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.
Y = a number
"is" means "equal to"
Equation:
Y - 8 = 94
Solving for Y:
Y - 8 = 94
Add 8 to both sides
Y = 102
Answer: Y = 102
Hope this helps!!
Answer:
6 chairs
8 desks
Step-by-step explanation:
First, we assume that all 14 items he bought were chairs, if that was to be true then the office manager would spend...
125 x 14 = 1750$
We see that he spent less then he should have so now we start to substitute desks instead of chairs, and we have to keep in mind that if we change 1 chair to a desk then the total will increase by...
515 - 125 = 390$
Now we just find the difference between the needed total and the total that we get if the office manager would by only chairs and then divide the result by 390 in order to find the number of desks, and so we get...
(4870 - 1750) / 390 = 3120 / 390 = 8 desks
And now that we know the number of desks we just subtract the number of desks from 14 and get the number of chairs, and so...
14 - 8 = 6 chairs
Answer:
Step-by-step explanation:
Number of students 10
Problem 1. $625 for the bus hire per friday, So 625*4=$2500
Problem 2. 2500/25=$100 each for the whole 4 weeks
Problem 3.
10 students tickets 220= 2200 for all tickets. The bus, 625/10 = $62.5*4= $250 dollars for the whole 4 weeks for the bus so in all each student pays $470 each
20 students, tickets 220=4400 for all tickets. The bus, 625/20=$31.25*4=$125 for the whole 4 weeks for the bus, so in all each student must pay $345 each
30 students, tickets 220 = 6600 for all tickets. The bus, 625/30 =$20.83*4=$83.32 for the whole 4 weeks for the bus, so in all each student must pay $303.32 each
41 students, tickets $160=$6560 for all tickets. The bus, because you need 2 buses at 625 each so $1250 for both buses 1250/41= 30.49*4=$121.96 for the whole 4 weeks for the bus. So in al each student must pay $281.96 each
Hope this is correct
Answer: Equilateral triangles are also right triangles sometimes. All angles of an equilateral are congruet sometimes.
