Consider the quadratic function f (x) = 2x² - 16x + 24. Complete the square to rewrite the function in the form
f(x)= a(x-h)² + k.
f(x) =
The quadratic function f(x) = 2x² - 16x + 24 can be rewritten in the vertex form f(x) = 2(x - 4)² + 4.
What is the vertex form of the given function?Given the function in the question:
f(x) = 2x² - 16x + 24
To determine the vertex form f(x) = a(x-h)² + k, we need to complete the square.
Factor out the leading coefficient of 2:
f(x) = 2x² - 16x + 24
f(x) = 2(x² - 8x + 12)
To complete the square, we need to add and subtract the square of half of the coefficient of x:
f(x) = 2[(x² - 8x + 16) - 4] + 8
Since (x² - 8x + 16) is a perfect square trinomial, we factored as (x - 4)².
f(x) = 2[(x - 4)² - 4] + 8
Now we can simplify and rewrite in the desired form:
f(x) = 2(x - 4)² - 4 + 8
f(x) = 2(x - 4)² + 4
Therefore, the vertex form is f(x) = 2(x - 4)² + 4.
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please help for this question
Trapezium T is reflected across line x = 3 to form trapezium U and reflected across line x = 7 to form tralpelzium V
The figure is attached
What is reflection over a lineReflection across a line is a geometric transformation which mirrors a point, shape or figure exactly across a pre-defined plane known as the Line of Reflection.
In other words, the size and general outline are kept in tact while orientations are adjusted. Furthermore, each corresponding point on either side of the Line of Reflection is found to be equidistant from the said axis and lies along a perpendicular line.
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Use the numbers in the multiplication equation 28 times 1/7 = 4 to write a division equation involving divison by a fraction
Changing the multiplication sign to a division sign, we will have 28 ÷ 7
Multiplication and division rule :-
Given the product of 28 and 1/7, we are to write a division equation involving division by a fraction.
Given,
28 * 1/7 = 4
Changing the multiplication sign to a division sign, we will have:
28 * 1/7 = 28/7
This can also be written as 28 ÷ 7
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A sale transaction on rental property closes on December 16. The landlord received the December rent of $713 on December 1. Assuming the closing day is the buyer's, and that the 365-day method is used for prorating, which of the following entries would appear on the settlement statement?
- To answer a question about a sale transaction on rental property that closes on December 16, you need to calculate how much rent the landlord owes to the buyer for the remaining days of December.
- You can use a formula called prorated rent to calculate the amount of rent that is proportional to the number of days that the buyer owns the property. Prorated rent splits the amount between the previous and new owners of a rental property.
- The formula for prorated rent is: Prorated Rent = (Monthly Rent / Number of Days in Month) x Number of Days Rent Owed
- In your case, the monthly rent is $713, the number of days in December is 31, and the number of days rent owed is 16 (from December 16 to December 31). The closing day is the buyer's, so the landlord owes rent for that day as well.
- Plugging these values into the formula, you get: Prorated Rent = (713 / 31) x 16 = 368.26
- This means that the landlord owes $368.26 to the buyer for the remaining days of December.
I hope this helps you answer your question.
improper integrals.
find the area under the curve
y = 1x^-2
from x = 7 to x = t and evaluate it for t = 10, t = 100.
then find the total area under this curve for x [tex]\geq[/tex] 7.
(a) t = 10
(b) t = 100
(c) Total area
1/7 square units make up the entire area under the curve from x = 7 to infinity.
To find the area under the curve [tex]y = x^{-2}[/tex] from x = 7 to x = t, we can integrate the function with respect to x:
[tex]\int\limits^7_t x^{(-2)} dx = [-x^{(-1)}] = [-1/t + 1/7][/tex]
To evaluate this expression for t = 10 and t = 100, we substitute these values:
[-1/10 + 1/7] = 0.0428 (rounded to four decimal places)
[-1/100 + 1/7] = 0.1328 (rounded to four decimal places)
To find the total area under the curve from x = 7 to infinity, we can integrate the function with respect to x from 7 to infinity:
[tex]\int\limits^7_t {x} x^{(-2)} dx \\= [-x^{(-1)}] \\= [0 - (-1/7)] \\= 1/7[/tex]
Therefore, the total area under the curve from x = 7 to infinity is 1/7 square units.
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members 1st federal credit union charges a $27 per check overdraft protection fee. On March 8, you had $1,400 in your account. Over the next four days, you wrote checks for: March 9, $1,380.15, March 10 $670 and $95.67, March 11, $130 and March 12, $87.60. How much will you pay in overdraft protection fees? How much will you owe the bank after March 12?
I have to add this problem
5/8+2/8
giving 10 points:)
The addition of the given fraction expression is 7/8.
In mathematics, an expression is a combination of numbers, symbols, and/or operators that represents a mathematical quantity or relationship. It can be a simple combination of numbers or a more complex combination involving variables, functions, or other mathematical constructs.
When adding fractions with the same denominator, you simply add the numerators and keep the denominator the same.
In this case, both fractions have a denominator of 8, so we can add their numerators:
5/8 + 2/8 = (5 + 2)/8 = 7/8
Thus, the sum of 5/8 and 2/8 is 7/8.
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2y+3y-18=-33?????????????????
Answer:
y=-3
Step-by-step explanation:
Answer:
Y = - 3
Step-by-step explanation:
So lets help you out here.....
First of all you should set up how you have to solve, let do this step by step...
Step 1 : 2y + 3y - 18 = - 33
Step 2 : Combine like terms... (2y + 3y = 5y)
Step 3 : Set up your new equation (5y - 18 = - 33)
Step 4 : Subtract negative 18 by negative 33 (- 18 - 33 = -15)
(PS: In a calculator - 18 - 33 is -51 but the 18 is also a negative so it would be - 15)
Step 5 : Divide (- 15 / 5 = - 3)
And that is how you solve this problem, have a great day!!!!!!
The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K= C + 273.15.
The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15. When solved for C, the equation is K - 273.15. Therefore, the correct option is option C.
Temperature is a unit of warmth or coldness that can be defined in the context of any number of arbitrary scales. It indicates the direction through which the energy from heat will naturally flow, i.e., through a hotter (body) to a colder (body) body. Temperature cannot be the same as a thermodynamic system's energy; for instance, a blazing match is significantly hotter than an iceberg.
K = C + 273.15
K - 273.15 = C + 273.15 - 273.15
K - 273.15 = C
Therefore, the correct option is option C.
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Your question is incomplete but most probably your full question was,
The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15.
When solved for C, the equation is
C = K – 273.15
C = 273.15 – K
C = K + 273.15
C = 273.15K
HELP ASAP!! ( failing my class lol pls help asappp )
What was the scale factor used?
Was the orientation preserved or changed?
Was congruence preserved or changed?
1) The scale factor of dilation is 1/3
2) The orientation is preserved in dilation of A to A'
3) The congruence is not preserved in dilation of A to A'
We know that the scale factor is nothing but the ratio of the size of the transformed image to the size of the original image.
Here from the attached graph we can observe that the square A is transformed to A'
The side length of square A is 18 units and the side length of square A' is 6
So, the scale factor would be,
r = A' / A
r = 6/18
r = 1/3
We know that a dilation preserves the shape and orientation of the figure, but changes the size of he figure.
So, the dilations do not preserve congruence, as it changes the size of a figure.
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PLEASE HELP
Part A:
List the three different types of visuals we use to organize all the possible outcomes in a sample space
1
2
3.
Part B:
Leena is arranging 3 different books in a row on a shelf. A detective story (D), a mystery story (M), and a comic book (C)
1. Pick one of the three types of visuals you listed in Part A to create a sample space for the arrangement of all possible outcomes for arranging the 3 books on a shelf. (1 point)
Fill in the Blank I will choose to create a
for this scenario
2. Create your visual either by hand or using technology
The three different types of visuals we use to organize all the possible outcomes in a sample space are:
Tree DiagramsTablesVenn DiagramsHow to explain the informationFor the second part of the question, select one of the three styles of graphical representation you listed in Part A to make a sample space for all probable results for putting the 3 books on a rack.
The table will show every feasible end result for setting up the 3 books on a rack.
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Al had ____ Pennie’s initially
AI initially had 786,432 pennies.
We have,
Let P be the initial number of pennies AI had.
According to the problem:
AI gives 3/8 of P pennies to Bev.
Bev gives 3/8 of what she got from AI to Carl.
Carl gives 3/8 of what he got from Bev to Dani.
Set up an equation to solve for P.
Let's start by finding how many pennies Dani gets from Carl:
Carl gives 3/8 of what he got from Bev to Dani, so Dani gets:
(3/8) x (3/8) x (3/8) x P pennies from Carl.
Next, let's find how many pennies Carl gets from Bev:
Bev gives 3/8 of what she got from AI to Carl,
So Carl gets (3/8) x (3/8) x P pennies from Bev.
Now we can substitute this expression for the number of pennies Carl gets from Bev into the expression for the number of pennies Dani gets from Carl:
Dani gets (3/8) x (3/8) x (3/8) x P pennies from Carl = (3/8) x (3/8) x (3/8) x (3/8) x P pennies from Bev = (3/8) x (3/8) x (3/8) x (3/8) x (3/8) x P pennies from AI.
We know that Dani gets 378 pennies, so we can set this expression equal to 378 and solve for P:
(3/8) x (3/8) x (3/8) x (3/8) x (3/8) x P = 378
Simplifying this expression:
P = 378 x (8/3) x (8/3) x (8/3) x (8/3) x (8/3)
P = 786,432
Therefore,
AI initially had 786,432 pennies.
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Look a tu the picture
The area of the composite figure in this problem is given as follows:
A = 87 ft².
How to obtain the area of the composite figure?When we want to obtain the area of a composite figure, we must add the areas of all the components of the figure.
The figure in this problem is composed as follows:
Rectangle of dimensions 10 ft and 6 ft.Rectangle of dimensions 10 - 4 = 6 ft and 9 - 6 = 3 ft.Right triangle of legs 10 - 4 = 6 ft and 6 - 3 = 3 ft.The areas are calculated as follows:
Rectangle: multiplication of dimensions.Right triangle: half the multiplication of the legs.Hence the area of the composite figure is given as follows:
A = 10 x 6 + 6 x 3 + 0.5 x 6 x 3
A = 87 ft².
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According to a National Center for Health Statistics, the lifetime odds in favor of dying from heart disease are 1 to 5, so the probability of dying from heart disease is
.
The probability of dying from heart disease is 0.1667 or 16.67%.
The odds in favor of an event are defined as the ratio of the probability of the event occurring to the probability of the event not occurring. In this case, the odds in favor of dying from heart disease are 1 to 5.
So, we can set up the following equation:
Odds in favor of dying from heart disease = probability of dying / probability of not dying
1/5 = probability of dying / probability of not dying
We can solve for the probability of dying by cross-multiplying:
probability of dying = odds in favor of dying from heart disease / (odds in favor of dying from heart disease + 1)
probability of dying = 1 / (1 + 5)
probability of dying = 1/6
Therefore, the probability of dying from heart disease is 0.1667 or 16.67%.
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5
Consider the following set of test scores for a history class:
100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40
Would it be better for the teacher to consider the mean or the median to interpret the overall results of the test?
The median because it better reflects that most students did not pass and the teacher should revisit the material.
The median because it is a passing score and shows most students passed the test.
The mean because it coincides with the mode and shows that most students passed the test.
The mean because it is higher and the teacher wants to feel good about the students.
1 point
Consider the following set that shows the high temperature in Orlando for the past 6 days:
91, 90, 90, 90, 84, 82, 81,90
The mode of these data would be type your answer.....
1 point
Consider the following set that shows the high temperature in Orlando for the past 8 days:
91, 90, 90, 90, 84, 82, 81,90
The median of these data would be type your answer.....
1) For the following set of test scores for a history class, 100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40, it would be better for the teacher to consider D) The mean because it is higher and the teacher wants to feel good about the students.
2) The mode of these data about the high temperatures in Orlando for the past 8 days would be 90.
3) The median of these data about the high temperatures in Orlando for the past 8 days would be 80.
What are the mean, mode, and median?The mean, mode, and median are three centers of measurement.
The mean refers to the average value in the data set, obtained as the quotient of the total value divided by the number of items.
The mode refers to the value that occurs most in the data set.
Lastly, the median is the middle value for a data set arranged in descending or ascending order.
1. Test Scores:
100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40
Total value = 660
Number of data items = 11
Mean = 60 (660 ÷ 11)
Median = 55
Mode = 60
2. High Temperature:
91, 90, 90, 90, 84, 82, 81, 90
Total Value = 698
Number of data items = 8
Mean = (87.25 (698 ÷ 8)
Median = 90
Mode = 90
3. High Temperature:
91, 90, 90, 90, 84, 82, 81,90
Median = 80 (81, 82, 84, 90, 90, 90, 90, 91)
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Find the quotient of
99 m² n³-81m³n²-18mn
__________________
3mn
The quotient of the expressions 99 m² n³-81m³n²-18mn and 3mn is 33mn² - 27m²n - 6
Finding the quotient of the expressionsFrom the question, we have the following parameters that can be used in our computation:
99 m² n³-81m³n²-18mn
__________________
3mn
To find the quotient of the expressions, we simply divide each term of the numerator by 3mn
Using the above as a guide, we have the following:
99 m² n³-81m³n²-18mn
__________________ = 33mn² - 27m²n - 6
3mn
Hence, the solution is 33mn² - 27m²n - 6
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A 100k
B 200k
C 300k
D 400k
The picture above shows 4 glass jars, all with the same number of gas molecules but at different temperatures.
Which of the jars would experience the greatest pressure?
O Jar A
O Jar B
O Jar C
O Jar D
Answer: The jar that would experience the greatest pressure is Jar D.
This is because the pressure of a gas is directly proportional to its temperature (according to the ideal gas law). Since all four jars have the same number of gas molecules, the jar with the highest temperature (Jar D) would have the greatest pressure.
Step-by-step explanation:
Match each equation with its y-intercept. ( 0 , b a ) ( 0 , c a ) ( 0 , b c ) ( 0 , c b ) ( 0 , a c ) ( 0 , a b ) Equations y-intercepts c x + b y = a arrowRight c x + a y = b arrowRight b x + a y = c arrowRight a x + b y = c arrowRight
The equation with the following y-intercepts are matched
a) c x + b y = a: (0, a/b)
b) c x + a y = b: (0, b/a)
c) b x + a y = c: (0, c/a)
d) a x + b y = c: (0, c/b)
Given data ,
Let the set of equations be represented by
c x + b y = a
c x + a y = b
b x + a y = c
a x + b y = c
Now , the y-intercept of the equation is when the value of x = 0
So , when x = 0
The y intercepts of the equation are
c x + b y = a: (0, a/b)
c x + a y = b: (0, b/a)
b x + a y = c: (0, c/a)
a x + b y = c: (0, c/b)
Hence , the equations are solved
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What is the equation of the line in the slope-intercept form?
Answer:
5y= -3x +15
Step-by-step explanation:
y=mx+c is slope Intercept form where M is slope and c is Intercept
The sum of three consecutive integers is 108. What are the integers?
Answer:
Step-by-step explanation:
hello :
let : x ,x+1 ,x+2 three consecutive integers
x +x+1 +x+2 = 108
3x =105
x = 105/3
x = 35
35 , 36 , 37
A civil patrol unit of 15 members includes 4 officers. In how many ways can 3 members be selected for a search and rescue mission such that at least 1 officer is included?
Step-by-step explanation:
There are 4 ways to select an officer
multiply this by the number of ways to select 2 others from the 15
4 * 15 C 2 = 4 * 15!/(2!13!) = 420 ways to select
The translation (x - 5,y + 11) is applied to a triangle. Maryanne makes a conjecture about the perimeter of the image of the triangle, tests the conjecture, and finds that it is true. What could have been her conjecture?
Answer: Maryanne's conjecture could have been that the perimeter of the image of the triangle will be the same as the perimeter of the original triangle.
Step-by-step explanation:
14. A clothing store has a cost of producing t-shirts at $4.50 per unit. The store also has a
monthly rent charge of $500. The store sells each t-shirt for $12.00 each.
Write an equation to model the store's profits each month:
Answer:
there gonna have to buy 120 to pay the rent
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Hitzu Company sold a copier (that costs $6,500) for $13,000 cash with a two-year parts warranty to a customer on August 16 of Year 1. Hitzu expects warranty costs to be 4% of dollar sales. It records warranty expense with an adjusting entry on December 31. On January 5 of Year 2, the copier requires on-site repairs that are completed the same day. The repairs cost $121 for materials taken from the parts inventory. These are the only repairs required in Year 2 for this copier.
1. How much warranty expense does the company report for this copier in Year 1?
2. How much is the estimated warranty liability for this copier as of December 31 of Year 1?
3. How much is the estimated warranty liability for this copier as of December 31 of Year 2?
4. Prepare journal entries to record (a) the copier’s sale; (b) the adjustment to recognize the warranty expense on December 31 of Year 1; and (c) the repairs that occur on January 5 of Year 2.
The warranty expense that the company report for this copier in Year 1 is $650.
The estimated warranty liability for this copier as of December 31 of Year 1 is $650
The estimated warranty liability for this copier as of December 31 of Year 2 is $556
How to calculate the valueThe warranty expense that the company report for this copier in Year 1 is:
= 13000 × 5%
= $650.
Also, the estimated warranty liability for this copier as of December 31 of Year 2 is $556
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Solve triangle ABC subject to the given conditions, if possible. Round the lengths of the sides and the measures of the angles (in degrees) to at least 2 decimal
places, if necessary.
a-13.9, b-15.2, c-25.7
The angles in the triangle are;
A = 26.67°, B = 29.06°, C = 124.27°
What is the solution of the triangle?We know that we have the triangle as ΔABC and a-13.9, b-15.2, c-25.7
Using the Cosine rule;
a^2 = b^2 + c^2 - 2ac CosA
(13.9)^2 = (15.2)^2 + (25.7)^2 - 2(15.2 * 25.7)Cos A
193.21 = 891.35 - 781.28CosA
193.21 - 891.35 = - 781.28CosA
Cos A = 193.21 - 891.35 / - 781.28
A = Cos-1 (193.21 - 891.35 / - 781.28)
A = 26.67°
Then;
c^2 = a^2 + b^2 - 2abCosC
(25.7)^2 = (13.9)^2 + (15.2)^2- 2(13.8 * 15.2)CosC
660.49 = 424.25 - 419.52CosC
660.49 - 424.25 = - 419.52CosC
C= Cos-1 (660.49 - 424.25 / - 419.52)
C = 124.27°
Then B;
180 - ( 26.67° + 124.27°)
= 29.06°
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Eric invested in a savings bond for 4 years and was paid simple interest at an annual rate of 4%. The total interest that he earned was $1120. How much did he invest?
Answer:
$7000
Step-by-step explanation:
For simple interest,
I = Prt,
where I = amount of interest earned
P = principal amount, the amount of the investment
r = annual interest rate (convert percent to decimal for calculations)
t = time (number of years)
I = Prt
We know I, r, and t, and we need to solve for P.
1120 = P × 4% × 4
Convert percent to decimal.
1120 = P × 0.04 × 4
Multiply on the right side.
1120 = 0.16P
Divide both sides by 0.16
7000 = P
Answer: $7000