Put the quadratic into vertex form and state the coordinates of the vertex. y= y= \,\,x^2+8x+41 x 2 +8x+41
Answers
The vertex form of the quadratic equation is y = (x + 4)² + 25, and the coordinates of the vertex are (-4, 25).
What is quadratic equation?A quadratic equation is a polynomial equation of degree 2, which means the highest power of the variable in the equation is 2.
Basic quadratic equation is : ax² + bx + c = 0
Quadratic equations can be solved using various methods, including factoring, completing the square, and using the quadratic formula.
The solutions of a quadratic equation are called roots, or zeros, of the quadratic function, which are the x-intercepts of the graph of the function.
To put the quadratic equation y = x² + 8x + 41 into vertex form, we need to complete the square by adding and subtracting a constant term. We can do this as follows:
y = x² + 8x + 41
y = (x² + 8x + 16) - 16 + 41 (add and subtract 16 inside the parentheses)
y = (x + 4)² + 25
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Related Questions
27. A factory worker has 5,500 puzzles to pack into cartons that each hold 785 puzzles. How many puzzles will be left over after the last box is full? A. 5 B.6 C.7 D.8
Answers
Answer:
C. 7
Step-by-step explanation:
5,500 divided by 785 = 7.006, which can be rounded to 7.
The number of puzzle will be left over after the last box is full is 5. Therefore, the correct answer is option A.
Given that, a factory worker has 5,500 puzzles to pack into cartons that each hold 785 puzzles.
The number of cartons required = 5500/785
The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Now,
785)5500(7
5495
__________
5
Here, the remainder is 5.
Therefore, the correct answer is option A.
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I need help please I can only find 2 of these solutions
Answers
Step 1: Isolate the Sin Operator
\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)
Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable
Note that since trig functions have 2 general solutions, this will give us one of our general solutions.
\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)
x₁= 0.48
Solving for x₂
Use the period identity for Sin Functions
\(sin(x)=sin(\pi -x)\)
X in this case is arcsin(0.25)
\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)
So our two general solutions are 0.48 and 5.52
Step 3: Period
Trig Functions have periodic behavior and this function period is
\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)
So our general solutions are
0.48±12k, where k is an integer
5.52±12k, where k is an integer
Let k=1, and we get our next set of solutions:
12.48 and 17.52
So our answer is 0.48,5.52,12.48,17.52
Use synthetic division to divide 2x^4 − 12x^3 + 18x^2 − 13x +20 ; x−4.
Answers
The result of the synthetic division of 2x^4 - 12x³ + 18x² - 13x + 20 by x - 4 is given by:
2x³ - 4x² + 2x - 5.
How does synthetic division works?In synthetic division, the coefficients of a polynomial are each divided by a value.This value is the zero of the divided polynomial, which goes into the far left box.For this problem, the polynomial is given by:
2x^4 - 12x³ + 18x² - 13x + 20.
Hence the coefficients are:
2, -12, 18, -13, 20.
The divisor is:
x - 4.
Hence the left coefficient is:
4.
From the image at the end of the answer, the resulting coefficients are given as follows:
2, -4, 2, -5, with a remainder of 0.
Hence the result is:
2x³ - 4x² + 2x - 5.
For the procedure, we consider that the coefficient 2, the first of the polynomial, is moved down, then multiplied with 4 and added with the next coefficient(-12), and this procedure happens until the last coefficient.
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The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 96
cm ^2 , what is the length of the diagonal?
Answers
Thee diagonal of the rectangle is 13.86 cm long.
What is the length of the diagonal of rectangle?We are given that;
Width of a rectangle is 9 less than twice its length. Thus, if length is L, then;
W = 2L - 9
Area formula for a rectangle is;
A = Length * Width
We are given area of rectangle = 96 cm²
Thus;
L(2L - 9) = 96
2L² - 9L = 96
2L² - 9L - 96 = 0
Using online quadratic equation calculator gives;
L = 9.53 cm
Thus;
W = 2(9.53) - 9
W = 19.06 - 9
W = 10.06 cm
The diagonal of the triangle will be gotten from Pythagoras theorem;
D = √(9.53² + 10.06²)
D = √192.0245
D = 13.86 cm
Thus, we conclude that the diagonal of the rectangle is 13.86 cm long.
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The following data give the distribution of the types of houses in a town containing 25,000 houses. Identify each category and its percentage on the circle graph. House Style Frequency Cape 6250 Garrison 10000 Split 8750
Answers
The categories and their Percentages on the circle graph would be as follows:
Cape: 25%
Garrison: 40%
Split: 35%
To represent the distribution of house types in a town containing 25,000 houses on a circle graph, we need to determine the percentage of each category.
The given data provides the following frequencies for each house style:
Cape: 6,250 houses
Garrison: 10,000 houses
Split: 8,750 houses
To calculate the percentage for each category, we divide the frequency of each house style by the total number of houses in the town (25,000) and multiply by 100.
Percentage for Cape: (6,250 / 25,000) * 100 = 25%
Percentage for Garrison: (10,000 / 25,000) * 100 = 40%
Percentage for Split: (8,750 / 25,000) * 100 = 35%
Therefore, the categories and their respective percentages on the circle graph would be as follows:
Cape: 25%
Garrison: 40%
Split: 35%
These percentages represent the proportion of each house style in the town and can be visually represented on a circle graph to provide a clear visualization of the distribution of house types.
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5. The Jones family orders four pizzas to eat. Each pizza is sliced into four parts. How many pizza slices do they get in total?
Answers
Answer:
16 slices
Step-by-step explanation:
Given :
Number of pizzas ordered = 4
Number of slices per pizza = 4
If 4 pizzas are each sliced into 4 parts ; the we have :
Pizza 1 = 4 slices
Pizza 2 = 4 slices
Pizza 3 = 4 slices
Pizza 4 = 4 slices
Total slices = (4 +4 +4 +4) = 16 slices
what’s the area of this triangle?
Answers
Answer:
hi there, the answer is
A=45 cm2
Step-by-step explanation:
A= 1/2 x 10 x 9
A=5 x 9
A=45 cm2
1. A target is divided into 100 squares colored in dark blue, white, and light blue. Amber throws a beanbag that lands on the target.
co
9 25
dark blue
What is the probability that it will land on a dark blue square?
26
white
light blue
Answers
The probability of landing on the dark blue target is 2/5.
Finding probabilityProbability is the ratio of required to the total possible outcomes of an event.
The required outcome = dark blue= 25Total possible outcomes= entire sample Space = 100P(dark blue ) = 40/100
divide through by 20
P(dark blue ) = 2/5
Therefore, the probability of landing on target is 2/5
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which is rights answer?
Answers:
A) 242.88 minutes
B) 4.08 minutes
C) 3.48 minutes
D) 3.97 minutes
Answers
The population of the average length in 2013 is (b) 4.08 minutes
How to predict the average length in 2013from the question, we have the following parameters that can be used in our computation:
The table of values
Using the least squares, we have the following summary
Sum of X = 9Sum of Y = 16.33Mean X = 1.5Mean Y = 2.7217Sum of squares (SSX) = 17.5Sum of products (SP) = 2.135The regression equation is
y = mx + b
Where
m = SP/SSX = 2.14/17.5 = 0.122
b = MY - bMX = 2.72 - (0.12*1.5) = 2.53867
So, we have
y = 0.12x + 2.54
In 2013, we have
y = 0.12 * 13 + 2.54
y = 4.1
Hence, the prediction is (b) 4.08 minutes
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The Wilson family spend $600 per month on groceries for their family.if this is 15% of their monthly budget, then what is their monthly budget?
Answers
Answer:
90
Step-by-step explanation:
SHOPPING-Three families recently ordered jeans from a catalogue. The Rodriguez family ordered twice as many jeans as the Gomez family, and the Jimenes family ordered 4 times as many
jeans as the Gomez family. Write an expression to show how many jeans the
families bought all together.
Answers
The answer would be 7x.
The numerical value of the volume of a sphere is equal to the numerical value of its surface area.
Find the exact value of the radius of this sphere.
Answers
Answer:
The radius of this sphere is \(3\).
Step-by-step explanation:
The volume of a sphere of radius \(r\) is:
\(\displaystyle V = \frac{4}{3}\, \pi\, r^{3}\).
The surface area of a sphere of radius \(r\) is:
\(A = \pi\, (2\, r)^{2}\).
Equate the right-hand side of these two expressions and solve for \(r\):
\(r = 3\).
In other words, the radius of this sphere is \(3\).
In two or more complete sentences, describe the transformation(s) that take place on the parent function f(x) = 3x to obtain the graph of f(x) = 3-x + 1 + 5.
Answers
There is a vertical stretch by a factor of 3. There is a reflection over the y axis. The graph moves left one unit and up by 5 units.
Hope this helps, and I provide an image in case it helps!
The adjacent sides of the parallelogram are (x + 3) and (x + 2). Find the perimeter of the parallelogram.
Answers
Answer:
P = 4x+10
Step-by-step explanation:
So a parallelogram has 2 set of sides which are parallel and equal. So if you're given two adjacent sides, that means you're given a side from each set of sides, which are equal. This means the perimeter is simply: 2(x+3) + 2(x+2). This can be further simplified by distributing the 2 which gives you the equation: 2x+6+2x+4, which further simplifies to 4x+10.
Solve the equation.
x(4x−11)=15
Answers
+11 +11
5x=26
/5 /5
x=5.2
hope this helps :)
A gear makes 50 revolutions each minute. It can be represented by the equation r-50t, where r is the total revolutions and t is the number of minutes. Which is the correct answer and explain.
Bennett says that it will take more than 7 minutes to make 300 revolutions
or
Betty says that 50 represents the constant of proportionality, k.
Answers
Answer: I believe Betty
Step-by-step explanation:
Betty because bennet says 300 divided by seven is 50 but is 42
Answer:
betty
Step-by-step explanation:
what is answer to this question please help
Answers
Answer:
5 > \(\sqrt{18\)
Step-by-step explanation:
The square root of 18 is approximately 4.24.
5 is greater than 4.24, so we can use the inequality sign >.
In how many ways can a store select 2 assistant managers out of 6 assistant managers to open and close the store?
Answers
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
6/2=3
Find the mean of the data set:
87,79,92,71,88,70,91,82,85
Round your answer to the nearest tenth.
Provide your answer below:
Answers
The mean of the data set is 82.77
How to calculate the mean of the data set?If we want to find the mean, we would have to put it at the back of our minds that the mean is the same as the average. As such, we would have to take the sum of all the values that have been listed in the data set and divide by the total number of the data.
The first step is to arrange the data set orderly from smallest to largest;
70, 71,79, 82,88,85,87,91,92
We have nine values in the data set thus the mean is;
70+71+79+82+88+85+87+91+92/9= 745/9= 82.77
Hence the mean of the data set is 82.77
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eddie has a steel rod that is 50 inches long. He uses a saw to cut off 2.75-inch pieces from the end of the rod. After cutting off a certain number of pieces, the steel rod is now 36.25 inches long. How many pieces did Eddie cut off the end of the steel rod?
a.) 4 pieces
b.) 5 pieces
c.) 7 pieces
Answers
Answer: B. 5 pieces
Step-by-step explanation:
36.25 + 2.75 = 39.00 + 2.75 = 41.75 + 2.75 = 44.50 + 2.75 = 47.25 + 2.75 = 50
what is the integer in the right side of -5
Answers
Step-by-step explanation:
-4 may be the corect answer
How many gallons each of 15% alcohol and 10% alcohol should be mixed to obtain 5 gal of 13% alcohol?
Answers
9514 1404 393
Answer:
3 gallons 15%2 gallons 10%Step-by-step explanation:
Let x represent the quantity of 15% alcohol required. Then (5-x) is the amount of 10% alcohol needed. The amount of alcohol in the mix is ...
0.15x +0.10(5-x) = 0.13(5)
0.05x +0.5 = 0.65 . . . . . . . simplify
0.05x = 0.15 . . . . . . . . . subtract 0.5
x = 3 . . . . . . . . . . . . . divide by 0.05
3 gallons of 15% alcohol and 2 gallons of 10% alcohol should be mixed.
6. Explain what must occur to the parent
function f(x) = x² to transform the
function to g(x) = (x-4)² +2.
Answers
Answer:
4 units right, 2 units up
Step-by-step explanation:
For \(g(x)=(x-4)^2+2\), the graph of \(f(x)=x^2\) would need to move 4 units to the right and 2 units up. Hence, the vertex would be \((4,2)\) if we compare the function g(x) with the form \(y=a(x-h)^2+k\).
during a single day at radio station WMZH,the probability that a particular song is played in 3/8.what is the probability that this thing will be played on exactly 2 days out of 3 days ?round to your nearest thousandth
Answers
The probability that the song will be played on exactly 2 days out of 5 days is approximately 0.164.
To find the probability that a particular song is played exactly 2 days out of 5 days at radio station WMZH, we can use the binomial probability formula.
The binomial probability formula is given by P(x) = C(n, x) * p^x * (1-p)^(n-x), where P(x) is the probability of x successful outcomes, n is the number of trials, p is the probability of a successful outcome on a single trial, and C(n, x) represents the binomial coefficient, which is the number of ways to choose x items from a set of n items.
In this case, we want to find the probability of the song being played exactly 2 days out of 5 days, so x = 2, n = 5, and p = 3/8.
Using the formula, we have:
P(2) = \(C(5, 2) * (3/8)^2 * (1 - 3/8)^(^5^-^2^)\)
C(5, 2) = 5! / (2! * (5-2)!) = 10
P(2) = 10 * (3/8)^2 * (5/8)^3
P(2) ≈ 0.164 (rounded to three decimal places)
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A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=-14x^2+1035x-10266
Answers
The price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit is 62.13
Quadratic equationy = -14x² + 1035x - 10266
solve the quadratic equation-14x² + 1035x - 10266 = 0
x = -b ± √b² - 4ac / 2a
= -1035 ± √1035² -4(-14)(-10266) / 2(-14)
= -1035 ± √1071225 - 574896 / -28
= -1035 ± √496329 / -28
x = 1035 / 28 ± √496329 / 28
x = 11.80 or 62.13
The maximum value of x is 62.13
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Suppose a company has fixed costs of $350 and variable cost of (0.49x + 1160) dollars per item.Suppose the selling price is (-0.51x+1340) dollars per unit.Find the cost function. C(x) =Find the revenue function. R(x) =Find the profit function. P(x) =
Answers
We have a fixed cost of $350 and a unit variable cost of 0.49x+1160.
We then can express the cost function as the sum of the fixed cost and variable cost:
\(\begin{gathered} C(x)=FC+VC \\ C(x)=350+(0.49x+1160)x \\ C(x)=350+0.49x^2+1160x \\ C(x)=0.49x^2+1160x+350 \end{gathered}\)The revenue function R(x) can be expressed as the selling price, -0.51x+1340, times the quantity, x:
\(\begin{gathered} R(x)=P(x)\cdot x \\ R(x)=(-0.51x+1340)x \\ R(x)=-0.51x^2+1340x \end{gathered}\)The profit function P(x) can be expressed as the revenue R(x) minus the cost C(x):
\(\begin{gathered} P(x)=R(x)-C(x) \\ P(x)=(-0.51x^2+1340x)-(0.49x^2+1160x+350) \\ P(x)=-0.51x^2+1340x-0.49x^2-1160x-350 \\ P(x)=(-0.51-0.49)x^2+(1340-1160)x-350 \\ P(x)=-x^2+180x-350 \end{gathered}\)Answer:
C(x) = 0.49x² + 1160x +350
R(x) = -0.51x² + 1340x
P(x) = -x² + 180x - 350
how to solve for reflection under transformation
Answers
Similarly, when a point is reflected across the line y = -x, the x-coordinates and y-coordinates change their place and are negated. Therefore, The reflection of the point (x, y) across the line y = x is (y, x). The reflection of the point (x, y) across the line y = – x is (-y, -x).
Hope this helps!
Match the correct word with it's definition
Answers
Answer:
Rule by a small group : Oligarchy
Rule by Citizens : Democracy
Rule by No one Anarchy
Rule by king or Queen : Monarchy
Consider the following equation:
cos x = x^3
Use your calculator to find an interval of length 0.01 that contains a root. (Enter your answer using interval notation.)
Answers
If the equation is cos x = x^3, the interval of length 0.01 that contains a root is [0.86, 0.87]
The given equation is
cos x = x^3
Move the term x^3 to the left hand side of the equation
cos x - x^3 = 0
Therefore the equation will be
f(x) = cos x - x^3
Here to find the interval of length 0.01 that contains a root, we have to use the intermediate value theorem
Plot the function in the graph
From the graph, we can see that the value of
x = 0.865
The interval of length = 0.01
Then the intervals will be 0.86 and 0.87
Therefore, the interval of length 0.01 that contains a root will be [0.86, 0.87]
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Quadrilateral ABCD has vertices A(–1, –2), B(–1, 3), C(4, 3) and D(4, –2). It’s dilated by a factor of 2 with the center of dilation at the origin. What are the coordinates of the resulting quadrilateral A’B’C’D
Answers
9514 1404 393
Answer:
A'(-2, -4)B'(-2, 6)C'(8, 6)D'(8, -4)Step-by-step explanation:
Dilation about the origin multiplies each coordinate value by the dilation factor.
A' = 2A = 2(-1, -2) = (-2, -4)
B' = 2B = 2(-1, 3) = (-2, 6)
C' = 2C = 2(4, 3) = (8, 6)
D' = 2D = 2(4, -2) = (8, -4)