the interest paid for borrowing qn amount of money for 3yrs at the rate of 4%is n108 find the amount of the money borrowed

We're given [tex]f(x) = 0[/tex] when [tex]x=-2[/tex] and [tex]x=3[/tex], so both [tex]x+2[/tex] and [tex]x-3[/tex] divide [tex]f(x)[/tex]

We're also told [tex]2x^2+3x+2[/tex] divides [tex]f(x)[/tex]. This quadratic does not have roots at -2 or 3, so we can factorize [tex]f(x)[/tex] as

[tex]f(x) = 2 (x + 2) (x - 3) (2x^2 + 3x + 2)[/tex]

where the leading coefficient is 2 because the full expansion should have a leading term of [tex]4x^4[/tex].

Now just expand [tex]f(x)[/tex] :

[tex]f(x) = 2 (x + 2) (x - 3) (2x^2 + 3x + 2)[/tex]

[tex]f(x) = 2 (x^2 - x - 6) (2x^2 + 3x + 2)[/tex]

[tex]f(x) = 2 (2x^4 + x^3 - 13x^2 - 20x - 12)[/tex]

[tex]f(x) = \boxed{4x^4 + 2x^3 - 26x^2 - 40x - 24}[/tex]

Answer:10X^2 +7

Step-by-step explanation:

The average rate of change is 4.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The rate of change in interval [0, 2]

r=[h(2)-h(0)]/2

h(2)=(2)²+2(2)-6

h(2)=4+4-6

h(2)=2

h(0)=(0)²+2(0)-6

h(0)=0+0-6

h(0)=-6

So, r=[h(2)-h(0)]/2

r=[2-(-6)]/2

r=(8)/2

r=4

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Answer:

(f+g)(x)

= |3x+5| + 13

Step-by-step explanation:

(f+g)(x) means

f(x) + g(x)

so you add the functions together.

|3x+5| + 6 + 7

And simplify.

|3x+5| + 13

16.39492

Step-by-step explanation:

First function; Initial value = 250; Decay; Decay rate = 11%

Second function; Initial value = 40; Growth; Decay rate = 11%

How to solve exponential decay functions?

1) The first function is;

40 = 250(0.89)^(x)

y = 250 (initial value)

Decay because 0.89 < 1

Thus;

Decay rate: (1 - 0.89) * 100 = 11%

2) The second function is;

250 = 40(1.11)^(x)

y = 40 (initial value)

Growth because 1.11 > 1 so growth

Growth rate: (1.11 - 1) * 100 = 11%

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The correct answer is option C which is the height of the plant increases by 2 mm for every hour of sunlight it receives.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

Given equation is as follows:-

Here x is the variable which depends on the amount of sunlight and 4 is the original height of the plant so as the sunlight varies the value of x changes and it increases the height of the plant by 2 mm.

The graph of the equation is also attached with the answer. Therefore the correct answer is option C which is the height of the plant increases by 2 mm for every hour of sunlight it receives.

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Answer: Option 1

Step-by-step explanation:

The second and third options do not contain the line y = 2x+6, so they can be eliminated.

Between the first and fourth options, only the first option shows the line y=2x+6 being shaded below, so it is the answer.

The graph of the inequality is graph A

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y ≥ ( 1/5 ) ( 4x - 1 )   be equation (1)

y ≤ 2x + 6   be equation (2)

Now , To graph the system of inequalities, we can start by graphing the boundary lines for each inequality and then determine which region of the coordinate plane satisfies both inequalities.

For the first inequality, y >= (1/5)(4x-1), we can start by graphing the line y = (1/5)(4x-1), which has a y-intercept of -1/5 and a slope of 4/5. We can draw this line as a solid line, since the inequality includes the "or equal to" condition:

And , for the second inequality, y <= 2x+6, we can graph the line y = 2x+6, which has a y-intercept of 6 and a slope of 2. We can also draw this line as a solid line, since the inequality includes the "or equal to" condition:

Hence , the inequality is solved and the solution to the system of inequalities is the shaded region above the line y = (1/5)(4x-1) and below the line y = 2x+6, including the boundary lines.

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Answer:

60

Step-by-step explanation:

1. parallel angle = 85

2. 180 - 85 = 95

3. 180 - (95+25) = 60

The coefficient of the variable Q is 36 , Option A is the correct answer.

The complete question is

The coefficient of 2(3)(6)Q is _____. a.36 b.18 c.12

Coefficient is the constant term written in front of  variable in an expression.

The expression given in the question is

2(3)(6)Q

The coefficient is 2 * 3 * 6 = 36

Therefore , the coefficient of the variable Q is 36 , Option A is the correct answer.

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The resulting equation on using the completing the square is y = (x+5)² - 25

The quadratic equation has a leading degree of 2. Given the equation below;

y = x^2+10x

Add the square of the half of coefficient of x to have;

y = x^2+10x + (10/2)²- (10/2)²
y = x^2 + 10x + 5² - 5²

y = x^2 + 10x  + 25 - 25

y = (x+5)² - 25

Hence the resulting equation on using the completing the square is y = (x+5)² - 25

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Answer:

80x = y

Step-by-step explanation:

Answer:

The answer is 33.31

Step-by-step explanation:

-41/2 ×-13/8

-41×-13 = 533

2×8=16

therefore, 533/16

ans= 33.31

I hope this helps.

1) [tex]\overline{EJ} \parallel \overline{KF}, \overline{JG} \parallel \overline{KH}, \overline{EF} \cong \overline{GH}[/tex] (given)

2) [tex]\overline{FG} \cong \overline{FG}[/tex] (reflexive property)

3) [tex]\overline{EG} \cong \overline{FH}[/tex] (segment addition postulate)

4) [tex]\angle JEF \cong \angle KFG, \angle JGE \cong \angle KHF[/tex] (if two parallel lines are cut by a transversal, the corresponding angles are congruent)

5) [tex]\triangle EJG \cong \triangle F\text{ }KH[/tex] (SAS)

Answer: 68.852459016393 or 68.9 if you round up

Step-by-step explanation:

If you add all the students subjects together you get a total of 41. Then if you add up the total of students who study physics, chemistry, and both you get 20. Then I put those numbers is a percentage calculator then boom you got your answer.

10. The missing conversion is 20.32 inches

11. Total number of red cars is 34

12. Total number of blue cars is 36

13. Total number of silver cars is 70

Ratio is the number of times a quantity is contained more  or less than another in a whole.

Analysis:

10. If 1 inch = 2.54cm

     Then 8 inches = 8 x 2.54cm = 20.32 cm

     First car park: Total number of cars = 60

     ratio of red:blue:silver = 1:2:3

     Total ratio = 1+2+3 = 6

     number of red cars = 1/6 x 60 = 10

     number of blue cars = 2/6 x 60 = 20 cars

     number of silver cars = 3/6 x 60 = 30

   second car park: Total number of cars = 80

    ratio of blue: red: silver = 2:3:5

    total ratio = 2+3+5 = 10

    number of red cars = 3/10 x 80 = 24

    number of blue cars = 2/10 x 80 = 16

    number of silver cars = 5/10 x 80 = 40

11.  Total number of red cars = 10+24 = 34

12.  Total number of blue cars = 20+16 = 36

13.  Total number of silver cars = 30+40 = 70

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Answer:

25.99

Step-by-step explanation:

SOH CAH TOA

(sin = opposite / hypotenuse

cos = adjacent / hypotenuse

tan = opposite / adjacent)

For the angle measurement provided (38 degrees), we know the opposite leg value, and we need to find the hypotenuse

the measurement of sin (opposite / hypotenuse) relates these two measurements

we can plug in our known values into sin:

sin = opposite / hypotenuse

sin (38) = 16 / x

(note: sin 38 = 0.61566147532, which we can round to 0.61566)

0.61566 = 16 / x

· x                   ·x           {multiply both sides by x to get rid of fraction}

0.61566(x) = 16

÷ 0.61566       ÷0.61566     {divide both sides by 0.61566 to isolate 1x}

x = 25.9883702043

{round to nearest hundredth}

x = 25.99

so, the measure of x is 25.99  {rounded to the nearest hundredth}

hope this helps!! have a lovely day :)

Answer:

cosx=adjacent/hypotenuse

triangle angle =180-(90+38)

=52°

cos(52°)=16/x

x=16/cos52

x≈23.373

Answer:

(2.5, - 10 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = (- 16, - 12 ) and (x₂, y₂ ) = (21, - 8 ) , then

midpoint = ( [tex]\frac{-16+21}{2}[/tex] , [tex]\frac{-12-8}{2}[/tex] ) = ( [tex]\frac{5}{2}[/tex], [tex]\frac{-20}{2}[/tex] ) = (2.5, - 10 )

Answer: c - (2 1/2 - 10)

Step-by-step explanation:

Answer:

check image below

Step-by-step explanation:

Answer:

Step-by-step explanation:

We solve an equation for a specific variable by using inverse operations to undo what is done to the variable. The resulting function is evaluated by substituting the given value for the variable.

__

We are given the equation ...

  6x -3y = 2

Solving for y, we get ...

  6x -2 = 3y . . . . . add 3y-2 to both sides

  2x -2/3 = y . . . . . divide by 3

  f(x) = 2x -2/3 . . . . write using functional notation

__

To find f(3), we use x=3 in the function.

  f(3) = 2(3) -2/3 = 6 -2/3

  f(3) = 5 1/3

Answer:

5000

Step-by-step explanation:

1000/2=5000

The bearing from C to A of the given travel path is gotten as; 100.63°

From the bearing image attached, we can use trigonometric ratios to get;

tanx = opp/adj

x = 53 + θ ---------- eqn(1)

opp = 119

adj = 59

Thus;

tan x = 119/59

tan x = 2.0169

x = tan⁻¹(2.0169)

x = 63.63°

From eqn (1), we have;

θ = x - 53

θ = 63.63 - 53

θ = 10.63°

Thus, the bearing from C to A = 90 + 10.63 = 100.63°

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The results that could be displayed are 3.9 ×10⁻⁶, 3.9 E-6 OR 0.0000039

From the question, we are to determine the results that could be displayed on the calculator screen

The given expression is

(2.6 × 10⁻²)(1.5 × 10⁻⁴)

= 2.6 × 1.5 × 10⁻²× 10⁻⁴

= 3.9 ×10⁻²⁺⁻⁴

= 3.9 ×10⁻²⁻⁴

= 3.9 ×10⁻⁶

= 3.9 E-6 OR 0.0000039

Hence, the results that could be displayed are 3.9 ×10⁻⁶, 3.9 E-6 OR 0.0000039

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Step-by-step explanation:

Hi There! Let me help you :)

Known

[tex] = \frac{ {6}^{ - 10} }{ {6}^{ - 4} } [/tex]

[tex] \: [/tex]

Asked

Simplify form.

[tex] \: [/tex]

Answer

[tex] = \frac{ {6}^{ - 10} }{ {6}^{ - 4} } [/tex]

[tex] = {6}^{ - 10 - ( - 4)} [/tex]

[tex] = {6}^{ - 6} [/tex]

[tex] = {6}^{ - 6} \: \text{or} \: \frac{1}{ {6}^{6} } [/tex]

There are 2 answers, it's A and C.

Answer:

Two angles and a side

Step-by-step explanation:

In order to prove triangles congruent, you'd have to either have an angle, angle, and then a side in that exact order for AAS or you can have two angles and a side in the middle of them for ASA.

The probability of rolling an even number on a number cube and spinning red or yellow on the spinner will be 1/4 or 0.25.

The complete question is given below.

I rolled a number cube and spun a spinner. The number cube is numbered 1 to 6. The spinner has 4 equal parts: red, blue, yellow, and green. What is the probability of rolling an even number on a number cube and spinning red or yellow on the spinner?

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Then the probability of rolling an even number on a number cube and spinning red or yellow on the spinner will be

The probability of getting even number on dice will be

Total event = 6 {1, 2, 3, 4, 5, 6}

Favorable events = 3 {2, 4, 6}

P₁ = 3/6

P₁ = 1/2

The probability of getting red or yellow will be

Total event = 4 {red, blue, yellow, green}

Favorable events = 2 {red, yellow}

P₂ = 2/4

P₂ = 1/2

Then the both event occur simultaneously, then we have

P = P₁ × P₂

P = 1/2 × 1/2

P = 1/4

P = 0.25

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The number of weeks by which the students in both classes will know how to write the same number of letters will be 4 weeks.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive.

Mr. McMillan has already taught his class 8 letters.

The students in Ms. Burke's class, who started the unit later, currently know how to write 12 letters.

Mr. McMillan plans to teach his class 4 new letters per week.

Ms. Burke intends to cover 3 new letters per week.

Eventually, the students in both classes will know how to write the same number of letters.

Then the number of weeks by which the students in both classes will know how to write the same number of letters will be

Let x be the number of the weeks and y be the total number of the letters.

Then the equation will be

y = 4x + 8 …1

y = 3x + 12 …2

Then by solving the equations 1 and 2, we have

x = 4 and y = 24

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Answer:

the answer pf x its 15

by adding the middle sum to 90 degreess and by dividing 6 and 90 you get 15

Answer:

5.9

Step-by-step explanation:

The distance between a point A and a point B is A-B.  (4.5) - (-1.4) is the same as 4.5 + 1.4 so your answer is 5.9

Answer:

Step-by-steDistance between

(

−

4.5

,

−

4.5

)

and  

(

3.5

,

3.5

)

 is

8

√

2p explanation:

Hence distance between

(

−

4.5

,

−

4.5

)

and

(

3.5

,

3.5

)

is given by

√

(

3.5

−

(

−

4.5

)

)

2

+

(

3.5

−

(

−

4.5

)

)

2

=

√

8

2

+

8

2

=

√

64

+

64

=

√

128

=

√

8

2

×

2

=

8

√

2

[tex](a+b)(a-b) = a^2 - ab + ba - b^2 = a^2 - b^2[/tex]

Since the middle terms cancel each other out, what is left is the difference of two squares.

In your example (x+6)(x-6) = x² -36