Answer:
<h2>
∠PQT = 72°</h2>
Step-by-step explanation:
According to the diagram shown, ∠OPQ = ∠OQP = 18°. If PQT is a tangent to the circle, it can be inferred that line OQ is perpendicular to line QT. Ths shows that ∠OQT = 90°.
Also from the diagram, ∠OQP + ∠PQT = ∠OQT;
∠PQT = ∠OQT - ∠OQP
Given ∠OQP = 18° and ∠OQT = 90°
∠PQT = 90°-18°
∠PQT = 72°
Answer:
x = - 5, x = - 3
Step-by-step explanation:
Given
x² + 15 = - 8x ( add 8x to both sides )
x² + 8x + 15 = 0 ← in standard form
Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)
The factors are 5 and 3, since
5 × 3 = 15 and 5 + 3= 8, thus
(x + 5)(x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x + 3 = 0 ⇒ x = - 3
Answer:
C
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
y = 2x² + 12x + 1
To express in vertex form use the method of completing the square.
The coefficient of the x² term must be 1 , thus factor out 2 from 2x² + 12x
y = 2(x² + 6x) + 1
add/ subtract ( half the coefficient of the x- term)² to x² + 6x
y = 2(x² + 2(3)x + 9 - 9) + 1
= 2(x + 3)² - 18 + 1
= 2(x + 3)² - 17 → C
Answer:
(p,r) = (1/3, 2/9)
Step-by-step explanation:
Here, we want to solve a system of equations
We can rewrite the second equation by dividing through by 2
So we have;
4p + 3r = 2
and
5p - 3r = 1
Add both equations:
9p = 3
p = 3/9
p = 1/3
Recall ;
5p - 3r = 1
3r = 5p - 1
Substitute the value or p here
3r = 5(1/3)-1
3r = 5/3 - 1
3r = 2/3
r = 2/9
So we have the solution set as;
(p,r) = (1/3 , 2/9)
