Answer:
10. x = 3 ± 2√6
11. x = 4 ± √6
12. 
and 
Step-by-step explanation:
10. Given the quadratic equation (x - 3)² + 14 = 38
We have to solve it by square root.
Now, (x - 3)² + 14 = 38
⇒ (x - 3)² = 38 - 14 = 24
⇒ (x - 3)² = (2√6)²
Now, square rooting both sides we get,
(x - 3) = ± 2√6
⇒ x = 3 ± 2√6 (Answer)
11. Given the quadratic equation x² - 8x + 10 = 0
We have to solve it by completing the square.
Now, x² - 8x + 10 = 0
⇒ x² - 2(4)(x) + 4² = 4² - 10
⇒ (x - 4)² = (√6)²
Now, square rooting both sides we get,
x - 4 = ± √6
⇒ x = 4 ± √6 (Answer)
12. Given the quadratic equation 5x² + 7x - 3 = 0
We have to solve it by quadratic formula.
Hence,
and 
⇒ and (Answer)
Answer:
x=-6 y=4
Step-by-step explanation:
-6+4=2
-6-4=10
19/2 = 9.5
(9.5)^2 = 90.25 = 9 + 81.25
x^2 - 19x + 9 = 0
x^2 - 19x + 90.25 - 81.25 = 0
(x - 9.5)^2 = 81.25
x - 9.5 = +/-sr(81.25)
I will let you finish from here
Answer:
13 sq cm.
Step-by-step explanation:
To find the area of this irregular figure, we will need to find the areas of a rectangle and triangle within this figure.
To find the area of the rectangle, we can simply do:
1 × 4= 4 sq cm.
Now, this is where it gets a little trickier. To find the area of the triangle, we will first need to determine the base and height.
We can see from the diagram that to find the base, we need to subtract:
7-4= 3 cm. This is the base of ONLY the triangle.
To find the height, we will need to do:
5+1= 6 cm. This is the total height of the entirety of the triangle.
We can now use the Triangle Area formula: 
(bh), to calculate the area of the triangle.
(6*3)= 9 sq cm.
Finally, add the areas of the rectangle and triangle together, giving you:
9+4= 13 sq cm.
