the simple fact that 94 is 49 backwards means nothing, anymore than say 001 and 100 are equal quantities or related other than in the digits.
so, 0.49 or 49/100 and 0.94 or 94/100, are two values, both are at the one hundredth level, so to see who is larger, we can nevermind the 100 and look at the numerator, 94 is clearly much larger than 49.
Jack and Susie want to save to buy a trampoline for their children. They each open a savings account that earns 1.5% a
year. Jack opens his account with $1,000, and Susie opens her account with $800.
X = number of years
The following functions represent the value of the savings accounts in x years
Jack's savings account: f(x) = 1000(1.015)*
Susie's savings account: g(x) = 800(1.015)
Which function represents the total amount Jack and Susie will save in x years?
200(1.015)
1800(1.015)
1800(1.015)2
1800(1.030)
Answer:
[tex]1,800(1.015)^{x}[/tex]
Step-by-step explanation:
we have
[tex]f(x)=1,000(1.015)^{x}[/tex]
[tex]g(x)=800(1.015)^{x}[/tex]
we know that
To find the function that represent the total amount Jack and Suzie will save in x years, adds f(x) and g(x)
so
[tex]f(x)+g(x)=1,000(1.015)^{x}+800(1.015)^{x}[/tex]
[tex]f(x)+g(x)=[1,000+800](1.015)^{x}[/tex]
[tex]f(x)+g(x)=1,800(1.015)^{x}[/tex]
Answer: 1,800(1.015)^{x}
Step-by-step explanation:
we have
f(x)=1,000(1.015)^{x}
g(x)=800(1.015)^{x}
we know that
To find the function that represent the total amount Jack and Suzie will save in x years, adds f(x) and g(x)
so
f(x)+g(x)=1,000(1.015)^{x}+800(1.015)^{x}
f(x)+g(x)=[1,000+800](1.015)^{x}
f(x)+g(x)=1,800(1.015)^{x}
Ethan rolls a 6 sided number cube. what is the probability that he gets a number less than 4?
A) 2/3
B) 1/2
C) 1/3
D) 1/6
B). 1/2
Step-by-step explanation:In this question, it's asking to find the probability of Ethan getting a side of the cube that is less than 4.
In this case, we know that Ethan is rolling a 6 sided number cube, meaning that the numbers on the cube will range from 1-6.
On the cube, we need to get the numbers that are less than 4.
1
2 ← These numbers are less than 4.
3
___
4
5
6
Knowing how many numbers are less than 4, we can solve the question.
We know that there are 3 numbers less than 4. So that will be our numerator.
There are 6 numbers in total, so that will be our denominator.
We can represent probability as a fraction.
Your fraction should look like this:
[tex]\frac{3}{6}[/tex]
We are not done yet, we would need to simplify the fraction.
To simplify, we would just divide the numerator and denominator by 3.
[tex]\frac{3}{6} \div \frac{3}{3}=\frac{1}{2}[/tex]
Once you're done solving, you should get [tex]\frac{1}{2}[/tex]
This means that answer choice B). 1/2 would be the correct answer.
I hope this helps you out.Good luck on your academics.Have a fantastic day!The probability that Ethan gets a number less than 4 by rolling the dice is 1/2.
What is the probability of an event?The probability of an event is the chance of happening that particular event.
The number of events in the sample space when rolling a dice is = 6.
The number of favorable events in that sample space = Getting a number less than 4 = 3.
Therefore, the probability of this particular event is
= 3/6
= 1/2
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The area of circle Z is 64 ft2.
What is the value of r?
r = 4 ft
r = 8 ft
r = 16 ft
r = 32 ft
The value of r that satisfies the given area is approximately 5.08 ft, which is closest to 4 ft.
Explanation:The area of a circle can be calculated using the formula A = πr², where A is the area and r is the radius. In this case, the area of the circle is given as 64 ft². So we can substitute the value of A as 64 ft² in the formula to find the value of r.
64 = πr²
To solve for r, we can divide both sides of the equation by π and then take the square root of both sides.
r² = 64/π
r = √(64/π)
To simplify further, we can approximate the value of π as 3.14.
r = √(64/3.14)
r ≈ 5.08 ft
Based on the given options, the value of r that is closest to 5.08 ft is 4 ft.
Answer:
ITS 8FT
Step-by-step explanation:
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 grams of an alloy that 52% copper with 78 grams of pure copper. How many grams of copper are in the resulting mixture? What percent of the resulting mixture is copper?
Answer:
See below in bold.
Step-by-step explanation:
The 50 grams of alloy contains 50 * 0.52 = 26 g of pure copper.
So the amount of copper n the mixture = 78 + 26 = 104 g.
The total mass of the mixture = 78 + 50 = 128 g.
% copper = 104 * 100 / 128
= 81.25%.
Final answer:
The resulting mixture contains 104 grams of copper, which constitutes 81.25% of the mixture.
Explanation:
To find out how many grams of copper are in the resulting mixture of the alloy, we need to calculate the amount of copper from both sources and add them together. The first source is 50 grams of an alloy that is 52% copper, and the second source is 78 grams of pure copper.
50 grams of 52% copper alloy contains 50 grams × 0.52 = 26 grams of copper.78 grams of pure copper is of course 78 grams of copper.Now, add the amounts of copper from both sources:
26 grams (from the alloy) + 78 grams (pure copper) = 104 grams of copper.
To determine what percent of the resulting mixture is copper, we add the total weight of the mixture (50 grams + 78 grams = 128 grams) and then calculate the percentage:
(104 grams copper / 128 grams total) × 100 = 81.25%
So, the resulting mixture contains 104 grams of copper and is 81.25% copper.
For Valentine's Day, Kelsey got a box of 24 chocolates. After one week, she'd eaten 5/8 of them. How many chocolates had Kelsey eaten?
Answer:
She had eaten 15 chocolates.
Step-by-step explanation:
[tex]\frac{5}{8} * 24 = \frac{120}{8} = 15[/tex]
Final answer:
Kelsey ate 15 chocolates out of the 24 after a week, which is 5/8 of the total. Jenny initially had 14 chocolates before eating two and giving half of the remainder to Lisa.
Explanation:
To solve how many chocolates Kelsey has eaten, we have to calculate 5/8 of 24. Since 24 chocolates multiplied by 5/8 equals 15, Kelsey ate 15 chocolates after one week.
Regarding the second question about Jenny and her chocolates:
If Lisa ends up with 6 chocolates, which represents half of the remainder after Jenny ate two, we can deduce that before giving half to Lisa, there were 12 chocolates.Adding back the two chocolates Jenny ate, she originally had 14 chocolates.In summary, the answer to how many chocolates Jenny initially had is 14.
Find the value of x if a linear function goes through the following points and has the following slope: (x,2), (-4,6), m=3
Answer:
X=-16/3 or 5.33
Step-by-step explanation:
The formula is y=mx+c
Substitute in values for gradient
6=-4×3+c
C=18
Y=3x+18
Substitute to find x
2=3x+18
-16=3x
X=-16/3
The slope of a line is the change in the y values over the corresponding x values.
The value of x, that makes the points a linear function is -16/3
Given that:
[tex]m = 3[/tex]
[tex](x_1,y_1) = (x,2)[/tex]
[tex](x_2,y_2) = (-4,6)[/tex]
The slope (m) of a line is calculated using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]3 = \frac{6-2}{-4-x}[/tex]
[tex]3 = \frac{4}{-4-x}[/tex]
Cross multiply
[tex]3 \times (-4 -x) = 4[/tex]
Divide by 3
[tex]-4 -x = \frac 43[/tex]
Add 4 to both sides
[tex]-x = \frac 43 + 4[/tex]
Take LCM
[tex]-x = \frac{4 + 12}3[/tex]
[tex]-x = \frac{16}3[/tex]
Divide by -1
[tex]x =-\frac{16}3[/tex]
Hence, the value of x is -16/3
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The second termn in a geometric sequence is 20. The fourth termn in the same sequense is 45/4, or 11.225. What is the common ratio in this sequence?
Answer:
t2=ar^(2-1)
20=ar
then
t4=ar^(4-2)
45/4=ar.r
45/4=20.r
45/80=r
Answer:
r=±0.75
Step-by-step explanation:
Given:
a2= 20
a4= 45/4
As a geometric sequence has a common ratio and is given by:
an=a1(r)^n-1
where
an=nth term
a1=first term
n=number of term
r=common ratio
Now
a2=20=a1(r)^(2-1)
20=a1(r)^1
20=a1*r
Also
a4=45/4=a1(r)^(4-1)
45/4=a1r^3
(a1*r)r^2=45/4
Substituting value of 20=a1*r
(20)r^2=45/4
r^2=45/4(20)
r^2=0.5625
r=±0.75!
A state is considering license plates that have two digits followed by four letters. Assuming no combinations are excluded, how many different plates are possible if no repetitions of letters or digits are allowed?
Answer:
32,292,000
Step-by-step explanation:
In your question, it asks how many license plate combinations we could make WITHOUT repeats.
We need some prior knowledge to answer this question.
We know that:
There are 26 letters in the alphabetWe can make 10 digits (0 - 9)With the information we know above, we can solve the question.
Since we CAN'T have repeats, we would be excluding a letter or number for each license plate.
We're going to need to multiply each "section" in order to find how many combinations of license plates we can make.
We decrease by one letter and one number in each section since we can't have repeats.
Now, we can solve.
Work:
[tex]26*25*24*23*10*9 = 32,292,000[/tex]
When you're done multiplying, you should get 32,292,000.
This means that there could be 32,292,000 different combinations of license plates.
I hope this helps you out.Good luck on your academics.Have a fantastic day![tex]10\cdot9\cdot26\cdot25\cdot24\cdot23=32292000[/tex]
What is the range of possible sizes for side x?
Answer:
1.6 < x < 9.6.
Step-by-step explanation:
Now x cannot be less than 5.6 - 4.0 = 1.6 as a triangle could not be formed if it were.
In fact x must be greater than 1.6.
Also x must be less than the sum of the other 2 sides.
So x must be less than 4.0 + 5.6 = 9.6.
Answer:
1.6 < x < 9.6
Step-by-step explanation:
The range of possible sizes for side x is 1.6 < x < 9.6.
What is the solution to the equation
-5 p = 24-p?
A distribution has the five-number summary shown below. What is the
interquartile range (IQR) of this distribution?
12, 21, 43, 62, 71
Answer:
the IQR is 41 because 62-21=41
A "True or False" test has five questions.
If you guess the answers, what is the
probability that you will get exactly two
correct?
Answer:
5/16.
Step-by-step explanation:
The probability of getting a correct answer on one question is 1/2 and the probability of getting it wrong is 1 - 1/2 = 1/2.
The probability of the first 2 being correct and the next 3 wrong = (1/2)^5 = 1/32.
There are 10 possible combinations of this ( first wrong the 2nd and third right and last 2 wrong, etc).
So the required probability is 10 * 1 /32
= 10/32
= 5/16.
The odds against Carl beating his friend in a round of golf are 7:5. Find the probability that carl will beat his friend.
In a game, the odds against Carl winning are 7:5. For every 7 games he loses, there are 5 games he wins. Therefore, the probability of Carl winning is 5 divided by the total of possible outcomes (5+7), which equals to 5/12.
Explanation:The subject of this question is Mathematics, specifically probability. The odds against Carl beating his friend in a round of golf are 7:5. To calculate the probability of Carl winning, we have to understand that the odds of an event occurring are the ratio of the possibility of the event happening to the possibility of the event not happening. If the odds are 7:5 against Carl winning, that means for every 7 games Carl loses, there are 5 games he wins.
To calculate the probability of Carl winning, we take the number of wins and divide it by the total number of outcomes. So the probability that Carl will beat his friend would be 5/(7+5) = 5/12.
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Simplify: ( y^−7 × y^−3 )−1 A. y−21 B. y 21 C. y−10 D. y 10
Answer:
D
Step-by-step explanation:
The rules we need to simplify this are:
[tex]a^x*a^y=a^{x+y}[/tex]
and
[tex](a^x)^y=a^{xy}[/tex]
Now, let's simplify the problem:
[tex](y^{-7}*y^{-3})^{-1}\\(y^{-10})^{-1}\\y^{10}[/tex]
Answer choice D is y^10, so that's correct.
The table below shows the future value of a certificate of deposit (CD), after x
years. Don states the applied interest is simple interest. True or false?
(number of years)
(future value)
$205.00
$210.00
$215.00
$220.00
$225.00
A. True
B. False
Answer:
A. True.
Step-by-step explanation:
The value increases by the same amount ($5) every year so it is simple interest.
Answer:True
Step-by-step explanation:
help with 1-9 , please!!!!
Answers:
1. 147+13=160
2. -55+(-31)= -55-31=-86
positive number and negative number= -negative number
3. 18+71=89
4. -14+21=7
Positive 7 because 21 is greater than -14
5. 12+(-56)= 12-56=-44
6. -4+18=14
7. -31+(-17)=-31-17=-48
8. 72+(-22)=72-22=50
9. 47+23=70
The sum of two polynomials is 8d5 – 3c3d2 + 5c2d3 – 4cd4 + 9. If one addend is 2d5 – c3d2 + 8cd4 + 1, what is the other addend?
Answer:
The second polynomial is:
[tex]6d^5-2c^3d^2+5c^2d^3-12cd^4+8[/tex]
Step-by-step explanation:
Given
[tex]Sum\ of\ polynomials=S=8d^5-3c^3d^2+5c^2d^3-4cd^4+9\\Polynomial\ 1=A=2d^5-c^3d^2+8cd^4+1\\Polynomial\ 2=B=?\\S=A+B\\B=S-A\\=8d^5-3c^3d^2+5c^2d^3-4cd^4+9-(2d^5-c^3d^2+8cd^4+1)\\=8d^5-3c^3d^2+5c^2d^3-4cd^4+9-2d^5+c^3d^2-8cd^4-1\\=8d^5-2d^5-3c^3d^2+c^3d^2+5c^2d^3-4cd^4-8cd^4+9-1\\=6d^5-2c^3d^2+5c^2d^3-12cd^4+8[/tex]
a jar contains 30 red marbles 50 blue marbles and 20 white marbles if you select one marble from the jar at random what is the theoretical probability of getting a red marble
Answer:
3/10
Step-by-step explanation:
P(red) = red marbles / total marbles
We have 30 red marbles
total marbles = (20 white+ 50 blue+ 30 red) = 100 marbles
P(red) = 30/100 = 3/10
Answer:
0.30 or 30%.
Step-by-step explanation:
This = number of re marbles / total number of marbles
= 30 / (30+50+20)
= 30 / 100
= 0.30.
What is the mean of 11,22,33
Answer:
22
Step-by-step explanation:
11+22+33=66
66/3
=22
Answer:
22
Step-by-step explanation:
The mean is just another word for average
Add up the three numbers and divide by 3
(11+22+33) /3 = 66/3 = 22
Identify the "c" value of the following quadratic equation given below.
-8 = 2(x + 9)^2
[tex]\bf -8=2(x+9)^2\implies -8=2(\stackrel{\mathbb{F~O~I~L}}{x^2+18x+81})\implies \cfrac{-8}{2}=x^2+18x+81 \\\\\\ -4=x^2+18x+81\implies 0=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+18}x\stackrel{\stackrel{c}{\downarrow }}{\boxed{+85}}[/tex]
Graph y < x2 - 3. Click on the graph until the correct graph appears.
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y< x^{2} -3[/tex]
The solution of the inequality is the shaded area below the dotted line of the quadratic equation [tex]y=x^{2} -3[/tex]
using a graphing tool
see the attached figure
The graph of the given function y < x² - 3 is attached below.
we have inequality that is a mathematical statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠).
Since we are given the inequality as;
y < x² - 3
We can write as;
y = x² - 3
These are used to describe relationships between quantities or to express constraints or conditions.
Therefore, the solution to the inequality is the shaded area below the dotted line of the quadratic equation.
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Write this expression as a single term: 2log2x + log2(x + 5).
[tex]\bf \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 2\log_2(x)+\log_2(x+5)\implies \log_2(x^2)+\log_2(x+5) \\\\\\ \log_2[x^2(x+5)]\implies \log_2(x^3+5x^2)[/tex]
The expression 2log2x + log2(x + 5) can be simplified to a single term, log2[x² × (x + 5)], by using properties of logarithms.
Explanation:
The subject of this question is the simplification of a logarithmic expression. In the mentioned expression, we have 2log2x + log2(x + 5), and we'll use the properties of logarithms to simplify it.
First remember that in terms of logarithms, mlogₐ(b) = log_a(b^m). So we can take the coefficient of the first term and use it as an exponent, which transforms '2log2x' into 'log2(x²)'.
Next, note the law that states logₐ(b) + log(c) ₐ= logₐ(bc). This means that we can combine the two terms under a singular logarithm to give us a single term: log2[x² × (x + 5)]. So, the simplified form of the expression 2log2x + log2(x + 5) is log2[x² × (x + 5)].
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HELP NEED IT PLEASE
Add all of the numbers together
2+3.5+2+3.5
5.5+5.5
= 11 cm
Answer is 11cm - second time
Answer:
11 cm
Step-by-step explanation:
The perimeter is equal to
P =2(l+w)
P = 2(2+3.5)
= 2(5.5)
= 11 cm
If r(x) = 2 – x2 and w(x) = x – 2, what is the range of (Wºr) (x)
(-∞,0]
(-∞,2]
[0,∞)
[2,∞)
Answer:
(-inf,2]
Step-by-step explanation:
[tex](w \circ r)(x)=w(r(x))[/tex]
[tex]w(2-x^2)[/tex] I replaced r(x) with 2-x^2
[tex](2-x^2)-x[/tex] I replace the x in w(x)=x-2 with 2-x^2
[tex]-x^2-x+2[/tex]
You can graph this to find the range.
But since this is a quadratic (the graph is a parabola), I'm going to find the vertex to help me to determine the range.
The vertex is at x=-b/(2a). Once I find x, I can find the y that corresponds to it by using y=-x^2-x+2.
Comparing ax^2+bx+c to -x^2-x+2 tells me a=-1, b=-1, and c=2.
So the vertex is at x=1/(2*-1)=-1/2.
To find the y-coordinate that corresponds to that I will not plug in -1/2 in place of x into -x^2-x+2.
This gives me
-(-1/2)^2-(-1/2)+2
-1/4 + 1/2 +2
Find a common denominator which is 4.
-1/4 + 2/4 +8/4
8/4
2.
So the highest y value is 2 ( I know tha parabola is upside down because a=negative number)
That mean then range is 2 or less than 2.
So the answer an interval notation is (-inf,2]
What is the value of x in the rhombus below?
Answer:
x = 17Step-by-step explanation:
We know:
1. Diagonals of a rhombus are perpendicular.
2. Diagonals divide the rhombus on four congruent right triangles.
3. The sum of measures of acute angles in a right triangle is equal 90°.
Therefore we have the equation:
(2x + 3) + (3x + 2) = 90 combine like terms
(2x + 3x) + (3 + 2) = 90
5x + 5 = 90 subtract 5 from both sides
5x = 85 divide both sides by 5
x = 17
The value of x is 17. This means that the angles formed by the diagonals of the rhombus are 37 degrees (2 * 17 + 3) and 53 degrees (3 * 17 + 2), and they indeed form congruent right triangles as required in the properties of a rhombus.
To find the value of x in the given equation, we start by understanding the properties of a rhombus and how its diagonals divide it into four congruent right triangles.
Given information:
Diagonals of a rhombus are perpendicular.
Diagonals divide the rhombus into four congruent right triangles.
Let's proceed with the steps to solve for x:
Step 1: Recognize that the angles formed by the diagonals are 2x + 3 and 3x + 2. Since these angles are congruent right angles, their sum is equal to 90 degrees.
Step 2: Set up the equation:
(2x + 3) + (3x + 2) = 90
Step 3: Combine like terms:
5x + 5 = 90
Step 4: Isolate x by subtracting 5 from both sides of the equation:
5x = 85
Step 5: Solve for x by dividing both sides by 5:
x = 85 / 5
x = 17
Hence, the value of x is 17. This means that the angles formed by the diagonals of the rhombus are 37 degrees (2 * 17 + 3) and 53 degrees (3 * 17 + 2), and they indeed form congruent right triangles as required in the properties of a rhombus.
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Which function describes this graph?
Α. y = x^2 - 2x +6
Β. y = (x-2)(x – 6)
C. y = (x - 4)(x - 4)
D. y = x^2 + 8x + 12
Answer:
D. x^2 + 8x + 12.
Step-by-step explanation:
The zeroes of the graph ( the x -intercepts) are -2 and -6 so we can write the function as (x + 2)(x + 6) = x^2 + 8x + 12.
The function y = x² + 8x + 12 describes this graph. This is obtained by using equation of parabola at the origin and transforming the graph to the required position as in the question by using rules of transformation of linear function.
What are the Rules of Transformation of Linear Function?
Rules of transformation of linear function are
f(x)+b - function is shifted b units upwardf(x)-b - function is shifted b units downwardf(x+b) - function is shifted b units to the leftf(x-b) - function is shifted b units to the right-f(x) - function is reflected over x-axisf(-x) - function is reflected over y-axisWhat is the required function?
Equation of parabola at the origin is y = x²
First the graph is shifted left 4 unitsBy the transformation we can rewrite the function in f(x+b) form;
that is ⇒ y = (x+4)² ⇒ y = x² + 8x +16
Next the graph is shifted 4 units downwardBy the transformation we can rewrite the function in f(x)-b form;
that is ⇒ y = x² + 8x +16 - 4 ⇒ y = x² + 8x +12
This is the required function.
Hence the function y = x² + 8x + 12 describes this graph.
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A(2,5),B(2,-3), and D(-6,5) are three verticals of square ABCD. What are the coordinates of the fourth vertex, c?
Answer:
(-6,-3)
Step-by-step explanation:
The explanation is in the picture. I really feel like the picture does a better job of explaining it then I could with words.
Answer:
C (-6,-3)
Step-by-step explanation:
A(2,5),B(2,-3), and D(-6,5)
AB has a length of 8 since the x coordinate is the same , we only worry about the y
5--3 = 5+3 = 8
AD has a length of 8 since the y coordinate is the same, we only worry about the x
2 --6 = 2+6 =8
Notice a pattern.
A and B have the same X
A and D have the same Y
B and C will need the same Y for it to be a square
C and D will need the same x
B has a y coordinate of -3
D has an x coordinate of -6
C will have coordinates of (-6,-3)
If we look at the attached graph of the 3 points, we see that to make the square, we need to add a point at (-6,-3)
5. A fan has three thin blades that spin to
produce a breeze. The diameter of the fan is
16 inches.
a. Determine the length of an arc between
two consecutive fan blades.
b. What is the area of each sector formed
by the radii passing through the center of
consecutive fan blades?
c. What is the angular velocity if the tip of
each blade in the fan moves 8m radians
in 2 seconds?
Answer:
a) The length of an arc between two consecutive fan blades is 16.76 inches
b) The area of each sector is 67.02 inches²
c) The angular velocity is 4m rad/sec
Step-by-step explanation:
* Lets explain how to solve the problem
- The fan has three thin blades that spin to produce a breeze
- The diameter of the fan is 16 inches
- The three blades divided the circle into three equal parts
- The circumference of the circle is 2πr
a)
∵ The diameter of the circle = 16 inches
∵ The radius of the circle is half the diameter
∴ The radius (r) = 1/2 × 16 = 8 inches
∵ The length of the circle = 2πr
∴ The length of the circle = 2π(8) = 16π
- The length of an arc between two consecutive fan blades is 1/3
the length of the circle
∴ The length of the arc = 1/3 × 16π = 16.76 inches
* The length of an arc between two consecutive fan blades is
16.76 inches
b)
- The area of a sector in the circle = [tex]\frac{x}{360}(\pi r^{2})[/tex]
where x is the central angle of the sector and r is the radius
of the circle
∵ The angle between each two consecutive blades = 360°/3
∴ x = 360°/3 = 120°
∵ r = 8 inches
∴ The area of each sector = [tex]\frac{120}{360}(\pi )(8^{2})=67.02[/tex]
* The area of each sector is 67.02 inches²
c)
∵ The angular velocity = Ф rad ÷ t, where Ф is the central angle
with radian measure and t is the time in seconds
∴ ω = Ф/t radian/second
∵ Ф = 8m radians
∵ t = 2 seconds
∴ ω = 8m ÷ 2 = 4m rad/sec
* The angular velocity is 4m rad/sec
Find the LCD for the following fractions:
(4/15x^3), (5/12x^2). answers: 25^3, 60x^3, 25x^5, 60x^5
Answer:
60x^3
Step-by-step explanation:
Given:
4/15x^3 and 5/12x^2
finding LCM of denominators (15x^3,12x^2)
for variable x, as x^3 is the heighest power so we'll keep x^3
now for the numeric part
15= 3*5
12=3*4
common factor is 3, so
3*4*5 =60
hence LCD= 60x^3!
h(x)=2x-4/3
o h^-1(x)= 3x-12/2
o h^-1(x)= 3/(2x-4)
o h^-1(x)= 3x+4/2
Answer:
[tex]\large\boxed{h^{-1}(x)=\dfrac{3x+4}{2}}[/tex]
Step-by-step explanation:
[tex]h(x)=\dfrac{2x-4}{3}\to y=\dfrac{2x-4}{3}\\\\\text{Exchange x to y and vice versa}:\\\\x=\dfrac{2y-4}{3}\\\\\text{Solve for y:}\\\\\dfrac{2y-4}{3}=x\qquad\text{multiply both sides by 3}\\\\2y-4=3x\qquad\text{add 4 to both sides}\\\\2y=3x+4\qquad\text{divide both sides by 2}\\\\y=\dfrac{3x+4}{2}[/tex]