The completed-square (vertex) form 2x² + 12x + 1 is 2(x+3)^2−17. Completing the Square is a technique to find maximum or minimum values of quadratic functions.
How to find completed-square ?Completing the square is a highly helpful technique or way to change a quadratic equation from also known as the "standard form," to its "vertex form,".
For some combinations of h and k, completing the square is a method for transforming a quadratic polynomial. In other words, the quadratic expression is completed by inserting a perfect square trinomial.
Finding the maximum or lowest values of quadratic functions can be done using the square method, sometimes known as "completing the square."
Use the form ax^2 + bx + c, to find the values of a, b, and c.
Consider the vertex form of a parabola.
a(x+d)^2+e
Find the value of d using the formula
d = b/2a.
d = 3
Find the value of e using the formula
e = c− b^2 / 4a.
e = −17
Substitute the values of a, d, and e into the vertex form 2(x+3)^2−17.
2(x+3)^2−17
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Nelson’s birthday party will be at the skating rink. The cost for each person is $ 25 . The cost of the room for the party is $ 50 . The function C ( x ) = 25 x + 50 models the total cost, C , where x is the number of people at the party. What is the maximum number of people who can be at the party for a budget of $ 600 ?
Answer:
24 people
Step-by-step explanation:
600 = 25x + 50 Subtract 50 from both sides of the equation
550 = 25x Divide both sides by 25
24 = x
Answer: x = 22
Step-by-step explanation:
We need to use trial and error for this.
20 - 25 seems like a reasonable range to substitute x with.
C(20) = 25(20) + 50
C(20) = 500 + 50
C(20) = 550.
This means that 20 is not the answer. Let's try 21.
C(21) = 25(21) + 50
C(21) = 525 + 50
C(21) = 575.
This means that 21 is also not the answer. let's try 22.
C(22) = 25(22) + 50
C(22) = 550 + 50
C(22) = 600.
This means that 22 is the maximum number of people for a budget of $600.
x = 22
HELP ME ASPPP PLEASE SHOW UR WORK PLEASE
Answer: -9
Step-by-step explanation:
FLOWERS The number of tulips in Paula's garden is 8 less than the number of marigolds. If there are 16 tulips, write and solve an equation to determine the number of marigolds m.
The number of marigold in the garden of Paula is 24.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of marigold be m.
In this case, the number of tulips in Paula's garden is 8 less than the number of marigolds. The number of marigold will be:
m - 8 = 16
m = 16 + 8.
m = 24
The number of marigold is 24.
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Nachelle has a points card for a movie theater.
She receives 50 rewards points just for signing up.
She earns 12.5 points for each visit to the movie theater.
She needs at least 170 points for a free movie ticket.
Write and solve an inequality which can be used to determine vv, the number of visits Nachelle can make to earn her first free movie ticket.
Step-by-step explanation:
#=number
Identify what is in the inequalityNachelle gets 50 points when signing up: 50+#x=#
Nachelle earns 12.5 points for each visit: 50+12.5x=#
Nachelle need at least 170 points: 50+12.5x=170
Now you have your inequality, solve.Subtract 50 from both sides: 50-50+12.5x=170-50
50-50 cancel out so now your left with 12.5x=170-50
Subtract the 170 and 50: 12.5x=120
Divide 12.5 from both sides: 12.5x÷12.5=120÷12.5
12.5x÷12.5 cancel out so the inequality is now x=120÷12.5
Divide 120 and 12.5: x=9.6
Since there is no such thing as 9.6 visits, round to 10.
Answer: Nachelle needs 10 visits in order to get her first free movie ticket.HELP NOW
The function f(x)=(1-x)^2-4 is decreasing only throughout the interval:
The function f(x)=(1-x)^2-4 is decreasing only throughout the interval is
-∞ < x < 1.
Given function:
f(x)=(1-x)^2-4
= 1 + x^2 - 2x - 4
= x^2 - 2x - 3
for decreasing:
f'(x) ≤ 0
2x - 2 - 0 ≤ 0
2x -2 ≤ 0
2x ≤ 2
x ≤ 1
-∞ < x < 1.
Therefore The function f(x)=(1-x)^2-4 is decreasing only throughout the interval is -∞ < x < 1.
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Antonio is ready to move out of his parent's house and live on his own. He found a great apartment that has all utilities included. His job as an assistant plumber requires him to have a car, but his hours are flexible enough to give him time on the weekends to have fun with his friends. What is the best way Antonio's budget can be modified to help him save enough for the $200 down payment and make the $500 monthly rental payment?
Monthly Budget
Old Budget
New Budget
Income
Wages
$1500
$1500
Expenses
Food
Cell Phone
Savings
Entertainment
Car Expenses
.
$250
$175
$200
$200
$300
.
$____
$____
$____
$____
$____
Net Income
$375
$____
a.
Antonio could keep his budget the same and hope he gets a raise at work.
b.
Antonio could reduce his monthly entertainment expenses by $100 to help pay the monthly rent. He could take $200 out of savings once for the deposit.
c.
Antonio could live at his parent’s house for one more month and save his net income. After one month of living at home, he would have enough additional money for the deposit and one year’s rent at the apartment.
d.
Antonio could reduce his monthly entertainment expenses by $75 and his food expenses by $50 to pay the monthly rent. He could take $200 out of savings once for the deposit.
Please select the best answer from the choices provided
A
B
C
D
The best way Antonio's budget can be modified to help him save enough is D. Antonio could reduce his monthly entertainment expenses by $75 and his food expenses by $50 to pay the monthly rent. He could take $200 out of savings once for the deposit
What is a budget?A budget is an estimate of revenue and expenses for a given period of time that is usually compiled and re-evaluated on a regular basis. A budget expresses intended expenditures as well as recommendations for how to meet them with resources.
Saving is the portion of one's income that is not spent on current expenses. In other words, it is money set aside for future use rather than being spent immediately. An expense is a cost incurred by businesses in the course of their operations. Wages, salaries, maintenance, rent, and depreciation are expenses.
In this case, the way to reduce the budget is illustrated.
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A line has the equation y - 4 = 3x + 11 Work out the gradient and the y-intercept of the line.
Answer: Gradient is 3 and y-intercept is 15
Step-by-step explanation:
by rearranging the equation so y is on 1 side we get:
y = 3x + 15
the gradient is the number before the x (coefficient)
the y intercept is the number that is not multiplied by the x, in this case 15
Determine the new coordinate location after (-3,7) on the graph y=-x^2 has undergone the following transformation: A reflection in the x axis followed by a vertical translation of 4 units up. What is the new coordinate?
Check the picture below.
notice the point, reflected over the x-axis and then shifted upwards, notice the parabola mentioned above, nowhere near it.
David works as a salesman and earns a basic salary of Rs 16 000 per month plus 8 % commission on his sales. If his total sales were rs 55 000 during last month, find his earnings for that month.
Answer:
$20400
Step-by-step explanation:
8 percent *55000 =
(8:100)*55000 =
(8*55000):100 =
440000:100 = $4400
16000+4400 =$20400
. A bag of marbles contains a ratio of 4 red marbles to 13 more blue marbles than
red marbles. If there are 51 blue marbles, how many red marbles are in the
bag?
The number of red marbles in the bag is 12.
We are given a bag. The bag contains two types of marbles. There are red and blue marbles in the bag. The ratio of marbles is four red marbles to thirteen more blue marbles than red marbles. Let the ratio of the number of red marbles to that of blue marbles be denoted by the variable "r".
r = 4/(13 + 4) = 4/17
The number of red marbles and blue marbles in the bag is 4x and 17x, respectively, where "x" is a variable. We know that the number of blue marbles in the bag is 51. We can write the following equation to find the value of "x".
17*x = 51
x = 51/17 = 3
Hence, the number of red marbles is 4x = 4*3 = 12.
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In the first week of July,1,020 a record people went to the local swimming pool. In the second week, 125 fewer people went to the pool than in the first week. In the third week, 145 more people went to the pool than in the second week. In the fourth week, 175 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
The percent decrease in the number of people who went to the pool over these four weeks is 15.2%.
How to calculate the percentage?The change regarding the people at the swimming pool for the number of weeks will be:
= 1020 - 125 + 145 - 175
= 865
The initial number of people is 1020.
Therefore, the percentage decrease will be:
= Decrease in number / Initial number × 100
= (1020 - 865) / 1020 × 100
= 155/1020 × 100
= 15.2%
The Percentage is 15.2%.
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Help Plssss!!!!!!!!!!
Simplifying Square Roots of Negative numbers
Answer:
10i
Step-by-step explanation:
using the fact that [tex]\sqrt{-1}[/tex] = i , then
[tex]\sqrt{-100}[/tex]
= [tex]\sqrt{100(-1)}[/tex]
= [tex]\sqrt{100}[/tex] × [tex]\sqrt{-1}[/tex]
= 10 × i
= 10i
= 0 + 10i ← in standard form
Bria and April were comparing text messages during lunch. April sent 20 messages today. April sent one fourth the amount of text messages sent by Bria. write a equation to determine how many text messages Bria sent.
answer:
0.25 (or 1/4) x 20 = 5
step-by-step explanation:
math. 0.25x20 = 5
Express using exponents and simplify any numerical coefficients: w · w · w
Answer:
w to the power of 3 or w^3
Step-by-step explanation:
For example, plug in a number for the variable given, and in this case, I used the number 2. When using the number 2, the question would become 2 * 2 * 2. It would be simplified as 2 to the power of 2 to the power of 3. That's how I got the answer of w to the power of 3.
what's 182.91% as a decimal
Answer:
1.8291
Step-by-step explanation:
which statistics about older workers are true?
Answer:Older workers are staying in the workforce longer.
Step-by-step explanation: I had the same question as you it should be right.
Write an equation for the translation of y = 4/x that has asymptotes at x = - 3
x and y = - 4.
Equation for the translation of y=4/x that has the given asymptotes.
x = -3 and y = -4 is y = [tex]\frac{4}{x+3} -4[/tex]
Given,
In the question:
The translation of y = 4/x that has asymptotes at x = - 3 and y = - 4.
Write an equation:
Now, According to the question:
What is asymptote?
A line that, in analytical geometry, is an asymptote of a curve is one where, when one or both of the x or y coordinates go to infinity, the distance between the curve and the line approaches zero. An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and similar settings.
According to the above statement:
The equation will be :
y = [tex]\frac{4}{x+3} -4[/tex]
Hence, Equation for the translation of y=4/x that has the given asymptotes.
x = -3 and y = -4 is y = [tex]\frac{4}{x+3} -4[/tex]
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Whitch set of paper towels is the better buy? 8 rolls for $8.73 or 14 rolls for $12.32?
9) Give the following expression in index form
a) √3
Answer:
nStep-by-stepkbexplanation:
Find the next two terms in this
sequence.
1, -3, 9, -27, 81, [ ? ],
Answer:
-243, 729
Step-by-step explanation:
[tex]f(x) = {( - 3)}^{x} [/tex]
x = 0, 1, 2, 3, .....
[tex]f(5) = {( - 3)}^{5} = - 243[/tex]
[tex]f(6) = {( - 3)}^{6} = 729[/tex]
3. Ben played at a friend's house for 2 hours
35 minutes. Later he played at a park for
1 hour 10 minutes. He played for another
1 hour 20 minutes in his backyard. How
long did Ben play in all?
Tell whether the relation, represented by the ordered pairs below, represents a function. Explain.
{ (-2, 4), (-1, 3), (0, 2), (-2, 0), (1, 1)
The relation represented by the ordered pair is not a function
How to determine the relation that is a function?The given parameter is represented as
{(-2, 4), (-1, 3), (0, 2), (-2, 0), (1, 1)}
As a general rule;
For a relation to be considered a function, the following must be true:
One x value must not point to several y values
Using the above as a guide, the ordered pair in the relation are not functions
This is because one x value must not point to several y values
Hence, (d) the ordered pair is not a function
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jack and bob leave their houses at 10:00 am walking toward each other. they meet at 10:30 am. if their houses are 7km apart, and jack is walking at 8 km/h , find bobs rate
URGENT
Bob is walking at the rate of 6 kilometer per hours
Jack and Bob leave their houses at 10:00 am walking toward each other and they meet at 10.30 am.
The distance between two houses = 7 kilometer
The speed of the Jack = 8 kilometer per hour
The distance traveled by Jack in 30 minutes = 8 / 2
= 4 kilometer
The remaining distance = 7 - 4
= 3 kilometer
Bob traveled 3 kilometers in 30 minutes
Then the speed of the Bob = 3 × 2
= 6 kilometer per hour
Hence, the Bob is walking at the rate of 6 kilometer per hours
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Giving 50 Points..!!
Estebe enlarged a 4 inch by 6 inch photograph by a scale factor of 5/2. What are the new dimensions of the photograph
Answer:
New photograph is 10 in by 15 in===================
Initial dimensions4 in and 6 in,and
Scale factor k = 5/2.Find new dimensionsw = 4*5/2 = 10 inl = 6*5/2 = 15 inA rival company offers you an annual salary of $36,000.Except for the pay, everything is identical between the companies. Do you accept or reject the rival company's offer, and why?
I will have to reject the offer of the rival company since it's lesser than $40560.
How to calculate the amountFrom the information, the person works a basic week of 40 hours and the basic rate is $19.50 per hour. It should be noted that there are 52 weeks in a year. The total amount will be:
= 40 × 19.50 × 52
= $40560
The rival company offers you an annual salary is $36000.
I'll reject the rival company's offer since it's lower.
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Complete question
You work a basic week of 40 hours and your basic rate is $19.50 per hour. A rival company offers you an annual salary is $36.000. Except for the pay, everything is identical between the conpanies. Do you accept or reject the rival company's offer, and why?
What number needs to be added to this set of numbers so the mean is 6? {3,4,7}
The finalized set is { 3 , 4 ,7 , 10 }
How is mean calculated ?Only numerical variables, whether continuous or discrete, can be used to calculate the mean. It is calculated by merely dividing the total number of values in a data set by the sum of all the values in the data set.
The given set is {3,4,7}
3 + 4 + 7 =14
To calculate the mean we divide the sum by the number of numbers present
So we must add 10
because if we add 10 to the set we get
3 + 4 + 7 + 10= 24
Thus the mean = [tex]\frac{24}{4}[/tex]
When we divide these two numbers we get :
mean = 6
Thus the finalized set is { 3 , 4 ,7 , 10 }
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The position of a 50 g oscillating mass is given by x(t)=(2. 0cm)cos(10t−π/4), where t is in s. If necessary, round your answers to three significant figures. Determine:.
Answer:their equal to 150
Step-by-step explanation:
took the test
What is the slope of the line?
4x -1 =3y + 5
Choose 1 answer:
B
413
2/3
32
314
Answer:
4/3
Step-by-step explanation:
so in y=mx+b form.
m=slope b=y-int
Subtract 5 from both sides to isolate y on a side.
4x-6=3y
Divide both sides by 3 to isolate y on one side.
(4/3)x-2=y
y=(4/3)x-2
m=4/3
b=-2
So the slope is 4/3
The coordinates of Quadrilateral EFGH and its image, Quadrilateral E'F'G'H', are given below.
H(-4, 2) H'(-4,-1)
Quadrilateral EFGH E(-5, 5) F(-3, 4) G(-2, 1) Quadrilateral E'F'G'H' E'(-5, 2) F'(-3, 1) G'(-2,-2)
Which single transformation could be used to map Quadrilateral EFGH to Quadrilateral E'F'G'H'?
O a translation of 3 units to the right
O a translation of 3 units up
O a translation of 3 units down
O a translation of 3 units to the left
Option (3) is correct. A translation of 3 units down.
What is translation of points?
A point's linear displacement from its starting position is referred to as translation. In an x - y coordinate plane, a point's coordinates are labelled with respect to the origin by first indicating the horizontal position and then the vertical position.
Given: The coordinates of Quadrilateral EFGH and its image, Quadrilateral E'F'G'H', are given below,
E(-5, 5) ⇒ E'(-5, 2)
F(-3, 4) ⇒ F'(-3, 1)
G(-2, 1) ⇒ G'(-2, -2)
H(-4, 2) ⇒ H'(-4, -1)
From above we can see that the y - coordinate of each point is decrease by 3.
Which is the translation of 3 units down.
Therefore, the single transformation a translation of 3 units down, could be used to map Quadrilateral EFGH to Quadrilateral E'F'G'H'.
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