Answer:
n³ + 4n² - 8n - 9
Step-by-step explanation:
(2n³ + 4n² - 7) + (-n³ - 8n - 2)
2n³ + 4n² - 7 - n³ - 8n - 2
2n³ - n³ + 4n²- 8n - 7 - 2
n³ + 4n² - 8n - 9
Please simplify 53/-18.75
Answer:
53/-18.75 = -2.82666
Step-by-step explanation:
hope this helps :)
Answer:
[tex] \frac{53}{ - 18.75} = \frac{5300}{ - 1875} = - 2.826[/tex]
I hope I helped you^_^
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.
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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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
44. Consider all rectangles with an area of 182 square feet. Letzbe the length of ene side of such a
rectangle
a) Express the perimeter as a function of
b) Use the graphing calculator to find the dimensions of the rectangle that
has the least perimeter. What is the least perimeter?
Answer:
Image result for 44. Consider all rectangles with an area of 182 square feet. Let's Be the length of one side of such a rectangle a) Express the perimeter as a function of b) Use the graphing calculator to find the dimensions of the rectangle that has the least perimeter. What is the least perimeter?
Divide the area of the rectangle by the width in order to find the length of 14 feet. The perimeter is the sum of the side lengths, which in this case is 14 feet + 4 feet +14 feet + 4 feet, or 36 feet.
Factorise 3x²+5x-12
Show working out
hi <3
i'm not sure of which method you will have been taught but i'll try to explain the method i was shown.
so, you need to multiply the coefficient of x^2 by the last value
3 x -12 = -36
now, you need to find two values that multiply to make -36 but add to make 5.
9 and 4 would work. it would have to be positive 9 and negative 4, as these would subtract to give the 5 that you need
now we have:
(x - 4)(x + 9)
however, we need to achieve the 3 from somewhere so it needs to be divided somewhere
9 is divisible by 3 so you can divide it there. as 4 cannot divide by 3, you would move the 3 up to be the coefficient.
thus, your final answer would be:
(3x - 4)(x + 3)
hope this helps :)
Answer:
it's gonna be 3(X*2 + 4X - 4)
Step-by-step explanation:
Just factor out 3 from the expression
_______insurance is a policy that protects the financial responsibility of
owning a vehicle.
Answer:
Liability car insurance
Help ASAP, I’ll give brainliest
Show work ty
Step-by-step explanation:
A
3(6+15)
=3(21)
=63
B
5[15-(6+1)]
=5(8)
=40
B
⅓(15)
=5
C
⅓(6+15)
=⅓(21)
=7
E
15/6
=2/1/2 or 2.5
W
2(6)(15-3)
=2(7)
=36
L
4(⅓+⅓+⅓)
=4(1)
=4
L
6/15 - 15/6
=36/90 - 225/90
= -189/90
= -21/10
a boat travels 24 km in 90 minutes what's the average speed?
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 ASAP
Graph JKL and its image after a reflection in the line y=3.
Then give the points of the image.
J (3,-5)
K (4, -1)
L (0, -3)
I need the new coordinates for the reflection of the pre image.
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.
Learn more:
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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.
SHOW PROOF OR NUN and brainlyiest
64 less than a triple a number
Answer:3n-64
Step-by-step explanation:
[17 - 7] × 6 + 2 + 56 - 8
Answer:
110
Step-by-step explanation:
[17 - 7] × 6 + 2 + 56 - 8
10 × 6 + 2 + 56 - 8
60 + 2 + 56 - 8
62 + 56 - 8
118 - 8
110
Answer:
110
Step-by-step explanation:
[17 - 7] × 6 + 2 + 56 - 8
(10) x 6 + 2 + 56 - 8
60 + 2 + 48
62 + 48
110
Thirty-six thousand four hundred fifteen in standard form
Answer:
30000 + 6000 + 400 + 15
Step-by-step explanation:
Find the sum S below:
[tex] \displaystyle \large{S = \frac{2}{1 \cdot 3} + \frac{2}{3 \cdot 5} + \frac{2}{5 \cdot 7} + ... + \frac{2}{(2n - 1)(2n + 1)} }[/tex]
Please show your work too. Thanks!
You can use the same technique I showed in another one of your questions (24467305).
Partial fractions:
[tex]\dfrac2{(2n-1)(2n+1)} = \dfrac a{2n-1} + \dfrac b{2n+1} \\\\ \implies 2 = a(2n+1) + b(2n-1) = (2a+2b)n + a- b \\\\ \implies \begin{cases}2a+2b=0 \\ a-b = 2\end{cases} \implies a = 1, b=-1[/tex]
Then we have a telescoping sum,
[tex]S = \displaystyle \sum_{k=1}^n \frac 2{(2k-1)(2k+1)} \\\\ S = \sum_{k=1}^n \left(\frac1{2k-1} - \frac1{2k+1}\right) \\\\ S = 1-\frac13 + \frac13 - \frac15 + \cdots +\frac1{2n-3}-\frac1{2n-1}+\frac1{2n-1}-\frac1{2n+1} \\\\ S = 1 - \frac1{2n+1} = \boxed{\frac{2n}{2n+1}}[/tex]
(And in case you were actually interested in an infinite sum, we can see that this converges to 1 as n goes to ∞.)
I HAVE 5 MIN SOMEONE HELP?
Answer:
35• 43 m square is correct answer
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
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
What is the answer to this?
Answer:
true
Step-by-step explanation:
5(1+2x)= 5 +10x =10x + 5
Answer:
Yes, they are eqivelant.
Step-by-step explanation:
5(1+2x) and 10x+5
The first step is to set them equal to each other, to see if they are equivelent.
5(1+2x) = 10x+5
Distribute the 5 to both terms in the parentheses by multiplying.
5(1) + 5(2x) = 10x +5
5 + 10x = 10x +5
The communative property of addition proves that these are equal.
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
What is the value of f(-2) and f(3)
Answer:
Step-by-step explanation:
When answering questions like this, we have to first decide which function we have to use. This is done by looking at the given domains (the x≤-2 etc). The first question ( f(-2) ), means we have to choose the function that applies to the x-coordinate -2. x=-2 is part of the section x ≤-2 since the sign means larger or equal to -2. Hence, we use the function 2x+8 to calculate f(-2). After finding this, the solving is relatively easy, just fill in the x-coordinate:
f(-2) = 2 * -2 + 8 = -4 + 8 = 4
The second one needs the same method. x=3 belongs in the section
-2 < x ≤ 3, since the final part means x is smaller or equal to 3, and in this case it is. Hence we use [tex]x^{2} -3[/tex] here:
f(3) = 3² - 3 = 9 - 3 = 6
I hope this helps! Feel free to reach out if you still have questions
Multi-Step Two friends compare the amount of change they
have in their pockets. Ashley has 12 nickels, 2 dimes, and
4 quarters. Beto has 10 nickels, 4 dimes, and 3 quarters.
Who has more money?
Answer:
Ashley
Step-by-step explanation:
Ashley:
12n (n=5) = 60+2u (u=10)=80
4 quarters equal a dollar
$1.80
Beto:
10n (n=5)= 50+ 4u (u=10) = 90
3 quarters equal .75
$1.65
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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The average weight of the top 5 fish at a fishing tournament was 13.1 pounds. Some of the weights of the fish are shown in the table.
Answer:
The Heaviest fish weigh 15.3(lb)
Step-by-step explanation:
14.9 +12.5+11.6+11.2+x/5=13.1
50.2+x/5=13.1
65/5=13
65.5/5=13.1
65.5 -50.2 = 15.3
the sum of two rational numbers is -8. if one of the is -8/17, find the other
Answer:
The other number is -128/17
Step-by-step explanation:
Let the unknown number be x,
[tex] \tt \longmapsto \: x + \frac{ - 8}{17} = - 8[/tex]
[tex] \tt \longmapsto \: x = \frac{ - 8}{1} + \frac{8}{17} [/tex]
[tex] \tt \longmapsto \: x = \frac{ - 136 + 8}{17} [/tex]
[tex] \tt \longmapsto \: x = \frac{ - 128}{17} [/tex]
What is the midpoint of segment AB when A is at (5,7) and B is at (3,1)?
Answer:
(4, 4)
Step-by-step explanation:
A (5,7) and B (3,1)
To find the midpoint of a line segment, use this formula.
[tex]midpoint =(\frac{x^1+x^2}{2} ,\frac{y^1+y^2}{2} )[/tex]
(x1, y1) = coordinates of first point
(x^2, x^2) = coordinates of second point.
Basically, you add the coordinates x^1 and x^2, then divide the sum by 2. That would be your first coordinate.
Next, you add y^1 and y^2, then divide the sum by 2. That would be your second coordinate.
[tex]midpoint-(\frac{5+3}{2} ,\frac{7+1}{2})[/tex]
[tex]midpoint = (4, 4)[/tex]
Therefore, the midpoint of segment AB is (4,4).
Let me know if you have any further questions.
The midpoint of segment AB, when point A is located at (5, 7) and point B is located at (3, 1), is (4, 4).
The midpoint formula states that the coordinates of the midpoint between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are given by:
Midpoint = [tex]((x_1 + x_2)/2, (y_1 + y_2)/2)[/tex]
The coordinates of point A are given as (5, 7), and the coordinates of point B are given as (3, 1).
Plugging in the coordinates:
x-coordinate of the midpoint = (5 + 3)/2 = 8/2 = 4
y-coordinate of the midpoint = (7 + 1)/2 = 8/2 = 4
Therefore, the midpoint of segment AB is (4, 4).
Thud, the midpoint of segment AB, when point A is located at (5, 7) and point B is located at (3, 1), is (4, 4).
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Which relation is a function of x?
Answer:
I think the graph is the fourth choice
I hope I helped you^_^
