The base of a triangle is (x + 7) inches long. The height of the triangle is (x – 4) inches long. If the area of the triangle is 13 square inches, what is the value of x.

x = 6, and x = -9

Step-by-step explanation:

Area of a triangle = 1/2 base* height = 13 square inches

Slot in the values of the base and height

13 = 1/2 ( x + 7 ) * ( x - 4 )

Expand

13 = 1/2 (x^2 - 4x + 7x - 28)

collect like terms

13 = 1/2 ( x^2 + 3x - 28 )

 cross multiply

13*2 = x^2 + 3x - 28

26 = x^2 + 3x - 28

Subtract 26 from both sides

0 = x^2 + 3x - 28 - 26

0 = x^2 + 3x - 28 - 54

rearrange

x^2 + 3x - 54 = 0

Two numbers which when multiplied gives -54 and when summed gives 3 are -6 and 9

x^2 - 6x + 9x - 54 = 0

x ( x - 6 ) + 9 (x - 6 ) = 0

(x - 6)(x + 9) = 0

x - 6 = 0

x = 6

x + 9 = 0

x = -9

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841

12

step-by-step explanation: