The maximum or minimum value of the function y = -2x² + 32x - 12 is (8, 116) and the range of the function y = -2x² + 32x - 12 lies in the interval
(−∞ ,116).
Given, the function is y = -2x2 + 32x - 12
According to the question we have to extract the maximum or minimum value of the function.
The maximum or minimum of a function which is a quadractic function occurs at the point x = -b/2a.
If a is negative, then the maximum value of the function is f(-b/2a).
If a is positive, then the minimum value of the function is f(-b/2a).
According to this, we can derive the general equation as
fmax(x) =ax²+bx+c occurs at x = -b/2a.
From the given equation, comparing we get
a = -2, b = 32, c = -12
Substitute the value of a and b in in the general equation and we get
x = -32/2(-2)
x = -32/-4
x = 8
Put x = 8 in the given general equation,
y = -2(8)² + 32(8) - 12
y = -2(64) + 256 - 12
y = -128 + 256 - 12
y = 256 - 140
y = 116
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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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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
You work in a jewelry store where you make a 13% commission for every sale. If you sell a $1350 ring, what will you make in commission?
Answer:1174.5
Step-by-step explanation:
.13 times 1350= 175.5$ so 1350-175.5= 1,174.5$
How many numbers in the set of consecutive integers from 1 to 99, Inclusive, have 3 as a factor but do not have 6 as a factor?
Graph the line of the given equation
Answer:
Step-by-step explanation:
See the attached image
please help asap!!
will mark brainliest :)
Answer:
Integer, Rational, Real
Step-by-step explanation:
Let's go through and define what each of these are:
Integer:
An integer is any number (including zero) that is positive or negative. Please note that it cannot be a decimal / fraction.
-1 is a whole, negative number. So, it is an integer.
Rational:
A rational number is any number that can be written as a ratio of 2 numbers. Ex: 1.5 can be 3/2
-1 can be written as -1/1, so it is a rational number.
Real
A real number is *any* number that is not imaginary (the number i is imaginary. i is [tex]\sqrt{-1}[/tex])
-1 has no i so it is a real number
Irrational
An irrational number is any number with a radical at it's end. Ex: 3 [tex]\sqrt{5}[/tex], and [tex]2\sqrt{2}[/tex]
-1 has no radical attached to it, so it is not an irrational number.
Whole:
A whole number is any number that has no decimal and is positive (though zero is included)
-1 has no negative, but is a negative number so it would not be counted as a whole number.
Natural:
Natural numbers were always confusing to me, but I hope this will help you. A natural number is any positive number starting at 1, and going forever. They always increase in a multiple of 1. Examples of natural numbers: 1, 2, 3, 4... It is called a natural number, because counting in multiples of ones is natural to us, like counting the amount of apples in a basket.
-1 is a negative number, so doesn't qualify for the characteristics of a natural number.
Let's go back through all of these explanations and see which ones we said -1 is:
Integer, Rational, Real
Mammoth Cave in Kentucky has a depth of −124.1 meters. Suppose a hiker traveled to the bottom of the cave. How many meters did the hiker descend?
Distance between starting and end point. The hiker descends the distance is [tex]124.1m[/tex]
What is depth?
The distance between the nearest end and farthest end of an object is its depth.
Here given that, the depth of the mammoth cave is [tex]-124.1m[/tex].
When the hiker is at the maximum depth it is traveling to the bottom of the cave.
As it is given the depth of the cave [tex]-124.1m[/tex]. Since the hiker is traveling down to the bottom and covering the total depth and the hiker must have covered the same distance corresponding to the depth in the cave which would be [tex]124.1m[/tex].
Hence, the hiker must have descended the distance that is [tex]124.1m[/tex]
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. 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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6. Multi-Step Problem A fish swims 12 miles
downstream in 2 hours. The fish swims back
upstream to the same point, but the trip takes
3 hours. Assume the speed of the current was
constant and the fish swam along the same
path.
a. Write a system of linear equations to
describe the situation.
b. Determine the speed of the fish in still
water.
c. Determine the speed of the current.
d. Writing If the speed of the current was
not constant, could you still calculate the
speed of the fish in still water?
The speed of the fish in still water is 5 Km/h.
The speed of the current is 1 km/hr.
Write the definition of speed.The speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined.For the given question.
Total distance travelled by fish = 12 miles.
Let the speed of the fish in still water be 'x km/h.'
Let the speed of the current be 'y km/hr'.
Time taken by fish in moving down steam is 2 hours.
Time taken by fish in moving up steam is 3 hours.
Use formula;
Distance = speed x time
Part a: system of linear equations
Down steam; 2(x + y) = 12 ...eq 1
Up steam; 3(x - y) = 12 ...eq 2
Part b: speed of the fish in still water.
Solve equation 1 an d 2 by elimination.
2(x + y) = 12
3(x - y) = 12
Divide equation 1 by 2 and multiply it by 3, Then add to eq 2.
6x = 30
x = 5
Speed of fish in still water = 5 Km/h.
Part c: speed of the current
Put value of x in eq 1.
x = 5
2y = 12 - 10
2y = 2
y = 1
Thus, speed of the current is 1 km/hr.
Part d: If the speed of the current is not constant than, then the value of speed of the fish in still water can not be found.
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a sample of 50 students was taken from the local university. these students spent an average of $170 on books this semester, with a standard deviation of $25.50. find the 95% confidence interval for the mean spent on books at this university?
TThe 95% confidence interval for the mean spent on books at this university is (160.711, 179.289).
In the given question we have to find the 95% confidence interval for the mean spent on books at this university.
A sample of 50 students was taken from the local university.
So n=50
These students spent an average of $170 on books this semester, with a standard deviation of $25.50.
So x=$170 and σ = $25.50
So the 95% confidence interval for the mean spent on books at this university.
CI=x ± [tex]z_{\alpha /2}[/tex]× σ/√n
Now finding the value of [tex]z_{\alpha /2}[/tex] for 99%=0.99 confidence interval.
[tex]\alpha[/tex] =1−0.99 = 0.01
[tex]\alpha[/tex]/2 = 0.01/2 = 0.005
[tex]z_{\alpha /2}=z_{0.005}[/tex]
[tex]z_{\alpha /2}[/tex] = 2.576
The z critical value at 99% confidence interval is 2.576.
Putting the value
CI=170 ± 2.576× 25.50/√50
CI=170 ± 2.576× 25.50/7.071
CI=170 ± 2.576×3.606
CI=170 ± 9.289
CI=(170 − 9.289, 170 + 9.289)
CI =(160.711, 179.289)
Hence, the 95% confidence interval for the mean spent on books at this university is (160.711, 179.289).
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I have 3 triangles and 1 circle. I want to add circles so that it is more likely that I will randomly choose a circle than a triangle. What's the smallest number of circles I should add?
Answer:
3
It should be 3 because well how to explain
the number of people infected with coronavirus doubles every 3.3 days. how many days does it take for the u.s. to go from one case (patient zero) to all 330,000,000 americans being infected.
It will take 96.7 days for the whole US population to get infected.
Given information;
The number of people infected with coronavirus doubles every 3.3 days as following;
1 → 2 → 4 → 8 → 16 → 32 → 64 → . . . . . . . . . . . . → 333,000,000
Let 'x' denotes number of 3.3 days passed the for cases 333,000,000.
⇒ [tex]2^x = 333,000,000[/tex]
For the above equation applying log on both sides. we get;
x(In 2) = In (330,000,000)
x = In (330,000,000)/(In 2)
x = 28.3
Therefore;
So, total no. of 3.3 days passed = 1 + x
= 1 + 28.3
= 29.3
And number of days for 1 to 330,000,000 = 29.3 * 3.3 days
= 96.7 days
Hence, it will take 96.7 days to infect the total population in US.
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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.Ms. Jackson is buying scientific calculators for her math class.
She tells the principal that a classroom set of 30 calculators would
cost $388.50. The principal wants to know the cost of purchasing
calculators for the entire school. How much would it cost to buy 300
calculators?
i need help asap, i dont remember learning this so i have no clue
The different ways used to display misleading information on a graph is done by skipping a number or doesn't begin at zero. There are incorrect labels on the graph. Data is missing.
What is a misleading graph?A misleading graph also referred to as a distorted graph, is one that presents data inaccurately, abusing statistics in the process and potentially leading to an incorrect conclusion.
Sometimes deceptive graphs are created on purpose, and other times it's just a matter of people not comprehending the data that goes into the graph. The "classic" varieties of deceptive graphs include those in which:
The vertical scale does not begin at zero, is too large or too little, skips digits, or all of the above.
The graph's labels need to be updated.
Data is omitted.
Thus, the different ways used to display misleading information on a graph are done by skipping a number or doesn't begin at zero. There are incorrect labels on the graph. Data is missing.
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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
Find an equation of variation in which y varie inverely a x and y=5 and x=17. Then find the value of y when x=10
Answer: If the graph of a relationship is a line or a ray through the origin, then it is proportional. If it is a line or ray that does not pass through the origin, then it is not proportional. Also, if it is not linear, then it is not proportional.
Step-by-step explanation:
8x + 18 = _ (4x + 9)
Answer:
2
Step-by-step explanation:
we can try 2 to distribute since 18 divided by 9 is 2
2(4x+9)
2(4x)+2(9)
8x+18
Hopes this helps please mark brainliest
EMERGENCY,
THIS IS QUESTION 1, GO ANSWER MY OTHER ONES UP UNTIL 10 ON MY PROFILE TOO. HELP ASAP
Answer:
A) Slope = 9/4, y-intercept = 2Step-by-step explanation:
The y-intercept is the y-coordinate with x = 0, this is 2 on the table:
b = 2,Use one more of points, (2, 6.5) to find the slope:
m = (6.5 - 2)/2 = 4.5/2 = 9/4The line is:
y = 9/4x + 2,Correct choice is A.
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 in9) Give the following expression in index form
a) √3
Answer:
nStep-by-stepkbexplanation:
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
Can anyone help!!!!
Question 5 only *
Answer:
Step-by-step explanation:
-3x^2 + 24x + 5 in the form 5 (6x - 3)^2 + 18
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?
Betsie is going to buy 250 envelopes
Here is some information about the cost of the envelopes
Letters2go Pack of 25 envelopes for £3.19
Value World Pack of 10 envelopes £1.99 Buy 2 packs get one free
Betsie wants to buy the envelopes for the best possible price
Which shop should Betsie buy the 250 envelopes from?
You must show how you got your answer.
At Letter2go, Betsie can purchase the 250 envelopes. As an example, 250 envelopes cost £31.9 in the Letter2go store but £33.17 in the Value World store.
What is an Expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
From Letters 2 go:
Pack of 25 envelopes for £3.19
If we look at the price of envelopes at shop 1, which is Value World,
The cost of a pack of 10 envelopes is £1.99.
Also, buy 2, get one is free
Which means that 1 pack = £1.99
2 packs = 2×£1.99 = £3.98
Also, with 2 packs Betsie get 1 pack free
So, Betsie gets 3 packs for £3.98.
1 pack = 10 envelopes
3 packs = 30 envelopes.
Hence,
In shop Value World:
30 envelopes = £3.98
1 envelope = £3.98/30
250 envelopes = (3.98/30)×250
So, 250 envelopes will cost £33.17 in Shop Value World.
From shop Letter 2 go:
25 envelopes = £3.19
1 envelope = £3.19/25
250 envelopes = (3.19/25)×250
Therefore, 250 envelopes in Store Letter 2 go should cost £31.9.
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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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Create a list of steps, in order, that will solve the following equation.
(x - 5)² = 25
Solution steps:
Add 5 to both sides
Multiply both sides by 5
Square both sides
Take the square root of both sides
Answer:
25
Step-by-step explanation:
5x5 =25 25-5=20
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
PLEASE HELP URGENT
Solve for the roots in simplest form using the quadratic formula:
4x^2+4x=3
Answer: x = 1/2 , -3/2
Step-by-step explanation:
Use the quadratic formula:
a=4
b=4
c=-3
x= -4 +- sqrt16-4(4)(-3) / 8
= -4 +- sqrt16+48 / 8
= -4 +- sqrt64 / 8
= -4 +- 8 / 8
Split it to (-4 + 8) / 8 and (-4 - 8) / 8
4/8 and -12/8 = 1/2 and -3/2
PLEASE HELP ASAP IM BEGGING pics below.
Please answer like a) (answer) and b) (answer)
TYSM
The expression of the given volume formula for the l will be 1 and l, in general, will be V/(wh).
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given volume expression,
V= lwh
a)
l = V/(wh)
l = 8/(2 × 4) = 1
b)
V= lwh
l = V/(wh)
Hence "The expression of the given volume formula for the l will be 1 and l, in general, will be V/(wh)".
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