If using the method of completing the square to solve the quadratic equation
x²+ 15x – 23 = 0, which number would have to be added to "complete the
square?
Answers
The number that we added to complete the square is (15/2)² = 225/4.
Define quadratic equationA quadratic equation is a polynomial equation of degree 2, which means that the highest power of the variable is 2. The general form of a quadratic equation is:
ax² + bx + c = 0
x²– 15x – 23 = 0
x² + 15x + (15/2)² - (15/2)² - 23 = 0
(x + 15/2)² - (23 + 225/4) = 0
(x + 15/2)² - 394/4 = 0
Now we can simplify the equation:
(x + 15/2)² = 394/4
(x + 15/2)² = 98.5
Finally, we can take the square root of both sides and solve for x:
x + 15/2 = ±√(98.5)
x = -15/2 ± √(98.5)
Therefore, the number that we added to complete the square is (15/2)² = 225/4.
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Related Questions
Will mark brainliest!! please give me the right answer
Answers
Answer:
2 1/4 or 9/4
Step-by-step explanation:
Because if you add up all the fractions and simplify them they equal 5/4 and if u add the 1 gallon to it it equals 1 5/4 but thats not it 5/4 also makes up a whole gallon its self with 1/4 left over
A 16-inch board is to be cut into three pieces so that the second piece is twice as long as the first plece and the third piece is 5 times as long as the first piece. If x
represents the length of the first piece, find the lengths of all three pieces.
What is the length of the first piece?
Answers
if the pieces are longer than each other then
x=5x+2x will be equal 7x
When a new charter school opened in 1995, there were 370 students enrolled. Write a formula for the equation N, representing the number of students attending this charter school t years after 1995, assuming that the student population:
Answers
ANSWER:
\(\begin{gathered} N=370+40t \\ \\ N=370-32t \\ \\ N=370+22t \\ \\ N=370-12t \\ \\ N=370 \\ \\ N=370+20t \end{gathered}\)STEP-BY-STEP EXPLANATION:
Given: Initial number = 370 students.
We can determine in each case taking into account that it would be a rate (that is, a slope) that is added to the equation.
Therefore:
Increased by 40 students per year:
\(N=370+40t\)Decreased by 40 students per year:
\(N=370-32t\)Increased by 44 students every 2 years:
\(\begin{gathered} N=370+\frac{44t}{2} \\ N=370+22t \end{gathered}\)Decreased by 48 students every 4 years:
\(\begin{gathered} N=370-\frac{48t}{4} \\ N=370-12t \end{gathered}\)Remained constant:
\(N=370\)Increased by 10 students every semester:
\(\begin{gathered} N=370+2\cdot10t \\ N=370+20t \end{gathered}\)I need help now!!!!!!
Answers
Answer:
6 weeks = 42 days
Step-by-step explanation:
6 weeks = 42 days Formula: multiply the value in weeks by the conversion factor '7'. So, 6 weeks = 6 × 7 = 42 days.
Toni & Warren are collecting foods for their
school's canned food drive. Toni started with 400
cans and collected 13 more each day. Warren
started with 40 cans and collected 22 more each
day. How long before Toni & Warren have the
same number of cans for their food drive?
Answers
Answer:
40 days
Step-by-step explanation:
Let d be the number of days.
\(400 + 13d = 40 + 22d\)
\(360 = 9d\)
\(d = 40\)
help please can you give me the answer and working out
Answers
The interquartile range is Q1 from Q3.
The lower quartile 25% and the upper quartile is 75%.
To find the quartile boundaries, we need to count the total number of observations in the dataset (which, in this case, is 44). Then, we multiply the desired percentage (25% for Q1 and 75% for Q3) by the total number of observations to get the number of observations that should be below the corresponding boundary.
To find Q1, we would calculate 0.25 x 44 = 11. We then locate the interval that contains the 11th observation and use the upper endpoint of that interval as the estimate of Q1. We repeat this process for Q3, using 0.75 x 44 = 33 as the number of observations that should be below the corresponding boundary.
Once we have estimated Q1 and Q3, we can then estimate the interquartile range by subtracting Q1 from Q3. This tells us how far apart the middle 50% of the data is, and gives us an idea of the variability of the dataset.
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as you consider the various factors involved in starting a group, what is the most important factor you have to judge?
Answers
As you consider the various factors involved in starting a group, the most important factor you have to judge is the group's purpose or goal.
Step 1: Identify the group's purpose or goal - This is crucial because it will guide all other decisions, including membership criteria, communication methods, and meeting schedules.
Step 2: Assess the needs and resources of potential members - This will help you understand their motivations and ensure the group can support their needs while accomplishing its goal.
Step 3: Establish clear membership criteria and expectations - This will ensure that everyone in the group is on the same page and committed to the same goals.
Step 4: Choose an appropriate communication method - This will facilitate smooth and efficient communication among group members.
Step 5: Develop a meeting schedule that works for all members - Regular meetings help keep the group on track and provide opportunities for collaboration and feedback.
By focusing on the group's purpose or goal, you can create a solid foundation for a successful and productive group.
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The box-and-whisker plot below represents some data set. What percenta data values are less than 66?
Answers
Given:
The a box-and-whisker plot if a data set.
To find:
The percentage of data values that are less than 66.
Solution:
From the given box-and-whisker plot, it is clear that the number 66 is the highest value of the data set.
It means all the values of the data set are less than 66 and no value can be more than 66.
All value means 100%.
Therefore, 100% of data values are less than 66.
Lara surveyed all of the 11th grade students at her school about the number of languages they speak and whether or not they have allergies. Here are her results:
Answers
Answer:
57.6% have allergies
42.4% have no allergies
Step-by-step explanation:
We only need to consider the students who speak two languages according to the question.
To find the percent with allergies, divide the number of students with allergies by the total number of students (that speak two languages).
19/33 = 0.5757 = 57.6%
To find the percent without allergies, divide the number of students without allergies by the total number of students (that speak two languages).
14/33 = 0.4242 = 42.4%
Check your work by adding the percentages to make sure they equal 100%
57.6 + 42.4 = 100
how to find the surface area
Answers
Answer:
364m^2
Step-by-step explanation:
Surface area is calculated by adding the area of each face.
Because this is a cubiod, there are 6 sides in pairs of identical area.
4m × 5m = 20m^2
4m × 18m = 72m^2
5m × 18m = 90m^2
90m^2 +72m^2 +20m^2 = 182m^2
This is 3 faces of the 6, so double it.
182m^2 ×2 = 364m^2
4. Show that the matrix [XX-X'Z(ZZ)-¹Z'X). where both the x & matrix X and the x matrix Z. have full column rank and m2, is positive definite. Discuss the implications of this result in econometrics.
Answers
To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.
Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:
A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'. The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric. Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v
Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.
When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.
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əz 22. Suppose z= z(x, y) is implicitly determined by ln(x+y+z) = x+2y+3z. Then dy (z.y.a)=(-1,5,-3)
Answers
the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).
n the given problem, we have an implicit equation ln(x+y+z) = x+2y+3z that defines z as a function of x and y. We are given the values dy = (-1, 5, -3).
To find the derivative dy/dx, we can use the total derivative formula and apply it to the implicit equation. The total derivative is given by dy/dx = - (∂F/∂x)/(∂F/∂y), where F = ln(x+y+z) - x - 2y - 3z.
Differentiating F partially with respect to x and y, we have (∂F/∂x) = 1/(x+y+z) - 1 and (∂F/∂y) = 1/(x+y+z) - 2.
Plugging in the given values of dy = (-1, 5, -3), we can calculate dy/dx = - (∂F/∂x)/(∂F/∂y) = -(-1)/(5-2) = 1/3.
Therefore, the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).
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Farmer Ed has 3,000 meters of fencing. and wants to enclose a reclangular plot that borders on a river. If Famer Ed does nat fence the side along the river, What is the largest area that can be enclos
Answers
Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.
What is the largest area that can be enclosed?To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.
Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.
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is the sqare of an odd number is always odd ?
Answers
Example : 3 square, 9 square , 5 square … etc
Step-by-step explanation:
Yes, the sqare of an odd number is always odd and apposite to that is, the sqare of an even number is always even.
for eg:-
even odd
2²=2x2=4 3²=3×3=9
4²=4×4=16 5²= 5×5=25
hope this helps you
have a nice day :)
true or false and why, if false explain, what is true.
Answers
Answer:
TRUE
Step-by-step explanation:
<8 and <3 are consecutive interior angles, and their sum is 180 degrees.
Thus, by Theorem, lines a and b are parallel.
The decimal 0.3 repeating represents 1/3. What type of number best describes 0.9 repeating, which is 3 times 0.3 repeating?
Answers
Answer:
4•5/5
Step-by-step explanation:
here 4.5 is numerator
and5 is denominator so
we divide4.5 by5
what is 3053 divided by 49
Answers
Answer:
62.30
Step-by-step explanation:
62.30
you divide the 3053 by 49
6 points
A car can travel 32 mi for each gallon of gasoline. The function d(x) = 32x
represents the distance d(x). in miles, that the car can travel with x gallons
of gasoline. The car's fuel tank holds 17 gal. How many miles can the car
travel?
Answers
Explanation
D(x)=32x and x would represent the amount of gallons the car has
D(x)=(32)(17)
544 miles
A sociologist polled a random sample of people and asked them their age and annual income. The two-way frequency table below shows the results. Annual income vs. age group Less than $50,000 At least $50,000 Total Ages 44 and under 148 68 216 Ages 45 and above 38 94 132 Total 186 162 348 Which of the following statements is true of those polled? Choose 1 answer: А A person with an annual income of less than $50,000 is more likely to be 45 years old or above. B A person in the 44 and under age group is more likely to to have an annual income of at least $50,000
Answers
Answer:
C A person with an annual income of at least \$50{,}000$50,000dollar sign, 50, comma, 000 is more likely to be 454545 years old or above
A person in the 44 and under age group is more likely to have an annual income of at least $50,000 is a correct statement.
We have given that,
A sociologist polled a random sample of people and asked them their age and annual income.
What is the annual income?
annual income is the amount of money you receive during the year into your bank account, before any deductions.
The two-way frequency table below shows the results.
Annual income vs. age group Less than $50,000 At least $50,000
Total Ages 44 and under 148 68 216 Ages 45 and above 38 94 132
Total 186 162 348
A person with an annual income of at least
\(=\$50000\\=$50,000dollar\)
Therefore statement b is true.
A person in the 44 and under age group is more likely to have an annual income of at least $50,000.
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Please help! will give brainliest!!
Answers
Answer:
c
Step-by-step explanation:
tHE ANSWER IS C
(a) Write 7.12% as a decimal.
(b) Write 0.019 as a percentage.
PLS HELP ME PLSS
Answers
Answer:
7.12 percent is .0712
and for .019 it's 1.9 percent
What is the process for doing the method of elimination for math systems?
Answers
Answer:
Elimination is the adding or subtracting of two equations used to solve them.
Step-by-step explanation:
Elimination is the adding or subtracting of two equations used to solve them.
Say you have this equation. \(\left \{ {{x + y=2} \atop {-x+y=6}} \right.\)
Notice that the x in both equations are opposites. After adding together we get.
x + y - x + y = 2 + 6
2y = 8
y = 4
x + 4 = 2
x = - 2
(- 2,4)
Say you decide to subtract the equations.
\(\left \{ {{x+y=2} \atop {x+2y=8}} \right.\)
x + y - x - 2y = 2 - 8
- y = - 6
y = 6
x + 6 = 2
x = - 4
(- 4, 6)
You can also multiply equations to make it easier to substitute.
\(\left \{ {{y+x=4} \atop {-2y+2x=8}} \right.\)
\(\left \{ {{2y+2x=8} \atop {-2y+2x=8}} \right.\)
2y + 2x - 2y + 2x = 8 + 8
4x = 16
x = 4
y + 4 = 4
y = 0
(4, 0)
the base of a triangle is shrinking at a rate of 3 cm/min and the height of the triangle is increasing at a rate of 9 cm/min. find the rate (in cm2/min) at which the area of the triangle changes when the height is 16 cm and the base is 12 cm.
Answers
The rate-of-change of area of triangle is changing when height is 16 cm and base is 12 cm is 30 cm²/min.
We know that the area of a triangle is given by the formula
⇒ A = (1/2)×b×h, where b = length of base and h = height,
We are given that the base is shrinking at a rate of 3 cm/min,
So, we have db/dt = -3 cm/min.
We are also given that the height is increasing at a rate of 9 cm/min,
So, we have dh/dt = 9 cm/min.
We need to find the rate at which the area of the triangle is changing with respect to time (dA/dt), when h = 16 cm and b = 12 cm.
⇒ dA/dt = (1/2)(db/dt)(h) + (1/2)(b)(dh/dt)
Substituting the values,
We get,
⇒ dA/dt = (1/2)×(-3)×(16) + (1/2)×(12)×(9),
⇒ dA/dt = -24 + 54,
⇒ dA/dt = 30 cm²/min
Therefore, the rate at which the area of the triangle is 30 cm²/min.
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please help 4x + 8 + 7x + 3
Answers
Answer:
11x + 11
Step-by-step explanation:
11x
11
=11x + 11
Answer:
11x + 1 1
Step-by-step explanation:
Simplify
Combine like terms
Answer and get Brainliest <3
Answers
Answer:
width = 9/2 inches, length = 18 inches
Step-by-step explanation:
Step-by-step explanation:
l = length
w = width
l×w = 81 in²
l = 2w + 9
we can use the identity of the second equation in the first equation :
(2w + 9)×w = 81
2w² + 9w = 81
2w² + 9w - 81 = 0
the general solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = w
a = 2
b = 9
c = -81
w = (-9 ± sqrt(9² - 4×2×-81))/(2×2) =
= (-9 ± sqrt(81 + 648))/4 =
= (-9 ± sqrt(729))/4 = (-9 ± 27)/4
w1 = (-9 + 27)/4 = 18/4 = 9/2 in
w2 = (-9 - 27)/4 = -36/4 = -9
a negative solution for a side length does not make any sense, so, width = 9/2 in is the only valid solution.
l = 2w + 9 = 2×9/2 + 9 = 9+9 = 18 in
so, the last answer option is correct.
A fair coin is tossed three times. What is the probability that two heads will be obtained in succession
Answers
Answer:
3/8
Step-by-step explanation:
the row numbers along the left side of a worksheet are as follows: 1 2 4 5 6. this indicates that row 3 is:
Answers
The row numbers along the left side of the worksheet are 1, 2, 4, 5, 6. We can observe that there is a missing number in the sequence, specifically the number 3. Therefore, based on the pattern, we can deduce that row 3 is missing from the worksheet.
Based on the given information, the row numbers along the left side of the worksheet are 1, 2, 4, 5, 6, with a missing number in the sequence, which is the number 3.
The presence of the numbers 1, 2, 4, 5, and 6 indicates that rows corresponding to those numbers exist in the worksheet. However, there is no row with the number 3 mentioned in the sequence. Thus, we can conclude that row 3 is missing from the worksheet.
It is important to note that the missing row could be intentional or accidental, but based on the given information, we can deduce that there is a discontinuity in the row numbering, specifically the absence of row 3.
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Given the function f(x)= 11−5x
2
. First find the Taylor series for f about the centre c=0. Which one of the following is the interval of convergence of the Taylor series of the given function f ? (− 5
11
, 5
11
) −[infinity]
5
5
(− 5
2
, 5
2
)
Answers
The correct answer among the given options is (-∞, ∞).
To find the Taylor series for the function f(x) = 11 - 5x² about the center c = 0, we can use the general formula for the Taylor series expansion:
f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)²/2! + f'''(c)(x - c)³/3! + ...
First, let's find the derivatives of f(x):
f'(x) = -10x, f''(x) = -10, f'''(x) = 0
Now, let's evaluate these derivatives at c = 0:
f(0) = 11, f'(0) = 0, f''(0) = -10, f'''(0) = 0
Substituting these values into the Taylor series formula, we have:
f(x) = 11 + 0(x - 0) - 10(x - 0)^2/2! + 0(x - 0)³/3! + ...
Simplifying further: f(x) = 11 - 5x². Therefore, the Taylor series for f(x) about the center c = 0 is f(x) = 11 - 5x².
Now, let's determine the interval of convergence for this Taylor series. Since the Taylor series for f(x) is a polynomial, its interval of convergence is the entire real line, which means it converges for all values of x. The correct answer among the given options is (-∞, ∞).
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ok there’s the science slides , and i think they are quite easy i just need some help bc im lazy . ik this is the math thing but
Answers
Answer:
just look up the answers on google
Step-by-step explanation:
The area of a rectangle is 14 1/2 sq cm and one side is 4 1/2 cm. how long is the other side?
Answers
Answer:
6cm*4.5cm = 27cm²
5cm*5cm = 25cm²
The first has a greater area - by 2 square centimeters.
Step-by-step explanation:
Answer:5 1/2
Step-by-step explanation:
4 1/2+4 1/2=9
14 1/2 -9=5 1/2