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Serggg [28]
3 years ago
11

Y=-5/4x-1 what is the slope and y intercept

Mathematics
1 answer:
pantera1 [17]3 years ago
8 0

Answer:

Slope = -5/4.    And y-int = (0,-1)

Step-by-step explanation:

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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
Martha took her family out to dinner. Their total bill was $32.58. She decided to leave their server a 20% tip. How much did Mar
MrMuchimi
$32.58 x 20% (0.2) = 6.156
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4 0
2 years ago
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10a3 what is the vocabulary for 10
dangina [55]

Answer:

Coefficient

Step-by-step explanation:

If it is 10a^3 (10 times the variable "a" cubed), then 10 is the coefficient.

3 0
2 years ago
The length of a pen is 5 more than its width.The perimeter is 26 m.Find the length and the width.
meriva
P=2l+2w

Since it is given that P=26m, length is 5 more than its width (w+5), we'll work it out in the perimeter formula.

26=2(w+5)+2w
26=2w+10+2w
26=4w+10
4w=26-10
4w=16
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Thus the width is 4m. Let's find the length.

l=w+5
l=4+5
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Answer: 54 liked best

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