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2 years ago

Write an equation of the line that passes through the point (2, 3) and is perpendicular to the line y = 1/2x - 1

1 answer:

6 0

Perpendicular means opposite and reciprocal (in reference to the slope).
The opposite of 1/2 is -1/2. The reciprocal of -1/2 is -2.

Now we know the slope we can plug the point they gave us into the X and Y positions to solve for b (in the point (2, 3) there is a X - Value (2) and a Y-value (3)

y= -2x+b
3= -2(2)+b
3= -4+b
1=b

Now we plug b and the slope in the generic y=mx+b equation:
y= -2x+1

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What is the expanded form for 102,200

solmaris [256]

Answer: 100,000 + 2000 + 200

Hope this helps!

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4 0

2 years ago

Read 2 more answers

Fitness Your goal is to take at least 10,000 steps per day. According to your pedometer, you have walked 527 4 steps. Write and

Archy [21]

The inequality is x + 5274 ≥ 10,000.

The total number of steps I have to take to reach my goal is 4726.

<h3>How many more steps do I have to take?</h3>

Here are inequality signs and what they mean:

> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to

Number of steps I have to take + number of steps I have taken ≥Total steps

X + 5274 + x ≥ 10,000

x ≥ 10,000 - 5274

x ≥ 4726

To learn more about inequality, please check: brainly.com/question/5031619

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5 0

1 year ago

The credit remaining on a phone card (in dollors) is a linear function of the total calling trime made with the card ( in minute

KATRIN_1 [288]

After 85 minutes of calls, there are $27.25 left on the card.

<h3>What is the remaining credit after 85 minutes of calls?</h3>

A linear equation in slope-intercept form is:

y = a*x + b

Where a is the slope.

If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope is:

$a = \frac{y_2 - y_1}{x_2 - x_1}$

In this case, we know that the line passes through the points (22, 36.7) and (52, 32,20)

(points of the form (time, dollars)).

So the slope is:

$a = \frac{32.2 - 36.7}{52 -22} = -0.15$

The linear equation is then:

y = -0.15*x + b

To find the value of b, we use the point (22. 36.7)

36.7 = -0.15*22 + b

36.7 + 0.15*22 = b = 40

Then the linear equation is:

y = -0.15*x +40

The amount remaining in the credit card after 85 minutes is given by evaluating the above equation in x = 85.

y = -0.15*85 + 40 = 27.25

This means that after 85 minutes of calls, there are $27.25 left on the card.

If you want to learn more about linear equations:

brainly.com/question/1884491

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7 0

1 year ago

Es 18 de junio de 1815, las tropas napoleónicas se encuentran justo adelante, tu eres el ingeniero en balística y el general Wel

Airida [17]

Answer:

89.1° or -1.4°

Step-by-step explanation:

1. Location:

You are on the Mont-Saint-Jean escarpment, near the Belgian town of Waterloo.

The French troops are about 50 m below you and 1.2 km distant.

2. Finding the firing angle

Data:

R = 1200 m

u = 600 m/s

h = -50 m (the height of the target)

a = 9.8 m/s²

We have two conditions.

Horizontal distance

(1) 1200 = 600t cosθ

Vertical distance

(2) -50 = 600t sinθ - 4.9t²

Divide each side of (1) by 600cosθ.

$(3) \, t =\dfrac{2}{\cos \theta}$

Substitute (3) into (2)

$-50 = 600t \sin \theta - 4.9t^{2} = 600 \left( \dfrac{2}{\cos \theta} \right ) \sin \theta - 4.9 \left( \dfrac{2}{\cos \theta} \right )^{2}\\\\(4) \, -50 = 1200 \tan \theta - \dfrac{19.6}{\cos^{2} \theta}$

Recall that

(5) sec²θ = 1/cos²θ = tan²θ + 1

Substitute (5) into (4)

$-50 = 1200 \tan \theta - 19.6 \left(\tan^{2} \theta}+ 1\right )$

Set up a quadratic equation

$\begin{array}{rcl}-50 & = & 1200 \tan \theta - 19.6\tan^{2} \theta -19.6 \\0 & = & 1200 \tan \theta - 19.6\tan^{2} \theta + 30.4\\0 & =&19.6\tan^{2} \theta - 1200 \tan \theta - 30.4\\0 & =&\tan^{2} \theta - 61.224 \tan \theta - 1.551\\\end{array}$

Solve for θ

Use the quadratic formula.

tanθ = 61.249 or -0.025

θ = arctan(61.249) = 89.1° or

θ = arctan(-0.025) = -1.4°

3 0

2 years ago

In a history class, students take a weekly multiple choice quiz consisting of 6 questions, each with 4 possible answers. if a st

Mademuasel [1]

There are 24 possible answers, 6 are correct answers and 18 are incorrect answers. By use of the hypergeometric distribution the probabilities of each possible number of randomly selected correct answers can be found, as follows:
P(0) = 0.1379, P(1) = 0.3819, P(2) = 0.341, P(3) = 0.1213, P(4) = 0.017, P(5) = 0.0008, P(6) = 0.000007.
The expected or mean number of correct answers is found from:
$E(X)=0\times0.1379+1\times0.3819+2\times0.341+3\times0.1213+4\times0.017$ $+5\times0.0008+6\times0.000007=1.4998$
The answer is: 1.4998

8 0

2 years ago