The volume of the dilated prism is calculated to be considering scale factor for the area as well as the height is 7558272 cm³.
What is the dilation or scale factor?The scale factor in the dilation of a mathematical object determines how much larger or smaller the image will be (compared to the original object).
Given that
The base area of prism = 8 cm²
Height of the prism = 6
Scale factor = 54
So enlarged area =( scale factor )² * previous area = 54²* 8 = 23328 cm²
Enlarged height = 54*6= 324 cm
Enlarged volume = enlarged area* enlarged height = 7558272 cm³
Thus, the volume of the dilated prism is 7558272 cm³.
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If italic sin open parentheses 2 x close parentheses equal italic cos open parentheses x plus 30 degree close parentheses comma what is the value of x?.
Using complementary angles, it is found that the solution to the trigonometric equation is of x = 20.
What are complementary angles?Complementary angles are two angles whose measures add to 90º.
If two angles a and b are complementary, we have that the sine of one is the cosine of other, that is:
[tex]\sin{a} = \cos{b}[/tex]
In this problem, the equation is:
[tex]\sin{(2x)} = \cos{(x + 30)}[/tex]
Hence, they are complementary, which means that:
[tex]2x + x + 30 = 90[/tex]
[tex]3x = 60[/tex]
[tex]x = \frac{60}{3}[/tex]
[tex]x = 20[/tex]
The solution to the trigonometric equation is of x = 20.
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The school store has 1500 pencils in stock and sells an average of 50 pencils per day. The manager reorders when the number of pencils in stock is 500.
The manager will have to reorder in ___________ days
Answer:
20 days
Step-by-step explanation:
50 × 10 is 500, so double that to the reorder point (1000) making it 20 days.
HELP NEEDED ASAP I NEED HELLLLPPP
Answer:
x = 14
Step-by-step explanation:
(4y - 10) + 3x = 180
in other hand: 4y - 10 = 9x + 12
so : (9x + 12) + 3x = 180
9x + 3x = 180 - 12
12x = 168
x = 168/12
x = 14
A square has a diagonal of length 12. Find the length of each side.
Answer:
3
Step-by-step explanation:
12÷4=3
Hope this will help you!
What is the value of x?
Enter your answer in the box.
Answer:
x = 68 feet is your answer
consider the figures on the coordinate plane
Answer:
B.Figures A and C
Step-by-step explanation:
because if you trust god god will give enlightenment and also your smart and Beautifull.
You want to know the mean number of hours music students at your school practice each week. At each of three music classes you randomly survey 10 students. Your results are shown. Use all three samples to make one estimate for the mean number of hours music students practice each week. Round to the nearest hundredth if necessary. Hours Practiced Each Week A: 6, 5, 5, 6, 4, 6, 8, 5, 2, 6 B: 0, 6, 6, 5, 4, 5, 6, 3, 4, 9 C: 4, 5, 6, 4, 3, 2, 2, 3, 12, 1 The mean of all the sample data is hours.
The mean of a dataset is the average of the dataset
The mean of all the sample data is 4.67 hours
How to determine the meanThe datasets are given as:
Week A: 6, 5, 5, 6, 4, 6, 8, 5, 2, 6
Week B: 0, 6, 6, 5, 4, 5, 6, 3, 4, 9
Week C: 4, 5, 6, 4, 3, 2, 2, 3, 12, 1
The mean of a dataset is:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
Week A
[tex]\bar x_A = \frac{6+ 5+ 5+ 6+ 4+ 6+ 8+ 5+ 2+ 6 }{10}[/tex]
[tex]\bar x_A =5.3[/tex]
Week B
[tex]\bar x_B = \frac{0+ 6+ 6+ 5+ 4+ 5+ 6+ 3+ 4+ 9}{10}[/tex]
[tex]\bar x_B = 4.8[/tex]
Week C:
[tex]\bar x_C = \frac{4+ 5+ 6+ 4+ 3+ 2+ 2+ 3+ 12+ 1}{10}[/tex]
[tex]\bar x_C = 4.2[/tex]
Calculate the mean for the three weeks
[tex]\bar x = \frac{5.3 + 4.8 + 4.2}{3}[/tex]
[tex]\bar x = 4.76[/tex]
Hence, the mean of all the sample data is 4.67 hours
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help on perimeter pls
Answer:
59
Step-by-step explanation:
pls don't take my word as a final answer pls if u can do some more research
Thanks for the help!!
9) pi/3 = 180 /3 = 60⁰
the other angle = 90-60=30⁰
10) 2pi/9 = 360/9 = 40⁰
the other angle = 90+40=130⁰
11) arc length = 2pi * r * (θ/360)
= 2pi * 16 * (270/360)
= 75.4 km
12)arc length = 2pi * r * (θ/360)
3 * 180/4 = 135⁰
135/360 =0.375
2pi * 6 * 0.375 =14.13 in
13) arc length = 2pi * r * (θ/360)
= 9 *2pi *(255/360) =40.05 mi
14)arc length = 2pi * r * (θ/360)
=23.56 mi
When 16 is added to a number, it gave Rony the number 12. What will be the number that was added to 16?
Answer:
- 4
Step-by-step explanation:
let the number be n , then
16 + n = 12 ( subtract 16 from both sides )
n = - 4
Answer:
[tex]\displaystyle -4[/tex]
Step-by-step explanation:
Use Deduction to figure this out:
[tex]\displaystyle \boxed{-4} = -16 + 12[/tex]
I am joyous to assist you at any time.
for p(x) = 5x^3-2x^2+3x-6.is x=-1 is a root of p(x)?is x=1 is a root of p(x)
Answer:
just x = 1 is a root.
Step-by-step explanation:
p(-1) = 5(-1)³ - 2(-1)² + 3(-1) - 6 = -5 - 2 - 3 - 6 = -26
so x= -1 isn't root for p(x)
p(1) = 5(1)³ - 2(1)² + 3(1) - 6= 5 - 2 + 3 - 6= 0
so x = 1 is a root for p(x)
What is the equation of the line that passes through the point (5, -6) and has a
slope of -3/5?
if u dont know the answer then dont say nothing if u do pls help
answer:
x = 0.875
explanation:
4 ( 5 - 7x ) = 6 - 12x20 - 28x = 6 - 12x20 - 6 = -12x + 28x14 = 16xx = 14/16x = 7/8x = 0.875a1 = -2 r=-2 Sn=22 Determine the number of terms of n in the series
A series can be an arithmetic series or geometric series
The series is undefined
How to determine the number of terms?The given parameters about the geometric series are:
a1 = -2 --- the first term
r=-2 --- the common ratio
Sn=22 --- the sum of n terms
The sum of n terms of a geometric series is represented as:
[tex]S_n = \frac{a(r^n - 1)}{(r-1)}[/tex]
Substitute known values
[tex]22 = \frac{-2((-2)^n -1)}{(-2-1)}[/tex]
This gives
[tex]22 = \frac{-2((-2)^n -1)}{(-3)}[/tex]
Divide both sides by -2
[tex]-11 = \frac{((-2)^n -1)}{(-3)}[/tex]
Multiply both sides by -3
[tex]33 = (-2)^n -1[/tex]
Add 1 to both sides
[tex](-2)^n = 34[/tex]
Take the natural logarithm of both sides
[tex]n\ln(-2) = \ln(34)[/tex]
Solve for n
[tex]n= \frac{\ln(34)}{\ln(-2) }[/tex]
The above number is a complex number.
Hence, the series is undefined
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Which equation is linear
Answer:
Step-by-step explanation:
How to identify a linear line:
has form: y = mx + c.A linear equation graphed looks like a straight line Has constant slope value.the degree of a linear function is oneBased on our previous information:
The answer is the first choice since the equation holds the form y = mx + c and has a degree of one and has a constant slope value.
Hope that helps!
I am taking a test tomorrow in math and it's on probability, I am having trouble with want that is can someone help and try and explain it to me better then my math teacher?? an example problem, If I have I have 8 M&Ms 2 red, 3 blue and 3 green, and it the change of getting a red M&M? I think it would be 2/8 but I know I probably wrong
Answer:
1/4
Step-by-step explanation:
probability is the number of possible solutions over the number of outcomes, so in this example, you would take the 2 possibilities of getting a red M&M, and pot it over all the possible M&Ms you could get, so it is 2/8, which simplifies to 1/4, so you are correct
Monomials. Pls hurry. I have a test.
(3p^7)^4
Answer:
81p^28
Step-by-step explanation:
3^4=81
7 times 4 =28
Which choice is a linear function?
Explain
Please Help
Answer:
Option C
Step-by-step explanation:
Given the following question:
Using the process of elimination, we can find the answer:
It's not option A, because in order for a table to be a linear function the change of x, and the change of y have to be constant. In this case our change in y goes through -2, to -1. Which means option A is not a linear function.
It's not option A because again in order for a table to be a linear function the change of x and the change of y have to be constant. In this case our change of x is constant but our change in y isn't.
It's not option D because in order to have a linear function, you have to be able to rewrite the function into slope intercept (y = mx + b) in this case we only have one real number which is 12, while having our x, and y variable. Which means option D isn't a function.
Which leaves option C or "4x + 3y = 12" which is your answer, because it can be rewritten in slope intercept form.
Hope this helps.
PLEASE HELP!!
The length of a square is 4x-3, find the area in terms of x
Answer:
16[tex]x^{2}[/tex]−24x+9
Step-by-step explanation:
A=s^2
s=4x-3
A=(4x-3)^2
(a-b)^2=a^2-2ab+b^2
A=16x^2-2(12x)+9
A=16x^2-24x+9
7/8-1/2 it’s a homework question and I can’t get it
Answer:
the answer is 3/8
Step-by-step explanation:
multiply 7 by 2, and get 14
multiply 1 by 8, and get 8
give both terms new denominators which will be 16
The new fraction will be [tex]\frac{14}{16} - \frac{8}{16}[/tex]
Now you can subtract the numerators which will give you 6/16
Now you would simplify the fraction
Divide the fraction by 2 and you get 3/8 which is your answer
Hope this helps:)
you have deposited $400 in a simple interest savings account which place 3% interest annually.
Find the amount of interest for 0, 5, 10, 15, and 20 years.
Add the interest to $400 and fill in the table round the amounts to the nearest dollar.
Answer:
0 years: $0
5 years: $460
10 years: $520
15 years: $580
20 years: $640
Step-by-step explanation:
can you guys please help me on my homework? It would mean a lot to me :)
Answer:
For the top half add all of the numbers of a given set together, then divide by how many numbers there are.
1.) 9
2.) 7
3.) 4
4.) 3
5.) 47.5
6.) 67 1/3
For the bottom half questions, literally the same thing.
7.) 9
8.) 34
9.) 66
10.) -28
11.) -21
12.) 3
Step-by-step explanation:
your welcome for doing you 2 minute homework
what is 1875 ÷ 125 (show ur work do long divison)
answer is 15 explained in image .
Camp Oaks gets 32 boxes of Orange juice and 56 boxes of apple juice. Each shelf in the cupboard can hold 8 boxes of juice. What is the least number of shelves needed for all the juice boxes.
Answer:
do 56x32=1792 then divide it by 8 1792/8=224 that is the least number of juice's for the shelves step-by-step explanation:
Quadrilateral A B C D is translated up and to the right and then is rotated 180 degrees about point Q to form quadrilateral X Y Z W. Quadrilateral ABCD is translated up and to the right, and then rotated about point Q. Which congruency statement is correct? ABCD ≅ WXYZ ABCD ≅ ZYXW ABCD ≅ WZYX ABCD ≅ ZWXY.
When a triangle is translated, the resulting triangle will be congruent to the original triangle.
The congruency statement is ABCD = ZYXW
Given
Quadrilateral ABCD is translated up and to the right and then is rotated 180 degrees about point Q to form quadrilateral XYZW.
Quadrilateral ABCD is translated up and to the right and then rotated about point Q.
What is translation?When a triangle is translated, the resulting triangle will be congruent to the original triangle.
From the complete question, corresponding points are:
Point A and point Z
Point B and point Y
Point C and point X
Point D and point W
This means that:
Points A and Z are corresponding.
Points B and Y are corresponding.
Points C and X are corresponding.
Points D and W are corresponding.
Hence, the congruency statement is ABCD = ZYXW
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Answer:
B
Step-by-step explanation:
How many dots are there at 100 minutes?
Answer:
I need more information.
Step-by-step explanation:
Answer:
401
Step-by-step explanation:
i know the answer cuz i did this before.
The pattern is that for every minute four dots are added diagnally. To find how many doths there are at 100 minutes we will multiply 4 x 100 and then add one for the dot e started at. 4 x 100 = 400 + 1 = 401
At 100 minutes there will be 401 dots.
What is the derivative of Cos(x) when x is measured in degrees?.
Answer:
- sinx
Step-by-step explanation:
This is a standard derivative and applies to angles in degrees or radians.
[tex]\frac{d}{dx}[/tex] (cosx ) = - sinx
Answer:
[tex]\huge\purple{- \frac{\pi}{180}\sin \: \bigg( \frac{\pi x}{180}\bigg)}[/tex]
Step-by-step explanation:
[tex]x \degree = \frac{\pi x}{180} \\ \\ \implies \: \cos \: (x \degree) = \cos \:\bigg( \frac{\pi x}{180}\bigg) \\ \\ \implies \: \frac{d}{dx} \cos \: (x \degree) = \frac{d}{dx} \: \cos \: \bigg( \frac{\pi x}{180}\bigg) \\ \\ = - \sin \: \bigg( \frac{\pi x}{180}\bigg)\frac{d}{dx} \bigg( \frac{\pi x}{180}\bigg) \\ \\ = - \sin \: \bigg( \frac{\pi x}{180}\bigg) \bigg(\frac{\pi}{180}\bigg) \\ \\ \huge \red{= - \frac{\pi}{180}\sin \: \bigg( \frac{\pi x}{180}\bigg)}[/tex]
25 POINTS. If 16 ounces of chlorine are needed in a 12,500-gallon pool, how many ounces of chlorine are needed in a 5,000-gallon pool?
7.6 ounces
3.2 ounces
6.4 ounces
5.9 ounces
Answer:
6.4 ounces
Step-by-step explanation:
Q6. NON-CALCULATOR
x + 2/3x +
x-2/2x =3
in file
Step-by-step explanation:
PLS HURRY!
What is the lowest value of the range of the function
shown on the graph?
5
4
- od
3
0-2
2-
Ο Ο
1
O 3
-5 -4 -3 -2 -11
1 2 3 4
5
х
-2
-3
-4
+ >
Answer: -2
Step-by-step explanation: