Simplify the complex expression to the standard form (a+bi). 8(5-9i)+2(5+2i)

Answer:

Step-by-step explanation:

first up, the perimeter is 4 side added up. so we do 72/4= which equals 18. we need to apply the 6 to the sides so we do 6/2=3 18/3=15 f=15 18+3= 21 one side is 15 & the other side is 21 to double check, 21+15*2= 72

Answer:

false

Step-by-step explanation:

question 4

0. 25 points

if py increases to 6 the vertical intercept will be the same and the slope will be steeper

the probability that the mean tire pressure of the sample is less than 69 psi 0.2030

The formula of the z-score is z = (x - μ)/σ, where

x is the score

μ is the mean

σ is the standard deviation

given,

a mean of 70 pounds per square inch

μ = 70

the standard deviation of 1.2 psi.

σ = 1.2

the sample is less than 69

x=69

so on substituting

z=(69-70)/1.2

z=-1/1.2

z=-0.83

The value corresponding to the z score is 0.2030 i.e 20.30%

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The first mechanic worked 20 hours and the second mechanic worked 5 hours

The work charge of first mechanic = $115 per hour

The  work charge of second mechanic = $55 per hours

Total number of hours they worked = 25 hours

The total amount they charged = $2575

Consider the number of hours that first mechanic work as x and second mechanic as y

Then the equations will be

x + y = 25

x = 25 -y

The second equation

115x + 55y = 2575

Here we have to use substitution method here

115(25-y) + 55y = 2575

2875 - 115y +55y = 2575

2875 -60y = 2575

60y = 2875 - 2575

60y = 300

y = 300 / 60

y = 5 hours

Then x = 25 - y

= 25 -5

= 20 hours

Hence, the first mechanic worked 20 hours and the second mechanic worked 5 hours

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a₁₁=1 of the given matrix.

Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array.

Given Matrix is [tex]\left[\begin{array}{cccc}1&3&8&5\\5&4&6&2\\6&7&1&8\\2&9&3&7\end{array}\right][/tex]

The matrix will be in the form[tex]\left[\begin{array}{cccc}a_{11} &a_{12} &a_{13} &a_{14} \\a_{21} &a_{22} &a_{23} &a_{24} \\a_{31} &a_{32} &a_{33} &a_{34} \\a_{41} &a_{42} &a_{43} &a_{44} \end{array}\right][/tex]

The given matrix is a 4 cross 4 matrix, which has 4 rows and 4 columns.

a₁₁ means it is the first element of first row and first element of first column.

By comparing the given matrix with standard form a₁₁=1

Hence, a₁₁=1 of the given matrix.

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After simplifying the percentage, if 120% of a is equal to 80% of b, then a+b is 5.

In the given equation,

If 120% of a is equal to 80% of b, then we have to find the value of a+b.

We firstly express the statement in the algebraic equation.

It is given in the statement that 120% of a.

We write it as 120%×a.

From the statement, 80% of b.

We write its as 80%×b.

Both are equal to each other.

So the expression should be

120%×a=80%×b

Divide by 12% on both side

120%/120% ×a=80%/120% ×b

Simplifying

a=80%/120% ×b

As we know that % means 100 but both number 80 and 120 have % sign. So the % sign emitted.

So a=80/120 ×b

Divide by b on both side

a/b=80/120 ×b/b

a/b=80/120

Simplifying the ration

a/b=2/3

Hence, the value of a=2 and b=3.

Now finding the value of a+b.

a+b = 2+3

a+b = 5

Hence, if 120% of a is equal to 80% of b, then a+b is 5.

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Answer:

a =-13/24 b = 5/3

Step-by-step explanation:

From given

8a + 5b = 4 (1)

3b = 5 (2)

Using (2)

b = 5/3

Putting the value of b into (1) gives

8a + 5(5/3) =4

8a + 25/3 = 4

8a = 4 - 25/3

8a = -13/3

a = -13/(3*8)

a = -13/24

Answer:

The original equation

Distributive property

subtract 5x from both sides

add 12 to both sides

divide both sides by -14

Answer: 90

Step-by-step explanation:

VolBigCube = 1.5x1.25x0.75 = 1.40625 in^3

VolSmallCube = 0.25x0.25x0.25 = 0.015625 in^3

VolBigCube/VolSmallCube = 1.40625/0.015625 = 90

The flour that Karina's mother has won't be enough for the recipe and she requires extra 3/20 together with the quality owed by the mother.

Flour is defined as a food product that is the main ingredient for baking of different recipes such as cakes, breads, plate pies just to mention a few.

The amount of flour needed by Karina for the recipe= 3/5 = 0.6.

The amount of flour owed by the mother = 3/7 = 0.45

The difference between the available flour = 0.6 - 0.45 = 0.15

This shows that extra flour of 0.15 or 3/20 is needed in addition to the quantity of flour owed by the mother to be able to make the recipe.

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The given system of equations has no solution.

What is substitution method?

In order to solve a system of equations, the substitution approach is typically utilized in mathematics. The first equation involving the variable must be solved using this procedure before the variable's value is substituted in the second equation.

Consider, the given system of equations,

y + 7 = 3x          ..(1)

6x - 2y = 12             ..(2)

From equation (1),

y = 3x - 7.

Substitute value of (y) in inequation (2),

6x - 2(3x - 7) = 12

6x - 6x - 14 = 12

            -14 = 12

It is not possible to solve -14 = 12.

Therefore, the given system of equations has no solution.

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The train will travel for approximately 50 kilometres in 1 hours.

The train travels 1 kilometre in 1 minute 20 seconds.

At this rate the number of kilometres the train will travel in 1 hour can be calculated as follows;

Therefore, lets convert 1 minutes and 20 second to hours.

20 seconds = 0.333333 minutes

Hence,

60 minutes = 1 hour

1.33333 minutes = ?

cross multiply

time in hours = 1.3333 / 60

time in hours = 0.02222221666

Therefore,

0.02 hours = 1 km

1 hours = ?

number of kilometres the train will travel in 1 hours = 1 / 0.02 = 50 km

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Answer: 4

Step-by-step explanation: x is multiplied by 4

The length of the guys wire to the nearest foot is 56 feet.

The pole 5 ft tall is used to support the guy wire for the tower, which runs from the tower to a metal stake in the ground.

The situations forms a right angle triangle.

Therefore, the length of the guy wire can be found as follows:

Using trigonometric ratios, we can find the angle the guy wire made with the ground.

tan ∅ = opposite / adjacent

tan ∅ = 5 / 1

∅ = tan ⁻¹ 5

∅ = 78.690067526

∅ = 78.69°

Therefore, let's find the length of the guy wire using the angle.

cos 78.69° =  adjacent / hypotenuse

0.1961172908 = 11 / h

h = 11 / 0.1961172908

h = 56.088884361

Therefore,

length of the guy wire = 56 feet

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Answer:

19 1/4

Step-by-step explanation:

1 3/4 × 11 = 7/4 × 11/1 = 77/4 = 19 1/4

Answer:

You need 8 picnic tables.

Step-by-step explanation:

You need 8 picnic tables because there are 30 friends and 4 sits at each table, and 4 x 8 is 32. There is 2 more extra seats. But it does fit all 30 friends.

The function f(x)  = [tex]-x^2 + 3x +11[/tex] of the value is 7.

Given,

In the question:

The function is given as:

f(x) = [tex]-x^2 + 3x +11[/tex]

To find the f(-1)

Now, According to the question:

The function is :

f(x) = [tex]-x^2 + 3x +11[/tex]

To put the value of x = -1 in above function's equation:

f(x) = [tex]-x^2 + 3x +11[/tex]

f(-1) = [tex]- (-1)^2 + 3(-1) +11[/tex]

Solve the equation:

Determine the sign:

f(-1) = -1 -3 +11

Calculate the sum or difference:

f(-1) =7

Hence, The function f(x)  = [tex]-x^2 + 3x +11[/tex] of the value is 7.

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The number she divides the 1572 and got an answer of 104, the remainder of 12 is 15.

It is the basic arithmetic operation, in which you are separating the number into some parts.

Given:

The dividend = 1572,

The quotient = 104,

The reminder = 12

Calculate the divisor by the following formula,

Dividend = Divisor × quotient + Reminder

Substitute the values,

1572 = Divisor × 104 +12

Divisor = 15

Therefore, the number she divides the 1572 and got an answer of 104, the remainder of 12 is 15.

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Answer:

65 cents

[tex]85 \div 17[/tex]

85/17 =5

so for 1 inch of wire is 5 cents but we want to know for 13 inches

so times 5 by 13

5cents*13=65cents

There are 2520 ways to seat 8 people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors.

There are a total of seven different ways for eight individuals to sit around a circular table: (8-1)!=7!. We are using the concept of circular permutation.

By using circular permutation we have,

7!=5040

All of the seating is included in these 5040 ways. Given that everyone has the same two neighbors, regardless of whether they are left or right neighbors, two seating are said to be equal. To achieve the desired outcomes, we must divide the total number of methods by 2.

5040/2

=2520 ways

Therefore, there are 2520 ways to seat 8 people around circular table where two seating are considered the same.

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Answer:

84 counters

Step-by-step explanation:

⅖ + ½ = 7/10

10 - 7 = 3

280 ÷ 10 × 3 = 84

Answer:

28

Step-by-step explanation:

1/2×280=140(red counters)

2/5×280=112(yellow counters)

140+112=252

280-252=28(green counters)

A. The bacteria sample that had a smaller initial population is;

Sample A; 100 bacteria.

B. The sample that was larger in the 5th week was;

Sample A; by 8,300.

An exponential function is defined by the general expression;

y = abˣ

where;

a is initial value.

b is rate of change.

For Sample A, the values of the above parameters are given as;

a = 100

b = 3

Thus, the exponential function is:

f(x) = 100(3)ˣ

In the 5th week, the population will be calculated as;

f(5) = 100 * 3⁵

f(5) = 24300.

For Sample B, the exponential function is expressed as:

g(x) = 500(2)ˣ

In the 5th week, the population will be;

g(5) = 500 * 2⁵

g(5) = 16000.

The difference of the larger population in Sample A and the smaller population in Sample B is;

24300 - 16000 = 8300.

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Answer:

8

Step-by-step explanation:

you divide so you can get the average

Answer:

in average she makes 8 friend in a week.

Step-by-step explanation:

You divide 80 by 9 that is 8 remaining 1, so yeah.

The inference rule is ({E and P} S1 {Q},{ not E and P} S2 {Q})/({P}if E then S1 else S2{Q}).

In the given question, we have to define the semantics (inference rule) of the if statement: {P} if (E) S1 else S2 {Q}.

A way of inferring the veracity of one assertion based on the significance of other assertions is known as an inference rule.

(S1, S2, ........, Sn)/S

According to the rule, if S1, S2,..., and Sn are real, then S's validity can be derived.

Given,

{P} if (E) S1 else S2 {Q}

The inference rule is

We know that if if E and P are true then it is S1 with postcondition {Q} or if E and P is false then it is else part that is S2 with postcondition {Q}

i.e. {E and P} S1 {Q},{not E and P} S2 {Q}

So the inference rule is:

({E and P} S1 {Q},{ not E and P} S2 {Q})/({P}if E then S1 else S2{Q})

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By using the properties of parallel lines, the result obtained is-

The correct options are first, second and fourth

What are parallel lines?

Two lines are said to be parallel if on extending them indefinitely, they will never intersect

Here,

From the figure,

For the first option,
m∠1=m∠5 [Corrosponding angles are equal]

First option is correct

For the second option,
m∠7=m∠11 [Corrosponding angles are equal]

Second option is correct

For the third option,
m∠5 ≠ m∠12 [ c is not parallel to b]

Third option is wrong

For the fourth option,
m∠4 = m∠5 [Alternate interior angle are equal]

Fourth option is correct

So the correct option are first, second and fourth

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Complete Question

The diagram has been attached

Answer: The answer is below

Step-by-step explanation:

If 1200 square centimeters of material is available to make a box with a square base and an open top,

The largest possible volume of the box is V = 4000cm^3.

We have 1200 cm^2 worth of material. This represents the surface area of a box with a square base and an open top.

the dimensions of the box.

Square base implies the length and width are the same.

Let x = length/width.

The box has a height as well.

Let h = height

the surface area ; S.

S = (area of base) + (area of 4 walls)

The area of the base is x^2

The area of one of the walls is length times height, or xh. Since there are 4 of them, it would be 4 times xh, or 4xh.

S = x^2 + 4xh

And we know that S = 1200cm^2, so

x^2 + 4xh = 1200

Let's solve for h.

4xh = 1200 - x^2

h = (1200 - x^2) / (4x)

we require the volume formula.

V = (length) x (width) x (height)

And we know all of these.

V = (x)(x)(h)

V = (x^2) h

putting h = (1200 - x^2) / (4x) in the formula

V = (x^2) ( 1200 - x^2)/(4x)

We get a cancellation,

V = x(1200 - x^2)/4

V = (1/4)x (1200 - x^2)

This will be our volume function, V(x).

V(x) = (1/4)(x)(1200 - x^2)

To maximize V(x), we must first take the derivative and then make it 0. Using the product rule (and ignoring the constant 1/4), we have

V'(x) = (1/4) [ (1200 - x^2) + (x)(-2x) ]

Simplify,

V'(x) = (1/4) [ 1200 - x^2 - 2x^2 ]

V'(x) = (1/4) [ 1200 - 3x^2 ]

V'(x) = (1/4) [ 3(400 - x^2) ]

V'(x) = (3/4) [ 400 - x^2 ]

To maximize, make V'(x) = 0, and solve for x.

0 = (3/4) [ 400 - x^2 ]

0 = 400 - x^2

x^2 = 400

x = +/- 20

Therefore,

x = { 20, -20 }

However, since x represents a dimension, it can never be negative, and we must discard the negative solution. That means

x = 20.

This tells us that the maximum volume occurs when x = 20. However, the question is asking WHAT the largest volume of the box is. Solving this is as simple as plugging x = 20 into our volume function, V(x).

V(x) = (1/4)(x)(1200 - x^2)

Therefore,

V(20) = (1/4) (20) (1200 - 20^2)

V(20) = (1/4) (20) (1200 - 400)

V(20) = (1/4) (20) (800)

V(20) = (20/4)(800)

V(20) = 5(800)

V = 4000cm^3

Hence the answer is, the largest possible volume of the box is V = 4000cm^3.

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Using midpoint theorem the value of DE is 4.

What is midpoint theorem?

 According to the midpoint theorem, "The line segment of a triangle linking the midpoint of its two sides is said to be parallel to its third side and is also half the length of the third side."

Here using midpoint theorem we know that ,

=> DE = 1/2 AB

Here DE=34-6x and AB=28-4x.

=> 34-6x=1/2(28-4x)

=>68-12x=28-4x

=> 12x-4x=68-28

=> 8x = 40

=> x =5.

Now put x=5 into DE then,

=> DE=34-6(5)=34-30 = 4.

Therefore using midpoint theorem value of DE is 4.

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The  probability of getting face card in all 4 attempts is 0.0018 approximately.

What are face cards?

Any of the twelve cards in a deck with an image of a face on it is referred to as a face card. King, Queen, and Jack are the face cards in this deck.

Main Body:

Jack, Queen, and King are face cards, each of the four suits has one of each, so 12 face cards.

12/52 is the chance that the first one will be a face card.

Then it’s 11/51, 10/50, and 9/49.

And the chance for all four is thus all four multiplied together.

(12 / 52) * (11 / 51) * (10 / 50) * (9 / 49) = 0.001828

Hence the probability of getting face card on all attempt is 0.0018

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The cost ruler is £ 1.5 and the cost of rubber is £ 1.0.

Cost of 01 ruler be x pound.

Cost of 01 rubber be y pound.

according to question,

[tex]5x + 3y = 5.5[/tex]         ------------------------------------ (1)

[tex]3x + 2y = 3.5[/tex]         ------------------------------------(2)

multiplying equation (2) by 2 and equation (1)

[tex]10x + 6y = 11[/tex]       -------------------------------------(3)

[tex]9x + 6y = 10.5[/tex]      -------------------------------------(4)

subtracting equation (4) by (3), we get

[tex]x = 0.5[/tex]

putting the value of [tex]x = 0.5[/tex] in equation (2),

3×0.5 + 2y = 3.5

⇒1.5 +2y = 3.5

⇒2y= 2.0

⇒y = 1

∴ the cost of ruler is £ 0.5 and the cost of £1.0

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