Answer:
x^3 +2x^2 -4x -8
Step-by-step explanation:
The factors of x^2 +4x +4 are (x +2)^2.
The factors of 4 -x^2 are -1(x -2)(x +2).
The least common denominator is the least common multiple of these, excluding the -1 multiplier. That multiple is ...
... (x +2)^2 × (x -2) = x^3 +2x^2 -4x -8
_____
Comment on the minus sign
When the given fractions are expressed using the denominator above, the second one will need to have its numerator sign adjusted. The two fractions are ...
7(x -2)/(x^3 +2x^2 -4x -8)-5(x +2)/(x^3 +2x^2 -4x -8)The LCD or Least Common Denominator for the fractions 7/(x^2 + 4x + 4) and 5/(4 - x^2) is the product of the distinct denominators after factoring, which is (x+2)^2(4 - x^2), given they have no common factors.
The acronym LCD refers to the Least Common Denominator, which in mathematics, is the least common multiple of the denominators of a set of fractions. It is used to find a common denominator so that the fractions can be combined or compared. For the fractions 7/x^2 + 4x + 4 and 5/4 - x^2, the LCD would be the product of the distinct denominators assuming they cannot be factored into common factors. In this case, assuming x^2 + 4x + 4 cannot be further factored (it is a perfect square: (x+2)^2), the denominators are x^2 + 4x + 4 and 4 - x^2 (since we consider x^2 to have a negative coefficient here). Consequently, if there are no common factors, the LCD is (x^2 + 4x + 4)(4 - x^2) or (x+2)^2(4 - x^2).
Which of the following is the graph of y= 2x2+3/4?
pre algebra 25=12+r r =? please show your work
[tex]25=12+r\\r=25-12\\r=13[/tex]
12 + r = 25 subtract 12 from both sides
12 - 12 + r = 25 - 12
r = 13A car's wheels spins at 1000 revolutions per minute. The diameter of the wheels is 23 inches. You want to know how fast the car is traveling, so what is the speed?Thank you
Answer:
72,220 inches per minute
Step-by-step explanation:
A car's wheels spins at 1000 revolutions per minute. The diameter of the wheels is 23 inches.
1 revolution = [tex]2\pi[/tex] radians
[tex]\frac{theta}{tome}=\frac{1000 \ revolution}{1 \ minuite} = \frac{1000* 2\pi }{1} =\frac{2000\pi}{1 \ minute}[/tex]
Speed [tex]V= \frac{r*theta}{t}[/tex]
r is the radius , theta is the angle and t is the time
We know diameter = 23 , then radius = 23/2
Speed [tex]V= \frac{23}{2}*\frac{2000\pi}{1}[/tex]
Value of pi = 3.14
speed = 23000* 3.14= 72220 inches/ minute
Answer:
72,220 inches per minute
Step-by-step explanation:
Michael and Imani go out to eat for lunch. If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill?
Answer:
The bill total is $27.32
Step-by-step explanation:
how to figure out tax amount: 25.30 x .08 = $2.024
add tax to cost of meal : 25.30 + 2.024 = $27.32
To calculate the total cost of the meal including an 8% tax, multiply the cost of the meal by the tax rate and add this to the original meal cost. The tax comes to $2.02. So, the total cost of the meal, including tax, is $27.32.
Explanation:The question asks how much the total bill is for Michael and Imani when they go out to eat for lunch. The food and beverages cost $25.30 and there is an 8% meal tax. To calculate the total cost of the meal including the tax, we can multiply the cost of the meal ($25.30) by the tax rate (8%) and add this to the original cost for the meal.
First, let's convert the tax rate from a percentage to a decimal. 8% is equivalent to 0.08 as a decimal. Then, we multiply $25.30 by 0.08:
$25.30 * 0.08 = $2.02
This amount ($2.02) is the tax on the meal. To get the total cost, add this tax amount to the cost of the meal:
$25.30 + $2.02 = $27.32
So, Michael and Imani's bill, including the 8% meals tax, will be $27.32.
Learn more about Tax calculation here:https://brainly.com/question/16200743
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Order least to greatest
Answer:
2 6/15, 2 4/9, 2 3/5, 2 2/3
Step-by-step explanation:
Make all the fractions improper fractions. So 2 2/3= 8/3, 2 6/15= 13/15, etc.
Then make all the denominators 45 and then order them from there.
The Organic Cafe ordered 45 boxes of sugar packets. Each box contained 37 packets of sugar. How many sugar packets in total did The Organic Cafe order?
Solve. Give your answer in scientific notation. (3.4x10^2)x(2x10^3)
A.1.4x10^-1
B.6.8x10^5
C.5.4x10^5
D.6.8x10^6
The solution in scientific notation si:
Option D: 6.8 * 10⁵
How to give the answer in scientific notation?
Scientific notation is a way of expressing very large or very small numbers. It involves writing a number as a product of a number between 1 and 10 and a power of 10.
For example, 800,000,000 can be written in scientific notation as 8 × 10⁸.
We are given the expression:
(3.4 * 10²) * (2 * 10³)
= (3.4 * 2) * 10² ⁺ ³
= 6.8 * 10⁵
Write as a fraction in lowest terms:
0.126126125= a/b
Answer:
a= 14
b= 111
just took it
Stan drove 3300m to the grocery store. The tires on his truck are 2.2m in circumference. How many rotations did each tire make on Stan's drive?
Answer:
1,500 rotations
Step-by-step explanation:
To answer this, divide 2.2 m into 3300 m. This results in 1500.
The wheels made 1,500 rotations each.
Match the products of complex numbers with their standard forms (need help :( )
Translate the word phrase into a math expression.
11 times the sum of a number and 15
11(y+15)
11+(y+15)
11y+15y
11y+15
Answer: 11(y+15)
Step-by-step explanation:
−
42
6
=
x
+
15
−
7
=
x
+
15
−
7
−
15
=
x
−
22
=
x
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the inverse of the given function.
27pionts
Answer:
D. f^-1(x) = log2(x -6)4x^2 -3 . . . . x ≤ 0B. √(x^5) -3√(x^3) -18√xStep-by-step explanation:
1. When you replace f(x) by x and x by y, you have
... x = 2^y + 6
The first thing you do is subtract 6; then you take the base-2 logarithm:
... (x -6) = 2^y
... log2(x -6) = y = f^-1(x)
You know that to get the y-term by itself, you must subtract 6. Anything else you do will operate on (x-6). Only answer choice D has that sort of construction.
2. When you swap x and y and solve for y, you have ...
... x = -1/2√(y+3)
... -2x = √(y +3) . . . . . . multiply by -2
... (-2x)^2 = y +3 . . . . . square
... 4x^2 - 3 = y = f^-1(x) . . . . subtract 3
The range of f(x) is (-∞, 0], so that is the domain of f^-1(x). That is, f^-1(x) is defined for x ≤ 0.
3. The product of the two functions is ...
... (x -6)(√x)(x +3) = (√x)(x^2 -3x -18)
Every term will have a factor of √x, and the coefficients will be 1, -3, -18. Only selection B matches those conditions.
Answer:
Question One: log_2(x - 6) = y
Question Two: First blank: 4 Second blank 0
Question Three: B
Step-by-step explanation:
f(x) = 2^x + 6
y = 2^x + 6 Interchange the x and y
x = 2^y + 6 Subtract 6 from both sides
x - 6 = 2^y Take the log of both sides
log(x - 6) = log 2^y The power can be multiplied by the log of 2
log(x - 6) = y log(2) Divide by the log of 2
log(x - 6)/log(2) = y This to me is the preferred answer. It allows you to calculate what the actual number is or graph it on Desmos
The answer I have given is equivalent to using base 2 as your log, but calculating that is not always easy.
log_2(x - 6) = y
Answer: D
Problem Two
You want the inverse of y = - 1/2 sqrt(x + 3) x ≥ - 3
Note: you cannot have any number less than -3 because if you do, you will be taking the square root of -x which involves complex numbers. In addition x ≥ -3 is a domain. You have to keep that in mind when doing this question.
y = - 1/2 sqrt(x + 3) Interchange the x and yx = - 1/2 sqrt(y + 3) Multiply by - 2-2x = sqrt(y + 3) Square both sides(-2x)^2 = sqrt(y + 3)^2 4x^2 = y + 3 Subtract 3 from both sidesy = 4x^2 - 3The domain and range of this is a little harder to figure out. The range of f(x) becomes the domain of f-1(x)
The range of f(x) is 0 <=y < - infinity
So the domain of f-1(x) <= 0
Answer: The first blank is 4 and the second one is 0
Graph: the graph is given you below the question. What it shows is the f(x) and f^-1(x) are symmetrical about y = x. Most inverses are. If you want to check your work, it is best to include a graph when doing inverses.
Red OriginalBlue inverseBlack: y = xProblem Three
The best way to begin this problem is to apply the associative property of multiplication and start by rewriting the givens as x^(1/2)[(x - 6)(x + 3)]. Do what is in the square brackets first.
x^(1/2) [x^2 - 6x + 3x - 18]x^(1/2) [x^2 - 3x - 18]Now deal with the x^(1/2) which must be multiplied by all three terms in the square brackets.
x^(1/2)*x^2: x^(2 + 1/2) = x^(4/2 + 1/2) = x^(5/2)x^(1/2)*(-3x): - 3 x^(2/2 + 1/2) = - 3x^(3/2)x^(1/2)*(-18): - 18x^(1/2)Result: x^(5/2) - 3x^(3/2) - 18x^(1/2)
Answer: √(x^5) - 3√x^3 - 18√x
Answer: B
For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answer:
Part a) The area of the figure is [tex]\frac{9}{2}(4+\pi )\ cm^{2}[/tex]
Part b) The perimeter of the figure is [tex]3(2+2\sqrt{2}+ \pi)\ cm[/tex]
Step-by-step explanation:
Step 1
Find the area of the figure
In this problem we have that
The figure ABC is the half of a square and the other figure is a semicircle
Find the area of the figure ABC
we have
[tex]AB=6\ cm, BC=6\ cm[/tex]
The area of the half square ABC is equal to find the area of triangle ABC
so
[tex]A1=\frac{1}{2}*6*6=18\ cm^{2}[/tex]
Find the area of the semicircle
The area of the semicircle is equal to
[tex]A2=\pi r^{2}/2[/tex]
we have that
[tex]r=6/2=3\ cm[/tex]
substitute
[tex]A2=\pi (3)^{2}/2[/tex]
[tex]A2=(9/2) \pi\ cm^{2}[/tex]
The area of the figure is equal to
[tex]18\ cm^{2}+(9/2) \pi\ cm^{2}= \frac{9}{2}(4+\pi )\ cm^{2}[/tex]
Step 2
Find the perimeter of the figure
The perimeter of the figure is equal to
[tex]P=AB+AC+length\ CB[/tex]
we have
[tex]AB=6\ cm[/tex]
Applying Pythagoras theorem
[tex]AC=\sqrt{6^{2}+6^{2}}\\AC=6\sqrt{2}\ cm[/tex]
Remember that
the circumference of a semicircle is equal to
[tex]C=\frac{1}{2}2\pi r=\pi r[/tex]
[tex]r=6/2=3\ cm[/tex]
[tex]C=\pi(3)[/tex]
[tex]C=3 \pi\ cm[/tex]
The perimeter of the figure is equal to
[tex]P=6\ cm+6\sqrt{2}\ cm+3 \pi\ cm[/tex]
Simplify
[tex]P=3(2+2\sqrt{2}+ \pi)\ cm[/tex]
Is 3x+12-2x equivalent to x+12. Use two properties of operations to justify your answer
Answer:
Step-by-step explanation:
Commutative property: 3x+12-2x = 3x-2x+12
Substitution property: 3x-2x+12 = x+12
x+12 = x+12
Subtraction property: x-x+12 = x-x+12
Substitution property: 12 = 12
Which of the following phrases are inequalities?
Answer:
B, C D
Step-by-step explanation:
Inequalities are the "alligators" < or > or the "alligators" with lines ≤ or ≥
< less than
>greater than
≤ less than or equal to
≥ greater than or equal to
ANSWERS:
B) 11 > (w - 4)^2 & C) y < 3^4 & D) 5 + 9 < 5 x 9
About this > inequality sign:
Greater thanMore thanAboveExceedsAbout this < inequality sign:
Less thanFewer thanBelowAbout this > inequality sign:
Greater than/Equal toNo less thanAt leastMinimum ofAbout this < inequality sign:
Less than/Equal toNo more thanAt mostMaximum OfSuppose you have $30 to spend on bags of tootsie rolls that are worth $3 and bags of lollipops worth $5. If you have to use all of their money, what combinations of candy bags can they buy?
Construct a linear equation and find/explain the y-intercept, x-intercept, and slope.
Finally, if you have $45 to spend on the candy, how would that impact everything?
Answer:
see below
Step-by-step explanation:
Let x = tootsie rolls
y = lollipops
Toosie rolls are 3 dollars and lollipops are $5 and you only have 30 dollars.
3x+5y =30
To find the x intercept, set y=0 and solve for x
3x +0 = 30
3x = 30
Divide by 3
3x/3 = 30/3
x = 10
The x intercept is 10. This means if you get no lollipops, you can have ten tootsie rolls.
To find the y intercept, set x=0 and solve for y
0 +5y = 30
5y = 30
Divide by 5
5y/5 = 30/5
x = 6
The y intercept is 6. This means if you get no tootsie rolls you can have 6 lollipops.
To find the slope, solve the equation for y
3x+5y =30
Subtract 3x from each side
3x-3x+5y = -3x+30
5y = -3x+30
Divide by 5
y = -3/5 x +30/5
y = -3/5 x +6
The slope is -3/5. For every three less lollipops you get, you can have 5 more tootsie rolls.
If you have $45 dollars instead of 30, this will change the x and y intercepts, but not the slope.
3x+5y =45
To find the x intercept, set y=0 and solve for x
3x +0 = 45
3x = 45
Divide by 3
3x/3 = 45/3
x = 15
The x intercept is 15. This means if you get no lollipops, you can have 15 tootsie rolls.
To find the y intercept, set x=0 and solve for y
0 +5y = 45
5y = 45
Divide by 5
5y/5 = 45/5
x = 9
The y intercept is 9. This means if you get no tootsie rolls you can have 9 lollipops.
To find the slope, solve the equation for y
3x+5y =45
Subtract 3x from each side
3x-3x+5y = -3x+45
5y = -3x+45
Divide by 5
y = -3/5 x +45/5
y = -3/5 x +9
The slope is -3/5. For every three less lollipops you get, you can have 5 more tootsie rolls.
How do you convert minutes to hours
Easy, just do 60 seconds which equals a minute. Since we know that now simply use 60 minutes to get you to an hour. If your doing minutes to hours make sure there is a 0 at the end.
find the unit rate 240 miles in 8 days
Answer:
30 miles per 1 day
Step-by-step explanation:
so 30 miles for each day and if you add 30 eight times which is the same as 30 times 8 you will get 240 miles hope it helps
1/8 of pizza costs 2 dollars. In an hour, 6 1/4 pizzas were sold. How much money was made at the food booth in that hour
Answer:
$12.50
Step-by-step explanation:
1) Mutliply 6 with 2
6*2= 12
2) multiply 1/4 with 2
1/4 * 2 =1/2
3) add 12 and 1/2
12+1/2 = 12.50
By converting the mixed number of pizzas sold to an improper fraction and multiplying by the price per whole pizza, we find the food booth made $100 in one hour from selling pizzas.
To determine how much money was made at the food booth in the given hour, we need to calculate the total sale of pizzas. Since 1/8 of a pizza costs $2, an entire pizza would cost 8 times that amount, which is $16 per pizza. It was stated that 6 1/4 pizzas were sold in that hour. To find the total, we multiply the price per pizza by the number of pizzas sold.
First, convert the mixed number 6 1/4 to an improper fraction to simplify the calculation: 6 1/4 is the same as (6 × 4 + 1) / 4, which is 25/4. Then, multiply the cost per pizza, which is $16, by the number of pizzas sold, which is represented by the fraction 25/4.
The equation for total money made is then $16 × {25}/ {4} = $100.
So, the food booth made $100 in that hour from selling pizzas.
If x=9 and y=−2, evaluate the following expression : 6x−8y
6(9)-8(-2)
6*9=54
8*(-2)=-16
54-16=38
38<-----
Answer:
70
Step-by-step explanation:
x=9 and y=−2, evaluate the following expression : 6x−8y
plug in
6(9) - 8(-2)
= 54 + 16
= 70
there are 100 officials at the race. you read that the total cost of all the officials for one day is 20 654. how much does each official get paid per day?
Answer:
$206.54
Step-by-step explanation:
Divide the number of officials by the total days pay to get the pay for each official working the race
If you are given a 4% raise and inflation is 1%, you are _____.
A you earn 3 percent more money
Step-by-step explanation:
4-1
Answer:
If you are given a 4% raise and inflation is 1%, you are making 3% more.
Step-by-step explanation:
If you are given a 4% raise and inflation is 1%, you are making 3% more.
[tex]4-1=3[/tex]
Or we can say you are making more money.
This is because you are given high percent of raise as compared to the low rate or percent of inflation, that shows you are on the positive side.
Complete the following sentence: Two events that are mutually exclusive...
Answer:
If two events are mutually exclusive then they cannot occur at the same time.
Step-by-step explanation:
If two events are mutually exclusive then they cannot occur at the same time.
For example: If you take a coin, the two possible outcomes on flipping a coin will be mutually exclusive as when you flip a coin, it cannot give both heads and tails at the same time.
Hence, the two mutually exclusive events cannot occur at the same time.
Your Food Cost s are $2,500. Your total food sales ae $17,500. What percent of your food sales do the food costs represent?
Answer:
the correct answer is 14.29%
Step-by-step explanation:
Erica babysits for 4.5 hours and is paid $27. If the people she babysits for have $34 to pay her, how long can they stay out?
Answer:
5 2/3 hours
Step-by-step explanation:
We can use a ratio to solve this problem
hours over money
4.5 hours x hours
------------- = ------------
27 dollars 34 dollars
Using cross products
4.5 * 34 = 27 * x
153 =27x
Divide each side by 27
153/27 = 27x/27
5.666666 hours
Keiko makes 8 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.
Answer:
8h = pStep-by-step explanation:
So if p is the total amount paid, and h is the amount of time spent working, it'll be worked out something like this.
The amount of money she makes per hour x the amount of time spent working = the amount she is paid.
Thus making it...
8 x h = p
but in algebra expressions, we don't normally use arithmetic symbols. So if we get rid of that, we get the answer of 8h = p.
:)
Jamal claims that the graph of f(x)+2 is equivalent to the graph of f(x+k).For the case where Jamals claim is correct, what must be the value of k?
A.-4
B.-1
C.1
D.2
Answer:
[tex]k=2[/tex]
Step-by-step explanation:
1) Rewriting:
[tex]f(x+k)=f(x)+2[/tex]
2) Suppose f(x)= ax (Linear function with b=0)
[tex]a(x+k)=ax+2\\a(x+k)=x+2\\ax+ak=x+2 \Rightarrow a=1\\x+k=x+2\\k=2[/tex]
3) Check the graph below
The correct option is D) 2.
Step-by-step explanation:
Given :
f(x) +2 and f(x +k)
Solution :
let, [tex]f(x) = ax[/tex] (linear function with b = 0)
so, [tex]f(x+k)=a(x + k)\;\;\;at,\; x=x+k[/tex]
Rewriting,
[tex]f(x+k)=f(x) + 2[/tex]
[tex]a(x + k) = ax +2[/tex]
[tex]k = 2 \;\;\;(at,\;a=1)[/tex]
Therefore, the correct option is D) 2.
For more information, refer the link given below
https://brainly.com/question/12431044?referrer=searchResults
Solve the system by the elimination method. 2x + y - 4 = 0 2x - y - 4 = 0 When you eliminate y, what is the resulting equation? x = 0 4x = -8 4x = 8
Answer:
Option C.
Step-by-step explanation:
System of the equation consists of two equations
2x + y - 4 = 0
2x + y - 4 + 4 = 0 + 4
2x + y = 4--------(1)
and 2x - y - 4 = 0
2x - y + 4 - 4 = 0 + 4
2x - y = 4------(2)
Now we will add these equations to eliminate y.
(2x + y) + (2x - y) = (4 + 4)
(2x + 2x) + (y - y) = 8
4x = 8
Therefore, resulting equation will be 4x = 8
Option C. will be the answer.
Which part of the proof does the fourth statement and reason represent?
Given: AB ≅ BC
BC ≅ EF
Prove: EG = AB + FG
It is part of the given information.
It is part of the argument.
It is the conclusion.
It is an assumption.
Answer:
Option B is correct.
Reason:It is an argument
Step-by-step explanation:
Given: [tex]AB \cong BC[/tex] and [tex]BC \cong EF[/tex]
By transitive property: a = b and b = c then, a =c
⇒[tex]AB \cong EF[/tex]
AB = EF [def of [tex]\cong[/tex] segment]
By Segment Addition Postulate states that given two points A and C, and a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation
AB + BC = AC.
Since, the line segment EG , F lies on the line segment;
then, by segment addition postulates we have;
EG = EF + FG
By substitution AB=EF
⇒ EG = AB + FG hence proved!
Since, in the fourth statement reason is: It is an argument
Answer:
B, it is an argument
Step-by-step explanation:
the function c=1.50(n-2)+5.50
Answer:
c =1.50n +2.50
Step-by-step explanation:
c=1.50(n-2)+5.50
The first step is to distribute the 1.5
c= 1.50*n -1.50*2 + 5.50
c = 1.50n - 3.0 +5.50
Now we need to combine like terms
c =1.50n +2.50