chapter 8
5.Find the circumference of each circle. Use your calculator's value of [pi]. Round your answer to the nearest tenth.

Take the base-5 logarithm on both sides and simplify.

[tex]x^{16 \log^3_5(x) - 68 \log_5(x)} = 5^{-16}[/tex]

[tex]\left(16 \log^3_5(x) - 68 \log_5(x)\right) \log_5(x) = -16[/tex]

[tex]16 \log^4_5(x) - 68 \log^2_5(x) + 16 = 0[/tex]

[tex]4 \log^4_5(x) - 17 \log^2_5(x) + 4 = 0[/tex]

Factorize the left side.

[tex]\left(4 \log^2_5(x) - 1\right) \left(\log^2_5(x) - 4\right) = 0[/tex]

Then

[tex]4 \log^2_5(x) - 1 = 0 \implies \log^2_5(x) = \dfrac14 \\\\ ~~~~~~~~ \implies \log_5(x) = \pm \dfrac12 \\\\ ~~~~~~~~ \implies x = \dfrac1{\sqrt5} \text{ or } x = \sqrt5[/tex]

or

[tex]\log^2_5(x) - 4 = 0 \implies \log^2_5(x) = 4 \\\\ ~~~~~~~~ \implies \log_5(x) = \pm 2 \\\\ ~~~~~~~~ \implies x = \dfrac1{25} \text{ or } x = 25[/tex]

and the product of these solutions is of course 1.

Answer:  $24

Step-by-step explanation:

14+14+14+14=56

56+24=80

80/5

16

The 5th shirt cost $24 if the average after the 5th shirt was purchased changed to $16 per shirt.

Let's consider the total cost of the first 4 shirts:

Total cost of first 4 shirts = 4 shirts * $14/shirt = $56

Now, let's assume the cost of the 5th shirt is "x" dollars. After purchasing the 5th shirt, the total cost of all 5 shirts would be:

Total cost of all 5 shirts = $56 + x

Given that the average price after the 5th shirt was purchased is $16, we can set up an equation using the average formula:

Average price = Total cost / Number of shirts

$16 = ($56 + x) / 5

Solving for x:

$16 * 5 = $56 + x

$80 = $56 + x

x = $80 - $56

x = $24

So, the cost of the 5th shirt (x) is $24. This means that the person purchased the 5th shirt for $24 in order to bring the average price of all 5 shirts to $16 per shirt.

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Corresponding angle postulate

Corresponding angles:

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position.

Here we need to prove ∠3 ≅ ∠7

From the properties of the two parallel line cut by the transversal line, these angle is corresponding angles.

i.e., ∠3 ≅ ∠7 (by the properties of the corresponding angles)

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A stadium has 20,000 reserved seats and 25,000 general admission seats. if reserved seats are $17.50 and general admission seats are $10.75. The total money taken is $618750

a stadium has 20,000 reserved seats

cost of reserved seats are $17.50

total cost of reserved seats are 20000 x $17.50

total cost of reserved seats = $350,000

the stadium has 25,000 general admission seats

cost of general admission seats are $10.75

total cost of general admission seats is 25000 x $10.75

total cost of general admission seats = $268,750

total money taken if tickets of all seats are sold is summation of cost of reserved seats and general seats

= $ 350000 + $268750 = $618750

Therefore the total money taken is $618750

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Answer:

  [-4, 0]

Step-by-step explanation:

You want the set -4 ≤ x ≤ 0 expressed using interval notation.

In interval notation, an interval is expressed as an ordered pair, with the first number of the pair being the lower end of the interval, and the second number being the upper end.

When the inequality symbol used to describe the interval is "less than" (<), the bracket used is a round bracket (parenthesis). When the symbol is "less than or equal to" (≤), a square bracket is used. The brackets need not be of the same kind.

When one end of the interval is an infinity (positive or negative), a round bracket is used.

The interval

  -4 ≤ x ≤ 0

is written using the ordered pair ...

  [-4, 0]

The number sequence x satisfying-4< x <0 is an interval containing -4,0 as well as all numbers between -4 and 0.

[-4, 0]

A graph for interval notation is created when we describe the solution set of an interval on even a number line.

Intervals are represented in rectangular brackets as well as parentheses, and two numbers are separated by a comma. The two numbers are referred to as the interval's endpoints. The number on the left represents the smallest element or lower bound.

Interval notation is a technique for representing any subset of the real number line. To write interval notation, we utilize different symbols depending on the type of interval.. For instance, the set of numbers x satisfying 1 x 6 is an interval containing 1, 6, and all values between 1 and 6.

The ordered pair is used to write the interval -4 x 0.

[-4, 0].

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Answer:

[tex]x = 1[/tex] or [tex]x = -5[/tex]

Step-by-step explanation:

[tex]4|2x + 4|-7 = 17\\\to4|2x + 4| = 24\\\to |2x + 4| = 6[/tex]

Case 1) 2x + 4 is positive
[tex]2x + 4 = 6\\\to 2x = 2\\\to x = 1[/tex]

Case 2) 2x + 4 is negative

[tex]2x + 4 = -6\\\to 2x = -10\\\to x = -5[/tex]

Using simple interest, the better deal is given by Bank B.

The options are missing, but they are given as follows:

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

A(t) = A(0)(1 + rt)

In which:

For Bank A, the balance, without the fee, will be given by:

A(1) = 500(1 + 0.1) = $550.

Removing the fee:

550 - 12 x 5 = $490.

For Bank B, the balance is given by:

A(1) = 500(1 + 0.02) = $510.

No fee, 510 > 490, hence Bank B offers the better deal.

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Answer: 9 + 6(x) = 7 - x

Answer:

→ 9 + (6 × x) = 7 - x

Answer:

11x - 16

Step-by-step explanation:

3x + (8x-16)

3x + 8x-16

11x - 16

The right option which completes the sequence is option d.

21.

Given, the series is 27, 3 , 24 , 7,......11, 18

There are 2 series in the given series,

1st series = 27 , 24 , ? , 18

2 nd series = 3 , 7 , 11

In the first series, the next term gets subtracted by 3.

27 - 3 = 24

24 - 3 = 21

21 - 3 = 18

In the second series, the next term gets added by 4.

3 + 4 = 7

7 + 4 = 11

hence the series is completed:

27,3,24,7,21,11,18

Therefore the sequence is completed.

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Answer:

13k + 49

Step-by-step explanation:

Hello!

Distribute -7 to -k and -7

Combine like terms (6k and 7k)

The simplified form is 13k + 49.

The most convenient method to graph the line is to plot the equation y = -3/2x + 6 to represent the equation 3x + 2y = 12

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The equation is given as

3x + 2y = 12

The above equation is a linear equation

All forms of equation can be conveniently plotted by a graphing utility

However, the best way is to start by simplifying the equation

So, we have

3x + 2y = 12

Divide through the equation by 2

So, we have

3/2x + y = 6

Make y the subject of the equation

So, we have

y = -3/2x + 6

This means that  we plot the equation y = -3/2x + 6 to represent the equation 3x + 2y = 12

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Answer:

Step-by-step explanation:

Answer:

6.984×10^8 km

Step-by-step explanation:

Your calculator can tell you the answer to this.

15.15×10^8 -8.166×10^8 = 6.984×10^8

The difference between the distances is about 6.984×10^8 km.

_____

Additional comment

If you're paying attention to significant figures, you must round this to 6.98×10^8 km. The precision of the Saturn distance does not allow any better precision in the difference.

Answer:

Step-by-step explanation:

Answer:

domain of the given function is i don't know sorry

Step-by-step explanation:

Answer:             4x +10

Step-by-step explanation:

Distribute the 2 to both terms

2*2x + 2*5

4x + 10

The  f(x) - k shifts the function g(x) by  √0.8x units downwards

Let us consider

f(x) = g(x) + k

g(x) = f(x) - k

where f(x) = √x and

          g(x) = √0.2x

Substituting these values in the above equation

√0.2x = √x - k

-k = -√x + √0.2x

k = √x - √0.2x

k = √0.8x

which means that the f(x) - k shifts the function g(x) by √0.8x units downwards.

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The solution of the system of equation by graphing is (1,2)

According to the question we have been given two equation which are :

       x + y = 3       and  y = 3x - 1

We need solve this system of equation by graphing that is we have to find the value of x and y from the graph.

For the solution of the system of equation from graph we need to find the intersecting point.

First we will plot the graph of both the equation

For , x+y = 3

      the coordinates are (0,3) and (1,2)

For, y = 3x-1

      the coordinates are (0,-1) and (1,2)

Hence the below image is the graph of both the equation

From the graph we will see the point where both the lines are intersecting.

Thus the point where they intersect is (1,2).

Hence the solution is (1,2)

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The commission for the sale of $33000 worth of items at 6 percent is $1980 and if the sale doubles than the commission would be $3960

Given that the commission rate is 6%

If the sales done is 33000 dollars then the commission received by the agent would be:

33000 * 0.06 = 1980

Now if the sale doubles we would have 33000 x 2

= 66000 dollars

then the commission received would be

66000 x 0.06

= $3960

Hence we would say that the commission for the sale of $33000 worth of items at 6 percent is $1980 and if the sale doubles than the commission would be $3960

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Answer:

yes, your answer is correct

Answer:

3 + 7 - (-10)

Step-by-step explanation:

> Option 1)

[tex]3 - 7 + (-10)\\\to 3 - 7 - 10\\\to -14[/tex]

> Option 2)
[tex]3 + 7 - (-10)\\\to 3 + 7 + 10\\\to 20[/tex]

> Option 3)

[tex]3 - 7 - (-10)\\\to 3 - 7 + 10\\\to 6[/tex]

> Option 4)

[tex]3 + 7 + (-10)\\\to 3 + 7 - 10\\\to 0[/tex]

Answer:

 the value of cos(x) is ±√3/2 and tan(x) is ±1/√3.

Step-by-step explanation:

Answer:

200 MPH

Step-by-step explanation:

You basically have to divide 400 miles by two hours, since you need the miles per hour.

*Please mark brainliest answer

Answer:

(22 × 3) - 62

Step-by-step explanation:

(22 × 3)-62

66 - 62

The answer is therefore 4

Answer:

.8976 per yard

Step-by-step explanation:

30-24.67=5.33

13÷5.33= 2.43 yards

Answer: 1

Step-by-step explanation:

The value of angle x in the triangle is 5

The given parameter is represented by the figure

By the external opposite angle of a triangle theorem, we have the following equation

22x + 3 = 6x + 4 + 79

Collect the like terms

So, we have

22x - 6x = 4 + 79 - 3

Evaluate the like terms

So, we have

16x = 80

Divide both sides by 16

So, we have

x = 5

Hence, the value of angle x in the triangle is 5

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