Answer:
slope = - 2
Step-by-step explanation:
Calculate the slope m using the slope formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 8) and (x₂, y₂ ) = (5, - 4)
m = 
= 
= - 2
The equation to be used to calculate the measure of ∠PQR in the cyclic quadrilateral is: (6x − 4)° + (2x + 16)° = 180°.
<h3>What are Opposite Angles in a Cyclic Quadrilateral?</h3>
A cylcic quadrilateral is a quadrilateral inscribed in a circle. The opposite angles are supplementary, that is they add up to give 180 degrees.
Thus, angles Q and O are opposite angles in the cyclic quadrilateral, which means they are supplementary.
Therefore, the equation to be used to calculate the measure of ∠PQR in the cyclic quadrilateral is: (6x − 4)° + (2x + 16)° = 180°.
Learn more about cyclic quadrilateral on:
brainly.com/question/10057464
The resulting equation has a leading degree of 2, hence the system of equation will have 2 solutions
<h3>Quadratic equations</h3>
Quadratic equations are equations that has a leading degree of 2. Given the following system of equations
y=2x
y=x^2+2
Equate to have:
2x = x^2+ 2
Equate to zero
x^2 - 2x +2 = 0
Since the resulting equation has a leading degree of 2, hence the system of equation will have 2 solutions
Learn more on system of equations here: brainly.com/question/14323743
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Answer:
HT = 17 cm
<T = 58°
<H = 32°
Step-by-step explanation:
✔️Find HT:
Since it's a right triangle, we would apply the Pythagorean Theorem given as c² = a² + b²
Where,
a = HW = 15 cm
b = WT = 8 cm
c = HT
Plug in the values:
HT² = 15² + 8²
HT² = 289
HT = √289
HT = 17 cm
✔️Find <T by applying trigonometric ratio formula:
Recall: SOH CAH TOA
Reference angle (θ) = <T
HW = 15 cm = Opposite side length
WT = 8 cm = Adjacent side length
Apply CAH:
Cos θ = Adj/Hyp
Substitute
Cos T = 8/15
T = 
T ≈ 58°
✔️Find <H:
Sun of interior angles of a triangle = 180°
Therefore,
m<H + m<T + m<W = 180°
Substitute
m<H + 58° + 90° = 180°
m<H + 148° = 180°
m<H = 180° - 148°
m<H = 32°
Answer:
b(t) = 70,000 + 3000t . . . . . salary after t years; t∈{0,1,2,3,4,5,6}
Step-by-step explanation:
We can let b(t) represent Benny's salary function with t being the number of completed years at the law firm, an integer. The function's domain includes only the first 6 years at the firm.
Since Benny gets the same raise each year, The function is linear. Its "y-intercept" is Benny's initial salary, and the rate of change is Benny's annual increase:
b(t) = 70,000 + 3,000t . . . . salary in dollars after t years with the firm
