200x 9, nine times two hundred,
13+13+13+13=52, not 43 .
<span>43 is a prime number therefore the only two factors are 1 and itself, Technically, you can say that 21.5 multiplied by 2 would be 43.</span>
Applying the trigonometry ratio and rationalization, the missing lengths are:
1. x = 12/√3; y = 2√3
2. x = 5√2; y = 5√2
3. b = 24
4. 4√3
5. 5√3
<h3>What are the Trigonometry Ratio?</h3>
The trigonometry ratios are represented as follow:
- SOH is sin ∅ = opp/hyp
- CAH is cos ∅ = adj/hyp
- TOA is tan ∅ = opp/adj.
1. To find x, apply SOH:
opp = 6
hyp = x
adj = y
∅ = 60°
Equation:
sin 60 = 6/x
x = 6/sin 60
x = 6/√3/2 (sin 60 = √3/2)
x = 6 × 2/√3
x = 12/√3
Rationalize
x = 12/√3 × √3 /√3
x = 12√3/3
x = 4√3
To find y, apply TOA:
tan 60 = 6/y
y = 6/tan 60
y = 6/√3 (tan 60 = √3)
Rationalize
y = 6/√3 × √3 /√3
y = 6√3 / 3
y = 2√3
2. To find x, apply SOH:
opp = x
hyp = 10
adj = y
∅ = 45°
Equation:
sin 45 = x/10
x = (10)(sin 45)
x = 10 × 1/√2 (sin 45 = 1/√2)
x = 10/√2
Rationalize
x = 10/√2 × √2 /√2
x = 10√2/2
x = 5√2
To find y, apply CAH:
cos 45 = y/10
y = (10)(cos 45)
y = 10 × 1/√2 (cos 45 = 1/√2)
y = 10/√2
Rationalize
y = 10/√2 × √2 /√2
y = 10√2/2
y = 5√2
3. To find b, apply Pythagorean theorem:
b = √(25² - 7²)
b = 24
4. 12/√3
Rationalize
12/√3 × √3 /√3
12√3/3
4√3
5. 15/√3 × √3 /√3
15√3 /3
5√3
Learn more about trigonometry ratios on:
brainly.com/question/10417664
Answer: 5cm and 8cm
Step-by-step explanation:
Perimeter of a rectangle = 2l + 2w
Area of a rectangle = l × w
where l = length
w = width
Therefore,
2l + 2w = 26 ...... i
l × w = 40 ...... ii
We can reduce equation i to l + w = 13.
l + w = 13 ....... i
l × w = 40 ....... ii
From i, l = 13 - w ...... iii
Put the value of l into equation ii
l × w = 40
(13 - w) × w = 40
13w - w² = 40
13w - w² - 40 = 0
w² - 13w + 40 = 0
w² -8w -5w +40 = 0
w(w - 8) -5(w - 8) = 0
(w - 5) = 0 and (w - 8) = 0
w = 0 +5 and w = 0 + 8
w = 5
l = 8
The dimensions are 5cm and 8cm
Answer:
$36.80
Step-by-step explanation:
15% of 32 = 0.15x32 = $4.80
32+4.80 because it was a tip being added to the bill
=36.80
