Lie is solving the quadratic equation by completing the square.
3x2 + 18x – 8 = 0
3x2 + 18x = 8
What should Lie do next?
Write the polynomial as a binomial squared.
Factor 3 out of the variable terms.
Isolate the variable x.
Add 8 to both sides of the equation.
Answer:
Factor 3 out of the variable terms
Answer:
Factor 3 out of the variable terms.
Step-by-step explanation:
To complete the square the coefficient on the x^2 term must be 1
Therefor
Factor 3 out of the variable terms.
Given: Line segment A B is parallel to line segment D C and Measure of angle 2 equals measure of angle 4
Prove: Line segment A D is parallel to line segment B C
A parallelogram has points A B C D. Angle D A B is angle 1, Angle A B C is angle 2, Angle B C D is angle 3, and angle C D A is angle 4.
A 2-column table with 7 rows. Column 1 is labeled statements and has entries line segment A B is parallel to line segment D C, measure of angle 2 = measure of angle 4, angle 1 and angle 4 are supplements, question mark, measure of angle 1 + measure of angle 2 = 180 degrees, angle 1 and angle 2 are supplements, line segment A D is parallel to line segment B C. Column 2 is labeled reasons with entries given, given, same side interior angles theorem, definition of supplementary angles, substitution, definition of supplementary angles, converse same side interior angles theorem.
m∠1 = m∠4
m∠2 = m∠3
m∠1 + m∠4 = 180°
m∠2 + m∠3 = 180°
Answer: (3)
Step-by-step explanation:
Angles 1 and 4 are supplementary, and their measures thus add to 180 degrees.
Answer:
Step-by-step explanation:
m∠2 + m∠3 = 180°
Jordan sold his used lawn tractor and accessories for $980. If he received nine times as much money for the lawn tractor as he did for the accessories, find how much money he received for the lawn tractor
Answer: \(\$882\)
Step-by-step explanation:
Given
Jordan sold lawn tractor and accessories for \(\$980\)
he receives 9 times more money for a tractor than for accessories
Suppose, he receives x amount for accessories
So, for tractor it is \(9x\)
total amount is
\(\Rightarrow 9x+x=980\\\Rightarrow 10x=980\\\Rightarrow x=\$98\)
He receives \(9x=\$882\) for tractor
Enter the phrase as an algebraic expression.
p divided by 8
The algebraic expression is
Answer: p/8
Step-by-step explanation: p is being divided by 8, meaning that in a fraction, p would be the numerator and 8 would be the denominator.
I hope this helps, have a good day.
Answer: The answer to this basic math question about translating the given basic algebraic phrase to the basic algebraic expression is \(\frac{p}{8}.\)
Step-by-step explanation: Mmmm, that was super extremely easy, so anyway, here is a basic step in order to translate the given basic algebraic phrase to the basic algebraic expression:
"p" is being divided by 8, meaning that it was in a fraction, "p" would be the numerator and 8 would be the denominator.
I hope that my full given answer with my full given step-by-step explanation is very helpful to your own basic math question about translating the given basic algebraic phrase to the basic algebraic expression, please mark me as Brainliest, take care, always be safe, and have a great holiday winter break, Merry Christmas and a happy new year! :D
Sincerely,
Jason Ta,
The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.
rotate point x (0,0)) 270 degrees clockwise about the origin then T<3,5>
here this probally will help
Answer:
5, 3
Step-by-step explanation:
use the power reducing formula to rewrite cos^4 x in terms of the first power of cosine. (hint : cos^4 x
We are to use the power reducing formula to rewrite cos⁴x in terms of the first power of cosine.
Here,
we have
cos⁴x
We can rewrite
cos⁴x as cos²x * cos²x
This is so because of the formula
(cos (A + B))(cos (A - B)) = cos²A - sin²BCos² x = (1 + cos 2x)/2 and cos 2x = 2cos²x - 1
Hence,
(cos⁴x) = (cos²x * cos²x) = (cos²x)(1 + cos 2x)/2
Again,
cos 2x = 2cos²x - 1
Therefore
(cos⁴x) = (cos²x * cos²x) = (cos²x)(1 + cos 2x)/2= (cos²x)(1 + 2cos²x - 1)/2= (cos²x)(2cos²x)/2= cos²x(cos²x)
This is in terms of the first power of cosine and is the required answer.
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Please help‼️ domain and range‼️
The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively
Calculating the domain and range of the graph?From the question, we have the following parameters that can be used in our computation:
The graph
The above graph is an exponential function
The rule of an function is that
The domain is the set of all real values
In this case, the domain is (-∝, ∝)
For the range, we have
Range = (0, ∝)
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4. There are major chords built on what three notes (with all white notes and no accidentals)? O CFG O ABC GEB OCDE
The three major chords built on white notes without accidentals are:
1. C major chord (C, E, G)
2. F major chord (F, A, C)
3. G major chord (G, B, D)
These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.
Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.
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What is the domain? I need help on this problem
The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x ≥ -6
How to determine the domain of the functionFrom the question, we have the following parameters that can be used in our computation:
\(f(x) = \sqrt{\frac{1}{3}x + 2\)
Set the radicand greater than or equal to 0
So, we have
1/3x + 2 ≥ 0
Next, we have
1/3x ≥ -2
So, we have
x ≥ -6
Hence, the domain of the function is (d) x ≥ -6
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find f(-2) for {(10,0),(-2,-5),(7,-2),(5,-9)}
Check the picture below.
a research scholar wants to know how many times per hour a certain strand of virus reproduces. he wants to construct the 85% confidence interval with a maximum error of 0.21 reproductions per hour. assuming that the mean is 12.4 reproductions and the standard deviation is known to be 2, what is the minimum sample size required for the estimate? round your answer up to the next integer.
The minimum sample size required for the estimate is 312.
To calculate the minimum sample size required for the estimate, we can use the formula for the margin of error of a confidence interval:
margin of error = z× (standard deviation / sqrt(n))
where z is the z-score corresponding to the desired confidence level, standard deviation is the known population standard deviation, and n is the sample size.
Rearranging this formula to solve for n, we get
n = (z × standard deviation / margin of error) ^ 2
Substituting the given values, we get
margin of error = 0.21 reproductions per hour
z-score for 85% confidence level = 1.44 (from standard normal distribution table or calculator)
standard deviation = 2 reproductions per hour
mean = 12.4 reproductions per hour
Therefore,
n = (1.44 × 2 / 0.21) ^ 2
n = 311.84
Rounding up to the nearest integer, the minimum sample size required is 312.
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What will be the output of the following code snippet and why? public static void main(string[] args) { int num = 2; int dividend = 5; dividend /= num; system.out.println(dividend); }
2 will be the output of the following code snippet.
What is a snippet in coding?
A code Snippet is a programming term that refers to a small portion of re-usable source code, machine code, or text. Snippets help programmers reduce the time it takes to type in repetitive information while coding. Code Snippets are a feature on most text editors, code editors, and IDEs.What does a code snippet look like?
Code snippets are templates that make it easier to enter repeating code patterns, such as loops or conditional-statements. In Visual Studio Code, snippets appear in IntelliSense (Ctrl+Space) mixed with other suggestions, as well as in a dedicated snippet picker (Insert Snippet in the Command Palette).The output will be 2 because when two integers are divided in Java, the decimal portion is always truncated.
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The complete question is -
The following snippet of code would produce what outcome? public static void main(String 2 [] args) { int day = 5; switch (day) { case 1: System.out.println("Monday "); case 2: System.out.println("Tuesday "); case 3: System.out.println("Wednesday "); case 4: System.out.println("Thursday "); case 5: System.out.println("Friday "); case 6: System.out.println("Saturday "); case 7: System.out.println("Sunday "); break; default: System.out.println("Invalid Day "); } } Invalid Day Friday Saturday Sunday Invalid Day Friday Friday Saturday Sunday What will be the output of the following code: int x = 20; int y = 40; if (x > 10) { if (y > 50) { System.out.println("Hello, Friend."); } else { System.out.println("Goodbye, Friend."); } } else { if (y > 50) { System.out.println("Hello, Enemy:"); } else { System.out.println("Goodbye, Enemy."); } } Hello, Friend. Hello, Enemy. Goodbye, Friend. Goodbye, Enemy.
Begin by graphing the absolute value function, . Then use transformations of this graph to graph the given function. h(x)= /x/ - 4
The value of the modulus function is g ( x ) = | x | - 4
What is Modulus Function?Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:
If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
Given data ,
Let the absolute value function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = | x | be equation (1)
Now , the function f ( x ) is shifted vertically down by 4 units
Down by d units: y = f(x) - d
Substituting the values in the equation , we get
Let the translated function be represented as g ( x )
g ( x ) = f ( x ) - 4
On simplifying the equation , we get
g ( x ) = | x | - 4
Hence , the transformed function is g ( x ) = | x | - 4
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4x + 6y = -8
-6x-6y = 24
what are the coordinate point where the two lines will intersect
Answer:
the point where the two lines intersect is (-8, 4)
Solve for x. 2(x-4)=17 a. X=1 b. X=2 c. X=12.5 d. X= 11
Answer:
c. x=12.5
Step-by-step explanation:
Equation Solving
Given the equation
2(x - 4) = 17
Solving for x implies doing several operations needed to have x isolated in the left part of the equation.
Dividing by 2:
x - 4 = 17/2
x - 4 = 8.5
Now we add 4:
x = 8.5 + 4
x = 12.5
Answer: c. x=12.5
Can these three side lengths form a triangle? 20ft, 20ft, 35ft
a. Yes
b. No
Answer:
A. yes
Step-by-step explanation:
These side lengths can form a triangle because a triangle can have 2 equal sides and an unequal one this triangle is called an isosceles triangle
what is the solution to this equation?4x+2(x+6)=36
5. A student surveyed 100 adults who took either vitamin C, zinc, or echinacea
supplements to prevent getting a cold. The adults were asked if they had a cold or no
cold in the last 30 days. The results are shown in the table.
vitamin C
zinc
no cold cold
41
echinacea
total
12
21
74
15
5
6
total
26
56
17
27
100
a. What proportion of adults in the survey took echinacea?
b. What proportion of adults who took vitamin C reported having a cold in the last
30 days?
c. What proportion of adults who reported having a cold took zinc?
The proportions for this problem are given as follows:
a) Took echinacea: 0.27.
b) Having a cold in the last 30 days, of those who took Vitamin C: 0.2679.
c) Took zinc, of those having a cold: 0.1923.
How to calculate the proportions?The proportions are calculated as the division of the number of desired outcomes by the number of total outcomes.
The survey is composed by 100 adults, and of those, 27 took echinacea, hence the proportion is of:
27/100 = 0.27.
56 adults took vitamin C, and of those, 15 reported a cold in the last 30 days, hence the proportion is of:
15/56 = 0.2679.
26 students had a cold in the last 30 days, and of those, 5 took zinc, hence the proportion is calculated as follows:
5/26 = 0.1923.
Missing InformationThe table is given by the image shown at the end of the answer.
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your friend, a male soccer player weighing 86 kg, is trying to determine how many carbohydrates should be consumed 2 hours before his soccer game. based on his weight, how many grams of carbohydrate would you recommend for your friend 2 hours before the soccer game?
In linear equation, The carbohydrate intake ranges between 129-286g
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
A diet with adequate proteins and carbohydrates can be given to an athlete (2-3 hours) before a sport.
Generally, 2-3g/kg body weight of Carbohydrates can be included in the diet (depending on the weight and height.
Here, the person weighs 86kgs (assuming the majority of the bodyweight is muscle mass)
Therefore, average carbohydrate intake can be – 85* 2 = 170g; or, 85*3 = 255g
Thus, the carbohydrate intake ranges between 129-286g
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jamie is 3 years less than three times Andys age. In five years the sum of their ages will be 59.How old are they now
Answer:
Andy : 13 years old and
Jamie: 36 years old
Step-by-step explanation:
Andy = x
Jamie = 3x - 3
In 5 years:
(X+5)+(3x-3+5) = 59
4x + 7 = 59
4x = 59 - 7
x = 52/4
x = 13
a false association between two variables that is actually due to the effect of a third variable is called a .
a false association between two variables that is actually due to the effect of a third variable is called a confounding variables.
What is a Variable?In the context of a mathematical problem or experiment, a variable is anything that may be altered. Typically, a variable is denoted by a single letter. Common generic symbols used for variables include the letters x, y, and z. An attribute that can be measured and have a wide range of values is called a variable. Size, age, wealth, place of birth, academic standing, and kind of housing are a few examples of factors. Both categorically and numerically can be used to categorise variables into two primary groups.
Third factors that affect both the independent and dependent variables are referred to be confounding variables. You risk overestimating the correlation between your independent and dependent variables if you don't take confounding factors into account.
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Triangle JKL is dilated by a scale factor of
2
2 to form triangle J'K'L'. What is the measure of side L'J'?
Step-by-step explanation:
If triangle JKL is dilated by a scale factor of 2, this means that all sides of triangle JKL are multiplied by 2 to form triangle J'K'L'.
Therefore, if the measure of side LJ is x, then the measure of side LJ' is 2x. Similarly, if the measure of side LK is y, then the measure of side L'K' is 2y.
To find the measure of side L'J', we can use the fact that the sum of the measures of the angles in any triangle is always 180 degrees.
In triangle JKL, the sum of the measures of angles J, K, and L is 180 degrees. This means that angle JKL is:
angle JKL = 180 - angle J - angle K
Since triangle JKL is dilated by a scale factor of 2, the corresponding angles in triangle J'K'L' are congruent to the angles in triangle JKL. Therefore, angle J'K'L' is also:
angle J'K'L' = 180 - angle J - angle K
Since angle J'K'L' is a straight line (180 degrees), we can find angle J'L'K' by subtracting angles J'K'L' and J'KL':
angle J'L'K' = angle J'KL' - angle J'K'L' = angle JKL - angle J'K'L'
Using the fact that corresponding angles in similar triangles are congruent, we have:
angle J'KL' = angle JKL
angle L'K'J' = angle LKJ
Therefore, angle J'L'K' is:
angle J'L'K' = angle JKL - angle J'K'L' = angle JKL - angle LKJ
Since triangle JKL is a triangle, we know that angle JKL + angle LKJ + angle LJK = 180 degrees. Therefore, we can rewrite the equation for angle J'L'K' as:
angle J'L'K' = (angle JKL + angle LKJ + angle LJK) - 2(angle JKL + angle LKJ)
Simplifying this equation, we get:
angle J'L'K' = angle LJK - angle JKL
Using the fact that corresponding angles in similar triangles are congruent, we have:
angle L'J'K' = angle LJK
angle J'L'K' = angle JKL
Therefore, triangle J'L'K' is similar to triangle JKL, and we can write the ratio of corresponding side lengths as:
L'J' / LJ = K'L' / KL
Since triangle JKL is dilated by a scale factor of 2, we have:
K'L' = 2LK
L'J' / LJ = 2L'K' / LK
Substituting L'K' = 2LK, we get:
L'J' / LJ = 4
Therefore, the measure of side L'J' is four times the measure of side LJ. If the measure of side LJ is x, then the measure of side L'J' is 4x.
The measure of side L'J' in the dilated triangle J'K'L' can be found by multiplying the length of the corresponding side in the original triangle by the scale factor of 2.
Explanation:In the field of Mathematics, specifically geometry, a dilation is a transformation that alters the size of a figure without changing its shape. If Triangle JKL is dilated by a scale factor of 2 to form Triangle J'K'L', every dimension of Triangle JKL is multiplied by this scale factor to get the corresponding dimension in Triangle J'K'L'.
Therefore, if you want to determine the measure of side L'J' in the new triangle, we need to know the length of the corresponding side in the original triangle (which is LJ). You would then multiply this length by the scale factor. The result would give you the length of side L'J'.
For example, if the length of side LJ in the original triangle is 4 units, the length of the corresponding side L'J' in the dilated triangle would be 4 * 2 = 8 units.
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Suppose at a particular moment earth and neptune are lined up with the sun. if we measure the distance between earth and the sun as 1.5 x 10^8 km and the distance between neptune and the sun as 4.5 x 10^9 km, what is the distance between earth and neptune?
The distance between Earth and Neptune is 4.35 x 10^9 km.
To find the distance between Earth and Neptune, we need to subtract the distance between Earth and the Sun from the distance between Neptune and the Sun.
Distance between Earth and Neptune = Distance between Neptune and the Sun - Distance between Earth and the Sun
Given:
Distance between Earth and the Sun = 1.5 x 10^8 km
Distance between Neptune and the Sun = 4.5 x 10^9 km
Substituting these values into the equation, we have:
Distance between Earth and Neptune = 4.5 x 10^9 km - 1.5 x 10^8 km
To subtract these values, we need to make sure they are in the same units. In this case, both values are already in kilometers, so we can subtract them directly:
Distance between Earth and Neptune = 4.5 x 10^9 km - 1.5 x 10^8 km
= 4.5 x 10^9 km - 0.15 x 10^9 km
= (4.5 - 0.15) x 10^9 km
= 4.35 x 10^9 km
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Please help if you can!! Suppose f(x) = x+ 2. Find the graph of
2f(x).
Click on the correct answer.
graph 1
graph 2
What is the x-intercept of the line below?
Answer:
(2,0) or 2
Step-by-step explanation:
The x-intercept is the point where the line intercepts or goes through the x-axis. The x-axis is the horizontal line that is labeled x.
Another way to find the x-intercept is to find the x value when the y value or f(x) equals zero.
15 first-year algebra students are learning how to solve two-step equations. the teacher notices that the students are not using precise mathematical language. which two instructional strategies should the teacher employ to encourage students to use precise mathematical language when completing this task? choose 2 answers
Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.
However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.
So the list goes as
1. Exponents
2. Roots
3. Multiplication
4. Division
5. additional
6. Subtraction
However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.
Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.
Furthermore, the preferred behavior norm for division and multiplication is different.
Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.
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The coordinates G(7, 3), H(9, 0), I(5, -1) form what type of polygon?
an obtuse triangle
an acute triangle
an equilateral triangle
a right triangle
Answer:
C is the answer
Step-by-step explanation:
Answer:
an equilateral triangle
Step-by-step explanation:
twelve cubes are stacked to make this figure
Answer:
rectangular prism
Step-by-step explanation:
Answer:
rectangular prism
Step-by-step explanation:
Select the equation that has a = 1 1/2 as its solution.
Answer:
1445
Step-by-step explanation:
hey
\(4\frac{1}{6} +a=5\frac{2}{3}\) is the equation that has a=\(1\frac{1}{2}\) as its solution.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
we need to find the equation which gives a=\(1\frac{1}{2}\)
Convert the mixed fraction to the improper fraction
a=3/2
\(4\frac{1}{6} +a=5\frac{2}{3}\)
Convert the mixed fraction to the improper fraction
25/6+a=17/3
Now take the variable on one side and constants on other sides
a=17/3-25/6
LCM of 3 and 6 is 6
a=34-25/6
a=9/6
The numerator and denominator are multiples of 3.
a=3/2
Hence, \(4\frac{1}{6} +a=5\frac{2}{3}\) is the equation that has a=\(1\frac{1}{2}\) as its solution.
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Angela sees a puzzle that uses a board with 20 holes drilled into it. There are 18 pegs in the holes, and the goal of the puzzle is to move the pegs by hopping them into the open holes until both holes are at one end of the board.
The correct answer is option C. as a p-type semiconductor with the pegs representing electrons and the holes representing positive charges.
What is semiconductor ?Between a conductor, like metallic copper, and an insulator, like glass, a semiconductor substance has an electrical conductivity value. While metals behave in the other direction, it loses resistance as its temperature rises. By adding impurities ("doping") to the crystal structure, one can change the material's conducting properties in advantageous ways. A semiconductor junction forms when a crystal contains two regions that have differing doping levels. The fundamental element of diodes, transistors, and the majority of contemporary electronics is the behavior of charge carriers, such as electrons, ions, and electron holes, at these junctions. The elements close to the so-called "metalloid staircase" on the periodic table, such as silicon, germanium, gallium arsenide, and others, are examples of semiconductors.
When a peg is moved, it can be thought of as an electron moving, and this peg (the electron) occupies a new hole (thus, it recombines with the hole), leaving behind a free hole. The holes indicate positive charges, while the pegs represent electrons.
Additionally, a p-type semiconductor has a higher concentration of holes than electrons, and the same is true for the puzzle (18 pairs of pegs (electrons-holes) and 2 open holes make up the puzzle, increasing the concentration of holes).
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