Given 4 1/10 -3 5/12 determine the product

Step-by-step explanation:

loga(x) calculates simply the exponent of a needed to get x as result.

so, 5 "to the power of the exponent of 5 needed to get 7" is 7 (we give 5 the exponent that it needs to create 7, so it creates 7).

the same thing with 2, where we give 2 the exponent it needs to create 1/49. so, it creates 1/49.

we get therefore

7 × 1/49 = 7/49 = 1/7

The recursive sequence that defines 5, -8, 5, is given by:

[tex]a_n = -a_{n-1} - 3[/tex]

In which the first term is of [tex]a_1 = 5[/tex].

A recursive sequence, in general terms, can be defined as follows:

[tex]a_n = f(a_{n - 1))[/tex]

In which the first term [tex]a_1[/tex] is given.

This rule means that the nth term of the sequence is a function depending on the previous term, the (n-1)th term of the function.

In the context of this problem, the sequence is given as follows:

5, -8, 5.

From the first to the second term, the number changed the signal and was subtracted by 3, and the same is true for the second to third term, as follows:

Then the recursive rule for the sequence is given as follows:

[tex]a_n = -a_{n-1} - 3[/tex]

With first term of [tex]a_1 = 5[/tex].

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Answer:

1≤x≤|R+

Step-by-step explanation:

since range is from the y axis

the starting point is 1 UpTo positive real numbers and it doesn't include 0

After evaluating the given fraction, the resultant answer is (C) 1¼.

So, 8 ÷ 6⅖:

Now, evaluate as follows

Which can also be written as 1¼.

Therefore, after evaluating the given fraction, the resultant answer is (C) 1¼.

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Given,

To find g(f(-2)). we first find the value of f(-2).

The value of f(-2) is,

So now to find the value of g(f(-2)),

So the value of g(28) is,

So the value of g(f(-2)) is 51.

Answer:

(x^3 + 3x^2 - 2x + 7)/x- 2

Expand the numerator in the above expression

(x^3 + 5x^2 - 2x^2 + 8x - 10x - 16 + 23)/(x - 2)

Rearrange the terms of the numerator in the above expression

(x^3 + 5x^2 + 8x - 2x^2 - 10x - 16 + 23)/(x- 2)

Factorize the numerator in the above expression

[x(x^2 + 5x + 8) - 2(x^2 + 5x + 8) + 23]/(x - 2)

Factor out x^2 + 5x + 8

[(x -2)(x^2 + 5x + 8) + 23]/(x - 2)

Split the fractions

(x -2)(x^2 + 5x + 8)/(x - 2) + 23/(x - 2)

Divide the common factors

(x^2 + 5x + 8) + 23/(x - 2) hope this help btw your welcome

Answer:

The answer is really option A. x^2 - x +2-5/x-1

Step-by-step explanation:

I just took the test and got it right :)

The length of the pole is 19.15 feet.

The angle of elevation is the angle created when an observer looks at an object placed above its height in relation to the eye level or the horizontal line. An angle of elevation is, for example, the angle created between the line of sight and the horizontal line when a man on Earth observes the Sun.

Given:

Angle made by straight road = 15°

Angle of elevation of the sun = 57°

Length of the shadow = 75 feet

∠ACB = 90° - 57° = 33°

∠CAB = 57° - 15° = 42°

Using Sine Law to find BC i.e.length of the pole.

[tex]\frac{BC}{sin A} = \frac{AB}{sin C}[/tex]

[tex]\frac{BC}{sin 42} = \frac{75}{sin 33}[/tex]

[tex]BC= \frac{75sin 42}{sin 33}[/tex]

BC ≅ 19.15 feet (to the nearest hundredth.)

Hence, the approximate length of the pole is 19.15 feet.

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Because the scaling factor is a whole number, which is 3, the enlargement of the dashed triangle is a dilatation.

Recall:

Thus:

For the dashed triangle, measure the separation between the points (2, -2) and (0, -2).

Using the coordinates (6, -6) and (0, -6) for the solid triangle, calculate the equivalent distance:

Scale factor = 6/2 = 3

The dilation is an enlargement because the scale factor is a whole number.

In conclusion, the enlarged dashed triangle indicates a dilatation because the scale factor, which is 3, is a whole number.

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Answer:

Step-by-step explanation:

[tex]\displaystyle\\A=\left[\begin{array}{ccc}-1&6\\-2&2\\4&9\\-5&-11\end{array}\right] \ \ \ \ \ \ \ \ \ B=\left[\begin{array}{ccc}-4&-1\\-8&8\\2&-7\\-6&5\end{array}\right] \\\\A+B=B+A\ (commutativity)\\\\\Rightarrow B+A=\left[\begin{array}{ccc}-4+(-1)&-1+6\\-8+(-2)&8+2\\2+4&-7+9\\-6+(-5)&5+(-11)\end{array}\right] \\\\\\ \Rightarrow B+A=\left[\begin{array}{ccc}-5&5\\-10&10\\6&2\\-11&-6\end{array}\right][/tex]

123°

180°-57°=<6=123°

Two pools are being filled with water. To start, the first pool had 728 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 23 liters per minute. Water is being added to the second pool at a rate of 37 liters per minute.

Let x be the number of minutes water has been added.

(a)

For each pool, write an expression for the amount of water in the pool after x minutes.

Amount of water in the first pool (in liters) = 23x + 728

Amount of water in the second pool (in liters) = 37x

(b)

Write an equation to show when the two pools would have the same amount of water.

this is when:

23x + 728 = 37x

subtract 23x from both sides:

23x + 728 - 23x = 37x - 23x

728 = 14x

divide both sides by 14:

728/14 = 14x/14

x = 52

So, pools are equal after 52 minutes.

Answer:

u = 115

Step-by-step explanation:

35 = u/5 + 12

35 - 12 = u/5

(35 - 12) * 5 = u

u = (35 - 12) * 5

u = 115

Answer:

x = 9

Step-by-step explanation:

given g(x) = - x and g(x) = - 9 , the equate right sides

- x = - 9 ( multiply both sides by - 1 )

x = 9

Answer: Quotient 142

Remainder 12

Step-by-step explanation:

The quotient is 142 and  the remainder is 12.

The long division method is as follows :

                                             [tex]142[/tex]

                                      [tex]39\sqrt{5550}[/tex]  

                                          -39                        

                                             165                       (3rd 5 taken down )

                                           -156    

                                                 90                     ( 0 taken down )

                                                -78  

                                                  12

step 1 : take the first two digits (55) of the divident , now multiply 39 with such a number that the product of those two must not go above 55 but should be closest to it.

step 2 : write the number on top and subtract the answer from 55.

step 3 :  Now bring down the third 5 and write it after the answer of the subtraction. So the number becomes 165.

step 4 : Again multiply 39 with such a number that the product of those two must not go above 165 but should be closest to it.

step 5 : write that number on top after the previous number and subtract the answer from 165.

step 6 : Now bring down the 0 and write it after the answer of the subtraction. So the number becomes 90.

step 7 : Again multiply 39 with such a number that the product of those two must not go above 90 but should be closest to it.

step 8 : write that number on top after the previous number and subtract the answer from 90.

We have to repeat these steps until all the digits from the divident are used and the remainder comes out to less than the divisor.

Here all the digits of divident are used and the remainder (12) is also less than the divisor (39), so we stopped.

Hence the quotient is 142 and the remainder is 12.

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A counterexample to show that 2a^2 = 72 where a = 6 is that a = -6 will still arrive at 72

This is a term that counters a statement. we can therefore say that counterexample is one that proves a statement to be false.

given data

2a² = 72

Conjecture: a = 6

The counterexample is a = -6

substituting a = -6 into the given equation

= 2a²

= 2 * ( -6 )^2

= 2 * ( 36 )

= 72

Since a = -6 gave same answer of 72 as a = 6 then a = -6 is the counterexample

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the ratio of action movies to all movies is 2: 5 .

In mathematics, a ratio illustrates how frequently one number appears in another. On a fruit tray, the ratio would be eight to six if there were eight oranges and six lemons.

Let Brayden has x number of  movies in total.

Total number of action movies in  his collection = 40% of x = 0.4 x

Other movies = 1 - 0.4x = 0.6 x

Ratio of action movies to all movies = 0.4x : x = 2: 5

Therefore the ratio of action movies to all movies is 2: 5 .

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Step-by-step explanation:

[tex]3 {}^{2} (189 \div 9) - 30 \\ 9 \times 189 \div 9 - 30 \\ 189 \div 1 - 30 \div 1 \\ 189 - 30 \div 1 \\ = 159[/tex]

according to bodmas

Answer:

159

Step-by-step explanation:

Using BODMAS - Bracket Of Division Multiplication Addition Subtraction

Step 1: Bracket

189/9=21

Hence [3^2 x (21)]-30

Step 2:

3^2= 9

Step 3: Calculate within parentheses [9* 21] :    189

9*21=189

Step 4: Open bracket

[189]-30=159

By 6.2 miles per hour, Sheri commutes more quickly.

We are given that,

John travels to work = 20km/hr

Sheri travels to work = 500m/min converting this into km/hr we get ,

1.61km/hr or 1 mile

John travels to work at the following rate:

[tex]\frac{20 km}{1 hr} * \frac{1 mile}{1.61km} = 12.42 miles/hr[/tex]

Sheri travels work at the following rate:

[tex]\frac{500m}{1min} *\frac{1km}{1000 m}*\frac{1mile}{1.61km}*\frac{60min}{1hr}=18.63 miles/hr[/tex]

Computing the difference between the two,

18.63 miles/hr - 12.42 miles/hr = 6.21 miles/ hr ≈ 6.2 miles/ hr

thus, by 6.2 miles per hour, Sheri commutes more quickly.

What are conversions in maths?

An amount that is multiplied or divided between one set of units and another is known as a conversion factor. In the event that a conversion is necessary, it must be carried out with the proper conversion factor to produce an equivalent value. For instance, when translating between inches and feet, 12 inches equals one foot.

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Answer:

1/2

Step-by-step explanation:

We know that each team has the following:

36Players + 3Coaches + ?Assistants = Sports League

We know that the ratio of assistants to players is 1/6, rewrite the equation accordingly:

36Players + 3Coaches + 6Assitants = Sports League

Now find the ratio of coaches to assistants:

3Coaches / 6Assistants = 1/2

The range of the function in this situation as required in the task content is; Choice D; 0 ≤ y ≤ 3.

It follows from the task content that the range of the function described by the situation is to be determined.

The set of all possible output values of a function, otherwise termed the dependent variable, y is called the Range.

It follows that since the distance he has remaining, y is a function of how long he has been riding the bike, x and it's said that; the boy lives 3 miles from the library; the range of the function described is; Choice D ; 0 ≤ y ≤ 3.

Please Note: The term, domain encompasses the set of all possible input values, otherwise termed the independent variable, x.

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Answer:

72 and 12

Step-by-step explanation:

substitute x = 3 into the expressions

2(x + 3)²

= 2(3 + 3)²

= 2(6)²

= 2 × 36

= 72

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

3(x - 1)²

= 3(3 - 1)²

= 3(2)²

= 3 × 4

= 12

Answer:

61608 i believe

Step-by-step explanation:

2% of 60400= 1208

60400+1208=61608

The formula for time, t = d/s which means time exists equivalent to distance divided by speed.

The times taken to travel 441 miles apart exists 8.25 hours

Time can be defined as the dimension based on which the evolution of any system takes place. It can be measured in terms of seconds, minutes, hours, days, weeks, months, and years.

The formula for time, t = d/s which means time exists equivalent to distance divided by speed.

Given: Train running in the opposite direction

Speed of one train (S1) = 65 mph

Speed of one train (S2)= 63 mph

Distance to be covered = 1056 miles

Train exists running in the opposite direction, so their relative speed = (S1 + S2)

Relative speed = (65 + 63) = 128 mph

Now, time is taken to travel 1056 miles apart

Time = Distance / relative speed

Time = 1056/128 = 8.25 hours

Therefore, the times taken to travel 441 miles apart exists 8.25 hours

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The total number of engineering students is 176 approximately among the 750 students enrolled in the college by using the proportionate formula.

It is mentioned here that a college has 19 students of engineering for every 81 students who got enrolled.

Therefore the ratio of engineering students to total number of students is as follows:

No. of engineering students = 19

Total number of students = 81

Ratio = [tex]\frac{19}{81}[/tex]

Now if the total number of students that the college has is 750 then the number of engineering students can be found by using the proportionate formula as the ratio of the engineering to the total students will remain same.

Total number of students = 750

Let the number of engineering students be y

Ratio = [tex]\frac{y}{750}[/tex]

Comparing it with the above ratio and using the proportionate formula,

[tex]\frac{19}{81} = \frac{y}{750}[/tex]

⇒ y = [tex]\frac{19*750}{81}[/tex]

⇒ y = 175.925

So approximately 176 were the engineering students among 750 students enrolled.

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The robot will take 0.15 hours to complete one task.

What is the unitary method of problem solving?
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. In the unitary method, the value of a unit quantity is determined before the values of other units are determined. Direct variation and inverse variation are its two different forms of variations. When there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other. If we increase one quantity in inverse variation, the value of another quantity will drop.

Given, time taken by robot to complete five tasks = 0.75 hours
Thus, time taken by robot to complete one task = (0.75/5) = 0.15 hours
Therefore, the robot will take 0.15 hours to complete one task.

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The scientific notation is 6.3 × [tex]10^{-3}[/tex]

The expression is ( 7 ×[tex]10^{-2}[/tex] )( 9 × [tex]10^{-2}[/tex])

Calculate the product or quotient

=63 × ([tex]10^{-2}[/tex] ×[tex]10^{-2}[/tex])

Simplify using the exponent rule with the same base [tex]a^{n} . a^{m}[/tex] = [tex]a^{n + m}[/tex]

=63 × [tex]10^{-2-2}[/tex]

=63 ×[tex]10^{-4}[/tex]

= 6.3 × [tex]10^{-3}[/tex]

Therefore the scientific notation is 6.3 ×[tex]10^{-3}[/tex].

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Answer:

10x^2 + 47.2x - 84.18

Step-by-step explanation:

You distribute both terms in the first set of parentheses (5x-6.9) to the terms in the second set (2x+12.2) So when you're doing it 5x gets multiplied by 2x and 12.2 and -6.9 gets multiplied by 2x and 12.2. Then you simplify as much as possible