Given the function f(x) = x² - x - 8, determine the average rate of change of the
function over the interval –4 < x < 3.

so for given expression x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

we can start by squaring the equation x²+(1/x)=3

so we have x⁴ + 2x² + (1/x)² = 9

x⁴ + 2x² + 1 = 9x²

x⁴ - 7x² + 1 = 0

Now we can factor it

(x²-1)(x²-1) = 0

so x² = 1

now we can substitute x² = 1 in the equation x⁴-2x³-x²-2x+1

x⁴-2x³-x²-2x+1 = x⁴-2x³-1-2x+1

= x⁴-2x³-2x-1

= (x⁴-2x³) - (2x+1)

= x⁴-2x³-2x-1

= (x²-x)² - (2x+1)

= (x-1)² - (2x+1)

so x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)

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Here's link[tex]^{}[/tex] to the answer:

bit.[tex]^{}[/tex]ly/3gVQKw3

Answer:

. The slope of the line indicates that test score and the time spent watching tv are negatively correlated

Answer:

C = 31

Step-by-step explanation:

always do the parenthesis first so (2+4) = 6

3² + 4(6) x 6 ÷ 8 + 4 (Use PEMDAS)

9 + 4(6) x 6 ÷ 8 + 4, multiply 4 and 6

9 + 24 x 6 ÷ 8 + 4, multiply 24 and 6

9 + 144 ÷ 8 + 4, divide 144 and 8

9 + 18 + 4, now just add

31.

Answer:

c) 31

Step-by-step explanation:

9 + 4(6) * 6 / 8 + 4

9 + 24 * 6 /8 + 4

9 + 144 / 8 + 4

9 + 18 + 4

= 31

Answer:  First, let's consider the rotation of 180 degrees clockwise. This can be thought of as a reflection over the x-axis, followed by a reflection over the y-axis.

The reflection over the x-axis will negate the y-coordinate, while the reflection over the y-axis will negate the x-coordinate. So after the rotation, the coordinates of point C will become (-5,-5)

Next, we'll consider the translation 5 units up. Translating a point up means that we'll add 5 to its y-coordinate. So the coordinates of point C'' will become (-5,-5) + (0, 5) = (-5, 0)

So the coordinates of C'' are (-5,0)

Therefore the answer is B.

Step-by-step explanation:

The various statements regarding the given scatter plot is checked and found to be true or false.

What is a scatter plot?

A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities.

1)The equation of the line is y = 2500x - 125.

From the graph we can take two points on the line,

( 2,2250) and ( 10,1250)

Standard equation of line is y = mx + b

where b is y - intercept and m is slope

m = [tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1}}[/tex] = [tex]\frac{1250 - 2250}{10 - 2}[/tex] = -125

From graph, b = 2500

Equation of line is

y = -125x + 2500

Therefore the given equation is false.

2) The group of hikers descends about 250 feet every minute.

      From the graph it is evident that for the interval between two points on y-axis is 250 feet and interval of x-axis is 1 minute.

So the hikers descend 250 feet every minute.

Therefore the given statement is true.

3) The hikers began at the elevation of 2500 feet.

     The x-intercept of the graph is 2500 feet.

      So the beginning elevation is 2500 feet.

 Therefore the statement is true.

4) The graph shows a negative association.

Since the line in the graph is going down and the slope is negative, the graph shows a negative association.

Therefore the statement is true.

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Answer:

x = 11 and x = -1

Step-by-step explanation:

We have x^2−10x = 11 and want to make a perfect square out of x^2−10x.

To do this, take half of the coefficient of x, square this half, and then add and then subtract the square immediately following x^2−10x:

Half of -10 is -5, and the square of -5 is 25.

x^2−10x = 11 becomes x^2 - 10x + 25 - 25 = 11

Rewrite x^2−10x + 25 as the square of a binomial:  (x - 5)^2.

Then we have (x - 5)^2 - 25 = 11.  Solve this for x -5:

(x - 5)^2 = 36.  Taking the square root of both sides, we get

x - 5 = ±6

Then x = 11 and x = -1

Answer:

<1 and  <2  are Complementary Angles

m<1  + <2  = 90 degrees

Step-by-step explanation:

<1 and  <2  are Complementary Angles

m<1  + <2  = 90 degrees

Have a great day!

Since, angle 1 and 2 sums up to make 90 degrees, hence Angle 1 and 2 are complementary angles.

Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complementary angles.

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. In the same way, complementary angles sum to 90 degrees.

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Answer:

16 ounces = 1 pint, 8 times 2 = 16

Step-by-step explanation:

Answer in explanation:

1 pint is 16 ounces so he could make 2 batches of lemonade with 1 pint of lemon juice.

(8 x 2 = 16

your answer is 2

Hope this helps!

Answer:

B 12

Step-by-step explanation:

Using pythagoras theorem

Answer:

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

Step-by-step explanation:

-x+5y=8

3x+7y=-2

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

3(-x+5y)=3(8)

3x+7y=-2

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

-3x+15y=24

3x+7y=-2

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

22y=22

y=22/22

y=1

-x+5(1)=8

-x+5=8

-x=8-5

-x=3

x=-3

Answer:

x=5, y=3

Step-by-step explanation:

y=x−2;4x+y=23

Step: Solve y=x−2 for y:

Step: Substitute x−2 for y in 4x+y=23:

4x+y=23

4x+x−2=23

5x−2=23(Simplify both sides of the equation)

5x−2+2=23+2(Add 2 to both sides)

5x=25

5x/5 = 25/5(Divide both sides by 5)

x=5

Step: Substitute 5 for x in y=x−2:

y=x−2

y=5−2

y=3(Simplify both sides of the equation)

angle ADC equals 74 degrees

Answer:

33 ounces

Explanation:

20% of 27.5 ounces is 5.5 ounces.

To find how much more juice the container has, we add 5.5 to 27.5, which equals to 33 ounces

Null hypothesis (H0): There’s no effect in the population. Alternative hypothesis (Ha or H1): There’s an effect in the population.

The null and alternative hypotheses are two opposing ideas that researchers use a statistical test to analyze evidence for and against: The null hypothesis (H0) states that there is no influence in the population. Alternative hypothesis (Ha or H1): There is a population effect.

Identify the null and alternative hypotheses.

As well as the sample size, specify.

Choose a suitable statistical test.

Gather information (note that the previous steps should be done prior to collecting data)

Based on the sample data, compute the test statistic.

Examine the null hypothesis, usually indicated by H0.

Always write the alternative hypothesis, which is usually marked by Ha or H1, with less than, greater than, or not equals symbols, i.e., (,>,or).

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The coeficient of x^3+y^4 in the algebraic expression is the number 2

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In the given expression we have the following:

2x^3+ 2y^4

As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 2.

2 is the coefficient of x^3+y^4

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Yes, 6/8 and 9/12 are equal. After simplifying both the fractions we got that both are equal and their value is 3/4.

Let's first try to understand what is a fraction.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

A fraction would be 5/10, for instance.

Here, the numerator is 5 and the denominator is 10.

6/8 is a fraction.

6/8 can be simplified further.

6/8 = 3/4

9/12 is also a fraction.

9/12 can be simplified further.

9/12 = 3/4

To compare 2 fractions first we try to make the same denominator.

we have the same value. so they are equivalent.

Given question is incomplete complete the question here:

Are 6/8 and 9/12 equivalent?

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Carman buy the video game in the cost of $45.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Carman has saved 80% of the money she needs to buy a new video game.

And, she saved the cost $36.

Let total cost of the video game = x

So, We can formulate;

⇒ 80% of x = $36

⇒ 80/100 × x = 36

⇒ 8x = 360

⇒ x = $45

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The population of the city grew from 2010 to 2020 by 13.37%.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

We have to given that;

In 2010, the population of a city was 237,000.

And, From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.

We know that;

Where, A = P (1+r)ⁿ

A = final population.

P = Initial population.

r = rate

n = time

Hence, The population in 2015 is, =

A = 237,000(1 + 0.076)⁵

A = 341829.629

And, The population in 2020 =

A = P (1 - r)ⁿ

A = 341829.629 (1 - 0.047)⁵

A = 268704.047

So, Percent grow = (268704.047 - 237,000) / 237,000 × 100

                           = 31704.047 / 237,000 × 100

                            = 13.37 %

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Answer:56

Step-by-step explanation:

Let ttt be the initial number of trees.

Hint #22 / 5

MacDonald now has t-5t−5t, minus, 5 trees and each one produced 210210210 oranges this harvest.

The total number of oranges produced is 210(t-5)210(t−5)210, left parenthesis, t, minus, 5, right parenthesis.

Hint #33 / 5

Since the trees produced a total of 417904179041790 oranges, let's set this equal to 417904179041790:

\qquad210(t-5)=41{,}790210(t−5)=41,790210, left parenthesis, t, minus, 5, right parenthesis, equals, 41, comma, 790

Now, let's solve the equation to find the initial number of trees (t)(t)left parenthesis, t, right parenthesis.

Hint #44 / 5

\begin{aligned}210(t-5)&=41790\\&\\ \dfrac{210(t-5)}{\blue{210}}&=\dfrac{41790}{\blue{210}}&&\text{divide both sides by $\blue{210}$}\\ \\ t-5&=199\\ \\ t-{5}\pink{+5}&=199\pink{+5}&&\pink{\text{add }} \pink{5} \text{ to both sides}\\ \\ t&=204\end{aligned}

210(t−5)

210

210(t−5)

​

t−5

t−5+5

t

​

=41790

=

210

41790

​

=199

=199+5

=204

​

​

divide both sides by 210

add 5 to both sides

​

Hint #55 / 5

The equation is 210(t-5)=41790.210(t−5)=41790.210, left parenthesis, t, minus, 5, right parenthesis, equals, 41790, point

MacDonald's farm initially had 204204204 orange trees.

Related content

There are  17/36 pounds of trail mix in each bag.

you need to first add the weight of the peanuts and M&M's together.

1[tex]\frac{17}{18}[/tex] + 1 [tex]\frac{5}{6}[/tex] =([tex]\frac{35}{18}[/tex]) +([tex]\frac{11}{6}[/tex]) =  [tex]\frac{35+33}{18}[/tex]    =[tex]\frac{68}{18}[/tex]

which can be simplified to 3 [tex]\frac{14}{18}[/tex]

So there are 3 [tex]\frac{14}{18}[/tex]pounds of trail mix altogether.

3 [tex]\frac{14}{18}[/tex]÷ [tex]\frac{8}{1}[/tex] =

[tex]\frac{68}{18}[/tex]  ÷  [tex]\frac{8}{1}[/tex]=[tex]\frac{68}{144}[/tex]

which can be simplified to [tex]\frac{17}{36}[/tex]

So there are [tex]\frac{17}{36}[/tex]pounds of trail mix in each bag.

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Answer:

23.88 feets

Step-by-step explanation:

C=2π2

=2×3.142×3.8

=23.8792 feets

rounded to the nearest TENTH

=23.88 feets

Answer:

Step-by-step explanation:

Answer is 6 units

Answer:

6 units fs

Step-by-step explanation:

The value of the polynomial "5x - 4x^2 + 3" at x =- 1 is -6.

The polynomial is 5x - 4x^2 + 3, and it is required to find its value at x = -1,

Now solve the polynomial by putting the value of x equal to -1:

5(-1) - 4(-1)^2 + 3        ,  x =  - 1

-5 - 4 ( 1 ) + 3             , squaring -1 gives + 1

minus 5 minus 4 plus 3

( - 9 + 3)

( - 6 )

Hence, is shown that the value - 6 is obtained when the given polynomial "5x - 4x^2 + 3" is solved for x = -1.

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The required two numbers are 9 and 41.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

Let x be the lesser number, and y be the greater number.

From the question, we know that:

x + y = 50 (Equation 1: The sum of the two numbers is 50)

y = 5x - 4 (Equation 2: The greater number is four less than five times the lesser number.)

The equation is to solve for one of the variables, and then substitute that value into the other equation to find the other variable.

Then, two numbers are x = 9 and y = 41.

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The equation y = 5x - 8 and y = 9x - 8 have one solution at

(0, -8)

The equation is solved simultaneously by elimination method as follows

y = 5x - 8

y = 9x - 8

subtraction the equations

0 = -4x - 0

-4x = 0

x = 0

substituting x = 0 into y = 5x - 8

y = 5x - 8

y = 5 * 0 - 8

y =0 - 8

y = -8

The solution of the equation is at the point (0, -8)

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