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2 years ago

Plss helpp its due tmr and i dont really get ittt

Mathematics

1 answer:

OlgaM077 [116]2 years ago

4 0

The orthocenter of the triangles ABC are (2, 0) and (3, 3)

<h3>How to determine the orthocenter?</h3>

<u>Question 8</u>

The coordinates are given as:

A(2,0); B(2, 4); C(6,0)

Calculate the slope of BC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(0 - 4)/(6 - 2)

m =-1

The perpendicular slope is:

n = -1/m

n = -1/-1

n = 1

The equation of the perpendicular line is

y = n(x - x1) + y1

Where:

(x1, y1) = (2,0)

So, we have:

y = 1(x - 2) + 0

y = x - 2

Calculate the slope of AC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

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

m =0

The perpendicular slope is:

n = -1/m

n = undefined

This means that the perpendicular line is a vertical line

The equation of the perpendicular line is

x = x1

Where:

(x1, y1) = (2,4)

So, we have:

x = 2

Substitute x = 2 in y = x - 2

y = 2 - 2

y = 0

So, we have:

(x, y) = (2, 0)

Hence, the orthocenter of ABC is (2, 0)

<u>Question 9</u>

The coordinates are given as:

A(1,1); B(3, 4); C(6,1)

Calculate the slope of BC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(1 - 4)/(6 - 3)

m =-1

The perpendicular slope is:

n = -1/m

n = -1/-1

n = 1

The equation of the perpendicular line is

y = n(x - x1) + y1

Where:

(x1, y1) = (1,1)

So, we have:

y = 1(x - 1) + 1

y = x

Calculate the slope of AC using:

m = (y2 - y1)/(x2 - x1)

So, we have:

m =(1 - 1)/(6 - 1)

m =0

The perpendicular slope is:

n = -1/m

n = undefined

This means that the perpendicular line is a vertical line

The equation of the perpendicular line is

x = x1

Where:

(x1, y1) = (3,4)

So, we have:

x = 3

Substitute x = 3 in y = x

y = 3

So, we have:

(x, y) = (3, 3)

Hence, the orthocenter of ABC is (3, 3)

<h3>How to solve for x?</h3>

<u>Question 18 - 20</u>

Line 2x and x+ 3 are congruent lines

So, we have:

2x = x +3

Solve for x

x= 3

Line 3x and 2x + 5 are congruent lines

So, we have:

3x = 2x +5

Solve for x

x = 5

Line 2x - 3 and x + 2 are congruent lines

So, we have:

2x - 3 = x + 2

Solve for x

x = 5

<u>Question 21 - 23</u>

Line x + 5 and 3x + 7 are congruent lines

So, we have:

x + 5 = 3x + 7

Solve for x

x = -1

Line x + 6 and 5x - 4 are congruent lines

So, we have:

x + 6 = 5x - 4

Solve for x

x = 2.5

Line x + 8 and 5x + 7 are congruent lines

So, we have:

x + 8 = 5x + 7

Solve for x

x = 1/4

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15. Ten less the quotient of a number and 3 is 6.

coldgirl [10]

Answer:

(n/3)-10=6

Step-by-step explanation:

Let n be the number

Quotient of n and 3 is n/3

10 less that this is (n/3)-10=6

7 0

3 years ago

Help please!! i need to find the value of x

Wewaii [24]

You have to subtract the degrees like in this picture:

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3 years ago

Read 2 more answers

La o ferma zootehnica sau rezervat pentru hrana vitelor 302340 kg de lucerna ?i cu 240003 kg de fan mai mult decât lucerna. Câte

kipiarov [429]

Salut!

Avem 302340 kg + 240003 kg = 542343 kg fan;

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Bafta!

3 0

3 years ago

How many degrees are each angle of a regular 7 sided shape?

Diano4ka-milaya [45]

Answer:

Step-by-step explanation:

Here is a diagram of a seven sided regular polygon. You use this diagram to find out how many degrees total are in the interior of a the heptagon. There are 5 such triangles which means that since each triangle has 180o the total amount of the interior angles must be 5 * 180 = 900

Since there are 7 interior angles, the answer to how large each one of them is is found by

900/7 = 129.57 which is slightly off because it is a rounded error.

In general, the size of the angles in a regular polygon

180(n - 2 ) / n

Where n is the number of degrees in each interior angle. For example for an 8 sided figure you would get

180(8 - 2) / 8 = 180 * 6/8 = 133 degrees.

6 0

3 years ago

Use sigma notation to represent the sum of the first seven terms of the following sequence -4,-6,-8.....

lina2011 [118]

Answer:Answer:

$\sum\left {{7} \atop {1}} \right -n(3+n)$

Step-by-step explanation:

Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;

The sum of an arithmetic series is expressed as $S_n = \frac{n}{2}[2a+(n-1)d]$

n is the number of terms

a is the first term of the sequence

d is the common difference

Given parameters

n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2

Required

Sum of the first seven terms of the sequence

$S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 = \frac{7}{2}[-8+(6)(-2)]\\\\S_7 = \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70$

The sum of the nth term of the sequence will be;

$S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n = \frac{-6n}{2} - \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)$

The sigma notation will be expressed as $\sum\left {{7} \atop {1}} \right -n(3+n)$ . <em>The limit ranges from 1 to 7 since we are to find the sum of the first seven terms of the series.</em>

3 0

3 years ago