Number 1
37.50 divide by 5.25 and the answer is 7
Answer:
square
Step-by-step explanation:
The opposite angles are congruent, the diagonals bisect each other, the opposite sides are parallel, the diagonals bisect the angles
False.
Multiplying two negatives gives a positive.
Step 1: Factor
![2 x^{2} - 3x -2](https://tex.z-dn.net/?f=2%20x%5E%7B2%7D%20-%203x%20-2)
1. <span> Multiply 2 by -2, which is -4.</span>
2. <span>Ask: Which two numbers add up to -3 and multiply to -4?
</span>3. <span>Answer: 1 and -4
</span>4. Rewrite
![-3x](https://tex.z-dn.net/?f=-3x)
as the sum of
![x](https://tex.z-dn.net/?f=x)
and
![-4x](https://tex.z-dn.net/?f=-4x)
![2 x^{2} +x-4x-2\ \textless \ 0](https://tex.z-dn.net/?f=2%20x%5E%7B2%7D%20%2Bx-4x-2%5C%20%5Ctextless%20%5C%200)
Step 2: <span>Factor out common terms in the first two terms, then in the last two terms.
</span>
![x(2x+1)-2(2x+1)\ \textless \ 0](https://tex.z-dn.net/?f=x%282x%2B1%29-2%282x%2B1%29%5C%20%5Ctextless%20%5C%200)
<span>
Step 3: </span>Factor out the common term
![2x+1](https://tex.z-dn.net/?f=2x%2B1)
![(2x+1)(x-2)\ \textless \ 0](https://tex.z-dn.net/?f=%282x%2B1%29%28x-2%29%5C%20%5Ctextless%20%5C%200)
Step 4: Solve for
![x](https://tex.z-dn.net/?f=x)
1. Ask: When will
![(2x+1)(x-2)](https://tex.z-dn.net/?f=%282x%2B1%29%28x-2%29)
equal zero?
2. Answer: When
![2x + 1 = 0](https://tex.z-dn.net/?f=2x%20%2B%201%20%3D%200)
or
![x-2=0](https://tex.z-dn.net/?f=x-2%3D0)
3. <span>Solve each of the 2 equations above:
</span>
![x=- \frac{1}{2} ,2](https://tex.z-dn.net/?f=x%3D-%20%5Cfrac%7B1%7D%7B2%7D%20%2C2)
<span>
Step 5: </span>From the values of
![x](https://tex.z-dn.net/?f=x)
<span>above, we have these 3 intervals to test.
x = < -1/2
-1/2 < x < 2
x > 2
Step 6: P</span><span>ick a test point for each interval
</span>For the interval
![x\ \textless \ - \frac{1}{2} ](https://tex.z-dn.net/?f=x%5C%20%5Ctextless%20%5C%20-%20%5Cfrac%7B1%7D%7B2%7D%20%0A)
Lets pick
![x=-1.](https://tex.z-dn.net/?f=x%3D-1.)
Then,
![2(-1) ^{2} -3 * -1 -2 \ \textless \ 0](https://tex.z-dn.net/?f=2%28-1%29%20%5E%7B2%7D%20-3%20%2A%20-1%20-2%20%5C%20%5Ctextless%20%5C%20%200)
After simplifying, we get
![3\ \textless \ 0](https://tex.z-dn.net/?f=3%5C%20%5Ctextless%20%5C%200)
, Which is false.
Drop this interval.
<span>
For this interval
![- \frac{1}{2} \ \textless \ x\ \textless \ 2](https://tex.z-dn.net/?f=-%20%5Cfrac%7B1%7D%7B2%7D%20%5C%20%5Ctextless%20%5C%20x%5C%20%5Ctextless%20%5C%202)
Lets pick
![x=0](https://tex.z-dn.net/?f=x%3D0)
. Then,
![2* 0^{2} - 3 * 0-2\ \textless \ 0](https://tex.z-dn.net/?f=2%2A%200%5E%7B2%7D%20-%203%20%2A%200-2%5C%20%5Ctextless%20%5C%200)
. After simplifying, we get
![-2\ \textless \ 0,](https://tex.z-dn.net/?f=-2%5C%20%5Ctextless%20%5C%200%2C)
which is true. Keep this <span>interval.
For the interval </span>
![x\ \textgreater \ 2](https://tex.z-dn.net/?f=x%5C%20%5Ctextgreater%20%5C%202)
Lets pick
![x = 3.](https://tex.z-dn.net/?f=x%20%3D%203.)
Then,
![2 * 3 ^{2} -3*3-2\ \textless \ 0.](https://tex.z-dn.net/?f=2%20%2A%203%20%20%5E%7B2%7D%20-3%2A3-2%5C%20%5Ctextless%20%5C%200.)
After simplifying, we get
![7\ \textless \ 0](https://tex.z-dn.net/?f=7%5C%20%5Ctextless%20%5C%200)
, Which is false. Drop this interval.
.Step 7: Therefore,
![- \frac{1}{2} \ \textless \ x\ \textless \ 2](https://tex.z-dn.net/?f=-%20%5Cfrac%7B1%7D%7B2%7D%20%5C%20%5Ctextless%20%5C%20x%5C%20%5Ctextless%20%5C%202)
Done! :)</span>
118.73 that's the answer, you have to use long multiplication. Hope I helped