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bezimeni [28]
3 years ago
14

What is the exact solution to the equation 2^x+2 =5^2x ? A) −2ln2/2ln5−ln2 B) −ln2/2ln5+ln2 C) ln2/2ln5+ln2 D) 2ln2/2ln5−ln2

Mathematics
1 answer:
GenaCL600 [577]3 years ago
4 0

Answer: D

<u>Step-by-step explanation:</u>

          2ˣ⁺² = 5²ˣ

      ln 2ˣ⁺² = ln 5²ˣ               <em>apply ln to both sides</em>

(x + 2) ln 2 = 2x ln 5            <em>apply exponent to coefficient log rule</em>

x ln 2 + 2 ln 2 = 2x ln 5       <em>distribute (x + 2) on left side</em>

2 ln 2 = 2x ln 5 - x ln 2        <em>subtract (x ln 2) from both sides</em>

2 ln 2 = x(2 ln 5 - ln 2)         <em>factor out (x) from right side</em>

\frac{2ln2}{2ln5 - ln2} = x                             <em>divide both sides by (2 ln 5 - ln 2)</em>


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Answer:

The unit rate is $8.89 /ft².

Step-by-step explanation:

Given:

$160 for 18ft².

So, by dividing with 18

\frac{160}{18} we get 8.888.

Now, round to nearest hundredth for $8.888 is $8.89.

Therefore, the unit rate is $8.89 /ft².

7 0
3 years ago
Name the place of the hylighted digits,then write the value of the digits 35.052
Alex
<span>Name the place of the hylighted digits,then write the value of the digits 35.052
Answer: tens</span>
3 0
3 years ago
RS = 6y+2, ST=3y +7, and RT=13y-23 What is the value of y? y =________ Find STand RT. ST =_______ RT =_______
svlad2 [7]

Answer:

<h2><em> y = 8, ST = 31 and RT = 81</em></h2>

Step-by-step explanation:

Given RS = 6y+2, ST=3y +7, and RT=13y-23, the vector formula is true for the equations given; RS+ST = RT

Om substuting the expression into the formula;

6y+2+3y +7 = 13y - 23

collect the like terms

6y+3y-13y+2+7+23 = 0

-4y+32 = 0

Subtract 32 from both sides

-4y+32-32 = 0-32

-4y = -32

y = -32/-4

y = 8

Since ST = 3y+7. we will substitute y = 8 into the exprrssion to get ST

ST = 3(8)+7

ST = 24+7

ST = 31

Similarly,

RT = 13y-23

RT = 13(8)-23

RT = 104-23

RT = 81

<em>Hence y = 8, ST = 31 and RT = 81</em>

6 0
3 years ago
Anika was shown a reduction of a complex figure.
Luba_88 [7]

Answer:

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Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Henry worked for 8 days, Jack worked for 9.5 days while Steffi worked for 6.5 days to complete a project. If the amount earned f
trasher [3.6K]

Answer:

The ratio in which the amount is shared is 16:19:13

Step-by-step explanation:

The given parameters are;

The number of days Henry worked = 8 days

The number of days Jack worked = 9.5 days

The number of days Steffi worked = 6.5 days

The sharing formula for the amount earned for the project = The ratio of the number of days worked by each one

The total number of days worked by all three = 8 days + 9.5 days + 6.5 days = 24 days

The fraction of the total number of days Henry worked = (8 days)/(24 days) = 1/3 = 16/48

The fraction of the total number of days Jack worked = (9.5 days)/(24 days) = 19/48

The fraction of the total number of days Steffi worked = (6.5 days)/(24 days) = 13/48

Therefore. the ratio in which the amount is shared = 16:19:13 (which is the same as the ratio of the number of days worked)

5 0
3 years ago
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