Which expression is equivalent to 1/4(8 - 6x + 12)?
Answers
The expression that is equivalent to 1/4(8 - 6x + 12) is 2 - 3x/2 + 6
What are algebraic expressions?
Algebraic expressions are simply defined as those mathematical expressions that are composed of terms, variables, their coefficients, their factors and constants.
These mathematical expressions are also comprised of arithmetic operations.
These operations are listed thus;
BracketParenthesesAdditionSubtractionMultiplicationDivisionFrom the information given, we have that;
1/4(8 - 6x + 12)
expand the bracket, we have;
8 - 6x + 12/4
Divide in group, we have;
8/4 - 6x/4 + 12/4
Divide the values
2 - 3x/2 + 6
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Related Questions
A 3-pack of raffle tickets costs $5.76. What is the unit price
Answers
Answer:
1.92
Step-by-step explanation:
to find the unit cost you just divide 5.76 by 3
5.76/3 = 1.92
Answer: 72
i looked it up it so it should be right
In Exercises 1 and 2, solve the system using the elimination method.2. x + y - 2 = -22x – y += = 8-x + 2y + 2: = 10
Answers
(1,3,-7)
1) Let's write the following system of linear equations, and then solve them by the elimination method.
The first thing to do is to proceed with the elimination of one variable. In this case, let's chose to start with
x-6y+2z=5 x -2
2x-3y+z=4
3x+4y-z=-2
2x-12y+4z=10
2x-3y+z=4
3x+4y-z=-2
Adding these two equations:
2x-3y+z=4
-2x+12y-4z=-10
----------------------------------
9y -3z =-6
Now getting the other equations, let's eliminate another variable, in this case, "x"
-2x+12y-4z=-10 x 3
3x+4y-z=-2 x 2
Adding them
-6x +36y -12z=-30
6x+8y-2z=-4
----------------------------
0 44y -14z=-34
2) Now that we have a simpler system of two variables "y" and " z" let's operate them. Choosing a factor that we can multiply and cancel out the y variable, in this case, let's pick the Least Common Multiple between 9 and 44 = 396, so let's multiply them by
9y -3z = -6 x 44
44y-14z=-34 x -9
396y -132z = -264
-396y+126z=-306
----------------------------
6z =-42
z=-7
Plugging into the equation 9y -3z =-6
9y-3(-7)=-6
9y +21 =-6
9y=27
y=3
And for x
x-6y+2z=5
x-6(3)+2(-7)=5
x+18-14=5
x+4=5
x=1
3) So the solution for that system is (1, 3, -7).
Find the perimeter of the figure.
Answers
Answer:
75
Step-by-step explanation:
9 + 9 + 9 + 9 + 9 + 30 = 75
Good luck on your assignment!
What is the approximate probability of exactly two people in a group of seven having a birthday on April 15? (A) 1.2 x 10^-18 (B) 2.4 x 10^-17 (C) 7.4 x 10^-6 (D) 1.6 x 10^-4
Answers
The approximate probability of exactly two people in a group of seven having a birthday on April 15 is (C) \(7.4 x 10^-^6\)
How we get the approximate probability?To calculate the probability of exactly two people in a group of seven having a birthday on April 15, we can use the binomial distribution formula:
\(P(X = k) = C(n, k) * p^k * (1 - p)^(^n^-^k^)\)
Where:
P(X = k) is the probability of exactly k successes (in this case, k = 2)n is the number of trials (in this case, n = 7)p is the probability of success in a single trial (in this case, p = 1/365, assuming that all days of the year are equally likely for a birthday)C(n, k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items (in this case, C(7, 2) = 21)So, plugging in the values, we get:
\(P(X = 2) = C(7, 2) * (1/365)^2 * (1 - 1/365)^(7 - 2)\)
\(= 21 * (1/365)^2 * (364/365)^5\)
\(= 2.38 x 10^-5\)
The probability of exactly two people in a group of seven having a birthday on April 15 can be calculated using the binomial distribution formula.
The formula takes into account the number of trials, the probability of success in a single trial, and the number of successes desired.
In this case, we want to find the probability that exactly two people in a group of seven have a birthday on April 15, assuming that all days of the year are equally likely for a birthday.
Plugging in the values into the formula gives us an approximate probability of \(7.4 x 10^-^6\), which is the answer (C).
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how many frequent flyer program members are reported in newspaper quintile v? remember to report your answer with regards to the (000) format!
Answers
The number of frequent flyer program members in newspaper quintile V.
The information related to that specific quintile.
Unfortunately, you didn't provide the required data to calculate the number of frequent flyer program members in newspaper quintile V.
To understand what the given data represents.
Since the question is asking for the number of frequent flyer program members in newspaper quintile V.
The data is provided, I will guide you through a step-by-step process to find the answer and ensure that it is reported in the (000) format, as you requested.
Please provide the relevant data, and I'll be more than happy to help you calculate the answer.
Once the information is given, I will walk you through a step-by-step procedure to identify the solution and make sure it is presented in the (000) format, as you asked, when I have the data.
Comprehend what the provided data means.
Given that the number of frequent flyers programmed members in newspaper quintile V is the subject of the issue.
Information pertinent to that particular percentile.
Unfortunately, you didn't supply the information needed to determine how many people in newspaper quintile V are members of frequent flyer programmed.
The pertinent information, and I'll be pleased to assist you in coming up with the solution.
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a person walks 35.00 north of west for 11.2 km. how far due north and how far due west would he have to walk to arrive at the same location?
Answers
To arrive at the same location, the person would have to walk 25 km due north and 6.2 km due west.
This can be calculated using the Pythagorean theorem: c² = a² + b², where c is the total distance and a and b are the distance traveled due north and due west, respectively.
In this case, c = 11.2 km and a = 35 km. Therefore, a² + b² = 11.2² and b = √(11.2² - 35²) = 6.2 km.
Therefore, the person must travel 25 km due north and 6.2 km due west to arrive at the same location.
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A roller-coaster is at the top of a 62-meter hill. the car and its passengers have a total mass of 1,088 kilograms. by the time the car reaches the bottom of the hill, its speed is 74 miles per hour (33 meters per second). how much kinetic energy does the car have at the bottom of the hill?
Answers
The kinetic energy of the roller coaster at the bottom of the hill is approximately 594,576 J.
The potential energy of the roller coaster at the top of the hill can be calculated as:
PE = mgh
where m is the mass of the car and its passengers, g is the acceleration due to gravity \((9.8 m/s^2\)), and h is the height of the hill (62 m). Thus, we have:
PE =\((1088 kg)(9.8 m/s^2)(62 m) = 670,720 J\)
At the bottom of the hill, all of the potential energy has been converted to kinetic energy. The kinetic energy of the roller coaster can be calculated as:
\(KE = (1/2)mv^2\)
where v is the speed of the roller coaster at the bottom of the hill. Thus, we have:
\(KE = (1/2)(1088 kg)(33 m/s)^2 = 594,576 J\)
Therefore, the kinetic energy of the roller coaster at the bottom of the hill is approximately 594,576 J.
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X
-4
O
3
START HERE
10
Y=8X-5
Y=-2X-1
Y-3X+2
Y=X-7
Y
-35
5 Y=2X+5
35
105
Y=10X+5
Y=-2X-1
X
-5
2.5
0
2.5
Equations of Lines Maze
Y
S
1 Y=-4X-5
-7
-0
X
2
1
0
I
h+X=A
h-X=A
Y
20
10
0
-10
Y=-6X-7
Y=4X+2
Y=6X+10
Y=-4X
X
2
5
7
10
Y=5X-5
Y=2X+1
Y
10
22
30
42
Y-X
Y=2X+7
Y=-X+4
Y=5X
Y=-2X+1
X
1
2
3
4
Y
9
.
Xb=A
0
15
Xh-=A
Finish
Answers
Answer:
Step-by-step explanation:
Given that the polynomial function has the Given zero, find the other zeros. f(x)=x^3-2x^2-11x+52; -4
Answers
ANSWER
The other two zeros are
• 3 + 2i
,• 3 - 2i
EXPLANATION
If the zeros of a polynomial are x1, x2, x3... the polinomial function can be written in a factored form,
\(P(x)=(x-x_1)(x-x_2)(x-x_3)\ldots\)Hence, if we know that one of the zeros of f(x) is -4, that means that (x + 4) is a factor. Thus, we can divide the polynomial by that factor,
So f(x) is,
\(f(x)=(x+4)(x^2-6x+13)\)To find the other two zeros now we just have to find the zeros of the second factor (x² - 6x + 13), which is much easier because we can simply use the quadratic formula,
\(\begin{gathered} ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}\)In this case a = 1, b = -6 and c = 13,
\(x=\frac{6\pm\sqrt[]{6^2-4\cdot1\cdot13}}{2\cdot1}\)\(x=\frac{6\pm\sqrt[]{36-52}}{2}\)\(x=\frac{6\pm\sqrt[]{-16}}{2}\)Note that the number under the radical is negative. Therefore the other two zeros are not real - in other words, in the real numbers set this function has only one zero: -4.
In the complex number set we know that i² = -1, so we can replace the minus sign under the radical by i²,
\(x=\frac{6\pm\sqrt[]{16i^2}}{2}\)And solve the square root,
\(x=\frac{6\pm4i}{2}\)We can distribute the denominator into the sum/subtraction,
\(x=\frac{6}{2}\pm\frac{4i}{2}\)And we get that the other two zeros are,
\(\begin{gathered} x_2=3+2i \\ x_3=3-2i \end{gathered}\)This agrees with the complex conjugate root theorem, which states that
Given the equation y = 3(2)x
Answers
Regarding the exponential function y = 3(2)^x, we have that:
We know that the graph has a y-intercept at (0,3), because the a-value is of 3.We know that the graph models exponential growth, because the b-value is of 2.The numeric value of the function at x = 3 is given as follows: 24.What is the exponential function?An exponential function is defined as follows:
y = ab^(x/n).
In which the parameters are defined as follows:
a is the initial value.b is the rate of change.n is the time needed for the rate of change.The function for this problem is given as follows:
y = 3(2)^x.
Hence the parameters are given as follows:
a = 3 -> y-intercept at (0,3).b = 2 > 1, hence exponential growth.At x = 3, the numeric value of the function is obtained as follows:
y = 3 x 2^3
y = 3 x 8
y = 24.
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What is the reasoning?
Answers
Answer:
yes, i agree. the right angle is 90 and 90+90=180. The law of the congruent angle states that if one angle in a the plane is right then the other connected must be as well, making line L 180.
Step-by-step explanation:
i badly explained it however you should get the answer correct with that. i think... use your brain in addition to mine.
27. Two of the smallest mammals on Earth
are the bumblebee bat and the Etruscan
Pygmy shrew. How much shorter is the
bat than the shrew?
Answers
Etruscsn small mammals on earth the Bumblebee bat
Find the real or imaginary solutions of the equation by factoring. x⁴+7x²=18 .
Answers
The real or imaginary solutions of the equation by factoring. x⁴+7x²=18 . The real solutions are x = ±√2 and the imaginary solutions are x = ±3i.
To find the real or imaginary solutions of the equation
x⁴ + 7x² = 18
by factoring,
we can rewrite the equation as
x⁴ + 7x² - 18 = 0.
Now, let's factor the equation.
We can rewrite it as
(x² - 2)(x² + 9) = 0.
To find the solutions, we set each factor equal to zero and solve for x.
From the first factor,
x² - 2 = 0,
we get x = ±√2.
From the second factor,
x² + 9 = 0,
we get x = ±3i,
where i is the imaginary unit (√-1).
So, the real solutions are x = ±√2 and the imaginary solutions are x = ±3i.
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Two less the quotient of a number and five.
What is the algebraic expression
Answers
x/5 - 2
you're dividing the number by 5 so you'll get x over 5
and then ur subtracting 2
a pollster is interested in knowing which presidential candidate voters prefer in the upcoming election. in an effort to obtain this information, 1000 voters are randomly selected and asked their preference. the sample in this situation is
Answers
To help account for variability, the pollster used a simple random sample.
Sampling is the selection of a subset (a statistical sample) of people from within a statistical population in statistics, assurance, and survey procedures. the population's characteristics that were sampled. Obtaining samples that are typical of the population being researched is the objective of statisticians.
In situations where it is not practical to evaluate the complete population, sampling offers insights and is more cost-effective and time-efficient than doing so.
Each observation gives a number for one or more characteristics of certain things or people, including their size, location, color, or weight.
In survey sampling, especially in stratified sampling, ratings can be added to the results to take into consideration the sample design. The practice is guided by conclusions from statistical theory and probability theory.
Since 1000 people are randomly selected , hence we can say that the preference is simple random sample.
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How many bit strings of length 9 do not have four consecutive
1s
Answers
The number of bit strings of length 9 that do not have four consecutive 1's is 381. Therefore, the number of bit strings of length 9 that do not have four consecutive 1's is 381.
Let's denote the number of bit strings of length n with no 4 consecutive 1s as a n . Then, let's find a formula that calculates a n for any integer n. A string of length n with no 4 consecutive 1s can end in 0 or 1. If it ends in 0, then it is enough that the first n - 1 bits contain no 4 consecutive 1s, so there are a n - 1 such strings. If it ends in 1, then the last three bits must be 101. The first n - 3 bits can be any string with no 4 consecutive 1s. So there are a n - 4 strings of length n that end in 101. Therefore, we have the recursive formula a n = a n - 1 + a n - 4 .
We also have the initial conditions a 0 = 1, a 1 = 2, a 2 = 4, a 3 = 7 . Using this recursive formula and the initial conditions, we can calculate a 9 :a 9 = a 8 + a 5 a 8 = a 7 + a 4 a 7 = a 6 + a 3 a 6 = a 5 + a 2 a 5 = a 4 + a 1 We can use the initial conditions to calculate all the values of a n up to a 9 . Finally, a 9 is the main answer, which is 381. Therefore, the number of bit strings of length 9 that do not have four consecutive 1's is 381.
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Determine the slope of the line
Answers
Step-by-step explanation:
(x₁, y₁) = (-3, -4) and (x₂, y₂) = (0, 4)
\(m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{ 4 - ( - 4)}{0 - ( - 3)} \\ m = \frac{4 + 4}{3} \\ m = \frac{8}{3} \)
#CMIIWwhat is 3 and 1/6 as an improper fraction
Answers
Answer:
Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer
she recorded data for the low temperature each day for a week in the table
Answers
The average low temperature for the week is -3°F.
How to solve thisIt is the total sum of the given values divided by the number of values.
We have,
Temperatures for one week:
Day Temperature
Sunday −5 °F
Monday −8 °F
Tuesday −6°F
Wednesday −8°F
Thursday −3 °F
Friday 2° F
Saturday 7° F
The average of the low temperature:
= [ -5 + (-8) + (-6) + (-8) + (-3) + 2 + 7 ] / 7
= (-5 - 8 - 6 - 8 - 3 + 2 + 7) / 7
= -30 + 9 / 7
= -21 / 7
= -3
Thus,
The average low temperature for the week is -3°F.
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christopher recoded the low temperature each day for 1 week and recorded his results in this table.
what average low of -5-8-6-8-3 2 7
The whiteboard is 4.5 feet in width.
1. How many inches wide is the whiteboard?
Answers
Answer: The board is 54 inches wide
The width of a whiteboard, in inches, is 54.
What is multiplication?Multiplication is a type of mathematical operation. The repetition of the same expression types is another aspect of the practice.
For instance, the expression 2 x 3 indicates that 3 has been multiplied by two.
We know that the width of the whiteboard is 4.5 feet.
However, if we need to express this width in inches, we have to convert feet to inches, as the two units are not directly comparable.
There are 12 inches in a foot.
Therefore, to convert a value in feet to inches, we can simply multiply the value by 12. In other words, 1 foot is equal to 12 inches.
So, to convert the width of the whiteboard from feet to inches, we can simply multiply the width (4.5 feet) by the conversion factor of 12 inches/foot as follows:
4.5 feet × 12 inches/foot = 54 inches
Therefore, the whiteboard is 54 inches wide.
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Consider the point (x,y) lying on the graph of the line 6x + 4y = 7. Let L be the distance from the point (x,y) to the origin (0,0). Write L as a function of x.
Answers
The distance L from the point (x, y) on the graph of the line 6x + 4y = 7 to the origin (0, 0) can be expressed as a function of x as L(x) = |(7 - 6x)/√(36 + 16)|.
To find the distance from a point to the origin, we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by √[\((x2 - x1)^2 + (y2 - y1)^2\)].
In this case, the point (x, y) lies on the line 6x + 4y = 7. We can rewrite this equation in terms of y as y = (7 - 6x)/4.
To find the distance from (x, y) to the origin (0, 0), we substitute the values into the distance formula:
L(x) = √[\((x - 0)^2 + ((7 - 6x)/4 - 0)^2\)]
= √[\(x^2 + (7 - 6x)^2/16\)]
= √[\(16x^2 + (7 - 6x)^2\)]/4
= √[\(256x^2 + (49 - 84x + 36x^2)\)]/4
= √[\((292x^2 - 84x + 49)\)]/4
Simplifying further, we get L(x) = |(7 - 6x)/√(36 + 16)|, which represents the distance from the point (x, y) to the origin (0, 0) as a function of x.
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help plz (asap) ..............................................................................
Answers
Answer:
oof u alone kid
Step-by-step explanation:
Colin was using the back of his book to check his homework answers. The answer that he had on his paper was −13 − (15 + 58). The correct answer, located in the back of the book, was −13 −15 + 58. Was Colin correct? Justify your response
Answers
Answer: No. Collin was wrong.
Step-by-step explanation:
From the question, we are informed that the answer that Collin had on his paper was −13 − (15 + 58) and the correct answer, located in the back of the book, was −13 −15 + 58.
Collin is wrong because he didn't take into cognisance the effect of minus on the bracket. Here, −13 − (15 + 58) will be equal to -13 -15 -18. This is because minus multiplied by plus equals to minus. He shouldn't have put the numbers in the bracket.
a committee of four people is formed by selecting members from a list of 12 people. how many different committees can be formed?
Answers
495 different committees can be formed by selecting 4 members from a list of 12 people.
In this case, we have 12 people to choose from and we want to form a committee of 4 people. The number of different committees that can be formed is represented by the combination formula:
C(n, r) = n! / [r! * (n - r)!]
Where n = total number of people (12), r = number of people in the committee (4), and ! represents the factorial function.
Applying the formula:
C(12, 4) = 12! / (4! * (12 - 4)!)
C(12, 4) = 12! / (4! * 8!)
C(12, 4) = (12 * 11 * 10 * 9 * 8!)/(4 * 3 * 2 * 1 * 8!)
The 8! in the numerator and denominator cancels out:
C(12, 4) = (12 * 11 * 10 * 9)/(4 * 3 * 2 * 1)
C(12, 4) = 11880/24
C(12, 4) = 495
So, 495 different committees can be formed by selecting 4 members from a list of 12 people.
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A grocery store clerk put only packages of glazed
donuts and packages of chocolate donuts on a
shelf. The ratio of the number of packages of
chocolate donuts to the total number of packages
on the shelf was 5 to 12. Which number could be
the number of packages of glazed donuts the clerk
put on the shelf?
A. 23 B. 18 C. 14 D. 32
Answers
Answer:
c. 14
Step-by-step explanation:
12 - 5 = 7
needs to be a multiple of 7 which 14 is
50 points if you get correct!!! PLEASE HELP ASAP!!!! Hypothesis: Water is always denser than oil and we can test this by pouring equal quantities of water and cooking oil together in a container. The water sinks to the bottom and the oil is on top because it's less dense. We decide to change one factor: temperature. We put the mixture in a freezer all night. In the morning we notice that the water, now ice with bubbles, has risen to the top of the mixture. The oil is not frozen but is now on the bottom. Choose the best probable analysis to fit result.
A. When water freezes gas bubbles form making it less dense than oil and reversing their positions.
B. Oil loses its viscosity when it is cooled and causing it to ooze beneath the ice.
C. When oil freezes it becomes denser.
D. Oil and water don't mix and eventually separate in the cold.
Answers
Answer:
I believe the answer is A.
Step-by-step explanation:
Answer:
A. When water freezes gas bubble from making it less dense than oil and reversing their positions.
Worth 60 points for a rapid reply- find the area of each regular polygon. Answers are rounded to the nearest whole number.
Answers
The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
How to calculate for the area of the polygonArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of octagon × (n)number of side.
apothem = s/[2tan(180/n)].
11 = s/[2tan(180/12)]
s = 11 × 2tan15
s = 5.8949
perimeter = 5.8949 × 12 = 70.7388
Area of dodecagon = 1/2 × 11 × 70.7388
Area of dodecagon = 389.0634 in²
Area of pentagon = 1/2 × 5.23 × 7.6
Area of pentagon = 19.874 in²
Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
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Solve 6X ^ 2 +5X -6 =0algebraically for the exact values of X
Answers
The exact values of x for the equation 6x² + 5x - 6 = 0 algebraically is x = 1/3 or -3/2.
To solve the equation 6x² + 5x - 6 = 0 algebraically for the exact values of x, we can use the quadratic formula, which states that the solutions to ax² + bx + c = 0 are given by:
x = (-b ± √(b² - 4ac))/2a
In this case, a = 6, b = 5, and c = -6.
Substituting these values into the quadratic formula gives us:
x = (-5 ± √(5² - 4(6)(-6)))/2(6)
x = (-5 ± √(25 + 144))/12x = (-5 ± √169)/12
x = (-5 ± 13)/12T
he solutions are therefore:
x = (-5 + 13)/12 or x = (-5 - 13)/12
x = 1/3 or x = -3/2
Algebraically, the solution of the equation is x = 1/3 or -3/2.
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I set z=t=0(x,y,z,t)
and I got a partial solution (0,1,0,0).
I solved two homogeneous matrices once for z=1
and t=0
, then for z=0
and t=1
and I got two solutions (1,1,1,0)
and (1,1,0,1).
Then, I got (0,1,0,0)+a∗(1,1,1,0)+b∗(1,1,0,1
)
Therefore, all possible results are (0,1,0,0),(1,0,1,0),(1,0,0,1),(0,1,1,1)
Would this be correct?
Answers
The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).
Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.
Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).
Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).
Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).
To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.
(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)
Expanding this expression, you get:
(0+a+b, 1+a+b, 0+a, 0+b)
Simplifying, you obtain the following set of solutions:
(0, 1, 0, 0)
(1, 2, 1, 0)
(1, 2, 0, 1)
Therefore, the correct set of possible results would be:
(0, 1, 0, 0)
(1, 2, 1, 0)
(1, 2, 0, 1)
Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.
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Classify each polygon by its number of sides.
Drag the choices into the boxes to correctly classify each polygon.
Answers
Answer choices for shape number 1:
A Pentagon
Answer choices for shape number 2:A Dodecagon
Answer choices for shape number 3:A Decagon
Sure hope this helps you