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3 years ago

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37. ABC has vertices A(0, 0) , B(0, 4) , and C(3, 0) . Write the equation for the line containing the altitude overline AR in st

andard form

1 answer:

Nutka1998 [239]3 years ago

4 0

Answer:

3x - 4y = 0

Step-by-step explanation:

The triangle Δ ABC has vertices A(0,0), B(0,4) and C(3,0).

Therefore, the equation of the straight line BC in intercept form will be

$\frac{x}{3} + \frac{y}{4} = 1$

⇒ 4x + 3y = 12

⇒ $y = - \frac{4}{3}x + 4$ .......... (1)

This is a equation in slope-intercept form and the slope is $- \frac{4}{3}$ .

Now, the altitude AR is perpendicular to equation (1) and hence its slope will be $\frac{3}{4}$ .

{Since, the product of slope of two mutually perpendicular straight line is always - 1}

Therefore, the equation of the altitude AR which passes through A(0,0) will be

$y = \frac{3}{4}x$

⇒ 4y = 3x

⇒ 3x - 4y = 0 (Answer)

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Hair colors are an example of which type of data?

kotykmax [81]

Answer:

Nominal data are used to label variables without any quantitative value. Common examples include male/female (albeit somewhat outdated), hair color, nationalities, names of people, and so on. In plain English: basically, they're labels (and nominal comes from "name" to help you remember). You have brown hair (or brown eyes).

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2 years ago

Workers in an office of 60 staff were asked their favourite type of take-away.

nikdorinn [45]

Answer:

a = 84°

b = 36°

c = 24°

d = 84°

e = 132°

Step-by-step explanation:

The parameters of the workers in the office are;

The number of staffs in the office = 60 staffs

The take-aways are pizza, curry, fish & chips, kebab and other

The frequency for the above take-aways = 14, 6, 4, 14, and 22 respectively

The variables for the angles representing the above take-aways on the pie chart = 'a', 'b', 'c', 'd', and 'e'; respectively

In order to find the size of the angles that represent each group of workers in the pie chart, we find the ratio of the group size to the total number of workers and we multiply the result by 360° as follows;

∠a = 360° × 14/60 = 84°

∠b = 360° × 6/60 = 36°

∠c = 360° × 4/60 = 24°

∠d = 360° × 14/60 = 84°

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3 years ago

CosA.cos2A.cos4A=sin8A/8sinA

alexgriva [62]

I assume you're supposed to establish the identity,

cos(A) cos(2A) cos(4A) = 1/8 sin(8A) / sin(A)

Recall the double angle identity for sine:

sin(2<em>x</em>) = 2 sin(<em>x</em>) cos(<em>x</em>)

Then you have

sin(8A) = 2 sin(4A) cos(4A)

sin(8A) = 4 sin(2A) cos(2A) cos(4A)

sin(8A) = 8 sin(A) cos(A) cos(2A) cos(4A)

==> sin(8A)/(8 sin(A)) = cos(A) cos(2A) cos(4A)

as required.

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3 years ago

What is the solution of √x-5 = x-11

PIT_PIT [208]

Hey!

To solve x in this equation we must first add five to both sides to get $\sqrt{x}$ on its own.

<em>Original Equation :</em>
$\sqrt{x} - 5 = x - 11$

<em>New Equation {Added 5 to Both Sides} :</em>
$\sqrt{x} =x-6$

Now we must square both sides of the equation.

<em>Old Equation :</em>
$\sqrt{x} =x-6$

<em>New Equation {Changed by Squaring Both Sides} :</em>
$x= x^{2} -12x+36$

And now we must solve the new equation.

Step 1 - Switch sides
$x^{2} -12x+36=x$

Step 2 - Subtract x from both sides
$x^{2} -12x+36-x=x-x$

Step 3 - Simplify
$x^{2} -13x+36=0$

Now we need to solve the rest of the equation using the quadratic formula.

$\frac{-(-13)+ \sqrt{(-13) ^{2}-4*1*36 } }{2*1}$

${13+ \sqrt{(-13)^{2}-4*1*36 }=13+ \sqrt{25}$

$\frac{13+ \sqrt{25}}{2}$

$\sqrt{25}=5$

$\frac{13+5}{2}$

$\frac{18}{2}$

9

$\frac{-(-13)- \sqrt{(-13) ^{2} -4*1*36} }{2*1}$

4

<em>So, this means that in the equation $\sqrt{x} -5=x-11$ ,</em> x = 9 <em>and </em>x = 4.

Hope this helps!

- Lindsey Frazier ♥

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3 years ago

I need help with dividing fractions

iVinArrow [24]

When you divide fractions, you want to use keep change flip.

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Let’s use 3/4 ÷ 2/3

Keep 3/4 the same, change the division sign into a multiplication sign, and flip 2/3 so that it is 3/2

It’ll look like this

3/4 x 3/2

Now just multiply the numerators, 2 x 3, then multiply the demoninators, 4 x 2.

You get 6/8

Simplify this number and you get 3/4.

If you have any further questions feel free to ask.

Hope this helps.

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3 years ago