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Misha Larkins [42]
2 years ago
12

Y= -x^2+10x-25 in factored form and what is the x intercept

Mathematics
1 answer:
Strike441 [17]2 years ago
5 0

Step-by-step explanation:

X-intercept, y = 0

0 = -x² + 10x - 25

-x² + 10x - 25 = 0

-(x² - 10x + 25) = 0

x² - 10x + 25 = 0

(x - 5)(x - 5) = 0

x = 5

(5,0)

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Find the distance between a point (–7, –19) and a horizontal line at y = 3.
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2 years ago
Among all pairs of numbers (x,y)such that 6x+2y=36 find the pair for which the sum of squares, x^2+y^2 is minimum.
lora16 [44]
First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.


The sum x^2+y^2 can be written as: x^2+y^2=(x+y)^2-2xy, 
<span>
from the binomial expansion formula: </span>(x+y)^2=x^2+2xy+y^2.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>

</span>x^2+y^2=(x+(-3x+18))^2-2x(-3x+18)=(-2x+18)^2+6x^2-36x=4x^2-72x+18^2+6x^2-36x=10x^2-108x+18^2.

This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.


At x=5.4, the expression 10x^2-108x+18^2, which is equivalent to x^2+y^2, takes it smallest value.

Substituting, we would find 10x^2-108x+18^2=10(5.4)^2-108(5.4)+18^2=291.6-583.2+324=32.4 This is the smallest value of the expression. 


For x=5.4, y=-3x+18=-3(5.4)+18=1.8.



Answer:   (5.4, 1.8)
8 0
2 years ago
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3) "she used 1/2 lb of flour ro make bread"
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From here you can solve for w using back substitution. 
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Anuta_ua [19.1K]
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