The end behaviour for the polynomial function h(x)=−x3+x4−2x+1 h ( x ) = - x 3 + x 4 - 2 x + 1 is: x→−[infinity], y→−[infinity] x → - [infinity] , y → - [infinity] and x→[infinity], y→[infinity] x → [infinity] , y → [infinity] x→−[infinity], y→[infinity] x → - [infinity] , y → [infinity] and x→[infinity], y→[infinity] x → [infinity] , y → [infinity] x→−[infinity], y→−[infinity] x → - [infinity] , y → - [infinity] and x→[infinity], y→−[infinity] x → [infinity] , y → - [infinity] Unable to tell.

Domain and Range of the given rational functions are:Given rational function f(x) = 3/(x-1)The denominator of f(x) cannot be zero.x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}

The range of f(x) is all real numbers except zero.Given rational function f(x) = (2x)/(x-4)The denominator of f(x) cannot be zero.x ≠ 4 Therefore the domain of f(x) is {x | x ≠ 4}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x+3)/(5x-5)The denominator of f(x) cannot be zero.5x - 5 ≠ 0x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}The range of f(x) is all real numbers except 1/5.Given rational function f(x) = (2+x)/(2x)The denominator of f(x) cannot be zero.x ≠ 0 Therefore the domain of f(x) is {x | x ≠ 0}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x^2+4x+3)/(x^2-9)For the denominator of f(x) to exist,x ≠ 3, -3

Therefore the domain of f(x) is {x | x ≠ 3, x ≠ -3}The range of f(x) is all real numbers except 1, -1. Function Domain Rangef(x) = 3/(x-1) {x | x ≠ 1} All real numbers except zerof(x) = (2x)/(x-4) {x | x ≠ 4} All real numbers except zerof(x) = (x+3)/(5x-5) {x | x ≠ 1} All real numbers except 1/5f(x) = (2+x)/(2x) {x | x ≠ 0} All real numbers except zerof(x) = (x^2+4x+3)/(x^2-9) {x | x ≠ 3, x ≠ -3} All real numbers except 1, -1

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Explanation:

Check out the diagrams below.

We'll start with the left diagram (marked "before") which is a right triangle with the horizontal leg of 25 feet and hypotenuse 65 feet.

Use the pythagorean theorem to find the vertical side x.

a^2 + b^2 = c^2

25^2 + x^2 = 65^2

625 + x^2 = 4225

x^2 = 4225 - 625

x^2 = 3600

x = sqrt(3600)

x = 60

The top of the ladder is 60 feet high when placed against the wall in this configuration.

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

If the upper end is moved down 8 feet, then x-8 = 60-8 = 52 feet is the new height of the ladder. Refer to the "after" in the diagram below.

Like earlier, we'll use the pythagorean theorem to find the missing side.

a^2 + b^2 = c^2

y^2 + 52^2 = 65^2

y^2 + 2704 = 4225

y^2 = 4225 - 2704

y^2 = 1521

y = sqrt(1521)

y = 39

The horizontal distance from the ladder base to the wall is now 39 feet.

Earlier it was 25 feet, so it has increased by 39-25 = 14 feet.

The probability that a 34 square foot metal sheet has at least 9 defects is 0.4308, rounded to four decimals.

Given that the sheet metal has an average of 7 defects per 20 square feet, we can find the rate parameter (λ) of the Poisson distribution as follows:

λ = (7 defects / 20 sq ft) = 0.35 defects per square foot

Let X be the number of defects in a 34 square foot metal sheet. Since X follows a Poisson distribution with rate parameter λ, we can find the probability that X is at least 9 defects using the cumulative distribution function (CDF) of the Poisson distribution:

P(X ≥ 9) = 1 - P(X < 9) = 1 - F(8)

where F(k) is the CDF of the Poisson distribution with rate parameter λ evaluated at k.

Using the Poisson distribution formula for F(k), we have:

F(k) = P(X ≤ k) = ∑(i=0 to k) [(λ^i * e^(-λ)) / i!]

Using a calculator or software, we can find that:

F(8) = P(X ≤ 8) = 0.5692

Therefore, we have:

P(X ≥ 9) = 1 - F(8) = 1 - 0.5692 = 0.4308

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The region between the line y = 1 and the graph of y = √(x + 1), 0 ≤ x ≤ 4 is revolved about the x-axis.We need to integrate this using the washer method. We start by finding the volume of the individual washers:V = π(R^2 - r^2)hWe need to find R, r, and h for this.

We can express the volume of the solid as follows:

V = ∫(πy^2)dx

Let's put it to the test now:

π∫[0,4][1 - (√(x + 1))^2]dx= π∫[0,4](1 - x + 1)dx= π∫[0,4](2 - x)dx= π[x(2 - x) - (1/2)(x^2)]|[0,4]= π(4 - (1/2)(16) - 0 + (1/2)(0))= (3π)/2

The volume of the region between the line y = 1 and the graph of y = √(x + 1), 0 ≤ x ≤ 4 is revolved about the x-axis is (3π)/2.2. The region between the lines x = 4, y = x - 2, and the x-axis in the first quadrant is revolved about the y-axis.We can express the volume of the solid as follows:

V = ∫(2πx)(x - 4)dx

Let's put it to the test now:

2π∫[0,2](x^2 - 4x)dx= 2π[((1/3)(2^3) - 4(1/2)(2^2)) - 0]= (4π)/3

The volume of the region between the lines x = 4, y = x - 2, and the x-axis in the first quadrant is revolved about the y-axis is (4π)/3.

The region between the x-axis and the line y = -x + 6 in the first quadrant is revolved about the y-axis.The volume of the solid is calculated as follows:

V = ∫(2πx)(-x + 6)dx

Let's put it to the test now:

2π∫[0,6](x^2 - 6x)dx= 2π[((1/3)(6^3) - 6(1/2)(6^2)) - 0]= (36π)/3= 12π

The volume of the region between the x-axis and the line y = -x + 6 in the first quadrant is revolved about the y-axis is 12π.4. The region between the x-axis and the graph of y = sin x, 0 ≤ x ≤ π is revolved about the line x = 2.Using the washer method, we can evaluate the volume of the solid. The equation we'll use is:

V = ∫(πR^2 - πr^2)dx

Let's put it to the test now:

π∫[0,π]((2 + sin x)^2 - 4)dx= π∫[0,π](4 + 4sin x + sin^2x - 4)dx= π∫[0,π](4sin x + sin^2x)dx= π(-4cos x - (1/3)cos^3x)|[0,π]= (16π/3)

The volume of the region between the x-axis and the graph of y = sin x, 0 ≤ x ≤ π is revolved about the line x = 2 is (16π/3).

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Given:

Consider the given sides are,

\(BD=21m\)

\(BC=25m\)

\(DE=40m\)

\(AB=xm\)

To find:

The measure of AB.

Solution:

Let x be the measure of AB.

From the given figure it is clear that,

\(\angle ADE \cong \angle ABC\)                 (Right angles)

\(\angle ADE \cong \angle ABC\)                  (Corresponding angles)

Two corresponding angles are congruent. So, by AA property of similarity,

\(\Delta ABC\sim \Delta ADE\)

Corresponding sides of similar triangle are proportional.

\(\dfrac{AB}{BC}=\dfrac{AD}{DE}\)

\(\dfrac{x}{25}=\dfrac{(x+21)}{40}\)

\(40x=25(x+21)\)

\(40x=25x+525\)

Isolating x, we get

\(40x-25x=525\)

\(15x=525\)

\(x=\dfrac{525}{15}\)

\(x=35\)

Therefore, the measure of AB is 35 m.

Answer:

x = 0

Step-by-step explanation:

y = x + 4 and y = 2x + 4

Let's solve

x + 4 = 2x + 4

-x  + 4 = 4

-x = 0

x = 0

So, there is only one solution is x = 0

Answer:

(8+-4)(6+-2)(5+-1)

Step-by-step explanation:

i.) 8+(-4)

8-4=4

ii) 6+(-2)

   6-2=4

iii) 5+(-1)

    5-1 = 4

HOPE THIS HELPS

Answer:

(8+-4)(6+-2)(5+-1)

Step-by-step explanation:

Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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The length of the side DA from secant theorem is; 10

From the cyclic diagram attached;

Since CA = 12.5 and CB = 4.5, it means that;

BA = 12.5 - 4.5 = 8

From the secant theorem, we know that;

The product of the secant and its exterior segment is equal to the square of the tangent segment.

Thus;

Length of DA = √(8 * 12.5)

Length of DA = 10

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Answer:

Inequality: 6r - 200 - 65 \(\geq\) 1000  and minimum of 211 people

Step-by-step explanation:

Let r = rides

6r - 200 - 65 \(\geq\) 1000

6r - 265 \(\geq\) 1000

6r \(\geq\) 1265

r \(\geq\) 210 \(\frac{5}{6}\)

Needs 211 people to make a profit of at least $1000

\(f(-2) = -4\) for the given piecewise function by using the equation \(f(x) = x - 2\)  if   \(x < 3.\)

A piecewise function is a mathematical function that is defined differently on different parts of its domain.

Instead of having a single formula that applies to the entire domain, a piecewise function has multiple formulas, each applying to a specific interval or subset of the domain.

To find f(-2) for the given piecewise function, we need to determine which piece applies to the input value o  \(f -2\), which is less than 3. Therefore, we use the first piece of the function, which is\(f(x) = x - 2 if x < 3.\)

Substituting x = -2 into this piece, we get:

\(f(-2) = (-2) - 2 = -4\)

Therefore, f(-2) = -4 for the given piecewise function.

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Answer:

y = 5/2 x - 4

Step-by-step explanation:

For slope-intercept form, just solve for y:

5x - 2y = 8

\(\frac{5x}{2} - \frac{8}{2} = \frac{2y}{2}\)

5/2 x - 4 = y or

y = 5/2 x - 4

The slope intercept form is y= 5/2x - 4.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have the Equation

5x - 2y = 8.

As, we know from the slope intercept form

y= mx + b

So, 5x - 2y = 8

5x - 8 = 2y

5/2x - 8/2 = y

y= 5/2x - 4

where slope is 5/2 and y intercept is -4.

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Answer:

it is algebraic expression

Answer:

the answer is no

Step-by-step explanation:

khan acadmy

Answer:

no

Step-by-step explanation:

did it on khan

Answer:

\(HD=5.5\)

Step-by-step explanation:

\(4(HD)=22 \implies HD=5.5\)

Answer:

Step 1:

The proportion of people who were caught after being on the 10 Most Wanted list can be estimated as:

(number of people caught) / (total number of suspected criminals)

Substituting the given values, we get:

169 / 434 ≈ 0.389 (rounded to three decimal places)

So the estimated proportion of people caught after being on the 10 Most Wanted list is 0.389.

Step 2:

To construct an 80% confidence interval for the population proportion of people caught, we can use the following formula:

p ± z* sqrt(p*(1-p)/n)

where p is the sample proportion, z* is the z-score corresponding to the desired confidence level (80% in this case), and n is the sample size.

Substituting the given values, we get:

0.389 ± 1.282 * sqrt(0.389*(1-0.389)/434)

Simplifying this expression, we get:

0.389 ± 0.049

Therefore, the 80% confidence interval for the population proportion of people caught is:

(0.340, 0.438)

Rounded to three decimal places, this becomes:

(0.340, 0.438)

Step-by-step explanation:

By reviewing your class notes.

Sure hope this helps!

Answer:

Step-by-step explanation:

Learn the material with examples, and do lots of problems. The more problems you solve, the more familiar you become with the problems and the faster and better you will answer the questions.

The option that needs to be corrected in this construction of a line parallel to line AB passing through C is C: the second arc should be centered at C.

The second arc should be centered at C because as it crosses passing through Line C, it is seen that it was not touching or intersecting AB and so one can say that it is parallel to it.

Looking at the other lines, we will see that they are all touching AB and are not running parallel to it.

Hence, The option that needs to be corrected in this construction of a line parallel to line AB passing through C is C: the second arc should be centered at C.

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Answer:

m∠B = 100°

a = 4.6

b = 7.36

Step-by-step explanation:

By applying sine rule in the given triangle,

\(\frac{\text{sin(A)}}{a}= \frac{\text{sin(B)}}{b}= \frac{\text{sin(C)}}{c}\)

Now substitute the values in the expression,

\(\frac{\text{sin(38)}}{a}= \frac{\text{sin(B)}}{b}= \frac{\text{sin(42)}}{5}\)

\(\frac{\text{sin(38)}}{a}= \frac{\text{sin(42)}}{5}\)

\(a=\frac{5\text{sin(38)}}{\text{sin(42)}}\)

a = 4.6

By applying triangle sum theorem in ΔABC,

m∠A + m∠B + m∠C = 180°

38° + m∠B + 42° = 180°

m∠B = 180° - 80°

m∠B = 100°

\(\frac{\text{sin(100)}}{b}= \frac{\text{sin(42)}}{5}\)

\(b=\frac{5\text{sin(100)}}{\text{sin(42)}}\)

b = 7.36

Answer:

Step-by-step explanation:

8√42 ÷ 2√7 is 8√42/2√7 in a fraction form

you want to take the square root out of the denominator, and so you would multiply the denominator by the numerator and itself.

8√42/2√7 * 2√7/2√7 = 4√6

The cost of the labor per hour is 115 hours.

The equation is going to be:

4.25x + 167 = 655.75

your x is going to be:115

The duration was 4.25 hours.

The parts cost 167.

Cost in full: 655.75

so the price per hour is x.

As a result, when you write your equation, the total number of hours (multiplied by the cost per hour) will be added to the cost of the parts, and the sum of these two amounts will be your total cost.

In order to solve the problem, you must deduct the cost of each component from the total cost. This should give you the following result: 4.25x = 488.75

After that, divide 4.25 by each side as you normally would.

The cost of labor per hour follows. 115

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Answer:

Step-by-step explanation:

3:3:2 = 3x +2x +3x = 8x

112 = 8x

x = 14

alex = 3x = 3(14) = 42

sara = alex = 42

henry = 2x = 28

Answer:

heres what i think..

Step-by-step explanation:

the triangles can be similar as long as they have the same angle,but different measurements, a similar triangle could be a translation,dilation, or enlargement, as long as they are at the same angle (not rotated, reflected, or transformed ect.).

CDE = CDB + BDA + ADE

CDE = 42° + 37° + 20°

CDE = 99°

hope it helps...!!!

Answer:99 degrees

Step-by-step explanation:

Angle CDB + Angle BDA + Angle ADE= Angle CDE

42+37+20=99

Answer: 19.2 is how long

Step-by-step explanation:

Answer:

16 minutes

Step-by-step explanation:

Basically I just found out what 10 percent of 20 was, which is 2, then multiplied 2 by 8, to get 16 minutes.

Answer:

The correct answer is not rational.

Step-by-step explanation:

Based on the illustration given above, the feet that she now need to ascend to get back to sea level is 40.5.

Note that the first descend was 20.6 - 12.5 =

8.1 feet

Then she drop 32.4 feet again

So to get back up she need to add:

= 32.4 feet + 8.1 feet

= 40.5

Therefore, based on the calculation given above, the feet that she now need to ascend to get back to sea level is 40.5.

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a. To solve the given initial value problem (IVP) using Laplace transforms, we can apply the Laplace transform to the differential equation and solve for the Laplace transform of the solution.

Taking the Laplace transform of the equation y'(t) + y(t) = (1-3), we have:

sY(s) - y(0) + Y(s) = (1-3)/s

Substituting the initial condition y(0) = 2, we have:

sY(s) - 2 + Y(s) = (1-3)/s

Now, rearranging the equation to solve for Y(s), we get:

Y(s) = (1-3)/s + 2/(s+1)

Simplifying further, we have:

Y(s) = (-2)/s + 2/(s+1)

b. To obtain the solution y(t), we can apply the inverse Laplace transform to Y(s) obtained in part (a).

Taking the inverse Laplace transform, we have:

y(t) = -2 + 2e^(-t)

Therefore, the solution to the given initial value problem is y(t) = -2 + 2e^(-t).

Explanation:

In the first part, we applied the Laplace transform to the differential equation and obtained the equation in terms of the Laplace transform Y(s). By rearranging the equation, we solved for Y(s) in terms of the given Laplace transform expression.

In the second part, we applied the inverse Laplace transform to Y(s) to obtain the solution y(t). The inverse Laplace transform of -2/s gives us a constant term of -2, while the inverse Laplace transform of 2/(s+1) gives us the exponential term 2e^(-t).

Therefore, the solution y(t) = -2 + 2e^(-t) satisfies the differential equation y'(t) + y(t) = (1-3) and the initial condition y(0) = 2.

a. To find the auxiliary equation for the given differential equation y'' - 4y' + 3y' - 12y = 0, we can substitute y = e^(rt) into the equation, where r is an unknown constant.

Substituting y = e^(rt) into the differential equation, we get:

r²e^(rt) - 4re^(rt) + 3e^(rt) - 12e^(rt) = 0

Factoring out e^(rt), we have:

e^(rt)(r² - 4r + 3 - 12) = 0

Simplifying further, we obtain:

e^(rt)(r² - 4r - 9) = 0

Therefore, the auxiliary equation for the given differential equation is r² - 4r - 9 = 0.

b. The auxiliary equation plays a crucial role in finding the solutions to the given differential equation. By solving the auxiliary equation, we can determine the types of solutions and their behavior.

The auxiliary equation for the given differential equation y'' - 4y' + 3y' - 12y = 0 is r² - 4r - 9 = 0. This is a quadratic equation in terms of the unknown constant r.

To solve the quadratic equation, we can use various methods such as factoring, completing the square, or using the quadratic formula. In this case, the quadratic equation does not factor easily, so we can use the quadratic formula:

r = (-(-4) ± √((-4)² - 4(1)(-9))) / (2(1))

Simplifying further, we have:

r = (4 ± √(16 + 36)) / 2

r = (4 ± √52) / 2

r = (4 ± 2√13) / 2

r = 2 ± √13

Therefore, the solutions to the auxiliary equation are r₁ = 2 + √13 and r₂ = 2 - √13.

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To determine the maximum voltage of the power supply without damaging the LED, we need more information about the LED's specifications. The resistance of the resistor alone cannot provide enough information to calculate the maximum voltage.

LEDs have a maximum forward voltage rating, beyond which excessive voltage can damage them. This rating varies depending on the type and color of the LED. Additionally, LEDs typically require a current-limiting resistor to prevent excessive current flow.

To calculate the appropriate current-limiting resistor value and maximum voltage for the LED, we need the following information:

Forward voltage (Vf) rating of the LED: This is the voltage required for the LED to operate correctly. It can typically be found in the LED's datasheet or product specifications.

Forward current (If) rating of the LED: This is the recommended operating current for the LED, usually specified in milliamperes (mA) or amperes (A).

With these values, we can determine the maximum voltage of the power supply using Ohm's law and the LED's characteristics:

Calculate the current (I) flowing through the LED:

I = If (recommended forward current)

Calculate the resistance value (R) for the current-limiting resistor:

R = (Vp - Vf) / I

Where Vp is the power supply voltage and Vf is the forward voltage of the LED.

Use the resistance value (R) obtained to find the maximum voltage:

Vp(max) = Vf + I x R

Please provide the forward voltage and forward current ratings of the LED for a more accurate calculation.

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Answer:

=======================

Let the speed of plane is x and speed of the wind is y.

The speed of the plane with the wind is x + y and speed of the plane against the wind is x - y.

Equation for speed:

Since the same amount of time spent in both cases, we can set equations:

Add up the two equations and solve for x:

Find y: