Answer:
1. (3x²y³z)²=9x⁴y⁶z²
2. (2m³n⁻⁴)³=8m⁹n⁻¹²
Step-by-step explanation:
Both questions require knowledge of two rules of indices/powers:
(xy)ᵃ=xᵃyᵃ (when numbers multiplied by each other are put to a power, that is equal to the product of each number to that power)
(xᵃ)ᵇ=xᵃᵇ (when a number to a power is put to another power, that is equal to the number to the power of the product of the powers)
1.
(3x²y³z)²
=(3²)(x²)²(y³)²(z²)
=(9)(x²⁽²⁾)(y³⁽²⁾)(z²)
=9x⁴y⁶z²
2.
(2m³n⁻⁴)³
=(2³)(m³)³(n⁻⁴)³
=(8)(m³⁽³⁾)(n⁻⁴⁽³⁾)
=8m⁹n⁻¹²
Hope this helps! :D
7 -3 2/5
= 7 -17/5
= 35/5 -17/5 (common denominator is 5)
= 18/5
= 3 3/5
The final answer is 3 3/5~
Answer:
<em>The height of the monument is 124.8 ft</em>
Step-by-step explanation:
<u>Right Triangles</u>
The ratios of the sides of a right triangle are called trigonometric ratios. The tangent ratio is defined as:
The figure attached below shows the different distances involved in the problem. We heed to find the value of h, the height from Daniel's eyes. Then we'll add it to the 6 ft where his eyes are located from the ground.
Taking the angle of 68° as a reference:
Solving for h:
Calculating:
h = 118.8 ft
The height of the monument is 118.8 ft + 6 ft = 124.8 ft
This question wants you to find a common denominator for the fractions.
This means finding the LCM, least common multiple, for 21 and 9.
This can be done by listing the multiples for each number until they meet at a common one.
9:
9
18
27
36
45
54
63
21:
21
42
63
This means the LCM of 21 and 9 is 63.
So the lowest possible common denominator is 63.
21 • 3 = 63
So you have to multiply the numerator of 2/21 by 3 as well.
2 • 3 = 6
2/21 = 6/63
Now do the same for 1/9.
9 • 7 = 63
Multiply the numerator, 1, by 7.
1 • 7 = 7
1/9 = 7/63
So in the first blanks, you would put 6/63 for what 2/21 is equal to and 7/63 for what 1/9 is equal to.
7/63 is greater than 6/63.
7/63 > 6/63
That means 1/9 > 2/21
So 2/21 < 1/9 is the answer to the last blank.
Hope this helps!
8:15 + 5:00 = 13:15
13:15 + 0:15 = 13:30
The turkey will be ready at 1:30pm