Tutor profile: Jeny B.
Based on the following standard form equation, determine the center and the radius of the circle. $$(x-6)^2+(y+7)^2=36$$
The equation for a circle in standard form is $$(x-h)^2+(y-k)^2=r^2$$ where r is the radius and (h,k) is the center of the circle. Using this formula, you can identify that $$h=6$$ and $$k=-7$$. To find r, you must take the square root of 36 which equals 6. Therefore, the equation is for a circle with the radius of 6 and a center at (6,7).
Identify the subject, direct object, and indirect object in the following sentence. Mary gave Shelly the sandwich.
The subject is the nun or pronoun that performs the verb in the sentence. The direct object is the thing that is being acted upon. The indirect object is the recipient of the direct object in the sentence. They often are inside prepositional phrases. So for the sentence above, first you locate the action of the sentence which is GAVE. Who is giving? MARY. So MARY is the SUBJECT of the sentence. Then you must ask what did Mary give? Mary gave a SANDWICH. So SANDWICH is the DIRECT OBJECT because it is what the verb is acting upon. So finally, who is receiving the sandwich? The answer is SHELLY. Shelly is receiving the sandwich so she is the INDIRECT OBJECT. You can also check this by seeing if you can move it to the end of the sentence and attach it with a preposition and it still makes sense. So you can change the sentence to Mary gave the sandwich to Shelly. This sentence still makes sense. Therefore, Shelly is the indirect object.
Complete the point-slope equation of the line through (-3,3) and (2,1) y-1=___
The point-slope formula is (y-Y)=m(x-X) where m=slope and (X,Y) is a point on the line. To finish the equation, first you must find the slope. The formula for slope is m=change in y/ change in x The change in y is found by subtracting the first y from the second, and the change in x is found by subtracting the first x from the second. SO for this problem, you plug in the two point and $$m=(1-3)/(2-(-3))$$ which can be simplified to $$m=(1-3)/(2+3)$$. Then you solve for m. $$m=(-2)/(5)=-(2/5)$$ The slope of the line is -2/5. Then, you need to plug in the slope and one of the two points. For this problem, It already plugged in Y=1, so the point you are using is (2,1). So you plug in m=-2/5 and X=2 to give you the answer of equation $$y-1=-2/5(x-2)$$
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