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WINSTONCH [101]
2 years ago
13

Can SOMEBODYYY please do the maths!!! PLeassssssssssssseeeeeeee

Mathematics
1 answer:
Anna11 [10]2 years ago
5 0

Answer:

<h2>see below</h2>

Step-by-step explanation:

<h3>Question-6:</h3>

we are given a equation

\sf \displaystyle \:   \log_{4}( - x)  +   \log_{4}( 6 - x)   = 2

to solve so

recall logarithm multiplication law:

\sf \displaystyle \:   \log_{4}( - x \times (6 - x))  = 2

simplify multiplication:

\sf \displaystyle \:   \log_{4}(  - 6 x +   {x}^{2} )  = 2

remember \displaystyle \log_{4}(4^2)=2

so

\sf \displaystyle \:   \log_{4}(  - 6 x +   {x}^{2} )  =     \log_{4}( {4}^{2} )

cancel out \log_4 from both sides:

\sf \displaystyle \:    - 6 x + {x}^{2}   =      {4}^{2}

simplify squares:

\sf \displaystyle \:    - 6 x + {x}^{2}   =      16

move left hand side expression to right hand side and change its sign:

since we are moving left hand side expression to right hand side there'll be only 0 left in the left hand side

\sf \displaystyle \:    - 6 x + {x}^{2}  - 16  =     0

rewrite it to standard form i.e ax²+bx+c=0

\sf \displaystyle \:      {x}^{2} - 6x  - 16  =     0

rewrite -6x as 2x-8x:

\sf \displaystyle \:      {x}^{2}   + 2x  -  8x  - 16  =     0

factor out x and 8:

\sf \displaystyle \:    x  {(x}^{}   +  2)  - 8(x   + 2) =     0

group:

\sf \displaystyle \:    (x    -  8){(x}^{}   + 2) =     0

\displaystyle \: x = 8 \\ x = - 2

\therefore \: x =  - 2

<h3>Question-7:</h3>

move left hand side log to right hand side:

\displaystyle \:   \log(x ) +  \log(x - 21)  = 2

use mutilation logarithm rule;

\displaystyle \:   \log( {x}^{2} - 21x)  = 2

\log(10^2)=2 so

\displaystyle \:   \log( {x}^{2} - 21x)  =  \log({10}^{2} )

cancel out log from both sides:

\displaystyle \:   {x}^{2} - 21x =  100

make it standard form:

\displaystyle \:   {x}^{2} - 21x  - 100=  0

factor:

\displaystyle \:   {(x} + 4)(x - 25)=  0

so

\displaystyle \:   x = 25

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what is the distance between the points (4, 5) and (10, 13) on a coordinte plane a. 12 units b. 8 units c. 10 units d. 14 units
qaws [65]

Answer:

<h2>10 units</h2>

Option C is the correct option

Step-by-step explanation:

Let the points be A and B

A ( 4 , 5 ) ------> ( x1 , y1 )

B ( 10 , 13 ) ------> ( x2 , y2 )

Now, let's find the distance between these points:

\sqrt{ {(x2 - x1)}^{2}  +  {(y2 - y1)}^{2} }

plug the values

= \:  \sqrt{(10 - 4) ^{2} +  {(13 - 5)}^{2}  }

Calculate the difference

=  \sqrt{ {(6)}^{2} +  {(8)}^{2}  }

Evaluate the power

=  \sqrt{36 + 64}

Add the numbers

=  \sqrt{100}

Write the number in exponential form with. base of 10

=  \sqrt{ {(10)}^{2} }

Reduce the index of the radical and exponent with 2

= 10 \: units

Hope this helps..

Best regards!!

7 0
3 years ago
pls help i need this now subtract -9 1/3 - ( - 1 1/3 enter your answer as a simplified fraction in the box
Neko [114]

Answer:

-8/1 or -8

Step-by-step explanation:

when you subtract a negative, it means add. so first lets add the one. we get -8 1/3. then we can add the 1/3. our final answer is -8

4 0
2 years ago
The expression 10a+6c gives the cost (in dollars) for a adults and c children to eat at a buffet restaurant.
lys-0071 [83]
Yikez that’s really hard
4 0
3 years ago
MARKING BRAINLEST!!!!!!!!!
lapo4ka [179]

Answer:

A  3^4 * 3^-4 / 3^6

C 1 / 3^6

Step-by-step explanation:

( 3^2 * 3^-2)

-------------------  all the the power of 2

           3^3

First simplify the numerator

We know a^b* a^c = a^(b*c)

( 3^(2+-2))

-------------------  all to the power of 2

           3^3

( 3^(0))

-------------------  all to the power of 2

           3^3

( 3^(0))

-------------------  all to the power of 2

           3^3

We know a^b/ a^c = a^(b-c)

3^(0-3)  all to the power of 2

3^-3 all to the power of 2

3^-3 ^2

We know that a^b^c = a^(b*c)

3^(-3*2)

3^ -6

We know the negative exponent takes if from the numerator to the denominator

1 / 3^6

The other correct choice is A

3^4 * 3^-4 = 3^0 which is 1

1/3^6 is the same answer

8 0
3 years ago
Read 2 more answers
What is the quotient of 78,600 + 12?
creativ13 [48]

The quotient of 78,600 and 12 is 6,550

7 0
3 years ago
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