2. David determines that 3 sqrt 2 cis(7pi/4) = -3+3i. When he considers the graphical representation of these numbers, he knows he made an error. Clearly explain in complete sentences what David observed, and where David made his mistake. State the correct rectangular equivalence of 3 sqrt 2 cis(7pi/4).

Answer:

required expression = 11x-5

Step-by-step explanation:

We have information about the following things :

Since units digit is 5 less than the tens digit, then the unit digit will become

x-5

Now we have these two things:

Now let us look at some two digit numbers like 29 , 43 and 78

in 29, tens digit is 2 and units digit is 9

29 is formed by multiplying the tens digit by 10 and multiplying the units digit by 1 like this : 29 = (2×10) + (9×1)

Similarly;

43 = (4×10) + (3×1)

78 = (7×10)+(8×1)

Now to get out two digit number from the question, we similarly need to multiply the tens digit with 10 and units digit with 1 and add them like this:

tens digit : x

Units digit : x-5

Hence the number is (x × 10) + [(x-5)×1] = 10x + x-5 = 11x-5

hence the required algebraic expression is 11x-5

Another way to summarize this proof is to say vertical angles are congruent.

Lines are shortest distance between two point and angles are forned from the intersection of two lines.

From the given figure, they are trying to prove that the angles ANR and VNE are equal. Since these angles are formed at the point of intersection, hence another way to summarize this proof is to say vertical angles are congruent.

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Answer:

Yes

Step-by-step explanation:

They are equivalent as 12d + 36 is the expanded form of 12(d + 3)

Answer:

Yes,

just factorize 12d+36 and since 12 is common

12(d+3)

The difference in the rate of change of both functions is: 15.

Rate of change of a linear function = change in y / change in x.

Function A is given as: y = 35x. The rate of change for function A is 35.

From the graph of function B, using two points, (1, 50) and (2, 100):

Rate of change = (100 - 50)/(2 - 1)

Rate of change = 50.

Therefore, the difference in the rate of change of both functions = 50 - 35 = 15.

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5x>25

x>5

Hope it helps!

Answer: Option (3)

Step-by-step explanation:

[tex]|-2x|=4\\\\|2x|=4\\\\|x|=2\\\\x=\pm 2[/tex]

The number line represents the solutions to  |-2x| = 4 is Number line C.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have Equation: |-2x| = 4

We know the value inside the mod is always positive.

So, 2x = ±4

x= ±4/2

x= ±2

Thus, the required number line is C.

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Answer:

  M/6 = G/5

Step-by-step explanation:

We are given a relation between the numbers of students in two different groups. That relation can be used to write an equation.

If we consider M&M buyers to be 6 in a group, then the number of those groups is ...

  M/6

Similarly, the number of groups who bought gum will be ...

  G/5

where there are 5 gum-buyers in each group.

The problem statement tells us that for each group of one kind, there is a matching group of the other kind. That is, the numbers of groups are equal:

  M/6 = G/5

A function assigns the values. The number 20 describes the cost that Bobby needs to pay for each extra ounce of letters.

A function assigns the value of each element of one set to the other specific element of another set.

In the given function y = 30 + 20(x - 1), the number 20 describes the cost that Bobby needs to pay for each extra ounce of letters.

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Answer:

210 ways

Step-by-step explanation:

7 P 3 = 210  ways

or    7 C 3 = 35     choices of 3 posters which can bearrranged in 6 different ways     6 * 35 = 210 ways

The two ways that can be used to find the area of a trapezoid include:

It should be noted that a trapezoid simply means a four sided shape that has parallel sides.

To find the area of the shape goes thus:

Find the length of each base.

Find the height of the trapezoid.

Substitute the values into the formula: A = (a + b) × h/2

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For finding the inverse of a function you have to write it as an ecuation.

[tex]y = 4x + 7[/tex]

Invert the values of x and y.

[tex]x = 4y + 7[/tex]

Our objetive now in this new equation is to clear y. First, subtract 7 in both sides of the equation.

[tex]x - 7 = 4y[/tex]

Then, divide both sides by 4.

[tex] \frac{x - 7}{4} = y[/tex]

Finally, invert the values of x and y again and put the equation like a function.

[tex] {f}^{ - 1} (x) = \frac{x - 7}{4} [/tex]

This is correct because f(x) = x is the axis of symmetry for both functions (green one).

Answer:

h(-8)= -14

Step-by-step explanation:

[tex]h(-8)=-2(-8+5)^2+4 \\h(-8)=-18+4=-14[/tex]

[tex]\huge\boxed{-14}[/tex]

We have the following equation:

[tex]h(f)=-2(f+5)^2+4[/tex]

Substitute in [tex]-8[/tex] for [tex]f[/tex] and simplify.

[tex]\begin{aligned}h(-8)&=-2(-8+5)^2+4&\textsf{Substitute.}\\&=-2(-3)^2+4&\textsf{Add.}\\&=-2\cdot9+4&\textsf{Simplify the power.}\\&=-18+4&\textsf{Multiply.}\\&=\boxed{-14}&\textsf{Add.}\end{aligned}[/tex]

The expression πr² = 6477 can be used to solve for the radius of the sphere.

It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.

[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]

Area of sphere A = 6477 square inches

A = 4πr²

A = 6477

4πr² = 6477

πr² = 6477

Thus, the expression πr² = 6477 can be used to solve for the radius of the sphere.

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The total length of the segment AC is the sum of AB and CB, which gives, CB = 9

The given parameters are;

Required: CB

Solution:

AC = AB + CB by segment addition property

Therefore;

AC = 17 = 32 + 3•x + 57 + 6•x = 89 + 9•x

17 = 89 + 9•x

[tex]x = \frac{17 - 89}{9} = - 8[/tex]

CB = 57 + 6•x = 57 + 6 × (-8) = 9

Therefore;

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Answer:

510

Step-by-step explanation:

Assume 2 numbers 500,500.. with a mean of 500

so if we add 10 to each of the two numbers, mean will be:

[tex]\frac{510+510}{2}=510[/tex]

Of course you can vary the set and the numbers and still get the same mean

Answer: A. (3x² + 4x-7)(x) + (3x² + 4x-7)(-2)

Step-by-step explanation:

The expressions are equivalent by the distributive property.

The coordinates represents a possible collision point of the objects according to equations r = 4cos(θ) and r = –1/ 2cos(θ)  cos(∅) are (-2,2π/3).

Given Equations  r = 4cos(θ) and r = –1 2cos(θ).

We have to find the coordinates of collision.

The first object is moving around the screen r = 4cos(θ).

The second object is moving around the screen r = –1 /2cos(θ).

According to question

Coordinate can be found out by equating both the equations.

4cos(θ) =–1 /2cos(θ)

2cos(θ)=-1

cos(θ)=-1/2

θ=[tex]cos^{-1} (1/2)[/tex]

=120°

θ=-2π/3

Therefore the two equations are equal when

θ=2π/3

we have

r=4 cos(2π/3)=-2

and r=-1+2 cos(2π/3)

r=-2

Hence the coordinates that represent the collision point are (-2,2π/3).

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Answer: Option A on EDGE

Just took test

Step-by-step explanation:

Using a calculator to find the approximate value of e in

F(e)=e^{2e} we have F(e)=229.6516. This is further explained below.

Generally, To approximate a function f (x) f (x) f (x) for values of x near to zero, one may use a power series known as a Maclaurin series.

In conclusion, Using your calculator to find the approximate value of e in

F(e)=e^{2e}

We have

F(e)=e^{2e}

F(e)=229.6516

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Answer:

b. 4.5 cm

a. 42 mm is the answer

The company should use the median to support their claims.

Measures of average commonly used are mean and median.

Mean is the sum of the numbers divided by the total number

Mean : (5 + 6 + 6 + 6 + 7 + 8 + 8 + 8 + 8 + 11) / 10 = 7.3

Median is the number at the center of the dataset when it is arranged either in ascending or descending order.

Median = 8

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Answer:

the last option

Step-by-step explanation:

please put brainliest

The amount of the portions can be made with one case will be 399.25 ounces.

Conversion means to convert the same thing into different units.

You buy tomatoes in 25 pounds (11.34 kg) cases.

We know that 1 pound (0.45 kg) is equal to 16 ounces (0.45 kg).

Then the number of the ounces in 25 pounds (11.34 kg) will be

⇒ 25 x 16

Multiply the numbers, then the expression will be

⇒ 400 ounces (11.33 kg)

In 25 pounds of tomatoes, there will be 400 ounces.

One portion of salad requires 0.75 ounces (0.02 kg) of tomatoes.

Then the amount of the portions can be made with one case will be

⇒ 400 – 0.75

⇒ 399.25 ounces

Thus, the amount of the portions can be made with one case will be 399.25 ounces.

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The economic order quantity is 385 and reorder point is 254.

a. Economic order quantity (EOQ)

EOQ=√2×D×C÷H

Where:

D =Annual Demand

S = Cost of Ordering

H=Holding cost

Hence:

EOQ=√2×5300×70÷.25×20

EOQ=√742,000÷5

EOQ=√148,400

EOQ=385

b. Reorder point

Reorder point=5300/250×12 days

Reorder point=254

c. Reorder point

Reorder point=5300/250×35 days

Reorder point=742

d. Reorder point

Reorder point=742-385

Reorder point=357

Therefore the economic order quantity is 385 and Reorder point is 254.

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The complete question is:

a. If the cost of the part is $20 per unit, what is the economic order quantity?

b. Assume 250 days of operation per year. If the lead time for an order is 12 days, what

is the reorder point?

c. If the lead time for the part is seven weeks (35 days), what is the reorder point?

d. What is the reorder point for part (c) if the reorder point is expressed in terms of the inventory on hand rather than the inventory position?

Using relations in a right triangle, it is found that:

cos(A) = 3/5 = 0.6.

The relations in a right triangle are given as follows:

In this triangle:

Hence:

cos(A) = 30/50 = 3/5 = 0.6.

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The product of 12, x, and y written in an algebraic expression is 12xy.

Algebraic expressions are mathematical expressions containing variables, coefficients, and their arithmetic operators such as addition, subtraction, multiplication, and division.

An algebraic expression can be used to interpret and solve mathematical word problems.

From the information given:

The algebraic expression can be translated as 12x × y = 12 xy.

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The algebraic expression that can be translated as product of 12, x and y is 12 xy.

Expressions are used to interpret mathematical problems

From the question given we are to translate the product of 12, x and y.

The product of 12 and x is 12x

The product of 12x and y is 12xy, hence the algebraic expression that can be translated as product of 12, x and y is 12 xy.

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Answer:

x = 0.76556443         x = -3.26556443

Step-by-step explanation:

You can use the quadratic formula to find the roots.

Answer:

913

Step-by-step explanation:

cylinder:

radius=5.6 height=7

first lets find the volume of the cylinder the formula for the volume of a cylinder is pi times radius squared times height. so after plugging in the height and radius you get 689.64242

cone:

radius=5.6 height=6.8

now the volume of the cone, the formula for the volume of a cone is pi times radius squared times height/3. so after plugging in the height and radius of the cone you get 223.31278

so 689.64242 + 223.31278= 912.9552 and that rounded to the nearest tenth is 913

Answer:

let's playthe games questiontag

Step-by-step explanation:

it is 8+1 people (8 students and 1 teacher).

a.

how many seating arrangements are possible ?

start with any of the 9 seats. there are 9 possibilities who will sit in that chair.

the next seat has then only 8 possibilities left. the next one 7. the next b one 6. and so on.

so, all possibilities are

9×8×7×6×...×1 = 9! = 362,880

b.

if the teacher is fixed to a specific seat, then this position is constant in all seating arrangements.

that means for the variable part we have only 8 people remaining.

and that gives us now only

8! = 40,320

possibilities

c.

how many combinations are there for the triplets, when they sit together, to arrange their internal sitting sequence ?

3! = 6

and we need to block these 6 combinations for each of the freely selectable seats as starting seat for such a block of 3.

to visualize this, let's give each seat an identifier.

we have the seats s1, s2, s3, ... s8, s9.

for all the combinations of these 9 seats, we need to eliminate the 6 combinations, where the triplets sit on s1, s2, s3.

and then the 6 combinations, where they sit at s2, s3, s4.

and then at s3, s4, s5. then at s4, s5, s6. ... s8, s9, s1. and s9, s1, s2.

it is not clear if b. still applies here (and the teacher has a fixed seat), or if we are back to the general a. scenario.

if we have again all 9 people picking their seats freely, and we only block the triplets from sitting together, then we need to block these 6 combinations for each of the 9 seats (as visualized above) giving us

9! / (9×3!) = 362,880 / 54 = 6,720 remaining possibilities.

if we have again the teacher blocking one fixed seat, then we need to block the 6 triplets combinations theoretically for each of the 8 remaining seats as above.

but : the teacher is now a separator disabling some of these blocks of 3.

e.g. let's say the teacher's seat is s9. then the teacher automatically separates the triplets in otherwise "illegal" blocks of 3.

s7, s8, s1 is now a valid seat combination for the triplets (because there is the fixed s9 in between).

the same for s8, s1, s2.

so, we need to eliminate the 6 combinations not for all 8 starting seats, but only for 6.

and that gives us

8! / (6×3!) = 40,320 / 36 = 1,120 remaining possibilities.