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Answer:

The directrix of the ellipse is:

x= -3.25 and x=9.25

Step-by-step explanation:

As we know that for any ellipse equation of the type:

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex] and a>b

The directrix is given by:

[tex]x=h\pm \dfrac{a}{e}[/tex]

where,

[tex]e=\sqrt{1-\dfrac{b^2}{a^2}}[/tex]

Here we have the equation of parabola as:

[tex]\dfrac{(x-3)^2}{5^2}+\dfrac{(y-2)^2}{3^2}}=1[/tex]

Hence, we have:

[tex]h=3,\ k=2,\ a=5,\ b=3\\\\and\\\\e=\sqrt{1-\dfrac{3^2}{5^2}}\\\\e=\sqrt{1-\dfrac{9}{25}}\\\\e=\sqrt{\dfrac{25-9}{25}}\\\\\\e=\sqrt{\dfrac{16}{25}}\\\\e=\dfrac{4}{5}[/tex]

Hence, we have: the directrix as:

[tex]x=3\pm \dfrac{5}{\dfrac{4}{5}}\\\\\\x=3\pm \dfrac{25}{4}\\\\Hence, x=9.25\ and\ x=-3.25[/tex]

Hence, the equation of directrix is:

x= -3.25 and x=9.25

Answer:

B

Step-by-step explanation:

On edge

Answer:

Te correct option B.

Step-by-step explanation:

The surface area of a cone is

[tex]A=\pi r(r+l)[/tex]

Where, r is the radius and l is slant height.

From the given figure it is noticed that the radius of the cone is 6 and slant height is 15.

The surface area of cone is

[tex]A=\pi \times 6\times (6+15)[/tex]

[tex]A=\pi \times 6\times 21[/tex]

[tex]A=126\pi[/tex]

The area of the cone is 126π units². Therefore option B is correct.

Varna's package weighs 3 pounds, priced at $7.50, matching Elliot's $12.50 package with 5 pounds at same unit price.

To find the weight of Varna's package of ground beef, we can set up a proportion based on the unit price.

Elliot's package:

Price: $12.50

Weight: 5 pounds

Varna's package:

Price: $7.50 (same unit price as Elliot's)

Weight: Let's call it x pounds

We can set up the proportion:

[tex]\[\frac{12.50}{5} = \frac{7.50}{x}\][/tex]

Now, we can cross multiply:

[tex]\[12.50x = 5 \times 7.50\]\[12.50x = 37.50\][/tex]

Now, let's solve for \( x \):

[tex]\[x = \frac{37.50}{12.50}\]\[x = 3\][/tex]

So, the weight of Varna's package of ground beef is 3 pounds.

Complete question:

Elliot buys a 5 pound package of ground beef for 12.50

1)varna buys a package of ground beef for 7.50 at the same unit price. 2)What is the weight of the package

Answer:

6.25

Step-by-step explanation:

I go to rsm and this answer worked

In scientific notation the product is written as  [tex](2.144)\times10^{12}[/tex].

Two scientific notation values are [tex]6.7\times10^6[/tex] and [tex]3.2 \times10^5[/tex].

We have to explain the steps to find the product of these values.

Scientific notation is a widely used floating-point system in which numbers are expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10.

For the product of the above values we multiply coefficients separately like

[tex](6.7\times3.2=21.44)[/tex]

and powers of 10 separately

[tex](10^6\times10^5=10^{11} )[/tex].

So,

[tex]6.7\times10^6 \times 3.2\times10^5=(6.7\times3.2)\times(10^6\times10^5)[/tex].

[tex]6.7\times10^6 \times 3.2\times10^5=(21.44)\times10^{11}[/tex]

Or, in scientific notation form,

[tex]6.7\times10^6 \times 3.2\times10^5=(2.144)\times10^{12}[/tex].

Hence, in scientific notation the product is written as  [tex](2.144)\times10^{12}[/tex].

For more details on scientific notation follow the link:

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The 7th term in the geometric sequence described by this explicit formula will be 31,250 so option (D) will be correct.

A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.

For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.

Given explicit formula is

[tex]a_{n}[/tex] = 2 × [tex]5^{(n-1)}[/tex]

Where n represents a number of terms and [tex]a_{n}[/tex] is an nth term in the GP series.

By substituting n = 7 into the formula

[tex]a_{7}[/tex] = 2 × [tex]5^{(7 - 1)}[/tex]

[tex]a_{7}[/tex] = 2 × 5⁶

[tex]a_{7}[/tex] = 2 × 15625 = 31250 hence, it will the correct answer.

For more information about the geometrical progression

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The circumference of a circular rug with a radius of 3 feet is equal to 18.84 feet.

Given the following data:

Mathematically, the circumference of a circle is calculated by using this formula:

Circumference = 2πr

Where:

r is the radius of a circle.

Substituting the given parameters into the formula, we have;

Circumference = 2 × 3.14 × 3

Circumference = 18.84 feet.

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Final answer:

After reflecting the origin (0,0) first across the line y=2, and then across the line x=-3, the final image of the point is at (-6,4).

Explanation:

The reflection of a point in the Cartesian coordinate system can be found using certain rules, depending on the line of reflection.

For the first reflection across L1: y = 2, imagine that every point has to move in a perpendicular motion to this line until it is on the opposite side but the same distance from L1.

The origin (0,0) will move up to (0,4) because it is 2 units away from y=2 and needs to move another 2 units up to be an equal distance on the opposite side of the line.

Next, for the reflection across L2: x = -3, use the same principle, but horizontally.

The point (0,4) is 3 units away from the line x=-3.

Reflecting over this line, you would move (0,4) to the left by 6 units (twice the distance from the line), giving us a final position of (-6,4).

The final position of the point O (0,0) after the two reflections is (-6,4).

The interest that will be charged after the first month is $1.875, calculated by multiplying the remaining balance of $125 by the monthly interest rate of 1.5%.

The subject at hand is centered around the concept of credit card interest calculation. In Caitlyn's case, the remaining balance after her payment is $375 - $250 which equals $125. This is the amount that will incur interest.

The APR (annual percentage rate) is 18%, but we must first convert this to a monthly rate by dividing by 12, which equals 0.015 (or 1.5%). The interest charged after the first month is calculated by multiplying the remaining balance by the monthly interest rate. Therefore, the formula to calculate the interest is $125 * 0.015, which equals $1.875.

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To solve the system of inequalities, we find the values of x that satisfy both conditions: x > 3 and x < -1.

To solve this problem, we need to find the values of x that satisfy the given inequalities:

4x+2 > 14

-21x+1 > 22

For the first inequality, subtracting 2 from both sides gives us:

4x > 12

Dividing both sides by 4, we get:

x > 3

For the second inequality, subtracting 1 from both sides gives us:

-21x > 21

Dividing both sides by -21 (and flipping the inequality sign), we get:

x < -1

Therefore, the values of x that satisfy both inequalities are:

x > 3 and x < -1

Final answer:

A cone cut with a plane parallel to its base forms a circular cross section, a concept that is part of the study of conic sections.

Explanation:

When a cone is cut with a plane parallel to its base, the cross section or plane section that is created is a circle. This concept falls under the study of conic sections, which also includes other shapes like ellipse, parabola, and hyperbola, all of which are formed by the intersection of a plane with a cone. If the cut is made closer to the apex, the circle will be smaller, and if it's made closer to the base, the circle will be larger, but all such cross sections remain circular as long as the cut is parallel to the base.

Answer:

6 inches.

Step-by-step explanation:

The distance between two cities is around = 600 miles.

Map has a scale of 0.3 inches = 30 miles.

Therefore, on the scale 1 inches = [tex]\frac{30}{0.3}[/tex] miles

                                                      = 100 miles

Since on the map, 100 miles = 1 inches

The distance of 600 miles =  [tex]\frac{600}{100}[/tex]

                                            = 6 inches

The scale distance between cities is 6 inches.

Answer:

D!!

Step-by-step explanation:

Hope it helps!!

The solution to the inequality 11x + 14 < -8 is x < -2. On a number line, this would be a circle at -2 with a line extending to the left.

To find the solution to the inequality 11x + 14 < –8, we will first subtract 14 from both sides, which gives us:

11x < -8 - 14

This simplifies to 11x < -22.

Next, we divide both sides by 11 for: x < -2

The solution is x < -2. On a number line, this would be represented by a circle around -2 (not filled in, because the inequality does not include 'equal to') with a line extending to the left (indicating 'less than').

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Answer:

polynomial x³ -6x² +8x .

Step-by-step explanation:

Given  :  polynomial function in standard form with zeros at 0, 2, and 4.

To find : Which of the following is a polynomial function.

Solution : we have given that

zeros at 0, 2, and 4.

x = 0 .

x = 2

x = 4

(x -0)(x -2) (x -4).

x (x-2)(x-4).

x( x² -4x -2x +8).

x (x² -6x +8).

x³ -6x² +8x .

Therefore, polynomial x³ -6x² +8x .

The range of sales that will earn at least $40 and at most $50 is represented by the inequalities x >= 40 and x <= 50. Hence, the range of possible sales is x such that 40 <= x <= 50.

The subject of this question is inequalities and the concept of a range of numbers in mathematics. Here, we're looking at a range of sales values that will result in the organizer earning between $40 and $50.

The two inequalities that represent this scenario are: x >= 40 and x <= 50.

To find the range of sales, we look at the values that satisfy both conditions. Therefore, the range of sales is all the sales amounts (x) such that: 40 <= x <= 50. This means that any amount of sales that is greater than or equal to $40 and less than or equal to $50 will meet the criteria.

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