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3 years ago

Which of the following is the x-intercept for 3y - 4x = 8?

Mathematics

1 answer:

expeople1 [14]3 years ago

3 0

The answer is E because 3 x 0 - 4 x -2 = 8

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Make b the subject of the formula P=2a+b

Gelneren [198K]

In order to make b the subject of this equation, we must isolate it on the left side. We can do this by following these steps:

$P = 2a+b$

Subtract b from both sides

$P - b = 2a+b-b$

$P-b=2a$

Subtract P from both sides

$P-b-P=2a-P$

$-b=2a-P$

Now, we have isolated b, but it is negative. We can fix this by multiplying both sides of the equation by -1.

$-(-b)=-(2a-P)$

$b=-2a+P$

Which is your final answer.
$b = -2a+P$ .
Hope that helped! =)

5 0

2 years ago

Read 2 more answers

I will give brainleist

Goshia [24]

Let's write the equation in standard from

$y = mx + b$

Where,

m is slope or rate of change
b is the y-intercept or initial value

<h3>Let's start by finding slope⤵️</h3>

$\boxed{ \sf \: m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1}}}$

x1, y1 = 0,12
x2, y2 = 1,13

$\tt \: m = \frac{13 - 12}{1 - 0}$

$\tt \: m = \frac{1}{1}$

$\tt \: m = 1$

b = 12

<h3>Equation⤵️</h3>

$\sf \: y = 1x + 12$

8 0

2 years ago

Read 2 more answers

What is the lateral and surface area? I will give the brainliest if you answer correctly and no links or you will be reported

jeyben [28]

Answer:

Lateral: 560

Surface Area: $560 + 96\sqrt{3}$

Step-by-step explanation:

Well, we know that the lateral area is just the surface area subtracted by the hexagon base of the figure. Thus, if we (1) find the area of one of the triangular faces and multiply by 6, we get the lateral area. And then, if we (2) add the area of the hexagonal base, we get the surface area.

Let's do (1) first to get the lateral area

They mention that the base of one of the triangular faces is 8 and its height (which is the slant height) is 20. So the area is simply 20 * 8/2 = 80

Then, we multiply by 6 because there are 6 of these triangles and get 560

So the lateral area is 560

Let's do (2) next to find the surface area

If we add the area of the hexagonal base to 560, we obtain the surface area

The hexagon is a regular hexagon with a length of 8. Now, the area of a hexagon $3\sqrt{3} * s^2 /2$ where $s$ is the side. We can obtain this formula if we separate the hexagon into 6 equilateral triangles.

Plugging in 8 for $s$ we get $96\sqrt{3}$

So the surface area is $560 + 96\sqrt{3}$

7 0

2 years ago

Examine today’s stock listing for SFT Legal, shown below.

grandymaker [24]

Answer:

its D

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Determine the above sequence converges or diverges. If the sequence converges determine its limit

marshall27 [118]

Answer:

This series is convergent. The partial sums of this series converge to $\displaystyle \frac{2}{3}$ .

Step-by-step explanation:

The $n$ th partial sum of a series is the sum of its first $n\!\!$ terms. In symbols, if $a_n$ denote the $n\!$ th term of the original series, the $\! n$ th partial sum of this series would be:

$\begin{aligned} S_n &= \sum\limits_{k = 1}^{n} a_k \\ &= a_1 + a_2 + \cdots + a_{k}\end{aligned}$ .

A series is convergent if the limit of its partial sums, $\displaystyle \lim\limits_{n \to \infty} S_{n}$ , exists (should be a finite number.)

In this question, the $n$ th term of this original series is:

$\displaystyle a_{n} = \frac{{(-1)}^{n+1}}{{2}^{n}}$ .

The first thing to notice is the ${(-1)}^{n+1}$ in the expression for the $n$ th term of this series. Because of this expression, signs of consecutive terms of this series would alternate between positive and negative. This series is considered an alternating series.

One useful property of alternating series is that it would be relatively easy to find out if the series is convergent (in other words, whether $\displaystyle \lim\limits_{n \to \infty} S_{n}$ exists.)

If $\lbrace a_n \rbrace$ is an alternating series (signs of consecutive terms alternate,) it would be convergent (that is: the partial sum limit $\displaystyle \lim\limits_{n \to \infty} S_{n}$ exists) as long as $\lim\limits_{n \to \infty} |a_{n}| = 0$ .

For the alternating series in this question, indeed:

$\begin{aligned}\lim\limits_{n \to \infty} |a_n| &= \lim\limits_{n \to \infty} \left|\frac{{(-1)}^{n+1}}{{2}^{n}}\right| = \lim\limits_{n \to \infty} {\left(\frac{1}{2}\right)}^{n} =0\end{aligned}$ .

Therefore, this series is indeed convergent. However, this conclusion doesn't give the exact value of $\displaystyle \lim\limits_{n \to \infty} S_{n}$ . The exact value of that limit needs to be found in other ways.

Notice that $\lbrace a_n \rbrace$ is a geometric series with the first term is $a_0 = (-1)$ while the common ratio is $r = (- 1/ 2)$ . Apply the formula for the sum of geometric series to find an expression for $S_n$ :

$\begin{aligned}S_n &= \frac{a_0 \cdot \left(1 - r^{n}\right)}{1 - r} \\ &= \frac{\displaystyle (-1) \cdot \left(1 - {(-1 / 2)}^{n}\right)}{1 - (-1/2)} \\ &= \frac{-1 + {(-1 / 2)}^{n}}{3/2} = -\frac{2}{3} + \frac{2}{3} \cdot {\left(-\frac{1}{2}\right)}^{n}\end{aligned}$ .

Evaluate the limit $\displaystyle \lim\limits_{n \to \infty} S_{n}$ :

$\begin{aligned} \lim\limits_{n \to \infty} S_{n} &= \lim\limits_{n \to \infty} \left(-\frac{2}{3} + \frac{2}{3} \cdot {\left(-\frac{1}{2}\right)}^{n}\right) \\ &= -\frac{2}{3} + \frac{2}{3} \cdot \underbrace{\lim\limits_{n \to \infty} \left[{\left(-\frac{1}{2}\right)}^{n} \right] }_{0}= -\frac{2}{3}\end{aligned}}_$ .

Therefore, the partial sum of this series converges to $\displaystyle \left(- \frac{2}{3}\right)$ .

8 0

3 years ago