What is the length of the missing leg?

After applying some properties of logarithm the correct expression for the given logarithmic equation we get is 3x = log₂ 10.

Use the concept of  logarithm defined as:

The logarithmic function is the opposite of the exponentiation of that function.

It can be mathematically defined as:

For [tex]x > 0 , a > 0[/tex], and [tex]a\neq1[/tex],

[tex]y= log_a x[/tex] if and only if x = ay

Then the function is given by

[tex]f(x) = log_a x[/tex]

Where a is the base of function.

The given expression is:

[tex]2^{3x} = 10[/tex]

Take log both sides,

[tex]\text{log } 2^{3x} = \text{log } 10[/tex]

Since we know that,

[tex]\text{ log} a^n = n\text{ log} a[/tex]

Therefore,

3x log 2 = log 10

Dividing both sides by 2

3x = log10/log2

Since we know that,

[tex]\text{log} _a b = \dfrac{\text{log}_c b}{\text{log}_c a}[/tex]

Therefore,

3x = log₂ 10.

Hence,

The correct expression is 3x = log₂ 10.

To learn more about logarithmic expression visit:

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Answer: D) The sum of a number and twelve

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Explanation:

r = an unknown number

r+12 = sum of the unknown number and 12

The term "sum" refers specifically to the result of an addition problem.

As another example, saying 2+3 = 5 has a sum of 5.

Answer:

Step-by-step explanation:

I think it's b

Answer:

C (3;-3)

Step-by-step explanation:

when you put the points on the orthonormal, try to write the parallel of BD, passing through A. then the parallel of AB passing through D. you will detect that it's a rectangle that have 4 angles. which is correct

I hope you would try it on your paper and am glad I helped

Answer:

x=6

Step-by-step explanation:

9(10)=15(×)

90=15×

90÷15=6

Answer:

17/25

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

even numbers between 6 and 25 = 6 8 10 12 14 16 18 20 22 24

multiples of 3 = 6 9 12 15 18 21 24

Answer:

Subtract 1/3 from 2/3 dont forget to add the variable h!

1/3h + 11 = 8

-11            -11

1/3h = -3

Now we multiply by 3 on both sides

H = -9

Answer:

Number of wooden carving = a

Total amount Sam spend = 1,200 + 4a

Total revenue of Sam = 15a

Number of wooden carving make to earn profit $4,300 = 500 carvings

Step-by-step explanation:

Given:

Sales price of each wooden carving = $15

Fixed cost = $1,200

Variable cost = $4 for each

Find:

Number of wooden carving make to earn profit $4,300

Computation:

Part 1

Assume

Number of wooden carving = a

Part 2

Total amount Sam spend = 1,200 + 4a

Part 3

Total revenue of Sam = 15a

Part 4

Total profit of Sam = Total revenue of Sam - Total cost of Sam

4,300 = 15a - [1,200 + 4a]

4,300 = 15a - 1,200 - 4a

11a = 5,500

a = 5,500 / 11

Number of wooden carving make to earn profit $4,300 = 500 carvings

Answer:

$324.19

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

Price = $475

Price tag down = 35%

Tax = 5%

So, price after tag down = $475 - ( $475 × 35%)

= $475 - $166.25 = $308.75

Now, we calculate tax value after price tag down,

Tax value = $308.75 × 5% = $15.44

So, we can calculate the bed cost by using following formula,

Bed cost = Price after tag down + Tax value

= $308.75 + 15.44

= $324.19

Answer:

Possible

Step-by-step explanation:

The rule for triangle side lengths is that the two shortest sides must add up to the longest side so it is possible because

3+7 = 10

Two short sides = The longest side

Answer:

possible

Step-by-step explanation:

3+7= 10

Answer:

Yes, Kylie's can have the same ratio of tulips to daisies as that of Jorge

Step-by-step explanation:

Complete question

Jorge planted flowers in his garden. He planted one row of 12 tulips

and one row of 36 daisies. Jorge's friend Kylie has a garden with 100 flowers in it. Kylie's garden contains tulips and daisies. Is it possible for Kylie's garden to have the same ratio of tulips to daisies as Jorge's garden? Explain why or why not

Solution

Ratio of Tulip to daises in Jorge garden is 12:36 = 1:3

Here the common factor is 12 for numerator and denominator i.e 4 * 3 or 2, 2, 3

Given, Jorge's friend Kylie has a garden with 100 flowers, 100 is divisible by 4 but not 3.

Hence, if we take  Ratio of Tulip to daises in Jorge garden as 3:9 (by only removing common factor 4), then the Ratio of Tulip to daises in Kylie  garden will have the same ratio is that of Jorge'sgarden

Answer:

45, 000 J o 45 KJ

Step-by-step explanation:

Recordemos que trabajo realizado = fuerza * distancia

En este caso, fuerza = peso del objeto

Por lo tanto, peso del objeto = 180 Kg * 10ms ^ 2 = 1800 N

Por eso;

Trabajo realizado = 1800 N * 25 m = 45, 000 J o 45 KJ

Answer:

[tex]height = \frac{24}{2} = 12 \: cm \\ adjacent = \frac{32}{2} = 16 \: cm[/tex]

We get a triangle of height 12 cm and adjacent 16 cm

[tex]side = \sqrt{ {12}^{2} + {16}^{2} } \\ = \sqrt{400} \\ = 20 \: cm[/tex]

Answer:

side=√(24/2)²+(32/2)²

=√12²+16²

=√400

= 20

9×9+6×6

81+36

√117

10.816

nearest tenth=10.8cm

Answer:

109.3 ft

Step-by-step explanation:

Remembering SOHCAHTOA

We would be using sin

sin = opposite / hypotenuse

sin 40 = x / 170

0.6428 = x/170

x =  0.6428  x 170 = 109.3 ft

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

Answer:

236+590=

Step-by-step explanation:

236

+590

700+120+6=820 ɨ tɦɨռҡ

Answer:

[tex]x=0.1 ~ft[/tex]

Step-by-step explanation:

[tex]cot30=\frac{B}{H} =\frac{B}{H}[/tex]

[tex]\frac{\sqrt{3} }{2} =\frac{B}{H}=H=\frac{16}{\sqrt{3} }[/tex]

[tex]sin70=\frac{X}{H} =\frac{P}{H}[/tex]

[tex]sin70=\frac{x}{\frac{16}{\sqrt{3} } }[/tex]

[tex]x=\frac{\sqrt{3} }{16 ~sin70}[/tex]

[tex]=0.1152[/tex]

[tex]x=0.1[/tex]

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hope it helps

have a great day!!

Answer: 9.7

Step-by-step explanation: I got this question right

70+30 = 100

B = 180 - 100 - 20

B = 60°

80+20 = 100

C = 180 - 100 - 30

C = 50

DB/sin100 = 8/sin(60)

8*sin(100)/sin(60)

DB = 9.0973

DC/sin(30) = 8/sin(50)

8*sin(30)/sin(50)

DC = 5.22163

x = [tex]\sqrt{5.22163^{2} +9.0973^{2} -2*5.22163*9.0973*cos(80)[/tex]

x = 9.7

Answer:

Less than

Step-by-step explanation:

EX:

1/2 * 1/2 = 1/4

1*1 = 1

2*2 = 4

when you multiply two fractions, you get a fraction of a fraction.

Answer:

x = 2

Step-by-step explanation:

OK so lets do it together.

2x = -2x + 8

Subtract 8 from both sides

2x - 8 = -2x

Add 2x to both sides

4x - 8 = 0

Add 8 to both sides

4x = 8

Divide each side by 4

x = 2

Check:

4 = -4 + 8

4 = 4

correct

If my answer is incorrect, pls correct me!

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Answer:

c

Step-by-step explanation:

280/2016 * 13000000

answer is option d 2.8 million

Answer:

70 cm^3

hope this helps

have a good day :)

Step-by-step explanation:

base=length and width so 7 x 10=70 cm3

Answer:

cos(16°)•10=x

option one: 9.613

Answer:

Step-by-step explanation:

[tex]sin ~x=sin~x \times \frac{cos~x}{cos~x} =\frac{sin~x}{cos~x} \times cos ~x=tan~x*cos ~x[/tex]

Answer:

132 sq units

Step-by-step explanation: