The difference of two numbers is 7. if the sum of the smaller number and the square of the larger number is 125, what is the value of the larger number?

larger = 11

Step-by-step explanation:

We will consider x = bigger, y = smaller

This means x - y = 7 (The difference of two numbers is 7)

This also means that x = 7 + y

And

y + x^2 = 125    (The sum of the smaller number and the square of the larger number is 125)

If we sustitute x = 7 + y in the second equation we get

y + (7+y)^2 = 125  

We can do the square of the binomial and get

y + 49 + 14y + y^2 = 125   (We substract 125 on both sides of the equation)

y + 49 + 14y + y^2 - 125 = 125 - 125

We get

y^2 + 15y - 76 = 0

We can make a factorization

(y+19)(y-4)= 0

y+19 = 0            y-4 = 0

y = -19               y=4

This means y=4 is the smaller number and x= 7+ y = 7 + 4 = 11

So x= 11 is the bigger number

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

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