f
(
x
)
=
−
x
2
+
6
x
+
13
f(x)=−x
2
+6x+13, determine the average rate of change of the function over the interval
−
1
≤
x
≤
5
−1≤x≤5.

Answer:

1.12*10^(-15)

Step-by-step explanation:

Answer:

1.12e-15

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

[tex] {(3x + 6)}^{2} [/tex]

Answer:

Step-by-step explanation:

a=175

r=2.8

The intersection of the sets of outcomes of events A and B is the set of all outcomes that are common in both events A and B. This is a concept from set theory in mathematics.

The correct answer to the given question is option B.

The correct statement that best describes the intersection of the sets of outcomes of events A and B is 'The intersection of the sets is the set of all outcomes in events A and B'.

In mathematical terms, the intersection of two sets, often denoted as A ∩ B, is the set of elements which are in both A and B.

Thus, the intersection of two sets of outcomes of events A and B, would consequently be the set of all outcomes that are common in both events A and B.

This is mainly a concept from set theory, a fundamental part of mathematics that deals with the study of sets, which are collections of objects.

For instance, if the set A = {1, 2, 3} and the set B = {2, 3, 4}, then A ∩ B = {2, 3}. In this example, 2 and 3 are the outcomes that are common in both events A and B.

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Answer:

C) 100

Step-by-step explanation:

line AC intersects line DB,

hence ∠AEB and ∠DEC are opposite angles and thus

∠AEB = ∠DEC

5x-10 = 4x+12   (subtract 4x from both sides)

5x - 4x - 10 = 12

x - 10 = 12    (add 10 to both sides)

x = 12 + 10 = 22 degrees

∠DEC = 4x+12

= 4(22) + 12

= 88 + 12

= 100 degrees

Answer:

Part a) see the explanation

Part b) The graph in the attached figure

Step-by-step explanation:

The complete question is

The length of a snake in a video game doubles every minute. the function f(x)=10*(2)^x represents the length of the snake in centimeters. the time x=0 represents when the game started.

a) label the correct axes with "length (cm)" and"time (minutes)"

b) graph f(x)=10*(2)^x

Part a) we know that

we have a exponential function of the form

[tex]f(x)=a(b^x)[/tex]

where

f(x) -----> the length of a snake in a video game in centimeters

x ----> the time in minutes

a is the initial value or y-intercept of the linear equation

b is the base of the exponential equation

In this problem

[tex]f(x)=10(2^x)[/tex]

so

[tex]a=10\ cm[/tex] ---> initial value, value of y when the value of x is equal to zero[tex]b=2[/tex] ----> factor growth

[tex]b=(1+r)\\r=b-1=2-1=1[/tex]

[tex]r=100\%[/tex] ----> percent rate of change

Is a exponential growth function

Part b) Graph the function

To graph the function we need different points

assume different values of x and find the values of f(x)

For x=0 ---->  [tex]f(0)=10(2^0)=10[/tex] ----> point (0,10)

For x=1 ---->  [tex]f(1)=10(2^1)=20[/tex] ----> point (1,20)

For x=2 ---->  [tex]f(2)=10(2^2)=40[/tex] ----> point (2,40)

For x=3 ----> [tex]f(3)=10(2^3)=80[/tex] ----> point (3,80)

For x=4 ---->  f(4)=10(2^4)=160 ----> point (4,160)

Plot the points, connect them and draw the graph

see the attached figure

Answer:

0.699 (=69.9%)

Step-by-step explanation:

Efficiency = total hits / total attempted

given total hits = 51 and total attempted = 73

Efficiency = 51/73 = 0.699 (=69.9%)

Introduction

Wrestling is a wonderful activity with many advantages for the student-athlete. It is a sport that is highly

competitive, exciting and satisfying. It is a sport that provides for individual and team competition. It is -

and should be - fun. Unfortunately, the practice of losing weight by not eating, restricting fluid intake and

over-exercising reduces the sport's fun. This information is presented to help clear up misconceptions

regarding wrestling and weight loss. I also hope to give some guidance to those who desire to manage

their weight properly in preparation for and during the wrestling season.

History and Stigma

For too long, the wrestling community has unthinkingly accepted the myth that to be a good wrestler, you

must cut weight. The generally accepted thinking is something like this: if your natural weight is 135

pounds, you may be a good wrestler at 135 pounds. But if you wrestle at 130 pounds, you'll be a better

wrestler. And if you can make it down to 125, you'll be a state champion. No facts support that widely held

view, yet wrestlers and parents subscribe to that faulty reasoning. Looking further back, many remember

the days that losing excessive weight was a specific practice and expectation among wrestlers. It was

supposed to teach sacrifice, commitment, and the idea of “No Pain, No Gain.”

Regardless of the current attitude of the majority of the wrestling community, the stigma that an unhealthy

loss of weight is a requirement of wrestling among outside observers sticks. The Virginia High School

League has followed national guidelines to establish rules that encourage healthy weight management

among wrestlers.

Current Regulations

Preseason weight certification is accomplished with three steps. The first is determining each wrestler’s

body fat percentage using skin fold calipers. Next, the wrestler completes a hydration test, to insure

against a dehydrated weight measurement, and the wrestler weighs in. The third step is the calculation of

the wrestler’s minimum wrestling weight based on 7% body fat for males and 12% for females. The

wrestler may not wrestle at a weight class below his minimum weight during the season. The wrestler is

also restricted from losing more then 1.5% body weight loss per week (official weigh-ins at certification,

matches, and tournaments are used for this calculation). A one-pound per month growth allowance is

provided to allow for the natural growth of this age group. The VHSL advises, and we have instituted,

daily weigh-ins before and after practice to monitor weight-loss and dehydration.

Additionally, the National Federation of State High School Associations has adopted several other rules to

guide coaches and wrestlers while managing their weight. Wrestlers are discouraged from wrestling at a

weight class more then one weight class above their certified weight.

The equation that models the situation of a wrestler's varying weight is w = x +/- 3.2, with x representing the normal weight. The minimum weight is 164.8 pounds and the maximum weight is 171.2 pounds.

To write an equation that models the situation, we can use the variables x and w to represent the normal weight and the varying weight, respectively. The equation can be written as w = x +/- 3.2, where the +/- sign represents that the weight can vary by as much as 3.2 pounds. Given that the normal weight is 168 pounds, the minimum weight would be 168 - 3.2 = 164.8 pounds, and the maximum weight would be 168 + 3.2 = 171.2 pounds.

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Option A

[tex](7 \times 10^{-3}) - (2.3 \times 10^{-6}) = 6.9977 \times 10^{-3}[/tex]

Solution:

Given expression is:

[tex](7 \times 10^{-3}) - (2.3 \times 10^{-6})[/tex]

To evaluate the expression, let us make the exponent of 10 same

[tex]2.3 \times 10^{-6} = 0.0023 \times 10^{-6+3} = 0.0023 \times 10^{-3}[/tex]

[ Here, decimal point is moved three times left, so add 3 ]

Therefore,

[tex](7 \times 10^{-3}) - (2.3 \times 10^{-6}) = (7 \times 10^{-3}) - (0.0023 \times 10^{-3})[/tex]

[tex]\text{Take the } 10^{-3} \text{ as common }[/tex]

[tex](7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 10^{-3}(7-0.0023)\\\\\text{ Solve for terms inside the bracket }\\\\(7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 10^{-3} \times 6.9977\\\\\text{Therefore, the simplified expression is: }\\\\(7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 6.9977 \times 10^{-3}[/tex]

Thus Option A is correct

Answer:

The rate of change for the interval shown in the table is 1 , so the function is a linear function.

Step-by-step explanation:

See the table attached.

The table shows selected points from a function.

Now, the given interval is x = 1 to x = 4.

For, x = 1, f(x) = 2 and for x = 4. the function f(x) = 5.

Therefore, the rate of change for the interval shown in the table i.e slope of the line is [tex]\frac{5 - 2}{4 - 1} = 1[/tex] and it is constant throughout the interval so the function is a linear function. (Answer)

The rate of change for the interval shown in the table is constant , so the function is a linear function.

Note the following important points:

1. Linear Function:

If the difference between y values remains constant for any pair of consecutive points ([tex]y_2-y_1 = y_3-y_2 = y_4-y_3,[/tex]and so on), the function exhibits a constant rate of change, indicating a linear function. In this case, the rate of change would be the difference between two y values divided by the difference between their corresponding x values (e.g., [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]).

2. Non-Linear Function:

If the difference between y values varies between consecutive points, the function would be non-linear. The specific type of non-linear function (e.g., quadratic, exponential) would require further analysis with more data points or additional information about the function's behavior.

In this case, as shown in the attached table, it is clear that

For [tex]x_1=1, y_1=f(x)=2[/tex].

For [tex]x_2=2, y_2=f(x)=3[/tex].

For[tex]x_3=, y_3=f(x)=4[/tex].

For [tex]x_4=, y_4=f(x)=5[/tex], and so on.

Thus the rate of change for the interval shown in the table or its slope is constant as evident from the following calculation.

[tex]\frac{(y_2-y_1)}{(x_2-x_1)}=\frac{3-2}{2-1}=1\\ \frac{(y_3-y_2)}{(x_3-x_2)}=\frac{4-3}{3-2}=1\\\frac{(y_4-y_3)}{(x_4-x_3)}=\frac{5-4}{4-3} =1[/tex].

So it is clear that, the rate of change for the interval shown in the table is constant , so the function is a linear function.

Answer:

The correct option:  x + y = 6

Step-by-step explanation:

In a Cartesian system or a coordinate system, the abscissa is the value of the horizontal (x) value and the ordinate is the value of the vertical (y) value.

So, The sum of the abscissa and the ordinate = x + y when written as an algebraic expression.

Since given that The sum of the abscissa and the ordinate is six

So,  the correct equation is x + y = 6

-8, 3.5, -1.15. -9 1/4

I hope this helped!

Answer:

[tex]f=6.8[/tex]  

Step-by-step explanation:

Given equation:

[tex]88.1-2.3f=72.46[/tex]

To solve for the unknown variable [tex]f[/tex].

Solution:

In order to solve for [tex]f[/tex], we will isolate [tex]f[/tex] alone on one side by carrying out math operations to both sides.

We have:

[tex]88.1-2.3f=72.46[/tex]

Subtracting both sides by 88.1

[tex]88.1-88.1-2.3f=72.46-88.1[/tex]

[tex]-2.3f=-15.64[/tex]

Dividing both sides by -2.3

[tex]\frac{-2.3f}{-2.3}=\frac{-15.64}{-2.3}[/tex]

∴ [tex]f=6.8[/tex]    (Answer)

huh cant see nun............

Answer:

Step-by-step explanation:

Consider A=60°, B=50°, C=y°=???

So, according to the measurement of angles of a triangle.

A+B+C= 180°

60°+80°+C= 180°

140°+C=180°

C=180°-140°

C=y°=40°

So, x is also 40° since x and y are vertically opposite angles.

Answer:

4

Step-by-step explanation:

7-3=4

then i just messed around with putting numbers to the 4th and got 4

The question asks for a number which, when raised to the 7th power and divided by the same number raised to the 3rd power, results in 256. By understanding the rules of exponents, we find that the number is 4 because 4^4 equals 256.

To solve this problem, it's important to know that when you divide two numbers with the same base and different exponents, you subtract the exponents. So, a number to the 7th power divided by the same number to the 3rd power equals that number to the (7-3)th = 4th power.

Therefore, the question is asking for a number which to the 4th power equals 256. The fourth root of 256 is 4 because 4^4 equals 256. So the answer is 4.

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Answer:

The total amount that Beyonce will pay for the chair is $9100.

Step-by-step explanation:

The Principal amount of chair  = $6500

Rate of interest  = 8%

Time = 5 years

Now, SIMPLE INTEREST  = [tex]\frac{P\times R \times T}{100}[/tex]

So, here calculating the interest on the chair, we get:

[tex]SI = \frac{6500 \times 5 \times 8}{100} = 2600[/tex]

So, the interest on the amount of chair for 5 years  is $2600.

Total amount of chair  = Original Amount of Chair + Interest Amount

                                      = $6500 + $2600 = $9100

Hence, the total amount that Beyonce will pay for the chair is $9100.

To find the total amount, calculate the interest and add it to the principal amount.

Simple interest is calculated using the formula: I = P * r * t, where I is the interest, P is the principal amount (loan), r is the annual interest rate, and t is the time in years. In this case, the principal amount (loan) is $6500, the annual interest rate is 8%, and the time is 5 years. So, the interest can be calculated as: I = 6500 * 0.08 * 5 = $2600.

To find the total amount that Beyonce will pay for the chair, we need to add the interest to the principal amount. The total amount is given by the formula: Total Amount = Principal + Interest. Therefore, Total Amount = 6500 + 2600 = $9100.

So, Beyonce will pay a total amount of $9100 for the chair, including the principal amount and interest.

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Answer:

Step-by-step explanation:

(a)

3x - 6y = -12.,......(1)

x - 2y = -8.…......(2)

from equation (2),by adding 2y to both sides, x= -8 + 2y.....(3)

Let's substitute the value of x in equation (1)

3(-8 + 2y) - 6y = -12

-24 + 6y - 6y = -12

6y - 6y = 12..,..(4)

From equation (4) we can see that both equations (1) and (2) has no solutions for x and y

(b)They are two parallel lines of slope of 2 and intercepts on y at 2 and 4

(a) The given system has no solution.

(b) The lines are parallel and never intersect.

To determine the solution of the system of equations using the substitution method, follow these steps:

Substitution Method

Interpretation of Result

Because the system of equations has no solution, we deduce that the lines represented by these equations are parallel and never intersect. Thus, they do not share any common points.

Therefore, the system of equations has no solution, and the lines are parallel.

Answer:

n + 8

Step-by-step explanation:

Next time add a picture please.

Answer:

19 - 28/n  

Step-by-step explanation:

i did the test ;)

Answer:

23/12x+7

Step-by-step explanation:

2 3/4=11/4

8 2/5=42/5

----------------

11/4x-5/6(x-42/5)

11/4x-5/6x+210/30

11/4x-5/6x+7

33/12x-10/12x+7

23/12x+7

Answer:

A.No, the probability of getting a 3 on a fair die does not change. It will always be

Step-by-step explanation:

Get a good grade!

Answer:

35

Step-by-step explanation:

An isosceles triangle always has two equal angles. As there cannot be another 110° (the triangle cannot have over 180° total), the other two angles must equal eachother. 180° - 110° = 70°. 70° represents the other two angles, so it needs to be divided in 2 to get the answer of 35°.

Answer:

Step-by-step explanation:

buys it for $ 45

well...you know the business is gonna want to make a profit...so they would have to sell it for more then they bought it for.

I would say $ 60 or $ 80

Final answer:

Given the wholesale price of $45, the sensible retail prices to charge customers would be $60 and $80, as they both allow for covering costs and earning a profit, unlike $20 and $40, which would incur losses.

Explanation:

The question involves understanding wholesale and retail prices, essential concepts in economics and business mathematics. When a company buys an item at a wholesale price, it usually marks up the price when selling it at retail to cover costs and generate profit. Given the wholesale price of $45, the retail prices that make sense to charge customers would be those higher than $45 because selling at a lower price would result in a loss.

Both $60 and $80 are above the wholesale price and would allow the company to cover additional costs and earn a profit. $20 and $40 would not make sense as they are below the wholesale price, leading to a loss per item sold.

The original number is 64

Step-by-step explanation:

The given is:

We need to find the original number

Assume that the unit digit of the number is x and the ten digit is y

∵ The unite digit of the number is x

∵ The ten digit of the number is y

∵ The sum of the two digits is 10

- Add x and y, then equate the sum by 10

∴ x + y = 10 ⇒ (1)

∵ The value of the number is x + 10y

- Reverse the digits means y will be the unit digit and x will

   be the ten digit

∴ The new number is y + 10x

∵ The new number is 18 less than the original number

- That means their difference is 18, (the original number minus

   the new number = 18)

∴ (x + 10y) - (y + 10x) = 18

- Simplify the left hand side

∴ x + 10y - y - 10x = 18

- Add the like terms in the left hand side

∴ -9x + 9y = 18

- Divide both sides by 9

∴ -x + y = 2 ⇒ (2)

Now we have a system of equation to solve it

Add equation (1) and (2) to eliminate x

∴ 2y = 12

- Divide both sides by 2

∴ y = 6

- Substitute the value of y in equation (1) to find x

∵ x + 6 = 10

- Subtract 6 from both sides

∴ x = 4

∵ The original number is x + 10y

∵ x = 4 and y = 6

∴ The original number = 4 + 10(6) = 4 + 60 = 64

The original number is 64

To check the answer reverse the digits of the number

∵ The new number is y + 10x

∴ The new number = 6 + 10(4) = 6 + 40 = 46

∵ The original number is 64

∵ The new number is 46

∵ 64 - 46 = 18

∴ The new number is less than the original number by 18

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Answer:

The original number is 64.

Answer:

186.111111111

Step-by-step explanation:

Answer: the answer is 186.111111

The bakery sold 23 bagels and 12 muffins.

Step-by-step explanation:

Given,

Cost of each bagel = $1.50

Cost of each muffin = $2.00

Total sold = 35

Revenue generated = $58.50

Let,

x be the number of bagels

y be the number of muffins

According to given statement;

x+y=35       Eqn 1

1.50x+2y=58.50    Eqn 2

Multiplying Eqn 1 by 2

[tex]2(x+y=35)\\2x+2y=70\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](2x+2y)-(1.50x-2y)=70-58.50\\2x+2y-1.50x-2y=11.50\\0.50x=11.50[/tex]

Dividing both sides by 0.50

[tex]\frac{0.50x}{0.50}=\frac{11.50}{0.50}\\x=23[/tex]

Putting x=23 in Eqn 1

[tex]23+y=35\\y=35-23\\y=12[/tex]

The bakery sold 23 bagels and 12 muffins.

Keywords: linear equation, elimination method

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Answer:

Step-by-step explanation:

Let the number be x and y

xy = 378.......(1)

x + y = 41......(2)

Making y as subject in (2)

y = 41 - x......(3)

Substitute it in (1)

x(41 - x) = 378

41x - x² = 378

x² - 41x + 378 = 0

x² - 27x - 14x + 378 = 0

(x² - 27x) - (14x - 378) = 0

x(x - 27) - 14(x - 27) = 0

(x -14)(x - 27) = 0

x - 14 = 0 or x - 27 = 0

x = 14 or x = 27

And y = 41 - x

When x = 14

y = 41 - 14 = 27

y = 27

When x = 27

y = 41 - 27 = 14

y = 14

The two numbers are 14 and 27.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Let the numbers are x and y.

Then,

the system of equations

xy = 378  {equation 1}

x + y = 41   {equation 2}

y = 41 - x

Then

x(41 - x) = 378

41x - x² = 378

x² - 41x + 378 = 0

x² - 27x - 14x + 378 = 0

(x² - 27x) - (14x - 378) = 0

x(x - 27) - 14(x - 27) = 0

(x -14)(x - 27) = 0

x - 14 = 0 or x - 27 = 0

x = 14 or x = 27

And y = 41 - x

When x = 14

y = 41 - 14 = 27

y = 27

When x = 27

y = 41 - 27 = 14

y = 14

Therefore, the  14 and 27 are the numbers.

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Answer:

Step-by-step explanation:

X + 61° = 90° {right angle}

X = 90° - 61°

X = 29°

The second option of $65 for 250 flyers is the better value as it offers a lower cost per flyer.

To determine which option is a better value, we need to calculate the cost per flyer for each option. For the first option of $30 for 100 flyers, the cost per flyer would be $0.30. For the second option of $65 for 250 flyers, the cost per flyer would be $0.26. Therefore, the second option is the better value as it offers a lower cost per flyer.

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