Suppose a conic section passes through the point (2, - 7). If the conic section has focus ( - 1, -3), directrix 2 = 3, then it is a ellipse parabola hyperbola cannot be determined.

Answer:

Hi, there for the graph it will be not a function

For the equation it is also not a function

Step-by-step explanation:

For the graph use   vertical line test to see if the x value are the same if they are that's means it is not a function.

The X value can't be the same and can't be used twice.

The reason why because given an equation, there should be only one corresponding y value for any x value.

Dividing two polynomials may produce another polynomial only when the divisor has a lower degree than the dividend. Otherwise, it will generally result in a rational function.

No, dividing two polynomials may not result in another polynomial. It can produce a rational function.

A polynomial is an algebraic expression consisting of terms with non-negative integer exponents. When two polynomials are divided, the result is not always a polynomial.

If the degree of the polynomial being divided (dividend) is higher than the degree of the polynomial dividing (divisor), then the result can be a polynomial with a lower degree. However, if the degree of the divisor is equal to or greater than the degree of the dividend, the result will generally be a rational function, which is a ratio of two polynomials.

A rational function has the form P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero. The division can introduce terms with negative or fractional exponents, making the result a rational function rather than a polynomial.

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The compass needle always points north because it is magnetic north pole.

Earth has magnetic field due to magnetic elements present in Earth's core in molten form. They are assumed to be in the form of giant bar to ease the calculations concerning magnetic field and polarity. The assumptions are geographic south pole harbours magnetic north pole and vice versa for the opposite pole.

So, we know that like poles attract each other and unlike poles repel each other. The north end of magnetic needle will point towards the magnetic south pole which is geographic north pole. Thus, we see compass needle directed to North pole.

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Answer:

x>=9

Step-by-step explanation:

so, we can plot this on a number line

the point at 9 is a solid dot, since brackets (not parenthasis) indicates that we including the number. the shaded part of the line extends all the way to positive infinity. the shaded part means that it is a solution, while the un-shaded parts aren't solutions to [9,infinity) it is x>=9 and not x>9 because 9 is included.

x>=9 is the answer

Answer:

The point (11, 5) is NOT on the parabola.

Step-by-step explanation:

Let \((x_0,y_0)\) be any point on the parabola

Let \((a, b)\) be the focus

Let \(y=c\) be the the directrix

Distance between \((x_0,y_0)\) and the focus: \(\sqrt{(x_0-a)^2+(y_0-b)^2}\)

Distance between \((x_0,y_0)\) and the directrix is \(|y_0-c|\)

Given:

Therefore:

Distance between \((x_0,y_0)\) and the focus: \(\sqrt{(x_0-6)^2+(y_0-4)^2}\)

Distance between \((x_0,y_0)\) and the directrix is \(|y_0-0|\)

Equate the two expressions and solve for \(y_0\):

     \(\sqrt{(x_0-6)^2+(y_0-4)^2}=|y_0-0|\)

\(\implies (x_0-6)^2+(y_0-4)^}=(y_0-0)^2\)

\(\implies {x_0}^2-12x_0+36+{y_0}^2-8y_0+16={y_0}^2\)

\(\implies {x_0}^2-12x_0-8y_0+52=0\)

\(\implies 8y_0={x_0}^2-12x_0+52\)

\(\implies y_0=\dfrac18{x_0}^2-\dfrac{12}{8}x_0+\dfrac{52}{8}\)

\(\implies y_0=\dfrac18{x_0}^2-\dfrac32x_0+\dfrac{13}{2}\)

Now rewrite with (x, y):

\(\implies y=\dfrac18x^2-\dfrac32x+\dfrac{13}{2}\)

Therefore, this is the equation of the parabola

To determine if the point (11, 5) is on the parabola, input x = 11 into the equation:

\(\implies y=\dfrac18(11)^2-\dfrac32(11)+\dfrac{13}{2}\)

\(\implies y=\dfrac{41}{8}\)

So the point (11, 5) is NOT on the parabola.

Given that the cost is $1.10 per pound, we can calculate the cost per servable pound by dividing the total cost ($1.10 * 4 pounds) by the servable weight (2 pounds). Therefore, the correct option is c. $2.20.

The original weight of the food item is 4 pounds, and the cost per pound is $1.10. Therefore, the total cost of the food item is 4 pounds * $1.10 = $4.40.

The servable weight of the food item is 2 pounds. To find the cost per servable pound, we divide the total cost ($4.40) by the servable weight (2 pounds):

Cost per servable pound = Total cost / Servable weight = $4.40 / 2 pounds = $2.20.

Hence, the cost per servable pound for this food item is $2.20. Therefore, the correct option is c. $2.20.

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Using the definition of descriptive and inferential statistics, it is found that this is an example of descriptive statistics.

In this problem:

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The length of the missing leg is approximately 72 centimeters.

To find the length of the missing leg, we can use the Pythagorean theorem.

According to the given information, we have a right triangle with two known sides:

One leg: 90 cm

Hypotenuse: 54 cm

Let's denote the missing leg as "x" cm.

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Therefore, we can set up the following equation:

\(90^2 + x^2 = 54^2\)

Simplifying the equation, we have:

\(8100 + x^2 = 2916\)

Subtracting 2916 from both sides:

\(x^2 = 8100 - 2916\)

\(x^2 = 5184\)

Taking the square root of both sides:

x = √5184

x ≈ 72 cm (rounded to the nearest tenth)

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Answer:

D. Normality of the estimator (e.g., sample mean)

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The question was incomplete. Check below the complete question.

Which of the following is the necessary condition for creating confidence intervals for the population mean? A. Known population parameter B. Normality of the population C. Known standard deviation of the estimator D. Normality of the estimator (e.g., sample mean)

Answer:

k = ± 4

Step-by-step explanation:

Given

x² - kx + 4 = 0 ← in standard form

with a = 1, b = - k, c = 4

The equation has equal roots, thus the discriminant

b² - 4ac = 0, that is

(- k)² - (4 × 1 × 4) = 0

k² - 16 = 0 ( add 16 to both sides )

k² = 16 ( take the square root of both sides )

k = ± \(\sqrt{16}\) = ± 4

The standard deviation of the sampling distribution is 0.00702.

In this case, we know that 8% of all adults in Ohio support the increase. We can use this information, along with the sample size of 1500, to calculate the standard deviation of the sampling distribution. The formula for the standard deviation of the sampling distribution is:

standard deviation = √ [(population proportion x (1 - population proportion)) / sample size]

Plugging in the numbers, we get:

standard deviation = √ [(0.08 x 0.92) / 1500]

standard deviation = √0.00004928

standard deviation = 0.00702

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Answer:

Lauren will have 13 pieces of wire, each 2/3 ft. long, and 1/3 ft. of wire left over.

To find g(-2), we'll substitute -2 for x in the equation g(x) = -4x² - 5x + 9. So,g(-2) = -4(-2)² - 5(-2) + 9g(-2). The value of g(-2) is -6.

To find g(-2), substitute -2 for x in the equation

g(x) = -4x² - 5x + 9 to get

g(-2) = -6 + 9g(-2)

We are given three functions as follows:

f(x) = (1/3)x - 5, g(x)

= -4x² - 5x + 9, and

h(x) = 1/(x - 8) + 3.

We are asked to find g(-2), which is the value of g(x) when x = -2.

Substituting -2 for x in the equation g(x) = -4x² - 5x + 9, we get

g(-2) = -4(-2)² - 5(-2) + 9.

This simplifies to g(-2) = -16 + 10 + 9 = -6.

Hence, g(-2) = -6.

The value of g(-2) is -6.

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The area of the rectangular parking lot is 929.03 square meters.

Use the formula for the area of a rectangle to calculate the area of the rectangular parking lot, which is given as:

Area = length × width

We know that the parking lot is 67.5 ft wide and 148 ft long, the area can be calculated as follows:

Area = 67.5 ft × 148 f

t= 9990 sq. ft

However, the question asks for the area in square meters, so we need to convert square feet to square meters. 1 square foot is equal to 0.092903 square meters, so we can use this conversion factor to convert square feet to square meters.

Area in square meters = Area in square feet × 0.092903

= 9990 sq. ft × 0.092903

= 929.03 sq meters

Therefore, the area is 929.03 square meters.

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Answer:

B

Step-by-step explanation:

The explanation is attached below.

Answer:

3 and 9

Step-by-step explanation:

let,the ratio be 3x and 1x

3x+1x=12

4x=12

x=12/4

x=3

3x=3*3=9

x=3

Hence,the ratio are 3 and 9

The blood platelet count is an illustration of normal distribution Approximately 95% of the data lies within 2 standard deviations of the mean. There are approximately 99.7% of women with platelet count between 65.2 and 431.8

The given parameters are:

μ = 248.5

\(\sigma = 61.1\\\)

(a) The percentage within 2 standard deviation of mean or between 126.3 and 370.7

Start by calculating the z-score, when x = 126.3 and x = 370.7

\(Z = \frac{(x-u)}{\sigma}\)

So, we have:

x = -2

Also,

x = 2

The empirical rule states that:

Approximately 95% of the data lies within 2 standard deviations of the mean.

Hence, there are approximately 95% of women with platelet count within 2 standard deviations of the mean.

(b) The percentage with platelet count between 65.2 and 431.8

Start by calculating the z-score, when x = 65.2 and x = 431.8

So, we have:

Z =-3

Also:

Z = 3

The empirical rule states that:

Approximately 99.7% of the data lies within 3 standard deviations of the mean.

Hence, there are approximately 99.7% of women with platelet count between 65.2 and 431.8

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Answer:

-6

Step-by-step explanation:

use PEMDAS

start with the exponent: (-4)^2=16

-12 / 3 * (-8 + 16 - 6) +2

then the parentheses: (-8+16-6)=2

-12 / 3 * 2 +2

next is multiplication/division, division comes first so: -12/3=-4

-4 * 2 +2

then multiplication: -4*2=-8

-8+2=-6

The value of g(4) in the function is -5 which is option b

To find the value of g(4) in the composite function, we need to evaluate the function when x = 4

In the first equation, since x is greater than 4 already, we can't use ot.

Let's proceed to the second equation;

g(x) = -2x + 3, x ≤ 4

Let's put the value x = 4 into the equation;

g(4) = -2(4) + 3

g(4) = -8 + 3

g(4) = -5

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Answer:

\(x=\frac{7}{30}\)

Step-by-step explanation:

Solve for x:

\(x+\frac{2}{3}=\frac{9}{10}\)

Subtract \(\frac{2}{3}\) on both sides

\(x=\frac{7}{30}\)

Answer:

X= 7/30

Step-by-step explanation:

subtract 2/3 from both sides.

X+ 2/3 = 9/10

X +2/3 -2/3 =9/10 -2/3

simplify the expression

X + 2/3 -2/3 =9/10 -2/3

X=7/30

Answer: The arc length, the radius, and the central angle of a circle are related by the formula:

arc length = radius x central angle

Therefore, we can find the central angle by dividing the arc length by the radius:

central angle = arc length / radius

In this case, the arc length is 30π units and the radius is 20 units, so:

central angle = (30π units) / (20 units) = 3π / 2 radians

This is the measure of the central angle in radians. In degrees, we can convert this angle by multiplying by 180/π:

central angle = (3π / 2 radians) x (180/π degrees per radian) ≈ 270 degrees

Therefore, without calculating, I think the measure of the central angle is approximately 270 degrees. This is because the arc length is more than three-quarters of the circumference of the circle (which has a circumference of 2πr = 40π units), so the central angle should be more than three-quarters of a full circle, which is 270 degrees.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

the company has been a long term solution to the point that 666666

Answer:

400000

Step-by-step explanation:

Answer:

\(c=85\)

Step-by-step explanation:

\(c=180-a-b\) where \(a=62\) and \(b=33\)

Step 1.  Substitute a for 62 and b for 33

\(c=180-(62)-(33)\)

Step 2. Subtract \((180 - 62)\)

\(c=118-33\)

Step 3. Subtract (again)

\(c=85\)

so c = 85

Answer:

angle ABC = 36 degrees

Step-by-step explanation:

6x = (4x+24)

2x = 24

x = 12

angle ABC = 180 -6x - (4x+24)

angle ABC = 180 - 6(12) - 4(12) - 24 = 36 degrees

Answer:

81π cubic units

Step-by-step explanation:

The formula for volume of cone is given by:

V = 1/3πr^2h, where

Step 1:  Find radius:

We know that the diameter, d, is simply twice the radius.  Thus, we can find the radius of the circular base by dividing the given diameter by 2:

d = 2r

d/2 = r

9/2 = r

4.5 units = r

Thus, the radius of the circular base is 4.5 units.

Step 2:  Find volume and leave in terms of pi:

We can find the volume in terms of pi by plugging in 4.5 for r and 12 for h and simplifying:

V = 1/3π(4.5)^2(12)

V = 1/3π(20.25)(12)

V = 1/3π(243)

V = 81π cubic units

Thus, the volume of the cone in terms of pi is 81π cubic units.

The Fundamental Theorem of Algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This theorem is important as it provides a way to prove the existence of solutions to polynomial equations and provides an analytical tool to find the exact location of the solutions.

This theorem is also known as the algebraic version of the Intermediate Value Theorem as it states that if a polynomial is continuous on a closed interval, then it must take on all values between its maximum and minimum.

The theorem can be easily proven by considering a single-variable polynomial of degree n and transforming it into a polynomial of degree n−1 with the same roots. By repeating this process, the polynomial can be reduced to a constant and hence, it must have at least one root.

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Answer:

b

Step-by-step explanation:

Answer:

The answer for question would be 3