All categories

2 years ago

The proof for the power property of logarithms appears in the table with an expression missing.

Mathematics

2 answers:

iVinArrow [24]2 years ago

7 0

Answer:

$log_{b}(b^{x r})$

Step-by-step explanation:

A picture of the question is shown in the figure attached. There we can see that the step corresponding to Properties of exponents is the option:

$log_{b}(b^{x r})$

which is equivalent to

$log_{b}((b^{x})^{r})$

Murljashka [212]2 years ago

5 0

Answer:

Step-by-step explanation:

on edge

You might be interested in

4.5m is ____ % of 90 cm; 90 cm is ____ % of 4.5m

Burka [1]

Answer: 5%

Step-by-step explanation:

Firstly, Convert metre to centimetre

100cm = 1m

Therefore,

4.5m = 450cm

If 450cm is X% of 90cm

That becomes :

450= X% × 90

450= 90X%

X% = 450/90

X% = 5%

4 0

2 years ago

Bill removed the ten of spades and the king of hearts from a deck of standard playing cards and threw them in the trash. There w

AveGali [126]

Answer:

Step-by-step explanation:

2 if you mean 1 of each so it would be 50 cards

3 0

2 years ago

7. All of the following are perfect square trinomials EXCEPT one. Which is it?

wolverine [178]

Answer:

All answers EXCEPT answer C. are perfect square trinomials.

Step-by-step explanation:

A perfect square trinomial is polynomial that satisfies the following condition:

$(a+b)^{2} = a^{2}+2\cdot a \cdot b + b^{2}$ , $\forall\,a,b\in\mathbb{R}$

Let prove if each option observe this:

a) $4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}$

1) $4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}$ Given

2) $(2\cdot x)^{2}+ 2\cdot (2\cdot x)\cdot (3\cdot y)+(3\cdot y)^{2}$ Definition of power/Distributive, associative and commutative properties.

3) $a = 2\cdot x$ , $b = 3\cdot y$ Definition of perfect square trinomial/Result.

b) $9\cdot a^{2}-36\cdot a + 36$

1) $9\cdot a^{2}-36\cdot a + 36$ Given.

2) $(3\cdot a)^{2}-2\cdot (3\cdot a)\cdot 6 + 6^{2}$ Definition of power/Distributive, associative and commutative properties.

3) $a = 3\cdot a$ , $b = 6$ Definition of perfect square trinomial/Result.

c) $x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}$

1) $x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}$ Given

2) $x\cdot y\cdot (1-4\cdot x+4\cdot x)$ Distributive property.

3) $x\cdot y \cdot 1$ Existence of the additive inverse/Modulative property.

4) $x\cdot y$ Modulative property/Result.

d) $a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}$

1) $a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}$ Given

2) $(a\cdot b)^{2}+2\cdot (a\cdot b)\cdot (2\cdot a^{2})+(2\cdot a^{2})$ Definition of power/Distributive, associative and commutative properties.

3) $a = a\cdot b$ , $b = 2\cdot a^{2}$ Definition of perfect square trinomial.

All answers EXCEPT answer C. are perfect square trinomials.

8 0

2 years ago

In ΔKLM, m = 59 cm, ∠L=111° and ∠M=60°. Find the length of l, to the nearest centimeter.

g100num [7]

Answer:

64 (or 63.6)

Step-by-step explanation:

You can figure out the <K by adding the first two angles (111+60) and getting 171 (subtracting that from 180 gives you a 9-degree angle for <K

Given three angles and 1 side, you can calculate the sides as follows:

k=m*sin (K) / sin (M) = 10.65

l=m*sin (L) / sin (M) = 63.60234

Since you're solving for l, the steps would be:

l=59 * sin (111) / sin (60)

l=59 * (0.934) / (0.866)

l=55.106 / 0.866

l=63.63

Hope this helps!

4 0

2 years ago

Students collected data about the capacities of their lungs by inflating balloons with a single breath. they measured the circum

marishachu [46]

The given data is the following:

Student Trial 1 Trial 2 Trial 3 Average
----------- -------- -------- -------- ------------
1 66.0 66.5 68.5 67.0
2 67.5 64.0 70.5 67.3
3 60.3 60.5 60.5 61.0
4 55.0 58.0 59.0 57.3

Let us check the reported averages.
Student 1:
Average = (66.0 + 66.5 + 68.5)/3 = 67.0 Correct
Student 2:
Average = (67.5 + 64.0 + 70.5)/3 = 67.3 Correct
Student 3:
Average = (60.3 + 60.5 + 60.5)/3 = 604 Incorrect
Student 4:
Average = (55.0 + 58.0 + 59.0)/3 = 57.3 Correct

Answer: Student 3

6 0

2 years ago

Read 2 more answers