Answer:
-5/2 is the reciprocal of -2/5, but the opposite would just be 5/2.
Step-by-step explanation:
The formula for the equation of a circle is (x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and <em>r</em> is the radius.
So we need to find the values of (h, k) in order to find the center of the circle.
If we simply line up the equation of our given circle with our formula,
we can see that -h = 3 or h = -3 and -k = -2 so k = 2.
So now we have our answer.
center ⇒ (-3, 2)
Answer:
x = 32°
Step-by-step explanation:
∆KLM is an isosceles triangle because it has two equal sides, KL & KM. Therefore, the angles opposite to each of the two equal sides, which are referred to as the base angles are congruent to each other.
m<KML = m<KLM = 58°
m<MKL = 180 - (58 + 58) (Sum of triangle)
m<MKL = 64°
m<JKM = 180 - m<MKL (linear pair theorem)
m<JKM = 180 - 64 (Substitution)
m<JKM = 116°
∆JKM is also an isosceles triangle with two equal sides. Therefore, it's based angles (x & <J) would also be equal to each other.
Thus:
x = ½(180 - m<JKM)
x = ½(180 - 116) (Substitution)
x = 32°
75-31= 44
44/75= 0.58666 or 58.7%
Subtract 31 from 75 since we're figuring out greater than or "equal to" we want to include the number 32 in our equation. If it was only "greater than" 32 then we'd subtract 32 from 75. Then you divide that number(44) by 75, which is all the possible outcomes you could have in this scenario. Move the decimal two places to the right to make it a percentage and you've got your answer.
Answer:
13 weeks; 98 dollars.
Step-by-step explanation:
Let's say x represents the number of weeks, and y the number of dollars. For Janelle, an equation to find out how much money she has is y = 20 + 6x. For April, the equation is y = 150 - 4x. Now we need to find how long it will take them to have the same amount of money, and how much that is. A new equation to figure that out is 150 - 4x = 20 + 6x. To solve, make it so the variable is only one side. Add 4x to both sides. You now get 150 = 20 + 10x. Then we continue solving. Subtract 20 from both sides to get 130 = 10x. Then divide both sides by 10 to get 13 = x. This means in thirteen weeks, they will have the same amount of money. To find out how much money they have, choose one (or both to be sure) of the equations and solve for y. For example, Janelle's equation is y = 20 + 6x. Fill in 13 for x to get y = 20 + 6(13). y = 20 + 78. y = 98. This means in 13 weeks, Janelle will have 98 dollars. To be sure, also check with April's equation. y = 150 - 4x. y = 150 - 4(13). y = 150 - 52. y = 98. Therefore, in 13 weeks, both people will have 98 dollars.
