Answer:
(x,y) = (8,7)
Step-by-step explanation:
Solve equation [2] for the variable x
[2] x = y + 15
Plug this in for variable x in equation [1]
[1] (y +15) + y = 1
[1] 2y = -14
Solve equation [1] for the variable y
[1] 2y = - 14
[1] y = - 7 By now we know this much :
x = y+15
y = -7
// Use the y value to solve for x
x = (-7)+15 = 8
Solution :
{x,y} = {8,-7}
Answer:
- (x-4.5)^2 +(y +5)^2 = 30.25
- x = (1/8)y^2 +(1/2)y +(1/2)
- y^2/36 -x^2/64 = 1
- x^2/16 +y^2/25 = 1
Step-by-step explanation:
1. Complete the square for both x and y by adding a constant equal to the square of half the linear term coefficient. Subtract 15, and rearrange to standard form.
(x^2 -9x +4.5^2) +(y^2 +10y +5^2) = 4.5^2 +5^2 -15
(x -4.5)^2 +(y +5)^2 = 30.25 . . . . . write in standard form
Important features: center = (4.5, -5); radius = 5.5.
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2. To put this in the form x=f(y), we need to add 8x, then divide by 8.
x = (1/8)y^2 +(1/2)y +(1/2)
Important features: vertex = (0, -2); focus = (2, -2); horizontal compression factor = 1/8.
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3. We want y^2/a^2 -x^2/b^2 = 1 with a=36 and b=(36/(3/4)^2) = 64:
y^2/36 -x^2/64 = 1
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4. In the form below, "a" is the semi-axis in the x-direction. Here, that is 8/2 = 4. "b" is the semi-axis in the y-direction, which is 5 in this case. We want x^2/a^2 +y^2/b^2 = 1 with a=4 and b=5.
x^2/16 +b^2/25 = 1
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The first attachment shows the circle and parabola; the second shows the hyperbola and ellipse.
A. Multiply the area of the original store by the percent increase then add that to the original amount.
1200 x 0.75 = 900
1200 + 900 = 2100
Answer: 2,100 square feet.
B. 2000 x 0.30 = 600
2000 + 600 = $2,600
2600 x 0.05 = 130
2600 + 130 = 2,730
Rent :$2,730
20,000 = P ( 1 + 0.1 )^4
20,000 = P * 1.1^4
20,000 = P * 1.461
P = 20,000 : 1.461 ≈ $13,689.25
Answer: Miranda needs to put now in the bank $13,689.25