Finding the slope passing through the points

The standard form of the complex numbers ( 7 − 5 i ) ⁢ ( 2 + 3 i ) is

Complex numbers are numbers that are represented of the form a + ib

a and b are real numbers. a is the real part and b is in the imaginary part

i = √-1

Opening up the parenthesis by multiplication  

( 7 − 5 i ) ⁢ ( 2 + 3 i )

= 14 +21i - 10i -15i^2

where i^2 = -1

= 14 +21i - 10i -15 * -1

= 14 +21i - 10i +15

= 29 + 11i

The equation is equal to 29 + 11i

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The equation that represents how many grams of the compound will remain after 4 hours is A(4) = 380 *(1 - 12.1%)⁴

From the question, we have the following parametersa:

Mass = 380 grams

Rate of decay= 12.1% per hour

These parameters can be represented using the following exponential equation

A(n) = A *(1 - r)ⁿ

Where

n = number of hours = 4

A  = Initial mass = 380

r = rate of decay = 12.1%

Substitute the known values in the above equation, so, we have the following representation

A(4) = 380 *(1 - 12.1%)⁴

Hence, the equation is A(4) = 380 *(1 - 12.1%)⁴

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Answer:    y=-1/2x+4

Step-by-step explanation:

The example of a complex fraction is the fraction that consisting fraction on the numerator or denominator or both, that is 4 / (1/6)

The simple fraction consist of both numerator and denominator as whole number. The term on the top is the numerator and the term on the bottom is called the denominator

The complex fraction is defined as the fraction that consisting fraction on the numerator or denominator or both

The example of the complex fractions are

4 / (1/6)

Here the numerator is the 4 and it is a whole number. The denominator is 1/6 that is a fraction

Therefore, the example of a complex fraction is 4 / (1/6)

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in essence, find "x" when y = 196

[tex]y = \cfrac{1}{25}x^2\qquad \stackrel{\textit{when y = 196}}{196=\cfrac{1}{25}x^2}\implies (196)(25)=x^2 \\\\\\ \sqrt{(196)(25)}=x\implies {\Large \begin{array}{llll} \stackrel{\frac{m}{h}}{70}=x \end{array}}[/tex]

There is no sufficient evidence to support that the population mean is less than 165.

What is mean ?

The average of a set of values is referred to as the mean in statistics and math. The simple arithmetic mean, geometric mean, and harmonic mean are some of the methods that can be used to calculate the mean. The simple arithmetic mean involves adding the numbers together and dividing the result by the number of observations.

From the given data

183, 152, 178 , 157 , 194 , 163 , 144 , 114 , 178 , 152 , 118 , 158

Mean = 157.5833

Standard deviation s = 24.39

  n = 12

Null hypothesis  [tex]H_{0}[/tex] : μ = 165

Alternative Hypothesis [tex]H_{1}[/tex] = μ < 165

Level of significance ∝ = 0.05

degree of freedom (df) = n - 1

                                (df) = 12 - 1

                                (df) = 11

critical value [tex]t_{0.05 , 11}[/tex] = -1.796 (left - tailed)

Test - statistics (t) = ( mean - μ ) / ( s / √n)

                         (t) = -1.053

p - value = 0.1574

p - value > Significance level (∝)

 0.1574 > 0.05

We fail to reject the null hypothesis

Critical value [tex]t_{0.05 , 11}[/tex] = -1.796

                   |[tex]t_{0.05 , 11}[/tex]| = 1.796

|test - statistics| < |critical value|

1.053 < 1.796

We fail to reject the null hypothesis

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Answer:

20

Step-by-step explanation:

197 rounded to the nearest 10 is 200.

10.3 rounded to the nearest 10 is 10.

So, 200 ÷ 10 = 20

Answer:

20

Step-by-step explanation:

We are rounding to the nearest 10.

197≈200

10.3≈10

After you have rounded the numbers, The equation simplifies a whole bunch.

200/10=20

Answer: Horizontal Translation

Step-by-step explanation:

Answer:

136

Step-by-step explanation:

solve the inside of the parentheses and you get -17, then multiply by -8

Answer:3

Step-by-step explanation:

since 7 is a number and b is to u should just put 3 windows cause u need to add them all up i think, not sure but just do that, why not,

The amount they earn from the sale of candy canes as required is; $6.75.

It follows from the task content that the amount earned by Raven and Tyler as in the task content is to be determined.

Since they sell their cups of hot chocolate for $2.25 in which case they sold 11 cups.

However, the question requires that the amount which they earn from the sale of candy canes is to be determined.

Therefore, since each candy cane is sold for $0.75, it follows that the amount earned on 9 candy cones is;

= 9 × $0.75

= $6.75

Ultimately, the amount earned from the candy canes is; $6.75.

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The rational root theorem, as its name suggests, is used to find the rational solutions of a polynomial equation (or zeros or roots of a polynomial function). The solutions derived at the end of any polynomial equation are known as roots or zeros of polynomials. A polynomial doesn't need to have rational zeros.

Rational root theorem, also called rational root test, in algebra, theorem that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the constant term (the one without a variable) must be divisible by the numerator.

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The value of x in the considered inequality's solution set is given by -10.

What is  inequality ?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

We have;

3(x - 4) ≥ 5x + 2

By solving;
3(x - 4) ≥ 5x + 2

3x - 12 ≥ 5x + 2

Adding -3x-2 on both sides we get ;

-12-2 ≥ 5x-3x

-14 ≥ 2x

Dividing both sides by 2,we get;

-14/2 ≥ 2x/2

-7 ≥ x

x ≤ -7

As a result, any numbers that are less than or equal to -7 comprise the solution set for this inequality.

There is currently only the value -10 in the solution set because -10 ≤ -7.

As a result, the value of x in the collection of solutions to the inequality under consideration is provided by -10.

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Answer:

Oh god, I don't really know much about this, but I am going to assume that the 25 represents the mn so maybe you have to put 25mn + 6600 on the first box?

Step-by-step explanation:

I just looked up how to do this. I think the form has to be a C=mn+b format. For the third box, I think you need to solve 54100=25mn+6600. On the second box I think you just need to solve C(3600)=25(3600)+6600. idrk

Answer:

y=-[tex]\frac{5}{3}[/tex]x-4

Step-by-step explanation:

find the slope m = [tex]\frac{y2-y1}{x2-x1}[/tex]

m=[tex]\frac{1-6}{-3+6}[/tex]

m=-[tex]\frac{5}{3}[/tex]

Use the slope and one of the points to solve for the y-intercept

y1=mx1+b

6=-[tex]\frac{5}{3}[/tex](-6)+b

6=10+b

b=6-10

b=-4

plug the values for m and b into y=mx+b

y=-[tex]\frac{5}{3}[/tex]x-4

Answer:

First find the slope.

m=y2-y1 / x2-x1

m= 1-6

-3-(-6)

m=-5

-3+6

m=-5

3

m= -1.6

y-y1=m(x-x1)

y-6= -1.6(x-(-6))

y-6= -1.6x+6

The number of sugar cups will be equal to 7.5 cups.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that the ratio of flour to sugar is 2 cups to 3 cups. The number of cops for flour is 5.

The number of sugar cups will be calculated as,

F / S = 2 / 3

5 / S = 2 / 3

S = ( 5 x 3 ) / 2

S = 7.5 cups

Therefore, the number of sugar cups will be equal to 7.5 cups.

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We isolate the variable in an equation by dividing both sides of the equation in which one side does not contain any variable.

According to the question,

We have the following information:

Isolating a variable by dividing each side of the equation in which one side does not contain any variable.

Now, in this case, it is clearly stated that the first step to isolate the variable from the equation is to perform division.

Now, this can be done as follows in the given equation:

2x = 14

Now, the variable x can be isolated by dividing both sides of the equation by 2:

x = 14/2

x = 7

Hence, we isolate the variable in an equation by dividing both sides of the equation in which one side does not contain any variable.

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Answer:

x

Step-by-step explanation:

x

Answer:

Step-by-step explanation:

the answer is 8

The slope of the line that passes through (2,4) , (9,10) is 6/7

From the question, the points are given as

(2,4) , (9,10)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (2,4) and (9,10)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (2,4) and (9,10)

Substitute the known values in the above equation

So, we have the following equation

Slope = (10 - 4)/(9 - 2)

Evaluate

Slope = 6/7

Hence, the slope of the line is 6/7

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21⁰

sin0=opp/hyp

sin0=5/14

0=(sin^-1)5/14

0=21⁰

Answer:

$300

Step-by-step explanation:

S = amount of $$ Shivani currently has

Y = ... Yamini currently has

1. If Shivani gives 60 to Yamini, the amounts with both will be equal:
   S - 60 = Y + 60

2. if Yamini gives 20 to Shivani, the amount with Shivani would become twice the amount left with Yamini: 2(Y-20) = S+20

3. Simplify both equations and solve the system:

   S = Y + 120
   S = 2Y - 60

   Y + 120 = 2Y - 60  ⇒  Y = 180

   S = 180 + 120 = 300

To solve a proof question, firstly you have to identify the question and visualize it and then try to connect the given conditions.

Mathematical proofs can be difficult, but can be conquered with the proper background knowledge of both mathematics and the format of a proof.

To solve a proof question you have to remember following steps:

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The exponential function showing the relationship between t and y is y = 310000(1.048)⁺

From the question, we have the following parameters that can be used in our computation:

Initial population = 310000

Rate of growth = 4.8%

These parameters can be represeted as

a = 310000 and r = 4.8%

An exponential function is represented as

y = a(1 + r)⁺

Substitute the known values in the above equation, so, we have the following representation

y = 310000 (1 + 4.8%)⁺

Evaluate

y = 310000(1.048)⁺

Hence, the function is y = 310000(1.048)⁺

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Answer:

x less than or equal to -2

Step-by-step explanation:

I believe that's the answer

Answer:

  x < -2

Step-by-step explanation:

You want the domain of a function graphed as a curve with an open circle at x=-2, which is the right end of the curve.

The domain is the horizontal extent of the graph. It is the set of values for which the relation is defined.

The open circle at (x, y) = (-2, 0) means that point is not part of the graph. All x-values to the left of that point have corresponding y-values, so the extent of the graph can be said to be ...

  x < -2

The domain of the relation is x < -2.

Answer:

-3 <-1

-3 is less than -1.

By using Unitary method it can be calculated that

4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint

 1 quart of blue paint is mixed with  [tex]3\frac{1}{3}[/tex] quarts of white paint

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

a) Here, Unitary method will be used

Blue Paint                   White Paint

(Quart)                          (Quart)

[tex]1\frac{1}{2}[/tex]                                     5

[tex]1\frac{1}{5}[/tex]                                     4

1                                        [tex]3\frac{1}{3}[/tex]

5 quarts of white paint is mixed with [tex]\frac{3}{2}[/tex] quarts of  blue paint

1 quart of white paint is mixed with [tex]\frac{3}{2} \times \frac{1}{5}[/tex] quarts of blue paint

4 quarts of white paint is mixed with [tex]\frac{3}{2} \times \frac{1}{5} \times 4[/tex] quarts of blue paint

4 quarts of white paint is mixed with [tex]\frac{6}{5}[/tex] quarts of blue paint

4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint

Again

[tex]\frac{3}{2}[/tex] quarts of blue paint is mixed with 5 quarts of white paint

1 quart of blue paint is mixed with  [tex]5 \div \frac{3}{2}[/tex] quarts of white paint

1 quart of blue paint is mixed with  [tex]\frac{10}{3}[/tex] quarts of white paint

1 quart of blue paint is mixed with  [tex]3\frac{1}{3}[/tex] quarts of white paint

c) Finally

  4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint

   1 quart of blue paint is mixed with  [tex]3\frac{1}{3}[/tex] quarts of white paint

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Using doubles plus one fact the sum of 8 + 8 + 1is equal to 17 it is done by simply adding 1 to the given number.

Doubles plus one fact is used to add numbers which are next to each other.

Doubles plus one fact is simply done by doubling the number and adding one to it.

The sum of 8 + 8 can be determined by using doubles plus one fact as:

Simply add 1 in 8 + 8 + 1 to get the result required.

8 + 8 + 1 = 17

Therefore by using doubles plus one fact the sum of 8 + 8 + 1 is equal to 17.

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