9.
((x - 2)2
The function f(x) = ax2 + bx
3x – 6
if x < -1
if - 1
if x 2
is continuous for all real values of x.
Find a and b.
Answers
Answer:
a = 0.3 and b = - 1.1
Step-by-step explanation:
(x - 2)² = x² -4x + 4
Hence, x² - 4x + 4 = 3x - 6
x² - 7x + 10 = 0
(x - 5)(x - 2) = 0
∴ x = 5 or 2
f(5) = 25a + 5b = 2 ----- (i)
f(2) = 4a + 2b = -1 ------ (ii)
(i) X 2: 50a + 10b = 4 ----- (iii)
(ii) X 5: 20a + 10a = -5 ---- (iv)
Subtract (iv) from (iii): 30a = 9
a = 0.3
Substitute a into (ii) to obtain b
4(0.3) + 2b = -1
2b = -1 - 1.2 = -2.2
∴ b = -1.1
Related Questions
Solve the equation for all values of x in simplist form (x-6)^2=-36
Answers
The complex solutions for the equation are x = 6 + 6i and x = 6 - 6i.
A quadratic equation is represented by the formula\((x - 6)^2 = -36\). To begin, we can get rid of the square term on the left side of the equation by taking the square roots of both sides. We do, however, introduce the idea of complex numbers because the right side is negative.
To solve the equation for all values of x in simplest form, we'll follow these steps:
1. Write down the given equation:\((x-6)^2 = -36\)
2. Since we have a squared term equal to a negative value, this implies that there are no real solutions (because the square of a real number is always non-negative). However, we can find complex solutions.
3. Take the square root of both sides of the equation:
\(\sqrt{((x-6)^2)} = \sqrt{(-36)} \\ x-6 = ± \sqrt{(-36)}\)
4. The square root of -36 can be simplified to 6i (where i is the imaginary unit):
x-6 = ± 6i
5. Add 6 to both sides of the equation to isolate x:
x = 6 ± 6i
So, the complex solutions for the equation are x = 6 + 6i and x = 6 - 6i.
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n+n+n=1 what is n?????
Answers
Answer:
1/3
Step-by-step explanation:
If you add all the n's, it would make 3n=1. Divide both sides by 3 and get n=1/3
Answer:
0.333 or 1/3
Step-by-step explanation:
0.333*3=1
What is the slope of a line that passes through the points (2,0) and (6,−12)
Answers
Answer:
slope = -3
Step-by-step explanation:
Slope formula: \(\frac{y2-y1}{x2-x1}\)
Given points: (2, 0), (6, -12)
(2, 0) = (x1, y1)
(6, -12) = (x2, y2)
To find the slope, input the two given points into the formula used to find slope:
\(\frac{-12-0}{6-2}\)
Simplify:
-12 - 0 = -12
6 - 2 = 4
\(\frac{-12}{4} = -\frac{3}{1}=-3\)
The slope of the line is -3.
Hope this helps :)
Huy is painting eight styrofoam cubes for a science project. the side length of the cube measures 6 1/2 inches. What is the total surface area that Huy will paint
Answers
Answer:
2028 square inches
Step-by-step explanation:
The side length of the styrofoam cube measures 6 1/2 inches.
Step 1
We find the surface area of a cube
The formula is given as
Surface Area = 6a²
Where a = Side length of the cube = 6 1/2 inches
Hence,
Surface area of a cube = 6 × (6 1/2inches)²
= 253.5 square inches
Step 2
Huy is painting eight styrofoam cubes for a science project.
The total surface area that Huy will paint is calculated as:
1 styrofoam cube = 253.5 square inches
8 styrofoam cubes = x
Cross Mulitiply
x = 8 × 253.5 square inches
x = 2028 square inches
Therefore, the total surface area that Huy will paint is 2028 square inches.
which of the following basic functions is equivalent to the piecewise-defined function f(x)= x if x≥0 −x if x<0 ? question content area bottom part 1 a. f(x)= 1 x b. f(x)=x c. f(x)=x2 d.
Answers
The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.
The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.
Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.
The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.
In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.
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Let A be a 4x4 matrix and suppose that det(A)=8. For each of the following row operations, determine the value of det(B), where B is the matrix obtained by applying that row operation to A.a) Interchange rows 3 and 1 b) Add -2 times row 3 to row 2 c) Multiply row 4 by 2Resulting values for det(B):
a) det(B) = 0
b) det(B) = 0
c) det(B) = 0
Answers
The resulting values for det(B) are 8, -8, 16
How to find the resulting values of det(B)?To determine the effect of each row operation on the determinant of the matrix, we can use the fact that the determinant is multilinear with respect to the rows. In other words, if we perform a row operation on a matrix, the determinant is multiplied by a scalar that depends on the row operation.
a) Interchanging rows 3 and 1 of A:
Let B be the matrix obtained by interchanging rows 3 and 1 of A. This row operation is equivalent to multiplying A by the permutation matrix P that interchanges rows 3 and 1. Since P is a permutation matrix, det(P) is either 1 or -1. In this case, interchanging rows 3 and 1 once is equivalent to applying P twice, so det(P) = 1. Therefore,
det(B) = det(PA) = det(P) det(A) = det(A) = 8
b) Adding -2 times row 3 to row 2 of A:
Let B be the matrix obtained by adding -2 times row 3 to row 2 of A. This row operation is equivalent to multiplying A by the matrix
I - 2 e_2 e_3^T,
where I is the 4x4 identity matrix, and e_2 and e_3 are the second and third standard basis vectors in R^4, respectively. The determinant of this matrix is -1 (it is a reflection matrix), so
det(B) = det((I - 2 e_2 e_3^T) A) = (-1) det(A) = -8.
c) Multiplying row 4 of A by 2:
Let B be the matrix obtained by multiplying row 4 of A by 2. This row operation is equivalent to multiplying A by the diagonal matrix D with diagonal entries 1, 1, 1, 2. The determinant of this matrix is 2, so
det(B) = det(DA) = 2 det(A) = 16.
Therefore, the resulting values for det(B) are:
a) det(B) = 8
b) det(B) = -8
c) det(B) = 16
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A bag contains 10 black, 15 white, and 25 blue marbles. What is the probability of randomly selecting one
marble that is NOT black?
Answers
Answer: 0.8 or 80%
Step-by-step explanation:
First find the total number of marbles:
10 + 15 + 25 = 50 marbles total
To find the number of marbles that are not black:
15 + 25 = 40 marbles that are not black
Set up ratio:
\(\frac{40}{50}\) = 0.8 or 80%
I need to figure out what c equals in the problem -3 - 3/4(c-4) =5/4
please help
Answers
Answer:
-54
Step-by-step explanation:
-3 -3/4(c-4)=5/4
\(\\\)
Answer:
Exact Form:
c = −5/3
Decimal Form:
c = −1.¯6
Mixed Number Form:
c = −1 2/3
Step-by-step explanation:
if the number of degrees of freedom for a chi-square distribution is 25, what is the standard deviation? round to four decimal places. standard deviation
Answers
The standard deviation for a chi square distribution for given degree of freedom is 7.0711.
The chi-square distribution is parameterized by the number of degrees of freedom (df). As the number of degrees of freedom increases, the shape of the distribution becomes more symmetrical and approaches a normal distribution.
The standard deviation (σ) of a chi-square distribution with k degrees of freedom is given by the formula:
σ = sqrt(2k)
Therefore, for a chi-square distribution with 25 degrees of freedom:
σ = sqrt(2(25)) = sqrt(50) ≈ 7.0711
Rounding this to four decimal places gives a standard deviation of approximately 7.0711.
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Solving Inequalities
Algebra 1
Answers
Answer:
b\(\geq\)-12
Step-by-step explanation:
Step 1- Subtract 10 from both sides of the inequality.
New inequality:
4b\(\geq\)-48
Step 2- Divide by 4 on both sides of the inequality, to get your answer.
Answer:
b\(\geq\)-12
3.75
Word form
please help
Answers
Answer:
three and seventy-five hundredths or three point seven five
Step-by-step explanation:
how do i mutiply 5 times 4
Answers
Answer:20
Step-by-step explanation
If you add 5 five times \(5+5+5+5+5 =\) When you do this you are multiplying just longer
What is 0.25 to the nearest whole number
Answers
Answer:
0
Step-by-step explanation: 0.25 rounded is 0
What is 0. 2 [5x + (–0. 3)] + (–0. 5)(–1. 1x + 4. 2) simplified?
Answers
The simplified form of the expression is 1.55x - 2.16.
To simplify the expression 0.2[5x + (-0.3)] + (-0.5)(-1.1x + 4.2), we can distribute the coefficients and simplify the terms.
First, distribute 0.2 to the terms inside the brackets: 0.2 * 5x + 0.2 * (-0.3) = x - 0.06.
Next, distribute -0.5 to the terms inside the second brackets: -0.5 * (-1.1x) + (-0.5) * 4.2 = 0.55x - 2.1.
Now, we can combine the simplified terms: (x - 0.06) + (0.55x - 2.1) = 1.55x - 2.16.
Thus, the simplified expression is 1.55x - 2.16.
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need this ASAP. pls answer this question
Answers
Answer:
this is ur answer so memories
Find the common difference of the arithmetic sequence. −16,−7,2,11
Answers
Answer:
Common difference is 9
Step-by-step explanation:
-16 + 9 = -7
-7 + 9 = 2
2 + 9 = 11
smallest to largest. Here are four decimal numbers: 0.9, 0.5, 0.8, 0.1
Answers
Answer:
0.1,0.5,0.8,0.9
Step-by-step explanation:
Is it true that If A is invertible, then detA^−1 = det A.
Answers
Yes,
It is true that if A is invertible, then det(A⁽⁻¹⁾) = det(A).
The determinant of a matrix and its inverse are closely related.
The determinant of a matrix is nonzero, then the matrix is invertible, and its inverse has the same determinant as the original matrix.
The following properties of determinants:
det(AB) = det(A)det(B) for any square matrices A and B
If A is invertible, then det(A⁽⁻¹⁾) = 1/det(A)
Using these properties, we can write:
det(A⁽⁻¹⁾) = det(A⁽⁻¹⁾)det(AI) = det(A⁽⁻¹⁾A) = det(I) = 1
And:
det(A) = det(AA⁽⁻¹⁾) = det(A)det(A⁽⁻¹⁾)
Multiplying both sides by det(A⁽⁻¹⁾), we get:
det(A)det(A⁽⁻¹⁾) = det(A⁽⁻¹⁾)det(A⁽⁻¹⁾) = det(A⁽⁻¹⁾)det(A)
det(A⁽⁻¹⁾) = det(A).
The determinant of a matrix and its inverse are closely related.
The determinant of a matrix is nonzero, then the matrix is invertible, and its inverse has the same determinant as the original matrix.
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Algebra 1 common assessment unit 2-1 SY23
Answers
Answer:
\(t1 {15y08 \frac{18 \gamma \gamma }{?} }^{2} \)
14. (10 points) Consider the transformation Y = g(x) = 2 - 3X, for the random variable X, where the cdf for X is Fx (x) = {1-03:18 ( e 1758} > 0 Find the cdf for Y. Hint: Make sure that you define the support of the random variable Y.
Answers
The cdf for Y is Fy(y) = 0.318(e^(1758(2-y)/3)).
How to calculate cumulative distribution function (cdf)?Consider the transformation Y = g(x) = 2 - 3X, for the random variable X, where the cumulative distribution function (cdf) for X is Fx(x) = {1-0.318 (e^1758)} > 0. We need to find the cdf for Y.To find the cdf for Y, we need to follow the steps given below:
Determine the support of the random variable Y.We know that X has a support of (0,∞).Therefore, the minimum possible value of g(x) = 2 - 3X is 2 - 3(∞) = -∞.The maximum possible value of g(x) = 2 - 3X is 2 - 3(0) = 2.The support of Y is (-∞, 2].
Define the cdf for Y.To define the cdf for Y, we need to use the this formula: Fy(y) = P(Y ≤ y)Since Y = 2 - 3X, we have X = (2 - Y) / 3.
Substituting this value of X in the expression for fx(x), we get: Fx(x) = P(X ≤ x) = P[(2 - Y) / 3 ≤ x] = P(Y ≥ 2 - 3x)Using the complement rule, we can write:P(Y ≤ y) = 1 - P(Y > y) = 1 - P(Y ≥ y) = 1 - P(2 - 3X ≥ y) = 1 - P(X ≤ (2 - y) / 3) = 1 - Fx[(2 - y) / 3]Substituting the value of Fx(x), we get:Fy(y) = 1 - Fx[(2 - y) / 3] = 1 - {1 - 0.318(e^(1758(2-y)/3))} = 0.318(e^(1758(2-y)/3))
Therefore, the cdf for Y is Fy(y) = 0.318(e^(1758(2-y)/3)).Thus, we can conclude that the cdf for Y is Fy(y) = 0.318(e^(1758(2-y)/3)).
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Death Valley National Park, in California and Nevada, is the site of the lowest elevation in the Western Hemisphere. Bad water Basin in the park is about 86 meters below sea level.
Answers
I forgot how to do this, can someone help me-
Answers
Step-by-step explanation:
1) x/20 = -9
By cross multiplication,
x = -180
2) -168 = -14k
k = -168/-14
k = 12
3) -5m = -50
m = 10
4) -320 = -20n
n = 16
5) -4 = x - 5
x = 1
6) -6(-8 + n) = -54
42 - 6n = -54
-6n = -54 -52
6n = 106
n = 17.6
7) 3(x - 9) = -3
3x - 27 = -3
3x = 24
x = 8
8) 9k + 3 = -78
9k = -81
k = -9
9)4 + (n/4) = 8
By taking LCM,
16 + n/4 = 8
16 + n = 32
n = 16
10) -5r + 7 = -73
-5r = -80
r = 16
Hope it helps.
Help please i dint get it pls answer
Answers
Answer: 7%
(Hope this is right.)
Step-by-step explanation:
Let's solve this using the information we have and an equation.
Shane: $32,000 - (Given)
Theresa: 18,000+14x, if x=1,160 - (Given)
---------------------------------------------------------------
Step two: (Theresa) 14(1,160) =16,240 (Algebra)
Step three: (Theresa) 18,000+16,240=34,240 (Algebra, given.) - cost of Theresa's car.
---------------------------------------------------------------
Finally,
They're asking for how much more she paid for her car as a percentage of what Shane paid.
34,240-32,000=2,240 and
2,240/32,000=0.07
0.07x100=7
Answer 7% more than what Shane paid.
What is the constant of proportionality in the graph below
Answers
Answer:
you need to show the graph in order to get an answer
Each container as twice as many lollipop as each packet. If there were 721 lollipop in 2 containers and 3 packets find the number of lollipop in a container.
Answers
The number of lollipops in a container is 206.
How to determine the numberThese are steps to find the number of lollipops in a container:
1. Let x be the number of lollipops in a packet and 2x be the number of lollipops in a container.
2. According to the given information, we have the equation: 2(2x) + 3x = 721
3. Simplify the equation: 4x + 3x = 721 7x = 721
4. Solve for x: x = 103
5. Substitute x back into the equation to find the number of lollipops in a container: 2x = 2(103) = 206 Therefore, the number of lollipops in a container is 206.
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what makes a good regression model? significant independent variables including the largest possible number of variables dropping all insignificant variables from the model a significant intercept and dependent variable
Answers
Significant independent variables makes a good regression model.
A reasonable high R-squared score makes sense if your regression model includes independent variables that are statistically significant. According to the statistical significance, shifts in the dependent variable are correlated with changes in the independent variables.
Accordingly, a high R-squared value shows that your model adequately accounts for the variation in the dependent variable.
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driving at a constant speed, sharon usually takes minutes to drive from her house to her mother's house. one day sharon begins the drive at her usual speed, but after driving of the way, she hits a bad snowstorm and reduces her speed by miles per hour. this time the trip takes her a total of minutes. how many miles is the drive from sharon's house to her mother's house?
Answers
The distance between her house and her mother's house =135 miles
Let the entire distance be 3x
Normally that takes 180 minutes
speed would be (3x)/180 = x/60 miles per minute
It would take 60 minutes to go the first distance of x and 276-60 = 216 minutes to the next 2x miles
She hits a bad snowstorm and reduces her speed by 20 miles per hour.
So her speed would be, (x - 20)/60 miles
for given situation we formulate an equation,
(x - 20)/60 = 2x/216
(x - 20)/10 = x/18
18x - 360 = 10x
8x = 360
x = 45 miles
So, the total distance would be:
3x = 3 × 45
= 135 miles
Therefore, the required distance is 135 miles
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. If A and B are two sets and A∪ B= A ∩ B, then
A= Φ
B= Φ
A=B
None of these
Answers
Answer:
A=B maybe ...
what is that symbols of a and b
drag the slope of each graphed line to the white box.
Answers
Answer:
A -1/2
B 2
C -1/4
D 3
Step-by-step explanation:
Hope this helps :p
The graph below shows the number of books the students in Mrs. Harold's class read this semester. Which two students together read as many books as Jesus?
A. Calvin and Kim
B. Mary and Kim
C. Horatio and Kim
D. Allison and Sori
Answers
Hi!
Jesus read 6 books.
Together Mary and Kim read 6 books.
Mary=4 books read, Kim=2 books read.
I hope this helps!
Feel free to give brainliest!
Answer:
D
Step-by-step explanation: