Complete the follow two column proof
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The percentage decrease in the price of the two bags of oranges is 25.1 %.

We have been told that the usual price of a bag of oranges was $4 and during the promotion, it became $5.99 for two bags of oranges. We need to find the percentage decrease here.

We can calculate that two bags before the promotion cost =  $4 × 2 = $8

As we already know, the two bags during the promotion cost = $5.99

The decrease in price can be calculated as well  =  $8 - $5.99 = $2.01

Percentage decrease = ($2.01 /  $8) * 100 %

Percentage decrease = 25.1 %

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The rectangular form of 6{(cos225°) +i(sin225°) }is -3√2-3i√2.The shape that complex numbers typically take is referred to as rectangle form: z = a + bi.

Polar notation depicts a complex number in terms of the lengths of the vector and the angular direction from the starting point. In rectangle notation, a complex number is represented by its vertical and horizontal dimensions. The system is referred to be rectangular because the angles made by the axes at the origin and the measurements at point p are both 90 degrees. As a result, the measurement results in a rectangle with sides Xp and Yp.

To determine  rectangular form, we obtain,

Let Z=6{(cos225°) +i(sin225°)}

Now, cos225°=-cos( 180°+45°)= -cos45°= -[tex]\frac{1}{√2}[/tex]

sin225°=-[tex]\frac{1}{√2}[/tex]

S0, 6{(cos225°) +i(sin225°)}= 6 ( -[tex]\frac{1}{√2}[/tex])+6i(-[tex]\frac{1}{√2}[/tex])=-3√2-3i√2.

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Answer:

A

Step-by-step explanation:

right on edge

Answer:

1.07 x 10^8

Step-by-step explanation:

Input x (0 1 2)-  Output y( 2 -1 -4) is ​represents the function y = -3x+2.The relationship between such a collection of input data and each output is how a function is defined.

A function is, to put it simply, a relationship between outputs in which each input is connected to exactly one output. For each function, there is a range, made the request, and domain. Typically, a function is written as f(x), where x stands for the output. It is possible for a function to be declared inside of a class, module, or other function.

To determine Function , we obtain,

y = -3x+2

y = -3(0)+2=2

y = -3(2)+2=-1

y = -3(2)+2=-4

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Answer:c

Step-by-step explanation:

Answer:

m∠FED = 80°

Step-by-step explanation:

The expression that can be used to determine if she has enough money to purchase the jeans would be discussed below.

The total amount of money given to Natalie by her mom= $40.

The original price of the jeans = $45

The discount percentage = 20% of 45

= 20/100 ×45/1

= 900/100 = $9

The price of the jeans after discount = $36

The percentage of tax deduction = 8% of 45

= 8/100 × 45

= 360/100

= $3.6

The price of the jeans after tax = 36+ 3.6 = $39.6

Therefore, the amount of money that the money gave to Natalie to purchase jeans will be enough.

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Answer:3

Step-by-step explanation:

The solution to the system of equation is x = -2 and y = -3.

System of equation can be solved using different method such as elimination method, graphical method and substitution method,

here we have,

Therefore, let's solve the system of equation by using substitution method.

-2x+ 7y = 15

6y=x

substitute the value of x in equation(i)

-2* 6y+ 7y = 15

or, -12y + 7y = 15

or, -5y = 15

or, y = -3

so, we get,

x = 6/ -3

or, x = -2

Hence, The solution to the system of equation is x = -2 and y = -3.

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Therefore, the n-th term of the sequence is 19 - 2n.

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant value to the previous term. This constant value is called the common difference of the arithmetic sequence. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is obtained by adding 3 to the previous term.

The nth term of an arithmetic sequence can be expressed using the following formula:

an = a1 + (n - 1)d

where an is the nth term of the sequence, a1 is the first term, n is the number of the term, and d is the common difference.

The sum of the first n terms of an arithmetic sequence can also be calculated using the formula:

Sn = n/2(2a1 + (n - 1)d)

where Sn is the sum of the first n terms, a1 is the first term, n is the number of terms, and d is the common difference.

Here,

The first term of the sequence is 17 and the common difference between consecutive terms is -2 (i.e. subtracting 2 from the previous term to get the next term). So, we can write the n-th term of the sequence as:

a_n = 17 + (n-1)(-2)

Simplifying this expression, we get:

a_n = 19 - 2n

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Answer:

36

Step-by-step explanation:

The requried solution to the system of equations is x = 7, y = 6.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

To solve the system of equations:

4x - 2y = 16 - - --  - -(1)

2x + 3y = 32 - - - - - - (2)

We can use the method of substitution:
Solve one of the equations for one of the variables in terms of the other variable.
Let's solve the first equation for y:

4x - 2y = 16

-2y = -4x + 16

y = 2x - 8

Substitute the expression found in step 1 into the other equation 2.

2x + 3(2x - 8) = 32

Solve the resulting equation for the remaining variable.

2x + 6x - 24 = 32

8x - 24 = 32

8x = 56

x = 7

Substitute the value of x into one of the original equations to find the value of the other variable.

Using the first equation:

4x - 2y = 16

4(7) - 2y = 16

28 - 2y = 16

-2y = -12

y = 6

Therefore, the solution to the system of equations is x = 7, y = 6.

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Try using Socratic and it may help

Using the fact that the figures are similar, we will get z = 4.

We know that the two figures are similar, then the correspondent quotients between sides must be equal.

That means that we can write the equation:

10/15 = z/6

And we can solve that equation for z, we will get:

z = 6*(10/15) = 4

That is the value of z.

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Answer:

[tex]x=3, x=\frac{17}{4}[/tex]

Step-by-step explanation:

The side opposite to the length of 20 is 7x - 11, whereas the side opposite to an unknown length is 4x - 2. To solve this unknown length, we are given 35 as the total length, so we can do 35-20 = 15, which is the opposite of the length of 4x-2.

Since we know the opposite sides of each side, we can set up these equations since we notice that the lengths are parallel based on what is diagrammed:

[tex]7x-11=20[/tex]

[tex]4x-2=15[/tex]

Now, let's solve for x in [tex]7x-11=20[/tex]:

[tex]7x-11=20[/tex]

[tex]7x=20+11\\7x=21\\x=3[/tex]

Let's solve for x in [tex]4x-2=15[/tex]:

[tex]4x-2=15[/tex]

[tex]4x=15+2\\4x=17\\x=\frac{17}{4}[/tex]

to determine the stability of the equilibrium solutions Consider the autonomous differential equation

dydt=f(y).

The equilibrium solutions are obtained by solving

f(y)=0 for y.

Let

c1,c2,⋯,cn

be the equilibrium solutions.

Plot

c1,c2,⋯,cn

on the real number line, and create a phase line using the signs of

f(y)

by drawing a left arrow on the interval where

f(y)<0

, and right arrows where

f(y)>0.

Use the phase line to determine the stability of the equilibrium solutions as follows.

If both arrows point toward the equilibrium solution, it is stable.

If both arrows point away from the equilibrium solution, it is unstable.

If one arrow points towards the equilibrium solution and one points away from it, it is semi-stable.

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Pythagorean theorem tells us how the side lengths of right triangles are related.

The Pythagorean theorem, also known as the Pythagorean identity, states that the sum of the squares of the lengths of the two sides forming the right angle is equal to the square of the length of the hypotenuse in any right triangle (the side opposite the right angle). In other words, the Pythagorean theorem can be used to calculate the length of the hypotenuse given the lengths of the two sides of a right triangle.

This relationship can be written as the equation:

[tex]a^2 + b^2 = c^2[/tex]

where a and b are the lengths of the legs, and c is the length of the hypotenuse. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

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The completed square form of the given equation is:

(x + 4)^2 + (y - 3)^2 = 40.

First to complete the square for the given equation:

x^2 + y^2 + 8x - 6y - 15 = 0

We need to group the x and y terms together and add and subtract some constants to make them into perfect squares.

x^2 + 8x + y^2 - 6y = 15

We can add and subtract constants inside the left side of the equation to make it into perfect squares, as follows:

x^2 + 8x + 16 + y^2 - 6y + 9 = 15 + 16 + 9

Now we can rewrite the left side of the equation as a sum of perfect squares:

(x + 4)^2 + (y - 3)^2 = 40

Therefore, the completed square form of the given equation is:

(x + 4)^2 + (y - 3)^2 = 40.

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The appropriate numerical measures of center and spread to describe a given distribution of a quantitative variable depend on the shape, symmetry, and presence of outliers in the data.

Measures of center include mean, median, and mode. The mean is affected by extreme values, while the median is resistant to outliers. The mode is useful when looking for the most common value or values in a distribution.

Measures of spread include range, interquartile range (IQR), variance, and standard deviation. The range is the difference between the maximum and minimum values, but it is sensitive to outliers. The IQR is the range of the middle 50% of the data and is resistant to outliers. Variance and standard deviation both measure the spread of the data around the mean, with the variance being the average squared deviation from the mean and the standard deviation being the square root of the variance.

In general, if the data is approximately symmetric and without outliers, the mean and standard deviation are appropriate measures of center and spread, respectively.

If the data is skewed or has outliers, the median and IQR are more appropriate. If the distribution has multiple modes, the mode may be useful to describe the distribution, but it should be used with caution as it may not be unique or well-defined for certain distributions.

Ultimately, the choice of measures of center and spread depends on the characteristics of the data and the research question being investigated. It is always a good practice to use multiple measures of center and spread and to visualize the distribution of the data using histograms or boxplots to gain a better understanding of the data.

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Answer:

7:55

Step-by-step explanation:

If the class is 30 minutes it would end at 7:15 then add 40 minutes to get 7:55.

The expression represents a correct solution to the equation 6(x+4)= 20 is x= -2/3

We know, that the equation is:

6(x+4)=20

6x + 24 = 20

Now, Subtract 24 from both sides

6x + 24 = 20

6x + 24-24 = 20-24

Simplify the expression in the equation

6x + 24-24 = 20-40

6x=-4

Divide both sides by the same factor

6x=-4

6x/6 =-4/6

Simplify the expression

Cancels numbers that are both numerators and denominators X=-4/6 X=-2/3

Therefore, the correct solution to the equation is x=-2/3

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Connie's total bill is sum of trail mix and water will be  $9.13.

What is sum ?
In mathematics, the sum refers to the result of adding two or more numbers together. It is a basic arithmetic operation, often used in many different mathematical concepts and calculations. The symbol for addition is '+', and the sum of a set of numbers is often represented using the capital Greek letter sigma (∑).

According to the question:

Connie's total bill would be the sum of the cost of the trail mix and the cost of the water, which is:

Total bill = cost of trail mix + cost of water

Total bill = $6.98 + $2.15

Total bill = $9.13

Therefore, Connie's total bill was $9.13.

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The solution of the Chinese Remainder Theorem can be calculated by using the formula: [tex]{\displaystyle x=\sum _{i=1}^{k}a_{i}M_{i}N_{i}.}[/tex]

According to the Chinese remainder theorem, if one knows the remainders of the Euclidean division of an integer n by multiple numbers, one may uniquely calculate the remainder of the division of n by the product of these integers, provided that the divisors are pairwise coprime (no two divisors share a common factor other than 1).

For example, if we know that the remainder of n divided by 3 is 2, the remainder of n divided by 5 is 3, and the remainder of n divided by 7 is 2, we may calculate the remainder of n divided by 105 (the product of 3, 5, and 7) without knowing the value of n. This tells us that if n is a natural number less than 105, then the only possible value of n is 23.

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the lateral surface area of the triangular prism with measurement of 5cm, 5cm, 4cm, 6cm and 12cm is 140 cm².

To find the lateral surface area of a triangular prism, we need to calculate the sum of the areas of all the rectangular faces of the prism. In this case, the triangular prism has two triangular faces and three rectangular faces. The triangular faces have dimensions of 5 cm (base) and 4 cm (height), while the rectangular faces have dimensions of 5 cm (width), 6 cm (height), and 12 cm (length).

To calculate the area of one of the triangular faces, we use the formula for the area of a triangle:

Area = (1/2) x base x height

In this case, the base is 5 cm and the height is 4 cm, so the area of one triangular face is:

Area = (1/2) x 5 cm x 4 cm = 10 cm²

Since there are two triangular faces, the total area of the triangular faces is: Total area of triangular faces = 2 x 10 cm² = 20 cm²

To calculate the area of one of the rectangular faces, we use the formula for the area of a rectangle: Area = length x width

In this case, the dimensions of the rectangular faces are 6 cm (height) x 5 cm (width) and 12 cm (length) x 5 cm (width), so the areas of these faces are: Area of one rectangular face = 6 cm x 5 cm = 30 cm²

Area of another rectangular face = 12 cm x 5 cm = 60 cm²

Since there are three rectangular faces, the total area of the rectangular faces is: Total area of rectangular faces = 30 cm² + 60 cm² + 30 cm² = 120 cm²

Finally, the lateral surface area of the triangular prism is the sum of the areas of the triangular and rectangular faces:

Lateral surface area = Total area of triangular faces + Total area of rectangular faces

Lateral surface area = 20 cm² + 120 cm² = 140 cm²

Therefore, the lateral surface area of the triangular prism is 140 cm².

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The value of 0.4375 in fractional form is 7/16.

Parts of a whole numbers are represented by fractions, where the denominator represents the entire object and the numerator the equal part.

By dividing a number by 10 for each digit after the decimal, we may eliminate the decimal and turn it into a fraction.

The decimal point is followed by four integers, thus we will divide it by 10,000.

= 4375 / 10000

Simplifying fraction yields the result

= 4375 ÷ 5 / 10000 ÷ 5

= 875 ÷ 5 / 2000 ÷ 5

= 175 ÷ 5 / 400 ÷ 5

= 35 ÷ 5 / 80 ÷ 5

= 7 / 16

In addition, they are comparable fractions.

The fractional equivalent of 0.4375 is 7/16.

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Complete question - what is 0.4375 as a fraction?

the expression equivalent to 7k+13-4K+10+5k-6 is 8k + 17. correct option: (B) 14+72

How to do and what is expression equivalent?

Simplifying the expression by combining like terms, we get:

7k + 13 - 4k + 10 + 5k - 6

= (7k - 4k + 5k) + (13 + 10 - 6)

= 8k + 17

Therefore, the expression equivalent to 7k+13-4K+10+5k-6 is 8k + 17. correct option would be : (B)

Two expressions are equivalent if they represent the same mathematical value for all possible values of the variables. In other words, if you substitute any value for the variables in both expressions, the resulting values will be the same.

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After 10 minutes, the first pool will contain a volume of 2267.5 liters of water and the second pool will contain 2702.5 liters of water.

It is important to first identify the information given in the question. We have the starting amounts of water in both pools, as well as the rates at which water is being added to each pool. Using this information, we can set up an equation to determine how much water will be in each pool after a certain amount of time.

Let t represent the amount of time in minutes that the pools are being filled. The equation for the first pool will be 1920 + 34.75t and the equation for the second pool will be 2500 + 20.25t.

To find out how much water is in each pool after a certain amount of time, we can simply plug in the value of t and solve for the amount of water. For example, if we want to know how much water is in each pool after 10 minutes, we can plug in t = 10 and solve:

First pool: 1920 + 34.75(10) = 1920 + 347.5 = 2267.5 liters
Second pool: 2500 + 20.25(10) = 2500 + 202.5 = 2702.5 liters

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Jen returned home was 11:02. Below, you will learn how to solve the problem.

When Jen left the house, it was 10:03, she was running errands for 59 minutes. To find out what time it was when she returned home, we need to add the 59 minutes to the time she left the house.

First, we need to convert the time she left the house to minutes, 10:03 is equal to 603 minutes (10 hours x 60 minutes per hour + 3 minutes).

Next, we add the 59 minutes she was running errands to the 603 minutes:

603 minutes + 59 minutes = 662 minutes

Finally, we convert the 662 minutes back to hours and minutes:

662 minutes ÷ 60 minutes per hour = 11 hours with 2 minutes remaining

So, the time when Jen returned home was 11:02.

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The complete ratio table is

Hours       Weeks

168              1

1008             6

840               5

How to complete the table?

The mathematical operation that would be used to determine the missing values are division and multiplication. In order to convert hours to weeks, divide by 168 hours. To convert weeks to hours, multiply by 168.

1008 hours to weeks = 1008 / 168 = 6 weeks

5 weeks to hours = 5 x 168 = 840 hours

Hence , The complete ratio table is

Hours       Weeks

168              1

1008             6

840               5

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Let's first determine how much Charlie will have in his savings account at the end of the summer if he doesn't withdraw any money. There are 12 weeks in the summer, so he would have:

$500 - $25/week x 12 weeks = $200

So if he withdraws money for more than 0 weeks, he will not have at least $200 in the account at the end of the summer. Therefore, he cannot withdraw any money from the account.

Answer:

12 weeks.

Step-by-step explanation:

Since Charlie has $500, but wants to spend $25 every week, we can set up a problem.

[tex]25[/tex] × [tex]12[/tex] [tex]= 300[/tex]

Thus, he can go 12 weeks and spend $300 while still managing to have $200 left in his account.

Hope it helped!