The radius of a circle is changing at the rate of 1/π inches per second. At what rate, in square inches per second, is the circle’s area changing when the radius is 5 inches?

1-Is the sum of two prime numbers always a prime number?

Solution:

No. Here is an example.

3 + 7 = 10 , 3 and 7 are prime numbers but not their sum 10.

2-Is the product of two prime numbers also a prime number?

Solution:

Never because it will have 1 and itself as factors and also the two numbers involved in the product.

Example: 7 × 11 = 77 ,77 has 1, itself, 7 and 11 as factors.

3-Which is the largest 3 digit prime number?

Solution:

Start with the largest three digit number 999.

4- Which is the smallest 2 digit prime number?

Solution

Start with the smallest 2 digit number 10.

10 is not a prime number

Answer: 11 is a prime number

The solution to the math problem is -6.

A math problem is a problem that can be represented, analyzed, and probably solved, with the techniques of arithmetic. This will be an actual-world problem, inclusive of computing the orbits of the planets inside the solar gadget, or trouble of a greater summary nature, such as Hilbert's problems.

The Collatz Conjecture is the only math problem no person can resolve it is straightforward and sufficient for almost every person to recognize but notoriously difficult to resolve.

= 19 - ( - 5 ) ²

= 19 - ( 25 )

= 19 - 25

= - 6

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Answer:

-2/8 or  -1/8

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

180-15

Hello!

the sum of the angles in the triangle = 180°

so the 3rd angle = 180° - 165° = 15°

The surface area of the rectangular prism is 396 square inches

He will need 504 tlles

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

7 in by 12 in by 6 in

The surface area of the rectangular prism is calculated as

Area = 2 * (7 * 12 + 7 * 6 + 12 * 6)

Evaluate

Area = 396

Hence, the area is 396 square inches

The number of tiles is 7 * 12 * 6 = 504

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Question

wants to tile the surface of a rectangular storage case that is 7 inches​ long, 12 inches​ wide, and 6 inches tall. If he uses all green​ tiles, how many tiles will he​ need?

Answer:

2050

Step-by-step explanation:

Using the reasoning abilities -

a) If the authorities also know that exactly one of the four suspects is telling the truth, the person who did it is David.

b) If the authorities also know that exactly one is lying, the person who did it is David.

What is reasoning?

Reasoning is the capacity to come to a conclusion from premises and known facts in a circumstance.

a) The reasoning for the scenario is given.

Suppose Alex is telling the truth.

Then Carol did it, which contradicts David's statement that Carol lied when she said that he did it.

Therefore, Alex is lying.

Suppose Jay is telling the truth.

Then David, Carol, and Alex did not do it, so Jay did it.

But this contradicts Carol's statement that David did it.

Therefore, Jay is lying. Suppose Carol is telling the truth.

Then David did it, which contradicts David's statement.

Therefore, Carol is lying.

This leaves us with David as the only person who could be telling the truth.

Therefore, David did it.

b) The reasoning for the scenario is given.

Suppose Alex is lying.

Then Carol did not do it, and neither did Jay, which means David must have done it.

But this contradicts David's statement that Carol lied when she said that he did it.

Therefore, Alex is telling the truth.

Suppose Jay is lying.

Then Carol, David, and Alex did not do it, which means that Jay did it.

But this contradicts Carol's statement that David did it.

Therefore, Jay is telling the truth.

Suppose Carol is lying.

Then David did not do it, which means that Carol, Alex, and Jay did not do it, which leads to a contradiction.

Therefore, Carol is telling the truth.

This leaves us with David as the only person who could be lying.

Therefore, David did it.

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Answer:

Goodluck

Step-by-step explanation:

Answer:

minimum, coordinates of vertex: (-3,-11)

explanation:

\(\sf y =x^2 +6x-2\)

x coordinates on vertex:

solving steps:

Find y-coordinate on vertex:

\(\sf y =x^2 +6x-2\)

\(\sf y =(-3)^2 +6(-3)-2\)

\(\sf y =-11\)

\(\mathrm{If}\:a < 0,\:\mathrm{then\:the\:vertex\:is\:a\:maximum\:value}\)

\(\mathrm{If}\:a > 0,\:\mathrm{then\:the\:vertex\:is\:a\:minimum\:value}\)

coordinates: (-3,-11) thus minimum

Answer:

vertex = (-3, -11)

minimum

Step-by-step explanation:

The vertex of a parabola is its turning point (stationary point).

Therefore, the x-coordinate of the vertex can be determined by differentiating the function, setting it zero and solving for x:

\(\dfrac{dy}{dx}=2x+6\)

\(\dfrac{dy}{dx}=0\implies 2x+6=0 \implies x=-3\)

Substitute found value for x into the original function to find the y-coordinate:

\(\implies (-3)^2+6(-3)-2=-11\)

Therefore, the vertex is (-3, -11)

As the leading term of the quadratic function (\(x^2\)) is positive, the parabola will open upwards, so the vertex is its minimum point.

The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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Answer:

5

Step-by-step explanation:

14-9=5

Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

Answer: 80%

Step-by-step explanation:

divide 120 by 150 and you get .8 then you move the decimal over 2

Answer:

w = -2 + 2z(2x-1)/y

Step-by-step explanation:

(2x-1)/y = (w+2)/2z

2z(2x-1)/y = w+2

-2 + 2z(2x-1)/y = w

The 164° and 81° located with the angle x at a point indicates that the size of the angle x is 115°

The angles that are arranged around a point add up to 360°. The angles at a point are the angles which together, produce a rotation of 360°.

The sum of angle at a point can be used to find the measure of the angle x as follows;

The addition of angles at a point = 360°

Therefore; 164° + 81° + x = 360°

Therefore; x = 360° - (164° + 81°) = 115°

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Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

Answer:

Step-by-step explanation:

To check whether the given credit card number is valid or not, we need to apply the Luhn algorithm or the mod-10 algorithm. The Luhn algorithm works by adding up all the digits in the credit card number and checking if the sum is divisible by 10 or not. If it is, then the credit card number is considered valid, otherwise, it is invalid.

Let's apply the Luhn algorithm to the given credit card number:

Step 1: Starting from the rightmost digit, double every second digit

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 16| | 6 | | 14| | 0 | | 0 | | 10|

Step 2: If the doubled value is greater than 9, add the digits of the result

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 7 | | 6 | | 5 | | 0 | | 0 | | 1 |

Step 3: Add up all the digits in the credit card number, including the check digit

5 + 4 + 2 + 4 + 9 + 8 + 1 + 3 + 2 + 7 + 2 + 0 + 0 + 0 + 8 + 5 + 1 = 61

Step 4: If the sum is divisible by 10, then the credit card number is valid, otherwise, it is invalid.

61 is not divisible by 10, therefore the given credit card number is invalid.

Hence, it can be concluded that 5424 9813 2720 0085 is an invalid MASTERCARD credit card number.

The time taken by the person to cover 260 miles will be 3 hours and 15 minutes.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that a person to drive 260 miles on a highway if she merges onto a highway at 7 p.m. and drives nonstop with her cruise control set at 80 mph.

The amount of time taken by the person to cover the distance of 260 miles with a speed of 80mph is,

Speed = Distance / Time

Time = Distance / Speed

Time = 260 / 80

Time = 3.25 or 3 hours 15 minutes

Therefore, the time taken by the person to cover 260 miles will be 3 hours and 15 minutes.

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14 and 20 and 18 and 24 are not perfect squares

Answer:

I am 93% sure its B

Step-by-step explanation:

Answer:

maa ki chut. na na na na na na na na na na na na na na na na na

Answer:

Assuming you mean like a savings account. A financial reserve is created to save money over time to cover events such as emergency surgery, etc.

I'd like to look at this as both a math joke and a warm message.

Thank you, love.

The 5 differentiation Rules are:

Power rule:

The power rule of derivatives says d/dx (xn) = n · xn - 1.

Sum and difference rule:

This rule says, the differentiation process can be distributed to the functions in case of sum/difference. i.e., d/dx (f(x) ± g(x)) = d/dx (f(x)) ± d/dx (g(x)).

Product rule:

The product rule is used to find the derivative of product of two functions. It says d/dx (f(x)) · g(x)) = f(x) d/dx (g(x)) + g(x) d/dx (f(x)). In other words, it can be written as (uv)' = u v' + v u'.

Quotient rule:

The quotient rule of derivatives is to find the derivative of a fraction where both numerator and denominator involve variable.

Chain rule:

The chain rule of derivatives is used to differentiate a composite function, or in other words, chain rule is used to find the derivative of a function that is inside the other function.

Hence we get the required answer.

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Answer:

1

Step-by-step explanation:

Parallel lines are two lines that if the lines were extended, wouldn't intersect ever.  Perpendicular lines, however, are lines that intersect at a 90-degree angle. AB and CD are parellel, and AB and EF are perpendicular.

Both angles 1 and 2 are supplementary and linear angles.

So, options (1) and (3) are the correct options.

If consider, ∠1 and ∠2 are supplementary. If two angles form a linear pair, the angles are supplementary. A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary.  

If consider complementary angles. They are equals if the two intersected lines by the transversal are parallel. In the figure, angles 1 and 2 are corresponding. The 1 is external and the 2 is internal. Angles that are on opposite sides of the transversal of two other lines.

If consider linear pair angles. The sum of angles of a linear pair is always 180 degrees. Consider the image as shown. Here angle 2 and angle 1 are said to be a linear pair because they are formed on the same line with a standard arm S and common vertex point Q. Also, the sum of angles 1 and 2 is equal to 180 degrees.

Two angles are said to be adjacent angles, if, they share a common vertex, a common side and they do not overlap. Observe the following figure to understand what adjacent angles look like. Angle 1 and 2 are adjacent because they have a common side BD and a common vertex B.

A pair of vertically opposite angles are always equal to each other. Also, a vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees. For example, if two lines intersect and make an angle, say X=45°, then its opposite angle is also equal to 45°.

We can see all images.

So, that

When two lines intersect each other at a point, angles formed on the point are called as linear pair.

Since pair of linear angles is supplementary, sum of linear angles will be 180°.

m∠1 + m∠2 = 180°

Therefore, both angles 1 and 2 are supplementary and linear angles.

Options (1) and (3) are the correct options.

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Answer:

\(y=x^2+6x-16\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given points on the curve:

The x-intercepts of a quadratic function are the points at which the line crosses the x-axis, so when y = 0.  

Therefore, the x-intercepts of the given function are -8 and 2.  

Substitute these into the intercept formula:

\(\implies y=a(x-(-8))(x-2)\)

\(\implies y=a(x+8)(x-2)\)

Substitute the other given point (-6, -16) into the equation and solve for a:

\(\begin{aligned} y&=a(x+8)(x-2)\\\textsf{When }(-6,-16)\implies -16&=a(-6+8)(-6-2)\\-16&=a(2)(-8)\\-16&=-16a\\\implies a&=1\end{aligned}\)

Therefore, the equation of the function in intercept form is:

\(y=(x+8)(x-2)\)

Expand to standard form:

\(\implies y=x(x-2)+8(x-2)\)

\(\implies y=x^2-2x+8x-16\)

\(\implies y=x^2+6x-16\)

Therefore, the quadratic function in standard form is:

\(\boxed{ y=x^2+6x-16}\)

Step-by-step explanation:

To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:

Write the function: f(x) = 1/x^3.

Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).

Differentiate the function: In our case, n = -3, so the derivative is:

f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.

Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.