Answer:
Step-by-step explanation:
Somebody plays 30 times
L+W = 30, where L and W are number of losses and wins, respectively.
L = 30-W
Net after 30 plays is $6
2W - 1L = 6
2W - (30-W) = 6
3W = 36
W = 12
W = 18
17 wins
Myron put $5000 in a 5 year CD paying 3% interest compounded monthly. After 2 years he withdrew all his money and as an early withdrawal penalty he paid back all the interest he made during the first year. How much money was Myron left with
Answer:
$7128.80
Step-by-step explanation:
First, create an equation.
Use the formula f(t)=P(1+b)^t
Plug in the information.
Time will equal months.
f(12)=5000(1+0.03)^12
Solve.
f(12) = 7128.80
Myron was left with $7128.80.
Hope this helps!
A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 17 doors is taken, and it is found that they have a mean of 2069 millimeters with a standard deviation of 24. Assume the population is normally distributed. Is there evidence at the 0.02 level that the doors are either too long or too short
There is not enough evidence at the 0.02 level that the doors are either too long or too short. So, the null hypothesis is accepted.
How to decide whether the null hypothesis is rejected or accepted?Using the p-value approach for the hypothesis test, whether the null hypothesis is rejected or accepted.
If the p-value is greater than the significance level then the null hypothesis is accepted.If the p-value is less than the significance level then the null hypothesis is rejected.Calculation:It is given that,
Sample size n = 17
Sample mean X = 2069
Standard deviation σ = 24
Population mean μ = 2058
Significance level α = 0.02
Hypothesis:
The null hypothesis: H0: μ = 2058
The alternative hypothesis: Ha: μ ≠ 2058
So, the z-test score for the given distribution is,
z-score = (X - μ)/(σ/√n)
On substituting,
z-score = (2069 - 2058)/(24/√17)
= 11/5.82
= 1.89
Thus, the p-value for the z-score of 1.89 is 0.0587 ≅ 0.06.
Since 0.06 > 0.02(significance level), the null hypothesis is accepted. So, there is no sufficient evidence that the doors are either too long or too short.
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Type the correct answer in the box. Use numerals instead of words.
What is the length of the diagonal shown in the rectangular prism? Round your answer to the nearest tenth.
7 ft
ft
4 ft
5 ft
The length of diagonal is 9.5 ft
What is Pythagoras theorem?
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
We will find the length of diagonal as shown below:
l= 7 ft
h= 5 ft
w= 4 ft
Let diagonal be d.
Let v be the diagonal of the base.
Using Pythagoras theorem
[tex]v=\sqrt{7^2+4^2}[/tex]
[tex]=\sqrt{49+16}[/tex]
[tex]v=\sqrt{65}[/tex]
For finding the value of d again using Pythagoras theorem
[tex]d=\sqrt{v^2+h^2}[/tex]
[tex]=\sqrt{(\sqrt{65})^2+5^2 }[/tex]
[tex]=\sqrt{65+25}[/tex]
[tex]=\sqrt{90}[/tex]
=9.4868
Rounding to nearest tenth
=9.5
Hence, the length of diagonal is 9.5 ft
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A rectangular box with a square base, an open top, and a volume of 32,000 cm3 is to be made. What is the minimum surface area for the box
the minimum surface area for the box is 4800 cm².
Forming the Equation of SurfaceArea
It is given that the given rectangular box is square-based and top is open. hence, it consists of square and 4 rectangles.
Let the side of the square be a, and height of the box be h.
Then, the total surface area of the box will be given by,
S = a² + 4ah _________ (1)
Also, it is given that the volume of the box is, V = 32000 cm³
The volume of the rectangular box, V = a² h
Eliminating One of the Variables From the Equation
The volume of the rectangular box, V = a² h
⇒ a² h = 32000
⇒ h = 32000/a² _______ (2)
Substituting this value of h in equation (1), we get,
S = a² +4a(32000/a²)
S = a²+128000/a
Minimizing the Surface Area Equation
To find the minima, put, dS/da = 0
dS/da = 2a-128000/a²
⇒ 2a-128000/a² = 0
Multiplying the whole equation with a², we get,
2a³-128000 = 0
⇒ 2a³ = 128000
⇒ a³ = 128000/2
⇒ a³ = 64000
⇒ a = 40 cm
Calculating the Minimum Surface Area
From, equation (2), h = 32000/(40)²
h = 32000/1600
h = 20 cm
Now, substituting the computed values of a and h in equation (1), we get,
S = (40)² +4(40)(20)
S = 1600 +3200
S = 4800 cm²
∴ The minimum surface area of the box is 4800 cm².
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Which sequence shows a pattern where each term is 1.5 times the previous term?
A: -4, 6, -9, 13.5
B: 10, 15, 25, 40
C: 98, 99.5, 101, 102.5
D: -200, -300, -450, -675
The sequence that shows a pattern where each term is 1.5 times the previous term is option D
How can series of numbers be in a Sequence ?Series of numbers can be in a sequence either in arithmetic or in geometric. In the above question, it is geometric because the sequence shows a pattern where each term is 1.5 times the previous term.
Let us test each option one by one.
Option A
1.5 x -4 = -6
But the next number in the series is 6
Option B
1.5 x 10 = 15
1.5 x 15 = 22.5
But the next number in the series is 25
Option C
1.5 x 98 = 147
But the next number in the series is 99.5
Option D
1.5 x -200 = -300
1.5 x -300 = -450
1.5 x -450 = -675
Therefore, the sequence that shows a pattern where each term is 1.5 times the previous term is option D
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Answer: D (-200,-300,-450,-675,...)
Step-by-step explanation:
Recognizing the pattern in a sequence is used to write the function that represents it.
The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x − 4)3 − 7. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?
(4, −7)
(−4, −7)
(4, 7)
(−4, 7)
Answer: (4,-7)
Step-by-step explanation:
when f(x) = [tex]x^3[/tex] the vertex is (0,0). when g(x)= [tex](x-4)^3-7[/tex] the vertex will be (4,-7). The equation is put into vertex form, in order for us to find the vertex (h,k), followed by [tex]y=a(x-h)^3+k[/tex]. With h=4 and k=-7.
Therefore, the answer is (4,-7)
Use the factor theorem to determine 2x^3+3x^2-5x-6 of the polynomials is divisible by(x+1)
The quotient of the polynomials [tex]2x^{3} +3x^{2} -5x-6[/tex] divided by (x+1) is [tex]2x^{2} -x-6[/tex].
Given two polynomials [tex]2x^{3}+3x^{2} -5x-6[/tex] and (x+1).
We have to determine whether [tex]2x^{3}+3x^{2} -5x-6[/tex] is divisible by (x+1).
Factors are the numbers which are multiplied to get the number whose factors are given. The factor theorem is a theorem which links factors and zeroes of a polynomial.
Polynomial is an expression of more than two algebraic terms may be in addition or subtraction.
We have to first find the factors of polynomial [tex]2x^{3}+3x^{2} -5x-6[/tex].
[tex]2x^{3}+3x^{2} -5x-6[/tex]=[tex]2x^{3}+3x^{2} -4x-x-6[/tex]
=[tex]x^{2}[/tex](2x+3)-2(2x+3)-x
=[tex](x^{2} -x-2)[/tex](2x+3)
=([tex]x^{2}[/tex]-x-2)(2x+3)
=[[tex]x^{2}[/tex]-2x+x-2](2x+3)
=[x(x-2)+1(x-2)](2x+3)
=(x+1)(x-2)(2x+3)
Because (x+1) is a factor of [tex]2x^{3}+3x^{2} -4x-x-6[/tex],so it is divisible by (x+1).
Hence using factor theorem we can say that [tex]2x^{3}+3x^{2} -4x-x-6[/tex]is divisible by (x+1).
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You spend 0.88 of your allowance this week. what percent of your allowance did you spend?
Answer: 88%
Step-by-step explanation: So, to convert the decimal into a percentage, multiply .88 by 100. And BOOM! you have 88% as your answer.
We spent 88% of your allowance this week.
Since we know that,
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
To find out what percentage of your allowance you spent,
Divide the amount you spent by your total allowance,
then multiply by 100 to get the percentage.
Here are the steps:
1. Identify the amount you spent: 0.88
2. Identify your total allowance: 1.00 (assuming your allowance is $1.00) 3. Divide the amount spent by the total allowance,
⇒ 0.88 ÷ 1.00 = 0.88 4.
Multiply the result by 100 to get the percentage,
⇒ 0.88 x 100 = 88%
Therefore, we spent 88% of your allowance this week.
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Look at the image below. 5.3, 5, 3. Find the area
Answer: 15 square units
Step-by-step explanation:
[tex]A=(5)(3)=15[/tex]
There is a pair of parallel sides in the following shape. What is the area of the shape
The calculated value of the total area of the figure is 49 square units
How to calculate the area of the figureFrom the question, we have the following parameters that can be used in our computation:
The figure
Where, we have
Shape = trapezoid
The total area of the trapezoid is calculated as
Area = 1/2 * Sum of parallel sides * Height
So, we have
Area = 1/2 * (11 + 3) * 7
Evaluate
Area = 49
Hence. the total area of the figure is 49 square units
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A car dealership needs a program to store information about the cars for sale. For each car, they want to keep track of the following information: number of doors (2 or 4), whether the car has air conditioning, and its average number of miles per gallon. Which of the following is the best design
The best object-oriented program design for this car dealership's software program is to use a single class Car, with three instance variables (fields):
numDoorshasAirmilesPerGallon.What is a class?A class can be defined as a user-defined blueprint (prototype) or template that is typically used by software programmers to create objects and define the data types, categories, and methods that should be associated with these objects.
In object-oriented programming (OOP) language, a class that is written or created to implement an interface in a software would most likely implement all of that interface's method declarations without any coding error.
In this scenario, the best object-oriented program design for this car dealership's software program is to use a single class Car, with three instance variables (fields):
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Complete Question:
A car dealership needs a program to store information about the cars for sale. For each car, they want to keep track of the following information: number of doors (2 or 4), whether the car has air conditioning, and its average number of miles per gallon. Which of the following is the best design?
(A) Use four unrelated classes: Car, Doors, AirConditioning, and MilesPerGallon.
(B) Use a class Car with three subclasses: Doors, AirConditioning, and MilesPerGallon.
(C) Use a class Car, with fields: numDoors, hasAir, and milesPerGallon.
(D) Use a class Car, with subclasses of Doors, AirConditioning, and MilesPerGallon.
(E) Use classes: Doors, AirConditioning, and MilesPerGallon, each with a subclass Car.
In which situation could the quotient of -24 divided by 3 be used to answer the question?
A. The temperature of a substance decreased by 24∘C per minute for 3 minutes. What was the overall change of the temperature of the substance?
B. A football team lost 24 yards on one play, then gained 3 yards on the next play. How many total yards did the team gain on the two plays?
C. Julia withdrew a total of $24 from her bank account over 3 days. She withdrew the same amount each day. By how much did the amount in her bank account change each day?
D. A cookie jar contains 24 cookies. Each child receives 3 cookies. How many children are there?
The situation in which the quotient of -24 divided by 3 be used to answer the question is;
Julia withdrew a total of $24 from her bank account over 3 days. She withdrew the same amount each day. By how much did the amount in her bank account change each day? AlgebraCheck all options:
A. The temperature of a substance decreased by 24∘C per minute for 3 minutes. What was the overall change of the temperature of the substance?
Temperature decrease = 24°C per minutes × 3 minutes
= 72°C decrease in temperature
B. A football team lost 24 yards on one play, then gained 3 yards on the next play. How many total yards did the team gain on the two plays?
Loss = -24 yards
Gain = 3 yards
Total gain = -24 + 3
= -21 yards
C. Julia withdrew a total of $24 from her bank account over 3 days. She withdrew the same amount each day. By how much did the amount in her bank account change each day?
Amount withdrawn per day = -$24 / 3
= -$8 per day
Change in her account per day = $8
D. A cookie jar contains 24 cookies. Each child receives 3 cookies. How many children are there?
Number of children = 24 cookies / 3 cookies
= 8 cookies per children
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equation of a line that passes through the points (4, 5) and (7, -7).
Answer:
y=-4x+21
Step-by-step explanation:
1. Draw these points on a graph.
2. Point A is (4,5) and Point B is (7,-7).
3. You find the slope (gradient) by the Change in Height/ Change in Horizontal distance.
4. Now put that slope and one point into the "Point-Slope Formula"
5. Simplify Algebraically.
Answer:
y = - 4x + 21
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 5 ) and (x₂, y₂ ) = (7, - 7 )
m = [tex]\frac{-7-5}{7-4}[/tex] = [tex]\frac{-12}{3}[/tex] = - 4 , then
y = - 4x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (4, 5 )
5 = - 16 + c ⇒ c = 5 + 16 = 21
y = - 4x + 21 ← equation of line
Abigail is investing in the stock market and has a maximum budget of $6,300 with which to purchase stock in two promising companies. stock in the software company currently sells for $42 per share. stock in the robotics company is currently trading at $8 per share. write the inequality in standard form that describes this situation. use the given numbers and the following variables
Answer:
The equation is 21x+4y<3150
Step-by-step explanation:
This question can be understood by the concept of inequalities.
Let x be the number of stocks of software company and y be the number of stocks of robotics company purchased.
Money invested in 1 stock of software company = $42
Money invested in 1 stock of robotics company = $8
Total expenditure on software company stock = 42*x
Total expenditure on robotics company stock = 8*y
So the total expenditure should be less than 6300
Hence the equation is
42x+8y<6300
21x+4y<3150
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HI! Ok so I specifically am having an issue solving this problem? I keep coming back to 2.32 when im solving it myself and when i've asked for help its also 2.32, 2.3 rounded to be exact but the issue is my program wont accept that?
Am I solving it right or is the program im using just bugging out on me.
maybe try using the 2 and dropping the decimal
The expression $\frac{4k 8}{4}$ simplifies to an expression of the form $ak b$ where $a$ and $b$ are integers. Find $\frac{a}{b}$ .
The value of integers a and b is 1 and 2 and the value of a/b is 1/2.
According to the statement
we have a given a expression 4k+8 / 4 and we have to simplify this expression in the form of ak+b and find the value of a/b where a and b are the integers.
An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Here 4k+8/4 becomes
4k/4 +8/4 -(1)
and general form is
ak+b -(2)
Now, compare these equations then we get
a = 1 and b = 2.
Now we find the value of a/b
then
a/b = 1/2.
So, The value of integers a and b is 1 and 2 and the value of a/b is 1/2.
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A typical decision support system (DSS) includes many components including a(n) _____ which allows decision makers to easily access and manipulate the DSS and to use common business terms and phrases.
A typical decision support system (DSS) includes many components including a(n) dialogue manager which allows decision makers to easily access and manipulate the DSS and to use common business terms and phrases.
What are the components of decision support systems DSS?Decision support systems, according to Management Study HQ, are made up of three essential parts: the database, the software system, and the user interface. DSS repository.What are the 4 parts of DSS?Data management, model management, knowledge management, and user interface management make up the majority of decision support systems.What type of decision-making does DSS support?Systems for supporting data-driven decision making are used by users to make choices about organizations, inventories, and goods.When evaluating recent and historical data to report on the state of a department or the company as a whole, managers may find data-driven decision support systems to be of the most use.Learn more about decision support system here:
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five more than the product of two and a number,
decreased by seven;
evaluate when a = 8
Key Words
five
more than
product
two
a number
decreased by
seven
Intro
Replace With
5
+
X
2
a
7
Write and evaluate the expression. Then, complete the
statements.
First, write the expression
Second,
Third,
The answer is
V
8 in for the variable, a
by using
Done
P
Answer:
It was difficult reading the question, as written. Check my assumptions.
Step-by-step explanation:
"five more than the product of two and a number,
decreased by seven"
---
Let the "number" be a.
We are told "five more than . ." means +5,
"the product of two and a number" means 2a,
"decreased by seven" mean -7
Put the statements together to obtain:
+5+2a-7
Simplify to 2a-2
Evaluate when a = 8:
2a-2
2(8)-2
16-2
= 14
Two consecutive positive integers have a product of 30. what are the integers?
The two consecutive integers are 5 and 6
How to find integers in an expression?let
the first integer = x
second integer = x + 1
Therefore,
x(x + 1) = 30
x² + x = 30
x² + x - 30 = 0
(x - 5)(x + 6) = 0
Therefore,
x = 5 and x = -6
Hence, let's use 5 because it's positive.
So, the numbers are 5 and 6
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Question 1 (1 point)
m2IJK-570 and mZIJL-20°. Find mZLJK.
3
→K
O a MZLJK-77°
Ob mZLJK-37°
Oc mZLJK-40°
Od mZLJK=-37°
Answer:
37°
Step-by-step explanation:
Subtract angle IJL from angle IJK.
100 POINTS!!! PLEASE HELP ASAP EXPERTS! PLEASE I'M BEGGING!!
The function H(t) = −16t2 + 64t + 12 shows the height H(t), in feet, of a baseball after t seconds. A second baseball moves in the air along a path represented by g(t) = 10 + 10.4t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
Answer:
A)
[tex]\begin{array}{|c|c|c|}\cline{1-3} t & H(t) & g(t)\\\cline{1-3} 1 & 60 & 20.4\\\cline{1-3} 2 & 76 & 30.8\\\cline{1-3} 3 & 60 & 41.2\\\cline{1-3} 4 & 12 & 51.6\\\cline{1-3} \end{array}[/tex]
Between 3 and 4 seconds.
B) The baseballs will collide between 3 and 4 seconds.
Step-by-step explanation:
Given functions:
[tex]H(t)=-16t^2+64t+12[/tex]
[tex]g(t)=10+10.4t[/tex]
Part ASubstitute the values of t = 1, 2, 3 and 4 into the two functions:
[tex]H(1)=-16(1)^2+64(1)+12=60[/tex]
[tex]H(2)=-16(2)^2+64(2)+12=76[/tex]
[tex]H(3)=-16(3)^2+64(3)+12=60[/tex]
[tex]H(4)=-16(4)^2+64(4)+12=12[/tex]
[tex]g(1)=10+10.4(1)=20.4[/tex]
[tex]g(2)=10+10.4(2)=30.8[/tex]
[tex]g(3)=10+10.4(3)=41.2[/tex]
[tex]g(4)=10+10.4(4)=51.6[/tex]
Create a table with the found values:
[tex]\begin{array}{|c|c|c|}\cline{1-3} t & H(t) & g(t)\\\cline{1-3} 1 & 60 & 20.4\\\cline{1-3} 2 & 76 & 30.8\\\cline{1-3} 3 & 60 & 41.2\\\cline{1-3} 4 & 12 & 51.6\\\cline{1-3} \end{array}[/tex]
The solution to H(t) = g(t) is between 3 and 4 seconds as:
When t = 3, H(t) > g(t)
When t = 4, H(t) < g(t)
To prove this, equate the equations and solve for t:
[tex]\implies -16t^2+64t+12=10+10.4t[/tex]
[tex]\implies -16t^2+53.6t+2=0[/tex]
Using the Quadratic Formula to solve for t:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\implies t=\dfrac{-53.6 \pm \sqrt{53.6^2-4(-16)(2)} }{2(-16)}[/tex]
[tex]\implies t=\dfrac{53.6 \pm \sqrt{3000.96}}{32}[/tex]
[tex]\implies t=3.39, -0.04\:\:(\sf 2\:d.p.)[/tex]
As time is positive, t = 3.39 s (which is between 3 and 4 seconds).
Part BWhen the two baseballs are at the same height they will collide.
Therefore, the baseballs will collide between 3 and 4 seconds (when t = 3.39 s).
A piece of plexiglass is in the shape of a semicircle with radius 2m. determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass
The dimensions of the rectangle having greatest area in the piece of plexiglass which is a semicircle is [tex]2\sqrt{2}[/tex] and [tex]\sqrt{2}[/tex].
Given radius of piece of plexiglass which is a semi circle equal to 2m.
We have to find the dimensions of the rectangle which is inscribed in the semi circle.
Draw a rectangle in a semicircle.
Suppose the length of rectangle be x and width be y.
Draw a line from the center to the vertex of the rectangle which forms a right angled triangle with sides x,y and 2.
[tex](x/2)^{2} +y^{2} =2^{2}[/tex]
y=[tex]\sqrt{16-x^{2} }/2[/tex]
Area of rectangle=2xy
=x[tex]\sqrt{16-x^{2} }[/tex]/2
Finding the derivative of area
d A/dx=1/2[x(-2x)/2[tex]\sqrt{16-x^{2} }[/tex]+[tex]\sqrt{16-x^{2} }[/tex]]
d A/dx=0
1/2[[tex]-2x^{2} /2\sqrt{16-x^{2} }+\sqrt{16-x^{2} } ][/tex]=0
Solving for x
[tex]\sqrt{16-x^{2}[/tex]=[tex]x^{2} /\sqrt{16-x^{2} }[/tex]
16-[tex]x^{2}[/tex]=[tex]x^{2}[/tex]
16=2[tex]x^{2}[/tex]
[tex]x^{2}[/tex]=8
x=2[tex]\sqrt{2}[/tex]
put the value of x in y=[tex]\sqrt{16-x^{2} }/2[/tex] to get the value of y
y=[tex]\sqrt{16-8} /2[/tex]
=[tex]\sqrt{8} /2[/tex]
= 2[tex]\sqrt{2} /2[/tex]
=[tex]\sqrt{2}[/tex]
Hence the dimensions of rectangle which is in a semi circle of radius 2 is [tex]\sqrt{2} and 2\sqrt{2}[/tex].
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Find the interval in which the function is negative.
f(x)=x²-3x - 4
1. (-∞0, -1)
II. (-1, 4)
HI. (4, ∞)
Oll only
III only
OLI
LIII
Answer:
II only
Step-by-step explanation:
The positive leading coefficient and even degree of f(x) tell you its graph is U-shaped and opens upward.
If there is an interval where the function is negative, it must lie between the two x-intercepts. The graph will be above the x-axis (f(x) > 0) for x-values outside that interval.
The only reasonable answer choice is ...
II (-1, 4) . . . . only
Function f is a rational function with a y-intercept at (0,2). if g(x) = 4f(x), which point represents the y-intercept of function g?
Answer:
(0,8)
Step-by-step explanation:
[tex]g(0)=4f(0)=4(2)=8[/tex]
A fair coin is tossed three times and is tails each time. What is the probability that the next toss will be
heads
The probability that the next toss will be heads is 1/8.
What is probability?The likelihood of an event occurring is described by probability. We frequently have to make forecasts about the future in real life. We may or may not be aware of the outcome of an event. When this happens, we declare that there is a chance the event will take place.
Using the probability formula, one can determine the likelihood of an event by dividing the favorable number of possibilities by the total number of options. Since the favorable number of outcomes can never be greater than the entire number of outcomes, the probability of an event happening can range from 0 to 1.
Probability of getting two tails and next heads in three tosses is,
=1/2*1/2*1/2
=1/8
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please help im in a rush
Answer:
a)
Surface Area: 172 cm^2
Volume: 112 cm^3
b) Surface Area
c) Volume
Step-by-step explanation:
What is the equation of the line through(4,2) and (0,-2)?
Answer:
y = x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 2 ) and (x₂, y₂ ) = (0, - 2 )
m = [tex]\frac{-2-2}{0-4}[/tex] = [tex]\frac{-4}{-4}[/tex] = 1
the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2
y = x - 2 ← equation of line
Rewrite the function by completing the square.
Answer:
f(x) = (x -6)² +14
Step-by-step explanation:
Completing the square involves writing part of the function as a perfect square trinomial.
Perfect square trinomialThe square of a binomial results in a perfect square trinomial:
(x -h)² = x² -2hx +h²
The constant term (h²) in this trinomial is the square of half the coefficient of the linear term: h² = ((-2h)/2)².
Completing the squareOne way to "complete the square" is to add and subtract the constant necessary to make a perfect square trinomial from the variable terms.
Here, we recognize the coefficient of the linear term is -12, so the necessary constant is (-12/2)² = 36. Adding and subtracting this, we have ...
f(x) = x² -12x +36 +50 -36
Rearranging into the desired form, this is ...
f(x) = (x -6)² +14
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Additional comment
Another way to achieve the same effect is to split the given constant into two parts, one of which is the constant necessary to complete the square.
f(x) = x² -12x +(36 +14)
f(x) = (x² -12x +36) +14
f(x) = (x -6)² +14
The dollar-mart grocery stores sales six bars of soap for $1. how many soaps can a customer buy with $9.
Answer:
54
Step-by-step explanation:
6 bars of soap = $1
x bars of soap = $9
We need to multiply both sides of the equation by the same amount so that $9 is on the right.
$1 x 9 = $9
6 x 9 = 54
So, you can buy 54 soaps with $9.
Hope this makes sense. Feel free to ask further if need be.
Determine the slope of a line that is perpendicular to a line with coordinates (4, -2) and (-1, 3).
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the line above
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{4}}} \implies \cfrac{3 +2}{-1 -4}\implies \cfrac{5}{-5}\implies \cfrac{1}{-1}\implies -1 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{-1}} ~\hfill \stackrel{reciprocal}{\cfrac{-1}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{-1}{1}\implies 1}}[/tex]