(x + 2)(x+4)²
———————
(x+4)
Answer:
(x + 2)(x + 4)
Step-by-step explanation:
for the denominator we have (x + 2)(x + 4)(x + 4).
divide the denominator by (x + 4), you would be left with (x + 2)(x + 4).
Subtract the expressions.
(7.43n − 2.2) − (6 + 10.5n)
−30.70n − 4.5
−3.07n − 8.2
9.63n − 4.5
17.93n + (−8.2)
The solution to the expression is (b) -3.07n - 8.2
How to subtract the expressions?From the question, we have the following parameters that can be used in our computation:
(7.43n − 2.2) − (6 + 10.5n)
Remove the brackets
So, we have
(7.43n − 2.2) − (6 + 10.5n) = 7.43n − 2.2 − 6 - 10.5n
Evaluate the like terms
(7.43n − 2.2) − (6 + 10.5n) = -3.07n - 8.2
Hence, the solution is (b) -3.07n - 8.2
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jane will toss a fair coin two times. if you know that the first coin toss resulted in heads, what would the probability be that both coins would land on heads? explain.
The probability that both coins will land on heads is 50%. In other words, each coin toss is an independent event and each coin has an equal chance of landing on either heads or tails.
This is because the result of the first coin toss does not influence the outcome of the second coin toss, meaning each toss is an independent event with a 50% chance of landing on heads.The probability that both coins will land on heads is 50%. This is because the result of the first coin toss does not influence the outcome of the second coin toss. In other words, each coin toss is an independent event and each coin has an equal chance of landing on either heads or tails. This means that the probability of both coins landing on heads is the same as the probability of either coin landing on heads, which is 50%. Therefore, the probability that both coins will land on heads is 50%.
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Sarah is 148 centimeters tall. How tall is Sarah in inches? Round to the nearest tenth inch.
Answer:
58.3
Step-by-step explanation:
divide the length value by 2.54
58.2677
Answer:
58,3 inches
Step-by-step explanation:
1 inch = 2.54 cm
[tex]148 \: cm \:*\:\frac{1\:inch}{2.54\: cm} = 58,267716535433070866141732283465\\\\148\: cm=58,3 \:inches[/tex]
Please helpppp me with thisss
Answer:
d = 0
Step-by-step explanation:
We have the equation
7.5d = 2.5d
We divided both sides by factors and get
d = 0
Value of d is 0.
According to question
7.5d=2.5d
Lin divides each side by 2.5d
∴7.5d÷2.5d=2.5d÷2.5d
⇒3=1
which is not possible and Lin is doing wrong
Elena subtract 2.5d from each side
∴7.5d-2.5d=2.5d-2.5d
⇒5d=0
⇒d=0
So Elena is right and the value of d is 0.
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If C is the line segment from (5,4) to, (0,0), find the value of the line integral:
The value of line integral of the line segment from (5,4) to, (0,0) is 90.
Given that C is the line segment from (5,4) to (0,0):-
So, our first task is to calculate the line segment
After calculating the line segment, we will be able to calculate the line integral
We know that the equation of line is -
y - y1 = (y1 - y2)/ (x1 - x2) * (x - x1)
So now,
y - 0 = (4 - 0)/ (5 - 0) * (x - 0)
y = 4/5 x
5x - 4y = 0 -----------> (1)
A line integral is used to calculate the area covered by that line
c1 = ∫₀⁴ 5x dx ------> (2)
c2 = ∫₀⁵ -4y dy -----> (3)
c1 = [ 5 x²/2 ]₀⁴ = 5 * ( 4² - 0)/2 = 40
c2= [ -4 y²/2 ]₀⁵ = -4 * ( 5² - 0)/2 = 50
The value of the line integral: c1 + c2 = 40 + 50 = 90
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suppose you want to encrypt the message 10101111 by encrypting the decimal number that corresponds to the message. what is the decimal number
To find the decimal number that corresponds to the message "10101111", you can convert the binary number to decimal.
By using the following formula:
decimal = [tex]sum(binary[i] X 2^{(n-i-1)})[/tex]
binary = converting binary number
i = index of the current digit in the binary number
n = total number of digits in the binary number
[tex]2^{(n-i-1)}[/tex] is the corresponding power of 2
use the following steps to convert the binary number "10101111"
Calculate the decimal value for each digit in the binary number:
binary[0] = 1, [tex]2^{(8-0-1)}[/tex] = [tex]2^7[/tex] = 128
binary[1] = 0, [tex]2^{(8-1-1)}[/tex] = [tex]2^6[/tex] = 64
binary[2] = 1, [tex]2^{(8-2-1)}[/tex] = [tex]2^5[/tex] = 32
binary[3] = 0, [tex]2^{(8-3-1)}[/tex] = [tex]2^4[/tex] = 16
binary[4] = 1, [tex]2^{(8-4-1)}[/tex] = [tex]2^3[/tex] = 8
binary[5] = 1, [tex]2^{(8-5-1)}[/tex] = [tex]2^2[/tex] = 4
binary[6] = 1, [tex]2^{(8-6-1)}[/tex] = [tex]2^1[/tex] = 2
binary[7] = 1, [tex]2^{(8-7-1)}[/tex] = [tex]2^0[/tex] = 1
Adding decimal values for each digit
Total decimal value = 1128 + 064 + 132 + 016 + 18 + 14 + 12 + 11
= 128 + 0 + 32 + 0 + 8 + 4 + 2 + 1
= 175
Hence, the decimal number that corresponds to the binary number "10101111" is 175.
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PLEASE HELP I AM SO BEHIND ON SCHOOL WORK !!!
Which equation represents the same line as the points in the table?
y=−3x+2y is equal to negative 3 x plus 2
y=−34x+83y is equal to negative 3 fourths x plus 8 thirds
y=2x−34y is equal to 2 x minus 3 fourths
y=−34x+2
Answer:
Use this site, it will help you in the long run.
Moussa is younger than Sophia. Their ages are consecutive even integers. Find Moussa's age if the product of their ages is 24.
Moussa's age if the product of their ages is 24 is 4 years.
How to calculate their age?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Moussa is younger than Sophia. Their ages are consecutive even integers.
Let the ages be x and x + 2.
This will be illustrated as:
x(x + 2) = 24
x² + 2x = 24
x² + 2x - 24 = 0
x² + 6x - 4x - 24 = 0
x(x + 6) -4(x + 6) = 0
x - 4 = 0
x = 4
x + 2 = 4 + 2 = 6
The ages are 4 and 6 years.
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If the product of Sophia age and Moussa age is 24, the age of Moussa is 4 years.
How to find the Moussa's age?Moussa is younger than Sophia. Their ages are consecutive even integers.
The product of there ages is 24. Moussa's age can be found as follows:
Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2.
Hence,
Let
x = age of Moussa
x + 2 = age of Sophia
Hence, the product of their age will be as follows:
x(x + 2) = 24
x² + 2x = 24
x² + 2x - 24 = 0
lets factorise the quadratic equation. The numbers one can multiply to get -24 and add to get 2 are -4 and 6. Therefore,
x² - 4x + 6x - 24 = 0
x(x - 4) + 6(x - 4) = 0
(x + 6)(x - 4) = 0
Therefore,
x = - 6 and x = 4
We can only use positive numbers.
Therefore, the age of Moussa is 4 years
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pls help having trouble!
Answer:
a is 30 degrees.
Step-by-step explanation:
The degree of a triangle is 180, which means that all the degrees in any triangle will always add up to 180. Since CB and DB are congruent, the angles C and D will be the same. This means that to get the answer, just subtract the value we already have from 180 and divide the sum by 2.
[tex]\frac{180-120}{2} = \frac{60}{2} = 30[/tex]
consider the proposed proof that all real numbers are equal to 0 below. which is the first line that contains an error?
A. Let x be a real number,B. Add x to both sides of the equation, then C. x - x = 0,D. Therefore, x = 0
A. Let x be a real number - This step states that we are selecting a real number for which we will prove that it is equal to 0. This step does not contain an error.
B. Subtract x from both sides of the equation - This step does not contain an error as it is the first step in the process of proving that the real number is equal to 0.
C. x - x = 0 - This step contains an error, as it doesn't provide enough information to prove that the real number is equal to 0.
D. Therefore, x = 0 - This step also contains an error, as it assumes that the proof is correct without providing any evidence.
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Consider the arithmetic sequence 3, -10, -23, -36
Can someone help me with 3C?
The graph of the first five terms can be seen in the image at the end.
How to graph the first 5 terms of the sequence?We know that we have an arithmetic sequence:
3, -10, -23, -36
The common difference is what we get when we subtract two consecutive terms, we will get:
d = -36 - (-23) = -3
Then the recursive relation is:
a(n) = a(n - 1) - 13
At the moment we know:
a(1) = 3
a(2) = -10
a(3) = -23
a(4) = -36
Then fifth term will be:
a(5) = a(4) - 13 = -36 - 13 = -49
Now to graph it, we use the "n-th" value as the input, then we need to graph the five points (1, 3), (2, -10), (3, -23), (4, -36), (5, -49).
The graph can be seen in the image below:
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if you use 1 pound of mirepoix in a recipe that yields 1 gallon of soup, how much mirepoix do you need to make 31/2 gallons of soup?
we need 31/2 pounds mirepoix to make 31/2 gallons of soup.
let we need x% (percent) of mirepoix to make 1 gallon of soup
given we have 1 pound of mirpoix which yeilds 1 gallon soup of soup
so total amount of mirepoix that required in the solution is = [tex]\frac{x}{100} *1 pound[/tex]
so x/100 = 1 gallon / pound
we will use this equation for further calculation
let we need y pounds of mirepoix to make 31/2 gallon of soup ans we know that x% of mirepoix is required for this solution.
so [tex]\frac{x}{100} * y = 31/2[/tex]
ans in the above equation x/100 =1 gallon / pound
so 1 * y= 31 /2
and hence y = 31/2 pounds
so we need 31/2 pounds of mirepoix to form requied amount of soup.
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You just signed a 2 years lease for a one bedroom apartment in Brooklyn. The rent is $2,657 per month pulse $200 security deposit. Thinking long-term, you are wondering if it is better to rent or own a property. How will the total amount of rent you pay change over time?
After the end of the lease period the pay, the rent would increase to $3030.83 approx.
What is a Lease agreement?A lease is a legal agreement by which the owner of a building, a piece of land, or something such as a car allows someone else to use it for a period of time in return for money.
Given here, a 2-year lease is - $2,657 per month plus a $200 security deposit. Now, the average increase in the rate in the U.S is 14.07%
thus, at the end of the two-year lease period, the new rent would be
= (1+14.07/100) × $2,657
= $3030.83
Hence, the new rent with a security deposit is $3030.83 + security deposit.
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Describe how to write 4x^2 + 8x - 10 = 0 in vertex form
Answer:
(2x + 1)^2 = 7
Step-by-step explanation:
To write the quadratic equation 4x^2 + 8x - 10 = 0 in vertex form, we need to first complete the square. To do this, we need to add and subtract the same value to the quadratic term and the linear term so that the resulting quadratic has the form (x - h)^2 = k.
In this case, we need to add and subtract the square of half of the coefficient of the linear term, which is 8/2 = 4. This gives us the equation:
4x^2 + 8x + 4 - 4 - 10 = 0
This simplifies to 4(x^2 + 2x + 1) - 14 = 0, which can be rewritten as (2x + 1)^2 - 7 = 0.
To put this in vertex form, we need to rewrite the right side of the equation as a perfect square, so we add 7 to both sides to get (2x + 1)^2 = 7.
Then, we take the square root of both sides to get 2x + 1 = ±√7. We can then solve for x to get x = -1/2 ± √7/2.
Therefore, the equation 4x^2 + 8x - 10 = 0 can be written in vertex form as (2x + 1)^2 = 7.
I the ytem of equation conitent and independent conitent and dependent or inconitent
The system of linear equations, y = 2x + 4 ;
2y = x + 6 has a unique solution and it is a consistent system of linear equations.
What is linear System of Equations and it's solution?An ordered pair that satisfies all equations of the system is the solution of the system. A system of linear equations can have one solution, no solution, or an infinite number of solutions. The systems of equations can be classified according to the number of solutions. If a system has at least one i.e unique solution, it is called consistent. We have, the system of equations is
y = 2x + 4 => 2x - y + 4 = 0 --(1)
2y = x + 2 => x - 2y + 6 = 0 --(2)
Comparing the equation (1) with a₁x + b₁y + c₁=0
and equation(2) with a₂x + b₂y + c₂=0
We get, a₁ = 2 , a₂= 1 , b₁ = -1 , c₁= 4 , b₂= -2 , c₂ = 2
Now, compute the ratio of coefficients of variables .
a₁/a₂ = 2/1 , b₁/b₂ = -1/-2 = 1/2 , c₁/c₂= 4/6 = 2/3
=> a1/a2 ≠ b1/b2 ,
here, both lines are intersect at a point and a unique solution exist for pair of linear equations. In such a case , the pair of linear equations is said to be consistent. Thus, system is consistent.
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Complete question:
Is the system of equation is consistent and
independent consistent and dependent or inconsistent?
y = 2x + 4 , 2y = x + 6
Mapleton School is having a Thanksgiving food drive to support their local food bank. The food bank is running low on soup, so they asked the students to make soup a large part of their donations. Bernard donated 30 cans, 15 of which were soup. Gwen donated 20 cans, 12 of which were soup. Did Gwen and Bernard donate the same ratio of soup cans to total cans?
Answer: No, Gwen's ratio is 3:5 soup to total, and Bernard's is 1:2 soup to total
Step-by-step explanation:
Bernard donates 30 cans, 15 of which are soup.
15soup/30cans = 1soup/2cans = 1 soup to 2 total cans
Gwen donates 20 cans, 12 of which are soup.
12soup/20cans = 3soup/5cans = 3 soup to 5 total cans
The tatue i 4. 6 meter high. The angle of elevation from the oppoite corner of the courtyard to the top of the tatue i 8
The statue is 4. 6 meter high. The angle of elevation from the opposite corner of the courtyard to the top of the statue is 8,Tan 8 = 4.6/opposite and opposite = 4.6/tan 8 = 5.8 meters
First, we calculate the opposite side of the triangle using the tangent function. To do this, we need to use the angle of elevation (8 degrees) and the height of the statue (4.6 meters). We use the tangent function to calculate this, which is written as:
tan 8 = 4.6/opposite
Solving for the opposite, we get:
opposite = 4.6/tan 8 = 5.8 meters
This means that the opposite corner of the courtyard to the top of the statue is 5.8 meters away.
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Angles 2 and 8 are what type of angles?
A. Same side interior angles
B. Alternate exterior angles
C. Alternate interior angles
D. Corresponding angles
Help!!!
Answer:
B. Alternate exterior angles
Step-by-step explanation:
Alternate exterior angles are angles that are outside two lines intersected by the transversal and are located on opposite sides of the transversal. Also, they have the same degree! So, the answer is B.
PLEASE HELP!!!!! 90 POINTS!!!!!
Graph the following system of equations.
2x + 4y = 8
2x + 6y = 18
What is the solution to the system?
There is no solution.
There is one unique solution, (−6, 5).
There is one unique solution, (−4, 4).
There are infinitely many solutions.
Answer:
There is one unique solution, (−6, 5).
Step-by-step explanation:
2x + 4y = 8
2x + 6y = 18
2x + 4y = 8 ==> solve for 2x
2x + 4y - 4y = 8 - 4y
2x = 8 - 4y
2x + 6y = 18 ==> solve for 2x
2x + 6y - 6y = 18 - 6y
2x = 18 - 6y
8 - 4y = 18 - 6y ==> 2x = 8 - 4y and 2x = 18 - 6y
8 - 4y + 6y = 18 - 6y + 6y ==> solve for y by first adding 6y on both sides to
remove negative y
8 + 2y = 18 ==> simplify
8 - 8 + 2y = 18 - 8 ==> isolate y
2y = 10
y = 5
2x + 4(5) = 8 ==> substitute 5 for y in 2x + 4y = 8
2x + 20 = 8
2x - 20 + 20 = 8 - 20 ==> subtract 20 on both sides to isolate 2x
2x = -12
x = -6
x = -6, y = 5 ==> (6, 5)
Answer: There is one unique solution, (−6, 5).
Domain: -4
BOOKMARK
Determine the domain and range for the following graph.
Answer:
Domain (interval notation) : [-4,4)
Range (interval notation): [1,4)
Domain (inequality notation): [tex]-4\leq x < 4[/tex]
Range (inequality notation): [tex]1\leq x < 4[/tex]
Step-by-step explanation:
Domain is the x-values of a function
Range is the y values of a function
Help me quickly please! (I will mark brainliest)
The graphs in this problem that show continuous data are given as follows:
Top right.Bottom left.What are continuous and discrete graphs?Continuous and discrete graphs have different formats to show the data, which are presented as follows:
For a continuous data, the data shown is all the real numbers in an interval, hence a continuous graph is represented by solid lines. This means that the second and third graphs in this problem, that is, the top right and the bottom left graphs represent continuous data.
For discrete data, only certain values are represented in an interval, hence the graph of discrete data is composed only by dots, which is the case for the first and last graphs in this problem, that is, the top left graph and the bottom right graph.
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Write a triangle congruence statement
Answer:
1. ΔCDE≅ΔJEH
2. ΔIHG≅ΔIHD
3. ΔIHJ≅ΔIXT
4. ΔIJT≅ΔJIH
5. ΔEFD≅ΔDKJ
6.ΔGWY≅ΔGHI
7. find and describe a case in which the land surface of an area in the u.s. has subsided due to groundwater withdrawal. if possible, give an estimate of how many feet the land surface subsided.
an instance where a region's u.s. land surface has changed subsided due to groundwater withdrawal. The land surface in the Central Valley has subsided by as much as 30 feet in distance some areas due to unsustainable groundwater withdrawals.
The most famous case of land subsidence due to groundwater withdrawal in the United States is the Central Valley of California. The land surface in the Central Valley has subsided by as much as 30 feet distance in some areas due to unsustainable groundwater withdrawals. In addition to land subsidence, the unsustainable withdrawals have caused significant groundwater depletion, surface water contamination, and reduced agricultural productivity.
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Which sentence does NOT contain an error in pronoun-antecedent agreement?
a. A large herd of buffalo thundered across the plain and left a cloud of dust in their wake.
b. When the crowd reached the center of town, the mayor was surprised by their size.
c.Our gymnastics team proved their skills during the individual floor exercises.
Answer:
a
Step-by-step explanation:
here is a famous problem: nn guests arrive at a party. each person is wearing a hat. we collect all hats and then randomly redistribute the hats, giving each person one of the nn hats randomly. what is the probability that at least one person receives his/her own hat?hint: use the inclusion-exclusion principle.
The probability that at least one person receives his/her own hat is 1 - (1/n)^n, using the inclusion-exclusion principle.
The inclusion-exclusion principle states that the probability of event A or B occurring is equal to the probability of event A plus the probability of event B minus the probability of event A and B occurring. In this case, the probability of at least one person receiving his/her own hat is the probability of one person receiving his/her own hat plus the probability of two people receiving their own hats minus the probability of three people receiving their own hats, and so on. This can be expressed mathematically as 1 - (1/n)^n, where n is the number of guests. This formula can be applied to any situation where a random event is being repeated multiple times with the same set of outcomes.1 - (1/10)^10 = 0.99.
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Given g(x)=-5x+2 find g(-4)
Answer:_18
replace _4 instead of x
-5*-4=_20
_20+2=_18
Step-by-step explanation:
Which algebraic expression is equivalent to this expression?
A. 135x+147
B. 24x+183
C. 24x+13
D. 24x+147
9(-2) +15(x + 11)
Answer:
15x +147
Step-by-step explanation:
In a board of directors composed of 14 people, how many different ways can one chief
executive officer, one director, and one treasurer be selected?
Answer:
2184
Step-by-step explanation:
This question involves permutations. We can solve it using the formula
[tex]\frac{n!}{(n-r)!}[/tex]
where n=14 (because we are choosing from 14 people)
and r=3 (because we are choosing 3 people)
and we are using the permutation formula because the order or placement in which these 3 people are choosing matters (having a person 1 being a director is different from having person 1 being a chief executive officer)
14!/(14-3)!
= 14!/11!
= 14 x 13 x 12
= 2184
(-10, -12), (-8, -8), (-6, -4), (-4, 0)
Find the slope of the line passing through the given points
Answer: the slope is [tex]\frac{4}{2}[/tex] which can be simplified to just 2.
Step-by-step explanation:
You can use the equation [tex]\frac{y2-y1}{x2-x1}[/tex] to find the slope of a line. In this case, I chose to use the coordinates (-4,0) and (-6,-4), it doesn't matter which you choose as the (x1,y1) and (x2,y2) coordinates. So, [tex]\frac{-4-0}{-6-(-4)}[/tex] becomes [tex]\frac{-4}{-2}[/tex] which is the same as [tex]\frac{4}{2}[/tex], which is equal to 2. you can repeat this with the other points given to check your answer.
The slope of the line passing through the given points is equal to 2 .
what is the slope of a line?The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line. The slope of a line is the measure of the tangent of the angle made by the line with the x - axis. It is represented by m: m = y₂-y₁ / x₂ - x₁
Given here, are the points P (-10, -12), Q(-8, -8), R(-6, -4),S (-4, 0)
Now the slope of a line is constant for any two points that lie on a line.
therefore, slope of the line that passes through P,Q,R,S is
m = -8-(-12) /-8-(-10)
= 2
or m= 0-(-4) /-4-(-6)
= 2
clearly the slope is equal to 2 in either case that's because the line passes through all the four points.
Hence, the slope of the line passing through the given points is equal to 2.
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