(4.23)(1.6) please multiple

Answer:

x = 6

Step-by-step explanation:

log2(x + 5) + log2(x − 5) = log2 11.

We know that loga (b) + log a(c) = log a( bc)

log2(x + 5) (x − 5) = log2(11)

Multiply

log2(x^2 -25) = log2(11)

Raise each side to the power of 2

2^log2(x^2 -25) = 2^log2(11)

x^2 - 25 = 11

Add 25

x^2 -25 +25 = 25+11

x^2 = 36

Taking the square root of each side

x = ±6

But x cannot be negative because then the log would be negative in log2(x-5) and that is not allowed

x = 6

Answer:

x = 6

Step-by-step explanation:

[tex] log_2[/tex] ( x + 5 ) + [tex] log_2[/tex]( ( x - 5 ) = [tex] log_2[/tex] 11

Determined the define range.

[tex] log_2[/tex] ( x + 5 ) + [tex] log_2[/tex]( ( x - 5 ) = [tex] log_2[/tex] (11), x ∈ ( 5, + ∞ )

We know that [tex] log_a ( b ) + log_a ( b ) [/tex] = [tex] log_a( bc) [/tex]

[tex] log_2[/tex] ( x + 5 ) ( x - 5 ) = [tex] log_2[/tex] ( 11).

[tex] log_2[/tex] ( ( x + 5 ) × ( x - 5 ) ) = [tex] log_2[/tex] ( 11).

Use indentity :- ( a + b ) ( a - b ) = a² - b².

[tex] log_2[/tex] ( x² + 25) = [tex] log_2[/tex] ( 11).

Since , the base of the logarithm are the same. set the arguments equal.

x² - 25 = 11.

Move constant to the right-hand side and change their sign.

x² = 11 + 25

x² = 36.

Take square root of each side.

√x² = √36

x = ± 6

x = 6

x = -6, x ∈ ( 5, + ∞ )

Check if the solutions is in determine range.

x = 6

Answer:

Yeah

Step-by-step explanation:

Answer:

350.85

Step-by-step explanation:

90.6*2 = 181.2

27*2 = 54 (diameter)

54*pi = 169.646003294

169.646003294 + 181.2 = 350.846003294

350.846003294 = 350.85

Answer:d

Step-by-step explanation:

Answer:

D

explanation:

i got it right on the test

Answer:

2/5=x

Step-by-step explanation:

-9=-10x-5

Add 5 to each side

-9+5=-10x-5+5

-4 = -10x

Divide by -10

-4/-10 = -10x/-10

2/5 =x

Answer:

0.4

Step-by-step explanation:

you take the -5 to the other side as positive and that is -4 = -10X and then you divide -4 by -10 and that is 0.4 hope that helps

Answer:

6, permutation

Step-by-step explanation:

Book 1, CD 1

Book 1, CD 2

Book 1, CD 3

Book 2, CD 1

Book 2, CD 2

Book 2, CD 3

There are 6 permutations.

Answer:

3

Step-by-step explanation:

9,8,3,2,5

3

3/5=0.6

0.6

Answer:

hope it helps

Step-by-step explanation:

Answer:

The "!" represents a factorial

Step-by-step explanation:

In math, a factorial when there is an ! followed by a number.

For example, 5! = 5 factorial.

To solve factorials, multiply every integer below the number before the factorial, including the number.

5! = 5 x 4 x 3 x 2 x 1 = 120.

Answer:

Rs 56250

Step-by-step explanation:

Given:

Cost price of laptop (CP) = RS 45000

Profit (P) = 24 % = 0.24

The selling price of dealer (SP) = Cost price of customer,

So,

Selling price of dealer = [tex]\tt CP + Profit \:Percentage \:of \:C.P[/tex]

Selling price of dealer = CP(1+ Profit %)

Substituting value

Selling price of dealer = 45000(1+0.24)

Selling price of dealer = 45000*1.24

Selling price of dealer = 56250

Therefore, the Customer paid Rs 56250 for the laptop.

Answer:

Rs 56,250

Step-by-step explanation:

To calculate how much the customer paid for the laptop, we need to determine the total price after the retailer added a 25% profit margin.

If the dealer purchased the laptop for Rs 45,000, then Rs 45,000 is 100%. If the dealer sells it to a customer at 25% profit, it was sold at 125% of its purchase price.

Therefore, to calculate how much the customer paid for the laptop, we need to find 125% of Rs 45,000:

[tex]\begin{aligned}\sf 125\%\;of\;45000&=\sf\dfrac{125}{100} \times 45000\\\\&=\sf\dfrac{125\times 45000}{100} \\\\&=\sf\dfrac{5625000}{100} \\\\&=\sf56250\end{aligned}[/tex]

Therefore, the customer paid Rs 56,250 for the laptop.

Answer:  C. Trey, Susie, Tucker, Jordan, Ashton

========================================================

Explanation:

The random sub-sequence 52197 66082 helps directly determine who we pick.

The digit 5 is first of that sequence, so we pick Trey first (as he's the 5th student). Then we pick student #2 next, who is Susie.

Up next is student #1, and that would be Tucker

Up next is student #9, but the list only goes high as 7. So we skip over 9

Jordan is next up since 7 is the next digit

Finally, the last selection is Ashton because 6 follows after.

--------------

In other words, the sequence 52197 6 will lead to these selections in the order provided.

Side note: if we wanted a 6th student, then we'd have to skip over the next 6 since we cannot pick Ashton twice. The 6th selection would be Jack since he's student #0

Answer:

missing angle <60 and side lengths 5, 5[tex]\sqrt{3}[/tex]

Step-by-step explanation:

we understand from the given information that  the triangle in question is a special right triangle

and since this is a special triangle the side lengths follows :

the side length that sees <90 is represented by 2x

the side length that sees <60 is represented by x[tex]\sqrt{3}[/tex]

and the side length that sees <30 is represented by x

2x = 10 so x = 5 and  x[tex]\sqrt{3}[/tex] = 5[tex]\sqrt{3}[/tex]

Answer:

true, to my knowledge concentric circles are just circles that all have one main center.

Step-by-step explanation:

Answer:

90n-72=0

Step-by-step explanation:

18×5n-18×4=0

Answer:

-36,36

Step-by-step explanation:

3x - 6(5x + 3) = 9x + 6

 Distribute:

3x - 30x - 18 = 9x + 6

Combine like terms:

-27x - 18 = 9x + 6

There are two possible ways to isolate x

On the left

Subtract 9x from each side

-27x - 18 -9x = 9x-9x + 6

-36x -18 = 6

On the right

Add 27x from each side

-27x - 18 +27x = 9x+27x + 6

-18 =36x+ 6

Answer:

(B) mn+3

Rule of algebra: *INTEGERS*

like sign➡ add

unlike sign➡ subtract

Step-by-step explanation:

Because the m2n2 is got subtract by m and n that's why it bacames a constant mn.

Answer:

[tex](m^{2} n^{2} -7)-(mn+4)[/tex]

[tex]=m^{2} n^{2} -7-mn-4[/tex]

[tex]m^{2} n^{2} -mn-11[/tex]

Option C is your answer

----------------------------------

Hope it helps...

Have a great day!!

Answer:

x:-4,-3,-2,-1,0,1

f(x):-10,0,0,-4,-6,0

from the table we can see when x=0, y=-6

Therefore the y-intercept will be (0,-6)

OAmalOHopeO

The y intercept of the continuous function in the table is given by the relation f ( 0 ) = -6

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

Let the values of x be x = { -4 , -3 , -2 , -1 , 0 }

Let the values of y be y = { -10 , 0 , 0 , -4 , -6 }

Now , the y intercept of the function is when the value of x = 0

So , when x = 0 , the value of y = -6

And , f ( 0 ) = -6

Therefore , the y intercept is ( 0 , -6 )

Hence , the y intercept of the function is ( 0 , -6 )

To learn more about function rule click :

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Answer:

C:The set of all possible outcomes

Answer:

(x-9)^2 +(y-12)^2 = 225

Step-by-step explanation:

First find the length of the radius

If is the distance from the center to the point

d = sqrt( (x2-x1)^2 + (y2-y1)^2 )

   = sqrt( (0-9)^2 + (0-12)^2)

   = sqrt ( 81+144)

  = sqrt(225)

  = 15

The equation for a circle is

( x-h) ^2+ (y-k)^2 = r^2

(x-9)^2 +(y-12)^2 = 15^2

(x-9)^2 +(y-12)^2 = 225

Answer:

-1/9^2 is the power notation for your questions

Step-by-step explanations

Answer:

16/20

Step-by-step explanation:

Since this is a right triangle

sin theta = opp side / hypotenuse

sin theta = 16/20

Answer:

A.

[tex]{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\ \\ { \tt{ \sin( \theta) = \frac{16}{20} }}[/tex]

Answer:

It's an isosceles triangle equal 2 sides so

it will be x+67 ° +67 ° =180° ( sum of angle in triangle)

x+134 °=180 °

x =180 - 134

x = 46 °

The measurement of the missing angles in the given triangle is 67.

Use the concept of isosceles triangle defined as:

A triangle with two equal-length sides is said to be isosceles.

An isosceles triangle has equal angles on either side of its equal sides.

In the given figure,

One angle is 67 degrees

And two sides are equal.

Let the missing angle is x°

Since the two sides of this triangle are equal,

So this is an isosceles triangle.

Then two opposite angles must be equal.

For a triangle,

The sum of interior angles = 180°

Therefore,

67° + 67° + x° = 180°

x° = 46°

Hence,

The measurement of the missing angle is 46°

To learn more about the triangle visit;

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SPJ4

Answer:

C

Step-by-step explanation:

Given:

The two exponential functions are shown in the given table.

To find:

The correct conclusion about the functions f(x) and g(x).

Solution:

The given functions are:

[tex]f(x)=2^x[/tex]

[tex]g(x)=\left(\dfrac{1}{2}\right)^x[/tex]

The function g(x) can be written as:

[tex]g(x)=\dfrac{1}{2^x}[/tex]

[tex]g(x)=2^{-x}[/tex]

[tex]g(x)=f(-x)[/tex]

It means the graphs of f(x) and g(x) are reflections over the y-axis. So, option B is correct.

Since [tex]g(x)\neq -f(x)[/tex], therefore the functions f(x) and g(x) are not the reflections over the x-axis. So, option A is incorrect.

The function f(x) is an increasing function because the base of the exponent is [tex]2>1[/tex]. The function g(x) is a decreasing function because the base of the exponent is [tex]\dfrac{1}{2}<1[/tex]. So, option C is incorrect.

At x=0 the value of f(x) is 1 and the value of g(x) is also 1. It means the functions has same initial values. So, option D is incorrect.

Therefore, the correct option is B.

We can conclude that g(x) is a reflection over the y-axis of f(x).

The two functions are:

You can see the graph of these functions at the end of the answer.

You can also notice that g(x) can be written as:

g(x) = (1/2)^x = 2^(-x) = f(-x)

Then this is a reflection over the y-axis, thing that you can also see in the graph below.

So the correct option is:

"The functions f(x) and g(x) are reflections over the y-axis."

If you want to learn more about reflections, you can read:

https://brainly.com/question/4289712

Answer: B

Step-by-step explanation:

Using slope formula, change in y (3) over change in x (2) is 3/2. So the equation would be y=3/2x.

it's true because it gives interset or compensation amount to the individuals or organizations which motivates people to save their money in a saving account

Answer:

x = 10

The both line crosses with a little hyphen, meaning those are same

Answered by GAUTHMATH

Answer:

Yes

Step-by-step explanation:

The roof is Rectangular :

Dimension of roof section : 7.2 m by 4.4 m

Area of roof = length * width

Area of roof = 7.2 * 4.4 = 31.68 m²

Dimension of solar panels = 1400 mm by 850 mm

Converting to m:

1000mm = 1 m

1400/1000 by 850/1000 = 1.4 m by 0.85 m

Area each solar panel = 1.4 * 0.85 = 1.19 m²

Gap left at each edge :

30cm gap about the 4 edges gives a square with side length 30cm:

30cm = 30/100 = 0.3m

Area of gap left = 0.3² = 0.09 m²

Total area that can be covered = (31.68 - 0.09) m² = 31.59 m²

Maximum number of panels that can be placed on roof section :

Total area that can be covered / area of panel

31.59 m² / 1.19 m²

= 26.54 panels

Answer:

m = (y2 - y1) / (x2 - x1) = (10 - 6) / (3 - 1) = 2    slope of line

y = m x + b standard form of straight line

y = 2 x + b      where b is the intercept at x = 0

b = y - 2 x

b = 6 - 2 = 4    from our first equation

Also, b = 10 - 6 = 4       check from second equation

y = 2 x + 4    is our equation

Check if y = 6 and x = 1 then

y = 2 * 1  + 4 = 6   verifying the first point given