What is the answer to 9(5x)

MArishka [77]

$\bf \begin{array}{ccll} term&value\\ \cline{1-2} s_4&18\\ s_5&18r\\ s_6&18rr\\ &18r^2 \end{array}\qquad \qquad \stackrel{s_6}{8}=18r^2\implies \cfrac{8}{18}=r^2\implies \cfrac{4}{9}=r^2 \\\\\\ \sqrt{\cfrac{4}{9}}=r\implies \cfrac{\sqrt{4}}{\sqrt{9}}=r\implies \boxed{\cfrac{2}{3}=r} \\\\[-0.35em] ~\dotfill$

$\bf n^{th}\textit{ term of a geometric sequence} \\\\ s_n=s_1\cdot r^{n-1}\qquad \begin{cases} s_n=n^{th}\ term\\ n=\textit{term position}\\ s_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=6\\ s_6=8\\ r=\frac{2}{3} \end{cases}\implies 8=s_1\left( \frac{2}{3} \right)^{6-1} \\\\\\ 8=s_1\left( \frac{2}{3} \right)^5\implies 8=s_1\cdot \cfrac{32}{243}\implies 8\cdot \cfrac{243}{32}=s_1\implies \boxed{\cfrac{243}{4}=s_1}$

5 0

3 years ago

Jaden says that two triangles are congruent if their interior angles are congruent. Is Jaden correct, and why?

Bogdan [553]

Answer:

No

Step-by-step explanation:

No. Congruent triangles should also have corresponding congruent side lengths.

5 0

2 years ago

5 types of kitchen accidents and how to prevent them

Shalnov [3]

Answer:

Cutting any kind of fruit or vegetable. Prevent this by wearing gloves in the kitchen.
Forgotten kitchen spills are a major tripping hazard. Prevent this by not spilling anything, or if when you do, clean it up right away.
Washing dishes can result in knicks of plates and bowls, even even washing a knife improperly can harm you. Prevent this by being extra cautious when washing anything.
Unstable cutting boards are asking for improper cuts. Prevent this by only cutting on a surface that is level, sturdy, and reliable.
Skin contact with Chile Powder, or any kind of harmful cleaning substance.

Thanks so much for letting me help!!

8 0

4 years ago

Read 2 more answers

Classify each sequence as arithmetic, geometric or neither

Karolina [17]

Answer:

Geometric sequence = ⁵/9, ⁵/3, 5, 15, 45. . .

Arithmetic sequence = 16, 11, 6, 1, -4 . . .

Step-by-step explanation:

A geometric sequence is a sequence of numbers, in which every number in the sequence after the first term is multiplied by a common ratio, which gives us the next term. The common ratio is the ratio of a term to the term before it.

On the other hand, an arithmetic sequence is a sequence of number have a common difference between each consecutive terms. This common difference is gotten by subtracting a term from the term before it.

Now let's examine each sequence given:

==>16, 11, 6, 1, -4 . . .

11 - 16 = -5

6 - 11 = -5

1 - 6 = -5

-4 - 1 = -5

This is an arithmetic sequence. The commons difference "-5" is the same

==>⁵/9, ⁵/3, 5, 15, 45. . .

⁵/3 ÷ ⁵/9 = ⁵/3 × ⁹/5 = ⁹/3 = 3

5 ÷ ⁵/3 = ⁵ × ⅗ = 3

15 ÷ 5 = 3

45 ÷ 15 = 3

The common ratio "3" is the same. This is a geometric sequence.

3 0

3 years ago

6. The equation of line A is 3x + 6y - 1 = 0. Give the equation of a line that passes through the

Pavel [41]

Step 1: Convert to slope-intercept form to find the slope of the line.

This isn't necessary if you know all the shortcuts, it just makes your life a bit easier.

$3x+6y-1=0\\6y=-3x+1\\y=-\frac{3}{6}x+\frac{1}{6}\\-\frac{1}{2}x+\frac{1}{6}$

Now we want to find the equations for our new lines. It's easiest to do this in slope-intercept form, so let's start finding the slope and y-intercept.

So for the perpendicular line, the slope is going to flip and change signs, this is aka its opposite reciprocal.
And for the parallel line, it'll stay the same.

$-\frac{1}{2}$ ⇒ $\frac{2}{1}=2$
$-\frac{1}{2}$ ⇒ $-\frac{1}{2}$

As for the y-intercept, just apply that slope until you get a point where x=0.

(5, 1) with a rise of 2 and a run of 1...let's work backwards to (0, b)
(5, 1), (4, -1), (3, -3), (2, -5), (1, -7), (0, -9).

(5, 1) with a rise of -1 and a run of 2...let's work backwards to (0, b)
(5, 1), (3, 0), (1, -1)...gonna have to take half a step here...(0, -1.5).

Now let's construct our equations in slope-intercept form.

$y = 2x-9\\y=-\frac{1}{2}x-\frac{3}{2}$

And now it's time to convert to general form!

Make sure we have common denominators...check.

Multiply by the denominator...

$y=2x-9\\2y=1x-3$

...check.

Aaaand bring everything over!

$\boxed{-2x+y-9=0}\\\boxed{-x+2y-3=0}$

7 0

3 years ago