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sergeinik [125]
3 years ago
14

Write the normal form of the equation of the line passing through (1, 2) and with a normal vector n = 3 - 41. Write its general

form. + Drag and drop your images or click to browse...
Mathematics
1 answer:
Crank3 years ago
7 0

Answer:

general form of  is 3x - 4y = -5

Step-by-step explanation:

Equation pass through given point P (1,2)

And normal vector is given as  \begin{bmatrix}1\\ 2\end{bmatrix}

nX = np

\begin{bmatrix}3\\ -4\end{bmatrix} \begin{bmatrix}x\\ y\end{bmatrix}  =   \begin{bmatrix}3\\ -4\end{bmatrix}  \begin{bmatrix}1\\ 2\end{bmatrix}

\begin{bmatrix}3\\ -4\end{bmatrix}  \begin{bmatrix}x\\ y\end{bmatrix} = -5

therefore general form is written as ax + by = k

3x - 4y = -5

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The cost to rent a surfboard at the beach is $10.25 an hour plus an insurance fee of $25. Keith spent $55.75 when renting a surf
goblinko [34]

Answer: Keith spent 3 hours renting the surfboard.

Step-by-step explanation:

h=hour

10.25h+25=55.75

55.75-25= 30.75

30.75/10.25= 3

and if you want to check you can do

10.25(3)+25=

which would equal to 55.75

4 0
2 years ago
Solve for x. x - 2(2 - 3/2 x) = 2(4 - x) + 1
STALIN [3.7K]

Answer:

x = 13/6

Step-by-step explanation:

We are the following expression;

       x - 2(2 - (3/2)*x) = 2(4 - x) + 1

       x - (4 - 3*x) = 8 - 2*x + 1

       x - 4 + 3*x = 8 - 2*x + 1

         4*x + 2*x = 9 + 4

             6*x = 13

              x = 13/6

8 0
3 years ago
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 436.0 gram setting. It
Vilka [71]

Answer:

We conclude that the machine is under filling the bags.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 436.0 gram

Sample mean, \bar{x} = 429.0 grams

Sample size, n = 40

Alpha, α = 0.05

Population standard deviation, σ = 23.0 grams

First, we design the null and the alternate hypothesis

H_{0}: \mu = 436.0\text{ grams}\\H_A: \mu < 436.0\text{ grams}

We use one-tailed(left) 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{429 - 436}{\frac{23}{\sqrt{40}} } = -1.92

Now, z_{critical} \text{ at 0.05 level of significance } = -1.64

Since,  

z_{stat} < z_{critical}

We reject the null hypothesis and accept the alternate hypothesis. Thus, we conclude that the machine is under filling the bags.

8 0
3 years ago
How many pairs are parelof
PtichkaEL [24]

Answer: what what’s the question

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
If you are using Cosine and need to solve for an unknown hypotenuse, you should...
kifflom [539]

Using cosine, we can find the hypotenuse by using the formula below;

hypotenuse = adjacent / cos ∅

<h3 /><h3 /><h3>Trigonometric ratios:</h3>
  • Trigonometric ratios are ratios of sides of a right angled triangle.
  • The simplest ratios are cosine, sine and tangent.

Using cosine, the hypotenuse side can be solved as follows:

cosine ∅ = adjacent / hypotenuse

cross multiply

hypotenuse cos ∅ = adjacent

divide both sides by cos ∅

hypotenuse cos ∅ / cos ∅ = adjacent / cos ∅

Therefore,

hypotenuse = adjacent / cos ∅

learn more on cosines here: brainly.com/question/10657732?referrer=searchResults

6 0
2 years ago
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