the volume of the simplex with vertices at the origin and the standard basis vectors in nn dimensions

Quadratic Equations in Single Variable

n²-3n+10=0

2x²+2x+1=0

25b²-16=0

f²-3f+2=0

1/3m +2m=4

a²=225

Linear Equation in single Variable

8-3k=12

5w+5=0

10u-5=8

Linear Equation in Two  Variable

2y-z=9

3r+2e=6

d=3e-7

It should be noted that an equation simply means the expression that's used to show the relationship between the variables.

In this case, the equation has been grouped.

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Group the given equations into two based on observed common properties.

Equations

n²-3n+10=0

8-3k=12

2y-z=9

2x²+2x+1=0

25b²-16=0

3r+2e=6

5w+5=0

f²-3f+2=0

d=3e-7

1/3m +2m=4

10u-5=8

a²=225

When you have two parallel lines (lines m and n) crossed by a transversal (porch stain) the angles 7 and 8 sum 180º and angles 1 and 8 are alternate exterior angles (have the same measure)

Then to find the measure of angle 1:

1. Find the measure of angle 8:

2. Alternate exterior angles have the same measure:

The patient will pay $452.20 in full today after applying the 15% discount.

If the patient receives a 15% discount for a visit to the healthcare provider and the total charge for the service is $532.00, the patient will pay 100% - 15% = 85% of the total charge.

To calculate the amount the patient will pay in full today, we need to find 85% of $532.00.

85% of $532.00 can be calculated as:

(85/100) * $532.00 = $452.20

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According to Siegler, the pattern of learning math concepts involves a gradual development and refinement of strategies. Siegler's theory, known as the overlapping waves model, suggests that learners use multiple strategies simultaneously and gradually shift towards more efficient ones over time. This process allows for a better understanding and application of math concepts, ultimately leading to improved problem-solving skills.

According to Siegler, the pattern of learning math concepts involves a gradual progression from using counting strategies to more efficient and accurate strategies. Children initially rely on counting strategies to solve math problems, such as counting fingers or objects. As they progress, they begin to use more advanced strategies, such as decomposition or mental math, which allow them to solve problems more quickly and accurately. Siegler also emphasizes the importance of practice and repetition in developing math skills and the role of feedback and instruction in promoting learning. Overall, Siegler's theory suggests that children's math skills develop through a combination of innate abilities and environmental factors, including exposure to math concepts and opportunities for practice and instruction in time.

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Diagonal of rectangle is changing by the rate of 4.373 in. /sec.

Rate of change (ROC) is the rate at which a variable changes over a particular period of time

To find the average rate of change, divide the change in the y-values ​​by the change in the x-values . Finding the average rate of change is especially useful for identifying changes in measurable values ​​such as average speed or average velocity.

A ratio is a special ratio in which the two terms have different units.

the calculation part is shown in the below picture attached .

so after seeing the solution we come to an answer of = 4.373 in./sec

therefore diagonal of rectangle is changing by the rate of 4.373 in. /sec

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To find f(7), we can use the fact that g(7)=4 and the limit given in the problem.

First, let's simplify the limit by factoring out the common factor of f(x):

limx→7[3f(x)+f(x)g(x)] = limx→7[f(x)(3+g(x))]

Since f and g are both continuous functions, we can evaluate the limit by plugging in the value of 7:

limx→7[f(x)(3+g(x))] = f(7)(3+g(7)) = f(7)(3+4) = 7f(7)

We know that this limit equals 28, so we can write:

7f(7) = 28

Solving for f(7), we get:

f(7) = 4

Therefore, f(7) = 4.

Let's solve for f(7) using the given information about the continuous functions f and g.

We know that g(7) = 4 and lim(x→7)[3f(x) + f(x)g(x)] = 28.

Since f and g are continuous functions, we can apply the limit properties:

lim(x→7)[3f(x) + f(x)g(x)] = 3 * lim(x→7)[f(x)] + lim(x→7)[f(x)g(x)] = 28.

Now, we need to find lim(x→7)[f(x)] and lim(x→7)[f(x)g(x)].

Since f is continuous, lim(x→7)[f(x)] = f(7).

For lim(x→7)[f(x)g(x)], we can use the property lim(x→7)[f(x)g(x)] = lim(x→7)[f(x)] * lim(x→7)[g(x)] = f(7) * g(7) = 4f(7) (since g(7) = 4).

Now we can plug these limits back into our original equation:

28 = 3 * f(7) + 4f(7).

Combining the terms, we get:

28 = 7f(7).

Now, we can solve for f(7):

f(7) = 28 / 7 = 4.

So, f(7) = 4.

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The weaker inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) holds for all positive integers n, but using mathematical induction, the basis step works, although the inductive step fails.

a) If we try to prove the inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) using mathematical induction, we can see that the basis step works. When n = 1, we have 1/2 < 1/√3, which is true.

Now, let's consider the inductive step. Assuming that the inequality holds for some positive integer k, we need to show that it also holds for k+1, i.e., we assume 1/2 · 3/4 ··· 2k-1/2k < 1/√(3k) and we want to prove 1/2 · 3/4 ··· 2k-1/2k · (2k+1)/(2k+2) < 1/√(3k+3).

If we attempt to manipulate the expression, we can simplify it to (2k+1)/(2k+2) < 1/√(3k+3). However, we cannot proceed further to prove this inequality, as it is not necessarily true. Therefore, the inductive step fails, and we cannot establish the original inequality using mathematical induction.

b) However, mathematical induction can still be used to prove the stronger inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n+1) for all integers greater than 1. We can start by verifying the case where n = 1, which gives us 1/2 < 1/√4, which is true.

Now, assuming the inequality holds for some integer k, we can multiply both sides of the inequality by (2k+3)/(2k+2) to get:

(1/2 · 3/4 ··· 2k-1/2k) · (2k+3)/(2k+2) < 1/√(3k+1) · (2k+3)/(2k+2).

Simplifying the expression on both sides, we have:

(2k+3)/(2k+2) < 1/√(3k+1) · (2k+3)/(2k+2).

We can observe that the right side of the inequality is less than 1/√(3k+3) by multiplying the denominator of the right side by (2k+3)/(2k+3). Hence, we obtain:

(2k+3)/(2k+2) < 1/√(3k+3).

This establishes the inequality for k+1, and thus, we have proven the stronger inequality using mathematical induction.

By verifying the case where n = 1 separately, we can conclude that the weaker inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) holds for all positive integers n, as it follows from the proven stronger inequality using mathematical induction.

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Answer:

\(\sf \dfrac{64}{343} \ cubic \ yard\)

Step-by-step explanation:

      \(\sf \boxed{\bf Volume \ of \ cube =a^3}\)

Here, a is the edge of the cube.

\(\sf a =\dfrac{4}{7} \ yard\)

 \(\sf Volume \ of \ cube = \dfrac{4}{7}*\dfrac{4}{7}*\dfrac{4}{7}\)

                          \(\sf =\dfrac{64}{343} \ cubic \ yard\)

Answer:

The answer is

B

D

F

Step-by-step explanation:

Squaring a fraction is like squaring a whole number really so you just square the fraction by multiplying it by itself.

Answer:

Equation of line that includes the point (-9, -8) has a slope of 5 in point-slope form is

\(y+8 = 5 (x + 9)\)

Step-by-step explanation:

Equation of line in point-slope form is given as

\(y-y_1 = m (x-x_1)\)  ---------- (1)

Here

\(m=5 \ \ \ and \ \ \ (x_1, y_1) = (-9, -8)\)

Substitute values in equation (1)

\(y+8 = 5 (x + 9)\)

Simplifying it further

\(y = 5x + 45 -8\)

\(y = 5x + 37\)

The algebraic expression for "The product of 9 and two more than a number" is 9(x + 2).

In the given word phrase, "a number" is represented by the variable x. The phrase "two more than a number" can be translated as x + 2 since we add 2 to the number x. The phrase "the product of 9 and two more than a number" indicates that we need to multiply 9 by the value obtained from x + 2. Therefore, the algebraic expression for this word phrase is 9(x + 2).

"A number": This is represented by the variable x, which can take any value.

"Two more than a number": This means adding 2 to the number represented by x. So, we have x + 2.

"The product of 9 and two more than a number": This indicates that we need to multiply 9 by the value obtained from step 2, which is x + 2. Therefore, the algebraic expression becomes 9(x + 2).

In summary, the phrase "The product of 9 and two more than a number" can be algebraically expressed as 9(x + 2), where x represents the number.

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Answer:

No, Because BC is not parallel to AD

Answer:

A turtle travels about 90 feet

Because if a turtle can travel 450 feet within 25 minutes, then dividing 25 by 450 is 18 feet per minute, but if you multiply 5 minute x 18 feet, you get 90 feet in all.

So, a turtle can travel 450 feet per 25 minutes,

18 feet per minute, and

90 feet per 5 minutes

Hope this helps and I hope it is right, I used my skill thinking to solve this. So, please let me know if it did help and you do get it.

The amount by which the population decreased from 2015 to 2020, to the nearest 100 people will be 101577.114.

We will use the concept of percentage to solve this problem. By using percentage we can write any number in multiples of 100 and we denote the percentage by the sign %. The population of the city in 2010 was 101000. Now the population grew by 6.2% so the population in 2015 will be

Population in 2015 = 101000 + 6.2% of 101000

Population in 2015 = 101000 + 6262

Population in 2015 = 107262

Now the population decreased from 2015 to 2020 by 5.3% and population in 2020 will be

Population in 2020 = 107262 - 5.3% of 107262

Population in 2020 = 107262 - 5684.886

Population in 2020 = 101577.114

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To solve this problem, we need to set up a system of equations based on the given information. Let's assume that the farmer needs x cubic yards of mix a and y cubic yards of mix b.

For phosphoric acid, the equation would be:
x * pounds of phosphoric acid in mix a + y * pounds of phosphoric acid in mix b = pounds of phosphoric acid required

For nitrogen, the equation would be:
x * pounds of nitrogen in mix a + y * pounds of nitrogen in mix b = pounds of nitrogen required

For potash, the equation would be:
x * pounds of potash in mix a + y * pounds of potash in mix b = pounds of potash required

We can solve this system of equations using substitution or elimination method. Once we find the values of x and y, we can calculate the total cost.

Since the question asks for the answer in more than 100 words, I'll provide an explanation for the solution process.

1. Set up the equations using the given information.
2. Solve the system of equations to find the values of x and y.
3. Substitute the values of x and y into the cost equation to find the total cost.

The solution to the problem is to blend x cubic yards of mix a and y cubic yards of mix b to meet the minimum monthly requirements at a minimum cost. The total cost can be calculated by substituting the values of x and y into the cost equation.

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Answer:

The sheet should be turned up 7.5cm on each side to obtain maximum volume.

Step-by-step explanation:

If we make a rectangular eavesdrop, by bending the sheet along dotted line, then.

Height of eaves trough = x cm

Length of eaves trough = 600 cm

Width of eaves trough =  (30 - 2x) cm

We know that Volume is given by:

V = Length · Width · Height

V = (x)(30 - 2x)(600)

V = -1200x² + 18000x

To maximize the volume, we take the derivative and put it equal to zero.

\(\frac{dV}{dx} =\frac{d}{dx}( -1200x^2 +18000x)=0\\\frac{d}{dx}( -1200x^2 +18000x) = 0\\-(2)1200x+18000=0\\-2400x+18000=0\\x=\frac{18000}{2400}\\ x=7.5cm\)

Answer:

24

Step-by-step explanation:

24

Answer:

y=-x

I found the points then simplified it down

Answer:

hmm maybe trying using 2y=5x-2

Step-by-step explanation:

how i came to this was just looking at point y which was just 2 and then since point x was at 5,-2 all i did was simply it into 2y=5x-2

maybe that's the answer if it is can i get brainlist ?! pretty please if not let me know so i can see what i got wrong

Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

Answer:

About $4.98

Step-by-step explanation:

The cost of 30 ounces of iced tea will be $4.98.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

18 ounces. of iced tea costs 2.99. Then the ratio of cost to weight is calculated as,

⇒ $2.99 / 18

⇒ $0.166 per ounce

Then the cost of 30 will be calculated as,

⇒ $0.166 x 30

⇒ $4.98

The cost of 30 ounces of iced tea will be $4.98.

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Answer:

equation: 2(2w + 2) = 60

length = 16

width = 14

Step-by-step explanation:

width = w

length = w + 2

perimeter = 2(w + w + 2) = 60

equation: 2(2w + 2) = 60

4w + 4 = 60

4w = 56

w = 14

width = 14

length = w + 2 = 14 + 2 = 16

length = 16

Answer:

C

Step-by-step explanation:

As x moves towards infinity, the y value is constant, it never changes.

Answer:

The answer is C, it doesn't show a change

The rate of change of airplane is 3/4 mile and takes 30 minutes to last.

Given, the airplane begins its descent at 1 1/2 miles above the ground.

after 15 minutes the airplane is 3/4 mile above the ground.

height of the airplane if the airplane continues to descend at this

rate = ?

the change in height of the airplane is :

change in height = current height - initial height.

= 1 1/2 - 3/4

= 3/2 - 3/4

Reduction to common denominator.

= 3×2-3/4

= 6-3/4

= 3/4 miles.

Since the rate of descending remains, 3/4 mile need another 15 minutes.

therefore, the entire descent last:

15+15

= 30 minutes.

Hence, the rate of change of airplane is 3/4 mile and takes 30 minutes to last.

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Answer:

Enter cost and tip percent to get a tip amount and total dinner amount. Also split the total amount; divide among any number of people. ... Money, Pay, Taxes. > Tip ... Enter your meal or dinner cost along with the tip percentage. ... To calculate a gratuity or tip on any calculator it is a simple multiplication. ... All rights reserved

Step-by-step explanation:

After eating at your favorite restaurant, you know that the bill before tax is $52.60 and that the sales tax rate is 8%. You decide to leave a 20% tip for the waiter based on the pre-tax amount. How much ... To figure out the tip, you need to find 20% of $52.60. 0.2 \times 52.6

The amount that each person should pay is  $22.06   .

Percentages can be stated as essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number. We can take as example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

here, we have,

in the question ,

it is given that

total number of persons = 3 person + 1 = 4 persons

cost of the meal = $72.50

sales tax percent = 6.75%

tip percent = 15%

So , the amount of sales tax = 6.75% of cost = 0.0675 * 72.50 = $4.89

and , the amount of tip is = 15% of cost

= 0.15 * 72.50

= 10.87

So , the total amount payable is = cost + sales tax + tip

= 72.50 + 4.89 + 10.87

= 88.26

since the total number of persons is 4 ,

the amount per person is = 88.26/4 = 22.06

Therefore , The amount that each person should pay is  $22.06   .

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Answer:

neither

Step-by-step explanation:

the slope of the first seems to be 1/5 while the second looks to be 2/5

The complement of set A, denoted by ​ A`, is the collection of all elements that belong to the universal set but are not part of set A. It's not necessary to mention the universe (also known as U) if it's understood which set of elements is being referred to.

The complement of a set A is the collection of all elements that belong to the universal set but not to set A. It is denoted as ​ A` and does not include any elements that are already in set A. The universal set, also known as U, contains all possible elements and is assumed to be known. Therefore, when referring to the complement of a set, it is not necessary to mention the universal set explicitly. The complement of a set is useful in determining the set of elements that are not part of a particular set, and it can be used in various mathematical operations.

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Answer:

my best guess would be B for sure