Write the quotient 135−i in the form a + bi.?

Answer:

15

Step-by-step explanation:

1. 2x + 3 = 33

2. 2x = 33 - 3

3. 2x = 30

4. x = 15

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{10}\\ a=\stackrel{adjacent}{8}\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{10^2-8^2}=b\implies \sqrt{36}=b\implies 6=b[/tex]

The warmest temperature or "maximum" temperature means we need to find the derivative of the function.

T = -(t^2)/2 + 8t + 32

dT/dt = -t +8

A maximum/minimum occurs when the derivate(gradient) = 0

Therefore, dT/dt = 0

0 = -t + 8

t = 8

Putting t = 8 back into the original equation gives.

T(8) = 64 degF

So the warmest temperature is 64 degF 8 hours after 6am so at 2pm

The height of the CN Tower on scale drawing is 0.05.

A scale is a group of levels or numbers that are applied to a certain system of measurement or comparison.

Given that,

The height of CN Tower = 550 m,

Also, the scale is 1/11000

Let the height of the CN Tower in the scale is x,

Then,

x/550 = 1/11000

⇒x= =550/11000

⇒x = 0.05

The height of the CN Tower on scale drawing is 0.05.

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1. If you multiply the first equation by 2, the number to multiply the second equation by eliminating the y terms when making a linear combination is -3.

2a) The price per pound of apples is $1.25.

b) The price per pound of bananas is $0.75.

A system of equations involves two or more equations solved together.

Such equations are also known as simultaneous equations.

5x + 3y = 8.5 ... Equation 1

3x + 2y = 5.25 ... Equation 2

Multiply Equation 1 by 2:

5x + 3y = 8.5 ... (x 2)

= 10x + 6x = 17 ... Equation 3

Multiply Equation 2 by -3:

3x + 2y = 5.25 ... (x -3)

-9x -6y = -15.75 ... Equation 4

Add Equations 3 and 4:

10x + 6x = 17

+

-9x -6y = -15.75

= x = 1.25

Substitute x = 1.25 in Equation 1:

5x + 3y = 8.5

6.25 + 3y = 8.5

3y = 2.25

y = 0.75

Check variables in Equation 2:

3x + 2y = 5.25

= 3(1.25) + 2(0.75) = 5.25

= 3.75 + 1.5 = 5.25

5.25 = 5.25

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5x + 3y = 8.5

3x + 2y = 5.25

1. If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination?

2. Complete the multiplication and add the equations. What is the result?

What is the price per pound of apples? $

What is the price per pound of bananas?

Answer: 12

Equation: 12 times 5 - 7.

Step-by-step explanation: 12 times 5 is 60 and take away 7 would be 53.

Hoped This Helped!

Answer: Total interest: $399

Balance = $2,299

Step-by-step explanation:

Total interest=

1900 * 7/100 * 3

= 133 * 3

= 399

Balance at maturity:

1900 + 399

= 2299

Mars travels at a rate of 24 km per second.

At this rate, Mars travel 480 km in 20 seconds.

What is speed?

The speed of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time.

Here, we have

Mars revolves around the sun, it travels at a rate of approximately 15 miles per second.

1 mile = 1.6 km (given)

15 miles = 15 ×1.6 = 24 km

So, Mars travels at a rate of 24 km per second.

In 20 seconds, Mars will travel 24×20 =480km

Hence, Mars travels at a rate of 24 km per second.

At this rate, Mars travel 480 km in 20 seconds.

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Regarding the data-set, we have that:

The dot plot shows the absolute frequencies of each observation, hence we have that:

The distribution is analyzed considering the mean and the median.

The mean is given by the sum of all observations divided by the number of observations, hence:

Mean = (2 x 3 + 3 x 2 + 4 x 3 + 5 x 5 + 6 x 4 + 7 x 2 + 10 x 1)/(3 + 2 + 3 + 5 + 4 + 2 + 1) = 4.85.

There are 20 observations, hence the median is composed by the mean of the 10th and of the 11 observation, which are both of five, hence the median is of five.

Since the median is greater than the median, the data distribution is left skewed.

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Answer:

5, skewed right

The transformation g(x) = -f(x) converts the graph of

f(x) = 8x^2 - 7 into the graph of g(x) = -8x^2 + 7.

What is transformation of graph?

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the change of algebraic equations, it is a typical kind of algebraic problem.

Given:  f(x) = 8x^2 - 7.

We have to find what kind of transformation converts the graph

f(x) = 8x^2 - 7 into the graph of g(x) = -8x^2 + 7.

Let,

f(x) = 8x^2 - 7

Multiply both sides by -1.

⇒ -f(x) = -8x^2 - (-7)

  - f(x) = -8x^2 + 7

Since g(x) = -8x^2 + 7

⇒    -f(x) = g(x)

⇒    g(x) = -f(x)

Therefore, the transformation g(x) = -f(x) converts the graph of

f(x) = 8x^2 - 7 into the graph of g(x) = -8x^2 + 7.

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Answer:

0.41

Step-by-step explanation:

$4.94/12=0.41

Answer: $0.39.

Step-by-step explanation: $4.94. Divided by 13 = $0.38

Answer:

28

Step-by-step explanation:

Draw a line segment.  Put A on one end and C on the other. Put B between these two points.  Mark the distance between A and B as 16 and the distance between B and C 12.  Add these two numbers together to get the distance of 28.

The whole plots he can make are 43/6=7.1666

A ratio in mathematics displays the multiplicative relationship between two numbers. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). In a similar vein, the proportion of oranges to the overall amount of fruit is 8:14, while that of lemons to oranges is 6:8 (or 3:4). (or 4:7).

A ratio can include any number of numbers as its components, including counts of people or things, weights, lengths, and times, among other values. Both numbers must be positive in the majority of situations.

Given, the covering land is 5(3/8) acres

That is 43/8 acres

By dividing the plots as 3/4 each, we get

(43/8)*(4/3)=43/6=7.1666

The whole plots he can make are 43/6=7.1666

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Answer:

Area = 12x + 66

Perimeter = 2x + 35

Step-by-step explanation:

Area= 12(5.5 + x)

= 12x + 66

Perimeter = 2[(5.5 + x)+12]

= 2(17.5 + x)

= 2x + 35

The depth of the deep end of the swimming pool is 9.50 feet.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Since the shallow end of a swimming pool is 3.75 feet below the pool's surface and the deep end of the pool is 5.75 feet deeper, the depth will be:

= -3.75 - 5.75

= - 9.50

It is 9.50 feet deep.

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(18a + 43) is an equivalent expression for the given expression i.e.

4(3a + 7) + 3(2a + 5).

Yes, the answers are same from both the expressions i.e. 133.

Given, an expression i.e. 4(3a + 7) + 3(2a + 5)

Now, we are asked to find an equivalent expression for the given expression.

So, on simplifying the given expression, we get

4(3a + 7) + 3(2a + 5)

12a + 28 + 6a + 15

12a + 6a + 28 + 15

18a + 43

So, (18a + 43) is an equivalent expression for the given expression i.e.

4(3a + 7) + 3(2a + 5)

Now, On putting the value of a = 5 in both the expressions, we get

4(3(5) + 7) + 3(2(5) + 5)

= 4(15 + 7) + 3(10 + 5)

= 4(22) + 3(15)

= 88 + 45

= 133

also in (18a + 43),

= 18(5) + 43

= 90 + 43

= 133.

Hence, (18a + 43) is an equivalent expression for the given expression i.e.

4(3a + 7) + 3(2a + 5).

Yes, the answers are same from both the expressions i.e. 133.

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The best option that analogizes Cavalieri's Principle is D. A short, wide glass that can hold the same volume of water as a tall, thin glass.

To describe the relationship between solids, Cavalier introduced parallel planes and area. If every plane parallel to these two planes intersects both regions in equal-area cross-sections, the two regions have equal volumes.

The volume of a prism is calculated by multiplying the area of the base by the height.

Cavalieri's principle, named after Bonaventura Cavalieri, is a modern implementation of the method of indivisibles in geometry. It is as follows: Case in two dimensions: Assume two plane regions are included between two parallel plane lines.

The Cavalieri's Principle describes the relationship between the volumes of two solids given their cross-sections and heights. When comparing the areas of two solids given their respective bases and heights, this principle comes in handy.

It states that the volumes of two or more solids are equal when their areas and lengths are the same.

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Answer:

C: A straight column of 10 pennies having the same volume as a leaning column of 10 pennies.

Step-by-step explanation:

Answer: a.

Step-by-step explanation:

The regression line, considering the points given in this problem, is defined as follows:

y = 2.16x + 13.61.

The linear regression equation is obtained inserting the points of the data, that can be given in a table or a in a scatter plot, into a linear regression calculator.

These points are composed by a value of x and a value of y, and these values are listed as follows:

Inserting these points into the linear regression calculator, the equation is given as follows:

y = 2.16x + 13.61.

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Answer:

  (b)  52y +15

Step-by-step explanation:

You want an algebraic expression for 15 more than the product of 52 and a number.

If y represents "a number", then "the product of 52 and a number" can be written as ...

  52 × y = 52y

The wording "15 more than ..." means the value 15 is added to the product. That makes the expression ...

  (b)  52y +15

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The equivalent fraction using the least common denominator for 5/6 is 25/30 and for  4/5 is 24/30  .

In the question ,

it is given that ,

the fraction is 5/6 and 4/5 ,

the least common denominator of 6 and 5 is 30 .

the first fraction is 5/6 ,

since the least common denominator is 30,

we multiply the numerator and denominator by 5 ,

we get

= (5×5)/(6×5)

= 25/30

the second fraction is 4/5 ,

since the least common denominator is 30,

we multiply the numerator and denominator by 6 ,

we get

= (4×6)/(5×6)

= 24/30

Therefore , The equivalent fraction using the least common denominator for 5/6 is 25/30 and for  4/5 is 24/30  .

The given question is incomplete , the complete question is

Write Equivalent fractions for 5/6 and 4/5 using the least common denominator .

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If the domain of a​ one-to-one function f is ​[6​,&​), the range of its​ inverse, f-1 ​of the one to one function is [6​, &​)

In mathematics, functions are said to be one-to-one functions, when one input value only give an output. No two input values give same output value in a one to one function

Usually in mathematics, functions may have two inputs which give same outputs however for one to one functions one input value gives only one output value

Relating this to domain (input values) and range (output values) and inverse.

The domain of a one to one function will be the range of inverse of the one to one function

This is among the property of one to one function

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Answer:

3/5 elimination

Step-by-step explanation:

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Using the concept of scientific notation we can write 5.14*10^5 to convert from 5.14*10^5.

What is scientific notation?

Using scientific notation, one can express extremely big or extremely small values.

When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.

For instance, 650,000,000 can be represented as 6.5 108 in scientific notation.

The scientific notation consists of a coefficient multiplied by 10 and raised to an exponent.

To convert to a real number, start with the base and multiply by 5 tens like this: 5.14 × 10 × 10 × 10 × 10 × 10 = 514000(there are only 4 zeros because you cancel one zero to remove the decimal) so we write 5.14*10^5 to convert from 5.14*10^5.

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Answer:

1. A

2. A, B, D

Step-by-step explanation:

The first one is pretty straightforward, divide 7^2 to both the denominator and numerator, so you get 1/7^2. 7^2 is 49, which is not 14, so A is false. Everything else produces 1/49 in some shape or form.

The second question is also relatively easy. A is correct because 1/4 is 4^-1 and (4^-1)^-1 is 4^1. B is also right because if you add all the exponents up, you basically get -5+6+1=2, and 2^2 is 4. C is wrong because (1/2)^2 is 1/4, not 4. D is correct because 2^(5-3) is 2^2, which is 4. E is wrong because 4^(4-2) is 4^2, which is 16, not 4.

Overall, it's not hard, nor does it take time, you just need to remember the basic formulas: [tex]\frac{1}{x^a} =x^{-a[/tex], [tex]x^a * x^b=x^{a+b[/tex], and [tex]\frac{x^a}{x^b} = x^{a-b[/tex]

Answer: -√7 because it will cancel out to equal 0

An investment that takes 2 years to increase in value by $50 and

10 years to increase in value by $250 situation is best modeled by an exponential function with time as the independent variable

Two or more expressions with an Equal sign is called as Equation.

We need to find the exponential function with time as the independent variable.

Exponential growth refers to the original value from the range increases by the same percentage over equal increments found in the domain.

an investment that takes 2 years to increase in value by $50 and

10 years to increase in value by $250

an investment that increases by a constant factor of 1.03, or at a

rate of 3%, every year

an investment that increases by $30 every year

an investment that increases by $1 every 2 weeks

Hence, an investment that takes 2 years to increase in value by $50 and

10 years to increase in value by $250 situation is best modeled by an exponential function with time as the independent variable

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Answer:

solve for the supplementary angles:

140 + x = 180

x = 40

then solve for 5x

40 + 5x = 90

5x = 50

x = 10

TADA!!

Answer: x = 10

Step-by-step explanation:

J - E has to be 180. 180 - 140 is 40. DHF has to be a 90 degree angle. 90-40 is 50. 5x, 50/5 is 10 so X would be ten.