6) Four pieces measuring 29.cm, 19.62cm, 32.49cm and 24.74cm are cut from a board that is 200cm long. Allowing 1cm for waste in cutting, what is the length of the remaining piece?

Answer:

0.01775

Step-by-step explanation:

The prove that the equation can be verified using the laws of exponents.

It follows from the task content that the equation given is; 2^(2x+4)= 16 • 2^(2x).

It follows from the laws of indices ; particularly, the product of same base numbers.

The evaluation is therefore as follows;

2^(2x+4)= 16 • 2^(2x)

2^(2x) • 2⁴ = 16 • 2^(2x)

2^(2x) • 16 = 16 • 2^(2x)

Hence, since LHS = RHS, it follows that the expression is mathematically correct.

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Answer:

Step-by-step explanation:4

Step-by-step explanation:

We do the ones that are in parenthesis first. Find out the exponent. 2 to the power of two is 4. 3-4=-1. Then we would add 5. 5+-1 would result of 4.

The mixture requires 200 ounces of 40% alloy.

A mixture is a physical combination of two or more substances that retain their identities and are blended as solutions, suspensions, or colloids.

x = amount of 40% copper

400 = amount of 70% copper

x + 400 = total amount of copper = amount of 60% copper

Set a correctly weighted mixture of x and 300 equal to the a weighted (x+300), in which the weights are decimal percentages;

0.4x + 0.7(400) = 0.6(x + 400)

Solve for x:

0.4x + 280 = 0.6x + 240

0.2x = 40

x = 200

x = 200 ounces of 40% copper.

Therefore, the amount of 40% alloy needed for the mixture is 200 ounces.

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The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65

A = -6 and B = 65

From the question, we are to express the given expression in the form (x + A)^2+B by completing the square

The given expression is

x² -12x + 101

Using the completing the square method

x² -12x + 101

Divide the coefficient of x by 2 and then square it

The coefficient of x is -12

Dividing by 2, we get

-12/2 = -6

Squaring

(-6)²

Now, add and subtract this value from the expression

x² -12x + (-6)² + 101 - (-6)²

Then, we can write that

(x - 6)² + 101 - (-6)²

(x - 6)² + 101 - 36

(x - 6)² + 65

Thus,

The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65

By comparison,

A = -6

and

B = 65

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Answer:

  64

Step-by-step explanation:

You have the recursive formula f(1)=1; f(n)=4f(n-1) and you want f(4).

The value of f(4) can be found a couple of ways. Perhaps the simplest is to compute the first 4 terms of the sequence using the recursive formula.

  f(1) = 1

  f(2) = 4·1 = 4

  f(3) = 4·4 = 16

  f(4) = 4·16 = 64

The value of f(4) is 64.

The multiplying factor of 4 on the previous term tells you this is a geometric sequence with a common ratio of 4. The explicit formula is then ...

  f(n) = f(1)·r^(n-1) . . . . . n-th term of sequence with common ratio r

  f(n) = 1·4^(n-1) . . . . . . formula for f(1)=1 and r=4

For n=4, this is ...

  f(4) = 1·4^(4-1) = 4^3

  f(4) = 64

Answer: -2.25

Step-by-step explanation:-2.25 because it is closer to 0

Answer:  1

Step-by-step explanation:

here only taking the power of x in account

we have

[tex]\frac{x}{y} + \frac{y}{x}-\frac{x}{y} - \frac{y}{x}[/tex]

=0

since  [tex]x^{0}[/tex] =1

so solution is 1

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The final answer for 2211₃ to convert into base 10 is 76₁₀.

Given 2211₃

Expand the number as below

2211₃ = 2 * 3³ + 2 * 3² + 1 * 3¹ + 1 * 3⁰

To convert base 3 to base 10 we need to expand form numbers as

2211₃ = 2 * 3³ + 2 * 3² + 1 * 3¹ + 1 * 3⁰

         = 2 * 27 + 2 * 9 + 1 * 3 + 1 * 1

         = 54 + 18 + 9 + 1

         = 76₁₀

Therefore, the Correct answer for 2211₃ to convert into base 10 is 76₁₀

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After solving for x in the constructed equation, 97100 bushels were harvested last year.

What is an equation?

Constructing equation to determine no. of bushels.

Bales from the previous year = x + 0.45 x

= 140795 1.45 x

= 140795 X

= 97100 bales

After solving for x in the constructed equation, 97100 bushels were harvested last year.

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Answer:97100

Step-by-step explanation:

Answer:  15 + |−6| = 21 steps

Its stated that Joy walked 15 steps forward, meaning it would be a positive value. Shaunte walking backwards would give a negative value.

Answer:

3452

Step-by-step explanation:

Simplify the expression, and add/muiltiply where necessary.

Answer: B

Step-by-step explanation:

∑ Hey, shadowwolf9764 ⊃

Answer:

1.52545155993

Round if needed: 1.53

Step-by-step explanation:

Given:

[tex]\frac{0.128\div 3.2+0.86}{\frac{5}{6}\cdot 1.2+0.8}+\frac{\left(1\:\frac{32}{63}-\frac{13}{21}\cdot 3.6\right)}{0.505\cdot \frac{2}{5}-0.002}[/tex]

Solution:

Convert Mixed Number to a improper fraction:

[tex]1\frac{32}{63}=\frac{95}{63}[/tex]

Now we have;

[tex]=\frac{\frac{0.128}{3.2+0.86}}{\frac{5}{6}\cdot \:1.2+0.8}+\frac{95}{63}[/tex]

Solving the first part:

[tex]\frac{\frac{0.128}{3.2+0.86}}{\frac{5}{6}\cdot \:1.2+0.8}=\frac{0.128}{7.308}[/tex]

Then we have;

[tex]=\frac{0.128}{7.308}+\frac{95}{63}[/tex]

Least common factor: 460.404

[tex]=\frac{8.064}{460.404}+\frac{694.26}{460.404}[/tex]

Now using this formula: [tex]\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]

[tex]=\frac{8.064+694.26}{460.404}[/tex]

Adding the numbers:

[tex]=\frac{702.324}{460.404}[/tex]

Next divide the numbers:

[tex]1.52545155993[/tex]

Hence, the answer is:

[tex]1.52545155993[/tex]

Round if needed:

[tex]1.53[/tex]

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The total cost paid by the senior citizen for 3 days = $50

The function representing the total cost of the annual pass is:

f(x) = 20x + 80

A senior citizen pays $20 less than half of this price for x days

The total cost paid by the senior citizen = [tex]\frac{f(x)}{2} -20[/tex]

The total cost paid by the senior citizen =[tex]\frac{20x+80}{2} -20[/tex]

Simplify the resulting expression:

The total cost paid by the senior citizen =10x + 40 - 20

The total cost paid by the senior citizen = 10x + 20

x represents the number of days

Substitute x = 3 into the resulting equation

The total cost paid by the senior citizen for 3 days  =10(3)+20

The total cost paid by the senior citizen for 3 days = $50

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The average change is 3 degrees per hour.

To calculate the average of any data we have to divide the change by the time taken for that change.

let us suppose there is a data 4,5,6,7 and 8.

Average of the data will be the sum of data divided by the number of terms.

Average=[tex]\frac{4+5+6+7+8}{5}[/tex]

            =[tex]\frac{30}{5}[/tex]

            = 6

So now we will calculate the average change in temperature per hour,

Given that there is a fall of 12 degrees in 4 hours.

Average change per hour=[tex]\frac{12}{4}[/tex]

                                        = 3 degrees per hour

So, the required change is 3 degrees per hour.

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The sequence is an AP with a = 11 and d = - 4 , 6th term is - 9 and formula is a + ( n - 1 ) d .

First Term = 11

Second Term = 7

Third Te3rm = 3

Fourth Term = - 1

Fifth Term = - 5

a ) Sequence is 11 , 7 , 3 , - 1 , - 5

b ) a + ( n - 1 ) d

    11 + ( 6 - 1 ) ( - 4 )

     11 + 5 ( - 4 )

 11 - 20 = - 9

c )    a + ( n - 1 ) d

where a is the first term , n is the tem no . and d is the common difference of an AP .

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So probability that kayla rolls an even number on the red cube and a multiple of 3 on the blue cube is 16.66 ≈ 16%

Given that we have red number cube and blue number cube so as we all know that Probability is the ratio of the favourable number of outcomes to the total number of outcomes is known as Probability.

First, find the possible outcomes.

Kalya has a red number cube and a blue number cube. Each number cube has faces labeled 1 through 6

So, possible outcomes =6×6 =36

Let, S be the sample space.

Then, ⁿ(s) =36

Let, E = the event of getting an even number on the red cube and a multiple of  on the blue cube.

E = (2,3),(2,6),(4,3),(6,3),(6,6)

Then,  ⁿ(E)=6

Let, P  is the probability of the event .

So, P(E)= [tex]\frac{n(E)}{n(S)}[/tex] = [tex]\frac{6}{36}[/tex] = [tex]\frac{1}{6}[/tex] = 16.67 percent or 16[tex]\frac{2}{3}[/tex]  %

Thus, the probability Kayla rolls an even number on the red cube and a multiple of  on the blue cube is 16.66 percent.

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Answer:

16%

Step-by-step explanation:

Answer:

126

Step-by-step explanation:

A number is divisible by 3 if its sum of digits is divisible by 3 (you can do it over and over again until it's one digit!).

A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8.

A number is divisible by 6 if it is divisible by 2 and by 3.

A number is divisible by 9 if its sum of digits is divisible by 9 (you can do it over and over again until it's one digit!).

So we need a number with last digit 0, 2, 4, 6, or 8 (because it's divisible by 6 hence by 2) and with a sum of digits divisible by 9 (because if it's divisible by 9 it's also divisible by 3).

130 is not divisible by 9, so the first digits must be 12X.

to get a number divisible by 9, we need to add a digit D so that 1+2+D is divisible by 9.

9 - 1 - 2 = 6

126 is divisible by 9 because it's sum of digits is 9. It's also divisible by 6, because it is divisible by 3 and its last digit is 6.

∠NSP ≅ ∠QSR, ∠MSP ≅ ∠PSR, ∠MSN ≅ ∠PSQ, ∠NSQ ≅ ∠MSP, ∠NSQ ≅ ∠PSR are the congruent angles.

∠NSP ≅ ∠QSR by the Congruent Complements Theorem. Because both are complementary to ∠PSQ.

∠MSP ≅ ∠PSR by the Right Angles Congruence Theorem. Because both ∠MSP = ∠PSR = 90°.

∠MSN ≅ ∠PSQ because they have the same measure. ∠MSN = ∠PSQ = 50°. Angles with same measure are congruent to each other.

∠NSQ ≅ ∠MSP by the Right Angles Congruence Theorem. Because ∠NSQ = ∠MSP = 90°.

∠NSQ ≅ ∠PSR by the Right Angles Congruence Theorem. Because ∠NSQ = ∠PSR = 90°.

Congruent Complements theorem states that if two angles are complementary (sum = 90°) to the same angle, then they are congruent.

Right Angles Theorem states that two right angles(90° angles) are congruent to each other.

Vertical Angles Congruence theorem states that two opposite angles formed between intersection of two lines are congruent. Here, ∠MSN is not congruent to ∠QSR because they are not vertical opposite angles.

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Answer:

x=4

Step-by-step explanation:

6+14=5x

Add 6 and 14 which is equal to 20.

You will get 20=5x which you will then divide by 5 inorder to solve for x.

X=4

Pull out like factors :

5x - 20 = 5 • (x - 4)

Solve : 5 = 0

This equation has no solution.

A a non-zero constant never equals zero

Solve : x-4 = 0

Add 4 to both sides of the equation :

x = 4

Answer:

24y^2

Step-by-step explanation:

4y x 6y =

24y ^2

24y to the second power

Answer: x = [tex]\frac{-31}{23}[/tex], y = [tex]\frac{-9}{23}[/tex], z = [tex]\frac{-83}{23}[/tex]

Step-by-step explanation :Solving system of equations

Given the following system of equation below

 - 4x + 2y + z =1 .......(1)

x − y + 3x =  −5 ........(2)

3x + y − 4z = 10.........(3)

first we solve eq 1 and eq 3:

we get, -13x + 9y = 14 ..........(4)

Now we solve eq 2 and eq 4 and get value of x and y:

we get,  x = [tex]\frac{-31}{23}[/tex] and y = [tex]\frac{-9}{23}[/tex]

finally we put value of x and y in eq 1 and get the value of z:

-4(-31/23) + 2(-9/23) + z = 1

106/23 + z = 1

z = 1 - 106/23

z =[tex]\frac{-83}{23}[/tex]

Hence the solution of equation is ([tex]\frac{-31}{23}[/tex], [tex]\frac{-9}{23}[/tex], [tex]\frac{-83}{23}[/tex])

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Answer:

the number is -1

Step-by-step explanation:

11 + 10x = 1  Subtract 11 from both sides

10x = -10  Divide both sides by 10

x = -1

Check:

11 + (10 x -1) = 1

11 + (-10) = 1