Find the missing terms in the<br>sequence 27, ? , 23, ? , 19,...<br>good luck

Find the equation of the line that passes through the points (-5,7) and (2,3)

Olegator [25]

Answer:

$y=-\frac{4}{7}x+4\frac{1}{7}$

Step-by-step explanation:

So, in order to solve this problem, I started off by drawing it out. On my graph that I have attached below, I first started out by locating the points (-5,7) and (2,3). Now, this is an optional step, but I highly encourage practicing your graphing skills by solving this problem on graph paper as well. Next, I connected the two points that I just graphed. This is the line that passes through (-5,7) and (2,3).

Now, here is where the actual solving starts. If you haven't already been taught this yet, I will introduce it to you now. I am going to find the equation of this line by filling in what I know in the equation y=mx+b, where m= the slope of the line, and b= y intercept.

Slope of the line: m= $\frac{y_{1} - y_{2} }{x_{1} - x_{2} } = \frac{7-3}{-5-2} = \frac{4}{-7}= -\frac{4}{7}$

If you haven't been taught how to find the slope of a line I recommend you find out.

Substitute the slope into the equation.

$y=-\frac{4}{7} x+b\\$

Now, we will solve for the 'b,' or y intercept.

We already have x and y values to use: (-5,7) or (2,3). I'll use x=2 and y=3 to solve for the y intercept.

$y=-\frac{4}{7} x+b\\\\3=-\frac{4}{7} *2+b\\\\3=-\frac{8}{7} +b\\b=3+\frac{8}{7} \\b=\frac{21}{7}+\frac{8}{7}=\frac{29}{7} =4\frac{1}{7} \\b=4\frac{1}{7}$

Last step: substitute the slope and y intercept into y=mx+b.

$y=mx+b\\y=-\frac{4}{7}x+4\frac{1}{7}$

That is the answer to this problem.

I hope this helps.

3 0

3 years ago

Julien's parents want $64,000 at the end of 3 years. They put their money in an account that yields 10% per year compounded mont

Leto [7]

Answer: $\$47,471$

Step-by-step explanation:

Given

Julien's parents want $64,000 at the end of 3 years

The rate of interest is 10% annually

Suppose they invested P amount initially

So, compound interest, compounded monthly is

$\Rightarrow A=P\left( 1+\frac{r}{n}\right)^{nt}\quad [\text{n=Numner of compounding periods}]\\\\\text{Insert the values}\\\Rightarrow 64,000=P\left( 1+\frac{0.10}{12}\right)^{12\times 3}\\\\\Rightarrow 64,000=P\left( 1+\frac{10}{12}\right)^{36}\\\\\Rightarrow P=\dfrac{64000}{1.3481}\\\\\Rightarrow P=\$\ 47,471.37\approx \$ 47,471$

7 0

3 years ago

Solve the following inequality for w 8w+8>-10w-5

Vlad [161]

Answer:

Step-by-step explanation:

8w+8 > -10w-5

18w + 8 > -5

18w > -13

w > -13/18

8 0

3 years ago

Because of a virus introduced into a bacterial culture, the population of the bacteria decreasedfrom 3000 to 1000 in 50 minutes.

Mamont248 [21]

Answer:

208

Step-by-step explanation:

Given that;

y= a(1 - b)^t

Where;

wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.

To obtain the constant b,

y= ae^-bt

Substituting values;

1000 = 3000 e^-b(50)

1000/3000 = e^b(50)

0.33 = e^b-(50)

ln (0.33) = ln(e^b(-50))

-1.1 = -50b

b= 1.1/50

b= 0.022

After two hours or 120 minutes;

y= 3000(1 - 0.022)^120

y= 207.8661772

y= 208

8 0

3 years ago

What are the names of the two angles? *

Vika [28.1K]

Answer:

C or the 3rd one

Step-by-step explanation:

7 0

3 years ago

Find the missing terms in thesequence 27, ? , 23, ? , 19,...good luck​

Find the missing terms in thesequence 27, ? , 23, ? , 19,...good luck