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2 years ago

Write an equation in slope-intercept form for the graph shown. (1,0) (0,-2)

Mathematics

1 answer:

AlladinOne [14]2 years ago

4 0

Answer:

y= 2x -2

Step-by-step explanation:

Slope-intercept form

y= mx +c, where m is the slope and c is they y-intercept

$\textcolor{violet}{\text{\textcircled{1} Find the slope}}$

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

$slope = \frac{0 - ( - 2)}{1 - 0}$

$slope = \frac{0 + 2}{1}$

slope= 2

$\textcolor{violet}{\text{\textcircled{2} \text{Substitute value of slope into m}}}$

y= 2x +c

$\textcolor{violet}{\text{\textcircled{3} Find c}}$

Given that the y-intercept occurs at (0, -2), c= -2.

$\textcolor{violet}{\text{\textcircled{4} Substitute the value of c into the equation}}$

y= 2x -2

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Write the denominator of the fractiona 7/20 as the product of prime factors

gtnhenbr [62]

Answer:

Step-by-step explanation:

prime factors of 20 = 2 * 2 * 5

$\frac{7}{20}=\frac{7}{2*2*5}$

5 0

3 years ago

Ms. Li spent $840 on a vacation. She spent 2/3 of the amount on a plane ticket and 1/2 of the remaining amount on food. How much

olya-2409 [2.1K]

$\bf 840\cdot \cfrac{2}{3}\impliedby \textit{on the plane ticket}
\\\\\\
\left( 840\cdot \cfrac{2}{3} \right)\cdot \cfrac{1}{2}\impliedby \textit{ on food}$

4 0

3 years ago

The dingram shows a spinner innde up of a picce of card in the shape of a regular pentagon, with a toothpick pushed through its

Anastaziya [24]

Answer:

a) $P(X \leq 3) = 0.99328$

b) 0.6957

Step-by-step explanation:

Let X represent the number of 4's when n = 5 independent spins

each has a probability of 0.2 (i.e p = 0.2)

This notation is represented as:

X $\approx$ Binomial (n = 5, p = 0.2)

Probability of $x$ number of 4's is:

$P(X=x)= (\left \ n \atop x \right) p^x (1-p)^{(n-x)}$

here; $(\left \ n \atop x \right)$ is the combinatorial expression

$(\left \ n \atop x \right)$ = $\frac{n!}{x!(n-x)!}$

$P(X \leq3), n =5 , p = 0.2$

$P(X \leq3) = 1-P(X > 3)$

So; let's first find:

$P(X > 3)$

$= P(3$

$P(X = 4) =( \left \ {{5} \atop {4}} \right. ) (0.2)^4 (1-0.2)^1 \\ \\ P(X = 4) = 5(0.2)^4(0.8)^1 \\ \\ P(X = 4) = 0.0064$

$P(X = 5) =( \left \ {{5} \atop {5}} \right. ) (0.2)^5 (1-0.2)^0 \\ \\ P(X = 5) = 5(0.2)^5(0.8)^0 \\ \\ P(X = 5) = 0.00032$

$P (X=4)+P(X = 5 ) \\ \\ = 0.0064 + 0.00032 = 0.006720 \\ \\ \approx 0.007$

$P(X > 3 ) = 0.00672 \\ \\ P(X \leq 3) = 1- P(X > = 3 ) \\ \\ =1 - 0.00672 \\ \\ = 0.99328$

$P(X \leq 3) = 0.99328$

Given that:

The ratio of boys to girls at birth in Singapore is quite high at 1.09:1

What proportion of Singapore families with exactly 6 children will have at least 3 boys?

Probability of having a boy = $\frac{1.09}{1+1.09}$ = 0.5215

Binomial Problem with n = 6

P(3<= x <=6) = 1 - P(0<= x <=2)

= 1 - binomial (6,0.5215,2)

= 0.6957

5 0

3 years ago

Please help me I’m really stuck

dalvyx [7]

Answer:

/ 3=/ 5 { alternate anglea}

/ 5+/6 =180° {straight angle}

/ 6=180-26

/ 6=154°

hope it helps

<h3>stay safe healthy and happy.</h3>

6 0

3 years ago

Find the absolute extreme of the function on the closed interval. y=9e^xsinx , [0,pi]

Molodets [167]

For convenience sake, I will let $y=f(x)=9e^{x}\sin x$

First, we evaluate the function at the endpoints of the interval.

$f(0)=9e^{0}\sin(0)=0\\\\f(\pi)=9e^{\pi}\sin(\pi)=0$

Then, we need to find the critical points.

We can start by taking the derivative using the power rule.

$f'(x)=9e^{x} \frac{d}{dx} \sin x+9\sin x \frac{d}{dx} e^{x}=9e^{x}(\cos x+\sin x)$

Setting this equal to 0,

$9e^x (\cos x+\sin x)=0$

Since $9e^x > 0$ , we can divide both sides by $9e^x$ .

$\cos x+\sin x=0\\\\\sin x=-\cos x\\\\\tan x=-1\\\\x=\frac{3\pi}{4}$

$f\left(\frac{3\pi}{4} \right)=9e^{3\pi/4}\sin \left(\frac{3\pi}{4} \right)=\frac{9\sqrt{2}e^{3\pi/4}}{2}$

So, the absolute minimum is $\boxed{\left(\frac{3\pi}{4}, \frac{9\sqrt{2}e^{3\pi/4}}{\sqrt{2}} \right)}$ and the absolute minima are $\boxed{(0,0), (\pi, 0)}$

3 0

2 years ago