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3 years ago

What is the slope intercept form of y-3=1/2(x-1)

Mathematics

1 answer:

gtnhenbr [62]3 years ago

7 0

<h3>Answer: y = (1/2)x + 5/2</h3>

Work Shown:

y - 3 = (1/2)(x-1)

y - 3 = (1/2)x - 1/2 .... distribute

y = (1/2)x - 1/2 + 3 .... add 3 to both sides

y = (1/2)x - 1/2 + 6/2 ... rewrite 3 as 6/2

y = (1/2)x + 5/2

This is in y = mx+b form

m = 1/2 = 0.5 is the slope

b = 5/2 = 2.5 is the y intercept

Side note: the original equation is in point slope form. The point we can read from this equation is (1, 3)

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A group of 54 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic

aliya0001 [1]

Answer:

P-value = 0.4846

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 4.73

Sample mean, $\bar{x}$ = 4.35

Sample size, n = 51

Alpha, α = 0.05

Sample standard deviation, s = 3.88

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 4.73\\H_A: \mu \neq 4.73$

We use Two-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{4.35 - 4.73}{\frac{3.88}{\sqrt{51}} } = -0.699$

Now, $z_{critical} \text{ at 0.05 level of significance } = \pm 1.96$

We can calculate the p-value with the help of standard normal table.

P-value = 0.4846

Since the p-value is higher than the significance level, we fail to reject the null hypothesis and accept it.

We conclude that this college has same drinking habit as the college students in general.

7 0

3 years ago

What is the slope of the line between (3,-4) and (-2, 1)?<br> O 1<br> 02.<br> O-2<br> O-1

natka813 [3]

Answer:

-1……..........................

4 0

3 years ago

Read 2 more answers

The steps below show the incomplete solution to find the value of m for the equation 4m − 2m + 4 = −1 + 13:

sasho [114]

Answer

Step-by-step explanation

Because subtract 4 from 4 and twelve

6 0

2 years ago

Read 2 more answers

The vertices of quadrilateral MNPQ are M(−3,−2),N(−1,4),P(2,4), and Q(4,−2). Translate quadrilateral MNPQ using the vector ⟨3,−4

timofeeve [1]

Answer:

M'(0,-6),N'(2,0),P'(5,0) and Q'(7,-6)

Step-by-step explanation:

We are given that the vertices of quadrilateral MNPQ are M(-3,-2),N(-1,4),P(2,4) and Q(4,-2).

We have to translate the quadrilateral MNPQ using vector <3,-4>

The translate the coordinates of vertices (x,y) using the vector <a,b> is given by the rule

$(x,y)\rightarrow (x+a,y+b)$

Using the rule

The new coordinates of M

$(-3,-2)\rightarrow (-3+3,-4-2)$

$(-3,-2)\rightarrow (0,-6)$

The new coordinates of N

$(-1,4)\rightarrow (2,0)$

The new coordinates of P

$(2,4)\rightarrow (5,0)$

The new coordinates of Q

$(4,-2)\rightarrow (7,-6)$

Hence, after translation the new vertices of quadrilateral are

M'(0,-6),N'(2,0),P'(5,0) and Q'(7,-6)

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3 years ago

In a marathon, Peter ran 15 more kilometers than half of the number Juan ran. Peter ran at most 36 km

emmainna [20.7K]

Answer: 42 km

Step-by-step explanation:

P=Peter. J=Juan

P=15+J/2

36=15+J/2

21=J/2

J=42 km

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2 years ago