Answer:
Volume: x(x+6)(x+2) Area: [tex]x^{2}[/tex] + 8x +12
Step-by-step explanation:
Volume Explanation:
To find the volume of a 3d figure, we must multiply the length, width, and the height. Therefore we multiply (x)(x+6)(x+2)= [tex]x^{3}[/tex] + 8[tex]x^{2}[/tex] + 12x. Simplify this equation and we will get x(x+6)(x+2) for the formula to find the volume of the 3D figure.
Area:
To find the area of a 2D figure, we must multiply length x height. Therefore, we multiply the equations (x+6)(x+2)= [tex]x^{2} + 2x + 6x +12[/tex] to get a final answer of [tex]x^{2} +8x +12[/tex]. This will be the formula when you find the area of the 2D figure in question.
What is the length of the track, in miles, around turn A? Round your answer to three decimal places.
Answer:
?
Step-by-step explanation:
Please explain-WHAT TRACKS?
Answer:
5.275
Step-by-step explanation:
Got the answer from Emma on Gauth Math
How many centimeters in 3.7 kilometers?
Answer:
370,000 centimeters
Step-by-step explanation:
1. There are 1000 meters in a kilometer.
2. 3.7 kilometers x 1000 = 3,700 meters
3. There are 100 centimeters in a meter
4. 3,700 x 100 = 370,000 centimeters
A spring supporting a mass of 30 kg compresses 0.6 m. how far does the spring compress when it supports a mass of 10 kg? 0.1 m 0.2 m 1.2 m 1.8 m
The spring .2m far when it is compressed on being supported by a mass of 10kg.
Given: Mass of 30 kg which compresses spring by 0.6m
To find: The compression of the spring when it is supported by a mass of 10 kg
Concept: Compression springs are coiled springs that hold mechanical energy in a compressed state. When these springs are subjected to compressive loads, they compress and shorten, capturing and storing significant potential force.
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
By using unitary method,
10 is 3 times less than 30.
so, 30/3=10
Also applying the same proportion over the lengths compressed,
we get, 0.6/3=.2
For more information about unitary method, visit
https://brainly.com/question/24587372
#SPJ4
Problem
(a) Expand and simplify [tex](x^2+2)^2[/tex]
(b) Hence fully factorise [tex]x^4+4x+3[/tex]
Please do not give me irrelevant answers.
Answer:
a)
[tex](x^{2} + 2)(x^{2} + 2)\\x^{4} + 2x^{2} + 2x^{2} + 4\\= x^{4} + 4x^{2} + 4\\[/tex]
b)
[tex](x +1)(x + 1)(x^{2} -2x +3) = (x + 1)^{2} (x^{2} -2x +3)[/tex]
Which equation is a function of x? x = 5 x = y squared 9 x squared = y x squared = y squared 16
The equation which is a function of x is x²=y.
Given an equation that is a function of x.
A function may be a relation between a collection of inputs and a collection of permissible outputs with the property that every input is said to precisely one output.
If we input a value of x then we get the output f(x) = y, which is the function of x.
We are given four options out of which we are to pick the one which may be a function of 'x'.
The first option is x=5 in which no term of y is included and its a constant. So, option 1 is not correct.
The second option is x=y²+9 in which y contains a power 2. So, option 2 is not correct.
The third option is x²=y in which y contains power 1. So, option 3 is correct.
The fourth option is x²=y²+16 in which y contains a power 2. So, option 3 is not correct.
Hence, the equation which is a function of x is x²=y.
Learn about functions from here brainly.com/question/16614909
#SPJ4
Solve the inequality.
[tex]5x - 7 \leqslant 13 \\ add \: 7 \: on \: both \: sides \\ 5x - 7 + 7 \leqslant 13 + 7 \\ 5x \leqslant 20 \\ divide \: both \: sides \: by \: 5 \\ \frac{5x}{5} \leqslant \frac{20}{5} \\ x \leqslant 4[/tex]
Interval: (-infinity,4]MATH: FINDING HALF LIFE PT 1
Answer:
15.4 years
Step-by-step explanation:
An investment is doubled when it is twice its initial value. The equation can be solved for the value of t that makes this true.
SetupIn the exponential equation for investment value, the factor y₀ is the initial value of the investment. We want to find t when y = 2y₀.
2y₀ = y₀·e^(0.045t)
SolutionDividing by y₀ gives ...
2 = e^(0.045t)
Taking natural logarithms, we have ...
ln(2) = 0.045t
Dividing by the coefficient of t gives its value:
t = ln(2)/0.045 ≈ 15.4
The investment will be doubled after 15.4 years.
__
Additional comment
The continuously compounded interest rate for this investment is 4.5%. The doubling time is 0.693 divided by this: 0.693/0.045 ≈ 15.4. This relationship holds for any sort of continuous compounding.
Graph the function g.
f(x) = -2(x-4)² +4
g(x) = f(x) - 1
O
Answer:
19
Step-by-step explanation:
fx=16+4
fx=20
gx= 20-1
gx=19
19
If f(x) = x³ - 2, find f(3).
[tex]f(x) = x {}^{3} - 2 \\ f(3) = 3 {}^{3} - 2 = 27 - 2 = 25[/tex]
[tex]f(3) = 25[/tex]
Umm I don’t have 10 as a option
Answer: Look for the closes thing to 10
Step-by-step explanation:
If a + a = a then a = 0. prove
a+a=a
→a+a-a=0
→a=0
(proved)
Step-by-step explanation:
[tex]a + a = a[/tex]
[tex]2a = a[/tex]
[tex]2a - a = 0[/tex]
[tex]a = 0[/tex]
Proved.
5. Kal Tire installs automobile tires on a first-come first-served basis. A random sample of 50 customers experienced an average wait time of 93.7 minutes. Assume that the standard deviation of total wait time for all customers is 20.6 minutes. Determine the margin of error for a 95% confidence interval for this sample.
5.7099 is the margin of error.
What is standard deviation ?
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.
Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
According to the question,
The standard sampling error of the sample mean is σₓ ,
The sampling distribution is: N (u,σₓ/n)
Therefore,
By using the standard deviation formula:
σₓ = √∑(xi -μ)/N
Where,
∑= population standard deviation
N= the size of the population
xi= each value from the population
μ =the population mean
So ,
σₓ = [tex]\frac{20.6}{\sqrt{50} }[/tex] = 2.913
Since, a = 1- 95% = 0.05
therefore [tex]Z\frac{a}{2}[/tex] = (1-0.005 x 2) = 1.959964
Here, the margin of error for a 95% confidence interval for this sample is given by:
[tex]Z\frac{a}{2}[/tex] * σₓ = 1.959964 x 2.913
= 5.7099
5.7099 is the margin of error for a 95% confidence interval for this sample.
Learn more about standard deviation here:
https://brainly.com/question/13905583
#SPJ1
Craig ran 4 days last week. His distances were
3.25, 6.5, 7.25, and 10.5 kilometers. What was
his average distance per day for the 4 days?
-76 * a number minus 61 is equal to -89 less than the number
Answer: -211/76
Step-by-step explanation:
to solve this word problem equation, we need to first convert the words to numbers and variables we can solve for:
we can replace "a number" for a variable such as x
this gives:
-76·x-61=x+89
now all you have to do is solve the equation and you're done!
What is √200in simplest form?
Answer:
10√2
Step-by-step explanation:
The square root of 200 in its simplest radical form is 10√2.
If we know the prime factorization of a number, we can write the radical form of the square root of that number. As a result, the prime factorization of 200 is 2 × 2 × 2 × 5 × 5.
As a result, the square root of 200 in the simplest radical form should be 10√2.
MATH: FINDING HALF LIFE PT 2..HELP!
The half life of the radioactive Rutherford-265 is;
13.1 hours.
What is the half-life of the radioactive Rutherford-265?It follows from the task content that the given function represents the decay function of the radioactive material. Since half-life corresponds to the point at which only half of the starting material remains, hence we have;
(1/2) = e ^(-0.053t)
By taking the natural log of both sides, we have;
-0.6931 = -0.053t
Hence, t = -0.6931/ -0.053 = 13.1 hours.
Read more on half-life;
https://brainly.com/question/25750315
#SPJ1
Trigonometry Maths Question
80 points up for grabs!
Will mark brainliest to whoever answers
Answer:
x = 35.537677791974°
y = 63.434948822922°
Step-by-step explanation:
let x be the measure of the angle of elevation of the sun.
tan(x) = 10/14
Then
x = tan⁻¹ (10÷14) = 35.537677791974°
………………………………………………
let y be the measure of the angle of elevation of the sun
where the shadow decreases to 5m.
tan(y) = 10/5 = 2
Then
y = tan⁻¹ (2) = 63.434948822922°
Answer:
a) 35.54°
b) 63.43°
Given following:
length of pole: 10 meterits shadow: 14 meterDetermining, the shadow is adjacent side and length of the pole is the opposite side. Hence, use the tan rule. Let the angle be x.
(a)
[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]
[tex]\sf tan(x) = \dfrac{10}{14}[/tex]
[tex]\sf x = tan^{-1}(\dfrac{10}{14} )[/tex]
[tex]\sf x = 35.54^{\circ \:} \quad (rounded \ to \ nearest \ hundredth )[/tex]
(b) If the shadow decreases to 5 meter.
[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]
[tex]\sf tan(x) = \dfrac{10}{5}[/tex]
[tex]\sf x = tan^{-1} (\dfrac{10}{5})[/tex]
[tex]\sf x = 63.43 ^\circ \quad (rounded \ to \ nearest \ hundredth)[/tex]
Hi, need help please to get my HS diploma...did not graduate :(
Which of the following equations is written in standard form?
Answer:
The first answer
4x-2y=0
Whats the correct answer answer asap for brainlist
a2 − 6) and (a2 + 4) are the factors of
Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial whose factors are (a²-6) and (a²+4) is a⁴ - 2a² - 24.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Example: x²+3x+5 is a polynomial.
The polynomial whose factors are (a²-6) and (a²+4) is,
P(x) = (a²-6)(a²+4)
= a⁴ + 4a² - 6a² - 24
= a⁴ - 2a² - 24
Hence, The polynomial whose factors are (a²-6) and (a²+4) is a⁴ - 2a² - 24.
Learn more about Polynomials:
https://brainly.com/question/27343162
#SPJ1
Xin and Yvonne are standing 42 m apart. If they walk towards each other, they will meet after 12 seconds. If they walk in the same direction, Yvonne will catch up with Xin after one minute. It is given that Xin and Yvonne walk at constant speeds ofx m/s and y m/s respectively.
Form a pair of simultaneous equations in x and y.
Answer:
12(x+y)=42
60(y-x)=42
Step-by-step explanation:
12(x+y)=42 (12 seconds, x+y speed each second, 42 metres)
60(y-x)=42 (1 minute = 60 seconds, x-y speed each second, 42 metres)
PLEASE HELP!!!!!!!!!!
Step-by-step explanation:
[tex] = - \frac{5}{9} - ( - \frac{14}{15} )[/tex]
[tex] = - \frac{5}{9} + \frac{14}{15} [/tex]
[tex] = - \frac{5 \times 5}{9 \times 5} + \frac{14 \times 3}{15 \times 3} [/tex]
[tex] = - \frac{25}{45} + \frac{42}{45} [/tex]
[tex] = \frac{ - 25 + 42}{45} [/tex]
[tex] = \frac{42 - 25}{45} [/tex]
[tex] = \frac{17}{45} [/tex]
sally has a pet snail that fell into a well.The well is 16 feet deep. Each day the snail climbs up 5 feet, but each night slides down 4 feet. How many days will it take Sallys snail to get to the top of the well
Answer:
16 days
Step-by-step explanation:
OK, The pet snail only moves a foot per day because at night it falls again, SO ima going with 16 days.
[<Answer>] (2):
Hello! I'm Avery. And I'm here to help! :)
----------------------------------------------------------------------------------------------------------
[<The Explanation>}:
Sally has pet snail that fell into a well.
(Depth of the well = 16 feet)
Snail climbs up 5 feet but each night it slides back down 4 feet.
So the snail climbs up per day = 5 feet - 4 feet = 1 feet.
Number of days snail took to reach at 11 feet = 11 × 1 = 11 feet
Remaining distance to cover by the snail = 16 - 11 = 5 feet
Number of days to cover remaining 5 feet to reach the top of the well = 1 day
Therefore, snail will take 12 days to reach the top of the well.
----------------------------------------------------------------------------------------------------------
[<Ending>] <3
Hope this helps and if it's wrong, you can't sue me! :D
Bye! Hope this works for you :)
Have a nice day! - Avery <3
find the domain and range of the exponential function h(x) = 125x. explain your findings. as x decreases, does h increase or decrease? explain. as x increases, does h increase or decrease? explain.
We have an exponential growth. The domain is the set of all real numbers and the range is R: (0, ∞).
What can we say about the exponential function?Here we have the exponential function:
[tex]h(x) = 125^x[/tex]
Notice that the base, 125, is larger than 1, which means that we have an exponential growth.
So, as x increases, also does h(x).As x decreases, also does h(x).Now, the domain of any exponential equation is the set of all real numbers.
For the range, as x tends to negative infinity, the function will tend to zero.
And as x tends to infinity, h(x) also tends to infinity.
So the range is R: (0, ∞).
If you want to learn more about exponential equations:
https://brainly.com/question/11832081
#SPJ1
Compare the process of solving |x – 1| + 1 < 15 to that of solving |x – 1| + 1 > 15. Check all of the following you included in your response. Both absolute values would need to be isolated first. You would need to write a compound inequality for each. Both compound inequalities would compare x – 1 to –15 and 15. The inequality with “<” would use an “and” statement, while the “>” would use an “or” statement.
The required Comparison of the inequalities are
The |x – 1| + 1 > 15 represents the value of x lies between 13<x<15.The range of values encompassing the region's junction is (-13, 15).
If x is more than or equal to 15, then x-11+1>15 indicates the value of x is greater than or equal to 13. None of the regions in the intersection are empty.What is inequality?When comparing two numbers, an inequality indicates whether one is less than, larger than, or not equal to the other.
We take into account the various variables of the inequality
|x – 1| + 1 > 15
Therefore
|-x-1|+1-1<15-1
|-x-1|-1 <14
13<x<15
The required region lies between the inequality -13 <x< 15.
Simplify the inequality Ix-11+1 > 15 we get,
|x-1|+1 > 15
|x+1| +1-1 >15-1
|x-1| > 14
x> 15
x<-13
If x has a value between -13 and x + 15, then the expression "|x-1|+1+115" is true. The range "(-13, 15)" contains the intersection of the region.If "|x-1|+1>15" then either "x >15" or "x-13" applies to the value of x. This region's intersection is unoccupied.Read more about inequalities
https://brainly.com/question/20383699
#SPJ1
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10< x <22
Using it's concept, the average rate of change of the function over the interval 10 < x < 22 is given by:
[tex]r = \frac{f(22) - f(10)}{12}[/tex]
What is the average rate of change of a function over an interval?It is given by the change in the output divided by the change in input.
Over the interval 10 < x < 22, the outputs are f(10) and f(22), hence the rate of change is given by:
[tex]r = \frac{f(22) - f(10)}{12}[/tex]
More can be learned about the average rate of change of a function at brainly.com/question/24313700
#SPJ1
Solve: −(23a−13)+53a=−4
Answer:
a = -17/30
Step-by-step explanation:
So the first step is to distribute the negative sign, if that's a bit confusing think of the negative sign as a -1 instead of just a negative sign, and then think of distributing that negative 1 to the 23a and -13.
Original Equation:
-(23a - 13) + 53a
Distribute negative sign
-23a + 13 + 53a
Group like terms:
(-23a + 53a) + 13
Simplify
30a + 13 = -4
Subtract 13 from both sides
30a = -17
Divide both sides by 30
a = -17/30
Early in 2022, Pina Company switched to a just-in-time inventory system. Its sales revenue, cost of goods sold, and inventory amounts for 2021 and 2022 are shown below.
The Inventory Turnover for 2021 is 5.9 times and for 2022 is 10 times.
Inventory turnover2021
Inventory Turnover = Cost of Goods sold / Average Inventory
Cost of Goods sold = $1,165,250/[($170,000+$225,000)/2]
Cost of Goods sold = $1,165,250/($395,000/2)
Cost of Goods sold = $1,165,250/197,500
Cost of Goods sold = 5.9 times
2022
Inventory Turnover = Cost of Goods sold / Average Inventory
Cost of Goods sold = $1,525,000/[($225,000+$80,000)/2]
Cost of Goods sold = $1,525,000/($305,000/2)
Cost of Goods sold = $1,525,000/152,500
Cost of Goods sold = 10 times
Therefore the Inventory Turnover for 2021 is 5.9 times and for 2022 is 10 times.
Learn more about Inventory Turnover here:https://brainly.com/question/12942515
#SPJ1
The complete question is:
Pina Colada Corp. switched to a just-in-time inventory system. Its sales and Inventory amounts for 2021 and 2022 are shown below.
2021 2022
Sales revenue $3,360,000 $3,900,000
Cost of goods sold 1,165,250 1,525,000
Beginning inventory 170,000 225,000
Ending inventory 225,000 80,000
Determine the inventory turnover for 2021 and 2022.
Give 3 reason why a rectangle is not a square
Answer:
A square is a rectangle but a rectangle is not a square. A square consists of four sides of equal lengths. A rectangle has two sides shorter than the two other sides.
Step 6: Patterns can provide a clear understanding of mathematical relationships. This can be seen very clearly in the form of multiplication tables. 3 x 2; 3 x 3; 3 x 4 are clearly examples of the relationship pattern found in multiplication. Provide two more examples of relationship patterns found in mathematics. Describe the pattern in each case. (NB: Do not use the multiplication tables). (8) Step 6 : Patterns can provide a clear understanding of mathematical relationships . This can be seen very clearly in the form of multiplication tables . 3 x 2 ; 3 x 3 ; 3 x 4 are clearly examples of the relationship pattern found in multiplication . Provide two more examples of relationship patterns found in mathematics . Describe the pattern in each case . ( NB : Do not use the multiplication tables ) . ( 8 )
Two more examples of relationship patterns found in mathematics are Geometric sequences and Fibonacci numbers.
What are mathematical patterns?Mathematical patterns are a sequence of repeated arrangements of numbers, shapes, colors, letters, etc.
Mathematical patterns are usually abstract.
What is a geometric sequence?A geometric sequence is a sequence of non-zero numbers. The first number is the product of multiplying a previous number by a fixed, non-zero number, called the common ratio.
A Geometric sequence may look like: 2, 4, 8, 16, 32, 64, 128, ..., where the common ratio is 2.
What is a Fibonacci sequence?
A Fibonacci number starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers.
The rule of the Fibonacci sequence is that each number is equal to the sum of the preceding two numbers, for example, 0, 1, 1, 2, 3, 5, 8, 13.
Learn more about mathematical patterns at https://brainly.com/question/854376
#SPJ1