Answer:
d is 8.4 units
m∠E is 40.3°
Step-by-step explanation:
Let us use the cosine rule to find the side d and then use the sine rule to find the measure of angle E
- Cosine rule is d² = e² + f² - 2(e)(f)(cos D)
- Sine rule is
In Δ DEF
∵ EF is represented by d
∵ DF = 6 units and is represented by e
∴ e = 6
∵ DE = 9 units and is represented by f
∴ f = 9
∵ m∠D = 65°
- Substitute the values of e, f and m∠D in the cosine rule above
∴ d² = (6)² + (9)² - 2(6)(9)(cos 65°)
∴ d² = 71.35722773
- Take √ for both sides
∴ d = 8.447320743
- Round it to the nearest tenth
∴ d = 8.4 units
Now let us use the sine rule to find m∠E
∵ 
- By using cross multiplication
∴ 8.4 × sin(E) = 6 × sin(65)
∴ 8.4 sin(E) = 6 sin(65)
- Divide both sides by 8.4
∴ sin(E) = 0.647362705
- Use 
to find m∠E
∴ E = (0.647362705)
∴ m∠E = 40.34305
- Round it to the nearest tenth
∴ m∠E = 40.3°
Answer: For each of the questions, the numerator gives you the whole number (integer) and the denominator gives you the fraction that it is being multiplied by.
1. It should be 2 times 1/5. Because if you multiply those, you will get back to the fraction of 2/5.
2. It is 5 times 1/12
3. It is 7 times 1/2
Answer: X = 62°, Y = 68°, Z = 50°
Step-by-step explanation:
From the given picture, the angles of Δ LPN are ∠L= 62° and ∠ N = 50°
By angle sum property of triangle ,
∠P=180°-(62°+50°)
⇒∠P=180°-112°
⇒∠P=68°
Hence, ∠P=68°
Since, ΔXYZ ∼ ΔLPN [given]
Also, the corresponding angles of similar triangle are equal.
Therefore, ∠L=∠X 62° , ∠P=∠Y=68° and ∠ N =∠Z= 50°
Answer:
x = ±1
Step-by-step explanation:
Step 1: Define variables
f(x) = x² + 1
f(x) = 2
Step 2: Substitute
2 = x² + 1
Step 3: Solve for <em>x</em>
0 = x² - 1
0 = (x - 1)(x + 1)
x - 1 = 0
x = 1
x + 1 = 0
x = -1
∴ x = ±1
5 5 2 2 0
ten thousands thousands hundreds tens ones
