Answer:
a(n) = 4⁽ⁿ⁻¹⁾ is the answer :))))) goodluck!
Step-by-step explanation:
a₁ = 1 = 4⁰
a₂ = 4 =4¹
a₃ =4 x 4=4²
a₄ =4 x 4² =4³
a(n) = 4⁽ⁿ⁻¹⁾
Rayna is building a tapered staircase using wooden boards. The bottom stair is 3 1/2 ft wide, and the top stair is 2 1/6 ft wide. Each stair is 4 in. Shorter than the one below. What is the total length of wooden boards rayna needs for the stair tops, in feet? Enter your answer as an improper fraction.
Sum of an arithmetic sequence is defined by the formula,
[tex]T_n=\frac{n}{2}[2a+(n-1)d][/tex]
Total length of the wooden boards will be [tex]14\frac{1}{6}[/tex] feet.
It's given in the question,
Width of the bottom stair = [tex]3\frac{1}{2}[/tex] feetWidth of the top stair = [tex]2\frac{1}{6}[/tex] feetEach stair is 4 inch shorter than the one below.Since, 1 inch = [tex]\frac{1}{12}[/tex] feet
Therefore, [tex]4[/tex] inch = [tex]\frac{4}{12}[/tex] feet
= [tex]\frac{1}{3}[/tex] feet
So, each stair is [tex]\frac{1}{3}[/tex] feet shorter than one below.
Now the sequence formed will be,
[tex]\frac{7}{2},[\frac{7}{2}-\frac{1}{3}],[\frac{7}{2}-\frac{2}{3}],......\frac{13}{6}[/tex]
[tex]\frac{21}{6},\frac{19}{6},\frac{17}{6}....\frac{13}{6}[/tex]
It's an Arithmetic sequence with common difference 'd' = [tex]-\frac{1}{3}[/tex] and first term 'a' = [tex]\frac{7}{2}[/tex] and nth term [tex]T_n=\frac{13}{6}[/tex]
If there are 'n' stairs, expression for the for the top stair of the arithmetic sequence will be,
[tex]T_n=a+(n-1)d[/tex]
[tex]\frac{13}{6}=\frac{21}{6}+(n-1)(-\frac{1}{3})[/tex]
[tex]\frac{13}{6}-\frac{21}{6}=-(n-1)\frac{1}{3}[/tex]
[tex]\frac{8}{6}=(n-1)\frac{1}{3}[/tex]
[tex]\frac{4}{3}=(n-1)\frac{1}{3}[/tex]
[tex](n-1)=4[/tex]
[tex]n=5[/tex]
Therefore, there are 5 stairs.
Now total length of the wooden boards = Sum of 5 terms of the sequence
= [tex]\frac{n}{2}[2a+(n-1)(d)][/tex]
= [tex]\frac{5}{2}[2(\frac{21}{6})+(5-1)(-\frac{1}{3})][/tex]
= [tex]\frac{5}{2}[\frac{21}{3}-\frac{4}{3}][/tex]
= [tex]\frac{17}{3}\times \frac{5}{2}[/tex]
= [tex]\frac{85}{6}[/tex]
= [tex]14\frac{1}{6}[/tex] ft
Therefore, total length of the wooden boards will be [tex]14\frac{1}{6}[/tex] ft.
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If the volume of a cube is 1,728 cubic inches, find the side length of each of its sides.
Recall that the volume of a cube equals (side)^3. We can create an equation to model this.
1728 in^3 = (side)^3
We can get the cube root of both sides.
12 in = side
Each side is 12 inches long.
Solve this equation: 3x – 5 - x = 134
Step 1: Simplify by combining like terms. Which terms can
be combined?
Answer:
(3x - x) :v
Step-by-step explanation:
3x - 5 - x =134
2x - 5 = 134
2x = 139
x = 139/2
in the figure below the measure of <1=5x°, the measure of <2=y°, and the measure of <3=85°. Find the value of each variable.
Answer:
180-85=95
180-95=85
5x=85
x=17
For given figure, x = 17° and y = 95°
What is an equation?"It is a mathematical statement which consists of equal symbol between two mathematical expressions."
For given question,
We have been given ∠1 = 5x°, the measure of ∠2 = y°, and the measure of ∠3 = 85°
we know, the sum of all the angles on one side of a straight line is always 180°
So, we get two equations.
∠1 + ∠2 = 180° .....................(i)
and ∠2 + ∠3 = 180° .....................(ii)
First we solve equation (ii) to find the value of ∠2
⇒ ∠2 + ∠3 = 180°
⇒ y + 85° = 180°
⇒ y = 95°
Now substitute this value of ∠2 in equation (i)
⇒ ∠1 + ∠2 = 180°
⇒ 5x° + y° = 180°
⇒ 5x° + 95° = 180°
⇒ 5x° = 85°
⇒ x = 17°
Therefore, x = 17° and y = 95°
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What is the multiplicative inverse of 1/2 ?
2
- 1/2
-2
Answer:
multiplicative inverse of 1/2 is 2
H. Tito started the week with a $20 in his lunch
account. If meals costs $2.30 each, write a linear
equation modeling Tito's account value. Can Tito
afford 9 meals?
Answer:
See Below
Step-by-step explanation:
Total money = $20
Cost of one time meal = $2.30
Linear equation = $20 - $2.3(x) Where x is the number of days
No, he can't afford 9 meals because 2.3 × 9 = 20.7. Which is out of his account's money
please help, this is geometry
Answer:
Step-by-step explanation:
The formula is the same almost as the previous question you posted.
You want to find the major arc. That's almost the whole circle. If it was the whole circle, the formula would be 2 * pi * r
But we only want a part of it. Just how big is the angle we use in the formula?
A circle has 360 degrees to go around it. We've cut out a slice of it that is 30 degrees.
The remaining part is 360 - 30 = 330
Arc length = angle / 360 * 2 * pi * r
r = 3 m
Arc length = 330 / 360 * 2 * pi * 3
Arc length = 0.9167 * 6 * 3.14
Arc length = 17.27
Find the scale factor of 1 inch = 9 feet
Answer:
9 ft = 9 × 12 = 108 in
ratio is 1:108
Step-by-step explanation:
An architect is hanging a large sign from a triangular shaped
ceiling and plans to hang the sign at a point located at the
centroid of the triangle.
A diagram of the triangular ceiling shown by A ABD was used
to determine the point on the ceiling where the sign will be hung,
which will be at point G. The length of one median of the
triangular ceiling, BE, is 45 feet.
What is the distance from one corner of the ceiling, at point B, to
the hanging point of the sign?
Enter your answer in the box.
Answer:
30 feet
Step-by-step explanation:
I just took the quiz :)
BRAINLIEST!! PLZ HELP
Given f (x) = x2 – 4 and g(x) = x + 3 then g (f (2)) =
Answer:
g (f(2)) = 3
Step-by-step explanation:
f (x) = x2 – 4
g(x) = x + 3
g (f (2)) =?
Find f(2) first
f (x) = x2 – 4
f (2) = 2^2- 4
= 0
Now put this in your g(x)
g(x) = x + 3
g (f(2)) = (f(2)) + 3
And u alredy know f(2) =0, so just put it in
g (f(2)) = 0 + 3
=3
Help please! Correct answer gets brainlesst
.
Here is a sketch of Noah's bedroom
He wants to create a scale drawing of his bedroom to show to his designer.
The actual length of wall A is 3.5 m.
He uses a scale of 1 m = 6 cm to draw his scale drawing.
How long should the length of wall A be on the scale drawing?
Answer:
21cm
Step-by-step explanation:
for every 1m, it is 6cm on the paper. thus, your answer would be 3.5÷1 which is 3.5
then multiply 3.5 by 6 which is 21
On a mountain, the temperature decreases by 6.5 °C for every 1000 metres increase in height. At 2000 metres the temperature is 10 °C. Find the temperature at 6000 metres
Answer:
30 degree c
Step-by-step explanation:
Is negative 5 a rational number or an irrational number
(Pleasee help me)
Answer:
Negative five is in fact a rational number.
Step-by-step explanation:
Rational numbers can either be negative or positive. An irrational number would be pi (3.14159 etc.)
The sum of 48 and itself,it's half and half of the half is added to 18
Evaluate the expression when a=
[tex] \frac{11 }{15} [/tex]
and c=
[tex] \frac{3 }{10} [/tex]
-2c+a
write your answer in simplest form
Answer:
[tex]\frac{2}{15}[/tex]
Step-by-step explanation:
Substitute the values for a and c into the expression
- 2c + a
= - 2× [tex]\frac{3}{10}[/tex] + [tex]\frac{11}{15}[/tex]
= - [tex]\frac{3}{5}[/tex] + [tex]\frac{11}{15}[/tex]
= - [tex]\frac{3(3)}{5(3)}[/tex] + [tex]\frac{11}{15}[/tex]
= - [tex]\frac{9}{15}[/tex] + [tex]\frac{11}{15}[/tex]
= [tex]\frac{2}{15}[/tex]
HELP ME I ONLY HAVE 15 MINUTES
... 30, 50, 100
... 180
... 50
A polynomial f (x) has the given zeros of 8, –1, and –3.
Part A: Using the Factor Theorem, determine the polynomial f (x) in expanded form. Show all necessary calculations. (3 points)
Part B: Divide the polynomial f (x) by (x2 – x – 2) to create a rational function g(x) in simplest factored form. Determine g(x) and find its slant asymptote. (4 points)
Part C: List all locations and types of discontinuities of the function g(x). (3 points)
The answer is "[tex]\bold{x^3-4x^2-29x-24, y=x-3,\ and\ x=2}[/tex]" and following are the complete solution to the given parts:
For point A)[tex]\to \bold{f(x)=(x-8)(x+1)(x+3)=(x^2-7x-8)(x-8)=(x^3-4x^2-29x-24)}[/tex]For point B)
[tex]\to \bold{x^2-x-2=(x-2)(x+1)}\\\\\to \bold{g(x)=\frac{(x-8)(x+1)(x+3)}{(x-2)(x+1)}}[/tex]
When [tex]x \neq -1[/tex] then
[tex]\to \bold{g(x)=\frac{(x-8)(x+3)}{x-2}}\\\\\to \bold{\lim_{n \to \infty} \frac{g(x)}{x}}[/tex]
So
For point C)
It is discontinuity when a [tex]\bold{x=2}[/tex] that is a vertical asymptote.
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Answer:
Part A:
x^3 - 4x^2 - 29x -24
(x + 1)(x - 8)(x + 3)
Part B.
(x + 1)(x - 8)(x + 3) / x^2 - x - 2= (x + 3)(x - 8) / x - 2
g(x)= (x + 3)(x - 8) / x - 2= y= x - 3
Part C.
x=2.
Step-by-step explanation:
See images for more information, it wouldn't let me post it.
Can someone please solve 14 and 15
On a coordinate grid. AB has endpoints A(4,– 2) and B(x, y). The midpoint of AB (-3,1). What is the x-coordinate of point B?
Answer: -10
Step-by-step explanation:
Formula for mid point is :
Mid point = ( (x1+x2)÷2 , (y1+y2)÷2) )
So, X1 = 4
X2 = X
Y1 = -2
Y2 = y
Now, use the formula
(-3,1) = ( (4 + x)÷2 , (-2+y)÷2) )
Now divide the sides for yourself to solve for midpoint for X and y separately
-3 = (4+x) ÷ 2 and 1 = (-2+y) ÷ 2
This is because 3 is the x coordinate of the mid point of A and B , so we equate it to (4+x) ÷ 2 because this expression basically gives us the x coordinate of mid point of A and B. So we already have the x coordinate of midpoint which is -3 so we can use this to find X coordinate of point B
So then we solve it by multiplying the 2 with -3 which gives -6
-6 = 4+X
Shift 4 on the other side and it will become negative 4
-6-4 = X
X = -10
Help! Perimeter and Area please.
19.5+24+7.5 = 19.5+__+24 = ___+24=___
Answer:
7.5, 27, 51
Step-by-step explanation:
19.5 + 24 + 7.5 = 19.5 + 7.5 + 24 = 27 + 24 = 51
Step-by-step explanation:
19.5+24+7.519.5+7.5+2427+2451hope it helps.stay safe healthy and happy...Read the sentence from section "The Tetractys" The Greeks made mathematics rigorous- everything had to be proved logically. Which of the following words, if it replaced the word "rigorous" in the sentence above, would CHANGE the meaning of the sentence? A exact B precise C thorough D appealing
Evaluate the function, f(x) = 3x²-8
f(5x)
Answer:
[tex]f(x)=3x^{2} -40fx[/tex] i think
Step-by-step explanation:
Write a function g whose graph represents a translation 3 units down followed by a vertical shrink by a factor of 1/3
of the graph of f(x) = x
If a function 'f' is translated by 'k' units down, image function 'g' will be,
g(x) = h(x) - 3If the function 'g' gets shrink by a factor 'm', the new function 'k' will be,
k(x) = [tex]m[g(x)][/tex] where, 0 < m < 1Following these rules image of the function 'f' given in the question will be g(x) = [tex]\frac{1}{3}x-1[/tex]
Function given in the question is,
f(x) = xIf the function f is translated by 3 units down, image function 'h' will be,
h(x) = f(x) -3
h(x) = x - 3
If the image function is vertically shrink by a factor of k, equation of the image function will be,
g(x) = [tex]k[h(x)-3][/tex]
where, k = [tex]\frac{1}{3}[/tex],
g(x) = [tex]\frac{1}{3}}(x-3)[/tex]
= [tex]\frac{1}{3}x-1[/tex]
Therefore, image function will be [tex]g(x)=\frac{1}{3}x-1[/tex].
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Which is a step in the process of calculating successive discounts of 8% and 10% on a $50 item?
a. take 2% of $50
b. take 8% of $46
C. take 10% of $46
d. take 18% of $50
Answer:
C. take 10% of $46
Step-by-step explanation:
I took it on edge
Find the distance between the given points: (2, -2) and (-4, 7)
Answer:
[tex]3\sqrt{13}[/tex]
Step-by-step explanation:
Hi there!
We want to find the distance between the points (2, -2) and (-4, 7).
To do that, we can use the distance formula.
The distance formula is given as [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We have everything needed to find the distance, but let's label the values of the points to avoid any confusion
[tex]x_1=2\\y_1=-2\\x_2=-4\\y_2=7[/tex]
Now substitute those values into the formula and solve
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{(-4-2)^2+(7--2)^2}[/tex]
Simplify
[tex]\sqrt{(-4-2)^2+(7+2)^2}[/tex]
[tex]\sqrt{(-6)^2+(9)^2}[/tex]
Square the numbers under the radical
[tex]\sqrt{36+81}[/tex]
Add the numbers under the radical together
[tex]\sqrt{117}[/tex]
Simplify the square root
[tex]3\sqrt{13}[/tex]
Hope this helps!
If a number is odd, then it is an integer and a prime number.
Which is a counterexample for the conditional?
A. –2
B. 2
C. 7
D. 9
Answer:
B. 2
it is the only odd prime number
Solve y = x + 4 for x
(9th-grade Algebra 1)
Answer:
[tex]x=y-4[/tex]
Step-by-step explanation:
Solve for x by simplifying two sides of the equation then isolating the variable.
Hope this helps!
solve the equation. determine whether or not the equation has one solution, no solution, or infinitely many solutions. 6c+3=c-12
Can someone help please ?
Answer:
This equation has no solution.
