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2 years ago

What is equivalent tox2+ 14x = -13

Mathematics

1 answer:

postnew [5]2 years ago

8 0

Answer:

X= 1 AND 13

Step-by-step explanation:

x2+14x = -13

by completing the square method

you add the square of half the coefficient of b to both sides

which is (14/2)^2

x^2+14x+(7^2) = -13 +(7^2)

x^2 + 7^2 = -13 + 49

x^2 + 7^2 = 36

(x + 7)^2 = 36

find the square root of both sides

(x+7) = + or - 6

x=7-6 ; 1

x= 7+6 ; 13

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3 years ago

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Leto [7]

For this case we have:

Question 1:

According to Heron's formula, the area of a triangle is given by:

$A=\sqrt{(s(s-a)(s-b)(s-c))}$

Where a, b and c are the sides of the triangle and s is the semi-perimeter of the triangle given by:

$s=\frac{(a+b+c)}{2}$

Let:

$a = 20mm\\b = 23mm\\c = 27mm$

We have s:

$s=\frac{(20+23+27)}{2}\\s=\frac{70}{2}\\s=35$

Substituting in the formula of the area:

$A=\sqrt{(35(35-20)(35-23)(35-27))}\\A=\sqrt{(35(15)(12)(8))}\\A=\sqrt{(50400)}\\A=224.5mm^2$

Thus, the area of the triangle is $A = 224.5mm ^ 2$

Answer:

$A = 224.5mm ^ 2$

Question 2:

The area of a traingule can be expressed as:

$A=\frac{(b*h)}{2}$

Where:

b: Base of the triangle

h: Triangle height

Let:

$b = 20m\\h = 18m$

Substituting the values in the expression we have:

$A=\frac{(20*18)}{2}\\A=\frac{360}{2}\\A=180m^2$

Thus, the area of the triangle is $A = 180m ^ 2$

Answer:

$A = 180m ^ 2$

Question 3:

It is known that the area of a rectangle is given by:

$A = l * w$

Where:

l: It is the length of the rectangle

w: It is the width of the rectangle

So:

$l = 9 feet\\w = 8 feet$

Substituting:

$A = (9 * 8) feet ^ 2\\A = 72 feet ^ 2$

Thus, the area of Laura's carpet is given by $A = 72 feet ^ 2$

Answer:

$A = 72 feet ^ 2$

Question 4:

We must take out the area of the outer wall, given by a rectangle, then:

$A = l * a$

Where:

l: It is the length of the rectangle

a: It is the height of the rectangle

We have:

$l = 48 feet\\a = 9 feet$

Substituting in the formula we have:

$A = (48 * 9) feet ^ 2\\A = 432ft ^ 2$

Thus, the area of the exterior wall is given by: $A = 432 feet ^ 2$

$432ft ^ 2> 400ft ^ 2$

So, a can of paint is not enough to cover the exterior wall.

Answer:

A can of paint is not enough to cover the exterior wall.

Question 5:

A regular hexagon is formed by 6 equal triangles. The area of the hexagon is given by:

$A=\frac{(perimeter* apothem)}{2}$

Where the perimeter is given by the sum of the sides, that is:

$perimeter = (10 + 10 + 10 + 10 + 10 + 10) cm\\perimeter = 60cm$

And the apothem is the height of each of the triangles that make up the hexagon, that is:

$apothem = 5cm$

Substituting in the formula:

$A=\frac{(60*5)}{2}\\A=\frac{300}{2}\\A=150cm^2$

Thus, the area of the hexagon is $A = 150cm ^ 2$

Answer:

$A = 150cm ^ 2$

7 0

3 years ago

What is equivalent tox2+ 14x = -13​

What is equivalent tox2+ 14x = -13