37.5*0.010=.375 (or press % button on calculator)
80*.375=30
Answer:
Option B.
{–9 + i√225 / 24, –9 – i√225 / 24}
Step-by-step explanation:
12a² + 9a + 7 = 0
Using formula method, the solutions to the equation can be obtained as follow:
Coefficient of a² (a) = 12
Coefficient of a (b) = 9
Constant (c) = 7
a = –b ±√(b² – 4ac) / 2a
a = –9 ±√(9² – 4 × 12 × 7) / 2 × 12
a = –9 ±√(81 – 336) / 24
a = –9 ±√(– 225) / 24
Recall
–225 = –1 × 225
Thus,
–9 ±√(– 225) / 24 = –9 ±√(–1 × 225)/24
Recall
√(–1 × 225) = √–1 × √225 = i√225
Thus,
–9 ±√(–1 × 225)/24 = –9 ± i√225/24
Therefore,
a = –9 ± i√225/24
a = –9 + i√225 / 24 or –9 – i√225 / 24
Therefore, the solutions to the equation are:
{–9 + i√225 / 24, –9 – i√225 / 24}
Given:
The graph of a figure and its image after dilation.
To find:
The scale factor.
Solution:
From the given graph it is clear that
ND = 3 units
N'D' = 6 units.
We know that,
![\text{Scale factor}=\dfrac{\text{Side of image}}{\text{Corresponding side of original figure}}](https://tex.z-dn.net/?f=%5Ctext%7BScale%20factor%7D%3D%5Cdfrac%7B%5Ctext%7BSide%20of%20image%7D%7D%7B%5Ctext%7BCorresponding%20side%20of%20original%20figure%7D%7D)
![\text{Scale factor}=\dfrac{N'D'}{ND}](https://tex.z-dn.net/?f=%5Ctext%7BScale%20factor%7D%3D%5Cdfrac%7BN%27D%27%7D%7BND%7D)
![\text{Scale factor}=\dfrac{6}{3}](https://tex.z-dn.net/?f=%5Ctext%7BScale%20factor%7D%3D%5Cdfrac%7B6%7D%7B3%7D)
![\text{Scale factor}=2](https://tex.z-dn.net/?f=%5Ctext%7BScale%20factor%7D%3D2)
Therefore, the scale factor is 2 and the correct option is A.
Answer:
a. 20
b. $15
Step-by-step explanation:
We can say that
represent the 30-day period, then we can write the next equation:
![55-2x=45-1.5x](https://tex.z-dn.net/?f=55-2x%3D45-1.5x)
Finding the
, we find the number of 30-day periods until the value of the cards will be equal, then:
![55-2x=45-1.5x\\55-45=-1.5x+2x\\10=0.5x\\\dfrac{10}{0.5}=x\\\\20=x](https://tex.z-dn.net/?f=55-2x%3D45-1.5x%5C%5C55-45%3D-1.5x%2B2x%5C%5C10%3D0.5x%5C%5C%5Cdfrac%7B10%7D%7B0.5%7D%3Dx%5C%5C%5C%5C20%3Dx)
Then is needed a 20 30-day periods to have the cards with equal value.
Now to know the walue of each card we have:
![55-2x\\55-2(20)\\55-40=15](https://tex.z-dn.net/?f=55-2x%5C%5C55-2%2820%29%5C%5C55-40%3D15)
Then each card will have a value of $15
The square root of thirteen is 3.6, and the square root of 14 is 3.7. I rounded to the nearest tenth. If your teacher wants you to round to something else, please let me know.