Tell whether the sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive
formula and an explicit formula to represent it.

3, 3.25, 3.5, 3.75,...
​

Answer:

[tex]x^{\frac{5}{12} }[/tex]

Step-by-step explanation:

In the question given we use the law of exponents;

[tex](a^{b})^{c} = a^{bc}[/tex]

If a base a is raised to a power b and the entire expression raised to a power c, the resulting expression is simply equal to the base a raised to the product of the two exponents b and c, that is bc.

In the case given,

a = x

b = 5/8

c = 2/3

To simplify the expression we simply multiply b and c;

bc = 5/8 * 2/3

     = 5/12

The simplified expression is thus;

[tex]x^{\frac{5}{12} }[/tex]

Answer:

The correct answer is ((x⁵/⁸)²/³) = x⁵/¹²

Step-by-step explanation:

Points to remember:-

Identity

(xᵃ)ᵇ = xᵃᵇ

Here it is given that, ((x⁵/⁸)²/³)

To find the value of ((x⁵/⁸)²/³)

(5/8) * (2/3) =  (5 * 2) /(8 * 3) = 10/24 = 5/12

By using identity (xᵃ)ᵇ = xᵃᵇ we can write,

((x⁵/⁸)²/³) = x⁽⁵/⁸⁾ˣ⁽²/³⁾

= x⁵/¹²    

Therefore the correct answer is ((x⁵/⁸)²/³) = x⁵/¹²

Answer:

5 if its a dice.

Step-by-step explanation:

On a dice, 5. The probability of it landing on 6 is 1/6

Answer:

15

Step-by-step explanation:

Since 9 questions is 60% of the exam, you must find 100%. You could find the value of 10% by dividing 60 by 6. You do the same to 9, divide by 6 to get 1.5. Now that you have the value of 10% you can multiply 10% by 10 to get 100. You also do the same to 1.5. Your answer should be 15, if not check your work again. Work hard!!

The total number of questions in the exam is 15 and this can be determined by using the unitary method.

Given :

Priya has completed 9 exam questions. This is 60% of the questions on the exam.

The unitary method can be used in order to determine the total number of questions in the exam.

According to the given data, Priya has completed 9 exam questions which are 60% of the questions on the exam. So, the 100% questions in the exam are:

[tex]= \dfrac{9}{60}\times 100[/tex]

Multiply 9 by 100 in the above expression.

[tex]=\dfrac{900}{60}[/tex]

Divide 900 by 60 in the above expression.

= 15 questions

So, the total number of questions in the exam is 15.

For more information, refer to the link given below:

https://brainly.com/question/21648365

The answer is -2. X is -2.

The area is the length x the height.

Length = 11.40 cm

Height = 6.90 cm

Area = 11.40 * 6.90 = 78.66 cm^2

The answer is D.

Answer:

Here the slope is 2.

Step-by-step explanation:

The first step here is to solve for y.  This will lead us to the correct slope value.  Subtracting 4x from both sides, we get -2y = 7 - 4x.

Dividing both sides by -2, we get y = -7/2 + 2x.  The coefficient of x is the slope.  Here the slope is 2.

The slope of a line parallel to the line 4x - 2y = 7 is 2. This is calculated by modifying the given equation into the form y = mx + b and determining the value of 'm', which represents the slope, and parallel lines share the same slope.

To find the slope of a line parallel to the given line, 4x - 2y = 7, we first need to put the given equation in the standard form y = mx + b, where 'm' represents the slope of the line.

We can do this by isolating 'y' in the equation. So, 4x - 2y = 7 becomes 2y = 4x - 7. Then, we divide the entire equation by 2 to solve for 'y', which gives us y = 2x - 7/2. Thus, the slope 'm' of this line is 2.

Lines that are parallel to each other have the same slope, so the slope of the line parallel to the given line is also 2.

https://brainly.com/question/32035102

#SPJ2

ANSWER

Midline y=-1

Period= 2π

Amplitude=3

Frequency=1

EXPLANATION

The given function completes one cycle on the interval 0 to 2π.

Therefore the period of the function is

[tex]2 \pi[/tex]

The midline divides the graph into two equal halves.

This line is y=-1

The cycle repeated once on the interval [0,2π] hence the frequency is 1.

The amplitude is the distance from the midline to the peak.

=2--1=3

Answer:

Step-by-step explanation:

[tex]30\cdot\dfrac{1}{6}=\dfrac{30}{6}=5[/tex]

Comparing the periods of the given cosine functions indicates that functions A) and C) both have the greatest period of π, which is longer than the period of function B), π/2.

To compare the periods of the given functions, let's first understand what the general form of a cosine function tells us about its period.

The general form is y = A cos(Bx + C), where A is the amplitude, B affects the period, and C is the phase shift.

The period of such a function is given by 2π / |B|.

For function A) y = 3cos(2x+1), B = 2, thus its period is π.

For function B) y=5cos(4x +8), B = 4, yielding a period of π/2.

Lastly, for function C) y=cos(2x+4) (4.3), assuming the (4.3) is an unrelated notation and focusing on the given cos component with B = 2, its period is also π.

The function with the greatest period among A, B, and C is thus A) and C), both having the same period of π, which is greater than the period of B).

The formula for finding the volume of a rectangular prism (the cargo area of the truck is the shape of a rectangle in 3D; a rectangular prism) is V = (l)(w)(h); where l = length, w = width, and h = height.

First, substitute the known values into the equation:

l = 8.5

w = 6

h = 10.5

V = (8.5)(6)(10.5)

(Note: .5 = 1/2)

Now, all we need to do is simplify:

V = 535.5 ft³ OR 535 1/2 ft³

(Note: ft³ is the condensed form of cubic feet)

You can pick whichever form your test directs you to use. They are both the same value though.

Hope this helps!

The volume of the cargo area of the truck is 519.75 cubic feet.

The volume of the cargo area of the truck can be calculated by multiplying its length, width, and height. Given the dimensions in feet are:

Length = 8 1/2 feet = 8.5 feet = 8 + 1/2 feet

Width = 6 feet

Height = 10 1/2 feet = 10.5 feet = 10 + 1/2 feet

To find the volume, we convert the mixed numbers to improper fractions and then multiply:

Length in fractions = 8 + 1/2 = 17/2 feet

Width in fractions = 6 = 6 * 2/2 = 12/2 feet

Height in fractions = 10 + 1/2 = 21/2 feet

Now, multiply the dimensions to find the volume:

Volume = Length * Width * Height

Volume = (17/2 feet) * (12/2 feet) * (21/2 feet)

Volume = (17 * 12 * 21) / (2 * 2 * 2) cubic feet

Volume = 4158 / 8 cubic feet

Simplifying the fraction, we get:

Volume = 519.75 cubic feet

Answer:

A.

Step-by-step explanation:

First, let's define the types of numbers.

Real numbers: a value that represents a quantity along a continuous line

ex: 1, 5, -6, 0.125, 45.5258,

Integer: Zero, any positive or negative number

ex: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5....

Whole numbers: a number without fractions [not negative]

ex: 0, 1, 2, 3, 4, 5.....

Rational numbers: any number that can be expressed as the quotient or fraction

ex: 1, 2, 3, 4, 5

Irrational numbers: any number that can't be expressed at the quotient or fraction

ex: pi, [3.14.... (never ending decimal)]  square root of 2....

Based on this information, the false statment would be A. I believe, because

pi is a real number and it is an irrational number.

I hope this helps!!! :)

Answer:

[tex]\large\boxed{B.\ 4x^2-41x+105}[/tex]

Step-by-step explanation:

[tex]f(x)=4x-\sqrt{x}\\\\g(x)=(x-5)^2\\\\f(g(x))\to\text{put}\ x=(x-5)^2\ \text{to}\ f(x):\\\\f(g(x))=f\bigg((x-5)^2\bigg)=4(x-5)^2-\sqrt{(x-5)^2}\\\\\text{use}\\(a-b)^2=a^2-2ab+b^2\\\sqrt{x^2}=|x|\\\\f(g(x)=4(x^2-2(x)(5)+5^2)-|x-5|\\\\x>5,\ \text{therefore}\ x-5>0\to|x-5|=x-5\\\\f(g(x))=4(x^2-10x+25)-(x-5)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\f(g(x))=(4)(x^2)+(4)(-10x)+(4)(25)-x-(-5)\\\\f(g(x))=4x^2-40x+100-x+5\\\\\text{combine like terms}\\\\f(g(x))=4x^2+(-40x-x)+(100+5)\\\\f(g(x))=4x^2-41x+105[/tex]

Answer: Option B

[tex]f(g(x)) = 4x^2 -41x + 105[/tex]

Step-by-step explanation:

We have 2 functions

[tex]f(x) = 4x -\sqrt{x}[/tex]

[tex]g(x) = (x-5)^2[/tex]

We must find [tex]f(g(x))[/tex]

To find this composite function enter the function g(x) within the function f(x) as follows

[tex]f(g(x)) = 4(g(x)) -\sqrt{(g(x))}[/tex]

[tex]f(g(x)) = 4(x-5)^2 -\sqrt{(x-5)^2}[/tex]

By definition [tex]\sqrt{a^2} = |a|[/tex]

So

[tex]f(g(x)) = 4(x-5)^2 -|x-5|[/tex]

Since x is greater than 5 then the expression [tex](x-5)> 0[/tex].

Therefore we can eliminate the absolute value bars

[tex]f(g(x)) = 4(x-5)^2 -(x-5)[/tex]

[tex]f(g(x)) = 4(x^2 -10x + 25) -(x-5)[/tex]

[tex]f(g(x)) = 4x^2 -40x + 100 -x+5[/tex]

[tex]f(g(x)) = 4x^2 -41x + 105[/tex]

20^2+21^2=29^2 can be used to determine if the triangle is a right triangle

Answer:

Step-by-step explanation:

The two smaller line lengths are squared separately and added. The square of the third line is noted. If squares of the two small ones equal the square of the largest one, you are working with a right angle triangle.

The one that puts into a formula what is stated above is B. D is close, but the longest line must be by itself.

Answer:

[tex]\large\boxed{\vec{u}\circ\vec{v}=121}[/tex]

Step-by-step explanation:

[tex]\vec{a}=<x_a,\ y_a>,\ \vec{b}=<x_b,\ y_b>\\\\\vec{a}\circ\vec{b}=x_ax_b+y_ay_b\\\\====================================\\\\\vec{u}=<8,\ 7>,\ \vec{v}=<9,\ 7>\\\\\vec{u}\circ\vec{v}=(8)(9)+(7)(7)=72+49=121[/tex]

Answer:

x = 3 + i+√5

x = 3 + i-√5

OR

x= 4 - √6

x= 4 +√6

Step-by-step explanation:

(x - 3)² +6=1​

(x - 3)² + 6 = 1

        -6   -6

sq root > (x - 3)²      = -5

x-3 = i±√5     (i because neg. number)

x = 3 + i±√5

since its ±

two possible answers

x = 3 + i+√5

x = 3 + i-√5

Or

(x - 3)² +6=1​

(x-3)+  √6= √ 1

x-3 = 1 - (±)  √6

x= 4 - (±)  √6

Answers

x= 4 - √6

x= 4 +√6

Answer:

x cannot equal -3, and x cannot equal -2

Step-by-step explanation:

Answer:

The excluded values of the rational expression are -3 and -2.

Step-by-step explanation:

If a ration function is defined as [tex]R(x)=\frac{p(x)}{q(x)}[/tex], then the excluded values of the rational function are those values for which q(x)=0.

The given rational expression is

[tex]\frac{x^2+2x-3}{x^2+5x+6}[/tex]

Factories the numerator and denominator.

[tex]\frac{x^2+3x-x-3}{x^2+3x+2x+6}[/tex]

[tex]\frac{x(x+3)-1(x+3)}{x(x+3)+2(x+3)}[/tex]

[tex]\frac{(x+3)(x-1)}{(x+3)(x+2)}[/tex]                .... (1)

Equate the denominator equal to 0.

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

Using zero product property,

[tex]x+3=0\Rightarrow x=-3[/tex]

[tex]x+2=0\Rightarrow x=-2[/tex]

Therefore the excluded values of the rational expression are -3 and -2.

Cancel out the common factors of equation (1)

[tex]\frac{x - 1}{x + 2}[/tex] for (x≠-3)

It means x=-2 is vertical asymptote and x=-3 is hole.

Answer:

[tex]f(x)=log_ex[/tex]

Step-by-step explanation:

By definition, we can write ln instead of log. WHEN??

Whenever the base of the logarithm is the number "e".

Hence, when we have:

[tex]Log_e[/tex]

We can write it in shortcut as:

[tex]Log_e=ln[/tex]

Hence, ln x can also be written as [tex]Log_ex[/tex]

Fourth answer choice is right.

Answer:

[tex]f(x) = log_e(x)[/tex]

Step-by-step explanation:

[tex]f(x) = ln x[/tex]

For logarithmic function ln(x) the base of ln is 'e'

[tex]f(x) = log_3(x)[/tex]

The base of log is 3 . so it is not equivalent to [tex]f(x) = lnx[/tex]

[tex]f(x) = log_{10}(x)[/tex]

The base of log is 10 . so it is not equivalent to [tex]f(x) = lnx[/tex]

[tex]f(x) = log_b(x)[/tex]

The base of log is b . so it is not equivalent to [tex]f(x) = lnx[/tex]

[tex]f(x) = log_e(x)[/tex]

The base of log is e . so it is equivalent to [tex]f(x) = lnx[/tex]

Answer:

The radius is [tex]r=5\ cm[/tex]

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises.

so

[tex]m<C =(1/2)[arc\ AB][/tex]

[tex]m<C =90\°[/tex]

substitute

[tex]90\°=(1/2)[arc\ AB][/tex]

[tex]arc\ AB=180\°[/tex]

That means----> The length side AB of the inscribed triangle is a diameter of the circle

Applying Pythagoras Theorem

Calculate the length side AB

[tex]AB^{2}=AC^{2}+BC^{2}[/tex]

[tex]AB^{2}=8^{2}+6^{2}[/tex]

[tex]AB^{2}=100[/tex]

[tex]AB=10\ cm[/tex] -----> is the diameter

Find the radius

[tex]r=10/2=5\ cm[/tex] -----> the radius is half the diameter

Answer:

Part A) The perimeter of the court is [tex]P=139.25\ ft[/tex]

Part B) [tex]5\ cans[/tex]

Step-by-step explanation:

Part A) we know that

The perimeter of the court is equal to the perimeter of the square plus the perimeter of semicircle

[tex]P=4D+\frac{\pi D }{2}[/tex]

we have that

[tex]D=25\ ft[/tex]

substitute

[tex]P=4(25)+\frac{(3.14*25)}{2}[/tex]

[tex]P=139.25\ ft[/tex]

Part B)

Find the area above the foul line (labelled II)

The area of a semicircle is equal to

[tex]A=\frac{\pi r^{2}}{2}[/tex]

we have

[tex]r=25/2=12.5\ ft[/tex]

substitute

[tex]A=\frac{(3.14)(12.5)^{2}}{2}[/tex]

[tex]A=245.31\ ft^{2}[/tex]

Round to the nearest whole number

[tex]A=245\ ft^{2}[/tex]

One can of paint covers 50 square feet of floor

so

Calculate how many cans of blue paint does the school need to purchase

[tex]245/50=4.9\ cans[/tex]

Round up

[tex]5\ cans[/tex]

Answer:

C. 1

Step-by-step explanation:

The line containing segment BC has a slope of 1 and a y-intercept of 5 (at point B). Thus, its equation is ...

y = x + 5

For the value of x = -4, the value of y is ...

y = -4 +5 = 1

Point (-4, 1) is on the line containing segment BC.

Answer:

C. 1

Step-by-step explanation:

Answer:

A) 14 cm^2

Step-by-step explanation:

Given

Rhombus ABCD

let the given length be diagonal 1, a= 8cm

diagonal 2,b= 3.5cm

Area of ABCD=?

Area of rhombus= ab/2

Putting the values in above :

Area of ABCD= 8(3.5)/2

                       =28/2

                       =14 !

Answer:

14cm^2

Step-by-step explanation:

Answer:

No Solutions

Step-by-step explanation:

-5x+10x+3=5x+6

5x+3=5x+6

5x=5x+3, which isn't true

ANSWER

The equation has no solution.

EXPLANATION

The given equation is

-5x+10x+3=5x+6

Group similar terms

-5x-5x+10x=6-3

-10x+10x=6-3

0=3

This statement is not true.

Hence the equation has no solution.

Answer:

[tex]m<FEH=86\°[/tex]

Step-by-step explanation:

we know that

The inscribed angle measures half that of the arc comprising

step 1

Find the measure of arc EF

[tex]m<FHE=\frac{1}{2}(arc\ EF)[/tex]

we have

[tex]m<FHE=45\°[/tex]

substitute

[tex]45\°=\frac{1}{2}(arc\ EF)[/tex]

[tex]arc\ EF=90\°[/tex]

step 2

Find the measure of arc EH

[tex]m<EGH=\frac{1}{2}(arc\ EH)[/tex]

we have

[tex]m<EGH=49\°[/tex]

substitute

[tex]49\°=\frac{1}{2}(arc\ EH)[/tex]

[tex]arc\ EH=98\°[/tex]

step 3

Find the measure of arc FGH

[tex]arc\ FGH=360\°-(arc\ EH+arc\ EF)[/tex]

substitute the values

[tex]arc\ FGH=360\°-(98\°+90\°)[/tex]

[tex]arc\ FGH=172\°[/tex]

step 4

Find the measure of angle FEH

[tex]m<FEH=\frac{1}{2}(arc\ FGH)[/tex]

we have

[tex]arc\ FGH=172\°[/tex]

substitute

[tex]m<FEH=\frac{1}{2}(172\°)=86\°[/tex]

now divide 76.5 by 8.5

76.5/8.5 = 9 hours

you can get 12 quarters

Answer:

I don't know either

Step-by-step explanation:

Polygons are categorized according to their side count. The following are the designations for polygons depending on the number of sides they exhibit:

3 sides: Triangles

4 sides: Quadrilaterals

Special cases of quadrilaterals include rectangles, squares, parallelograms, rhombuses, and trapezoids.

5 sides: Pentagons

6 sides: Hexagons

7 sides: Heptagons or Septagons

8 sides: Octagons

9 sides: Nonagons

10 sides: Decagons

Polygons are classified based on the number of sides they possess. Here are the names for polygons with different numbers of sides:

Triangles: The simplest polygon with three sides, often classified based on angles as equilateral, isosceles, or scalene.

Quadrilaterals: Four-sided polygons, encompassing various shapes with specific characteristics. For example, squares have equal sides and right angles, while rectangles have opposite sides of equal length and right angles.

Pentagons: Five-sided polygons, commonly found in geometry and nature.

Hexagons: Six-sided polygons frequently seen in beehives and some crystal structures.

Heptagons or Septagons: Seven-sided polygons, less commonly encountered in everyday geometry.

Octagons: Eight-sided polygons, often used in architecture and design.

Nonagons: Nine-sided polygons, less commonly discussed but still defined geometrically.

Decagons: Ten-sided polygons, exhibiting symmetry and regularity in shape.

The question probable may be:

What is the name of the polygon​

Which has :

3 sides - ?

4 sides - ?

5 sides - ?

6 sides - ?

7 sides - ?

8 sides - ?

9 sides - ?

10 sides - ?

A frequency polygon is a statistical tool used in mathematics to represent the distribution of data visually, much like a line graph, but specifically connected to a histogram. They are particularly helpful for interpreting continuous data and spotting trends within datasets.

Although the question seems to be incomplete, it appears to ask about the terminology used in mathematics, particularly pertaining to polygons. However, if we connect the dots with the provided reference, it seems the actual topic is 'frequency polygons' in the context of statistics. A frequency polygon is a graphical representation of data in statistics, where it's used to illustrate the distribution of a dataset and is similar to a line graph. It is typically made by connecting the midpoints of the tops of bars of a histogram with straight lines, making the data visually easy to interpret. By doing so, it helps in understanding how values are distributed over an interval and is often used to compare different sets of data on the same graph.

Continuous data can sometimes be difficult to analyze, but frequency polygons simplify this by offering a clear, visual interpretation. They are helpful in identifying trends and patterns in data which are not immediately obvious when looking at a table of values or a histogram alone.

I and II

When a graph has a solid line, solutions lie ON that line, whereas if it was a dotted line, solutions lie only on the shaded side of that line, not the line itself.

Answer:

is the last one if not the second option would  be the 2 second

Step-by-step explanation:

Answer:

The volume of the pyramid is one third the volume of the rectangular prism

or

The volume of the prism is three times the volume of the pyramid

Step-by-step explanation:

step 1

Find the volume of the rectangular prism

The volume is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the prism

Find the area of the base B

[tex]B=5^{2}=25\ in^{2}[/tex]

substitute

[tex]Vprism=25h\ in^{3}[/tex]

step 2

Find the volume of the square pyramid

The volume is equal to

[tex]V=(1/3)Bh[/tex]

where

B is the area of the base

h is the height of the pyramid

Find the area of the base B

[tex]B=5^{2}=25\ in^{2}[/tex]

substitute

[tex]Vpyramid=(1/3)25h\ in^{3}[/tex]

Remember that

[tex]Vprism=25h\ in^{3}[/tex]

substitute

[tex]Vpyramid=(1/3)Vprism[/tex]

The volume of the pyramid is one third the volume of the rectangular prism

or

[tex]Vprism=3Vpyramid[/tex]

The volume of the prism is three times the volume of the pyramid