First Part
Given that
[tex]Volume = \frac{4}{3} \pi r^{3}[/tex]
We have that
[tex]Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{Diameter}{2})^{3} = \frac{4}{3} \pi 9^{3} = 972\pi cm^{3} \approx 3053.63 cm^{3}[/tex]
Second Part
Given that
[tex]Volume = \frac{4}{3} \pi r^{3}[/tex]
If the Diameter were reduced by half we have that
[tex]Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{r}{2}) ^{3} = \frac{\frac{4}{3} \pi r^{3}}{8}[/tex]
This shows that the volume would be [tex]\frac{1}{8}[/tex] of its original volume
Step-by-step explanation:First Part
Gather Information
[tex]Diameter = 18cm[/tex]
[tex]Volume = \frac{4}{3} \pi r^{3}[/tex]
Calculate Radius from Diameter
[tex]Radius = \frac{Diameter}{2} = \frac{18}{2} = 9[/tex]
Use the Radius on the Volume formula
[tex]Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi 9^{3}[/tex]
Before starting any calculation, we try to simplify everything we can by expanding the exponent and then factoring one of the 9s
[tex]Volume = \frac{4}{3} \pi 9^{3} = \frac{4}{3} \pi 9 * 9 * 9 = \frac{4}{3} \pi 9 * 9 * 3 * 3[/tex]
We can see now that one of the 3s can be already divided by the 3 in the denominator
[tex]Volume = \frac{4}{3} \pi 9 * 9 * 3 * 3 = 4 \pi 9 * 9 * 3[/tex]
Finally, since we can't simplify anymore we just calculate it's volume
[tex]Volume = 4 \pi 9 * 9 * 3 = 12 \pi * 9 * 9 = 12 * 81 \pi = 972 \pi cm^{3}[/tex]
[tex]Volume \approx 3053.63 cm^{3}[/tex]
Second Part
Understanding how the Diameter reduced by half would change the Radius
[tex]Radius =\frac{Diameter}{2}\\\\If \\\\Diameter = \frac{Diameter}{2}\\\\Then\\\\Radius = \frac{\frac{Diameter}{2} }{2} = \frac{\frac{Diameter}{2}}{\frac{2}{1}} = \frac{Diameter}{2} * \frac{1}{2} = \frac{Diameter}{4}[/tex]
Understanding how the Radius now changes the Volume
[tex]Volume = \frac{4}{3}\pi r^{3}[/tex]
With the original Diameter, we have that
[tex]Volume = \frac{4}{3}\pi (\frac{Diameter}{2}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{2^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{2 * 2 * 2} = \frac{4}{3}\pi \frac{Diameter^{3}}{8}\\\\[/tex]
If the Diameter were reduced by half, we have that
[tex]Volume = \frac{4}{3}\pi (\frac{Diameter}{4}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{4^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 4 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 2 * 2 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{8 * 8} = \frac{\frac{4}{3}\pi\frac{Diameter^{3}}{8}}{8}[/tex]
But we can see that the numerator is exactly the original Volume!
This shows us that the Volume would be [tex]\frac{1}{8}[/tex] of the original Volume if the Diameter were reduced by half.
Which of the binomials below is a factor of this expression?
121A^2 - 64B^2
A. 121A + 8B
B. 11A + 8B
C. 121A + 32B
D. 11A + 32B
Answer: 11A+8B
Step-by-step explanation:
a right triangle with a long leg (x+7) and a short leg with (x) and the hypothenuse is 13
Answer:
Area is 30cm^2 if thats what your asking
Step-by-step explanation:
Answer:
X = 5
Step-by-step explanation:
You need to use the Pythagorean theory to solve this question.
[tex] {13}^{2} = {x}^{2} + {(x + 7)}^{2} [/tex]
[tex]169 = {x}^{2} + ( {x}^{2} + 14x + 49)[/tex]
[tex]169 = 2 {x}^{2} + 14x + 49[/tex]
[tex]0 = 2 {x}^{2} + 14x + 49 - 169[/tex]
[tex]0 = 2 {x}^{2} + 14x - 120[/tex]
Now simply the equation by dividing everything by 2.
[tex]0 = {x}^{2} + 7x - 60[/tex]
[tex]0 = (x - 5)(x + 12)[/tex]
Now, you can find the possible solutions by setting each bracket to 0.
[tex]0 = x - 5[/tex]
[tex]5 = x[/tex]
OR
[tex]0 = x + 12[/tex]
[tex] - 12 = x[/tex]
However, a measurement on a triangle cannot be negative. Therefore, we can ignore -12 and say that the answer is x = 5.
Choose the multiplication problem that correctly shows partial products.
A) A
B) B
C) C
Answer:
B
Step-by-step explanation:
62x4=248
4x2=8
6x4=24 and carry the 0 and get 240
240+8=248 and you get B
A bag of chocolates is labeled to contain 0.384 pounds of chocolates. The actual weight of the chocolates is 0.3798 pounds. Are the chocolates heavier or lighter than the weight stated on the label?
Based on the information given the chocolates stated on the label is 0.0042-ounce lighter.
Weight:
Using this formula
Chocolate weight=Current weight-Actual weight
Where:
Current weight=0.384
Actual weight=0.3798
Let plug in the formula
Chocolate weight=0.384-0.3798
Chocolate weight=0.0042 ounce
In conclusion, the chocolates stated on the label are 0.0042-ounce lighter.
How can i find the answer to this question: simplify (7^5)^3
Answer:
Option D
Step-by-step explanation:
Given the following question:
[tex](7^5)^3[/tex]
To find the answer we simply have to apply the exponent rule and multiply the exponents.
[tex](7^5)^3[/tex]
[tex](a^b)^c=a^{bc}[/tex]
[tex]5\times3=15[/tex]
[tex]=7^{15}[/tex]
Your answer is "7^15" or option D.
Hope this helps.
Answer:
7^15
Step-by-step explanation:
We know that a^b^c = a^(b*c)
7^5^3
7^(5*3)
7^15
What is the slope-intercept equation for this line?
y = [?]x + ( )
Answer:
y=-x-3
Step-by-step explanation:
in what rate of interest rupees 4000 amounts to Rupees 6000 in 2 years
Answer:
Ans:25%
Step-by-step explanation:
In what rate of interest Rs 4000 amounts to Rs 6000 in 2 years? Ans:25%
What is the slope-intercept equation for this line?
y = [?]x+ [?]
Answer:
y= -x-3
Step-by-step explanation:
Teddy has two sisters. One of them is 3 years older than Teddy, the other one is 7 years younger than her only brother. How old was the older sisters when the younger sister was born
Lets let Teddy be x.
Sister 1: x+3
Sister 2: x-7
If we subtract the younger sister (sister 2) from the older sister (sister 1), we get:
x+3 - (x-7) = x+3 - x + 7 = 10
The older sister was 10 years old when the younger sister was born.
Remington is installing a fence around his
rectangular yard. His yard is 20 feet long
by 45 feet wide. If the fencing he picked
out costs $25 per foot, how much money
will be spent on the fence?
Answer:
$3,250
Step-by-step explanation:
Find the perimeter of the yard ( the distance around the yard).
A rectangle has two sides of each dimension.
The perimeter is 20 + 20 + 45 + 45 = 130 feet.
Now multiply the total feet by the cost per foot:
130 feet x 25 per foot = $3,250 total.
Find the area of the shaded polygons
NEED ASAP PLEASE!! THANK YOU
Answer:
168
Step-by-step explanation:
area of a trapezoid is
((a+b)/2)*h
((8+16)/2)*14
12*14 =
168
5. The graph of each function contains the given point. Find the value of 'c'.
y = -5x2 + c (2,-14)
42. A triangle has an area of 14 square inches. The height of the triangle is three inches more than the
base. What are the base and height of the triangle?
43. Jill has a small treasure box that is 6 inches long. It can hold a volume of 72 inches cubed, and the
width of the box is 5 inches less than twice the height of the box. What are the dimensions of the box?
44. Jessie is mowing her back yard that is in the shape of a right triangle. The shortest side is 7 meters
shorter than the second side, and the hypotenuse is 13 meters long. What are the lengths of the two
sides?
Answer:
Question 42
area of a triangle = 1/2 × base × height
Given:
area = 14 in²height = x + 3base = xSubstituting given values into the formula:
⇒ 14 = 1/2 × x × (x + 3)
⇒ 28 = (x + 3)x
⇒ 28 = x² + 3x
⇒ x² + 3x - 28 = 0
⇒ (x - 4)(x + 7) = 0
⇒ x = 4, x = -7
As length is positive, x = 4 only.
⇒ height = 4 + 3 = 7 in
⇒ base = 4 in
-----------------------------------------------------------------------------------------
Question 43
volume of a cuboid = length x width x height
Given:
volume = 72 in³length = 6 inheight = xwidth = 2x - 5Substituting given values into the formula:
⇒ 72 = 6 × (2x - 5) × x
⇒ 12 = (2x - 5)x
⇒ 12 = 2x² - 5x
⇒ 2x² - 5x - 12 = 0
⇒ (x - 4)(2x + 3) = 0
⇒ x = 4, x = -1.5
As length is positive, x = 4 only.
⇒ height = 4 in
⇒ width = 2(4) - 5 = 3 in
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Question 44
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = x - 7b = xc = 13 mSubstituting given values into the formula:
⇒ (x - 7)² + x² = 13²
⇒ x² - 14x + 49 + x² = 169
⇒ 2x² - 14x - 120 = 0
⇒ x² - 7x - 60 = 0
⇒ (x - 12)(x + 5) = 0
⇒ x = 12, x = -5
As length is positive, x = 12 only.
⇒ one leg = 12 m
⇒ other leg = 12 - 7 = 5 m
what value makes 3k– 6 < 12 true?
Answer: Any number smaller than 6
3k - 6 < 12
(Add six to both sides)
= 3k < 18
(Divide by 3 on both sides)
= k < 6
Also a side note that may be helpful in other similar problems: If you are dividing or multiplying by a negative number you have to flip the inequality sign.
BCD and EFG are shown below. Which of the following statements is true? Look at picture.
Answer:
(b) ∠EGF ≅ ∠BDC
Step-by-step explanation:
Angles D and G are both marked with double arcs, indicating they are congruent:
∠EGF ≅ ∠BDC
__
Other choices:
BD is the short segment between the marked angles. It has no "decoration." EF is the longer segment with a single hash mark decoration. These are not corresponding parts, so are not congruent. There is no right angle in these triangles, so the Pythagorean theorem is not applicable.
__
CD is the longest side, with no decoration. EF is the middle-length side with a single hash mark decoration. These are not corresponding sides.
Answer:
I don't know I'm sorry soo just try to work it out if u don't know how than ask someone you know okay, ur welcome.
What happens to the coordinates of a shape when the shape reflects about the x-axis? What happens to the
coordinates when the shape reflects about the y-axls? Explain.
Hey there!
Here's what happens to the coordinates of a point when it's reflected around the x-axis:
(x, y) --> (x, -y) or (x, -y) --> (x, y)
So the point's x-coordinate hasn't changed.
Here's what happens to the coordinates of a point when it's reflected around the y-axis:
(x, y)--> (-x, y) or (-x, y) --> (x, y)
So the point's y-coordinate hasn't changed.
Hope everything is clear.
Let me know if you have any questions!
Always remember: Knowledge is power!
Find the value of x. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth.
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{24+x}\\ a=\stackrel{adjacent}{24}\\ b=\stackrel{opposite}{32}\\ \end{cases}\implies (24+x)^2~~ = ~~24^2+32^2 \\\\\\ (24+x)(24+x)~~ = ~~24^2+32^2\implies \stackrel{F~O~I~L}{24^2+48x+x^2}~~ = ~~24^2+32^2 \\\\\\ 48x+x^2=32^2\implies x^2+48x-32^2=0\implies x^2+48x-1024=0 \\\\\\ (x-16)(x+64)=0\implies x= \begin{cases} 16~~\textit{\Large \checkmark}\\\\ -64 \end{cases}[/tex]
notice, we didn't use -64, since the value of "x" must be a positive value.
Cassie has 10 1/2 feet of string to make 15 beaded bracelets. She needs 9 inches of string for each bracelet. Does she have enough string to make all the bracelets? Explain. (1 foot = 12 inches)
Answer:
unfortunately one person will be without a bracelet
Please solve with explanation high points
Answer:
a. -2x^2 + 3x+5=y
b.-x^2 +5x-4=y
c.-x^2 +6x-12=y
Step-by-step explanation:
a.y=-2x^2 +bx+c
the points P and Q lie on curve
[tex]\left \{ {{-b+c=2} \atop {b+c=8}} \right.[/tex]
=> b=3, c=5
b. delta = b^2 +4c
x1= [tex]\frac{-b+\sqrt{b^{2}+4c } }{-2}[/tex] =4
=> [tex]b-\sqrt{4c+b^{2} }[/tex]=8
x2=[tex]\frac{-b-\sqrt{b^{2}+4c } }{-2}[/tex]=1
=>2=b+[tex]\sqrt{b^{2}+4c }[/tex]
suppose : [tex]\sqrt{b^{2}+4c }[/tex] = a
=> [tex]\left \{ {{a+b=2} \atop {-a+b=8}} \right.[/tex]
=> a=-3
b=5
a=-3 => [tex]\sqrt{b^{2}+4c }[/tex] =-3 => b^2 +4c =9 =>5^2 +4c=9 => c=-4.
c.vertex (3;-3)
[tex]\frac{-b}{-2}[/tex]=3 => b =6
[tex]\frac{-D}{4a}[/tex]=[tex]\frac{-b^{2}+4ac}{-4}[/tex] =-3 =>-b^2+4ac=12 => c=-12.
Which of these describes an angle?
Extends in both directions with no end
The amount of turn between two straight lines that have a common endpoint, or vertex
A part of a line that connects two endpoints
Has a start point but no endpoint
i need help with this problem
Answer:
Disagree
Step-by-step explanation:
because it looks like less than 45
Phoebe rounded a number to the nearest tenth and got 6.5. When she rounded it to the nearest whole number, she got 7. Which number could be the number she rounded?
Answer:
6.7
please give brainliest
Divide.
4^2.4^6
O 4-3
O 4^3
O 4-4
O 4^4
The answer is C, 4^4
Step-by-step explanation:
no, the answer is definitely NOT 4⁴.
4² is smaller than 4⁶, right ?
so, 4²/4⁶ must be smaller than 1.
remember, what we do with exponents when we multiply terms ? we add the exponents.
like 4²×4⁶ = 4⁸
and when we divide terms ? we subtract the exponents.
4²/4⁶ =
[tex] {4}^{ - 4} [/tex]
because 2 - 6 = -4
A bead is formed by drilling a cylindrical hole of 2mm diameter through a sphere with an 8mm diameter. Estimate the volume of the bead to the nearest whole?
Volume of the bead = Volume of the sphere - volume of the cylindrical hole = 242.95 mm³.
What is the Volume of a Sphere and a Cylinder?Volume of a sphere = 4/3πr³Volume of a cylinder = πr²hVolume of the bead = Volume of the sphere - volume of the cylindrical hole
= 4/3π(4³) - π(1²)(8)
= 268.08 - 25.13
Volume of the bead = 242.95 mm³
Learn more about volume of sphere on:
https://brainly.com/question/22807400
The answer to this math question is?
Answer:
58 seconds
Step-by-step explanation:
Very very easy, no formulas or +,- required here.
You can see that the swim times go till 44 on the line, that is the lowest, that means the FASTEST swim time. But we need the slowest swim time. That we can find by finding where does the line end in the right side. We can see it ends between 56 and 60, and if we calculate, then we can find out that the bar in the middle represents 58, so hence, her slowest timing for her swim time is 58 seconds.
So hence, your answer is 58 seconds!
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If you see someone without a smile, give them one of yours!
Thanks!
~MiniMeteorologist~
Have a great day!
:D
Alexandra deposited $1,000 in
a savings account
Her
savings account pays 3.5% simple
interest. How much interest will the
account earn in 5 years?
My answers are
A. 35.00
B. 145.00
C . 175.00
D . Not here
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (1000)(0.035)(5)\implies I=175[/tex]
Use the graph of triangle JKL to answer A and B
a. Reflect JKL over the x-axis. Record the coordinates of
the original and new image below.
b. Describe what happened to the x and y coordinates
once they were reflected.
2 Use the coordinates of triangle QRS to answer a-b.
Answer:
a) J':(-7,7) K':(-5,2) L':(-2,3)
b) The x coordinates remained the same, the y coordinates swapped from negative to positive.
Step-by-step explanation:
Aside: I'm using J', K', and L' to denote the new locations of J,K,L after the reflection.
When an object is reflected over the x-axis, it means it's positive points will flip to negative y space, and negative points will flip to positive y space.
That said, J, for instance, will have the same X-coordinate, but its Y-coordinate will flip from negative to positive. Doing this with every vertex mirrors the triangle over the X-axis.
Therefore, J:(-7,-7) will become J':(-7,7), and likewise with K and L becoming K':(-5,2) and L':(-2,3).
Answer:
Step-by-step explanation:
find the average of the following numbers -34 and -37
Answer:
35.5 is the average of 34 and 37
Step-by-step explanation:
Answer:
-35.5
Step-by-step explanation:
-34 + -37 = -71
-71/2 = -35.5
I hope this helps!
Select the correct answer.
Which of the equations below represents a line perpendicular to the x-axis?
OA
I = 3
OB.
= = 3y
Зу
Ос.
1 = Y
=
OD
r = -3y
Answer:
0D r equals -3y
hope ts helpful
What is the slope of the line defined by the equation y = 5x + 3?
A) 3/5
B) 5/3
C) 3
D) 5
Answer:
D) 5
Step-by-step explanation:
5 is the rise. x or 1 is the run. (0,3) is the start location.