Express the following in simplest a + bi form.
V9+1-36
O
-91
O
3 - 61
3 + 6
91

Answer: The slope is -2 and the y-intercept is (0,1)

Step-by-step explanation:

The given problem can be exemplified in the following diagram:

The trajectory of the boat can be divided into two distinct right triangles, as shown in the figure. The difference between each of the sides of the right triangle form another right triangle that will allow us to determine the total distance using the Pythagorean theorem.

Solving the operation:

Now using the sine function:

Solving the operations:

This can be exemplified in the following diagram:

Using the Pythagorean theorem:

Replacing the values:

Solving the operations:

Taking square root to both sides:

Therefore, the total distance is 313 miles.

The cost price of the shorts is K22.50.

To find the cost price of the shorts, we need to reverse calculate the original price before the markup and taxes were applied.

Let's assume the cost price of the shorts is represented by C.

The markup of 17% is applied to the cost price, which means the selling price (including the markup) is 117% of the cost price.

117% of the cost price C can be calculated as (117/100) * C.

GST (Goods and Services Tax) is also included in the selling price. GST is typically calculated as a percentage of the selling price. In this case, the selling price of the shorts including GST is K29.25.

Since the GST is included in the selling price, we can subtract it from the selling price to obtain the selling price before GST.

Let's assume the GST rate is R% (as a decimal), then the selling price before GST can be calculated as:

Selling price before GST = Selling price - (Selling price × R)

In this case, the selling price before GST is K29.25, and the GST rate is 17% (0.17 as a decimal). Substituting these values into the equation, we have:

K29.25 = Selling price - (Selling price × 0.17)

Simplifying the equation

K29.25 = Selling price × (1 - 0.17)

K29.25 = Selling price × 0.83

Selling price = K29.25 / 0.83

Now we can substitute the selling price in terms of the cost price:

K29.25 / 0.83 = (117/100) × C

Simplifying the equation:

C = (K29.25 / 0.83) × (100/117)

Calculating the cost price C:

C = K22.50

Therefore, the cost price of the shorts is K22.50.

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The solution to the system of linear equation (x, y) are (0, 2) and the graph is attached below

The linear equations are;

2y = 6x + 4...eq(i)

y = -2x + 2 ...eq(ii)

From eq(ii)

y = -2x + 2

Put eq(ii) into eq(i)

2(-2x + 2) = 6x + 4

-4x + 4 = 6x + 4

6x + 4x = 4 - 4

10x = 0

x = 0

Put x = 0 into eq(ii)

y = -2(0) + 2

y = 2

The solution are (x, y) , (0, 2)

Kindly find the attached graph below

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With the Application of Integral calculus the volume of  solid generated is π.

what is integral calculus?

We study integrals and their characteristics in the calculus area known as integral calculus. A crucial idea is integration, which is the opposite of difference. The fundamental theorem of calculus establishes a connection between integral and differential calculus.

v = 2π∫0√π/2xcosx2dx

  = π·sinx20√π/2

v = π

Hence the volume of  solid generated when the region enclosed by the given curves is revolved about the y-axis is π

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Answer:

y=50+12x y=100+9x

Step-by-step explanation:

Answer:

Answer below

Step-by-step explanation:

x=-4

3×(-4)+5= -7

x=-2

3×(-2)+5= -1

x=0

3×(0)+5= 5

x=2

3×(2)+5= 11

hope this helps!

Answer:

I think it would be 5 I'm honestly not 100% sure though!

Answer:

167 pairs

Step-by-step explanation:

Represent jeans with J and shirts with S

\(S = 2J\)

\(Amount = \$500\) --- Maximum

Required

Determine the number of pair of jeans he can buy

To represent as an inequality, we have:

\(S + J \leq Amount\)

\(S + J \leq 500\)

Substitute 2J for S

\(2J + J \leq 500\)

\(3J \leq 500\)

Divide through by 3

\(J \leq 500/3\)

\(J \leq 167\)

Hence, without exceeding $500, Jess can buy 167 pairs of jeans

Answer:

7

Step-by-step explanation:

30( 7 ) + 14( 12 ) =448 \(\leq\) 500

The sum of the infinite geometric sequence is 3 3/4

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

The geometric sequence

In the geometric sequence, we have

First term, a = 3/5¹⁻¹

a = 3

Also, we have

Common ratio, r = 1/5

The sum of the infinite geometric sequence is calculated as

Sum = a/(1 -  r)

So, we have

Sum = 3/(1 -  1/5)

Evaluate

Sum = 3 3/4

Hence, the sum of the infinite geometric sequence is 3 3/4

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The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Hey girl! It's me again to explain this to you :)

Number 21.) If we start from our y-intercept -2 and move up 2 on our y-axis we get to point (0,0). If we move over 1 space to the right, we are on (1,0), which is the x-intercept.

Slope: 2/1 or just 2

Y-intercept: -2

You didn't ask for this but i'm gonna write it anyways. The equation for this line is y=2x-2

Number 22.) If we start from our y-intercept 2 and move down 2 on your y-axis we get to point (0,0). If we move over 1 space to the right, we are on (1,0), which is the x-intercept.

Slope: -2/1 or just -2

Y-intercept: 2

Again you didn't ask for this but the equation for this line is y=-2x+2

Hope this helped you understand and again make this brainliest and reply if you need more help or have any more questions :)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

sin  (  3pi / 4 )

 =  sin   (   pi   -   pi  /  4   )

 =  sin   (   pi / 4  )

 = 1/root(2)

  =  root(2) / 2

Answer:

x=y-6/3y+1

Step-by-step explanation:

3xy+x=y−6

Step 1: Factor out variable x.

x(3y+1)=y−6

Step 2: Divide both sides by 3y+1.

x(3y+1)

3y+1

=

y−6

3y+1

It should be noted that to calculate the rate of change on a graph, you need to determine how much the dependent variable (y) changes for a given change in the independent variable (x). This is also known as the slope of the graph.

Here are the steps to calculate the rate of change on a graph:

Identify two points on the graph that you want to calculate the rate of change between. These points can be any two points on the line or curve.

Determine the change in the dependent variable (y) between the two points. This is the difference between the y-values of the two points.

Let's call this change in y as "Δy".

Determine the change in the independent variable (x) between the two points. This is the difference between the x-values of the two points.

Let's call this change in x as "Δx".

Calculate the rate of change (or slope) using the formula:

slope = Δy/Δx

This formula gives you the average rate of change between the two points.

An overview was given as your information is incomplete.

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Each cut piece measures 6.25 meters in length.

One of the fundamental mathematical operations is division, in which a bigger number is divided into smaller groups with the same number of components.

One of the fundamental mathematical operations is division, in which a bigger number is divided into smaller groups with the same number of components.

Given

The thread was divided into 4 equal pieces after being cut at 25 meters.

= 25/4 \s = 6.25.

The thread was divided into 4 equal pieces after being cut at 25 meters.

= 25/4 \s = 6.25.

Each cut piece measures 6.25 meters in length.

The complete question is,

A 25 meter distance. Cindy cut the string into four equal pieces. each component's quality.

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The graph that represents the function y= tanx is Option A.

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and   negative infinity, creating a wave-  like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

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Answer:

x = 1

y = 5

z = 2

Step-by-step explanation:

System of equations:

6x - 2y + z = -2

2x + 3y - 3z = 11

x + 6y = 31

Isolate one variable in any of the equations:

x + 6y = 31

x = 31 - 6y

Plug in this value for x in another equation:

6(31 - 6y) - 2y + z = -2

186 - 36y - 2y + z = -2

186 - 38y + z = -2

-38y + z = -188

z = -188 + 38y

Plug in these values in the remaining equation:

2(31 - 6y) + 3y - 3(-188 + 38y) = 11

62 - 12y + 3y + 564 - 114y = 11

626 - 12y + 3y - 114y = 11

626 - 9y - 114y = 11

626 - 123y = 11

-123y = -615

y = 5

Plug in value of y into our other answers to solve for x and z:

x = 31 - 6(5)

x = 31 - 30

x = 1

z = -188 + 38(5)

z = -188 + 190

z = 2

Check your work:

6x - 2y + z = -2

6(1) - 2(5) + 2 = -2

6 - 10 + 2 = -2

-4 + 2 = -2

-2 = -2

Correct!

*Note there are several ways to solve for these types of problems. I used substitution*

Answer:

63

Step-by-step explanation:

5 tens=50, and 13 ones=13. 50+13=63

Answer:34.63

Step-by-step explanation:

Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

The loss percentage is 91%.Given that Venessa bought 80 apples for 4$, out of these apples, 25% were rotten and had to be thrown away. Venessa sold the remaining apples at 6 cents per apple.To calculate the profit or loss percentage, we need to determine the cost price, selling price, and the number of apples sold.

Cost price (CP) = 4 $.Selling price (SP) = 80 × 0.75 × 6 cents= 36 cents = 0.36 $.Now, let's calculate the profit.Profit = SP – CP= 0.36 $ – 4 $= – 3.64 $Loss = CP – SP= 4 $ – 0.36 $= 3.64 $.

Therefore, Venessa incurred a loss of $3.64 when she sold 80 apples at 6 cents per apple.Now let's calculate the loss percentage Loss Percentage = (Loss / CP) × 100= (3.64 / 4) × 100= 91%.

Therefore, the loss percentage is 91%.Note: If the result obtained after the subtraction of SP from CP is negative, it means there is a loss, and the percentage of loss can be calculated by (loss/CP) × 100.

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Answer: It is a reflection of Reflections of You (second location) in the x-axis.

Step-by-step explanation: Based on the given information, the relationship between the new location (The Gridiron) and the previous locations can be determined.

The correct answer is:

   It is a reflection of Reflections of You (second location) in the x-axis.

The coordinates of the first three checkpoints of The Gridiron (A''(0,−5), B''(9,−5), and C''(4,−5)) indicate that they have the same y-coordinate (-5) as the corresponding checkpoints in the second location, Reflections of You. However, there is no indication of a reflection in the y-axis or any transformation related to the first location, Transformation Fitness Studios. Therefore, the correct answer is that The Gridiron is a reflection of Reflections of You in the x-axis.

The equation for the line of best fit is: C. y = 0.894x + 0.535.

In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;

x          y            x²        y²          xy__

5          4          25        16       20

6          6           36       36       36

9          9           81        81        81

10         11          100       121       110

14          12        196       144      168  

Sum                  438       398     415

Next, we would calculate the mean of the x and y variables as follows;

Mean = [∑(x)]/n

Mean = 44/5

Mean, \(\bar{x}\) = 8.8

Mean = [∑(y)]/n

Mean = 42/5

Mean, \(\bar{y}\) = 8.4

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4

∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²

∑(x - \(\bar{x}\))² = 50.8

Now, we can determine the slope coefficient for the line of best fit:

Slope (b) = 45.4/50.8

Slope (b) = 0.894.

Lastly, we would determine the intercept (a) as follows;

\(a = \bar{y} - b\bar{x}\)

a = 8.4 - (0.894)8.8

a = 0.535

Therefore, the required equation is y = 0.894x + 0.535.

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