Answer:
y = (3/2)x - 5/2
Step-by-step explanation: 5 + 2x
-2x-3y=5, solved for y, is y = ------------- , with a slope of -2/3. A line
-3
perpendicular to this one has a slope which is the negative reciprocal of -2/3, that is, +3/2. Using the slope-intercept formula, we calculate the y-intercept of the line that is perpendicular to the given one and passes through (1/3, -2): y = mx + b => -2 = (3/2)(1/3) + b, or
-2 = 1/2 + b. Thus, b must be -2 1/2, or -5/2.
The desired equation is y = (3/2)x - 5/2.
Answer:
a) 5.83 cm
b) 34.45°
Step-by-step explanation:
a) From Pythagoras theorem of right triangles, given right triangle ABC:
AB² + BC² = AC²
Therefore:
AC² = 5² + 3²
AC² = 25 + 9 = 34
AC = √34
AC = 5.83 cm
b) From triangle ACD, AC = 5.83 cm, AD = 4 cm and ∠A = 90°.
From Pythagoras theorem of right triangles, given right triangle ACD:
AD² + AC² = DC²
Therefore:
DC² = 5.83² + 4²
DC² = 34 + 16 = 50
DC = √50
DC = 7.07 cm
Let ∠ACD be x. Therefore using sine rule:
Answer:
10 and 15, 20 and 25, and 35 and 45.
Step-by-step explanation:
Answer Z=2
The math …..
Multiple ( ) first
15z -21 -18z +22 = 32z - 52 -17
Combine like terms
-3z + 1 = 32z -69
Move like terms to isolate Z
-35z = -70 two negative make positive
35z = 70
Divide both sides by 35 to isolate Z
Z = 2
Answer:
f(x) = (x + 10)(x + 4)(x - 1)
Step-by-step explanation:
Given the zeros of a polynomial, say x = a and x = b, then
the factors are (x - a) and (x - b)
The polynomial is then the product of the factors
f(x) = (x - a)(x - b)
Here the zeros are x = - 10, x = - 4 and x = 1, thus the factors are
(x - (- 10)), (x - (- 4)) and (x - 1), that is
(x + 10), (x + 4) and (x - 1)
f(x) = (x + 10)(x + 4)(x - 1)
