Which number completes the table...? 24 54 84 114 14 19

A triangle has two angles that measure 18.6 degrees and 113.4 degrees respectively. what is the measure of the third angle?

spin [16.1K]

Answer:

$x = 48$

Step-by-step explanation:

$18.6 + 113.4 + x = 180$

$132 + x = 180$

$x = 180 - 132$

$x = 48$

5 0

3 years ago

!!!!!!Plss Help Me!!!!!!!

dimulka [17.4K]

Write the problem as an equation:

5n <65

Solve for n by dividing both sides by 5:

n <13

Because the inequality does not contain an equal sign, n (13) is not included in the answer so there would be an open circle on the number 13

The correct answer would be A.

3 0

3 years ago

Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

$3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)$

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

$4^n+17$ is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

$4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17$

$3\cdot 4^k$ is divisible by 3 and

$4^k+17$ is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

4 0

3 years ago

Plz Help due in 10 min If triangle ABC has the following angle measurements, what is the value of x?

Nookie1986 [14]

Answer:

Step-by-step explanation:

4x-17+3x+8+x+13=180

8x+4 =180

8x=176

X=22

5 0

3 years ago

Read 2 more answers

Suppose that a function f(x) is defined for all real values of x except at xequals=c. can anything be said about the existence

Margaret [11]

we are given that

f(x) is defined for all values of x except at x=c

Limit may or may not exist

case-1:

If there is hole at x=c , then limit exist

case-2:

If there is vertical asymptote at x=c , then limit does not exist

Examples:

case-1:

$\lim_{x \to c} \frac{x^2-cx}{(x-c)}$

We can simplify it

$\lim_{x \to c} \frac{x(x-c)}{(x-c)}$

$=\lim_{x \to c} x$

$=c$

so, we can see that limit exist and it's value defined

case-2:

$\lim_{x \to c} \frac{1}{(x-c)}$

Left limit is

$\lim_{x \to c-} \frac{1}{(x-c)}$

$=-\infty$

Right Limit is

$\lim_{x \to c+} \frac{1}{(x-c)}$

$=+\infty$

so, we can see that left limit is not equal to right limit

so, limit does not exist

4 0

3 years ago