I really need help with these questions please help

The ratio of monomial expressions that best estimates the behavior of 2x^4 + 7x + 19/8x^2-14 as x → ±∞ is 1/4 * x^2.

what is a function?

In mathematics, a function is a relationship between two sets of values, called the domain and the range, where each value in the domain is associated with a unique value in the range.

a. The term with the highest degree in the numerator of the rational function is 2x^4. As x becomes very large or very small, this term dominates the behavior of the function. Therefore, the best monomial expression that estimates the behavior of 2x^4 + 7x + 19 as x → ±∞ is 2x^4.

b. Similarly, the term with the highest degree in the denominator of the rational function is 8x^2. As x becomes very large or very small, this term dominates the behavior of the function. Therefore, the best monomial expression that estimates the behavior of 8x^2-14 as x → ±∞ is 8x^2.

c. To find the ratio of monomial expressions that best estimates the behavior of the rational function as x → ±∞, we divide the expression from part (a) by the expression from part (b):

(2x^4) / (8x^2) = 1/4 * x^(4-2) = 1/4 * x^2

Therefore, the ratio of monomial expressions that best estimates the behavior of 2x^4 + 7x + 19/8x^2-14 as x → ±∞ is 1/4 * x^2.

d. Based on the answer to part (c), as x → ±∞, the ratio 1/4 * x^2 becomes very large in magnitude, but its sign depends on the sign of x. As a result, the function f(x) also becomes very large in magnitude as x becomes very large in either the positive or negative direction. Therefore, we can say that as x → ±∞, f(x) → ±∞.

e. Based on the answer to part (d), we can conclude that there is no horizontal asymptote for f.

Therefore, the ratio of monomial expressions that best estimates the behavior of 2x^4 + 7x + 19/8x^2-14 as x → ±∞ is 1/4 * x^2.

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The ratio of monomial expressions that best estimates the behavior of 2x⁴ + 7x + 19/8x² - 14 as x → ± ∞ is 1/4 * x².

What is a function?

A function is a relationship between two sets of values, called the domain and the range, where each value in the domain is associated with a unique value in the range.

a. The term with the highest degree in the numerator of the rational function is 2x⁴. As x becomes very large or very small, this term dominates the behavior of the function. Therefore, the best monomial expression that estimates the behavior of 2x⁴ + 7x + 19 as x → ±∞ is 2x⁴.

b. Similarly, the term with the highest degree in the denominator of the rational function is 8x².

As x becomes very large or very small, this term dominates the behavior of the function.

Therefore, the best monomial expression that estimates the behavior of 8x² - 14 as x → ±∞ is 8x².

c. To find the ratio of monomial expressions that best estimates the behavior of the rational function as x → ±∞, we divide the expression from part (a) by the expression from part (b):

(2x⁴) / (8x²) = 1/4 * x⁽⁴⁻²⁾ = 1/4 * x²

Therefore, the ratio of monomial expressions that best estimates the behavior of 2x⁴ + 7x + 19/8x² - 14 as x → ±∞ is 1/4 * x².

d. Based on the answer to part (c), as x → ±∞, the ratio 1/4 * x² becomes very large in magnitude, but its sign depends on the sign of x. As a result, the function f(x) also becomes very large in magnitude as x becomes very large in either the positive or negative direction. Therefore, we can say that as x → ±∞, f(x) → ±∞.

e. Based on the answer to part (d), we can conclude that there is no horizontal asymptote for f.

Therefore, the ratio of monomial expressions that best estimates the behavior of 2x⁴ + 7x + 19/8x² - 14 as x → ±∞ is 1/4 * x².

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Answer:

2.6

Step-by-step explanation:

The χ² = (observed - Expected)²/Expected

The expected wins :

n = 6

(45+33+44+39+42+37) / 6 = 40

χ² = (45-40)²/40 + (33-40)²/40 + (44-40)²/40 + (39-40)²/40 + (42-40)²/40 + (37-40)²/40

χ² = 0.625 + 1.225 + 0.4 + 0.025 + 0.1 + 0.225

χ² = 2.6

Answer:  the number that can be placed in the box to make the statement true is 3.

Step-by-step explanation:

To make the statement true, we need to find a number that, when added to 7, equals 10. From the given options, the number that satisfies this condition is 3.

If we substitute 3 for the box in the statement, it becomes:

If +7=10, then 10-7=3.

Answer:

The answer is : x>4

Step-by-step explanation:

3(5-x)<5x-17

15-3x<5x-17

-3x-5x<-17-15

-(3x+5x)<-(17+15)

3x+5x>17+15

8x>32

x>\(\frac{32}{8}\)

x>4

First, you should simplify the function expression.

3(x2 + 10x + 5) - 5(x-k) = 3x2 + 30x + 15 - 5x + 5k = 3x2 +15x +15 +5k

In order for the polynomial to be divisible by x, all terms need to divide by x with no remainder.  The first two terms clearly divide by x.  However, the last two do not.  In order for this to work out where k is constant, 5k would have to cancel out the  +15 term, leaving nothing to divide by x.

So: 15 + 5k = 0

5k = -15

k = -3

Step-by-step explanation:

as I don't see any equations or graphs here I can only answer in general :

f(x) is the patent function.

g(x) is the transformed function.

g(x) = -6f(x-7)

the "-" reflects the curve over the x-axis (what was positive is now negative and vice versa).

the factor 6 stretches the curve up and down by the factor 6 (everything is now 6 times larger or smaller).

and the argument "x-7" relates x (for the new function) with "x-7", meaning that now things are happening at x, that were originally happening at x-7, so they happen now "later" (more to the right on the x-axis) than before - hence a shift to the right.

Answer:

its D

Step-by-step explanation:

took the test :)

Answer:

B.9x

Step-by-step explanation:

A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted. Some terms contain variables with a number in front of them. The number in front of a term is called a coefficient.

Answer:

your answer is going to be -158

Step-by-step explanation:

(5)-(3)^2+7×-22=-158

Answer:

Step-by-step explanation:

The length of material needed for the border is the perimeter of the backyard play area

How to calculate the length of material needed

The area of the play area is given as:

The area of a trapezoid is calculated using:

Where L1 and L2, are the parallel sides of the trapezoid and H represents the height.

The given parameter is not enough to solve the length of material needed.

So, we make use of the following assumed values.

Assume that the parallel sides are: 25 feet and 31 feet long, respectively.

While the other sides are 10.2 feet and 8.2 feet

The length of material needed would be the sum of the above lengths.

So, we have:

Using the assumed values, the length of material needed for the border is 74.4 feet

Answer:

Let x be the distance traveled by you to the north and y be the distance traveled by your friend to the west. Let d be the distance between you and your friend at time t. Then, we have:

d^2 = x^2 + y^2

Taking the derivative of both sides with respect to time, we get:

2d (dd/dt) = 2x(dx/dt) + 2y(dy/dt)

Simplifying this expression, we get:

dd/dt = (x(dx/dt) + y(dy/dt)) / d

Since you are driving north at a constant speed v and your friend is driving west at a constant speed w, we have:

dx/dt = v and dy/dt = -w

Substituting these values and simplifying, we get:

dd/dt = (v^2 + w^2)^0.5

Therefore, the speed of separation between you and your friend at time t is the square root of the sum of the squares of your speeds.

To find the second derivative of the distance between you and your friend, we take the derivative of dd/dt with respect to time:

d^2d/dt^2 = (v dv/dt + w dw/dt) / (v^2 + w^2)^0.5

Since v and w are constant, their derivatives with respect to time are zero, so the second derivative of the distance between you and your friend is zero.

Suppose you wait for an hour (i.e., t = 1 hour) before driving off to the north. Then, at time t > 1 hour, the distance between you and your friend is given by:

d = (vt)^2 + ((t-1)w)^2)^0.5

Taking the derivative of both sides with respect to time, we get:

dd/dt = 2v^2t / (2((vt)^2 + ((t-1)w)^2)^0.5)

Simplifying this expression, we get:

dd/dt = v / ((v^2 + ((t-1)w)^2)^0.5)

Therefore, the speed of separation between you and your friend at time t (greater than one hour) is given by v divided by the square root of the sum of the squares of your speed and your friend's speed.

The second derivative of the distance between you and your friend is given by:

d^2d/dt^2 = -vw(t-1) / ((v^2 + ((t-1)w)^2)^1.5)

The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

Answer:

10

Step-by-step explanation:

After hour, pay increases by 10.

The denominator is zero (0/0 is undefined), we cannot determine the exact value of f(-3) using this equation.

To solve the given equations, we need to find the value of the function f(x) for specific values of x.

"If f(x) / (x - 2) = x³ + 2x - 4 + 13/(x - 2), what is f(2)?"

To find f(2), we can substitute x = 2 into the equation and solve for f(2).

Plugging in x = 2, we get:

f(2) / (2 - 2) = 2³ + 2(2) - 4 + 13/(2 - 2)

Since the denominator is zero (2 - 2 = 0), the equation is undefined. Therefore, there is no solution for f(2) in this case.

"If f(x) / (x + 3) = 3x² - 4x + 2, what is f(-3)?"

To find f(-3), we can substitute x = -3 into the equation and solve for f(-3).

Plugging in x = -3, we get:

f(-3) / (-3 + 3) = 3(-3)² - 4(-3) + 2

Simplifying, we have:

f(-3) / 0 = 3(9) + 12 + 2

f(-3) / 0 = 27 + 12 + 2

f(-3) / 0 = 41

Additional information or context is needed to solve for f(-3).

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The value of vertical asymptotes is, x = 9

And, The value of Horizontal asymptotes is,

y = - 4

We have to given that;

Expression is,

⇒ j (x) = 1/(x - 9) - 4

Now, We can simplify as,

⇒ j (x) = 1/(x - 9) - 4

⇒ j (x) = (1 - 4(x - 9)] / (x - 9)

⇒ j (x) = [1 - 4x + 36] / (x - 9)

⇒ j (x) = (- 4x + 37) / (x - 9)

Hence, For vertical asymptotes make denominator zero.

As, x - 9 = 0

x = 9

And, Here degree of numerator and denominator both are one.

Hence, Horizontal asymptotes is,

y = - 4 / 1

y = - 4

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Answer:

The slope is 2

Step-by-step explanation:

In order to find slope of the line, we need to take two coordinates from this graph. Lets take (3,3) and (2,1)

Method 1: Count the slope

We can count the slope using the technique \(\frac{rise}{run}\) that will give us an answer.

Counting the slope, we get \(\frac{2}{1}\) which can be simplified to just 2.

Method 2: Slope formula

We can use the formula \(\frac{y2-y1}{x2-x1}\) to find the slope without counting by simply plugging in the coordinates and evaluate.

\(\frac{1-3}{2-3}\)

Evaluate

\(\frac{-2}{-1}=2\)

Thus, our slope is 2 and the equation of the line will be \(y=2x-3\)

Answer:

This answer would be 1/8

Step-by-step explanation:

All of the colors are equal and there are 4 colors and 3 numbers if you try putting it together then yes it does equal 1/8 because it is equal and it fits just right for both spinners.

Answer:

16

Step-by-step explanation:

Step 1: Write down the function \(f(x)=7x^2+2x+3.\)

Step 2: Write down the limit definition of the derivative:
\(f'(x)= lim_{h0} \frac{f(x+h)=f(x)}{h} .\)

Step 3: Substitute the function \(f(x)\) into the limit definition:
\(f'(x)=lim_{h0} \frac{(7(x+h)^2+2(x+h)+3)-(7x^2+2x+3)}{h}.\)

Step 4: Simplify the expression inside the limit:
\(f'(x)=lim_{h0}\frac{7x^2+14xh+7h^2+2x+2h+3-7x^2-2x-3}{h} .\)

Step 5: Combine like terms:
\(f'(x)=lim_{h0} \frac{14xh+7h^2+2h}{h} .\)

Step 6: Factor out an \(h\) from the numerator:
\(f'(x)=lim_{h0} \frac{h(14x+7h+2h}{h} .\)

Step 7: Cancel out the \(h\) in the numerator and denominator:
\(f'(x)=lim_{h0}(14x+7h+2).\)

Step 8: Evaluate the limit as \(h\) approaches 0:
\(f'(x)=14x+2.\)

Step 9: Substitute \(x=1\) into the derivative:
\(f'(1)=14(1)+2=14+2=16.\)

The Slope of the tangent line to the curve \(f(x)=7x^2+2x+3\) at \(x=1\) would be \(16.\)

Answer: length = 12 width = 15

12 times 2 = 24

12 + 3 = 15

15 times two is 30

30 plus 24 is 54

The ratio 81:108 can be simplified to 9:13. To find the simplest form of the ratio, you can divide both numbers by the greatest common factor. The greatest common factor of 81 and 108 is 9, so you can divide both numbers by 9 to get the simplified ratio of 9:13.

The estimated value of 2/3 is roughly 0.67, of 1 it is 1 and for 0 it is 0.

What does a estimate mean?

A number given to a demographic parameter that was taken from the a statistical sample. A pricing estimate for the job that needs to be done. 3. an assessment or view of the essence, character, or trait of an object or a person.

What is an illustration of an estimate?

To make computations simpler, an estimate is an approximate estimation of the real value, amount, or quantity.

For 2/3, on dividing we get the value as 0.67.

Since 1 is a number and doesn't need to be rounded or approximated, the guess is 1.

Since it is a number without a fractional component, the approximation of 0 also is 0.

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Given:

radius = 6ft

area of a sector = 59.66 ft²

π = 3.14

Find: central angle (missing one)

Solution:

To solve for the central angle given radius and area of a sector, we have the formula below:

Let's plug in the given data above to the formula.

Then, solve for θ.

Therefore, the measure of the central angle is 190 degrees.

To summarize:

radius = 6ft

central angle = 190 degrees

area of a sector = 59.66 ft²

Answer: The question requires an understanding of how to compose and decompose multi digit numbers. The expanded form 70,000 + 4,000 + 70 + 2 corresponds to the number 74,072, which is the population of Davidson County.

(sorry if i'm wrong)

:(

Given:

x - 4y = -3

4x - 2y = -12

To determine if the point (3, 1) lies on both of the lines in the system of equations:

Substitute (3, 1) in the first equation, we get

3 - 4(1) = -3

3 - 4 =-3

-1 = -3

But,

Substitute (3, 1) in the second equation, we get

4(3) - 2(1) = -12

12 - 2 = -12

10 = -12

But,

Hence, the answer is, No.

The point (3, 1) does not lie on both of the lines in the system of equations.

The function is defined as g(x) = f (√3x² + 4 ), where "f" is an unknown function.

A function is a mathematical object that assigns a unique output or value for each input. In other words, given an input, a function produces exactly one output.

To understand this function and its properties, we need to first identify and verify the domain and range of the function. The domain of a function is the set of all possible inputs for which the function produces a real output. In this case, the domain of "m" is the set of all real numbers "x" such that the expression √3x² + 4 is real.

Next, we need to understand the composition of functions. In this case, "m" is defined as the composition of two functions, "g" and "f."

The composition of two functions "f" and "g" is defined as "f(g(x))," which means that the output of "g" is used as the input for "f." In other words, we first evaluate "g" for a given value of "x," and then use the output of "g" as the input for "f."

Finally, we can evaluate the function "m" for a specific value of "x" by first evaluating "g" and then "f."

To do this, we simply substitute the value of "x" into the expression for "g" and then evaluate "f" with the resulting output.

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The value of the test statistic is given as follows:

z = 4.47.

The equation to calculate the test statistic using the z-distribution is given as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

The parameters for this problem are given as follows:

\(\overline{p} = 0.59, p = 0.5, n = 618\)

p = 0.5 as the most term means that we are testing if the proportion is either less than or greater than 0.5.

Then the test statistic is obtained as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.59 - 0.5}{\sqrt{\frac{0.5(0.5)}{618}}}\)

z = 4.47.

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Answer:

41.93 degrees

Step-by-step explanation:

The value g(7) of the function g(x) = 7  / 8 x  - 1 / 2 is 45 / 8.

A function relates each element of a set with exactly one element of another set (possibly the same set).

In a simpler term, a function relates an input to an output.

Therefore, let's find the value of g(7) for the function below:

g(x) = 7  / 8 x  - 1 / 2

Hence,

g(7) = 7 / 8 (7)  - 1 / 2

g(7) = 49 / 8  - 1 / 2

g(7) =  49 - 4 / 8

Therefore,

g(7) = 45 / 8

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Part A: The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5

Part B: The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).

Part C: the length of each of the five pieces of wood cut by Warren is 3.8 feet.

It is made up of two mathematical objects, with an equals sign (=) between them. Equations are used to represent relationships between unknown variables and can be solved to find their values.

Part A:

The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5, where x is the length of each piece of wood.

Part B:

The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).

This equation can be used to calculate how much wood Warren has cut off from the original 4.5 feet of wood, which is the length of each of the five pieces of wood.

Part C:

Solving the equation from Part A:

x + 0.7 = 4.5

Subtract 0.7 from both sides:

x + 0.7 - 0.7 = 4.5 - 0.7

x = 3.8

Therefore, the length of each of the five pieces of wood cut by Warren is 3.8 feet.

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