Answer:

Step-by-step explanation:


















Hence, the correct answer is 
The density of the gold sample is 19.3g/cm³
Let the mass of the gold sample be represented by m
m = 579 g
Let the volume of the gold sample be represented by V
V = 30 cm³
Let the density of the gold sample be represented by ρ
The formula for the density is:


The density of the gold sample is 19.3g/cm³
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We have,
x+y:x-y=3:2
To prove that, x+ y : x - y = 3:2.
x+y=3
And,
x+y = 2
Adding (1) and (2), we get
x+y+x-y=3+2
⇒2x=5
⇒ x =
Put x = in (1), we get
+y=3
⇒ y=3-=
x+y:x-y=
=3:2
So, x+y:x-y=3:2.
Answer:
No
Step-by-step explanation:
<u>Use synthetic division</u>
-5 | 1 -4 3 7
____<u>-5 45 -240</u>
1 -9 48 | -233
Since the remainder is not 0, then x+5 is not a factor of the polynomial
Answer:
a) (i)
, (ii)
, (iii)
, (iv)
, (v)
, (vi)
, (vii)
, (viii)
; b)
; c) The equation of the tangent line to curve at P (7, -2) is
.
Step-by-step explanation:
a) The slope of the secant line PQ is represented by the following definition of slope:

(i)
:




(ii) 




(iii) 




(iv) 




(v) 




(vi) 




(vii) 




(viii) 




b) The slope at P (7,-2) can be estimated by using the following average:



The slope of the tangent line to the curve at P(7, -2) is 2.
c) The equation of the tangent line is a first-order polynomial with the following characteristics:

Where:
- Independent variable.
- Depedent variable.
- Slope.
- x-Intercept.
The slope was found in point (b) (m = 2). Besides, the point of tangency (7,-2) is known and value of x-Intercept can be obtained after clearing the respective variable:



The equation of the tangent line to curve at P (7, -2) is
.