Ayesha has a theory about 2 digit numbers that have a larger tens digit than ones digit she says that reversing the digits and subtracting the reversed number from the original number will always generate a number that is a multiple of 9 is ayesha right? If so why do you think this works? If not,why not?

Answer:

[tex]A) 7[/tex]

Step-by-step explanation:

[tex]-2x+4=2\left(4x-3\right)-3\left(-8+4x\right)[/tex]

[tex]2\left(4x-3\right)-3\left(-8+4x\right)[/tex]

[tex]2 (4x - 3)[/tex]

[tex]\longrightarrow8x-6[/tex]

[tex]\longrightarrow 8x-6-3\left(-8+4x\right)[/tex]

[tex]-3 (-8 + 4x)[/tex]

[tex]\longrightarrow 24-12x[/tex]

[tex]8x-6+24-12x[/tex]

Combine like terms:

[tex]8x-12x-6+24[/tex]

Add: [tex]8x-12x=-4x[/tex]

Add: [tex]-6+24=18[/tex]

[tex]\longrightarrow-2x+4=-4x+18[/tex]

Subtract 4 from both sides:

[tex]\longrightarrow-2x+4-4=-4x+18-4[/tex]

[tex]\longrightarrow-2x=-4x+14[/tex]

Add 4x to both sides:

[tex]\longrightarrow-2x+4x=-4x+14+4x[/tex]

[tex]\longrightarrow2x=14[/tex]

Divide both sides by 2:

[tex]\longrightarrow\frac{2x}{2}=\frac{14}{2}[/tex]

[tex]\longrightarrow x=7[/tex]

____________________________

OAmalOHopeO

Answer:

1 + 1 = 2

2 - 1 = 1

The line's slopes are cute

Step-by-step explanation:

I hope your lines enjoy their equations, you are a great parent to your lines. =D

The rate of change of radius of the circle when the radius is 10 cm is

dr / dt = 1/2π cm / sec

What is implicit differentiation?

In mathematics, differentiation is the process of determining the derivative, or rate of change, of a function. Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function based on one of its variables. The process of finding the derivative of dependent variable in an implicit function by differentiating each term separately

Given data ,

Oil is poured on a flat surface and it spreads out forming a circle

The area of the circle is increasing at a rate of 10 cm²/sec

Let the area of the circle be = A

So , the equation is dA² / dt² =  10 cm²/sec

The area of the circle = πr²

So , dA² / dt² = 2π dr / dt

2πr dr / dt = 10 cm²/sec

Substituting the value of r in the equation , we get

2π x 10 dr / dt = 10 cm²/sec

20π dr / dt = 10 cm²/sec

Divide both sides of the equation be 20π

dr / dt = ( 1/2π ) cm / sec

Therefore , the rate of change of radius of the circle is ( 1/2π ) cm / sec

Hence , The rate of change of radius of the circle when the radius is 10 cm is dr / dt = 1/2π cm / sec

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area = H/2*(b1+b2)

8.1 = 1.5/2*(6.7 +b2)

8.1=0.75*(6.7+b2)

10.8=6.7+b2

b2=10.8-6.7

b2=4.1m

The shaded region is by assumption the region which is not covered by the semicircle in in given rectangles.

The area of the shaded region is given by 15.48 sq. ft.

A semicircle is a circle cut in half. Thus, one circle produces two semicircle.

Firstly we will find the area of the rectangle and then subtract the area of the semicircle to find the are of the shaded region.

Since the radius of the semicircle is equal to width of the rectangle(6 ft), thus the length of the diameter of the circle( twice the radius which is 12 ft) serves as length of the considered rectangle.

Thus, we have:

[tex]\text{Area of the given rectangle\:} = 6 \times 12 = 72 \: \rm ft^2[/tex]

Since the semicircle is having radius of 6 ft, thus:

[tex]\text{Area of semicircle} = \dfrac{\pi r^2}{2} = \dfrac{3.14 \times 6^2}{2} = 56.52 \: \rm ft^2[/tex]

Thus, area of the shaded region will be equal to area of rectangle - area of semicircle = 72 - 56.52 = 15.48 sq. ft.

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Answer:

Step-by-step explanation:

the answer is a

there is a 1/2 probability of getting heads on any one flip

 since the first one landed on heads you have a 1/2 probability f getting a 2nd one

Probability = 1/2

The third derivative of the function is [tex]y^{'''}=\dfrac{\left(3y^2+12xy-x\right)y''+y'\left(6yy'+12xy'+12y-1\right)-\left(6y-1\right)y'-6yy'}{\left(3y^2+x\right)^2}-\dfrac{2\left(6yy'+1\right)\left(\left(3y^2+12xy-x\right)y'-y\cdot\left(6y-1\right)\right)}{\left(3y^2+x\right)^3}[/tex]and the value at the point x = 1 is 42

How to determine the third derivative at the point x = 1

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

[tex]x^2 + xy + y^3 = 1[/tex]

Differentiate implicitly

So, we have

[tex]3y^2y' + xy'+y+2x=0[/tex]

Make y' the subject of formula

So, we get

[tex]y'=-\dfrac{y+2x}{3y^2+x}[/tex]

Differentiate the second time

Using a graphing tool, we have

[tex]y''=\dfrac{\left(3y^2+12xy-x\right)y'-6y^2+y}{\left(3y^2+x\right)^2}[/tex]

Differentiate the third time to get the third derivative

Using a graphing tool, we have

[tex]y^{'''}=\dfrac{\left(3y^2+12xy-x\right)y''+y'\left(6yy'+12xy'+12y-1\right)-\left(6y-1\right)y'-6yy'}{\left(3y^2+x\right)^2}-\dfrac{2\left(6yy'+1\right)\left(\left(3y^2+12xy-x\right)y'-y\cdot\left(6y-1\right)\right)}{\left(3y^2+x\right)^3}[/tex]

Recall that

x = 1

Calculating y, we have

[tex]1^2 + (1)y + y^3 = 1[/tex]

[tex]1 + y + y^3 = 1[/tex]

[tex]y^3 + y = 0[/tex]

Factorize

[tex]y(y^2 + 1) = 0[/tex]

So, we have

y = 0 or [tex]y^2 + 1 = 0[/tex]

The equation [tex]y^2 + 1 = 0[/tex] will give a complex solution

So, we have

x = 1 and y = 0

Calculating y', we have

[tex]y'=-\dfrac{0+2(1)}{3 * 0^2+1}[/tex]

[tex]y'=-\dfrac{2}{1}[/tex]

y' = -2

Calculating y", we have

[tex]y''=\dfrac{\left(3y^2+12y-1\right)y'-6y^2+y}{\left(3y^2+1\right)^2}[/tex]

[tex]y''=\dfrac{\left(3(0)^2+12(1)(0)-1\right)(-2)-6(0)^2+0}{\left(3(0)^2+1\right)^2}[/tex]

[tex]y''=\dfrac{\left2}{1}[/tex]

y" = 2

Calculating y", we have

[tex]y^{'''}=\dfrac{\left(3y^2+12xy-x\right)y''+y'\left(6yy'+12xy'+12y-1\right)-\left(6y-1\right)y'-6yy'}{\left(3y^2+x\right)^2}-\dfrac{2\left(6yy'+1\right)\left(\left(3y^2+12xy-x\right)y'-y\cdot\left(6y-1\right)\right)}{\left(3y^2+x\right)^3}[/tex]

Simplifying the denominators, we have

[tex](3y^2 + x)^2 = (3(0)^2 + 1)^2 = 1[/tex]

[tex](3y^2 + x)^3 = (3(0)^2 + 1)^3 = 1[/tex]

So, we have

[tex]y^{'''}=\dfrac{\left(3y^2+12xy-x\right)y''+y'\left(6yy'+12xy'+12y-1\right)-\left(6y-1\right)y'-6yy'}{1}-\dfrac{2\left(6yy'+1\right)\left(\left(3y^2+12xy-x\right)y'-y\cdot\left(6y-1\right)\right)}{1}[/tex]

Divide

[tex]y^{'''}=[\left(3y^2+12xy-x\right)y''+y'\left(6yy'+12xy'+12y-1\right)-\left(6y-1\right)y'-6yy']-[2\left(6yy'+1\right)\left(\left(3y^2+12xy-x\right)y'-y\cdot\left(6y-1\right)\right)][/tex]

Simplifying each term:

[tex](3y^2+12xy-x)y''+y'(6yy'+12xy'+12y-1)-(6y-1)y'-6yy' = (3(0)^2+12(1)(0)-(1))(2) + (-2)(6(0)(-2) +12(1)(-2) + 12(0) - 1) - (6(0) - 1)(-2) - 6(0)(-2)[/tex]

[tex](3y^2+12xy-x)y''+y'(6yy'+12xy'+12y-1)-(6y-1)y'-6yy' = 46[/tex]

Also, we have

[tex]2(6yy'+1)((3y^2+12xy-x)y'-y(6y-1)) = 2(6(0)(-2) + 1)((3(0)^2 + 12(1)(0) - 1)(-2) - 0(6(0)-1))[/tex]

[tex]2(6yy'+1)((3y^2+12xy-x)y'-y(6y-1)) = 4[/tex]

So, the expression becomes (by substitution)

[tex]y^{'''}= 46 -4[/tex]

This gives

[tex]y^{'''}= 42[/tex]

Hence, the third derivative at the point x = 1 is 42

Answer:

6 to the tenth power over 7 to the sixth power

Step-by-step explanation:

Given phrase,

6 to the fifth power over 7 cubed all raised to the second power,

[tex]\implies (\frac{6^5}{7^3})^2[/tex]

By using [tex](a^m)^n=a^{mn}[/tex]

[tex]=\frac{6^{5\times 2}}{7^{3\times 2}}[/tex]

[tex]=\frac{6^{10}}{7^6}[/tex]

= 6 to the tenth power over 7 to the sixth power

Simplify the expressions

(6⁵/7³)² = 2143588816/117649

(6⁷/7¹⁰) = 279936/282475249

(6¹⁰/7⁶) = 60466176/117649

(6³/7) = 216/7

(12⁵/14³) = 90855/1001

To simplify the given expressions, we can calculate the numerical values and perform the necessary operations. Let's evaluate each expression:

(6⁵/7³)²:

First, calculate the numerator and denominator:

Numerator: 6⁵ = 6 × 6 × 6 × 6 × 6 = 7776

Denominator: 7³ = 7 × 7 × 7 = 343

Now, substitute the values into the expression and square the result:

(7776/343)² = (7776/343) × (7776/343) = 2143588816/117649

The simplified form is 2143588816/117649.

(6⁷/7¹⁰):

Calculate the numerator and denominator:

Numerator: 6⁷ = 6 × 6 × 6 × 6 × 6 × 6 × 6 = 279936

Denominator: 7¹⁰ = 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 = 282475249

Substitute the values into the expression:

279936/282475249

This expression cannot be simplified further.

(6¹⁰/7⁶):

Calculate the numerator and denominator:

Numerator: 6¹⁰ = 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 = 60466176

Denominator: 7⁶ = 7 × 7 × 7 × 7 × 7 × 7 = 117649

Substitute the values into the expression:

60466176/117649

This expression cannot be simplified further.

(6³/7):

Calculate the numerator and denominator:

Numerator: 6³ = 6 × 6 × 6 = 216

Denominator: 7

Substitute the values into the expression:

216/7

This expression cannot be simplified further.

(12⁵/14³):

Calculate the numerator and denominator:

Numerator: 12⁵ = 12 × 12 × 12 × 12 × 12 = 248832

Denominator: 14³ = 14 × 14 × 14 = 2744

Substitute the values into the expression:

248832/2744 = 90855/1001

The simplified form is 90855/1001.

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Simplify 6 to the fifth power over 7 cubed all raised to the second power. 6 to the seventh power over 7 to the tenth power 6 to the tenth power over 7 to the sixth power 6 cubed over 7 12 to the fifth power over 14 cubed

(6⁵/7³)²

(6⁷/7¹⁰)

(6¹⁰/7⁶)

(6³/7)

(12⁵/14³)

To find the perpendicular line's equation, first find the negative reciprocal of the original line's slope. Next, use the point-slope form with the given point. Lastly, rearrange the equation into standard form, resulting in x + 4y = 22.

To find the equation of a line that is perpendicular to another line and passes through a given point, you need to perform a series of steps. The first line's equation is given as 4x - y = 2. Firstly, solve for y to put it in slope-intercept form, y = mx + b. Here, the equation becomes y = 4x - 2, so the slope (m) is 4. The slope of the perpendicular line will be the negative reciprocal of this, which is -1/4.

The next step is to use the point-slope form of the line, which is y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes. For the point (2,5), the equation of the line is y - 5 = -1/4(x - 2). Multiplying both sides by 4 to clear the fraction gives 4y - 20 = -x + 2.

Finally, rearrange the equation to get it into standard form, Ax + By = C, giving us x + 4y = 22. This is the standard form of the equation we were seeking.

The derivative of f(x) at x = -1 is -8.

Derivative is the rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.

According to the given problem,

f(x) = [tex]\frac{8}{x}[/tex]

Derivative of f(x),

⇒ f'(x) = [tex]-\frac{8}{x^{2} }[/tex]

At x = -1,

⇒ f'(-1) =  [tex]-\frac{8}{(-1)^{2} }[/tex]

          = -8

Hence, we can conclude, the derivative of f(x) at x = -1 is -8.

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Answer:37

Step-by-step explanation:

12•12=144

35•35=1225

1225+144=1369

Square root 1369=37

Answer:

A. 0.135%

Step-by-step explanation:

We have been given that adult male heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The average basketball player is 79 inches tall.  

We need to find the area of normal curve above the raw score 79.

First of all let us find the z-score corresponding to our given raw score.

[tex]z=\frac{x-\mu}{\sigma}[/tex], where,

[tex]z=\text{z-score}[/tex],

[tex]x=\text{Raw-score}[/tex],

[tex]\mu=\text{Mean}[/tex],

[tex]\sigma=\text{Standard deviation}[/tex].

Upon substituting our given values in z-score formula we will get,

[tex]z=\frac{79-70}{3}[/tex]

[tex]z=\frac{9}{3}[/tex]

[tex]z=3[/tex]

Now we will find the P(z>3) using formula:

[tex]P(z>a)=1-P(z<a)[/tex]

[tex]P(z>3)=1-P(z<3)[/tex]

Using normal distribution table we will get,

[tex]P(z>3)=1-0.99865 [/tex]

[tex]P(z>3)=0.00135[/tex]

Let us convert our answer into percentage by multiplying 0.00135 by 100.

[tex]0.00135\times 100=0.135%[/tex]

Therefore, approximately 0.135% of the adult male population is taller than the average basketball player and option A is the correct choice.

The vertical asymptotes of the function y = 2cot(3x) + 4 are  A.x = π/3  C. x = 2π D.x = 0

The function is given as:

y = 2cot(3x) + 4

The above function is a cotangent function, represented as:

y = Acot(Bx +C) + D

By comparison, we have:

B = 3

The vertical asymptotes are then calculated using:

[tex]x = \frac{\pi}{B}n[/tex], where n are integers

Substitute 3 for B

[tex]x = \frac{\pi}{3}n[/tex]

Using the above format, the vertical asymptotes in the options are  A.x = π/3  C. x = 2π D.x = 0

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To find the interest Candis would make from a 15,400% interest rate on a $220 investment for one year, we calculate using the simple interest formula, resulting in $33,880.

The question asks us to determine how much interest Candis would make from a payday loan with an effective interest rate of 15,400% if she invested $220 for a year. To calculate the interest earned, we can use the formula for simple interest which is I = Prt, where I is interest, P is principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years.

Converting 15,400% to a decimal, we get 154. Then, apply the formula:

I = $220 × 154 × 1

This gives us:

I = $33,880

Therefore, Candis would make $33,880 in interest after one year, which corresponds to option D.

Answer:

True

Step-by-step explanation:

Given statement : The base of an exponential function cannot be a negative number.

We need to check whether the given statement is true or not.

The general form of an exponential function is

[tex]f(x)=ab^x[/tex]

where, a is the initial value and b is the base of exponential function.

The value of base b is always greater than 0 because

1. The terms like [tex](-3)^\frac{1}{2}[/tex] is an imaginary number and it make no sense. So, the base of an exponential function cannot be a negative number.

2. It b=0, then [tex](0)^x=0[/tex], which is a constant function. So, the base of an exponential function cannot be 0.

It means b>0.

Therefore, the given the given statement is true.

Final answer:

The base of an exponential function must be positive, as a negative base can lead to undefined values when raised to non-integer exponents. The rate of growth of an exponential function with a positive base near one can be approximated by 1+x for small x. Bases for exponential functions can often be connected to Euler's number e (approximately 2.71818).

Explanation:

The statement that the base of an exponential function cannot be a negative number is true. The base of an exponential function needs to be positive because a negative base can lead to undefined or complex values when raised to a fractional or irrational exponent. For example, the exponential function with base e (where e is the Euler's number, approximately equal to 2.71818) demonstrates natural growth, and its rate of growth for small x values approximates to 1+x. This approximation indicates how for a small change in x, the change in the value of the function is nearly proportional when the base is a positive number close to one.

Considering other bases, they can be related to base e using the identity ax = eln(a)x, where a is a positive real number, and ln(a) is the natural logarithm of a. Thus, whether for common or natural bases, the exponential function is well-defined only for positive bases.