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Brilliant_brown [7]
3 years ago
13

Simplify (2x + y)(x - 2y) - (x + 2y)(2x - y) as much as possible.

Mathematics
1 answer:
snow_tiger [21]3 years ago
4 0

Answer:

-6xy

Step-by-step explanation:

(2x-y)x(x-2y)-(x+2y)X(2x-y)

remove the parentheses

2x^2-4xy+xy-2y^2-(2x^2-xy+4xy-2y^2)

collect terms

2x^2-4xy+xy-2y^2-(2x^2+3xy-2y^2)

remove the parentheses

2x^2-4xy+xy-2y^2-2x^2-3xy+2y^2

remove the opposites, collect the terms to get -6xy

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Solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!​
Misha Larkins [42]

Answer:

[0.25, 2]

Step-by-step explanation:

We have

4t² ≤ 9t-2

subtract 9t-2 from both sides to make this a quadratic

4t²-9t+2 ≤ 0

To solve this, we can solve for 4t²-9t+2=0 and do some guess and check to find which values result in the function being less than 0.

4t²-9t+2=0

We can see that -8 and -1 add up to -9, the coefficient of t, and 4 (the coefficient of t²) and 2 multiply to 8, which is also equal to -8 * -1. Therefore, we can write this as

4t²-8t-t+2=0

4t(t-2)-1(t-2)=0

(4t-1)(t-2)=0

Our zeros are thus t=2 and t = 1/4. Using these zeros, we can set up three zones: t < 1/4, 1/4<t<2, and t>2. We can take one random value from each of these zones and see if it fits the criteria of

4t²-9t+2 ≤ 0

For t<1/4, we can plug in 0. 4(0)²-9(0) + 2 = 2 >0 , so this is not correct

For 1/4<t<2, we can plug 1 in. 4(1)²-9(1) +2 = -3 <0, so this is correct

For t > 2, we can plug 5 in. 4(5)²-9(5) + 2 = 57 > 0, so this is not correct.

Therefore, for 4t^2 ≤ 9t-2 , which can also be written as 4t²-9t+2 ≤ 0, when t is between 1/4 and 2, the inequality is correct. Furthermore, as the sides are equal when t= 1/4 and t=2, this can be written as [0.25, 2]

8 0
3 years ago
Starting at home, Michael traveled uphill to the gift store for 24 minutes at just 10 mph. He then traveled back home along the
kondaur [170]
We can figure out how long Michael's trip took by realizing that 30 mph is 3 times 10 mph.  Because of this, the trip home will take 1/3 the amount of time it took to go up the hill.  This makes the equation 24 + 8 = 32 minutes for the whole trip.

Now we need to figure out how long the trip was.  We can do this by multiplying 10 minutes by 24/60, which equals 4.  This means that Michael went 4 miles there, and 4 miles back.  So Michael went a total of 8 miles.

Now we know that Michael went 8 miles in 32 minutes.  Now, we multiply 8 by 60/32.  This gives us 15, so Michael went 15 miles per hour on average in the trip.
4 0
3 years ago
What is the area of this figure?
Luden [163]

Answer:

The area of this figure is 24mm.

Step-by-step explanation:

4mm*3mm=12mm

1mm*6mm=6mm

3mm*4mm=12mm/2mm=6mm

6mm+6mm+12mm=24mm

3 0
2 years ago
What are two ratios equivalent to 10:85
guajiro [1.7K]

Answer:

2 : 17

1 : 8.5

6 0
3 years ago
How to solve y=−8x? is the y axis zero or is it one?
Vinvika [58]

y=-8x

To find x-intercept/zero, substitute y=0

0=-8x

solve the equation for x

x=0

now we do the same only different way ok

0=-8x

swap the sides of the equation

-8x=0

divide both sides of the equation by -8

x=0

PLEASE MARK ME AS BRAINLIEST

6 0
3 years ago
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