Answer:
(5, 2 ) and (- 1, 8 )
Step-by-step explanation:
Given the equations
y = - x + 7 → (1)
y = 0.5(x - 3)²
= 0.5(x² - 6x + 9)
y = 0.5x² - 3x + 4.5 → (2)
Substitute y = - x + 7 into (2)
- x + 7 = 0.5x² - 3x + 4.5 ( subtract - x + 7 from both sides )
0 = 0.5x² - 2x - 2.5 ( multiply through by 2 ) , then
x² - 4x - 5 = 0 ← in standard form
(x - 5)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 1 = 0 ⇒ x = - 1
Substitute these values into (1) for corresponding values of y
x = 5 : y = - 5 + 7 = 2 ⇒ (5, 2 )
x = - 1 : y = -(- 1) + 7 = 1 + 7 = 8 ⇒ (- 1, 8 )
Answer:
x = 116° , y = 20°
Step-by-step explanation:
Since, measure of angle subtended on the center of the circle is twice the measure of angle subtended on the circumference of the circle.
Now, by angle sum property of a quadrilateral.
Answer:
x + 600 ≥ 2400
Step-by-step explanation:
Given:
Amount needed = $2,400
Amount they had = $600
Find:
Amount they need
Computation:
Assume;
Amount they need = x
x + 600 ≥ 2400
Answer:
a. 30 b. 96 c. 46
Step-by-step explanation:
a. Multiply the 3 and 2 first, then add. Inside the parentheses= 15, so 15 x 2= 30
b. 5+3=8 2+4=6 8x6=48 48x2= 96
c. 2+4=6 3x6=18 18+5= 23 2x23=46
