The standard form of the equation of the quadratic function is y = -1/8x^2 + 1/4x - 41/8
How to find the standard form of the equation of the quadratic functionFrom the question, we have the following parameters that can be used in our computation:
(h, k) = (1, -5)
(x, y) = (5, -7)
A quadratic function is represented as
y = a(x - h)^2 + k
So, we have
y = a(x - 1)^2 - 5
Given that
(x, y) = (5, -7)
We have
-7 = a(5 - 1)^2 - 5
This gives
16a = -2
So, we have
a = -1/8
Recall that
y = a(x - 1)^2 - 5
So, we have
y = -1/8(x - 1)^2 - 5
Expand
y = -1/8(x^2 - 2x + 1) - 5
This gives
y = -1/8x^2 + 1/4x - 41/8
So, the required equation is y = -1/8x^2 + 1/4x - 41/8
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1.9 unit conversions
Change 24 in./s to ft/min.
After unit conversion of 24 in./s into ft/min the value will be 120
What are Units ?To measure and compare various things we use one term which is known as a unit. When all of the measuring units are the same, comparison is simple. Depending on their intended usage, different units can be categorized.
For example, for length measurement we use units like:- meter, centimeter, inch, miles.
Given that,
A rate = 24 in./s
The value of rate in ft./min. = ?
It is known that,
1 feet = 12 inches
And 1 minute = 60 second
So,
1 inches = 1/12 feet
1 second = 1/60 minute
⇒ 24 in./s
⇒ 24 ((1/12)ft / (1/60)sec)
⇒ 24 × 60/12
⇒ 24 x 5
⇒ 120
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a researcher records the change in weight (gain or lost) during the first semester of college for each individual in a sample of 25 freshmen, and calculates the average change in weight. this average is an example of a . group of answer choices
The average change in weight calculated by the researcher for the sample of 25 freshmen is an example of a statistic.
A statistic is a numerical summary of a sample that is used to make inferences about a population. In this case, the sample is the 25 freshmen, and the population could be all freshmen entering college.
The average change in weight is a statistic because it summarizes the data collected from the sample, and is used to make conclusions about the population.
It represents the typical or average amount of weight gained or lost by the freshmen in the sample during their first semester in college.
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a steel plate contains 20 bolts. assume that five bolts are not torqued to the proper limit. four bolts are selected at random, without replacement, to be checked for torque. (a) what is the probability that all four of the selected bolts are torqued to the proper limit?
The probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.
To calculate the probability that all four of the selected bolts are torqued to the proper limit, we need to find the number of combinations of 4 bolts out of 20 that have been torqued to the proper limit.
Let's call the number of proper bolts n = 20 - 5 = 15.
The number of combinations of 4 proper bolts out of 15 is given by the binomial coefficient nCk, where n is the number of bolts and k is the number of bolts selected.
nCk = n! / (k! (n - k)!).
So, the number of combinations of 4 proper bolts out of 15 is:
15C4 = 15! / (4! (15 - 4)!) = 15! / (4! 11!) = 1365.
Therefore, the probability of selecting all 4 proper bolts out of 20 is:
P = number of combinations of 4 proper bolts / number of combinations of 4 bolts = 1365 / 20C4 = 1365 / 4845 = 0.28
So, the probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.
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QUESTION FOR FOR LIH04
v=1/3(3.14) times 64 times 18
please this is so urgent
Select the correct answer.
What is the domain of the exponential function shown in the graph?
Answer: Choice D
Explanation:
The notation [tex]-\infty < \text{x} < \infty[/tex] says x is anything between negative infinity and positive infinity. Basically x is any real number. This is because the curve stretches forever to the left and right. Any number can be the x input.
When I add a number to another number four times as big the results is 30, find the first number
By using a system of equations of two variables we concluded that the first number was 6
Let the numbers be x and y and their sum gives z
The equation for the sum of 2 numbers:
x + y = z -(1)
We know, z = 30 and y = 4 times x = 4x
Putting values of y and z in equation (1), we get
x + 4x = 30
Solving for x, we get
5x = 30
x = 30/5 = 6
To get the value of y, put the value of x in y = 4x and we get
y = 4 x 6 = 24
So the real equation was
6 + 24 = 30
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Determine the intercepts of the line. Do not round your answers. y+1=3(x − 4) x-intercept: (_,_) y-intercept: (_,_)
The intercepts of the line are x intercept: (4.3,0) y-intercept: (0,-13)
How to determine the intercepts of the lineFrom the question, we have the following parameters that can be used in our computation:
y+1=3(x − 4)
To calculate the x-intercept, we set y to 0
So, we have the following representation
0+1=3(x − 4)
This gives
x - 4 = 1/3
So, we have
x = 4.33
To calculate the y-intercept, we set x to 0
So, we have the following representation
y + 1 = 3(0 − 4)
This gives
y + 1 = -12
So, we have
y = -13
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The function,y=−16x2+32x+48, represents the height, in feet, of a firework x seconds after it is launched.
After how many seconds does the firework hit the ground?
Enter your answer in the blank.
x=□seconds
The number of seconds does the firework hit the ground is 3 seconds
How to determine the valueFrom the information given, we have the quadratic function;
y = -16x² + 32x + 48
To determine the value of x , let's reduce the expression, we get;
-2x² + 4x + 6
Now, let's factorize the terms
Multiply the coefficient by the constant and find the pair factors
-2x² + 6x - 2x + 6
Factorize in pairs, we get;
-2x(x -3) - 2(x -3)
Then, we have the expressions
-2x - 2 = 0
solve for x
x = -1
x - 3 = 0
x = 3
Hence, the value is 3 seconds
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Answer:
3
Step-by-step explanation:
i took the test
PLEASE HELP DUE TOMORROW:
Ok, so I know the answer is 9 but I'm not sure how to actually get that answer, and this assignment requires me to show work.
The mean of x, y, and z is 55. If x+y=107 then what does z equal?
Answer:
The value of z is 58
Step-by-step explanation:
The mean is the average of a set of numbers. Mean = (sum of the numbers)/(the number of numbers).
We are told that the mean of x+y+z is = 55.
We can wriote this as:
55 = (x+y+z)/3
We learn that x+y = 107. So lets enter that number for x + y:
55 = (x+y+z)/3
55 = ((x+y)+z)/3
55 = ((107)+z)/3 [Substitution]
55 = (107+z)/3
165 = 107+z [Multiply both sides by 3]
z = 58 [Simplify]
CHECK:
Is the mean of x, y, and z 55?
55 = (x+y+z)/3 ?
55 = ((107)+z)/3 ? [Since we know x+y = 107]
55 = ((107)+58)/3 ? [Since z=58]
55 = (165)/3) ?
55 = 55 YES The value of z is 58
The percentage B(t) of women ages 25 and older in the United States who hold a bachelor's degree or higher t years after 1990 can be approximated by
B(t) = 0.48t + 18.
Using an inequality, determine those years for which more than 40% of women ages 25 and older in the United States will hold a bachelor's degree or higher.
Please help!!
Answer:
he inequality to determine the years in which more than 40% of women ages 25 and older in the United States will hold a bachelor's degree or higher is:
0.48t + 18 > 40
Subtracting 18 from both sides:
0.48t > 22
Dividing both sides by 0.48:
t > 45.83
So, for years t greater than 45.83, more than 40% of women ages 25 and older in the United States will hold a bachelor's degree or higher.
Step-by-step explanation:
Can you please answer the question???
The volume of given triangular prism is 24,000 cubic yards.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Here, the dimensions of base are 30 yards and 20 yards.
Here, area = 1/2×30×20
= 300 yd²
Volume of a triangular prism = Area of base triangle × Length of the prism.
= 300×80
= 24,000 yd³
Therefore, the volume is 24,000 yd³.
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Find the lengths of the diagonals of rectangle WXYZ.
WY = 24x-8
XZ = -18x+13
The length of each diagonal is ___ units.
In rectangle WXYZ, the length of each diagonal are 40.97 units and 39.98 units.
To find the lengths of the diagonals of rectangle WXYZ, we can use the Pythagorean theorem.
The diagonal WX is the hypotenuse of right triangle WXY, so we have:
WX^2 = WY^2 + XY^2
Similarly, the diagonal YZ is the hypotenuse of right triangle XYZ, so we have:
YZ^2 = XY^2 + XZ^2
Substituting the given values for WY and XZ, and x = 2, we get:
WY = 24(2) - 8 = 40
XZ = -18(2) + 13 = -23
Plugging these values into the equations above and simplifying, we get:
WX^2 = 40^2 + XY^2
YZ^2 = XY^2 + (-23)^2
Since XY is a common side of both triangles, we can solve for it by setting the two expressions for XY^2 equal to each other:
40^2 + XY^2 = XY^2 + (-23)^2
Simplifying, we get:
40^2 + 23^2 = 2XY^2
XY^2 = (40^2 + 23^2) / 2 = 1039
Substituting this value for XY^2 in the equations for WX^2 and YZ^2, we get:
WX^2 = 40^2 + 1039 = 1679
YZ^2 = 1039 + (-23)^2 = 1598
Taking the square roots, we get:
WX = sqrt(1679) ≈ 40.97
YZ = sqrt(1598) ≈ 39.98
Therefore, the length of each diagonal of Rectangle are approximately 40.97 units and 39.98 units.
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_____The given question is incomplete, the complete question is given below:
Find the lengths of the diagonals of rectangle WXYZ.
WY = 24x-8
XZ = -18x+13
x= 2
The length of each diagonal is ___ units.
subsitute (-3,3) 2y+x=3 y=x+0
Answer:
Point (-3, 3) is not a solution to the system of equations
2y+x=3
y=x+0
Step-by-step explanation:
2y + x = 3
y = x + 0
2(3) + (-3) = 3
6 - 3 = 3
3 = 3
The point works in the first equation.
3 = -3 + 0
3 = -3
The point does not work in the second equation.
jack's favorite number is 836. jill subtracts a secret number from 836 and her answer is the smallest possible combination of all the digits from jack's favorite number. what is the secret number?
The secret number is 564 as we solve it by given question.
jack's favorite number is 836 so here we have number 836 and
jill subtracts a secret number from 836 and her answer is the smallest possible combination of all the digits from jack's favorite number
so here we have a number 836
let we subtract x from 836 to get a number which is smallest number by using 836
the number which we can make by using these 3 degits are
368, 386, 638, 683, 836, 863 anf from all these numbers the smallest number which can be using 836 is 368
as given in question we have 836 and we will subtract x and get 368 so
836 - x = 368
x = 836 - 368
x = 564
the secrets number is 564.
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What is the greatest common factor : 21, 35, 56
Answer:
7
Step-by-step explanation:
Find the value of "x" and "y". State which angle pair theorem (s) you need.
(4)*
3x
y
(5x – 64)°
X =
4 =
theorem:
4.
about 45 of every 300 apples picked at the newbury apple orchard are rotten, if 3560 apples were picked one week, about how many apples were rotten?
about 45 of every 300 apples picked at the Newbury apple orchard are rotten, if 3560 apples were picked one week, about 534 many apples were rotten. We drew this answer with the help of algebra,
45/300 = x/3560
x = 3560*(45/300) = 534
At the same rate, about 534 rotten apples can be expected in the week's pickings.
Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions. In algebra, we use numbers like 2, −7, 0.068 etc., which have a definite or fixed value. In algebra we use variables like x, y, and z along with numbers.
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8.70% of is 14?
O 10
O 20
O 30
O 50
A 6
6
-foot ribbon is cut into 4
4
equal pieces.
Which equation shows how to find the length of each piece?
The equation shows how to find the length of each piece is L = R / N and the length of each piece is 1.5 feet.
To find the length of each piece, we can use the following equation:
Length of each piece = Total length of the ribbon / Number of pieces
In mathematical terms, we can represent this equation as:
L = R / N
Where,
L is the length of each piece
R is the total length of the ribbon (66 feet in this case)
N is the number of pieces (44 in this case)
In this problem, we are given a 66-foot ribbon and we are asked to cut it into 44 equal pieces. We need to find out the length of each piece.
Using this equation, we can easily find the length of each piece:
L = 66 / 44
L = 1.5 feet
Therefore, each piece of the ribbon is 1.5 feet long.
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Jane has 4.8 pints of juice.
Tim has 7.4 pints of juice.
About how many pints of juice do they
have in all?
Answer:
12.2 pints
Step-by-step explanation:
In all means add. Add the two decimals together.
4.8 + 7.4
12.2 pints
Starting with the number 10, build a sequence of 5 numbers.
Answer:
Step-by-step explanation:
To build a sequence, you have to create a rule. For example, if the rule is +2, then you add 2 to 10 to get 12, and then you add 2 to 12 to get 14, and so on. Your sequence would then be 10, 12, 14, 16, 18.
Huw investigates the opinion of the public about their local primary schools. He visits his town centre and administers a questionnaire to 120 people over the course of several days.
What type of sampling is this?
The type of sampling that Huw is using is called Convenience Sampling.
Explanation:
Convenience sampling is a non-probability sampling technique where the sample is selected based on ease of access and availability. In Huw's case, he is administering the questionnaire to people who happen to be in the town centre, which is convenient for him. The sample is not selected randomly, and therefore does not accurately represent the population as a whole. Convenience sampling is often used in quick, informal surveys where the researcher does not have the resources or time to conduct a more rigorous, randomized sampling method.
what is the period of the function f(x) shown in the graph?
Answer:
8π
Step-by-step explanation:
The period of a function f(x) is the x-distance between two repeating points of the function
Looking at the function graph given we see that the function reaches a peak value(called amplitude) at x = -6π and then again reaches this value at x = 2π
So the x-distance is 2π - (-6π) = 2π + 6π = 8π
From 2π, the function reaches its maximum value again at 10π giving the period once again as 10π - 2π = 8π
Sophia is trying to pick out an outfit for the first day of school. She can choose from 2 pairs of pants, 2 t-shirts, and 4 pairs of shoes. How many different outfits does Sophia have to choose from?
The number of many different outfits Sophia has to choose from should be 16.
What is arithmetic?
Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction.
Here, we have
Given: Sophia is trying to pick out an outfit for the first day of school. She can choose from 2 pairs of pants, 2 t-shirts, and 4 pairs of shoes.
She can choose from 2 pairs of pants, 2 t-shirts, and 4 pairs of shoes.
So here the number of distinct outfits should be like
= 2 × 4 × 2
= 16
Hence, the number of many different outfits Sophia has to choose from should be 16.
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Answer:16
Step-by-step explanation:Total outcomes
=
Total outcomes=
2‾
pants
×
2‾
t-shirts
×
4‾
shoes
pants
2
×
t-shirts
2
×
shoes
4
Fundamental counting principle
=
=
16
y = -2x + 1
4x + 2y = -1
(0, -3)
(-3,0)
No solution
Infinitely many solutions
The given equations having infinitely many solutions.
What is Solutions of system of equation?
A solution to a system of equations is a collection of variable values that satisfy all of the equations at the same time. To solve a system of equations, one must determine all of the sets of variable values that compose the system's solutions.
The solution to the system of equations y = -2x + 1 and 4x + 2y = -1 can be determined graphically by plotting both equations on the same set of axes and finding the points of intersection.
If there is exactly one point of intersection, then that point represents the unique solution to the system. If there are no points of intersection, then the system has no solution. If there are infinitely many points of intersection, then the system has infinitely many solutions.
Based on the information you provided, the system has two points of intersection: (0, -3) and (-3, 0). This means that the system has two solutions, and the solution set is the set of all points on the line that passes through these two points.
Therefore, The given equations having infinitely many solutions.
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Transcribed image text: Question 4 A certain automotive dealer sells only cars and trucks, and the ratio of cars to trucks on the lotis 11 to 33. If there are currently 51 trucks for sale, how many cars does the dealer have for sale! 34 68 136 272 thierronse
If the ratio of cars to trucks on the lot is 11 to 33 and there are currently 51 trucks for sale, then there are 17 cars for sale
The ratio of cars to truck on the lot = 11 : 33
Total number of trucks for sale = 51 truck
Consider the number of cars for sale = x
Then the ratios will be
11/33 = x / 51
Cross multiply the terms in the equation
33x = 51 × 11
33x = 561
Move 33 to the right hand side of the equation
x = 561 / 33
Divide the terms
x = 17
Therefore, the number of cars does the dealer have for sale is 17
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please help me i dont understand
Answer:
x=15°
∡Q= 75°
Step-by-step explanation:
supplementary angles means the sum of the angles =180°
so, 5x+105°=180°
5x=75°
x=15°
∡Q= 75°
Transformation Question
Translate point (5, -6) based on vector V.
V:(-2,10)
The updated positions are (5, -6) + (-2, 10) = (3, 4)
Describe vector.A vector is a mathematical concept that has both magnitude and direction. The vector's size is determined by size. An arrow-depicted line serves as this representation. The vector's magnitude is represented by the line's length, and its direction is shown by the arrow. additionally referred to as geometric, Euclidean, spatial, or just "vectors."
You can add the components of the vector to the corresponding components of the point to translate point (5, -6) based on vector V:(-2,10).
The updated positions are (5, -6) + (-2, 10) = (3, 4)
Thus, the translated message is (3, 4).
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