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3 years ago

HELP ME PLEASE-

Mathematics

1 answer:

polet [3.4K]3 years ago

4 0

Answer:

Step-by-step explanation:

if a is less than zero then b will from 4 down to negative infinity

so b < 4

Does this help at all? ask me some questions if you really want to learn about math ;)

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the vertex of the parabola represented by f(x)=x^2-2x+6 has coordinates (1,5). Find the coordinates of the vertex of the parabol

Sever21 [200]

$Plug \ in \ x+3 \ into \ f(x) \ to \ get \ g(x)
\\\ g(x) = (x+3)^2-2(x+3)+6
\\\ g(x)= x^2+6x+9 -2x-6+6
\\\ g(x) = x^2+4x+9
\\\ -\frac{b}{2a} --\ \textgreater \ vertex
\\\ \frac {-4}{2}
\\\ x \ coordinate = -2, plug \ it \ back \ into \ g(x)
\\\ (-2)^2+4(-2)+9
\\\ 4-8 + 9
\\\ y \ coordinate = 5
\\\ \boxed{(-2,5)}$

5 0

3 years ago

Find the sum of the given arithmetic series. 24 + 48 + 72 + 96 +...+ 480

Alja [10]

Answer:

5040

Step-by-step explanation:

The given series is :

24 + 48 + 72 + 96 +...+ 480

The first term, a= 24

Common difference, d = 24

The last term, $a_n=480$

Let there are n terms in the AP.

So,

$a_n=a+(n-1)d\\\\480=24+(n-1)24\\\\480=24+24n-24\\\\n=20$

There are 20 terms in the series. The sum of 20 terms is :

$S_{20}=\dfrac{n}{2}(2a+(n-1)d))\\\\=\dfrac{20}{2}\times (2(24)+19(24))\\\\=5040$

So, the sum of the given arithmetic series is equal to 5040.

8 0

3 years ago

3.1 Find the equation of the line passing through (4, 5) and parallel to the line 3x – 2y = 4.

valentinak56 [21]

$\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}$

<em>Find the equation of the line passing through (4, 5) and parallel to </em>

<em />

<em> </em> $\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}$

First of all, We need to convert this equation from standard form (ax+by=c) into slope-intercept form (y=mx+b).

$\rightarrow$ First, add 2y on both sides:-

$\Large\textsf{3x+2y=4}$

$\rightarrow$ Now, subtract 3x on both sides:-

$\Large\textsf{2y=-3x+4}$

$\rightarrow$ Divide by 2 on both sides

$\Large\text{$y=-\displaystyle\frac{3}{2}x +2$}$

$\rule{300}{3}$

Now, let's find the equation of the line that's parallel to the given line.

Remember, if lines are parallel to each other, then their slope's the same.

So the slope of the line that's parallel to the line whose equation we just found, is

$\Large\text{$-\displaystyle\frac{3}{2}$}$

Now let's write the equation in point-slope form:-

$\hookrightarrow\sf{y-y_1=m(x-x_1)}$

Replace numbers with letters, as follows:-

$\sf{y-5=-\displaystyle\frac{3}{2} (x-4)}$

The equation above is the equation in point-slope form.

Incase you need it converted to slope intercept form, refer to the steps below ~

Multiply -3/2 times x and -4:-

$\hookrightarrow\sf{y-5=-\displaystyle\frac{3}{2} x-6}$

Now, Add 5 on both sides:-

$\hookrightarrow\sf{y=\displaystyle\frac{3}{2} x+1}$

$\Uparrow\sf{Our\:equation\:in\:slope\;intercept\;form}$

<h3>Good luck with your studies.</h3>

#TogetherWeGoFar

$\rule{300}{1}$

4 0

2 years ago

Of the town's 42 firefighters, 16 volunteered for the special rescue team. Express the portion who did not volunteer.

Doss [256]

42 firefighters in total.

16 volunteered for the special rescue team.

n + 16 = 42

or it could be this way:

42 - 16 = n

8 0

3 years ago

Explain whether a bar graph double bar graph or circle graph is the best way to display the following set of data

erica [24]

I would say a circle graph would be best to use

8 0

3 years ago