Expand each logarithm.
log a²

Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.. The inequality that represents the given situation is 13x - 9 > 4.5x + 8

Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

From the question, we are to determine the inequality that represents the given situation

From the given information, we have that

The length of the laptop is given by 13x - 9 units

and The width of the laptop is given by 4.5x + 8 units

If the length is greater than the width, then we can write that

13x -9 > 4.5x + 8

Hence, the inequality that represents the given situation is 13x - 9 > 4.5x + 8

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If a scientist has 315 cells in a container and she expects the number of cells to triple in one day then the number of cells the scientist will have after one day is equal to 945.

The number of cells the scientist will have after one day can be figured out using multiplication. Multiplication is one of the four parts of arithmetic. It can be considered as the opposite of division and can be defined as the repeated addition of the same number or groups of equal sizes.

The number of cells the scientist will have after one day can be calculated as follows;

Number of cells = 315

As it is expected to triple, which means that it is expected to increase three times in amount.

Therefore;

3 × number of cells in the container

3 × 315 = 945

Hence, the number of cells the scientist will have after one day is calculated to be 945.

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Answer:

14y - 6

Step-by-step explanation:

given factored expression

2(7y - 3) ← multiply each term in the parenthesis by 2 to give original

= 14y - 6 ← expression before being factorised

Answer:

45%

Step-by-step explanation:

15 x 3 = 45

The depth of the box once the sand is poured into it is 2 feet

Volume of the box = length × height × width

20 = 5 × 2 × x

20 = 10x

x = 20/10

x = 2 feet

Therefore, the depth of the box once the sand is poured into it is 2 feet

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Using multiple line and angle theorems, the values of each of the 14 angles are given.

Using the geometry theorems :

1.)

∠2 is a right angle = 90°

2.)

∠1 + ∠2 + ∠3 = 180° (sum of angle on a straight line)

90 + ∠1 + 54° = 180°

∠1 = (180 - 144) = 36°

(∠2 and ∠5) ; (∠3 and ∠6) ; (∠1 and ∠4) are vertically opposite ;

Hence,

∠4 = 36°

∠5 = 90°

∠6 = 54°

∠3 = ∠8 = 54° (corresponding angles)

∠9 + ∠8 = 180° (sum of angle on a straight line)

∠9 = (180 - 54) =126°

∠7 = ∠9 = 126° (vertically opposite angles)

∠8 = ∠10 = 54° (vertically opposite angles)

∠4 = ∠13 = 36° (corresponding angles )

∠12 + ∠13 = 180° (sum of angle on a straight line)

∠12 = (180 - 36) =126°

∠11 = ∠13 = 36° (vertically opposite angles)

∠12 = ∠14 = 126° (vertically opposite angles)

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Answer:

2 ≤ x ≤ 3 where x represents the number of hours walking

Step-by-step explanation:

The distance to walk in miles can be modeled as the following inequality

Let x represent the number of hours Blake will be walking.

To cover 10 mi at 5 mph, Blake will take 10/5 = 2 hours
To cover 15 mi at 5 mph, Blake will take 15 /5 = 3 hours

The actual number of hours walked must lie within these limits

So

2 ≤ x ≤ 3 where x represents the number of hours walking

Here we will show you how to calculate the angle in degrees made by the hour hand and minute hand on a 12-hour clock at 11:12.

Before we continue, note that a clock is shaped like a circle and is composed of 360 degrees.

There are 60 minutes in an hour, and 360 degrees divided by 60 minutes is 6. Therefore, the minute hand moves 6 degrees per minute.

As you can see, the hour hand and minute hand showing 11:12 on the clock make an angle. We used the hands to make the pie chart below so it is easier to visualize what we are calculating.

The hour hand and minute hand on a clock showing 11:12 actually make two angles: The hour hand to the minute hand is outlined in blue, and the minute hand to the hour hand is outlined in red.

360 - (336 - 72) = 96 degrees

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Number of cats cannot be a decimal value, therefore, Total number of stray cats in the city today are 2686, rounded off from 2686.29.

As per the question statement, a certain city had 300 stray cats in 1999, and the number of cats are growing by 10% every year since then.

We are required to calculate the total number of stray cats in the city today.

To do so, we will need to know the formula of compound interest which goes as [tex]A=[P*(1+\frac{R}{100})^n][/tex]

Where, A = Final Amount i.e., (Principle + Interest).

P = Principle on which Interest in compounded

R = Rate of Compound Interest per annum

n = Time period of interest.

Here, (P = 300), (R = 10) and [n = (2022-1999) = 23]

Using these values of P, R and n in the above-mentioned formula to calculate the amount in the case of compound interest, we get,

Total number of stray cats in the city today (T) = [tex][300*(1+\frac{10}{100})^{23} ][/tex]

[tex]or, T=[300*(\frac{100+10}{100})^{23} ]\\or, T=[300*(\frac{110}{100})^{23}]\\or, T=[300*(\frac{11}{10})^{23}]\\or, T=2686.29[/tex]

Since, number of cats cannot be a decimal value, therefore, Total number of stray cats in the city today are 2686, rounded off from 2686.29.

Compound Interest: Compound interest means that the interest increases exponentially, rather than increasing linearly over time, or in simpler words, it is a continuous interest on principal plus interest.

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After solving, the factors of equation 3x²+10x+8 are:

So,

Given the equation: 3x²+10x+8

Then,

Factors are: (x+2) and (3x+4)

Therefore, after solving, the factors of equation 3x²+10x+8 are:

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Step-by-step explanation:

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The amount spent on calculators is $310 which is option (b) .

It is given that half people ordered $29.95 calculator which means that 5 people have ordered $29.95 per calculator then , amount is given by

    (number of people ) × cost per calculator = total amount spent

       [tex]5\times29.95=\$149.75[/tex]

It is given that least expensive calculator was $19.95 and the most expensive calculator was $39.95.

Mean will be [tex]=\frac{least\ + \ most}{2}[/tex]

                      [tex]=\frac{19.95+39.95}{2} \\\\=\frac{59.9}{2} \\\\=29.95[/tex]

so the other 5 people have spent an average of amount [tex]=5\times29.95[/tex]

                                                                                 [tex]=\$149.75[/tex]

Total amount spent on calculators will be [tex]=149.75+149.75=\$299.5[/tex]

which is approximately equal to $310 which is option (b) .

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Using the Pythagorean Theorem, we have that the distance from home plate to second base is about 127 feet.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared of the triangle, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

The distance between each consecutive base is of 90 feet, hence the distance from home plate to 2nd base is the hypotenuse of a right triangle in which the legs are of 90 feet, being the distances from home plate to 1st base and 1st base to 2nd base.

Then:

h² = 90² + 90²

h = sqrt(90² + 90²)

h = 127 feet.

The distance from home plate to second base is about 127 feet.

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The number of days for which the costs are the same is 6 days.

Let the number of days be represented by d.

A rental car agency charges a flat fee of $131.00 plus $49.00 per day to rent a certain car. This will be

131 + 49d

Another agency charges a fee of $77.00 plus $58.00 per day to rent the same car. This will be

77 + 58d

Equate both equations

131 + 49d = 77 + 58d

Collect like terms

58d - 49d = 131 - 77

9d = 54

Divide

d = 54 / 9

d = 6 days.

Therefore, the number of days for which the costs are the same is 6 days.

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The steps to express a fraction as a decimal is the reverse of the steps required to write a decimal as a fraction, with the resulting fraction being simplified further as follows;

To write a decimal as a fraction gives a fraction having all the digits of the decimal up to the last nonzero digit in the numerator, and 10 raised to the power, the number of places to the decimal point is moved up to the right of the last non zero digit, and vice versa.

Starting from question 2, we have;

2. 0.3 is ten times as great as 0.03, given that we have;

10 × 0.03 = 0.3

0.003 is 1/10 of 0.03, given that we have;

1/10 × 0.03 = 0.003

Expressing the decimals as fractions gives;

3. 0.001 = 1/1000

4. 0.05 = 5/100 = 1/20

5. 0.512 = 512/1000 = 64/125

6. 0.309 = 309/1000

Writing the fractions as decimals gives;

7. 2/1,000 = 0.002

8. 34/100 = 0.34

9. 508/1000 = 0.508

10. 99/1,000 = 0.099

Independent practice

Writing the decimals as fractions

11. 0.007 = 7/1,000

12. 0.08 = 8/100 = 2/25

13. 0.065 = 65/1,000 = 13/200

14. 0.9 = 9/10

15. 0.832 = 832/1,000 = 104/125

16. 0.203 = 203/1,000

17. 0.78 = 78/100 = 39/50

18. 0.999 = 999/1,000

19. 434/1,000 = 0.434

20. 3/10 = 0.3

21. 873/1,000 = 0.873

22. 17/1,000 = 0.17

23. 309/1,000 = 0.309

24. 5/1,000 = 0.005

25. 6/100 = 0.06

26. 999/1,000 = 0.999

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Answer:

Point G

Step-by-step explanation:

It is point G because since you mirrored it and flipped it, you need to flip figure one and if you move it to where figure two is, in the same place, the new point R is where point G is, so G corresponds to R

P.S. someone else aske the same question

Answer:

-45.5

Step-by-step explanation:

8x+4 -10x +5 = 100

x = - 91/2

Answer:

Step-by-step explanation:

Answer:

3 hours and 25 minutes

Step-by-step explanation:

Since these times are both AM, you can just change the form to 8.35 and 5.50 and subtract.

8.35- 5.50 = 2.85

And since there are max of 60 minutes in an hour, you take the 60 minutes from the 85 minutes, and you're left with 3 hours and 25 minutes.

Hope this helped :D

Answer:

i think 165 minutes which would be 2.75 converted in hours

Step-by-step explanation:

Answer:

might be C

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

2(4)=8, and a negative number times a positive number results in a negative number.

Answer:

  (3/2, 9/2)

Step-by-step explanation:

You want the midpoint of the line segment with end points R(4, 3) and S(-1, 6).

The coordinates of the midpoint will be the average of the end point coordinates:

  M = (R +S)/2

  M = ((4, 3) +(-1, 6))/2 = (4 -1, 3 +6)/2 = (3, 9)/2

  M = (3/2, 9/2) . . . . coordinates of the midpoint

Answer:

(2)

15x8.66666667=130.00000005

Step-by-step explanation:

to get the are in square feet you have to Length (in feet) x width (in feet) = area in sq. ft.

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{9 + x}{15}=\cfrac{15}{9}\implies \cfrac{9 + x}{15}=\cfrac{5}{3}\implies 27+3x=75 \\\\\\ 3x=48\implies x=\cfrac{48}{3}\implies \boxed{x=16}[/tex]

The outcome of -2 g(x) + f(x) is 4 x -2  x ² and the domain is  [ 0 , 2 ] .

Given,

f (x) = x - 2 and g (x) = x² - 3 x + 2

The question states to find the summation of the function f, that is, f (x) = x - 2, and function g, that is, g (x) =  x² - 3 x + 2

Performing the addition operation on these functions is just like simple addition.

This means that when we add the two functions f (x) and g (x), we get

f (x) + g (x) = x - 2 + x² - 3 x + 2

=> f (x) + g (x) = x ² - 2 x

This implies that the summation or addition of the two functions f (x) and g (x) gives x ² - 2 x

needed result = -2 g(x) + f(x) = -2 ( x² - 2 x ) = -2  x ² + 4x = 4 x -2  x ²

To find domain,

y = 4 x -2  x²

=> 4x -2 x²  ≥   0

=> 2 x * ( 2 - x )  ≥   0

=> 2 x ≥ 0 and 2 - x  ≥   0

=>x  ≤ 2 and  x ≥   0

=> the final Domain = [ 0 , 2 ]

Therefore, we get the result of -2 g(x) + f(x) as 4x -2  x ² and the domain as  [ 0 , 2 ] .

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to get the equation of any straight line, we simply need two points off of it, let's use those two from the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-6}{0 +4} \implies \cfrac{ -6 }{ 4 }\implies -\cfrac{3}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{3}{2}}(x-\stackrel{x_1}{(-4)}) \implies y -3=-\cfrac{3}{2} (x +4) \\\\\\ y-3=-\cfrac{3}{2}x-6\implies {\LARGE \begin{array}{llll} y=-\cfrac{3}{2}x-3 \end{array}}[/tex]

Answer:

1. 600000+90000+ 6000

2. 6000+ 300

3. 6x+ 33x

4.

5.

6.

7. 75

8. 21

9. -5x

10. 3x

11. 10 km

12. 4.6

13.

14.

15. $3.5

16.$1.5

17. 4x-1=3x-5

+1 +1

4x= 3x-4

-3x -3x

x=-4

18. 3x-3=27-2x

+3 +3

3x= 30-2x

+2x +2z

5x= 30

/5 /5

x= 6

19. 0.5

20. 1

Answer:  X = 4

Step-by-step explanation: