The volume of a cone varies jointly with the area of the base and the height. When the area of the base is 27 cm2 and the height is 6 cm, the volume is 54 cm3. Therefore, the area of the base is _____ cm2 when the height is 12 cm and the volume is 124 cm3.

On the attached diagram red curve is the graph of the quadratic function [tex]y = 2(x - 2)^2 + 2.[/tex] As you can see this graph has no intersections with x-axis, this means that there are no solutions.

If you translate red curve 2 units down, you obtaine the graph (blue curve) of the function [tex]y = 2(x - 2)^2[/tex] and this graph has one common point with x-axis. This means that there will be exactly one solution.

Answer: k=-2 (you add -2 to the function [tex]y = 2(x - 2)^2 + 2[/tex] to obtain the function [tex]y = 2(x - 2)^2[/tex]).

Answer: 0 ZERO

Step-by-step explanation:

Final answer:

After purchasing an album for $12.99 from the $50 gift card, the remaining balance is $37.01, which allows the purchase of 37 more single tracks, assuming each track costs $1.

Explanation:

To determine how many songs can be bought with a $50 gift card after purchasing an album for $12.99, we need to subtract the cost of the album from the total amount on the gift card. So, we have:

Subtracting the cost of the album from the gift card amount gives us:

$50 - $12.99 = $37.01

Assuming that each single track costs $1 as per the scenario provided, we can divide the remaining balance by the cost per single track:

$37.01 ÷ $1 per track = 37 tracks

This means that you can purchase 37 more single tracks with the remaining balance on the gift card.

To solve for b in the equation 7b divided by 12 equals 4.2, multiply both sides by 12 and then divide by 7, resulting in b being equal to 7.2.

To solve the equation 7b ÷ 12 = 4.2 for b, we must isolate b on one side of the equation. We can begin by multiplying both sides of the equation by 12 to cancel out the division by 12 on the left side. This results in the equation 7b = 4.2 × 12. To find the value of b, we then divide both sides of the equation by 7:

Therefore, the value of b is 7.2.

To find the value of b in the equation 7b/12 = 4.2, multiply both sides by 12 and then divide by 7 to get b = 7.2. The value of b is 7.2.

The student is asking how to find the value of b in the equation 7b divided by 12 equals 4.2. To solve for b, you can follow these steps:

Therefore, the value of b is 7.2.

Answer:

C: y(x + 4)(x – 6)

Step-by-step explanation:

I took the test on Edge -2022

A cyclic quadrilateral is a quadrilateral whose vertices all touch the circumference of a circle.

Opposite angles in a cyclic quadrilateral add to 180 degrees. Quadrilateral ABCD is a cyclic quadrilateral.

< A+<C=180

Substituting <A and <B values given in figure:

x+2+x-2=180

Adding like terms:

2x=180

Dividing both sides by 2

x=90°

<A=x+2=90+2=92°

<C=x-2=90-2=88°

<D=x-10=90-10=80°

<B+<D=180

<B=180-80=100°

The angles of the quadrilateral ABCD are

<A=92°

<B=100°

<C=88°

<D=80°

The system of equations 4x-y=4(x+1) and y=6 has no solution.

To determine the solution(s) of the system of equations, let's analyze each equation:

Equation 1: 4x - y = 4(x + 1)

Equation 2: y = 6

To simplify Equation 1, we can distribute 4 on the right side:

4x - y = 4x + 4

By rearranging terms, we have:

- y = 4

Comparing Equation 2 with this result, we see that the two equations are contradictory. Equation 2 states that y = 6, while the modified Equation 1 states that y = -4. This means there is no value of y that can simultaneously satisfy both equations.

Thus, the system of equations has no solution.

Therefore, the correct answer is C. no solution.

To know more about system of equations, refer here:

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To find h(x) = f(x) - g(x), we substitute and simplify the given functions. The result is h(x) = 2 × 3ˣ - 3²ˣ. This solution involves basic algebraic manipulation and exponent rules.

Let's start by defining the given functions:

We need to find h(x) = f(x) - g(x). Substitute the expressions for f(x) and g(x):

Now simplify the expression inside the parentheses:

Combine like terms:

Thus, the function h(x) = 2 × 3ˣ - 3²ˣ is found by subtracting g(x) from f(x).

Each cat would get approximately 6.67 ounces of cat food, which falls between 6 and 7 ounces. The calculation is done by dividing the total amount of food (20 ounces) by the number of cats (3).

The Philips family had to split 20 ounces of cat food among their 3 cats. To find out how much food each cat gets, we need to divide the total amount of food by the number of cats. Calculating this, 20 ounces ÷ 3 cats equals approximately 6.67 ounces per cat. Even though this is a decimal, if we consider whole numbers, the amount each cat gets falls between 6 and 7 ounces, since 6.67 is more than 6 and less than 7.

When dealing with fractions and division, it's essential to understand the concept of division and be able to find averages. The task at hand may often find itself related to dividing a quantity evenly among a number of recipients, much like in scenarios where we have to split a pie or determine individual portions.

To divide 20 ounces of cat food equally among three cats, each cat gets approximately 6.67 ounces. The amount of food per cat lies between the whole numbers 6 and 7.

The question is asking how to divide 20 ounces of cat food equally among three cats. To find out how much each cat would get, you divide the total amount of cat food by the number of cats:

This calculation shows that each cat would get approximately 6.67 ounces of food. This value lies between the whole numbers 6 and 7. Therefore, when the Philips family divides the cat food, each cat gets a little more than 6 ounces but less than 7 ounces of food.

probability  = number of favourable outcomes / total number of outcomes

probability of spinning any number = 1/3

probability of tossing a coin = 1/2

probability of compound event = 1/3 * 1/2 * 1/3 = 1/18

probability of spinning an odd number, flipping heads, then spinning a yellow is  = 2/3*1/2*1/3 = 1/9

Final answer:

The solution set to the given inequality '-3x < 5.92 - 15.4' is {5, 10}.

Explanation:

The student's question seems to be about solving an inequality to find which values from a given set satisfy it. While the inequality itself appears to be incorrectly written or has a typo, I'll assume it's meant to be '-3x < 5.92 - 15.4'.

We can begin by simplifying the right side of the inequality:

5.92 - 15.4 = -9.48

So the inequality becomes:

-3x < -9.48

To solve for x, we divide both sides by -3, remembering to reverse the inequality sign because we are dividing by a negative number:

x > 9.48 / 3

x > 3.16

Now we can compare this result to the set of numbers given: (-10, -5, 0, 5, 10).

The only numbers greater than 3.16 are 5 and 10.

Therefore, the solution set to the inequality is {5, 10}.

To find out the face value of a simple discount note that will provide a proceed of $24,700 with an 8% discount rate for 180 days, use the formula FV = P / (1 - (r * t)). Plug in the given values and compute the answer. The result is the required face value and should be rounded to the nearest cent.

To find out the face value of a simple discount note, we can use the formula FV = P / (1 - (r * t)) where FV represents the face value, P is the proceeds, r is the discount rate, and t is the time in years.

In the problem, P = $24,700, r = 8% or 0.08 (expressed as a decimal), and t = 180/365 because there are 365 days in a year and the note is for 180 days. Let's substitute these values into the formula:

FV = 24700 / (1 - (0.08 * (180/365))

When you calculate the expression on the right, the answer will be the face value required to get a proceed of $24,700 with an 8% discount rate for 180 days. Round to the nearest cent for your final answer.

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Answer: Volume of an oblique cylinder is 2011.43 sq.m.

Step-by-step explanation:

Since we have given that

Radius of a cylinder = 8 meters

Height of a cylinder = 10 meters

Cavelieri's Principle states that volume of an oblique cylinder is same as the volume of right circular cylinder with equal radius and height.

As we know the formula for "Volume of cylinder":

[tex]Volume=\pi r^2h\\\\V=\frac{22}{7}\times 8\times 8\times10\\\\V=\frac{14080}{7}\\\\V=2011.43[/tex]

Hence, Volume of an oblique cylinder is 2011.43 sq.m.

To find the polynomial difference, Lorne transformed the subtraction into addition of the opposite, combined like terms, and simplified the expression to get the result of -9x³ + 5x² + 6x - 10.

To find the difference between the two polynomials, Lorne correctly followed the steps of subtraction by changing the subtraction to the addition of the opposite. The process is outlined below:

Add the opposite of the second polynomial to the first polynomial by changing the sign of each term in the second polynomial.

Combine like terms by adding the coefficients of terms with the same degree of x.

Rearrange the terms in descending order of their degrees.

Write down the final simplified form of the polynomial.

By following these steps, the result would be:

Step 1:

(-3x³ + 5x² + 4x - 7) + (-6x³ + 2x - 3)

Step 2:

(-3x³ + 5x² + 4x - 7) + (-6x³) + 2x + (-3)

Step 3:

[(-3x³) + (-6x³)] + [4x + 2x] + [(-7) + (-3)] + [5x²]

Step 4:

-9x³ + 6x + (-10) + 5x2

Step 5:

-9x³ + 5x² + 6x - 10

Lorne subtracted [tex]6x^{3} - 2x + 3[/tex] from [tex]-3x^{3} + 5x^{2} + 4x - 7[/tex]. So, the main answer is 5. [tex]-9x^{3} +5x^{2} +6x-10.[/tex]

The steps Lorne used to find the difference between [tex]-3x^{3} +5x^{2} +4x-7[/tex] and [tex]6x^{3} -2x+3[/tex] are:

[tex]1. (-3x^{3} +5x^{2} +4x-7)+(-6x^{3} +2x-3)\\2. (-3x^{3} )+5x^{2} +4x+(-7)+(-6x^{3} )+2x+(-3)\\3. [(-3x^{3} )+(-6x^{3} )]+[4x+2x]+[(-7)+(-3)]+[5x^{2} ]\\4. -9x^{3} +6x+(-10)+5x^{2} \\5. -9x^{3} +5x^{2} +6x-10[/tex]

So, the main answer is 5. [tex]-9x^{3} +5x^{2} +6x-10.[/tex]

Lorne first added the two polynomials by combining like terms, then simplified the result by collecting like terms. The final expression represents the difference between the two polynomials after combining and simplifying.

COMPLETE QUESTION:

Lorne subtracted [tex]6x^{3} - 2x + 3[/tex] from [tex]-3x^{3} + 5x^{2} + 4x - 7[/tex]. Use the drop-down menus to identify the steps Lorne used to find the difference.

[tex]1. (-3x^{3} +5x^{2} +4x-7)+(-6x^{3} +2x-3)\\2. (-3x^{3} )+5x^{2} +4x+(-7)+(-6x^{3} )+2x+(-3)\\3. [(-3x^{3} )+(-6x^{3} )]+[4x+2x]+[(-7)+(-3)]+[5x^{2} ]\\4. -9x^{3} +6x+(-10)+5x^{2} \\5. -9x^{3} +5x^{2} +6x-10[/tex]