The general form of the equation of the quadratic function is, [tex]y=(x + 6)^2 - 1[/tex]
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given that the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function.
(h, k) = (−6, −1), (x, y) = (−9, 8)
The General vertex form of a quadratic,
f(x)=
[tex]y=a(x-h)^2 + k[/tex]
Where,a = focus,
h = x-coordinate of vertex,
k = y-coordinate of vertex.
As the point (−9, 8) lies on the curve, therefore it must satisfy the curve equation.
[tex]y=a(x-h)^2 + k\\\\8=a(-9-(-6))^2 - 1[/tex]
a = 1
∴ Then the equation becomes,
[tex]y=(x + 6)^2 - 1[/tex]
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16. Model Real Life Your aunt and uncle
buy 2 personal watercrafts for $3,495
each. They make 10 equal payments
for the watercrafts. What is the amount
of each payment?
7
TR
The amount of each payment is $699.
What is payment?
Payment refers to the exchange of something of value as a condition of a contract. While one party pays money and receives something else of value, the other party gets paid in return for delivering a good or service. Physical currency was once the most common form of payment, but nowadays most forms of payment use technology.
Given: Buy 2 personal watercrafts for $3,495 each.
So, the price for 2 watercrafts is, 2 x $3495 = $6990
They make 10 equal payments for the watercrafts.
So each payment is of $6990/10 = $699.
Hence, the amount of each payment is $699.
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What is the range of the data set below? * Data Set 13 44 54 2 25 17 7
Answer: 52
Step-by-step explanation:
To find the range of a data set, we subtract the smallest value from the largest value.
54 - 2 = 52
Please help me on this.
Explain why it has no real solution
Answer:
Step-by-step explanation:
[tex]\sqrt{2x+1} = -4 -1[/tex]
[tex]\sqrt{2x-1} = -5[/tex]
the number under a square root is always 0 or a positive number, so it can’t be equal to a negative number
In triangle DEF, line DE is congruent with line FD and the measurement of angle F is 55. Find the measurement of angle E. (isosceles triangle)
Step-by-step explanation:
because it is an isoceles triangle (both legs are equally long), E and F are the side angles in the baseline.
and because both leg sides are equally long, also both side angles must be equally large
therefore,
angle E = angle F = 55°.
PLEASE I REALLY NEED HELP!!! 100 points if answer right
y=1/3x+4 is perpendicular to y=-3x-4,
y=2/5x-7 is perpendicular to y=-5/2x+7,
y=-5/2x+8 is perpendicular to y=2/5x+6,
y=-2x+6 is perpendicular to y=1/2x+3 and
y=7/5x-9 is perpendicular to y=-5/7x-11.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We know that the product of slopes of perpendicular lines is -1.
mM=-1
m is slope of one line and M is the slope of perpendicular line.
M=-1/m
y=1/3x+4
The perpendicular line is y=-3x-4
y=2/5x-7
The perpendicular line is y=-5/2x+7
y=-5/2x+8
The perpendicular line is y=2/5x+6
y=-2x+6
The perpendicular line is y=1/2x+3
y=7/5x-9
The perpendicular line is y=-5/7x-11.
Hence, the lines with corresponding perpendicular lines are
y=1/3x+4---> y=-3x-4
y=2/5x-7-----> y=-5/2x+7
y=-5/2x+8----->y=2/5x+6
y=-2x+6---->y=1/2x+3
y=7/5x-9-----> y=-5/7x-11.
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100 POINTS WILL GIVE BRAINLIEST What is the target percent change for Growth Domestic Product?
A. 2-3% growth per period
B. 1-5% growth per period
C. 3-6% growth per period
Answer:A
Step-by-step explanation:
Question 1:
Joe and Sara are each running a 5k. In the age/ability group that Joe is running in, the average run time is 22:30 minutes/seconds with a standard deviation of 4 minutes. In the age/ability group that Sara is running in, the average run time is 31:15 minutes/seconds with a standard deviation of 6 minutes.
Joe's run time is 19:45. Sara's run time is 28:20. Compute the z-scores for each and thus make a claim about who ran a better race compared to their age/ability group.
Question 2:
Suppose a data set has a mean 50 and standard deviation 5. If the Z-score of a data value is -2, what is the actual score?
1. The z-scores are given as follows:
Joe: Z = -0.6875.Sara: Z = -0.49.Due to the lower z-score, Joe had a better time.
2. The actual score is of 40.
What are z-scores?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.Considering the mean and the standard deviation for his distribution, and also that 15 seconds = 0.25 minutes, the z-score for Joe is obtained as follows:
Z = (19.75 - 22.5)/4
Z = -0.6875.
For Sara, the z-score is calculated as follows:
Z = (28.33 - 31.25)/6
Z = -0.49.
Joe had a better time, as his lower z-score means that a lower percentage of runners spent less time than him, that is, a lower percentage of runners ran faster than him.
For item 2, the actual score is calculated as follows:
-2 = (X - 50)/5
X - 50 = -10
X = 40.
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Suppose that sin(a) = 4/6 and cos(b) =1/5 define in the first quadrant, determine cos(a-b). (round to 4 decimal places)
The value of the cosine of the angle of (a - b) will be 0.80.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
It is a function that repeats itself in a particular time interval.
Suppose that sin(a) = 4/6 and cos(b) = 1/5.
Then the value of 'a' is given as,
sin(a) = 4/6
sin(a) = 2/3
a = 41.81°
Then the value of 'b' is given as,
cos(b) = 1/5
b = 78.46°
Then the value of the cosine of the angle of (a - b) will be given as,
⇒ cos(41.81° - 78.46°)
⇒ cos(-36.65°)
⇒ cos 36.65°
⇒ 0.80
The value of the cosine of the angle of (a - b) will be 0.80.
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Shelby is walking through her favorite store and sees a shirt she likes being sold for $80.00. She then notices the store is having a 45% off sale on all items. Excited to purchase the shirt, she grabs it and goes to the cash register. As she’s taking out her wallet, she finds a coupon for 25% off (that is applied after the store’s sale). What is the final price of the shirt that Shelby pays after the two discounts?
a. $9.00
b. $33.00
c. $28.00
d. $52.00
first we go 45+25=70 so now 80-70=$10.00
Did you mess up one of the answer because I did it two ways and got 10.00?
Good afternoon! I have a survey for you guys to take. I would appreciate it if you do, because I use it for my schoolwork.
Knowing that the Bacon Cheeseburger meal is about 1000 calories and that you are supposed to consume between 2000 and 3000 calories per day, would you still eat Jack in the Box? Thank you beforehand!
1. I would eat there often
2. I would eat there sometimes
3. I would eat there rarely
4. I would not eat there ever
Answer:
Step-by-step explanation:
2, i would eat there sometimes!
Answer:
3. I would eat there rarely.
Step-by-step explanation:
Please give brainliest!!!
What is the value of x in |6|=x
Answer and Step-by-step explanation: I used demos and got (6,0) as my answer.
A tank has an intake valve and a release valve. The rate of follow through each valve is inversely proportional to the area of its cross-section. The cross-section area of the input can be described by the equation, f(x)= x^2+2x+1; The cross-section area of the release can be described by the equation, f(x)= x^2+4x+3. If the proportion constant is equal for the input and output, find x such that the volume of material in the tank remains constant.
Answer:
x = - 1------------------------------
The volume will remain constant if both input and output cross - sections are equal:
x² + 2x + 1 = x²+ 4x + 34x - 2x = 1 - 32x = - 2x = - 1Tommy does 28J of work to push the pencil over 4m. How much force did he use?
Answer:
Given that,
Tommy does 28 joules of work for pushing up the pencil.And, the distance is 4 meter.We know that
Work = Force × distance
So, the force = work ÷ distance
= 28 ÷ 4
= 7 newtonsTherefore we can conclude that the force that he used is 7 newtons.
I think of a number,take away 4 and multiply the result by 2.
The number that is thought in the form of expression will be 2x - 4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Let the number be 'x'. Then the expression is given as,
⇒ (x - 4) × 2
Simplify the expression, then we have
⇒ (x - 4) × 2
⇒ 2x - 4
The number that is thought in the form of expression will be 2x - 4.
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jonah and haley made brownies to bring as a class treat. some were plain and some had sprinkls the class ate 3/4 of one pan and 1/6 of another pan of plain brownies they ate 5/6 of one pan and 1/10 of another pan of brownies with sprinkles. if the brownies were the same sie dud the class eat more plain brownies or more brownies with sprinkles
Answer:
5/6
Step-by-step explanation:
he class ate 3/41 = <<3/41=3/4>>3/4 of one pan of plain brownies
They also ate 1/61 = <<1/61=1/6>>1/6 of another pan of plain brownies
The total amount of plain brownies they ate is 3/4 + 1/6 = <<3/4+1/6=5/6>>5/6
The class ate 5/61 = <<5/61=5/6>>5/6 of one pan of brownies with sprinkles
They also ate 1/101 = <<1/101=1/10>>1/10 of another pan of brownies with sprinkles
The total amount of brownies with sprinkles they ate is 5/6 + 1/10 = 5/6 + 1/10 = 41/60
The class ate more plain brownies because 5/6 > 41/60. Answer: {5/6}.
use the theorem in sec. 77, involving a single residue, to evaluate the integral of f (z) around the positively oriented circle |z|
The integral of f (z) around the positively oriented circle |z|
[tex]\int\limits^_ {} \,[/tex]f(z) dz = -8πi/3
What is integral?In mathematics, an integral lends numerical values to functions to represent notions like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.
With the exception of the point where z = z, where f(z) is analytic within and on C, let C be the smooth, simple closed curve except at z =z , then ,
[tex]\int\limits^_ {} \,[/tex] f(z) dz = 2πi [ res f(z)] z = [tex]z_{1}[/tex]
here f(z) is singular at z = -1,
res [tex]f(z)_{z = -1}[/tex] = [tex]\lim_{z\to \-1} z+1 f(z)_[/tex]
[tex]\lim_{z\to \-1}[/tex] [tex]z^{3}[/tex](1-3z)/(1+2[tex]z^{4}[/tex])
when z = -1 then f(z) = -4/3
Therefore [tex]\int\limits^_ {} \,[/tex]f(z) dz = 2πi (-4/3)
[tex]\int\limits^_ {} \,[/tex]f(z) dz = -8πi/3.
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Find the Area of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place. Please hurry!!!
The area of the given figure is 68.6
Calculating the area of a figureFrom the question, we are to determine the area of the given figure.
Area of the given figure = Area of the semicircle + Area of the rectangle + Area of the semicircle
Area of a semicircle = 1/2πr²
Where r is the radius
Area of a rectangle = Length × Width
From the given diagram,
The diameter of the semicircle is 4
Thus,
Radius, r = 4/2 =
r = 2
Length of the rectangle is 14
and the width of the rectangle is 4
Therefore,
Area of the figure = 1/2π(2)² + 14 × 4 + 1/2π(2)²
Area of the figure = 1/2π×4 + 14 × 4 + 1/2π×4
Area of the figure = 2π + 56+ 2π
Area of the figure = 4π + 56
Area of the figure = 68.566
Area of the figure ≈ 68.6
Hence, the area is 68.6
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and are right triangles. Find h. Use a proportion and show work.
In a triangle, The value of ''h'' will be;
⇒ h = 2.7 m
What is mean by proportion?
A proportion is a fraction of a total amount, in which two ratios are set equal to each other.
Given that;
The triangle is right triangle.
The values are,
AB = 6 m
BD = 12 m
BC = 0.9 m
DE = h m
Now,
Since, The triangle is right triangle.
Hence, By using definition of proportional we get;
⇒ AB / BC = AD / ED
Substitute all the values, we get;
⇒ 6/0.9 = (6 + 12) / h
⇒ 6 / 0.9 = 18 / h
⇒ h = 18 × 0.9 / 6
⇒ h = 2.7 m
Thus, The value of h = 2.7 m
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Please answer soon!!
Which angles are coterminal with 3л/2?
Select each correct answer.
A. 11л/2
B. -л/-2
C. -7л/-2
D. л/2
Answer:
A, C
Step-by-step explanation:
You want to know which answer choices are angles that are coterminal with 3π/2.
CoterminalAngles are coterminal when their terminal rays lie in the same position. In general, any angle will be coterminal with angles that are an integer multiple of 2π added to the original.
That is, an angle is coterminal with all angles that have the same value modulo 2π.
For the given angle and each of the answer choices, the attachment calculates the coefficient of π modulo 2. The ones that match the given angle are ...
A. 11π/2 mod 2π = 3π/2
C. -7π/-2 mod 2π = 3π/2
__
Additional comment
Both -π/-2 and π/2 match the angle π/2, which is not the same as 3π/2.
Of course, the minus signs in numerator and denominator cancel, so -7π/-2 is the same as 7π/2.
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The developer of the city park shown plans to put a decorative fence around the park. The budget allows for at least 399 feet of fencing but no more than 798 feet to be used.
The possible lengths of the side x + 30 are given as follows:
199.5 - x ≤ x + 30 ≤ 399 - x.
How to obtain the perimeter of a rectangle?The perimeter of a rectangle of base b and height h is given by the equation presented as follows:
P = 2(b + h).
The dimensions in the triangle in this problem are given as follows:
x.x + 30.The budget allows for at least 399 feet of fencing, hence:
2(x + x + 30) ≥ 399
x + x + 30 ≥ 199.5.
x + 30 ≥ 199.5 - x.
The budget allows for no more than 798 feet to be used, hence:
2(x + x + 30) ≤ 798
x + x + 30 ≤ 399
x + 30 ≤ 399 - x.
Then the range of values that can be assumed by the side with dimensions x + 30 is given as follows:
199.5 - x ≤ x + 30 ≤ 399 - x.
Missing InformationThe park has a rectangular format, with dimensions x and x + 30.
It asks for the possible lengths of the side with dimensions x + 30.
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what is 2/50 as a percentage’s
Answer:
4%
Step-by-step explanation:
2/50= 4/100
4/100= 0.04 or 4%
PLEASE HELP
Two swimming pools are being drained so that they can be repaired. The two equations below describe the depth of the two pools, d, as a function of time in hours, t.
d=5 - 1/4t. d=7 - 1/3t
Ted wants to know when the two pools will reach the same depth. He solves the system by equating the two equations for d and then solving for t. The solution he finds is t = 24, so he concludes that after 24 hours the pools will be the same depth. Is Ted’s conclusion reasonable? Why or why not?
A. Yes, Ted’s conclusion is reasonable. Setting the two equations equal and solving for t will solve for the time when the two pools are at the same depth.
B. Yes, Ted’s conclusion is reasonable. Substituting into both equations yields the same value for d, which is the depth of the pools.
C. No, Ted’s conclusion is not reasonable. Ted failed to take into account the limits on the domain and range of the two functions.
D. No, Ted’s conclusion is not reasonable. Ted made a math error when he was finding a common denominator when solving for t.
Yes, Ted’s conclusion is reasonable.
Setting the two equations equal and solving for t will solve for the time when the two pools are at the same depth.
Option A is the correct answer.
What is an equation?An equation is a mathematical statement made up of two expressions connected by an equal sign.
We have,
d = 5 - (1/4)t ____(1)
d = 7 - (1/3)t ____(2)
Now,
The time at which the depth d is the same.
Make (1) and (2) equal.
5 - (1/4)t = 7 - (1/3)t
(1/3)t - (1/4)t = 7 - 5
(4t - 3t)/12 = 2
t = 2 x 12
t = 24
Thus,
Yes, Ted’s conclusion is reasonable.
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A Consumer with a 10 years loan, will have to make 125 payments.
A. True
B. False
Answer:
False
Step-by-step explanation:
Assuming monthly payments
12 payments per year X 10 years = 120 payments
Andrew buys 8 bottles of cranberry juice at the corner store for a total cost of $5.68. If each bottle costs the same amount, how much is 6 bottles of juice?
Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 cup of white paint. Elena has 2/3 cup of white paint. How much purple paint can she make?
Elena can make 20/3 cups of purple paint
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
WE are given that Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 cup of white paint.
Since Elena has 2/3 cup of white paint. then;
1 1/2 cups of red paint (1 1/2=1.5)
1/2 cup of white paint (1/2=0.5)
Then the ratio is 3:1.5:0.5
Means every 0.5 cups of white paint Elena makes 5 cups of purple paint (3+1.5+0.5)
Let x the number of cups of purple paint
5/ 0.5 = x / (2/5)
x = 20/3 cups of purple paint
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Hong had 8/9
of a spool of yarn. He used 2/5
of his yarn for a project. What fraction of the spool was used for the project?
Answer: 16/45 of the spool
Step-by-step explanation:
2/5 of 8/9
2/5 * 8/9 = 16/45 (multiply numerators, and multiply denominators)
Cannot be further simplified.
Answer:
18/45
Step-by-step explanation:
Multiply both denominators to get a common denominator, in this case, it would be 45.
(8/9)*5=40/45
(2/5)*9=18/45
If n represents a power of 10, what is the value of n when 0.006 is rounded to the nearest power of 10?
Enter your answer in the box.
Answer:
The value of n is [tex]10^{-3}[/tex]
What is log function?
The logarithm (log) function is a mathematical function used to determine the logarithm of a number. The logarithm of a number is the exponent to which a particular base must be raised in order to produce that number. For example, the logarithm of 8 with base 2 is equal to 3 because 2 to the third power is 8. In mathematics, the logarithm of a number can be expressed as logbX, where b is the base and X is the number.
Step-by-step explanation:
We can write -
0.006 = 6 x 10^-3
10ⁿ = 6 x 10^-3
[tex]10^{n+3}[/tex] = 6
log([tex]10^{n+3}[/tex]) = log(6)
(n + 3) log 10 = log (6)
n +3 = log(6)/log(10)
n + 3 = 0.78
n = -3 + 0.78
n = -3 (approx.)
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please help!!!!!!!!!!!!!!!!!!
Answer:
1x2=2 3x3x1=3
Step-by-step explanation:
Find the measure of angle 2
a 50°
b 90°
c 140°
d 40°