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3 years ago

What do the vertical lines mean?

Mathematics

1 answer:

zhenek [66]3 years ago

3 0

The vertical lines are absolute values, the number in between them, if negative turns positive.

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Co-ordinate Geometry

saul85 [17]

Answer:

The value of a = 14

Step-by-step explanation:

Given

(x₁, y₁) = (2, 4)

(x₂, y₂) = (6, a)

(x₃, y₃) = (-1, 1)

A = 9 sq.units

Area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) is:

$A=\frac{\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right|}{2}$

substituting the values (x₁, y₁) = (2, 4), (x₂, y₂) = (6, a), (x₃, y₃) = (-1, 1), A = 9 in th formula

$A=\frac{\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right|}{2}$

$9=\frac{\left|2\left(a-1\right)+6\left(1-4\right)+-1\left(4-a\right)\right|}{2}$

Multiply both sides by 2

$\frac{2\left|2\left(a-1\right)+6\left(1-4\right)-1\left(4-a\right)\right|}{2}=9\cdot \:2$

simplify

$\left|2\left(a-1\right)+6\left(1-4\right)-1\left(4-a\right)\right|=18$

As the area is always positive.

$2\left(a-1\right)+6\left(1-4\right)-1\cdot \left(4-a\right)=18$

$2\left(a-1\right)-18-\left(4-a\right)=18$

Add 18 to both sides

$2\left(a-1\right)-18-\left(4-a\right)+18=18+18$

simplify

$2\left(a-1\right)-\left(4-a\right)=36$

$3a-6=36$

$3a=42$

Divide both sides by 3

$\frac{3a}{3}=\frac{42}{3}$

$a=14$

Thus, the value of a = 14

7 0

2 years ago

If one pie is shared equally by 6 people, then each person will get<br> what fraction of the pie?

amid [387]

Answer: Each person will take $\dfrac{1}{6}$ of the pie.

Step-by-step explanation:

Given : One pie is shared equally by 6 people.

The total number of persons = 6

Now, the fraction of the whole pie each person will take :-

$\dfrac{\text{Number of pie}}{\text{total persons}}\\\\=\dfrac{1}{6}$

Therefore, the fraction of the whole pie each person will take= $\dfrac{1}{6}$

3 0

2 years ago

Start with the value of 25, double it, and then calculate the percent increase.

Zanzabum

Answer: 100%

Step-by-step explanation:

If you start with 25 and double it you will get 50 and 25 is half of 50 so the percent increase will be 100%.

7 0

2 years ago

Round 689 to the nearest ten

Rama09 [41]

Answer:

690

Step-by-step explanation:

the 8 is in the tens place

so we look at the 9

it is 5 or higher

so we round the 8 up to 9

690

4 0

2 years ago

How does the HA theorem look like

Goryan [66]

Answer:

The HA Theorem states; If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another triangle, then the two triangles are congruent. ... They are both facing with their hypotenuses to the right, which means their right angles are to the left -- HA!

Step-by-step explanation:

8 0

2 years ago