The height of Moyo and that of
Adamu differs by 9. The difference of the squares of their height is 120.
Find their heights.​

Answer:

The answer to number 9 is: 148.16

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Explanation:

There are two approaches.

The slightly longer approach will have us take 6% of 420 to get 0.06*420 = 25.20

So 25.20 is the amount of tax you pay on top of the original $420. The total bill is 420+25.20 = 445.20 dollars

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The shortcut is to multiply 420 by 1.06 to get 420*1.06 = 445.20

The 1.06 multiplier indicates an increase of 6%

We can think of it it as 1.06 = 1 + 0.06 = 100% + 6%

The quadratic sequence answered  this way .

Quadratic sequences are sequences that include an term. They can be identified by the fact that the differences between the terms are not equal, but the second differences between terms are equal.

According to the question

Quadratic sequences are given the next term is :

1> 7 11 17 25  

First difference between terms

11 - 7 = 4

17 - 11 = 6

25 - 17 = 8  

Second difference between terms

6 - 4 = 2

8 - 6 = 2

Therefore, next term : First last difference + Second difference  + Last Term

                                   : 8+2 = 10

                                   : 25 + 10 = 35

2> 6 12 22 36

First difference between terms

12 - 6 = 6

22 - 12 = 10

36 - 22 = 14

Second difference between terms

10 - 6 = 4

14 - 10 = 4

Therefore, 1st next term : First last difference + Second difference  + Last Term

                                     :  14 + 4 = 18

                                     :  36+ 18 = 54

2nd next term : First last difference + Second difference  + Last Term

                                     :  18 + 4 = 22

                                     :  22 + 54 = 76

3rd next term : First last difference + Second difference  + Last Term

                                     :   22 + 4 = 26

                                     :   76 + 26 = 102

4th next term : First last difference + Second difference  + Last Term

                                    :    26 + 4 = 30

                                     :   76 + 26 = 102

3> nth term of a quadratic sequence = [tex]n^{2} - 2n + 8[/tex]

first three terms of this sequence :

1st term of the sequence : n = 1

substituting value of n

[tex]1^{2} - 2 + 8[/tex]

= 7

2nd term of the sequence : n = 2

substituting value of n

[tex]2^{2} - 2*2 + 8[/tex]

= 8

3rd term of the sequence : n = 3

substituting value of n

[tex]3^{2} - 2*3 + 8[/tex]

= 17 - 6

= 11

4> Quadratic sequence has an nth term :  [tex]2n^{2} + 3n -1[/tex]

6th term of the sequence : n = 6

substituting value of n

[tex]2(6)^{2} + 3*6 -1[/tex]

36*2 + 18 -1

= 89

5> Quadratic sequence has an nth term : [tex]n^{2} - 6n + 7[/tex]

term = 23

therefore,

23 = [tex]n^{2} - 6n + 7[/tex]

0 = [tex]n^{2} - 6n - 16[/tex]

solving the equation

[tex]n^{2} - (8-2)n - 16 = 0[/tex]

n(n- 8) + 2 (n - 8) = 0

(n-8) (n+2) = 0

n = 8 , -2

As term can not be negative , so n = 8

Therefore, term 8 of Quadratic sequence  : [tex]n^{2} - 6n + 7[/tex] is 23 .

6> First 5 terms of a quadratic sequence :

4 11 20 31 44

expression for the nth term of this quadratic sequence:

As general form of quadratic sequence is : [tex]an^{2}+bn +c[/tex]

now for n= 1

a + b + c = 4 -------------------(1)

now for n= 2

[tex]a2^{2}+b*2 +c[/tex] = 11

4a + 2b + c = 11 ---------------------------(2)

now for n= 3

[tex]a3^{2}+b*3 +c[/tex] = 20

9a + 3b + c = 20  ----------------------------------(3)

solving equation (1) , (2) & (3)

a = 1 , b = 4 , c = -1

now , substituting the value in general equation

[tex]= n^{2}+4n -1[/tex]

Hence, The nth term of this quadratic sequence [tex]= n^{2}+4n -1[/tex]

7>The first 5 terms of a quadratic sequence : 4 10 18 28 40

the nth term of this quadratic sequence :

As general form of quadratic sequence is : [tex]an^{2}+bn +c[/tex]

now for n= 1

a + b + c = 4 -------------------(1)

now for n= 2

[tex]a2^{2}+b*2 +c[/tex] = 10

4a + 2b + c = 10 ---------------------------(2)

now for n= 3

[tex]a3^{2}+b*3 +c[/tex] = 18

9a + 3b + c = 18  ----------------------------------(3)

solving equation (1) , (2) & (3)

a = -4 , b = 18 , c = -10

now , substituting the value in general equation

[tex]= -4n^{2}+18n -10[/tex]

Hence, The nth term of this quadratic sequence [tex]= -4n^{2}+18n -10[/tex]

8>First 5 terms of a quadratic sequence : 9 17 29 45 65

the nth term of this quadratic sequence :

As general form of quadratic sequence is : [tex]an^{2}+bn +c[/tex]

now for n= 1

a + b + c = 9 -------------------(1)

now for n= 2

[tex]a2^{2}+b*2 +c[/tex] = 17

4a + 2b + c = 17 ---------------------------(2)

now for n= 3

[tex]a3^{2}+b*3 +c[/tex] = 29

9a + 3b + c = 29  ----------------------------------(3)

solving equation (1) , (2) & (3)

a = 2 , b = 2 , c = 5

now , substituting the value in general equation

[tex]= 2n^{2}+2n +5[/tex]

Hence, The nth term of this quadratic sequence [tex]= 2n^{2}+2n +5[/tex]

9> Pattern is not given (incomplete question)

10> The nth term of a sequence is : [tex]n^{2} + 3n[/tex]

Two consecutive terms in the sequence have a difference of 38

The two terms of the sequence  :

N2 - N1 = 38

substituting n as n2 and n1

[tex](N_{2}) ^{2} + 3N_{2} - (N_{1}) ^{2} - 3N_{1}[/tex] = 38

[tex](N_{2}) ^{2} - (N_{1}) ^{2} + 3N_{2} - 3N_{1} = 38[/tex]

[tex](N_{2} - N_{1} ) (N_{2} + N_{1})+ 3(N_{2} - N_{1}) = 38[/tex]

[tex](N_{2} - N_{1} ) [N_{2} + N_{1}+ 3] = 1*38\\\ (as (N_{2} - N_{1} = 1 ) consecutive terms)[/tex]

now,

[tex](N_{2} - N_{1} ) = 1 ,\\\ [N_{2} + N_{1}+ 3] = 38[/tex]

solving both equations

[tex]N_{2} =18\\ N_{1} = 17[/tex]

Hence, two terms of sequence are 18th and 17th the whose difference in 38 .

11> The sequence:  [tex]n^{2} - 4n + 21[/tex]

To proof  the sequence is positive always

As n cannot be negative

let n = 0

substituting the value in equation we get

+ve

As we conclude in equation +ve part is larger than -ve part always ,

so this equation is always be +ve for any value of n .

Hence, The quadratic sequence answered  this way .

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Answer:

He or she got around -32 points per turn.

Step-by-step explanation:

-288 points (the total) divided by the player's 9 turns equals -32. This means that they got negative 32 points on average every round.

Answer:

x=7

Step-by-step explanation:

divide both sides by -8

Answer:

Divide each term by −8 - 8 and simplify.

x = 7x = 7

Answer:

[tex]q= -\frac{23}{8 }[/tex]

Step-by-step explanation:

hope this helps have a good rest of your day :) ❤

the answer is d (x+v). hope this helps :))

Answer:break my kneecaps

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

2*2 + 3*6 + 4*x + 5*8 + 6*1 = 84

4*x = 16

x = 4

Right, 8 is the biggest frequency

Answer:

18c - 30d + 36

Step-by-step explanation:

6(3c - 5d + 6)

6 × 3c = 18c

6 × -5d = -30d

6 × 6 = 36

Answer:

12 + t

Hope This Helped :)

Answer:

sebastian has 12+t trophies.

Answer:

5.0 cm

Step-by-step explanation:

Volume of a cylinder = πr²h

Height,h = 12.75 cm

π = 3.14

Radius,r = r

Volume of the cylinder = 1,000 cm³

Volume of a cylinder = πr²h

1000 = 3.14 × r² × 12.75

1000 = 40.035r²

r² = 1000/40.035

r² = 24.978

r = √24.978

r = 4.99 cm

Approximately 5.0 cm

Answer:

115

Step-by-step explanation:

5\color{red}{x}+\color{blue}{168}=

5x+168=

\,\,\color{purple}{743}

743

-\color{blue}{168}\phantom{=}

−168=

\,\,-\color{blue}{168}

−168

Subtract 168 from both sides

5\color{red}{x}=

5x=

\,\,575

575

\frac{5\color{red}{x}}{5}=

5

5x

​

=

\,\,\frac{575}{5}

5

575

​

Divide both sides by 5

\color{red}{x}=

x=

\,\,\boxed{\color{red}{115}}

115

​

Answer:

1/12

Step-by-step explanation:

3/4 turns to 9/12 of the cake is left before

2/3 turns to 8/12

9/12 minus 8/12 is 1/12

Answer:

900.000 000 + 5050.000 000 + 9.000 + 600 + 20 + 7

=900+5050+9+600+20+7=6586 is standard one

Answer: The weight = 33.75kg

Step-by-step explanation:

Given that  

one cubic metre of ice weight is 80 kg

which is mathematically written as

1m³ of ice = 80 kg

Therefore 75 cm length of  cubical  block of ice =???

First

changing  75 cm to meters, we have  75/100 = 0.75 m

Volume of block = l³= 0.75³ = 0.421875m³

Given that

1m³ = 80kg

0.421875m³=  0.421875 x 80

= 33.75kg

Answer:

Solving two step inequalities

Solving Two Step Linear Inequalities. To solve a two-step inequality, undo the addition or subtraction first, using inverse operations , and then undo the multiplication or division. The inverse operation of addition is subtraction and vice versa.

Answer:

rectangular prism

Step-by-step explanation:

Answer:

36x + 24y = 423 (1)

41x + 38y = 585.75 (2)

x =$5.25

y = $9.75

Step-by-step explanation:

x = the number of student tickets sold

y = the number of adult tickets sold

36x + 24y = 423 (1)

41x + 38y = 585.75 (2)

Multiply (1) by 38 and (2) by 24

1368x + 912y = 16,074 (3)

984x + 912y = 14,058 (4)

Subtract to eliminate y

1,368x - 984x = 16,074 - 14,058

384x = 2,016

x = 2,016/384

x = 5.25

Substitute x = 5.25 into (1) to find y

36x + 24y = 423

36(5.25) + 24y = 423

189 + 24y = 423

24y = 423 - 189

24y = 234

y = 234/24

y = 9.75

x =$5.25

y = $9.75

2.673 × 10^4 is a scientific number, and the number as an ordinary number is 26730

The number in scientific form is given as:

2.673 × 10^4

Express 10^4 as 10000

2.673 × 10^4 = 2.673 × 10000

Evaluate the product

2.673 × 10^4 = 26730

Hence, 2.673 × 10^4 as an ordinary number is 26730

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Answer:

6:8:10

Step-by-step explanation:

Answer:

The answer is n = 17

Step-by-step explanation:

Divide both sides by the numeric factor on the left side, then solve.

Hoped this helped!

brainly, please?

Answer:

b^(-4/5) ...............

Answer: 56%

Step-by-step explanation: To write the fraction 28/50 as a percent, remember that a percent is a ratio that compares a number to 100.

So we need to find a fraction that's equivalent

to 28/50 that has a 100 in the denominator.

To do this, we set up a proportion.

So we have 28/50 = n/100.

To find the value of n, we first find the fraction that

is equivalent to 28/50 that has a denominator of 100.

If we multiply both the numerator and denominator of

28/50 by 2, we can see that 28/50 = 56/100.

So 28/50 is equal to 56/100 or 56%.

Answer:

10%

Step-by-step explanation:

we want to find what % of 34 is 37.40

so, we will use the following equation:

[tex]\frac{part}{whole} = \frac{percent}{100}[/tex]

for this scenario:

part = 37.40

whole = 34

percent = x

now plug in:

[tex]\frac{37.40}{34} = \frac{x}{100}[/tex]                         cross multiply

34x = (37.40)(100)

34x = 3740                      divide both sides by 34

x = 110%

now we know that with tax, we paid 110% of the video game's price

110 - 100 = 10%

so the percent sales tax is 10%

just to check...

34 • 1.10 = $37.40

or

34 • .10 = 3.40

34 + 3.40 = 37.40

Answer:

25

Step-by-step explanation:

30÷6=5

5×5= 25

.........