq%20%5Cbigg%28%20a%20%3D%20%5Cdfrac%7BW%20-%207b%7D%7B4%7D%5Cbigg%29%20%20)
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This option is not correct
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<u>Option 2 : </u>
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![\sf \bigg( a = \dfrac{W - 4b}{7} \bigg) \neq \bigg( a = \dfrac{W}{7} - 4b \bigg)](https://tex.z-dn.net/?f=%5Csf%20%5Cbigg%28%20a%20%3D%20%5Cdfrac%7BW%20-%204b%7D%7B7%7D%20%20%5Cbigg%29%20%5Cneq%20%5Cbigg%28%20a%20%3D%20%5Cdfrac%7BW%7D%7B7%7D%20-%204b%20%5Cbigg%29%20%20)
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This option is not correct
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<u>Option 3 :</u>
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![\sf \bigg( a = \dfrac{W - 4b}{7} \bigg) = \bigg( a = \dfrac{W - 4b}{7}\bigg)](https://tex.z-dn.net/?f=%5Csf%20%5Cbigg%28%20a%20%3D%20%5Cdfrac%7BW%20-%204b%7D%7B7%7D%20%20%5Cbigg%29%20%3D%20%5Cbigg%28%20a%20%3D%20%5Cdfrac%7BW%20-%204b%7D%7B7%7D%5Cbigg%29%20%20)
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This option is correct
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<u>Option 4 :</u>
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![\sf \bigg( a = \dfrac{W - 4b}{7} \bigg) \neq \bigg( W = \dfrac{W}{7} - 28b \bigg)](https://tex.z-dn.net/?f=%5Csf%20%5Cbigg%28%20a%20%3D%20%5Cdfrac%7BW%20-%204b%7D%7B7%7D%20%20%5Cbigg%29%20%5Cneq%20%5Cbigg%28%20W%20%3D%20%5Cdfrac%7BW%7D%7B7%7D%20-%2028b%20%5Cbigg%29%20%20)
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This option is not correct
<u>______________________</u>
![\sf{\bold{\green{\underline{\underline{Answer}}}}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cbold%7B%5Cgreen%7B%5Cunderline%7B%5Cunderline%7BAnswer%7D%7D%7D%7D%7D%20)
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- Correct answer = option C
Step-by-step explanation:
![- \frac{1}{4} \times ( - \frac{6}{11} )](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%5Ctimes%20%28%20-%20%20%5Cfrac%7B6%7D%7B11%7D%20%29)
![\frac{1}{2} \times \frac{3}{11}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%20%20%5Cfrac%7B3%7D%7B11%7D%20)
![\frac{3}{22}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B22%7D%20)
Answer:
seven eights of a number = 7/8 × a number
let the unknown number be = x
![\frac{7}{8} \times x = 63](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B8%7D%20%20%5Ctimes%20x%20%3D%2063)
![x = 63 \div ( \frac{7}{8} )](https://tex.z-dn.net/?f=x%20%3D%2063%20%20%5Cdiv%20%28%20%5Cfrac%7B7%7D%7B8%7D%20%29)
![x = 63 \times \frac{8}{7}](https://tex.z-dn.net/?f=x%20%3D%2063%20%5Ctimes%20%20%5Cfrac%7B8%7D%7B7%7D%20)
![x = \frac{504}{7}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B504%7D%7B7%7D%20)
![x = 72](https://tex.z-dn.net/?f=x%20%3D%2072)
Answer:
A. First graph
Step-by-step explanation:
2x - y = 8 in slope intercept form is y = 2x - 8
x - y = 2 in slope intercept form is y = x - 2
The first graph matches the slope intercept form equations.