Answer:
Step-by-step explanation:
Let x be the number.
6 times the number = 6*x = 6x
Sum of 6 times of a number and twelve = 6x + 12
Three-fourths of the sum of 6 times of a number and twelve = [tex]\frac{3}{4}(6x +12)[/tex]
[tex]\frac{3}{4} ( 6x + 12) = \frac{3}{4}*6x + \frac{3}{4}*12\\\\[/tex]
[tex]= \frac{3}{2}*3x + 3*3\\\\=\frac{9}{2}x + 9[/tex]
Find the volume of the solid whose base is the region Ix I Iy I < 1 and whose vertical cross sections perpendicular to the y-axis are semicir- cles (with diameter along the base) g
Answer:
volume of the solid = [tex]\frac{\pi }{3}[/tex]
Step-by-step explanation:
As given , the region : |x| + |y| [tex]\leq[/tex] 1
when y [tex]\geq[/tex] 0 ,
|x| + y = 1
⇒|x| = 1 - y
when y ≤ 0 ,
|x| - y = 1
⇒|x| = 1 + y
The given region is the rectangle with sides (0, 5) , (0, -5), (5, 0), (-5, 0)
As given , the vertical cross section are semicircle
As we know that the area of semi circle = [tex]\frac{1}{2}[/tex][tex]\pi x^{2}[/tex]
Now,
Volume = [tex]\int\limits^0_-1 {\frac{\pi }{2} (1+y)^{2} } \, dy[/tex] + [tex]\int\limits^1_0 {\frac{\pi }{2} (1-y)^{2} } \, dy[/tex]
= [tex]\frac{\pi }{2} (\frac{(1+y)^{3} }{3} )[/tex] - [tex]\frac{\pi }{2} (\frac{(1-y)^{3} }{3} )[/tex]
= [tex]\frac{\pi }{6}[/tex][1-0] - [tex]\frac{\pi }{6}[/tex][0-1]
= [tex]\frac{\pi }{6} + \frac{\pi }{6} = 2\frac{\pi }{6} = \frac{\pi }{3}[/tex]
⇒volume of the solid = [tex]\frac{\pi }{3}[/tex]
Volume of the solid is the value of the capacity of the object that can be hold by it. Thus the value of the volume of the given solid is,
[tex]V=\dfrac{\pi}{3} [/tex]
Given information-The vertical cross sections of the solid is perpendicular to the y-axis.
The region of the base is,
[tex]|x|+ |y|\leq 1[/tex]
VolumeVolume of the solid is the value of the capacity of the object that can be hold by it.
When the value of the variable y is greater than or equal to zero than the value of the x is,
[tex]|x|=1-y[/tex]
When the value of the variable y is less than or equal to zero than the value of the x is,
[tex]|x|=1+y[/tex].
Given inequality makes a square with the corners (1,0), (0,1),(-1,0),(0,-1).
Now the limit for the given solid is between 0 to 1 and area is equal to the semicircle which is,
[tex]A=\dfrac{\pi x^2}{2} [/tex]
Thus the volume of the solid whose area bounded by the region 1 to -1 and vertical cross section is semicircle can be given as,
[tex]V=\int\limits^1_0 {\dfrac{\pi x^2}{2} } \, dx [/tex]
[tex]V=\dfrac{\pi}{2} [\;\;\int\limits^1_0 {(1+y)^2} \, dy +\int\limits^1_0 {(1-y)^2} \, dy ][/tex]
[tex]V=\dfrac{\pi}{2} [\;\;\dfrac{\int\limits^1_0 {(1+y)^3}}{3} \, +\dfrac{\int\limits^1_0 {(1-y)^3} \, }{3} ][/tex]
[tex]V=\dfrac{\pi}{6} [\;\;\ {(1-0)^3} \, +{(0-1)^3} \, ][/tex]
[tex]V=\dfrac{\pi}{3} [/tex]
Thus the value of the volume of the given solid is,
[tex]V=\dfrac{\pi}{3} [/tex]
Learn more about the volume of the solid here;
https://brainly.com/question/2254156
Pls help quick………… Math
A surf shop charges $6 to rent a wetsuit and $12 per hour to rent a surfboard. Write a function to model the cost, c, to rent a wetsuit and surfboard for h hours.
Answer:
c(h)=12h+6
because the swimsuit only needs to be paid for once, whereas the surfboard is charged on an hourly basis
What force is affected when the distance between two objects remains the name and the mass of each object is doulod?
HELP quick
Answer:
gravitational force or A the first one
Step-by-step explanation:
Answer:
Step-by-step explanation:
it a
What is the slope of the line? question 3
Answer:
slope =1
Step-by-step explanation:
hope it help you
Answer:
Undefined.
Step-by-step explanation:
The x-coordinates of the points along the straight line are always 1.
slope = change in y-coordinate/change in x-coordinate.
Since the change in x-coordinate is 0 (1-1=0), the denominator in the above will be 0 and the fraction (i.e. the slope) would be undefined.
help due in 15min
Simplify each expression
2(x + 4) - 3(y + 2x)
2d + 3(4d + 2k) - 3k
5(4m - 2r + 7) + 4m + 3r
Answer:
The last lines are the final answers, if you need a deeper explanation let me know but I wanted to make sure you understood and got it in time.
Step-by-step explanation:
2(x+4)-3(y+2x)
2x+8-3y-6x
-4x-3y+8
2d+3(4d+2k)-3k
2d+12d+6k-3k
14d+3k
5(4m-2r+7)+4m+3r
20m-10r+35+4m+3r
24m-7r+35
I hope I didn't get anything wrong in a hurry!
what is the decimal rounded to the nearest thousand of 369/460
Answer:
Step-by-step explanation:the answer is 0.8020
I will give brainiest to whoever answers correctly !!
Answer:
April 25 150 days
Step-by-step explanation:
f(x) = –22 + 10x – 2
Find f(-5)
Answer:
f(-5) = -74 you have to change the x to -5 and then solve
Julie's manager proposes a new pay rate. The manager says that Julie can make her original pay rate for the first
hours she works each day and that for any hours over the first 8 in each day she will be paid double ber bourly
rate. Explain how you would find her weekly earnings using this method
Step-by-step explanation:
Because he always do that non sense thing by this true method and always shout it when they will go from their house
HELP MY MOM IS GOING TO KILL ME
Answer:
−a2+17b
Step-by-step explanation:
What is the radian measure of an angle equal to 225 ?
A city has a population of 390,000 people. Suppose that each year the population grows by 6%. What will the population be after 15 years?
Use the calculator provided and round your answer to the nearest whole number.
Answer:
uh 351,000? im not sure..
Step-by-step explanation:
What is 86 + (-32) ?
Answer:
54
Step-by-step explanation:
Answer:
54
Step-by-step explanation:
Adding a negative number is the same thing as subtracting a positive number, so 86 + (-32) is the same thing as 86 - 32, which is 54.
i give 10 points and brainliest
Answer:(5,-9)
Step-by-step explanation:
Enter the product.
0.76 x 1,000 =
Answer:
760
Step-by-step explanation:
this is the answer you just add zeros and move the decimal
What is the volume of the rectangular prism?
Answers:
2/9 FT 3
10 FT 3
1 1/9 ft 3
3 1/3 FT 3
Answer:
3 1/3 FT 3
Step-by-step explanation:
im not sure if this right but i tried lol
Answer:
There is not enough info you need to add a picture of the box to measure it.
I'll give the brainiest IF you answer this correctly.
Answer:
Um the North China Plain
Step-by-step explanation:
Is dis math...
Please can you help on this question?!!!!!
Answer: let's try 2.2 for the first one (sorry if i make you get it wrong but i tried)
Step-by-step explanation:
Find 3.5% of 950 g.
Answer:
33.25 g
Step-by-step explanation:
Answer:
33.25 g
plz refer to the picture
alicia runs 5 miles in 40 minutes, if she ran at the same rate. how long would it take her to run 2 miles
Answer:
15 miles
Step-by-step explanation:
if she runs 5 miles in 40 minutes her average speed is 5÷40 = 0.125 miles per min
2 hours = 60 mins × 2 = 120 mins
if she runs 0.125 miles per minute, then 2 hrs = 120 mins × 0.125 = 15 miles
5. In the right triangle shown below, the length of side AB is x, the length of side BC is x + 2, and the length of the
hypotenuse AC is x + 4. Use this information to find the length of each side. (Use the Pythagorean theorem to get
an equation, and solve for x.)
I need an answer quick!!!
It’s from the problem set to lesson 17 M.1
Answer:
[tex]AB = 6[/tex] [tex]BC = 8[/tex] [tex]AC = 10[/tex]
Step-by-step explanation:
The picture of the triangle is missing.
Given
[tex]AC = x + 4[/tex]
[tex]BC = x + 2[/tex]
[tex]AB = x[/tex]
Required
Find x
When Pythagoras theorem is applied, we have:
[tex](AC)^2 = (BC)^2 + (AB)^2[/tex]
This is so, because AC is the hypotenuse
So, we have:
[tex](x+4)^2 = (x+2)^2 + x^2[/tex]
Open brackets
[tex]x^2 + 4x + 4x + 16 = x^2+2x + 2x + 4 + x^2[/tex]
[tex]x^2 + 8x + 16 = x^2+4x + 4 + x^2[/tex]
Collect Like Terms
[tex]x^2 -x^2 - x^2 + 8x -4x + 16 - 4 = 0[/tex]
[tex]- x^2 + 4x + 12 = 0[/tex]
Expand:
[tex]- x^2 + 6x -2x+ 12 = 0[/tex]
Factorize:
[tex]-x(x -6) -2(x- 6) = 0[/tex]
[tex](-x -2)(x- 6) = 0[/tex]
Split
[tex]-x - 2 = 0[/tex] or [tex]x - 6 = 0[/tex]
[tex]-x = 2[/tex] or [tex]x = 6[/tex]
[tex]x =-2[/tex] or [tex]x = 6[/tex]
Because [tex]BC = x + 2[/tex] and [tex]AB = x[/tex]
[tex]x =-2[/tex] can not be considered.
Hence:
[tex]x = 6[/tex]
Substitute 6 for x in
[tex]AC = x + 4[/tex]
[tex]BC = x + 2[/tex]
[tex]AB = x[/tex]
[tex]AC = 6 + 4[/tex]
[tex]AC = 10[/tex]
[tex]BC = 6 + 2[/tex]
[tex]BC = 8[/tex]
[tex]AB = 6[/tex]
Find the remainder when f(x) = (3x + 10x² + x - 2) divided by (x + 3)
What interval notation represents the data graphed below?
A. [-∞, -2) U [4, ∞]
B. [-∞, -2] U (4, ∞]
C. (-∞, -2] U (4, ∞]
D. (-∞, -2) U [4, ∞)
Answer: Choice D
[tex](-\infty, -2) \cup [4, \infty)[/tex]
=====================================================
Explanation:
The left portion is the interval (-∞, -2)
This is a shorthand way of saying [tex]-\infty < x < -2[/tex]
The curved parenthesis says "do not include this endpoint as part of the solution set". Note the open hole at x = -2 in the diagram.
In contrast, the value x = 4 is included (due to the filled in circle), so we use a square bracket for this endpoint. Therefore, the right-hand portion is represented by [4, ∞) which translates to [tex]4 \le x < \infty[/tex]
Negative and positive infinity will always use a parenthesis, and never a square bracket. This is because we can only approach infinity but never reach it, so we cannot include it as an endpoint.
All of this builds up to the full interval notation to be [tex](-\infty, -2) \cup [4, \infty)[/tex]
The only square bracket is near the 4; everything else is a curved parenthesis. This is why choice D is the final answer.
HELP FAST PLS-
10 is what percent of 118?
PLEASE SHOW ALL YOUR WORK
Answer:
10 is ≈8.47% of 118
Step-by-step
(10/118)(100)
write the standard number 723,600 in scientifict notation
Answer:
723,600 = 7.236 × [tex]10^{5}[/tex]
Step-by-step explanation:
Scientific notation is a way to express numbers in a form that makes numbers that are too small or too large more convenient to write. It is commonly used in mathematics, engineering, and science, as it can help simplify arithmetic operations.
Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens. The girls plan to play as many games as they can before running out of tokens. Let m represent the number of games that require 2 tokens; n represent the number of games that require 3 tokens; and p represents the number of games that require 4 tokens.
Janie plays the 3-token game four times. Write two equivalent expressions to represent the number of tokens that Janie will need to play each of the three games at least one time.
12
3 + 3 + 3 + 3 = 12
3 x 4 = 12
Thanks!! <3
if Pentagon ABCDE was dilated to create Pentagon A'B'C'DE', what rule was used?
a- (x,y) -> (-5,7y)
b- (x,y) -> (5/2x,5/2y)
c- (x,y) -> (5x,5y)
d- (x,y) -> (5/2x,7/3y)
Answer:
B [tex](x,y) \rightarrow \left(\frac{5}{2}x,\frac{5}{2}y\right)[/tex]
Step-by-step explanation:
Dilations
Given a point A(x,y) and a scale factor k the dilated image of A, called A' is calculated as A'=(kx,ky), assuming the same scale factor is applied in both axes.
The pentagon ABCDE was dilated to create pentagon A'B'C'D'E'. To find the dilaton rule used, we must find two clear points where the coordinates of both axes can be easily read from the graph.
Point C(-2,0) maps to C'(-5,0). This gives us the scale factor for the x-axis of -5/(-2)= 5/2.
The y-coordinate of E is 2 and the y-coordinate of E' is 5. This gives us the same scale factor for the y-axis of 5/2.
Thus, the rule to dilate the pentagon is:
B [tex]\mathbf{(x,y) \rightarrow \left(\frac{5}{2}x,\frac{5}{2}y\right)}[/tex]
Geometry pls halp... I have been asking this single question for over half an hour
Answer:
first one is SAS
Step-by-step explanation:
if tñ=2ñ+3, find S10
Answer:
[tex]S_{10}=280[/tex]
Step-by-step explanation:
Given that,
[tex]t_n=2n+3[/tex] ...(1)
We need to find the value of [tex]S_{10}[/tex].
Put n = 1 to find the first term.
[tex]t_1=2(1)+3=5[/tex]
Put n = 2 to find the second term.
[tex]t_2=2(2)+3=7[/tex]
Put n = 3 to find the third term.
[tex]t_3=2(3)+3=9[/tex]
Put n = 10 to find the tenth term.
[tex]t_{10}=2(10)+3=23[/tex]
It means we need to find the sum of 5,7,9,.....,23.
The formula for the sum of n terms is given by :
[tex]S_=\dfrac{n}{2}(a+a_n)[/tex]
We have, n = 10, a = 5 and [tex]a_n=23[/tex]
So,
[tex]S=\dfrac{10}{2}(5+23)\\\\S_{10}=10\times 28\\\\=280[/tex]
So, the value of [tex]S_{10}[/tex] is equal to 280.