Show that x^5-5x^3+5x2+-1=0 has 3 equal roots and find that root

Answer:

x-3

Step-by-step explanation:

martin =  x

jennifer = x-3

connor = 2x

what is jennifer's age?

Answer:

To find the perimeter and area of the square garden shed without graphing the coordinates, you can use the distance formula to calculate the length of one side of the square. The distance formula is d = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of two points. Using this formula with the coordinates of two adjacent corners of the square, such as (-2,8) and (1,8), we find that the length of one side of the square is 3 units. Since all sides of a square are equal in length, the perimeter is 4 times the length of one side, or 12 units. The area of a square is equal to the length of one side squared, so the area of the square garden shed is 9 square units.

This problem is different from finding the perimeter and area of the base of a house because it involves a square shape rather than a more complex shape. However, you can use similar strategies to solve both problems by calculating distances between points and using geometric formulas to find perimeter and area. The specific formulas used may vary depending on the shape of the base of the house.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 10891.31\\ P=\textit{original amount deposited}\\ r=rate\to 2.9\%\to \frac{2.9}{100}\dotfill &0.029\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &12 \end{cases}[/tex]

[tex]10891.31 = P\left(1+\frac{0.029}{4}\right)^{4\cdot 12} \implies 10891.31=P(1.00725)^{48} \\\\\\ \cfrac{10891.31}{1.00725^{48}}=P\implies 7700\approx P[/tex]

By answering the given question, we may state that Therefore, the equivalent inequality is: x < 2

A relationship between two terms or values which is not equal is known as an inequality in mathematics. Inequality follows imbalances, therefore. In mathematics, an inequality makes a link among two quantities that are not equal. Egality and inequality are different. Use the not similar symbol most frequently when two components are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two parts until only the variables are left, one can solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left & right.

inequality using basic algebraic operations:

5(2x-6)+6(3-x)<2x+4

10x-30+18-6x < 2x+4

4x - 8 < 0

4x < 8

x < 2

Therefore, the equivalent inequality is:

x < 2

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Situation 1:

Dependent variable: Distance traveled (d)

Independent variable: Speed (s)

Situation 2:

Dependent variable: Speed (s)

Independent variable: Distance traveled (d)

The dependent variable is the variable being studied or measured in an experiment or observation. It is the output or response that is being examined based on changes in the independent variable.

An independent variable is a variable that is manipulated or controlled by the experimenter in order to observe the effect on the dependent variable. It is also sometimes called the predictor variable.

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Accοrding tο given proportional data when d = 25, the value οf W is 95.

Relatiοnships between the twο variables that are prοpοrtiοnal οccur when their ratiοs are equal. Anοther apprοach tο cοnsider is that in a prοpοrtiοnal relatiοnship, οne variable is cοnsistently equal tο the οther's cοnstant value. This parameter is referred tο as the "cοnstant οf prοpοrtiοnality".

Accοrding tο the given infοrmatiοn:

Using the prοpοrtiοnality relatiοn W ∝ d, we can set up the fοllοwing prοpοrtiοn:

W/d = k, where k is the cοnstant οf prοpοrtiοnality.

Tο sοlve fοr k, we can use the values given in the prοblem:

133/35 = k

Simplifying, we get:

k = 3.8

Nοw, we can use this value οf k tο find the value οf W when d = 25:

W/25 = 3.8

Simplifying, we get:

W = 95

Therefοre, accοrding tο given infοrmatiοn when d = 25, the value οf W is 95.

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As per the given temperature, the new reading is  0°F

The formula for converting Fahrenheit to Celsius is (°F - 32) x 5/9 = °C. We can use this formula to determine the new temperature in Celsius and then convert it back to Fahrenheit.

First we have to convert the initial temperature to Celsius

(-20°F - 32) x 5/9 = -28.89°C

Now we have to add 20 degrees Fahrenheit to the initial temperature

-20°F + 20°F = 0°F

And then we have to convert the new temperature to Celsius

(0°F - 32) x 5/9 = -17.78°C

When we convert the new temperature from Celsius back to Fahrenheit

-17.78°C x 9/5 + 32 = 0°F

Therefore, the new reading on the thermometer will be 0 degrees Fahrenheit, which indicates that the temperature has risen by 20 units on the Fahrenheit scale.

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Answer: 20.1 m

Step-by-step explanation:

using  the formula circumference = 2pi r:

[tex]126=2\pi r[/tex]

divide 2 pi on both sides

[tex]r=\frac{126}{2\pi }[/tex]

r = 20.05

r = 20.1 m

Answer: Its B.) −5 ≤ y ≤ 2

Step-by-step explanation: The graph shows one part of the interval increasing which is the y value and stops at 3. The X interval which is the decreasing interval stops at -5. So this would be -5 greater then or equal to y greater then or equal to 2.

Sorry if wrong! Have a nice day :)

Step-by-step explanation:

disculpa, te recomiendo acercar más la foto para porder

te ayudar

Answer:

[tex]y^2 = x^3 / 2^{3/2}[/tex] or [tex]y = x^{3/2} / 2^{3/4}[/tex]

Step-by-step explanation:

We can use the identity [tex]cos^3(t) = cos(t)*cos^2(t) and sin^3(t) = sin(t)*sin^2(t)[/tex] to rewrite the given parametric equations in terms of x and y:

[tex]x = 2cos(t)*cos^2(t) = 2x^2 - 2y^2[/tex]

[tex]y = 2sin(t)*sin^2(t) = 2xy^2[/tex]

Solving for y in terms of x, we get:

[tex]y = x^{3/2} / 2x^{3/4}[/tex]

Therefore, the cartesian equation of the curve is:

[tex]y = x^{3/2} / 2^{3/4}[/tex]

or, equivalently:

[tex]y^2 = x^3 / 2^{3/2}[/tex]

Answer:

The probability of selecting a face card or a spade when randomly selecting one card from a standard deck of cards is 11/26 or approximately 0.423.

Step-by-step explanation:

Part A

No, selecting a face card and selecting a spade when randomly selecting one card from a standard deck of cards are not mutually exclusive events. This is because there are face cards that are also spades, so there is an overlap between the two events.

Part B

The probability of selecting a face card or a spade when randomly selecting one card from a standard deck of cards can be calculated as follows

P(face card or spade) = P(face card) + P(spade) - P(face card and spade)

Part C

The probability of selecting a face card or a spade when randomly selecting one card from a standard deck of cards can be calculated as follows

P(face card or spade) = P(face card) + P(spade) - P(face card and spade)

P(face card or spade) = 12/52 + 13/52 - 3/52

P(face card or spade) = 22/52

P(face card or spade) = 11/26

Hence, the probability of selecting a face card or a spade when randomly selecting one card from a standard deck of cards is 11/26 or approximately 0.423.

Answer:

9

Step-by-step explanation:

1 dozen -12

there dozen - 36

thus

red blocks -4

36/4

= 9

Answer:

∠ ABC = 38°

Step-by-step explanation:

given AB = DB then Δ ABD is isosceles with base angles congruent, that is

∠ BDA = ∠ BAD = 71°

the sum of the 3 angles in Δ ABD = 180° , so

∠ ABC + 71° + 71° = 180°

∠ ABC + 142° = 180° ( subtract 142° from both sides )

∠ ABC = 38°

Answer: 5/81

Step-by-step explanation:

F(4) = 5 * (1/3) ^ 4

F(4) = 5 * 1/81

F(4) = 5/81

To make things easier, consider the residue when each integer between equation 1 and 60 is divided by 5. The remainders might be one, two, three, or four.

A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.

0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0 (if all answers are wrong or not attempted) (if all answers are incorrect or not attempted)

5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 60 (assuming all answers are accurate) (if all answers are correct)

10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 120 (assuming all answers are accurate and attempted twice) (if all answers are correct and attempted twice)

. The impossible scores may be obtained by locating all the numbers between 1 and 60 that cannot be stated as a sum of 0, 5, or 10.

To make things easier, consider the residue when each integer between 1 and 60 is divided by 5. The remainders might be one, two, three, or four.

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Answer:

Proved

Step-by-step explanation:

In triangles ABD and CBD,

Angle CDB = Angle ADB (given in Question)
Angle CBD = Angle ABD ( Angle Bisector Therom)
BD = BD ( Common side)

Therefore Triangle ABD is congruent to Triangle CBD by ASA

Hope it helps :)

It is untrue to say that the exponential function f(x) has a base of 3.

A mathematical function termed an exponential function has the formula f (x) = axe, where x is a variable and a constant called the base of the function, which must be greater than 0. The most often used exponential function basis is the transcendental number e, or approximately 2.71828.

An exponential function has the form f(x) = bx for b > 0 and b 1. Like in any exponential expression, the base is b and the exponent is x. Bacterial growth serves as an example of an exponential function. Some bacteria grow by two per hour.

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The answer will be as follows after answering the supplied question It is equation worth noting that this equation is a cubic polynomial.

A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.

The degree n Lagrange polynomial that passes through n+1 unique points (x0,y0), (x1,y1),..., (xn,yn) is given by:

[j=0 to n] L(x) [i=0 to n, ij] * yj (x - xi)/(xj - xi) (xj - xi)

We have 5 points in our situation, thus n = 4. We get the following results by plugging the provided points into the Lagrange polynomial formula:

[tex]L(x) = 1*(x-2)(x-3)(x-4)(x-5)/(-1123) + 2(x-1)(x-3)(x-4)(x-5)/(1123) + 4(x-1)(x-2)(x-4)(x-5)/(1123) + 4(x-1)(x-2)(x-4)(x-5)/(1123) (2123)+ 12(x-1)(x-2)(x-3)(x-4)/(432*1)[/tex]

When we simplify this expression, we get:

[tex]L(x) = x^3/3 - 3x^2/2 + 11x/6 - 1[/tex]

As a result, the equation of the curve passing through the given locations is:

[tex]y = x^3/3 - 3x^2/2 + 11x/6 - 1[/tex]

It is worth noting that this equation is a cubic polynomial.

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According to the figure and using the corresponding angle theorem we have that

Corresponding angles are pairs of angles that are formed when a straight line intersects two parallel lines.

They are located on opposite sides of the transversal (the line that intersects the parallel lines) and in corresponding positions. Corresponding angles have the same degree measurement as each other.

angle 1 = 82 degrees corresponding angles are equal

angle a = 58 degrees corresponding angles are equal

angle a and angle 2 are linear pair hence angle a and angle 2 are supplementary angles

hence we have that

angle a + angle 2 = 180 degrees

58 + angle 2 = 180

angle 2 = 180 -58

angle 2 = 122 degrees

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Beth will need approximately 3365.76 [tex]cm^{2}[/tex] of plastic wrap to cover all 12 jars of jam.

What is a Circle?

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.

So now, to calculate the surface area of each jar, we need to find the area of the circular top and the area of the rectangular side.

The area of the circular top can be calculated using the formula for the area of a circle:

[tex]A=\pi r^{2}[/tex], where r is the radius of the circle.

The diameter of the jar is given as 7 cm, so the radius is half of that:

r = [tex]\frac{7}{2}[/tex] cm = 3.5 cm

Therefore, the area of the circular top is:

A_top = [tex]\pi r^2[/tex] = π[tex](3.5)^{2}[/tex] = 38.48 [tex]cm^{2}[/tex]

The area of the rectangular side can be calculated using the formula for the area of a rectangle:

A_side = base x height

The base of the rectangle is the circumference of the circular top, which can be calculated using the formula:

C = 2πr

C = 2π(3.5) = 22 cm

So the base of the rectangle is 22 cm, and the height is 11 cm, since that is the height of the jar.

Therefore, the area of the rectangular side is:

A_side = base x height = 22 cm x 11 cm = 242 [tex]cm^{2}[/tex]

To find the total surface area of each jar, we can add the area of the circular top and the area of the rectangular side:

A_total = A_top + A_side = 38.48 [tex]cm^{2}[/tex]+ 242 [tex]cm^{2}[/tex] = 280.48 [tex]cm^{2}[/tex]

For 12 jars, the total surface area of plastic wrap needed would be:

Total area = 12 x A_total = 12 x 280.48 [tex]cm^{2}[/tex] = 3365.76 [tex]cm^{2}[/tex]

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To minimize the distance walked, and the minimum distance is 31.8% of the total circumference of the circle.

If we draw a line segment from A to B, it will intersect the circle at two points, C and D. We can find the distance AC and the distance BD by using the Pythagorean theorem.

Let r be the radius of the circle, and let x be the distance we walk in and then out of the circle.

Then, we have:

AC = √(r^2 - (x/2)^2)

BD = √(r^2 - (x/2)^2)

The total distance we walk is AC + BD + AB. Since AB is fixed, we want to minimize AC + BD.

AC + BD = 2√(r^2 - (x/2)^2)

To minimize this expression, we need to maximize the value inside the square root. That means, we need to set (x/2)^2 to be as small as possible.

In other words, we want x to be as large as possible.

The maximum value of x is the diameter of the circle, which is 2r.

If we walk in and out of the circle along the diameter, then AC and BD are both equal to r, and the total distance we walk is 2r + AB.

Therefore, the percentage of the total circumference that we walk in and out of the circle is:

2r / (2πr) * 100% = 100/π ≈ 31.8%

So, we need to walk in and out of the circle at two points that are opposite to each other, along a diameter, to minimize the distance walked, and the minimum distance is approximately 31.8% of the total circumference of the circle.

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Answer:

c ≈ 11.2

Step-by-step explanation:

Using the distance formula, we have:

c = √[(x2 - x1)² + (y2 - y1)²]

c = √[(-7 - 3)² + (1 - (-4))²]

c = √[(-10)² + 5²]

c = √(100 + 25)

c = √125

c ≈ 11.2

Therefore, the distance between the two points is approximately 11.2 units.

[tex]\sqrt{(-7-3)^{2} + (1-(-4))^{2} } = \sqrt{(-10)^{2} + (5)^{2} } = \sqrt{100 + 25} \\[/tex]

[tex]= \sqrt{125} = 5\sqrt{5} =11.2[/tex]

Answer:

The measure which changes the most is the mean and the new value is 84°

The correct answer option is option B

Step-by-step explanation:

How to calculate mean and median?

Given data set:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Median = (100 + 105) / 2

= 205/2

= 102.5°

Mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12

= 965 /12

= 80.4°

Range = Highest value - lowest value

= 105 - 57

= 48°

Interquartile range = Third quartile - First quatile

= 88.5° - 74°

= 14.5°

If 58° is changed to 101°

101, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Median = (100 + 105) / 2

= 205/2

= 102.5°

Mean = (101 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12

= 1008 /12

= 84°

Range = Highest value - lowest value

= 105 - 57

= 48°

First quartile = (71 + 77) / 2

= 148/2

= 74°

Third quartile = (95 + 82)/2

= 177/2

= 88.5°

Interquartile range = Third quartile - First quatile

= 88.5° - 74°

= 14.5°

Therefore, the new mean is 84°

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The true statements about the functions A and B are

Given that

Function B: y = 3x + 4

A linear equation is represented as

y = mx + c

Where

Rate of change = m

y-intercept = c

Using the above definition, we have the following summary for function B

Rate of change = 3 and y-intercept = 4

For function A (the table), we have

Rate of change = (10 - 2)/(3 - 1)

Rate of change = 4

While the y-intercept is

y-intercept = 2 - 4

y-intercept = -2

So, we have

                                             Function A                Function B

Rate of change                         3                                4

y-intercept                                4                                -2

By comparing the features, we have the following true statements

C. The y-intercept of Function A is greater than the y-intercept of Function B.

E. The rate of change of Function A is less than the rate of change of Function B.

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Complete question

Function A and Function B are linear functions. Function A is represented by the table of values. Function B is represented by the equation.

Function A

x 1   3    4    7

y 2  10  14 26

Function B

y = 3x + 4

Which statements about the properties of Function A and Function B are true? Select each correct statement.

A. The y-intercept of Function A is equal to the y-intercept of Function B. B. The y-intercept of Function A is less than the y-intercept of Function B. C. The y-intercept of Function A is greater than the y-intercept of Function B.

D. The rate of change of Function A is equal to the rate of change of Function B.

E. The rate of change of Function A is less than the rate of change of Function B.

F. The rate of change of Function A is greater than the rate of change of Function B.

Answer:

Dry your hands from the soap and try twisting the lid of the pan. This will cause it to start to turn. If you put it in the freezer it will be harder to take it off. My guess is by twisting the lid, you would be able to cause enough friction to take the lid off.

Step-by-step explanation:

If this doesn't work try tilting the lid and then lifting it

Answer:

Try soaking it in hot water. The pot only if possible. The top is smaller and if the  pan expands it should loosen up

Answer:

Mr Drake is right.

Step-by-step explanation:

Because you first decreased it by 10% of the ORIGINAL value.

You then increased it by 10% of the DECREASED value.

The percentages are the same percentages, but on different base amounts.

Simple example:

$100 decreased by 10% of $100 ($10) is $90.

$90 increased by 10% of $90 ($9) is $99.

Answer:

Mr Drake Is correct

Step-by-step explanation:

When you increase something by 10%, you multiply the original value by 1.1. When you decrease it by 10%, you multiply the increased value by 0.9. So the final amount is:

original value x 1.1 x 0.9 = 0.99 x original value

Therefore, the new amount will be slightly smaller than the original amount, and Mr. Drake is correct.

Answer: p+3

Step-by-step explanation:

if p=12 and you need the answer to be 15, all you need to do is find 12+_= 15. Since 12+3=15 your answer would be p+3.

Answer:

number 2 is 4

Step-by-step explanation:

Based on the given question, Molly needs a loan of $1,000

A loan occurs when one or more people, businesses, or other entities lend money to other people, businesses, or other entities.

The recipient incurs a debt and is often responsible for both the principal amount borrowed as well as interest payments until the debt is repaid.

How to calculate the amount of loan that Molly needs?

Molly has a $2500 down payment saved for a purchase

The dealer's cash allowance is $1500, this will be deducted from her total

The amount of loan that Molly needs can be calculated by subtracting the dealer's cash allowance from Molly's down payment

Loan= Down payment-cash allowance= 2500 - 1500= 1000

Hence Moly needs a loan of $1,000

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