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Elanso [62]
3 years ago
6

7(3x/1)=-1its distributive property but I don't know how to solve it​

Mathematics
1 answer:
Lelu [443]3 years ago
7 0
7(3x/1)=-1
7(3x)=-1
21x=-1
21x/21=-1/21
X=-1/21

Answer: -1/21
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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
3 years ago
25-20x+4x² heh help pls and hurry :((
yulyashka [42]
25- 20x + 4x^2
=4x^2 - 20x + 25
=4x^2 - x(10+10) +25
=4x^2 - 10x - 10x + 25
=2x(2x - 5) - 5( 2x - 5)
=(2x - 5)(2x - 5)
=(2x - 5)^2
6 0
2 years ago
Read 2 more answers
Which object would hold about 2 cups of liquid when completely filled?
Setler [38]
D. the bottle of water
7 0
3 years ago
What is the value of x in the equation
Alex

Answer:

D) 57

Step-by-step explanation:

1/3x- 1/2 = 18 1/2

1/3x = 19

(3) * 1/3x = 19 (3)

x = 57

8 0
3 years ago
Read 2 more answers
Sita Rahim drove due north for 3 hours at 46 miles per hour. From the
Phantasy [73]

Answer:

224 miles

Step-by-step explanation:

What you would do is take the 3 hours times the 46 mph to get 138 miles.

3*46=138

Next, multiply the 2 hours by the 43 mph to get 86 miles.

2*43=86

Lastly, you're going to add the two.

138+86=224 miles.

6 0
3 years ago
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