Step-by-step explanation:
1. if to rewrite the given equation, then
y= -3(x+5)²+1;
2. the vertex of the parabola is (-5;1) and it is the highest point. Then
3. domain: x is any value, x∈(-∞;+∞);
range: y not greater than 1, y∈(-∞;1].
For the parabola f(x) = -3x² - 30x - 74, the domain is all real numbers (-∞, ∞), and the range is also all real numbers (-∞, ∞).
To determine the domain and range of the given parabola f(x) = -3x² - 30x - 74, we need to understand the behavior of parabolas.
The domain of a function represents all the possible x-values for which the function is defined. In this case, there are no restrictions on the x-values for the given quadratic function. Therefore, the domain is all real numbers, expressed as (-∞, ∞).
The range of a function represents all the possible y-values that the function can produce. For a parabola, if the coefficient of the squared term (in this case, -3) is negative, the parabola opens downward. Since the coefficient is negative, the parabola will have a maximum value. In this example, there is no minimum or maximum specified; thus, the range will also be all real numbers.
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Divide. Write your answer on the simplest form.
7/15 ÷ 3/10
Answer:
14/9
Step-by-step explanation:7/15 divided by 3/10 equals 14/9
Consider a collection of envelopes consisting of two red envelopes three blue envelopes one green envelope and one yellow envelope if two envelopes are selected at random with replacement determine the probability that at least one envelope is red envelope
The probability that at least one envelope is red envelope is 2/7.
Given:
A collection of envelopes consisting of two red envelopes three blue envelopes one green envelope and one yellow envelope if two envelopes are selected at random with replacement.
Total = 2 + 3 + 1 + 1
= 5 + 2
= 7
Number of possible outcomes = 7
Number of favorable outcomes = 2
Probability that at least one envelope is red envelope is = 2/7
= 0.2857
Therefore the probability that at least one envelope is red envelope is 2/7.
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A baseball is hit into the air, and its height h in feet after t seconds is given by h(t)=-16t^2+ 32t+ 1
a What is the height of the baseball when it is hit?
(b) After how many seconds does the baseball reach its maximum height?
(c) Determine the maximum height of the baseball.
a) The ball was struck from a height of one foot.
b) It took the object one second to reach its highest point.
c) The baseball may fly up to a height of 17 feet.
Determining the maximum height of an object using functions.Given the function that represents the height of an object in air expressed as;
h(t)=-16t^2+ 32t+ 1
a) The ball is hit at the point where the time is zero. Equating the function to zero.
h(0) = -16t^2+ 32t+ 1
h(0) = -16(0) + 32(0) + 1
h(0) = 1 feet
Hence the ball was hit at the height of 1 feet
b) At maximum height, the velocity of the object is zero. Hence;
v(t) = -32t + 32
v(t) = 0 = -32t + 32
32t = 32
t = 32/32
t = 1sec
Hence the object reach its maximum height after 1 seconds.
c) Substitute t = 1 into the function to have:
h(1)=-16(1)^2+ 32(1)+ 1
h(1) = -16 + 33
h(1) = 17 feet
The maximum height reached by the baseball is 17 feet.
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Need soon pls! Super easy
Answer:
choose 2nd option
Step-by-step explanation:
Use the annuity formula to determine the accumulated amount in the annuity if $80 is invested for 40 years at 6.0% compounded semiannually .
The accumulated amount in the annuity if $80 is invested for 40 years at 6% is $25,709.04.
What is the accumulated amount?An annuity is when a series of payment is made over a specified period of time. An annuity can either be an ordinary annuity or a beginning annuity. An ordinary annuity is when the series of payment is made at the end of the period. A beginning annuity is when the annuity payment is made at the beginning of the period.
In this question, the annuity would last for 40 years and payments would be made twice a year.
The formula that can be used to determine the accumulated amount is:
Accumulated amount = annuity factor x payment
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = annual interest rate / number of compounding = 6% / 2 = 3%n = number of payment period = number of years x number of compounding = 2 x 40 =80 yearsAccumulated amount = $80 x [{(1.03^80) - 1} / 0.03]
Accumulated amount = $80 x 321.36302
Accumulated amount = $25,709.04
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. What is the present value of an annuity that pays $100 per month for 10 years if money worth 6%
compounded monthly?
The present value of an annuity is $736.01
We know that the formula for Present Value of Annuity:
PV = P * [1 - (1 + r)^(-n)]/r
where, PV = present value of an ordinary annuity
P = value of each payment
r = interest rate per period
n = number of periods
From given data:
P = $100, n = 10 and r = 0.06
So, the present value would be,
PV = 100 * [1 - (1 + 0.06)^(-10)]/0.06
PV = 100 * 7.3601
PV = $736.01
Therefore, the present value of an annuity is $736.01
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suppose that $36,000 is deposited in an account and the balance increases to $39,786.15 after 2.5 years. how long will it take for the account to grow to $51,806.67? Assume continous compounding
It will take about _ years for $36,000 to grow to $51,806.67
It will take about 9.1 years for $36000 to grow with interest to $51806.67 after continuous compounding .
What is continuous compounding?
The process of continuously compounding involves calculating interest and reinvested it into the balance of an account over an infinite number of periods. When they specifically state that the amount is "compounded continuously" in a problem, they should use the continuous compounding formula. The mathematical constant "e" is used in this formula, and its value is roughly equal to 2.7182818. Here is the formula for continuous compounding.
Here the Principal P = $36000 , Total amount A= $39786.15 and
Time t=2.5 yrs.
Now using continuous compounding formula,
=> A = P[tex]e^(rt)[/tex]
=> 39786.15 = 36000*[tex]e^(r*5/2)[/tex]
=> r = 0.04 = 4%
Now A=51806.67 and Again using continuous compounding formula ,
=> A = P[tex]e^(rt)[/tex]
=> 51806.67 = 36000*[tex]e^(0.04*t)[/tex]
=> t =9.1 years.
Therefore it will take about 9.1 years for $36000 to grow to $51806.67 .
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PLS HELP! 50 points
Help please. Need it soon as possible
Answer:
Step-by-step explanation:
1=205
2=63
3=45
4=5
graph this problem and post the answer
A graph of the given set of functions has been plotted and shown in the image attached below.
What is a function?In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable to an output variable.
What is a graph?In Mathematics, a graph is a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).
By critically observing the graph of this set of functions (see attachment), we can reasonably infer and logically deduce that they both represent parallel lines, with function f(x) being transformed to produce function h(x).
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can someone pls help me i don’t get this
The 23 members of the westview journalism club are trying to raise at least 2,100 to buy new publishing desgin software. The members have already raised 1180. How much should each student still raise, on average, to meet the goal?
PLEASEE ASAAPP
Based on the number of members in the Westview Journalism Club, the amount that each student should raise on average to meet the goal is $40.
How to find the average amount?The amount that the students would have to raise is the amount that is remaining from the amount already raised. This can be found as:
= Amount that club needs to raise - Amount already raised
= 2, 100 - 1, 180
= $920
The average amount that each student has to raised to meet the target would then be based on the number of students in the club which is 23 members.
The average amount is therefore:
= Amount that still needs to be raised / Number of students in the Westview Journalism Club
= 920 / 23
= $40
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The following angles are supplementary to each other.
m∠A = (4x + 30)° and m∠B = (2x − 30)°
Determine x.
15
20
30
60
According to the sum of the given supplementary angles, we find out that the value of x is 30.
It is given that ∠A and ∠B are supplementary where,
∠A = (4x + 30)° and,
∠B = (2x - 30)°
We have to find out the value of x.
We know that two supplementary angles add up to 180°.
Since ∠A and ∠B are supplementary angles, therefore
∠A + ∠B = 180°
=> (4x + 30) + (2x - 30) = 180°
=> 6x = 180°
=> x = 30
Thus, for the given supplementary angles, the value of x is 30.
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**According to the sum of the given supplementary angles, we find out that the value of x is 30.
It is given that ∠A and ∠B are supplementary where,
∠A = (4x + 30)° and,
∠B = (2x - 30)°
We have to find out the value of x.
We know that two supplementary angles add up to 180°.
Since ∠A and ∠B are supplementary angles, therefore
∠A + ∠B = 180°
=> (4x + 30) + (2x - 30) = 180°
=> 6x = 180°
=> x = 30 **
In ΔNOP, \overline{NP} NP is extended through point P to point Q, m∠OPQ = (6x-15)∘, m∠PNO=(2x+18)∘ , and m∠NOP=(2x−13)∘. What is the value of x?
Mae has $215 in her account and withdraws $120 one time. Each month her balance is below $100, she pays a $7 fee. Write an equation to express her balance for the next x months, if she makes no deposits or withdrawals .
Answer: 930$ and the expression is 1000$ - 70$ = 930$
Step-by-step explanation:
if she has under 100 dollars in her bank account every month for 10 months therefore multiplying it by 10 giving you 1000 but we cant forget about the 7$ monthly fee. 7 times 10 = 70 1000- 70 = 930$
Answer:
Step-by-step explanation:
Triangle DEF, with vertices D(3,-5), E(8,-6), and F(4,-2), is drawn inside a rectangle, as shown below.
The area of triangle DEF, in square units, is given as follows:
4.08 units squared.
What is the area of a triangle?The area of a triangle is given by half the multiplication of it's base by it's height, as follows:
Area = 0.5 x base x height.
We consider the base as the segment DE, hence it's length is given by the distance between these two points, obtained as follows:
[tex]b = \sqrt{(8 - 3)^2 + (-6 - (-5))^2}[/tex]
[tex]b = \sqrt{26}[/tex]
b = 5.1 units.
The midpoint of the base is given as follows:
(5.5, -5.5).
As it is obtained with the mean of the coordinates.
The height is the distance between the midpoint of the base and the other vertex, hence:
[tex]h = \sqrt{(5.5 - 4)^2 + (-5.5 - (-5))^2}[/tex]
h = 1.6 units.
Hence the area of the triangle is obtained as follows:
Area = 0.5 x 5.1 x 1.6 = 4.08 units squared.
Missing InformationThe problem asks for the area of the triangle, as shown in the image given at the end of the answer.
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A square shape garden has a side of 6 feet. What is its area?
A weightlifter lifts
72
k
g
. Which of the following weights is the same as
72
k
g
?
(
1
k
g
=
1
,
000
g
)
720 g
720,000 g
72,000 g
30,000 g
Answer:
I think 72,000 because since the weightlifter is lifting 72 and it is kg. It is turned into grams. multiplied by 1000 so 72000
The perimeter of a quadrilateral (four-sided polygon) is 29 inches. The longest side is twice as long as the shortest side. The other two sides are equally long and are 2 inches longer than the
shortest side. Find the length of all four sides.
The length of the shortest side is ____?
the length of each of the two equal sides is____?
and the length of the longest side is___?
The length shortest side of the quadrilateral is 5 inches
The length longest side of the quadrilateral is 10 inches;
The length of the other two sides of the quadrilateral will be 7 inches.
What is the perimeter of a quadrilateral?
The length of a quadrilateral's boundary, or what remains after joining all four of its sides to form a single line segment, is referred to as the quadrilateral's perimeter. As a result, a quadrilateral's perimeter is measured in the same linear units as its sides, such as meters, inches, centimeters, etc. We are aware that a quadrilateral's perimeter can be calculated by summing all of its side lengths. This can be stated using a straightforward formula. For instance, the formula for a quadrilateral ABCD's perimeter can be written as,
AB + BC + CD + DA = The perimeter
Let the length shortest side of the quadrilateral be x;
So, According to the question,
length longest side of the quadrilateral will be: 2x;
length of the other two sides of the quadrilateral will be (x +2) inches.
We have given that:
The perimeter of the quadrilateral is 29 inches.
So,
⇒ 2x + (x+2) +(x+2)+x = 29
⇒5x + 4 = 29
⇒5x = 29-4
⇒5x = 25
⇒x =5;
Hence,
the length shortest side of the quadrilateral is 5 inches
length longest side of the quadrilateral is 10 inches;
length of the other two sides of the quadrilateral will be 7 inches.
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A manufacturer knows that their items have a normally distributed length, with a mean of 13.6 inches, and standard deviation of 2.4 inches. If one item is chosen at random, what is the probability that it is less than 13.1 inches long?
If one item is chosen at random, the probability that it is less than 13.1 inches long is equal to 0.4176.
How to determine the probability?First of all, we would determine the z-score of this data set. Mathematically, the z-score of a given sample score in a normal distribution can be calculated by using this formula:
Z-score = (x - μ)/σ
Where:
x represents the sample score.σ represents the standard deviation.μ represents the mean score.Substituting the given parameters into the formula, we have;
Z-score, z = (13.1 - 13.6)/(2.4)
Z-score, z = -0.5/2.4
Z-score, z = -0.208
If one item is chosen randomly, the probability that it would be less than 13.1 inches long is given by this mathematical expression:
P(x < 13.1) = P(z < -0.208)
P(z < -0.2083) = 0.4176.
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Use the function, to match each key feature listed below.
The parabola have a vertex of (-1, -64), it's x-intercept is (3, 0), (-5, 0), it's y-intercept is (0, -60) and it's axis of symmetry is x = -1
ParabolaThis is a curve formed by the intersection of a cone with a plane parallel to a straight line in its surface. It can also be defined as a curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed line. In mathematics, it is a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.
f(x) = 4x² + 8x - 60
The vertex = (-1, -64)
The x-intercept = (3, 0), (-5, 0)
The y-intercept = (0, -60)
The axis of symmetry = x = -1
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For every dozen bagels you buy, the cost increases $15. Which equation represents the cost, y, and the number of bagels, x?
a. y=1.25 + x
b. y=15x
c. x=15y
d. y=1.25x
The equation that represents the cost, y, and the number of bagels, x is D. y=1.25x
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.
It should be noted that 1 dozen = 12
The equation the represents the information will be:
y = (15/12) × x
y = 1.25 × x
y = 1.25x
where x = number of bagels
The equation is y = 1.2x.
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Help please i need your help
There are 28 groups of 1/5 are in 5.
And, The solution of the expression 5 ÷ 4/5 will be 25/4.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
There is a number line shown in figure.
Now,
In a number line,
The groups of 1/5 in 5 = 28 - 0
= 28
Thus, There are 28 groups of 1/5 are in 5.
And, The expression is,
⇒ 5 ÷ 4/5
Solve aa;
⇒ 5 × 5/4
⇒ 25 / 4
Thus, There are 28 groups of 1/5 are in 5.
And, The solution of the expression 5 ÷ 4/5 will be 25/4.
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Which pairs of fractions include a fraction equivalent to 1/2 and a fraction equivalent to 3/4 help me PLEASE
Answer:
4/8 and 8/16
Step-by-step explanation:
Multiply 1/2 and 3/4 to find a common fraction between them (4/8) then multiply that fraction by any number greater than 1 to find another fraction equivalent
Jonathan, Lucas, and Kiley are in a book
club. This past week, Lucas read six less
pages than Kiley read. Jonathan read two
times the amount of pages that Lucas.
read., Altogether, they read 122 pages.
how many pages did each person read? PLS HELP ME
Answer:
Lucas 29
Kiley 35
Jonathan 58
Step-by-step explanation:
Kiley = Lucas + 6
Jonathan = 2 x Lucas
Kiley + Lucas + Jonathan = 122
1. Replace Kiley and Jonathan with information we have
K + L + J = 122
(L+6) + L + (2L) = 122
4L + 6 = 122
4L = 122 - 6
L = 116/4 = 29
2. Replace Lucas with 29, you have
Kiley = 29 + 6 = 35
Jonathan = 2 × 29 = 58
Brett and Julian sign up to run in the Memorial Day race in their town. There are two different events at this race, a 5k and a 10k. Brett signed up for the 5k and Julian signed up for the 10k. Think of when both Brett and Juan would have finished 3/5 of their races. How many kilometers has each person run at this point?
The number of kilometers that Brett and Julian would have run at the 3 / 5 point are:
Brett - 3kmJulian - 6 km How to find the number of kilometers?Brett is running the 5k race at the Memorial Day race which means that when he runs 3 / 5 of the race, he would have ran a total of :
= Distance on Brett's race x Proportion ran
= 5 x 3 / 5
= 15 / 3
= 3 km
Julian on the other hand, is in the 10 k race which means that when they get to 3 / 5 of the race, they would have ran:
= 10 x 3 / 5
= 30 / 5
= 6 km
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Sari put $1230 in a savings account at a simple interest rate of 4.5% per year. Avi put $1105 in a savings account at a simple interest rate of 5.5% per year. Who will have earned more interest after 4 years? How much more?
Answer:
Avi
$21.61
Step-by-step explanation:
I = Prt
Sari: I = Prt = $1230 × 0.045 × 4 = $221.40
Avi: I = Prt = $1105 × 0.055 × 4 = $243.01
$243.01 - $221.40 = $21.61
Answer:
Avi
$21.61
It takes 1 3/4 of a pint of paint
to paint one wall of a room
and 1 4/5 of a pint of paint for
the second wall. How
many pints of paint are
used on the two walls?
3 11/20
Step-by-step explanation:
1 3/4+1 4/5=
7/4+9/5=
7/4x5/5=35/20
9/5x4/4=36/20
35/20+36/20=71/20=3 11/20
what is the point slope for the top and slope intercept for the bottom? TIA
Answer:
It looke like the point given is (1,2) and the slope is 3
Point slope form: y - 2 = 3(x -1)
Slope Intercept form: y = [tex]\frac{-1}{3}[/tex]x + 1
Step-by-step explanation:
Point slope As they name implies, you need a point and a slope. The picture is a little hard to read, but it looks like the point plotted is (1,2) The slope is the change in y over the change in x. It looks like from that point to get back on the line only using horizontal and vertical moves, we would move up three and 1 to the right to get back on the line at point (2,5).
The point slope form of a line is:
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex]) Plug in 2 for [tex]y_{1}[/tex] and 1 for [tex]x_{1}[/tex] amd 3 for m
y = 2 = 3( (x-1)
Slope intercept form: As the names implies we need a slope and a yi-intercept.
The slope is [tex]\frac{-1}{3}[/tex]. Select a point on the line. If you can only move veritacl and horizontal. You would move down 1 unit and three units to the right. The y intercept is where the line crosses the y axis. In this case 1
y = [tex]\frac{-1}{3} x + 1[/tex]
From the chart, estimate (roughly) the number of transistors per IC in 2012. Using your estimate and Moore's Law, what would you predict the number of transistors per IC to be in 2040?
The estimates for the number of transistors per IC, using an exponential function, are given as follows:
2012: 4,194,304,000.2040: 6.87 x 10¹³.What is the format of an exponential function?The format of an exponential function is presented as follows:
[tex]y = ab^\frac{x}{n}[/tex]
In which the parameters of the function are listed as follows:
a is the initial value of the function.b is the rate of change of the function.n is the period relative to the rate of change.Moore's Law states that the number of transistors per IC doubles every two years, hence the values of parameters b and n both have values of two, hence:
b = 2, n = 2.
The number of transistors per IC in the reference year of 1972 was of 4000, hence the initial value is of:
a = 4000.
Then the exponential function is:
[tex]y = 4000(2)^{\frac{x}{2}}[/tex]
2012 is 2012 - 1972 = 40 years after 1972, hence the estimate is given as follows:
[tex]y = 4000(2)^{\frac{40}{2}} = 4,194,304,000[/tex]
2040 is 68 years after 1972, hence hence the estimate is given as follows:
[tex]y = 4000(2)^{\frac{68}{2}} = 6.87 \times 10^{13}[/tex]
Missing InformationThe chart is given by the image at the end of the answer.
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