Answer: a) x = 2 and -4 b) p = 4.12 and -2.4
Step-by-step explanation:
a) Using the completing the square me those to solve x²+2x = 8
firstly, we divide the equation by the coefficient of x² to give
x²+2x=8
Secondly, we need to get the constant of the equation x²+2x by adding the value gotten from dividing coefficient of x by 2 and squaring it i.e(2/2)² to give 1 as the constant
The equation becomes
x²+2x+1-1= 8
Note that 1 was subtracted just to ensure the question isn't altered
(x²+2x+1)-1 = 8
(x+1)(x+1)-1= 8
(x+1)(x+1)= 8+1
(x+1)² = 9
Squaring both sides of the equation
√(x+1)² = +/-√9
x+1 = +/-3
x = +3-1 = 2
x = -3-1 = -4
therefore x = 2 and -4
b) Using the same funny concept to solve the equation
7p² − 12p + 4 = 0
7p²-12p = -4
Dividing by coefficient of p²
p²-12/7p= -4/7
Completing the equation at the right hand side i.e p²-12/7p
We will add the square of half of the coefficient of p to both sides of the given equation (-12/7×1/2)² = (-12/14)²
= 144/196
p²-12/7p+144/196 = -4+144/196
(p-12/14)² = 640/196
Squaring both sides
√(p-12/14)² = +/-√640/196
p-12/14 = +/-3.26
p = +3.26+12/14 = 4.12
and p = -3.26+12/14 = -2.4
<u>Answer:</u>
The quen is as following:
ABC is a right triangle at C,
Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1
If CH is an altitude to AB and CL is an angle bisector of ∠ACB, find m∠HCL.
<u>The solution is: m∠HCL = 30°</u>
<u>Step-by-step explanation:</u>
See the attached figure.
∵The triangle is right at C ∴∠C = 90°
∴∠A + ∠B = 90° ⇒(1)
∵ Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1
∴∠A = 5 times ∠B
Substitute at (1)
∴ 5 ∠B + ∠B = 90° ⇒⇒⇒ ∴∠B = 15° and ∠A = 75°
∵CL is an angle bisector of ∠ACB
∴ ∠ACL = 90°/2 = 45°
∵ CH is an altitude to AB ⇒ ∠CHA = 90°
At the triangle AHC:
∠ACH = 180° - (∠CHA + ∠CAH) = 180° - (90° + 75°) = 15°
<u>∴ ∠HCL = ∠ACL - ∠ACH = 45° - 15° = 30°</u>
Answer:
80 ounces
Step-by-step explanation:
For 1 pound, it's 16 ounces.
Therefore, if you multiply the pounds by 5, you also have to multiply the ounces by five.
16x5= 80
1x5= 5
Therefore, the bag weighs 80 ounces
Answer:
<u>The knitting club has 7 members </u>
Step-by-step explanation:
1. Let's check the information provided to us to answer the question correctly:
Cost of new patterns book = US$ 3.50
Cost of set of knitting needles for each member = US$ 3.20
Cost of set of a ball of yarn for each member = US$ 3.20
2. Write and solve an equation to determine how many members the knitting club has.
Number of members of the knitting club = x
For solving for x, we can use this equation:
3.50 + 3.20x + 5.40x = 63.70
8.60x = 63.70 - 3.50
8.60x = 60.20
x = 60.20/8.60
x = 7
<u>The knitting club has 7 members </u>
Answer: Yes
Step-by-step explanation:
1. -8 (3) - 2(2) < 6 (Add in the co-ordinated where they belong)
2. -24 -4 < 6 (Simplify)
3. -28 <6
-28 is smaller than 6, so the answer will be yes!