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3 years ago

Given triangle ABC with vertices A(−3, 0), B(0, 6), and C(4, 6).

Mathematics

1 answer:

Slav-nsk [51]3 years ago

3 0

Answer:

-1/2x+y-8=0, y-0, 7/6x+y-6=0

Step-by-step explanation:

First we find the slope of side AB:

6-0/0-(-3) =2

Altitude CD is perpendicular to AB:

slope of CD=-1/slope of AB = -1/2

Since the altitude CD passes through the point C(4, 6), using the point-slope form of the equation of a line, the equation of CD is:

y-6= -1/2*(x-4)

-1/2x+y-8=0

This is the required equation of the altitude from C to AB. The rest of the equations are solved in the same way. Good luck!

You might be interested in

* Find the length of BD. A

denpristay [2]

9514 1404 393

Answer:

BD = 17

Step-by-step explanation:

The Pythagorean theorem can be used twice:

BC^2 + AC^2 = AB^2

BC = √(AB^2 -AC^2) = √(25^2 -24^2) = √49 = 7

Likewise, ...

DC = √(AD^2 -AC^2) = √(26^2 -24^2) = √100 = 10

Then ...

BD = BC +DC = 7 + 10

BD = 17

7 0

3 years ago

Can someone help me find the area thanks 20 points

mezya [45]

Step-by-step explanation:

To find the area of a rectangle and a parallelogram, use the formula:

$a = l \times h$

(Area = Length x Height)

Q4.

$a = 1 \frac{1}{4} \times 3\frac{1}{4} = 4 \frac{1}{16}$

Q6.

$a = 1 \frac{2}{3} = 3 \frac{1}{2} = 5 \frac{5}{6}$

6 0

4 years ago

If last year, nadia earned $31,025. of that amount, she spent $3612.59 on food. what percent of her income went to food, to the

Free_Kalibri [48]

First make an equation
x% of 31,025= 3612.59

Then isolate x by dividing both sides by 31,025

x= 3612.59÷31,025

Divide to get your answer

x= .116

Last make you answer a percent and round

x= 11.6%

8 0

4 years ago

I need help with 1-3 please and help!

Ghella [55]

Answer:

Q : 3

10x - 11 = 120 - 11 = 109°

3x - 2 = 36 - 2 = 34°

3x + 1 = 36 + 1 = 37°

Q ; 2

3x - 5 = 27 - 5= 22°

7x + 5 = 63 + 5 = 68°

And 90°

Q1 :

∠1 = 92°

∠2 = 42°

∠3 = 113°

Step-by-step explanation:

Solution for Q : 3

As the angle of all three is given as ,

10x - 11

3x - 2

3x + 1

We know sum of all the three angles of triangle = 180 °

So, (10x - 11) + (3x - 2) + (3x + 1) = 180°

Or, 16x - 12 = 180°

Or 16x = 192°, So , x = 12

So, all three angles are 10x - 11 = 120 - 11 = 109°

3x - 2 = 36 - 2 = 34°

3x + 1 = 36 + 1 = 37°

Solution for Q - 2

Given angles are

3x - 5

7x + 5

90°

We know sum of all the three angles of triangle = 180 °

so ,(3x - 5) + (7x + 5) + 90 = 180°

or 10x = 180 - 90 = 90°

SO, x = 9°

SO, all the three angles are 3x - 5 = 27 - 5= 22°

7x + 5 = 63 + 5 = 68°

And 90°

Solution for Q : 1

From,

the shown fig it is clear that

The ∠2 = 42° ( opposite vertical angles )

so, in left triangle

50° + ∠2 + ∠1 = 180°

Or, 50° + 42° + ∠1 = 180° ( sum of all angles of triangles = 180°)

Or, ∠1 = 92°

Again

From right figure triangle

∠2 + 25° + ∠3 = 180°

Or, 42° + 25° + ∠3 = 180

Or, ∠3 = 113°

3 0

3 years ago

The equation of a parabola is given.

Leokris [45]

We have that
y = -5/8 x²- 3x + 4----> multiply by 8----> 8y=-5x²-24x+32
8y-32=-5x²-24x

Factor the leading coefficient

8y-32=-5*(x²+4.8x)

Complete the square Remember to balance the equation by adding the same constants to each side.

8y-32=-5*(x²+4.8x+5.76-5.76)
8y-32-28.8=-5*(x²+4.8x+5.76)
8y-60.8=-5*(x+2.4)²
8*(y-7.6)=-5*(x+2.4)²
-(8/5)*(y-7.6)=(x+2.4)²
-(1.6)*(y-7.6)=(x+2.4)²

is a vertical parabola-----> open down
The standard form is (x - h)² = 4p (y - k)

the vertex is the point (-2.4,7.6)
4p=-1.6
p=-1.6/4----> p=-0.40

the directrix is
y= k - p-------> 7.6-(-0.40)----> y=7.6+0.40----> y=8

the answer is
y=8

4 0

4 years ago