The value of a in the quadratic equation x² + 2x +4 = (x + 2)² + a( x + 2) + b is equal to -2.
How to solve the constant "a" in the quadratic equation.We shall first expand the right hand side and express it in form of the left hand side of the quadratic equation, and then compare their coefficients to derive the value of the constant as follows;
Left hand side; {open brackets}
(x + 2)² + a( x + 2) + b = x² + 4x + 4 + ax + 2a + b
(x + 2)² + a( x + 2) + b = x² + 4x + ax + 4 + b {group like terms}
(x + 2)² + a( x + 2) + b = x² + (4 + a)x + 4 + b
such that :
x² + 2x +4 = (x + 2)² + a( x + 2) + b, then;
x² + 2x +4 = x² + (4 + a)x + 4 + b
by comparing coefficients, we have that;
4 + a = 2
a = 2 - 4 {subtract 4 from both sides}
a = -2
Therefore, for all values of x, the constant a = -2 for the quadratic equation x² + 2x +4 = (x + 2)² + a( x + 2) + b.
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Solve the inequality.
-2d + (-5) ≤ 17
Answer:
d ≥ −11
Step-by-step explanation:
Step 1: Add 5 to both sides.
−2d−5+5 ≤ 17+5
−2d ≤ 22
Step 2: Divide both sides by -2.
−2d/−2 ≤ 22/−2
d ≥ −11
Which of the following is true about k-means clustering Group of answer choices A tree diagram is used to illustrate the steps in the clustering analysis We choose the value for k before doing the clustering analysis It is a type of hierarchical clustering The cluster analysis will give us an optimum value for k In a cluster analysis, the distance between the clusters should be: Group of answer choices Maximized Minimized Even Zero THANK YOU :)
Prior to performing the clustering analysis, we select the value for k, the statement regarding k-means clustering is accurate and the minimum distance between the clusters should be used.
Data is divided into groups (clusters) using cluster analysis that is relevant, practical, or both. If creating meaningful groups is the goal, the clusters should reflect the data's inherent structure. However, cluster analysis can occasionally merely serve as a valuable starting point for other tasks, including data summarization. In a wide range of disciplines, including biology, statistics, pattern recognition, information retrieval, machine learning, and data mining, cluster analysis has long been crucial, whether for understanding or usefulness. Cluster analysis has been used to solve numerous practical issues.
Hartigan (1975, pp 90-91) provides the following general guideline when determining the number of clusters. When (sum(k$withinss)/sum(kplus1$withinss)-1)*(nrow(x)-k-1) is more than 10, it is justified to add the extra group if k is the result of k-means with k groups and kplus1 is the result with k+1 groups.
As a result, choice B is the appropriate response.
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dylan and sam start at the same point and begin jogging in different directions. dylan is jogging east at a speed of 4 miles per hour. sam is jogging south at a speed of 3 miles per hour. after how many hours will they be exactly 15 miles apart?
After 3 hours Dylan and Sam will be exactly 15 miles apart .
In the question ,
it is given that ,
the speed at which Dylan is jogging in east = 4 miles per hour .
the speed at which Sam is jogging in south = 3 miles per hour .
the distance covered by Dylan is = 4t
the distance covered by Sam is = 3t
we have to find the time when they are 15 miles apart .
Since Dylan walks in east and Sam walks in South , it forms a right triangle , so , it will satisfy the Pythagoras Theorem ,
(3t)² + (4t)² = 15²
9t² + 16t² = 225
225 = 25t²
t² = 225/25 = 9
t = 3
Therefore , the time taken will be 3 hours .
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Write the rationalized expression of:
Sqrt(9)/(sqrt(3)+sqrt(x))
The rationalized expression would be [tex]\sqrt{3}+\frac{\sqrt{9} }{\sqrt{x}}[/tex].
What is a rationalized expression?
A rationalized expression is an expression that has been written in a simplified form which eliminates any radicals (square roots, cube roots, etc.) from the denominator. The denominator is made a rational number, meaning it can be expressed as a fraction with an integer numerator and denominator. This is done by multiplying both the numerator and the denominator by the radical of the denominator. This process is called rationalization.
The given expression is
[tex]=\frac{\sqrt{9}}{\sqrt{3}+ \sqrt{x} } \\\\=\frac{\sqrt{9} }{\sqrt{3} }+ \frac{\sqrt{9} }{\sqrt{x}}\\\\=\frac{3 }{\sqrt{3} }+\frac{\sqrt{9} }{\sqrt{x}}\\\\=\sqrt{3}+\frac{\sqrt{9} }{\sqrt{x}}[/tex]
Hence, the rationalized expression would be [tex]\sqrt{3}+\frac{\sqrt{9} }{\sqrt{x}}[/tex].
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How Many Intersections Are There Of The Graphs Of The Equations Below? 3x+30y = 36 None One Two Infinitely Many
The number of points of intersection for the graphs of the equations is infinite.
Point of intersection refers to the point at which two lines intersect on a graph. The graph of the equation refers to the visual demonstration of the equation obtained by plotting all the points of an equation on a graph. If there is only one variable, the graph is on a number line. If there are two variables, the graph is on the coordinate plane. If there are three variables, the graph is in three-dimensional coordinates.
Simplifying the given equations:
i) x/2 + 5y = 6
x + 10y = 12
ii) 3x + 30y = 36
3(x + 10y) = 36
x + 10y = 12
As the equations are equal lines, they will intersect at infinite times.
Note: The question is incomplete. The complete question probably is: How many intersections are there of the graphs of the equations below? x/2 + 5y = 6 3x + 30y = 36 none one two infinitely many
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Please help me Limited time I’ll give brainliest
Answer: C - I agree
D - Square root 50 lies between integers 7 and 8
E - Find the closest integer to 40
Step-by-step explanation: C - 7/9 will be 0.77777778 which you can simplify to 0.777
D - The square root of 50 is 7.07106781187 so it is between the integers 7 and
E - The square root of 40 is 6.32455532034 which so find the clossest integer to 40
Rose is mailing a package of magazines and
chips to her kids at camp. The package weighs
a total of 9 pounds and has 14 items inside. The
magazines each weigh 1 pound and the chips
each weigh .5 pounds. How many magazines, x,
and chips, y, is Rose mailing in the package?
x + y = 14
x + 0.5y = 9
a test often conducted to initially identify and evaluate
Tests are frequently used to initially determine and assess potential worker safety and health issues.
What are two good measures of safety and health program effectiveness?The following factors are essential to a good workplace safety and health program: Leadership and management commitment. Accountability. Concern for safety.
An idea or rule that directs behaviors, processes, or tools with the goal of reducing the possibility or incidence of harm to people, property, or the environment.
In order to protect people's bodily, mental, and material health as well as the community's overall wellbeing, safety is the condition in which risks and circumstances that could cause harm are under control. It is a necessity for daily existence and is required by both individuals and communities in order to realize their objectives.
Workplace safety procedures are established practices that describe how to carry out duties with the least amount of danger to people, property, and working conditions. The processes cover work-related duties that deal with safety issues, safety gear, and work-area safety precautions.
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tell whether each point is on the graph of f(x)=|x|.If it is, give the coordinates of another point with the same y value. (11,11)
The point (11,11) will lie on the graph of the function f(x) = IxI
What is coordinate?
The x-coordinate informs us of a point's separation from the y-axis, which is the vertical axis. The abscissa is another term for the x-coordinate. The y-coordinate shows how far a point is from the horizontal axis, or x-axis. The term "ordinate" also applies to the y-coordinate.
the function: f(x) = IxI
The function will have every positive and negative integer contained within itself.
So coordinates of another point with the same y value (11,11) will lies on the graph so as (-11,11).
Hence point (11,11) will lie on the graph of the function f(x) = IxI
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Please help, thank you. -10 points
Answer:
C
Step-by-step explanation:
3y+3=3y-3
taking the 3y from the right to the left and the 3 in the left to the right
3y-3y= -3-3
0=-6
taking the 3y from the left to the right and the 3 in the right to the left
3+3=3y-3y
6=0
-the amount of regular unleaded gasoline purchased every week at a gas station follows the normal distribution with mean 50000 gallons and standard deviation 10000 gallons. the starting supply of gasoline is 74000 gallons, and there is a scheduled weekly delivery of 47000 gallons. (a) find the probability that, after 11 weeks, the supply of gasoline will be below 20000 gallons. (b) how much should the weekly delivery be so that after 11 weeks the probability that the supply is below 20000 gallons is only 0.5%?
(A) The probability that, after 11 weeks, the supply of gasoline will be below 20000 gallons is 0.2643.
(B) 52854.8 gallons should be the weekly delivery so that after 11 weeks the probability that the supply is below 20000 gallons is only 0.5%.
Given,
u = 50000
s = 10000
n = 11
Starting supply = 74000
Weekly delivery = 47000
Total supply for 11-week = 74000 + 11*47000
= 591000
(A) If more than 20,000 gallons of gasoline are purchased overall in these 11 weeks, the supply will fall below that amount.
591000 - 20000 = 571000
We need to find, P(T > 571000) = P(z > [tex]\frac{571000-11(50000)}{\sqrt{1110000} }[/tex])
= P(z > 0.63)
= 1 - 0.7357
= 0.2643
(B) Unknown schedule delivery = A
Total gasoline should be more than = 74000 + 11*A - 20000
Probability = 05%
z-value corresponding it = 2.575
P(T > 74000 + 11*A - 20000) = 0.05
[tex]\frac{74000+11A-20000-11(50000)}{\sqrt{1110000} } = 2.575[/tex]
A = 52854.8
Hence, 52854.8 gallons should be the weekly delivery be so that after 11 weeks the probability that the supply is below 20000 gallons is only 0.5%.
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A diver is at a certain depth in the ocean. After ascending 10 3/4 feet, the diver is now at a depth of -56 1/2 feet, Write and solve an equation to determine the diver’s initial depth.
Equation to determine the diver’s initial depth is [tex]x + 10 \frac{3}{4} = 56\frac{1}{2}[/tex].
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
In algebra, an equation is a condition on a variable. It is satisfied only for a definite value of the variable.
The equation in one variable means the equation containing only one variable. Let’s have a look at the below equations.
Let the distance of diver at a certain depth be x.
After some time he ascends [tex]10\frac{3}{4}[/tex] feet.
The final position of diver is : [tex]56\frac{1}{2}[/tex] feet.
Using given information we get the required equation: [tex]x + 10 \frac{3}{4} = 56\frac{1}{2}[/tex].
where x = distance of diver at a certain depth.
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3 lines are shown. A line with points T, R, W intersects a line with points V, R, S at point R. A line extends from point R to point Z between angle V R W. Angle V R T is (5 x) degrees and angle T, R, S is (25 x + 30) degrees. In the diagram, what is the measure of AngleWRS? 5° 7.5° 25° 37.5°
The measure of ∠WRS is 25°.
What is meaning of intersect point?
A graph intersection is a location where two or more graphs meet. It is a point that is the answer to an equational system. The intersection of two curves is the sole application of the TI series.
Given the points on a line are T, R, W.
The points on another line are V, R, S.
Both lines intersect at R.
Then another line that extends from point R to point Z between ∠VRW.
The angle ∠VRT is 5x° and the angle ∠TRS is (25x + 30)°.
∠VRS is a linear angle means ∠VRS = 180°.
Again,
∠VRS = ∠VRT + ∠TRS
Putting the value of ∠VRS, ∠VRT, ∠TRS
180° = 5x° + (25x + 30)°
180 = 30x + 30
Subtract 30 from both sides:
150 = 30x
Divide both sides by 30:
x = 5.
∠WRS is vertically opposite angle of ∠VRT.
Therefore ∠WRS = ∠VRT = 5x° = (5×5)° = 25°
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A cylindrical wooden column is 3 m high and 28 cm in diameter use value π to calculate the mass in kf of the column if the density of the wood is 0.8g/cm^3
Answer:
1.478 kg
Step-by-step explanation:
Considering density=mass/volume, when we rearrange, we get mass=density*volume. Therefore, as we are given the density, we just need to find the volume to know the mass. The volume of a cylinder is πhr^2, and our radius is 28/2=14, so the volume of the cylinder is π*3*14^2=588π. Then, 588π*0.8=470.4π which is about 1477.8052 g. Then, to convert to kg, we can divide this by 1000 and get about 1.478 kg.
HELP MEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A. 147.5
B. 430.2
Step-by-step explanation:
A. 2001
2001 - 1998 = 3
y = 122.1(1.065)³
y = 147.49
y = 147.5
B. 2018
2018 - 1998 = 20
y = 122.1(1.065)²⁰
y = 430.23706225
y = 430.2
I hope this helps!
Arrange these from greatest to least greatest PLEASE HELP ME ANSWER THIS QUESTION
Answer: 37, 15, 12, 0, -6, -8, -23
Step-by-step explanation:
So, the higher the negative number, the lower the value is. Hope this helps!
Which of the following is the basis of diminishing marginal utility Mcq?
O MCN = TFCN - TFCN-1
O MCN = ACN - ACN-1
O MCN = AVCN - AVCN-1
O MCN = TCN - TCN-1
MCN= ACN-ACN-1 is the basis of diminishing marginal utility.
What is marginal utility?
The additional pleasure a consumer has from owning one extra unit of an item or service is known as marginal utility. Economists utilize the idea of marginal utility to estimate the quantity of a good that consumers will buy.
When positive marginal utility occurs?When the overall utility is increased by the consumption of an additional item, positive marginal utility occurs. On the other side, negative marginal utility arises when the overall utility is reduced by the consumption of one extra unit.
According to the law of diminishing marginal utility, as consumption rises, the marginal utility gained from each additional unit decreases, all other things being equal. The incremental improvement in utility brought on by consuming one more unit is known as marginal utility. An economic term for happiness or contentment is "utility."
So
MCN= ACN-ACN-1
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The ratio of men to women working for a company is 2 to 3. If there are 135 employees total, how many men
work for the company?
Answer:
Step-by-step explanation:
men = 2x
women = 3x
2x+3x=135
5x=135
x=27
27(2)=men
54 men
(1 point) how many strings of four decimal digits (note there are 10 possible digits and a string can be of the form 0014 eth., i., can start with zeros.) (a) end with an even digit? (can repeat digits.) 5000 (b) begin with an odd digit? (can repeat digits.) 5040
(a) 10⁴ strings of four digits which end with an even digit.
(b) 10⁵ strings of four digits which begin with an odd digit.
(a)There are 10 choices ranging from 0 to 1,2...9 for the first three digits of the string that ends in an even number and four possibilities ranging from 2,4,6,8, for the last digit.
According to the product rule there are 4000 strings that terminate in an odd number or 10 × 10 × 10 × 4.
(b) Also there are 10 choices ranging from 0 to 9 for the last three digits of the string that ends in an odd or even number and 5 possibilities ranging from 1,3,5,7,9 for the first digit .
According to the product rule there are 5000 strings that terminates in an even number or 10 × 10 × 10 × 5.
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in october, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. the bookstore believes that the two groups spent the same amount. what is an appropriate test value for a z test?
As per the sampling, an appropriate test value for a z test is 0.808
Sampling:
In math, sampling means selecting the group that you will actually collect data from in your research.
Given,
In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. the bookstore believes that the two groups spent the same amount.
Here we need to find the appropriate test value for a z test.
As per the given question, first we must know the definition of z test,
The term z-test means statistical test that can be used to determine whether two population means are different.
And it is used when the variances are known or the sample size is large.
And the formula of the z value, the test statistic for two population with large sample size is given by,
z = [x₂ - x₁] / √[(s₁²/n₁) + (s₂²/n₂)]
From the question we have, x1=$320, x2=$310, s1=$62, s2=$73, n1=60 and n2 = 60.
When we apply the value then we get the z value as
=> z = [310 - 320] / √[(62²/60) + (73²/60)]
=> 0.808
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a spring has a natural length of 18 inches and a force of 20 lbs is required to stretch and hold the spring to a length of 24 inches. what is the work required to stretch the spring from a length of 21 inches to a length of 26 inches?
The work required to stretch the spring is 91.6 Ibs-inch
What is work?
Work is defined as force applied across a distance. Work examples include pushing an object against gravity, driving a car up a hill, and lowering a captive helium balloon. Work is the mechanical expression of energy.
Δx : displacement from equilibrium position
f = k Δ x (force due to spring = -kΔx)
where, k is the spring constant
Given,
f = 20ibs
Δx = 24 -18 Inches = 6 inches
∴ k = 20/6 ibs/inch
Now, PE stored in spring = 1/2 k (Δx)²
Δx : displacement from equilibrium position
Work done = change in PE
= 1/2K (Δx₂)² -1/2k (Δx₁)²
given,
Δx₁ = 21-18 inches = 3 inches
Δx₂ = 26-18 inches = 8 inches
∴work done = 1/2 * 20/6 (8² - 3²)Ibs-inches
=10/6 *5*11
work done = 91.6 ibs-inch
The spring must be stretched with 91.6 Ibs-inch of force.
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HELPP!!!
angles of a triangle
Math
help please! Thank u.
Answer:
Step-by-step explanation:
40/20= 20
39/x=x
that woudl be how you would find it
Determine which integer will make the inequality 2(n + 2) < 5(n − 1) true.
S:{10}
S:{3}
S:{2}
S:{0}
Hence, when [tex]n=10[/tex] the given inequality is true.
What is the inequality?
An inequality is said to be sharp if it cannot be relaxed and still be valid in general.
Here given that,
Which integer will make the inequality [tex]2(n + 2) < 5(n -1)[/tex] true.
So,
[tex]2(n + 2) < 5(n-1)[/tex]
When
[tex]n=10\\\\\\2(10+2) < 5(10-1)\\\\2(12) < 5(9)\\\\24 < 45[/tex]
Hence, when [tex]n=10[/tex] the given inequality is true.
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assume that x1, x2, x3, and x4 are independent random variables. read the following statements. (a) the joint pmf or pdf for x1, x2, x3, and x4 is f1(x1)f2(x2)f3(x3)f4(x4). (b) if x1, x2, x3, and x4 are identically distributed then they are considered to be a random sample of size n. (c) if x1, x2, x3, and x4 have the same mean and variance then they are called a statistic. (d) identically distributed x1, x2, x3, and x4 can be thought of as measurements on outcomes of 4 random experiments. now choose the correct answer. group of answer choices all statements (a), (b), (c), and (d) are correct. statements (a) and (d) only are correct. statements (a), (b), and (c) only are correct. statements (a) and (b) only are correct. none of these answers are correct. statements (a), (b), and (d) only are correct.
On solving the provided question we got to know that, favorable cases for X4 to be the least is that = 0.25
What is probability?Probabilities are mathematical justifications of the probability that an event will happen or that a proposition is true. A number between 0 and 1, where 0 often indicates impossibility and 1 normally indicates certainty, denotes the likelihood of an event.
[tex]X1, \\X2, \\X3[/tex]
can be arranged in 3! Ways so, in tottal 6 ways
[tex]Hence, there are 6 cases where X4 is the lowest.[/tex]
Total no. of cases on which [tex]X1, X2, X3, X4[/tex] be arranged are 4! = 24
Favorable cases for [tex]X4[/tex] to be the least = [tex]6/24 = 1/4 = 0.25[/tex]
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What is the correct order of steps for bisecting segment AB?
A. Draw a line from point C to point D.
B. Keeping the compass the same width, place the compass on point B, and swing an arc above and below the segment.
C. Place points C and D on the intersection of the arcs created above and below segment AB.
D. Place the compass on point A, and open it wider than half the distance of the segment.
E. Swing an arc above and below the segment.
Answer: E
Step-by-step explanation:
answer please!!!! woopp
Answer:
1. infinite
2. no
3. one
4.no
Consider the parent function f (x) below.
Answer:
see the attachment
Step-by-step explanation:
You want graphs of f(x -5) and f(x)+2 and their asymptotes, given exponential function f(x).
f(x-5)The subtraction of 5 from the argument x causes the graph to be shifted to the right 5 units. The horizontal asymptote at y=0 is unchanged.
f(x)+2The addition of 2 to every function value causes the graph to be shifted up 2 units. The horizontal asymptote is likewise shifted up 2 units to y=2.
The red and blue graphs are attached. The asymptotes are dashed lines.
Find (f + g)(x) when f(x) = x - 2 and g(x) = 2x - 7.
Answer:
3x-9
Step-by-step explanation:
Just add the two together. (x-2) + (2x-7)= 3x-9
How do you find the sum of the arithmetic series 1 + 3 + 5 + ... + 27?
Answer:
sum = 196
Step-by-step explanation:
the sum to n terms of an arithmetic series, when the first and last terms are known is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( first term + last term)
we require to find the number of terms in the series
the nth term of an arithmetic series is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d = a₂ - a₁ = 3 - 1 = 2 , then
1 + 2(n - 1) = 27 ( subtract 1 from both sides )
2(n - 1) = 26 ( divide both sides by 2 )
n - 1 = 13 ( add 1 to both sides )
n = 14 ← number of terms in the series
Then
S₁₄ = [tex]\frac{14}{2}[/tex] (1 + 27) = 7 × 28 = 196
