Is the following number rational or irrational? -3+π
Choose 1 answer:
A)Rational
B)Irrational​

Answer:

Step-by-step explanation:

[tex]16=2^4\\\\8=2^3\\\\16^{2n-3}=8^{4n}\\\\(2^4)^{2n-3}=(2^3)^{4n}\qquad\txt{use}\ (a^n)^m=a^{nm}\\\\2^{(4)(2n-3)}=2^{(3)(4n)}\iff4(2n-3)=12n\qquad\text{use the distributive property}\\\\(4)(2n)+(4)(-3)=12n\\\\8n-12=12n\qquad\text{subtract}\ 8n\ \text{from both sides}\\\\-12=4n\qquad\text{divide both sides by 4}\\\\\dfrac{-12}{4}=\dfrac{4n}{4}\\\\-3=n\to n=-3[/tex]

Answer:

B

Step-by-step explanation:

The vertex form of an absolute value function is f(x)=a|x-h|+k where (h,k) is the vertex.

a is positive means the absolute value function will face up.

a is negative means the absolute value function will face down.

So looking at the picture we see the vertex is (2,3) and all of the choices have a is 1.

So plugging in 2 for h and 3 for k and 1 for a into f(x)=a|x-h|+k

f(x)=|x-2|+3.

B.

The correct function represent in the graph are,

⇒ y = |x - 2| + 3

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph of the function shown in image.

Now, Let the parent function is,

⇒ y = |x|

Clearly, the function is move 2unit left and 3 unit up.

Hence, The correct function represent in the graph are,

⇒ y = |x - 2| + 3

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Answer:

[tex] \sqrt{\frac{668}{\pi} } [/tex] feet  given the area is 167 ft squared

Step-by-step explanation:

Since our sector as a central angle of 90 degree then it is only a 4th of the whole circle.  The area of a circle is pi*r^2.  We will only be using a 4th of that since are sector is only a 4th of the circle.

So the formula will be using for the area of our sector is A=1/4 *pi*r^2.

We are given the area is 167 so replace A with 167.

167=1/4 * pi *r^2

Multiply both sides by 4.

167*4  =pi * r^2

668=pi * r^2

Divide both sides by pi

668/pi =r^2

Square root both sides

[tex] \sqrt{\frac{668}{\pi} } =r [/tex]

so shes 72 i think

hope i'm right

Answer: 58 would be my guess, but need more info

Answer:

(f-g)(x) = 4x - x^(-5)

Step-by-step explanation:

Please, enclose that negative exponent inside parentheses:  g(x)=x^(-5).  No need to type in the " + " in f(x)=4x^+1.

g(x) is to be subtracted from f(x).  Write f(x):

f(x)=4x

followed by the negative of g(x):  -g(x) = -x^(-5)

and now combine these two results:

 f(x)=4x

-g(x)= -x^(-5)

---------------------

(f-g)(x) = 4x - x^(-5)

The expression for (f-g)(x) is (f-g)(x) = 4x² + 1 - 1/x⁵

A function is a mathematical formula that describes how the dependent variable and independent variable are related. The dependent variable's value varies in the function together with the independent variable's value.

To find (f-g)(x), we need to subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x)

We are given:

f(x) = 4x² + 1

g(x) = x⁻⁵ = 1/x⁵

Substituting these values into the expression for (f-g)(x), we get:

(f-g)(x) = f(x) - g(x) = (4x² + 1) - (1/x⁵)

Simplifying the expression, we can write:

(f-g)(x) = 4x^2 + 1 - 1/x⁵

Therefore, the expression for (f-g)(x) is:

(f-g)(x) = 4x² + 1 - 1/x⁵

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Answer:

-33 or 33

Step-by-step explanation:

The seventh term of an AP is written as:

[tex]a + 6d[/tex]

The eleventh term of an AP is written as:

[tex]a + 10d[/tex]

If the 7th term is 11 times the 11th term, then;

[tex]a + 6d = 11(a + 10d)[/tex]

Expand to get:

[tex]a + 6d = 11a + 110d[/tex]

[tex]11a - a = 6d - 110d[/tex]

[tex]10a = - 104d[/tex]

[tex] \frac{a}{d} = - \frac{104}{10} [/tex]

[tex] \frac{a}{d} = - \frac{52}{5} [/tex]

We must have a=-52 and d=5

Or

a=52 and d=-5

For the first case, the 18th term is :

[tex] - 52 + 5 \times 17 = 33[/tex]

For the second case,

[tex]52 - 5 \times17 = - 33[/tex]

Answer:

6.5

Step-by-step explanation:

3! = 6

0! = 1

2! = 2

1! = 1

6 + 1/2*1 = 6.5

So all of the given answers are wrong.

Final answer:

The Pythagorean theorem relates the lengths of the legs and hypotenuse of a right triangle. By substituting the given values into the equation, we can solve for x using the theorem. The rounded value of x is 3.6 (B).

Explanation:

The Pythagorean theorem relates the length of the legs of a right triangle, labeled a and b, with the hypotenuse, labeled c. The relationship is given by: a² + b² = c². This can be rewritten, solving for c: c = √(a² + b²).

In this case, we want to find the value of x using the Pythagorean theorem. Let's say that the lengths of the legs are 3 and x. Substituting these values into the theorem, we have:

3² + x² = c²

Now, we can solve for x by rearranging the equation:

x² = c² - 3²

x = √(c² - 3²)

Rounding to the nearest tenth, we can find the value of x to be approximately 3.6 (B).

Final answer:

The Pythagorean theorem allows us to calculate the length of the hypotenuse of a right triangle by squaring the lengths of the other two sides, adding them together, and then taking the square root. To round to the nearest tenth, we calculate and then round the final result accordingly.

Explanation:

To use the Pythagorean theorem to find x and round to the nearest tenth, we need to establish the components of the equation. The theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula is written as a² + b² = c².

However, the problem provided does not include the initial lengths to insert into the equation; hence, we cannot compute the value directly. Nonetheless, I can illustrate with a hypothetical example:

If we have a right triangle with legs of lengths 9 (a) and 6 (b), then the hypotenuse (c) can be found as follows:

c = √(9² + 6²)
c = √(81 + 36)
c = √117
c = 10.82, round off to the nearest tenth would be c = 10.8

In this example, we squared the lengths of the legs, added them together, and took the square root of the result to find the hypotenuse to the nearest tenth. The same steps apply to any right-angled triangle where you are given the lengths of the legs and need to find the hypotenuse using the Pythagorean theorem.

Answer:

The multiplicative inverse is -5/3

Step-by-step explanation:

Multiplicative inverse means we want to end up with 1

-3/5 * what =1

Multiply by 5 to clear the fraction

-3/5 * what *5 = 1*5

-3 * what = 5

Divide by -3 to isolate what

-3*what /-3 = 5/-3

what = -5/3

The multiplicative inverse is -5/3

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ H(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad K(\stackrel{x_2}{10}~,~\stackrel{y_2}{7}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{10+2}{2}~~,~~\cfrac{7+1}{2} \right)\implies \left( \cfrac{12}{2}~,~\cfrac{8}{2} \right)\implies (6,4)[/tex]

Answer:

Option D y=3

Step-by-step explanation:

The question in English is

Which of the following functions is a constant function?

we know that

A constant function is a function whose output value is the same for every input value

so

Verify each case

case A) y=x+1

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case B) y=x+2

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case C) x=y+3

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case D) y=3

This is a constant function

Is a function whose output value is the same for every input value

Answer:

The graph intersect the y-axis at (0,4.5)

The graph intersect the x-axis at (-3.6,0)

Step-by-step explanation:

The equation is;

-4y=-5x-18

Dived every term by -4

[tex]\frac{-4y}{-4} =\frac{-5x}{-4} -\frac{18}{-4} \\\\\\y=\frac{5}{4}x+\frac{9}{2}[/tex]

plot using a graph tool to view the liner graph as below

ANSWER

The diagonal of the square is 6 units.

EXPLANATION

A diagonal of a square divides the square into two congruent right isosceles triangles.

Let the sides of the square be 's' units. Then, the Pythagoras Theorem says that, the sum of the squares of the shorter legs will be equal to the square of the hypotenuse.

Let the diagonal which is the hypotenuse be 'd' units.

Then,

[tex] {d}^{2} = {s}^{2} + {s}^{2} [/tex]

[tex] \implies \: {d}^{2} = 2{s}^{2}[/tex]

From the question, the side length of the square is

[tex]s = 3 \sqrt{2} \: units[/tex]

We plug in this value to obtain:

[tex]\implies \: {d}^{2} = 2{(3 \sqrt{2} )}^{2}[/tex]

Or

[tex]\implies \: {d}^{2} = 2 \times { {3}^{2} (\sqrt{2} )}^{2}[/tex]

[tex]\implies \: {d}^{2} = 9 \times 2 \times 2 = 36[/tex]

We take the positive square root of both sides to get:

[tex]d = \sqrt{36} [/tex]

[tex]d = 6 \: units[/tex]

Answer:

The y-intercept is the point (0,2)

see the attached figure                

Step-by-step explanation:

we have

[tex]3y=-5^{x}+7[/tex]

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

substitute in the equation and solve for y

[tex]3y=-5^{0}+7[/tex]    

[tex]3y=-(1)+7[/tex]

[tex]3y=6[/tex]

[tex]y=2[/tex]

therefore

The y-intercept is the point (0,2)

using a graphing tool

see the attached figure                      

Answer: For Plato users plot a point on 2 at the y intercept.

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{x + 5}\ >\huge\text{ 10}[/tex]

[tex]\huge\text{First you'll need to SUBTRACT by 5}[/tex][tex]\huge\text{on each of your sides!}[/tex]

[tex]\huge\text{x + 5 - 5}>\huge\text{ 10 - 5}[/tex]

[tex]\huge\text{Cancel out: 5 - 5 because it equals to 0}[/tex]

[tex]\huge\text{Keep: 10 - 5 because it gives us the result of 5}[/tex]

[tex]\huge\text{x}>\huge\text{5}[/tex]

[tex]\huge\text{It's an (o)(p)(e)(n)(e)(d) circle} \checkmark[/tex]

[tex]\huge\text{Starts off with \#5}\checkmark[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: A.}}}[/tex] [tex]\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

[tex]\Large\textnormal{A. First graph}[/tex]

Step-by-step explanation:

[tex]\Large\textnormal{First, subtract by 5 from both sides of equation.}[/tex]

[tex]\displaystyle x+5-5>10-5[/tex]

[tex]\Large\textnormal{Then, simplify, to find the answer.}[/tex]

[tex]\displaystyle 10-5=5[/tex]

[tex]\Large \boxed{x>5}[/tex], which is our answer.

[tex]\Large\textnormal{The correct answer is A.}[/tex]

Answer:

[tex]\$420.43[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=7.5\ years\\ P=\$300\\ r=0.045[/tex]  

substitute in the formula above  

[tex]A=300(e)^{0.045*7.5}[/tex]  

[tex]A=\$420.43[/tex]  

Answer:

130°

Step-by-step explanation:

Since there are 360 degrees is a circle, measure of AXC = 260 means the measure of Arc AC is:

360 - 260 = 100

Now if we were to draw 2 lines, one from A to X and another from C to X, we would have an intercepted angle at X originating from AC.

The theorem is when the intercepted angle is at the opposite side of the circumference, the angle is HALF THAT OF THE ARC.

So, half of 100 is 50.

Angle X and Angle B add up to 180, hence Angle ABC is 180 - 50 = 130

Answer: The crop yield increased by 9 pounds per acre from year 1 to year 10.

Step-by-step explanation:

To solve this we are using the average rate of change formula: Av=\frac{f(x_2)-f(x_1)}{x_2-x_1}, where:

x_2 is the second point in the function

x_1 is the first point in the function

f(x_2) is the function evaluated at the second point

f(x_1) is the function evaluated at the first point

We know that the first point is 1 year and the second point is 10 years, so x_1=1 and x_2=10. Replacing values:

Av=\frac{-(10)^2+20(10)+50-[-(1)^2+20(1)+50]}{10-1}

Av=\frac{-100+200+50-[-1+20+50]}{9}

Av=\frac{150-[69]}{9}

Av=\frac{150-69}{9}

Av=\frac{81}{9}

Av=9

Since f(x) represents the number of pounds per acre and x the number of years, we can conclude that the crop yield increased by 9 pounds per acre from year 1 to year 10.

Final answer:

To identify which function the graph represents, analyze the shape and pattern of the graph. The correct function could either be a polynomial such as y = x^4, which has a sharply rising curve, or a logarithmic function with a declining curve due to having a base between 0 and 1, like y = log(1/4)x, but not y = log1x as this is not mathematically valid.

Explanation:

The question requires the identification of a function based on its graph. Since the properties of functions are known, such as the logarithmic function increasing as x increases, and the behavior of exponential functions and their inverses, we can analyze the options given. The function y = log1x is not valid as the base of a logarithm cannot be 1. The function y = x4 is a polynomial function with a graph that rises sharply for positive and negative values of x. Lastly, y = log(1/4)x represents a logarithmic function with base 1/4, which is a declining curve because the base is between 0 and 1.

To choose the correct function that a graph represents, one should look for key characteristics such as the shape of the graph, increase or decrease pattern, as well as specific points like asymptotes or intercepts. If the graph is increasing as x increases and resembles a typical logarithmic curve, the correct choice is a logarithmic function. If the given graph is a sharp rising curve for all x-values and looks like a polynomial, then y = x4 would be correct. The given functions need to be analyzed based on their mathematical properties to select the one that best describes the graph in question.

Answer:

101

Step-by-step explanation:

The theorem to use this is the intercepted arc theorem, which tells us that if we take 2 points on the circumference of a circle and create an angle in the opposite side of the circumference, that angle is HALF that of the ARC intercepted.

If we look at 100 degree angle, we see the ARC intercepted is 99 degree and a degrees. According to theorem, we can say:

99 + a = 2(100)

99 + a = 200

a = 200 - 99

a = 101

Answer:

Step-by-step explanation:

11C4 = 11! / (7!*4!) = 11 * 10 * 9 * 8 * 7!/ 7! * 4!

11C4 = 11*10 * 9 * 8 / 24

11C4 = 11*10 * 3

11C4 = 330

========

You can't do the second one. Permutations and Combinations always give an answer greater than 1 and integers.

Answer:

  50 million

Step-by-step explanation:

You don't need to go to the trouble to find the value of k in e^(kt). Rather, you can use the given ratio directly.

When t = years after 1990, the population of 49 million took 12 years to achieve. The estimate desired is for 16 years after the year 1990. The appropriate exponential formula for the population is ...

  P = 46·(49/46)^(t/12)

Then for t=16, this is ...

  P = 46·(49/46)^(16/12) ≈ 50.04 . . . .  million

The population in 2006 is estimated at 50 million.

_____

The form of the exponential equation we used above is ...

  f(x) = (baseline value)·(ratio to baseline)^(x/(interval corresponding to ratio))

have you finished this yet? im doing it rn and i need help on some of them. if you havent i can help you with a couple answers

Answer:

The answer would be option B and option C

∠DEF and ∠FED describe an angle with a vertex at E.

The correct answers are option (B) and option (C)

For given question,

We need to find the correct angle with a vertex at E.

We know that the vertex is the common point of the rays of an angle.

It is always written at the middle in an angle.

So, ∠DEF and ∠FED describe an angle with a vertex at E.

The correct answers are option (B) and option (C)

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Answer:

3.7

Step-by-step explanation:

Inversely means we are taking the constant and dividing it.

So y varies inversely with x means "y=k/x".

k is a constant.  We can find the constant if they give us a point on this curve.

The constant is a number that doesn't change no matter your input and output.

[tex]y=\frac{k}{x}[/tex]

So they actually give us k=8.88 and y=2.4 so let's input this:

[tex]2.4=\frac{8.88}{x}[/tex]

We need to solve this equation for x.  You can do your favorite thing in cross-multiply. But how, Freckles?  Well just slap a 1 underneath that 2.4.  You can do that because 2.4/1 is still 2.4.

[tex]\frac{2.4}{1}=\frac{8.88}{x}[/tex]

Cross-multiply:

[tex]2.4x=8.88(1)[/tex]

[tex]2.4x=8.88[/tex]

Divide both sides by 2.4:

[tex]x=\frac{8.88}{2.4}[/tex]

[tex]x=3.7[/tex] when [tex]y=2.4[/tex].

Answer:

9*4

Step-by-step explanation:

We can Factor out a 9 from each term

9 + 27

9 (1+3)

9 (4)

9*4

Answer:

The price of 4 apples is Rs 28

Step-by-step explanation:

The price of 1 dozen apple is Rs 84

12 apples =Rs 84

1 apple = Rs 84÷12

1apple =Rs 7

Again

Price of 4 apples = Rs 7 × 4

= Rs 28 Ans,,

Answer: There Ya go

Explanation:

Answer:

D. X+5y=7

passes through both coordinates

Answer:

all work is shown and pictured

Answer:

C 8

Step-by-step explanation:

The average rate of change is given by

f(x2) -f(x1)

---------------

x2-x1

x2 = -3  and x1 = -5

Looking at the graph

f(x2) = f(-3) = 1

f(x1)= f(-5) =-15

Substituting these values into the equation

1 - (-15)

---------------

-3 - (-5)

1+15

----------

-3 +5

16

----

2

8

Answer: OPTION C.

Step-by-step explanation:

You need to use this formula:

[tex]averate\ rate\ of\ change=\frac{f(b)-f(a)}{b-a}[/tex]

Knowing that we need to find the average rate of change for the given quadratic function, for the interval from [tex]x=-5[/tex] to [tex]x=-3[/tex], we need to find their corresponding y-coordinates.

We can observe in the graph that:

For [tex]x=b=-5[/tex] →  [tex]y=f(b)=-15[/tex]

For [tex]x=a=-3[/tex] → [tex]y=f(a)=1[/tex]

Therefore, substitituting, we get:

 [tex]averate\ rate\ of\ change=\frac{-15-1}{-5-(-3)}=8[/tex]