What is the standard equation of this ellipse: Vertices: (0,12)
(0,-12) Foci: (0,8) (0,-8). Why do I keep getting
(x^2)/80+(y^2)/144?

The end behavior is that as x moves toward negative infinity, f(x) moves toward negative infinity and as x moves toward positive infinity, f(x) moves toward positive infinity. F(x) only has one x-intercept, which is x = 3.

The given function is f(x) = -x³ + 2x² + 3

1. End behavior:

As the leading coefficient of f(x) is negative, -x^3 dominates the behavior of the function as x moves towards -∞ or +∞. Therefore, the end behavior of the function is:

2. X-intercepts:

To determine the x-intercepts of the function, we have to calculate the equation f(x) = -x^3 + 2x^2 + 3 = 0. We can factor out a common factor of -1 to simplify the equation:

-x^3 + 2x^2 + 3 = 0

x^3 - 2x^2 - 3 = 0

Applying synthetic division or long division, one of the roots of this equation is x = 3. We can then factor out (x - 3) using polynomial division to find the other two roots:

x^3 - 2x^2 - 3 = (x - 3)(x^2 + x + 1)

The factor of x^2 + x + 1 has no real roots, so the only x-intercept of f(x) is x = 3.

3. Positive/negative:

To determine the sign of f(x) for different values of x, we can look at the sign of each factor in the polynomial:

Putting these together, we can make the following sign chart for f(x):

x                         f(x)

x < 0                   -

0 < x < 3                  +

x > 3                  -

4. Multiplicity: The single root of f(x) has multiplicity 1 and is given by x = 3. This indicates that at x = 3, the graph of f(x) crosses the x-axis and switches signs.

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The equation f(x) = 0 has four complex zeros: ±2i and 1 ± √2i, each with a multiplicity of 1.

To solve the equation f(x) = 0, we need to factor the polynomial f(x) into linear factors and then find the zeros of the equation.

Step 1: Factor the polynomial f(x) into linear factors.
f(x) = x ^ 4 + 2x ^ 3 + x ^ 2 + 8x - 12
= (x^2 + 4)(x^2 - 2x + 3)

Step 2: Find the zeros of the equation by setting each factor equal to zero and solving for x.
x^2 + 4 = 0
x^2 = -4
x = ±√(-4)
x = ±2i

x^2 - 2x + 3 = 0
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
x = (-(-2) ± √((-2)^2 - 4(1)(3)))/(2(1))
x = (2 ± √(-8))/2
x = (2 ± 2√2i)/2
x = 1 ± √2i

State the multiplicity of each zero.
The zeros of the equation are ±2i and 1 ± √2i. Each zero has a multiplicity of 1.

Use the table from your calculator to find any real zeros, then use synthetic division to find the remaining zeros.
There are no real zeros in this equation, as all of the zeros are complex numbers. Therefore, there is no need to use the table from the calculator or synthetic division to find the remaining zeros.

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Using two-point form, the equation of the line passing through the points A and B is x = 5.

The two-point form of a line is given by:
y - y₁ = [(y₂ - y₁)/(x₂ - x₁)] (x - x₁)
where (x₁, y₁) and (x₂, y₂) are two points on the line.

Given points A(5, 5) and B(5, -5), we can plug in the values into the equation:
y - 5 = [(-5 - 5)/(5 - 5)] (x - 5)

Simplifying the equation gives us:
y - 5 = (-10/0) (x - 5)

Notice that the slope (y₂ - y₁)/(x₂ - x₁) is equal to -10/0(indeterminate). This means that the line is a vertical line passing through x = 5.

The standard form of a line is Ax + By = C. So, the standard form of the equation of the line passing through points A and B is: x = 5.

Therefore, the equation of the line passing through the two points is x = 5.

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Find a positive value of c so that the following trinomial is factorable. [tex]x^2-4x+c[/tex], The value of [tex]c[/tex] will be given by [tex]c=4[/tex].

To find a positive value of c so that the trinomial [tex]x^2-4x+c[/tex] is factorable, we need to use the formula for the sum of two squares. This formula states that [tex](a-b)^2=a^2-2ab+b^2[/tex].

In this case, we can let [tex]a=x[/tex] and [tex]b=2[/tex], so the formula becomes [tex](x-2)^2=x^2-4x+4.[/tex]

Comparing this formula to the given trinomial, we can see that the value of c must be 4 in order for the trinomial to be factorable.

Therefore, the positive value of c that makes the trinomial [tex]x^2-4x+c[/tex] factorable is [tex]c=4[/tex].

In factored form, the trinomial becomes [tex](x-2)^2[/tex].

Answer: [tex]c=4.[/tex]

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The bus’s speed on the level road was 72 mph if the bus traveled on a level road for 6 hours at an average speed of 20 miles per hour.

The given data is as follows:

The bus traveled on road time = 6 hours

Average speed = 20 miles/hour

Time spent on the winding road = 3 hours

Entire trip distance =  534 miles

The equation will be written as:

(x+20) * (6) + (x)(2) = 534

Now, "x" is the average speed on the winding road.

solving for x value,

6x + 120 + 2x = 534

8x = 534 -120

x = 414/8

x = 52

Now,  we calculated the average speed for the winding road.

The average speed for the level road is calculated as:

u1 + v1 = 52 + 20 = 72

Therefore we can conclude that the bus’s speed on the level road was 72 mph.

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a) The expected payout for the insurance company is $182.

b) If the insurance company wants to charge 15% over the expected payout, the insurance company should charge the insured $27.30.

In a game of chance, the expected payout is the expected value of the game minus the cost.

For the insurance company, the expected payout is the probability-weighted value of the insurance undertaking.

The expected payout is the product of the amount to be paid to the insured family and the probability or chance of the insured dying.

The amount the insured family will receive = $130,000

The chance of the insured dying = 0.0014

The expected payout = $182 ($130,000 x 0.0014)

Charge over the expected payout = 15%

The amount the insurance company should charge the person = $27.30 ($182 x 15%)

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Answer:

D. x > 0, x ≤ 4, y ≥ 1 and y < 4

a) (TRUE)

If b is a linear combination of the columns of the matrix A, then the linear system Ax = b has a unique solution.

b) (FALSE)

If {u, v, w} is linearly independent, then {u+w, v + w} is linearly independent.

c) (FALSE)

If V = span{V1, V2, V3} and dim(V) = 2, then {V2, V3} is a basis of V.

a) If b is a linear combination of the columns of matrix A, then the linear system Ax = b has a unique solution. This is (always) true because if b is a linear combination of the columns of matrix A, then it can be written as Ax.

Therefore, if A is invertible, then x = A^(-1)b is a unique solution to Ax = b.

b) If {u, v, w} is linearly independent, then {u+w, v+w} is linearly independent. This is (possibly) false because {u+w, v+w} is linearly dependent if u = -v = w.

Therefore, {u+w, v+w} is not linearly independent.

c) If V = span{V1, V2, V3} and dim(V) = 2, then {V2, V3} is a basis of V.

This is (possibly) false because {V2, V3} is a basis for V if and only if V2 and V3 are linearly independent and span(V).

However, dim(V) = 2 implies that V is a 2-dimensional subspace of R^3, so {V1, V2, V3} cannot be linearly independent.

Therefore, {V2, V3} is not necessarily a basis for V.

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The value of x in the chord is 4.8 units

From the question, we have the following parameters that can be used in our computation:

The circle

Next, we calculate the radius using each chord using the Pythagoras theorem

Using the above as a guide, we have the following:

r² = x² + (37/2)²

r² = 13² + (28/2)²

By substitution, we have

x² + (37/2)² = 13² + (28/2)²

So, we have

x² = -(37/2)² + 13² + (28/2)²

Evaluate

x² = 22.75

Take the square root

x = 4.8

Hence, the value of x is 4.8 units

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The current thrοugh the 2.5 οhm resistοr is 2.4 A.

Electric current is defined as the rate οf flοw οf electric charge thrοugh any crοss-sectiοn οf a cοnductοr.

Tο calculate the current thrοugh a 2.5 οhm resistοr cοnnected acrοss a 6.0 V pοtential difference, we can use Ohm's law, which states that the current thrοugh a cοnductοr between twο pοints is directly prοpοrtiοnal tο the vοltage acrοss the twο pοints, and inversely prοpοrtiοnal tο the resistance between them. The mathematical expressiοn fοr Ohm's law is:

V = I x R

where V is the vοltage, I is the current, and R is the resistance.

We can rearrange this fοrmula tο sοlve fοr the current I:

I = V / R

Substituting the given values, we get:

I = 6.0 V / 2.5 οhm

I = 2.4 A

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By answering the above question, we may state that Without having both  expressions the original concept and Megan and Mindy's drawings, it is impossible to tell which drawing is mistaken.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.  

If Megan and Mindy both depicted the entire playground, then their pictures ought to match. Their designs ought to depict the remaining 4/6 of the playground if the plan they viewed only showed 2/6 of it.

You may assess a drawing's accuracy by contrasting it with the first design that Megan and Mindy viewed. They are correct if their designs depict the remaining 4/6 of the playground and the original plan matches. Their drawings are incorrect if they do not reflect the original design or do not depict the remaining 4/6 of the playground.

Without having both the original concept and Megan and Mindy's drawings, it is impossible to tell which drawing is mistaken.

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Tyler takes 32 minutes to read 24 pages.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Tyler reads 3/4 pages per minute. Then the ratio of pages to minutes is given as,

Ratio = (3/4)/1

Ratio = 3:4

If he read 16 minutes, then the number of pages is calculated as,

(3/4) x 16

3 x 4

12 pages

Tyler has to read 24 pages for homework. Then the number of minutes is given as,

24 / (3/4)

24 x (4/3)

8 x 4

32 minutes

Therefore, it takes 32 minutes to read 24 pages.

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The sample size needed to ensure that the probability that the sample mean differs from the population mean by more or less then 2.0 hours is less than at a 90% confidence level is 127.

The sample size needed to ensure that the probability can be calculated using the formula:
n = (zα/2)2 2 / (E2)

Where n is the sample size, is the population standard deviation (12.4 hours in this case), E is the margin of error (2.0 hours in this case) and zα/2 is the critical value from a z-table corresponding to the 90% confidence level (1.645 in this case).

Thus, n = (1.645)2 (12.4)2 / (2.0)2 = 126.8

Therefore, the sample size needed to ensure that the probability that the sample mean differs from the population mean by more or less then 2.0 hours is less than at a 90% confidence level is 127.

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The best forecast is the one with the lowest MSE level. In this case, the "3 Month Moving Average" has the lowest MSE level of 2.1, making it the best forecast. Therefore, the correct answer is B. 3 Month Moving Average.

One common metric used to compare forecasting methods is the Mean Squared Error (MSE). The MSE measures the average squared difference between the actual values and the forecasted values, so a lower MSE indicates a better fit.

In this case, we have four different forecasting methods and their respective MSE values. The 3 Month Moving Average has the lowest MSE of 2.1, which suggests it is the best forecasting method among the four options.

Thus, the answer is B. 3 Month Moving Average.

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It is one of the most fundamental curvilinear geometric shapes, a cylinder has historically been thought of as a three-dimensional solid. It is considered a prism with a circle as its base in basic geometry.

the area of mathematics that focuses on the characteristics and connections between points, lines, surfaces, solids, and their higher dimensional equivalents.

We can find the solution this way,

The volume of water in the Cylinder before marbles were dropped in =

The volume of water in the Cylinder After marbles were dropped in -

Volume of marbles

So, we can write it as,

Volume of water before = Volume of water after - Volume of Marbles

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b=7

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

If you travel 200 miles in four hours, then your average speed for the trip is 50 miles per hour. This is calculated by dividing the total distance traveled (200 miles) by the total time taken (4 hours).

So, if you travel 200 miles in four hours, your average speed is 50 mi/h.

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Answer:

16

Step-by-step explanation:

8-4x times y^2, x=3 and y=-2

First, plug in both variables. Since x=3, you would substitute 4x in the equation to 4(3). You would do the same to y, but instead it would be in replace of y^2. So it would be -2^2. You now have a new equation:

8-4(3) times -2^2

Next, you start solving the equation. You should follow PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction). This method is sometimes controversial, but it still works for this problem.

Start by multiplying 4 times 3 which equals 12. Then I solve the exponent. The exponent -2^2 is the same as -2 times -2. The -2 is the number that gets multiplied, and the exponent is how many times -2 gets multiplied times itself. -2 times -2 is 4. You can plug your new numbers back in the equation now.

8-12 times 4

The equation is much easier to solve now. 8-12 is -4. -4 times 4 is 16.

The answer is 16.

The length of the midsegment of the given trapezoid is 16.

A trapezoid is necessarily a convex quadrilateral in Euclidean geometry. The parallel sides are called the bases of the trapezoid.

Given is a trapezoid TUVW, with bases UV and TW given by expressions, 3x-1, 8x and the midsegment XY is 3x+7.

We need to find the length of the midsegment,

We know,

Midsegment = (base 1 + base 2) / 2

Therefore,

XY = UV+TW / 2

3x+7 = 3x-1 + 8x / 2

6x+14 = 11x-1

5x = 15

x = 3

XY = 3(3)+7 = 16

Hence, the length of the midsegment of the given trapezoid is 16.

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The product of the polynomials is 4x^(2)-28x+49, which is a single polynomial in standard form.

A polynomial is an expression consisting of variables, constants and coefficients, in which the exponents of the variables are either whole numbers or zero. It can be written in the form of a summation, where each term is the product of a coefficient and a variable raised to a power.

To multiply the polynomials using a special product formula, we can use the formula for squaring a binomial, which is (a-b)^(2)=a^(2)-2ab+b^(2). In this case, a=2x and b=7.

So, we can plug these values into the formula and simplify:

(2x-7)^(2) = (2x)^(2)-2(2x)(7)+(7)^(2)

= 4x^(2)-28x+49

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c) 2x^-3 + 5x^-1 - x

A polynomial is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication, and raised to non-negative integer powers.

Answer:

Only the (a) and (c) can be classified as polynomials here.

Reason is that  a polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division by a variable. A polynomial can have one or more terms, where each term contains a product of a coefficient and a variable raised to a non-negative integer power. For example, 2x^3 + 5x^2 - 3x + 7 is a polynomial with four terms.

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Anne and Maya drive for 2 1/2 hours.

A mixed fraction is a combination of a whole number and a proper fraction. For example, 2 1/3 is a mixed fraction, where the whole number is 2 and the proper fraction is 1/3.

To convert an improper fraction into a mixed fraction, Divide the numerator by the denominator and write down the whole number result as the whole number part of the mixed fraction.

Write down the remainder as the numerator of the fractional part of the mixed fraction.

Here we have

Anne and Maya each drive the same amount of time to complete the 5-hour trip.  

Let both of them be derived for 'x' hours

=> x + x = 5 hours

=> 2x = 5 hours

=> x = 5/2

Hence, Anne and Maya drive for 5/2 hours

Here 5/2 can be converted as 2 1/2  

Therefore,

Anne and Maya drive for 2 1/2 hours.  

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For the inequality y ≤ -2/3x + 6 the graph is plotted with the points (0, 6) and (9, 0).

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The inequality y ≤ -2/3x + 6 is already in slope-intercept form (y = mx + b), where the slope is -2/3 and the y-intercept is 6.

To find some possible solutions for this inequality, we can choose any value of x and then solve for y.

Let's choose x = 0 -

y ≤ -2/3(0) + 6

y ≤ 6

So when x = 0, any y value less than or equal to 6 will satisfy the inequality.

This gives us the solution set -

{(x, y) | y ≤ 6}

Now choose a value of y to find another point that satisfies the inequality. Let's choose y = 0 -

0 ≤ -2/3x + 6

2/3x ≤ 6

x ≤ (6 × 2)/3

x ≤ 9

So when y = 0, any x value less than or equal to 0 will satisfy the inequality.

Therefore, some possible solutions for the inequality y ≤ -2/3x + 6 are -

(0, 6) and (9, 0).

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Answer:

i do not know

Step-by-step explanation:

mmmmdjfhyhbwsdhsiayjbe

Answer:

The number of minutes that could have passed if the pool now has less than 74 gallons of water left is greater than 9 minutes.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The amount of water remaining in the pool after x minutes is given by:

110 - 4x

We want to find the number of minutes, x, such that the pool now has less than 74 gallons of water left.

110 - 4x < 74

To solve for x, we can first subtract 110 from both sides of the inequality:

-4x < 74 - 110

Simplifying, we get:

-4x < -36

Divide both sides of the inequality by -4,

x > 9

Therefore, the number of minutes that could have passed if the pool now has less than 74 gallons of water left is greater than 9 minutes.

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For (a): 52 + 35/10m, rationalizing the denominator gives the result (25√2 + 6√5)/10.
For (b): 33x + 3y/3xy, rationalizing the denominator gives the result √3(x+y)/xy.

To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of a binomial expression is the same expression with the sign between the terms changed. For example, the conjugate of (a+b) is (a-b) and the conjugate of (a-b) is (a+b). By multiplying by the conjugate, we eliminate any radicals in the denominator.

(a) 5/√2 + 3/√5

  = (5/√2)(√2/√2) + (3/√5)(√5/√5)

  = (5√2)/2 + (3√5)/5

  = (25√2 + 6√5)/10

(b) (3√3x + 3√y)/(3√xy)

  = (3√3x + 3√y)(3√xy)/(3√xy)(3√xy)

  = (9x√3xy + 9y√3xy)/(9xy)

  = (9√3xy(x+y))/(9xy)

   = √3(x+y)/xy

Therefore, the rationalized denominators are (a) (25√2 + 6√5)/10 and (b) √3(x+y)/xy.

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The length of line BC is 10cm ,The area of the circle is 78.5 cm² and The circumstance of Circle  is  31.4 cm.  

Part-1

To Find the length of BC, We have the lenghts of CD=8cm and DE=12cm

To find out length. We have to make a perpendicular line construction joins AE.

Triangle AED forms a right angled triangle.

As we all know pythagoras theorem.

Pythagoras formula c²=a²+b²

To findout radius of circle

Let AE=AC=r  

      AD=CD+AC

      AD=8+r

                               AD²=AE²+DE²

Submit all values in the above equation.

                               (8+r)²=r²+12²

(a+b)²=a²+b²+2ab use the formula

                             64+r²+16r=r²+144

Cancel r² each other.

                             64+16r=144

                                    16r=144-64

                                     16r=80

                                         r=5

Radius of the circle    r=5cm

Therefore , the value of BC=2AC

                                       BC=2r

                                        BC=2*5

                                        BC=10cm

The length of line BC is 10cm

Part-2

To find out area of the circle

We have the formula for area of circle.

                                       Area=πr²

                                         Area=(22/7)*5*5

                                         Area=78.5 cm²

The area of the circle is 78.5 cm².

To find out the circumstance of Circle

We have the formula for circumstance of circle.  2πr

                              circumstance=2*(22/7)*5

                              circumstance=31.4 cm

The circumstance of Circle  is  31.4 cm.  

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The decimal multiplier to increase by 6.1% is 1.061.

What is multiplication ?

Multiplication is a mathematical operation used for finding the result of adding a number to itself a certain number of times. It involves multiplying two or more numbers to find their product. For example, 2 times 3 is equal to 6, written as 2 x 3 = 6. In multiplication, the numbers being multiplied are called factors, and the result is called the product. Multiplication is often denoted by the symbol "x" or a dot ".".

A decimal multiplier is a factor that is used to increase or decrease a number by a certain percentage. It is commonly used in financial calculations such as interest rates, discounts, and taxes.

To find the decimal multiplier to increase by a certain percentage, you can use the following formula:

Decimal multiplier = 1 + (percentage increase/100)

For example, if you want to increase a number by 6.1%, the decimal multiplier would be:

Decimal multiplier = 1 + (6.1/100)

Decimal multiplier = 1.061

This means that to increase a number by 6.1%, you would multiply it by 1.061. For example, if you had a number of 100, to increase it by 6.1%, you would multiply it by 1.061 to get 106.1.

On the other hand, if you wanted to decrease a number by a certain percentage, you would use a decimal multiplier that is less than 1. For example, to decrease a number by 10%, the decimal multiplier would be 0.9, which means you would multiply the number by 0.9 to get the new decreased value.

Therefore, decimal multiplier to increase by 6.1% is 1.061.

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Answer:

Step-by-step explanation:

2(2x+2) + 2(x+4) = 36

4x+4 +2x+8 =36

6x+12= 36

6x = 36-12

6x =24

x = 4

longer side = 10