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3 years ago

Which of the following is the correct graph of the linear equation below? y+2=1/5(x-1)?

Mathematics

2 answers:

Ierofanga [76]3 years ago

7 0

Y + 2 = 1/5(x - 1)
y + 2 = 1/5x - 1/5
y = 1/5x - 1/5 - 2
y = 1/5x - 1/5 - 10/5
y = 1/5x - 11/5

slope = 1/5
y int = (0,-11/5)....for graphing purposes, -11/5 = - 2 1/5
x int = (11,0)

Vesnalui [34]3 years ago

7 0

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$y+2=1/5(x-1)$ -----> linear equation in point slope form

we know that

the line passes through the point $(1,-2)$

the slope is equal to $m=1/5$

To plot the line find the intercepts

<u>Find the y-intercept</u> ----> (value of y when the value of x is equal to zero)

$y+2=1/5(0-1)$

$y=-11/5=-2.2$

The y-intercept is the point $(0,-2.2)$

<u>Find the x-intercept</u> ----> (value of x when the value of y is equal to zero)

$0+2=1/5(x-1)$

$x=11$

The x-intercept is the point $(11,0)$

Plot the intercepts to graph the linear equation

see the attached figure

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3x²-9x+1+0 Find the discriminant

Sindrei [870]

Answer:

$\boxed{D = 69}$

Step-by-step explanation:

The given quadratic equation is:

$3x^2-9x+1 = 0$

Comparing it with the standard form of Quadratic Equation $ax^2+bx+c = 0$ , we get:

a = 3, b = -9 and c = 1

Discriminant = b² - 4ac

D = (-9)²-4(3)(1)

D = 81 - 12

D = 69

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3 years ago

Side legnths for x^2 -4x -12

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I hope this helps you

x^2-4x-12

x -6

x +4

(x-6)(x+4)

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3 years ago

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the

defon

Answer:

Price of widget to break even= $37.9

Step-by-step explanation:

We are told that the equation representing the amount of profit, y, made by the company, in relation to the selling price of each widget, x is;

y = -8x² + 348x - 1705

Now, the company will break even when it has made no profit. That is when, y = 0

Thus;

0 = -8x² + 348x - 1705

Rearranging,

8x² - 348x + 1705 = 0

Using quadratic formula ;

x = [-b ± √(b² - 4ac)]/2a

x = [-8 ± √(-348² - 4•1•1705)]/(2 x 8)

x = $5.63 or $37.87

We'll use $37.87 because it is the highest price for which no profit is made, and higher price means that we could sell least number of products to earn a certain amount of money.

We are told to approximate to nearest cent. Thus,

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3 years ago

A motorboat takes 5 hours to travel 100mi going upstream. The return trip takes 2 hours going downstream. What is the rate of th

Temka [501]

The boat went 5hours upstream, let's say it has a "still water" speed rate of "b", it went 100miles... however, going upstream is going against the current, let's say the current has a speed rate of "c"

so, when the boat was going up, it wasn't really going "b" fast, it was going " b - c " fast, because the current was eroding speed from it

now, when coming down, the return trip, well the length is the same, so the distance is also 100miles, it only took 2hrs though, because, the boat wasn't coming down "b" fast, it was coming down " b + c " fast, because the current was adding speed to it, so it came down quicker

now, recall your d = rt, distance = rate * time

$\bf \begin{array}{lccclll}
&distance&rate&time\\
&-----&-----&-----\\
upstream&100&b-c&5\\
downstream&100&b+c&2
\end{array}
\\\\\\
\begin{cases}
100=(b-c)5\\
\qquad \frac{100}{5}=b-c\\
\qquad 20=b-c\\
\qquad 20+c=\boxed{b}\\
100=(b+c)2\\
\qquad 50=b+c\\
\qquad 50=\boxed{20+c}+c
\end{cases}$

solve for "c", to see what's the current's speed

what's "b"? well 20+c = b

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3 years ago

Given that an intercepted arc has length 6pi inches and a central angle is pi/3, find the radius

MA_775_DIABLO [31]

$\bf \textit{arc's length}\\\\
s=r\theta \quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad radians\\
------\\
s=6\pi \\
\theta =\frac{\pi }{3}
\end{cases}\implies 6\pi =r\left( \frac{\pi }{3} \right)\implies \cfrac{6\pi }{\frac{\pi }{3}}=r
\\\\\\
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3 years ago