Answers
Answer:
[tex]\textsf{Vertex form}: \quad f(x)=(x-4)^2+2[/tex]
[tex]\textsf{Standard form}: \quad f(x)=x^2-8x+18[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
From inspection of the given graph:
vertex = (4, 2)y-intercept = (0, 18)Substitute the vertex and point (0, 18) into the vertex formula and solve for a:
[tex]\begin{aligned}y&=a(x-h)^2+k\\\implies 18&=a(0-4)^2+2\\18&=a(-4)^2+2\\18&=16a+2\\16a&=16\\a&=1\end{aligned}[/tex]
Substitute the found value of a and the vertex into the formula:
[tex]\implies y=1(x-4)^2+2[/tex]
[tex]\implies f(x)=(x-4)^2+2[/tex]
To write the equation in standard form, expand the brackets:
[tex]\implies f(x)=(x-4)^2+2[/tex]
[tex]\implies f(x)=(x-4)(x-4)+2[/tex]
[tex]\implies f(x)=x^2-8x+16+2[/tex]
[tex]\implies f(x)=x^2-8x+18[/tex]
Related Questions
The volume of a cube with side s is s3. Edna bought a cube-shaped jewelry box that has 7-inch sides. What is the volume of the jewelry box?
Answers
The volume of the jewelry box will be;
⇒ 343 inch³
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The volume of a cube with side s = s³
And, Edna bought a cube-shaped jewelry box that has 7-inch sides.
Now,
Since, Edna bought a cube-shaped jewelry box that has 7-inch sides.
Hence, The volume of the jewelry box = 7³
= 7 x 7 x 7
= 343 inch³
Thus, The volume of the jewelry box will be;
⇒ 343 inch³
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In ARST, r = 71 cm, /T=48° and /R=37°. Find the length of t, to the nearest 10th of
a centimeter.
Answers
In the given triangle, the length of side t is 87.7 cm
Calculating the length of a side in a triangleFrom the question, we are to determine the length of t.
From the given information,
r = 71 cm
∠T = 48°
∠R = 37°
From the law of sines, we can write that
t / sin T = r / sin R
t / sin 48° = 71/sin 37°
t = (71 × sin 48°)/sin 37°
t = 87.6736
t ≈ 87.7 cm
Hence, the length of t is 87.7 cm
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F(x)=(x+2)^2 (x-3) graph the function
Answers
The value of the equation f ( x ) is
f ( x ) = x³ + x² - 8x - 12
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
f ( x ) = ( x + 2 )²( x -3 ) be equation (1)
Now , on simplifying the equation , we get
f ( x ) = ( x + 2 )²( x -3 )
f ( x ) = ( x² + 4x + 4 ) ( x - 3 )
Now , multiplying each term with ( x - 3 ) , we get
f ( x ) = ( x - 3 ) x² + ( x - 3 ) 4x + ( x - 3 ) 4
f ( x ) = x³ - 3x² + 4x² - 12x + 4x - 12
On simplifying the equation ,we get
f ( x ) = x³ + x² - 8x - 12
Now , the value of the equation f ( x ) = x³ + x² - 8x - 12
On graphing the equation , we get
The graph of the equation f ( x ) = x³ + x² - 8x - 12 is shown below
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Are travels 120 miles and one and a half hours what is the average speed for miles per hour
Answers
Answer: 80
Step-by-step explanation:
You have 120 miles in one and a half hour
120÷1 1\2 =80 is your speed
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 0.70L to 0.14L
Answers
Answer:
5
Step-by-step explanation:
0.7/0.14
7/10×100/14
7×100/10×14
5
if f(x)=2x+6 , g(x)= - 5x - 9 what is the product of and g?
Answers
Answer:
f(x) * g(x) = -10x2 - 48x - 54
Step-by-step explanation:
(2x+6) * (-5x-9)
-10x2 - 18x - 30x - 54
-10x2 - 48x - 54
A professor had students keep track of their social interactions
for a week. The number of social interactions over the week is
shown in the following grouped frequency distribution. What is
the class width?
The class width is
Answers
The class width of the distribution is 4
What is class width?Class width is the difference between the Upper class limit and the Lower class limit of a class interval.
Class Width = Upper Class Limit − Lower Class Limit. For example: For a class interval, 163−175, Class Width =175−163=12.
Similarly for a class interval of 75-79, the class width is 79-75= 4.
The upper class limit is 79 and the lower class limit is 75.
The class limit for all the frequency distribution is constant.
Therefore the class width of the distribution is 4
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what are steps to solving 30,002-28,596
Answers
Answer:
1,406
Step-by-step explanation:
5 divided by 1135………
Answers
Answer:
227
Step-by-step explanation:
just divide it by how many times it goes into 1135
Answer:
227
Step-by-step explanation:
Simplify Oa Ob Oc Od 10x² -32 4
Answers
Answer:
Step-by-step explanation:
Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. 5x2 + 14x - 3 < 0 The solution set is O A. (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) O B. The solution set is the empty set. Which number line below shows the graph of the solution set? O A. В. + -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 7 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4. 7 8 C. + + + + + + + D. + -8 -7 -6 -5 -4 -3 -2 -1 1 3 4 7 8 -8 -7 -6 -5 -4 -3 -2 -1 1 3 4 5 7 8 E. F. + + + + -7 -6 -3 -2 -1 1 2 3 6 -8 -7 -6 -5 -4 -3 -2 -1 1 3 5 6 7 8 OG. →O H.
Your car has a 15 gallon tank and can run on fuel with added
ethanol. The fuel contains either 13 percent ethanol or 69 percent
ethanol. How much of 69% percent ethanol fuel should you use so
that your tank is 40 percent ethanol?
Answers
Answer: 7.5
Step-by-step explanation:
the tank is 15 gallons and you can get 13 percent ethanol or 69 percent ethanol, so you simply just get 7.5gallons of 69 percent and then 7.5 gallons of 13 percent
.69 divided by 15 is .046
.13 divided by 15 is .008
The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.
What is mixture?A mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the form of solutions, suspensions and colloids.Given is that a car has a 15 gallon tank and can run on fuel with added
ethanol. The fuel contains either 13 percent ethanol or 69 percent
ethanol.
The amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is given by -
{x} = 69% of 15 - {40% of 15}
{x} = (69/100 x 15) - (40/100 x 15)
{x} = 10.35 - 6
{x} = 4.35
Therefore, the amount of 69% percent ethanol fuel should you use so that your tank is 40 percent ethanol is equivalent to 4.35 gallons.
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A canoe rental service charges a $20 transportation fee and $30 dollars an hour to
rent a canoe. Write and graph an equation representing the cost, y, of renting a canoe
for x hours. What is the cost of renting a canoe for twelve hours?
Answers
The graph of the equation y = 30x + 20 is shown below.
It would cost $380 for 12 hours.
How to Write and Graph an Equation?The equation of a graph can be written as y = mx + b, if we know the slope of the graph (m) and the y-intercept (b) which is the point on the y-axis that the line will intercept.
Therefore:
Slope/unit rate (m) = $30 per hour
Rental service charges is the y-intercept (b) = $20
To write the equation, substitute m = 30 and b = 20 into y = mx + b:
y = 30x + 20
See the attachment below for the graph of the equation.
Substitute x = 12 into the equation y = 30x + 20 to find the cost of renting canoe for 12 hours:
y = 30(12) + 20
y = $380
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The length of a rectangle is 3ft longer than its width.
If the perimeter of the rectangle is,58ft find its length and width.
Answers
The length and width of the rectangle is 16 ft and 13 ft respectively.
What is the dimensions of the rectangle?The perimeter of a rectangle = 2(length + width)
Perimeter of the rectangle = 58 ftWidth of the rectangle = w ftLength of the rectangle = (w + 3) ftThe perimeter of a rectangle = 2(length + width)
58 = 2{(w + 3) + w}
58 = 2(w + 3 + w)
58 = 2(3 + 2w)
open parenthesis
58 = 6 + 4w
subtract 6 from both sides
58 - 6 = 4w
52 = 4w
divide both sides by 4
w = 52/4
w = 13
Hence,
Width of the rectangle = w ft
= 13 ft
Length of the rectangle = (w + 3) ft
= 13 + 3
= 16 ft
Therefore, the dimensions of the rectangle is given by 16 ft and 13 ft respectively
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How is solving a real-world problem with a system of equations similar to solving a real-world problem with a single equation in one variable? How is the process different?
Answers
Answer:In this concept, you will learn to solve real-world problems by writing and solving single-variable equations.
Step-by-step explanation:In this concept, you will learn to solve real-world problems by writing and solving single-variable equations.
hope it helps
:)
7. Casey bought a 15.4-pound turkey and an 11.6-pound ham for Thanksgiving and paid $38.51. Her
friend Jane bought a 10.2-pound turkey and a 7.3-pound ham from the same store and paid $24.84.
Find the cost per pound of turkey and the cost per pound of ham.
Answers
Answer:
t = 1.195pounds.
Step-by-step explanation:
The cost per pound of Turkey and Ham are: 1.195pounds and 1.733pounds respectively.
By observing the question, we must notice this is a word problem and can be written mathematically thus;
For Casey:
15.4t + 11.6h = 38.51
For Jane:
10.2t + 7.3h = 24.84
Therefore, to find the cost per pound of Turkey and Ham, the pair of equations need to be solved simultaneously.
Therefore, we can make t the subject of the formula in equation (2) as follows;
t = (24.84 - 7.3h)/10.2
Therefore, we can substitute the value of t into equation (1) to get;
15.4{(24.84 - 7.3h)/10.2} + 11.6h = 38.51
37.51 - 11.023h + 11.6h = 38.51
0.577h = 1
h = 1.733pounds
Therefore, by substituting the value of h into equation 1, we get the value of t to be;
t = 1.195pounds.
Simplify this equation please
48
Answers
Answer:
Please look at the attached image, thank you so much! Hope this helps! :D
Step-by-step explanation:
Answer:
6.92820323028, rounded would be 6.92. Even more rounded would be 7.
Step-by-step explanation:
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 9 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
lcd by inspection and division of 1/4, 3/32, 5/48, and 1/8
Answers
Part a: the LCD is measured to be 96 utilizing the inspection method.
Part b: By division of prime numbers: 96.
Explain the term LCD of the Fractions?The LCD of above fractions can be calculated using one of two methods. The inspection method is a name for the first technique. With this approach, the denominator's multiples are acquired, and the result is determined by selecting a common multiple from the pool of available multiples.The division by prime numbers is the name of the second approach. To acquire the LCD, find a prime number which divides the following fractions.The given number are-
1/4, 3/32, 5/48, and 1/8
Part a:
Find the multiples of the provided fractions' denominators, which are 4, 32, 48, and 8.
4 = 4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88, 92, 96.
32 = 32, 64, 96, 128, 160, 192, 224, 256, 288 ,320.
48 = 48, 96, 144, 192, 240, 288, 336, 384, 432 and 480.
8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
The computation shows that 96, which really is divisible by 4, 32, 48, and 8, is the lowest common multiple.
As a result, the LCD is measured to be 96 utilizing the inspection method.
Part b: By division of prime numbers:
Determine the factors of the given fractions' denominators, 4, 32, 48, and 8.
4 = 2, 2
32 = 2, 2, 2, 2 and 2.
48 = 2, 2, 2, 2 and 3.
8 = 2, 2 and 2.
The generated number, 96, can be divided by the provided fractions' denominators.
As a result, the outcome is 96.
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Assume gas cost $3.70 a gallon. Write an equation representing the total amount you need to spend on the car for the trip, after paying for a one time tune-up of $100.
Answers
The equation which can represent the total amount you need to spend on the car for the trip will be C = 3.70x
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Also an equation is a set of variables that are constrained through a situation or case.
Given that the 1 gallon is $3.70
x gallons = $3.70x
So, C = 3.70x
This will be the cost of x gallons
Hence "The equation which can represent the total amount you need to spend on the car for the trip will be C = 3.70x".
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No
0.7
What’s the percentage
Answers
Answer: 70%
Step-by-step explanation:
0.7
----- x 100% = 70%
1
Answer:
70%
Step-by-step explanation:
When turning a decimal into a percent always bring the decimal point two places to the right.
0.7.0.
070%
70%
Patrick is in a grocery store parking lot, 90meters away from his car. If he pushes his shopping cart at a constant velocity of 2meterspersecond toward his car, how much time will it take him to get one-third of the way to his car?
Write your answer as a whole number.
Answers
15 seconds of time will it take him to get one-third of the way to his car
What is Distance?The length along a line or line segment between two points on the line or line segment.
Given,
Patrick is in a grocery store parking lot, 90meters away from his car
Patrick pushes his shopping cart at a constant velocity of 2meterspersecond toward his car.
We need to find time will it take him to get one-third of the way to his car
one-third of the way to his car means 1/3 of 90 which is 30 meters.
Speed =Distance/ Time
Time=Distance/speed
=30/2
=15 units.
Hence, 15 seconds of time will it take him to get one-third of the way to his car
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Will mark brainliest
Answers
The solution is Option D.
The equation of the line is y = 28x
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the total distance traveled by the car y = 476 miles
Let the total amount of gasoline x = 17 gallons
So , the equation of line is given by
y = mx + c
where m is the slope
Slope m = y /x
Substituting the value for y and x in the equation , we get
Slope m = 476 / 17
= 28
Therefore , the equation of line is y = 28x and the graph is given below
Hence , The equation of the line is y = 28x
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Convert 170 gallons into cubic feet. Round
your answer to the nearest tenth.
*Note: you must use these exact conversion factors to
get this question right.
Answers
Answer:22.7
Step-by-step explanation: 170/7.481=22.724234728 rounded to the nearest tenth is 22.7
two packages of cookies cost $9.50. How much do seven packages cost?Try using a proportion to solve or finding unit rate?
Answers
Answer:
$33.25
1 package is $4.75
Step-by-step explanation:
9.5 divided by 2 is 4.75, that is how much one package costs.
4.75 times 7 is 33.25, that's seven packages worth.
Find the equation for the line that passes through the point (−2,0), and that is parallel to the line with the equation y=−12x−72
Answers
The linear equation parallel to y = -12x - 72 that passes through (-2, 0) is:
y = -12x - 24
How to find the linear equation?A general linear equation is written as:
y = m*x + b
Where m is the slope, and b is the y-intercept.
And two lines are parallel only if the lines have the same slope and a different y-intercept.
So, if we want to find a line parallel to:
y = -12x - 72
Then the slope of our line must be -12, then our line is something like:
y = -12x + b
Now we know that the line must pass through (-2, 0), replacing that in our line we get:
0 = -12*-2 + b
0 = 24 + b
-24 = b
The linear equation is:
y = -12x - 24
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SOLVE U
2u - 2/3 = - 3/4u+3
U =
Answers
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The value of u is 4/3
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
2u - 2/3 = -(3/4)u + 3
Add 2/3 on both sides.
2u = -(3/4)u + 3 + 2/3
Add (3/4)u on both sides.
2u + (3/4)u = 3 + 2/3
(8u + 3u) / 4 = (9 + 2)/3
11u/4 = 11/3
u/4 = 1/3
u = 4/3
Thus,
The value of u is 4/3
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The price for 7/8 of a pound of almonds is $6.65 . What is the cost of 3 and 1/2 pounds at the same rate?
Answers
The cost of 3 and 1/2 pounds of almond at the same rate is $26.60.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In the illustration given as m/n, it should be noted that m is the numerator and n is the denominator.
Since the price for 7/8 of a pound of almonds is $6.65, the fraction per pound will be done by dividing the amount for a pound by 7/8.
= $6.65 ÷ 7/8
= $7.6
The cost of 3 and 1/2 pounds at the same rate is:
= 3 1/2 × $7.6
= $26.60
In conclusion, the cost is $26.60.
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Julie likes to make bead necklaces. She has 296 beads altogether, but has 32 more round beads than square beads. How much of each bead does she have?
Answers
A student is using colored beads to make a model of magnesium hydroxide, Mg(OH)2. Magnesium atoms are
represented by orange beads, oxygen atoms by green beads, and hydrogen atoms by blue beads.
Model bead color key.
Magnesium orange beads O (orange)
Oxygen green beads O (green)
Hydrogen blue beads O (blue)
What combination of beads should the student use for the model?
Answers
The combination of beads that the student will use to make a model of magnesium hydroxide, Mg(OH)₂ is
Magnesium orange beads - 1Oxygen green beads - 2Hydrogen blue beads - 2What is model of molecule?Molecule models depict the positions of the various atoms, roughly to scale, and typically with color coding, as well as how they are joined together.
These models are helpful tools for visualizing the structures and shapes of groupings of atoms, which is vital for understanding the behavior of molecules
Over the course of the development of contemporary atomic theory, models have been employed to represent atom configurations.
The model of magnesium hydroxide, Mg(OH)₂ will require the atoms in the ratio:
Magnesium : Oxygen : Hydrogen = 1 : 2 : 2
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Given the function f (x)= x2 −5x + 6 , evaluate
Answers
Actually 20 is the answer
If the variance of the data values in a sample is 289, what is the standard
deviation of the data values?
O A. 17
OB. 19
OC. 18
O D. 16
Answers
Answer:
17
Step-by-step explanation: ..