Correct answers only for number 31

Mathematics

1 answer:

Ivahew [28]3 years ago

6 0

base: b

height: b

A = 1/2 (b · b) = 1/2(b²) = b²/2

sum is six less than area

b + b = 6 - ↔b²/2

2b = b²/2 - 6

4b = b² - 12 <em>multiplied by 2 to clear the denominator</em>

0 = b² - 4b - 12

0 = (b - 6)(b + 2)

0 = b - 6 0 = b + 2

b = 6 b = -2 (Negative so disregard)

A = b²/2 = (6)²/2 = 36/2 = 18

Answer: 18 units²

You might be interested in

The base is a right triangle with a leg of 12 in. and hypotenuse of 15 in.

EastWind [94]

Answer:

V = 540 inches ^3

Step-by-step explanation:

The area of the base is found be finding the other leg

a^2 +b^2 = c^2

12^2+b^2 = 15^2

144 +b^2 = 225

b^2 = 225-144

b^2=81

Take the square root of each side

b = 9

We can find the area of the triangle

B = 1/2 (9*12)

B =54

The Volume is given by

V = Bh

V = 54*10

V = 540 inches ^3

7 0

3 years ago

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find

Blababa [14]

$After\ adding\ equations\ and\ simplifying:\\\\One\ solution:\\\\x=number\\ example: x=2\\\\ infinitely\ many\ solutions:\\\\ Left\ side=\ Right\ side\\ example:\\ 2=2\\\\ No\ solutions:\\\\2 \neq 5$ $\left \{ {{x+3y=9} \atop {3x-y=7}\ \ |*3} \right.\\\\ \left \{ {{x+3y=9} \atop {9x-3y=21}} \right.\\+--------\\\\Addition\ method:\\\\10x=30\ \ |:10 \\\\x=3\\\\x+3y=9\\\\3y =9-x=9-3=6\\\\y=2\\\\ \left \{ {{y=2} \atop {x=3}} \right.$