Which expressions are equivalent to -56z+28?

A triangle is drawn on a coordinate plane. Point A is at (2,6), Point B is at (4,10), and Point C is at (8,5). What is the midpo

juin [17]

Answer:

I(3,8)

Step-by-step explanation:

to answer this question we must use this relation :

let I be our midpoint
I( $\frac{2+4}{2}$ ; $\frac{6+10}{2}$ )
I(3,8)

5 0

4 years ago

Help help help math math

solniwko [45]

Answer:

y=-1/2x-3

Step-by-step explanation:

Let's pick two points for slope.

$\frac{-1+3}{-4-0}$

$\frac{2}{-4}$

For the y-inctercept, the line intersect at the y-axis at (0,-3)

CHECK:

$y=-\frac{1}{2} (-4)-3$

$y=2-3$

$y=-1$

6 0

3 years ago

n is a positive integer with exactly two different divisors greater than 1, how many positive factors does n^2 have? A. 4 B. 5 C

Evgesh-ka [11]

Answer:

C. 5

Step-by-step explanation:

Remember that for any integer $n$ , the integers $1 \text{and} n$ are both divisors (or factors) of $n$ . First, we will prove that n is a square, and then we will compute the factors of the n².

In this case, the integer n has exactly two different divisors greater than 1. It's impossible that $n=1$ , since 1 doesn't have positive factors greater than 1. Then $n>1$ , therefore $n$ itself is one of the required divisors. Denote by $a$ the other divisor greater than 1, and note that to satisfy the condition on the divisors, $a$ .

Because a divides n, there exists some integer $k$ such that $n=ak$ . We must have that $k>1$ , if not, then $k\leq 1$ , which implies that $ak=n\leq a$ , which contradicts the part above.

Now, $k>1$ and, by definition of divisibility, k divides n. Then k must be equal either to n or a, since we can't have three different divisors of this kind. If $k=n$ then $n=an$ and by cancellation, $1=a$ which is a contradiction. Therefore $k=a$ and $n=a^2$ .

We have that $n=(a^2)^2=a^4$ . We can write n as $n=a^3a=a^2a^2=a^4 \cdot 1$ . From the first equation, a divides n and a³ divides n. From the second equation, a² divides, and from the last one, 1 divides n and a⁴=n divides n. Thus n has exactly 5 positive factors.