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The distance between the two centers is 10.

The discriminant needs to be greater than 0.

$\Delta = b^2- 4ac = 225 - 32c > 0$

$c < \frac{225}{32}$

225/32 is equal to 7.03125, so c can be any integer from 1 to 7. The sum is 28.

$-3(1+4i) + i(-2-i) = (-3-12i) + (-2i +1)= \boxed{-2 - 14i}$

Here are the sums of the digits of the numbers you listed in order:

1, 8, 2, 5, 6, 10, 6, 12, 6, 7, 8, 7, 20, 13, 7, 11, 12, 9, 12, 15, 16, 13, 13, 16, 17

Count the ones that are odd.

Diameter= 0.4 cm ==> $V = \frac{4}{3}\pi r^3 = \frac{4}{3} \pi \cdot 2^3 = \frac{32}{3} \pi$, or about 33.51 cm^3.

Each lead ball has a mass of (33.51)(11.3) = 378.663 g.

So, 5000 balls have a mass of 1,893,315 g or 1,893 kg.

The medians intersect at the centroid.

Using telescoping series, the sum becomes 9/2.

This is a geometric sequence with starting term 3/16 and common ratio 4.

The third term is c(3) = c(1) * 4^2 = 3.

You can simply plug this into your calculator.

$\sec(19^{\circ}) = \boxed{1.057}$

The answer is D.

1. 196 = 14^2 = 2^2 * 7^2

2. GCD(7a^3, 54a^2) = a^2

3. GCD(108, 162) = 54

Primero: $15.10

Usar dinero: $1.40

Total: 15.10 - 1.40 = $13.70

I am sorry.

$15x^2 + 31x + 2 = \boxed{(15x+1)(x+2)}$

Depending on which way you wanted to format the question:

m^4  = 5^4 = 625

4m = 5 * 4 = 20

13  * 12 * 47 = 7332 days

(avg cloudless days in a month   x    months in a year    x    years)

There are 180/2pi or roughly 6.28 radians in a complete revolution (360 degrees).

48 radians is equivalent to about 2720 degrees, which is equivalent to 200 degrees. Paul is in the 3rd quadrant. 

"4 more than p" ==> p+4

"the quotient of n and 8"  ==>  n/8

I recommend checking out wolframalpha.com or desmos.com.

nickel (III) sulfate

$\log_a{b} = c \quad \rightarrow \quad a^c = b$

$\frac{\sqrt{12x+15x^2}}{\sqrt{3x}} = \sqrt{\frac{12x+15x^2}{3x}} = \sqrt{\frac{(3x)(4+5x)}{3(x)}} = \boxed{\sqrt{4+5x}}$

Factor: x^2 + 4x - 12 = (x + 6)(x - 2)

The width is x-2 units.

$7a^7 \cdot a^7 = \boxed{7a^{14}}$

C to F: (0°C × 9/5) + 32 = 32°F

F to C: (32°F − 32) × 5/9 = 0°C

Replace the numbers with ones of your choosing.

$99^2 = (100 - 1)^2 = 100^2 - 2(100) +1 = \boxed{9801}$