(a) The inverse of A is:
A⁻¹ = [-2 1 0
1 0 1
1/2 0 1]
(b) The solution to the system of linear equations is x = [-3, 2, 3/2].
To find the inverse of A, we can use Gaussian Elimination. We can start by adding the first row to the second row. This gives us:
```
[1 0 1 4
1 1 2 -3
1 1 3 1]
```
Next, we can subtract the second row from the third row. This gives us:
```
[1 0 1 4
1 1 2 -3
0 0 1 2]
```
Finally, we can divide the third row by 2. This gives us the row reduced form of the matrix:
```
[1 0 0 -2
0 1 0 1
0 0 1 1/2]
```
As we can see, the third column of the row reduced matrix is the inverse of the first column of the original matrix. Therefore, the inverse of A is:
```
A⁻¹ = [-2 1 0
1 0 1
1/2 0 1]
```
We can now use this inverse to solve Ax=b. We can write this equation as:
```
[1 0 1 4
1 1 2 -3
1 -1 1 1] * x = [4 -3 1]
```
Multiplying both sides of this equation by A⁻¹, we get:
```
x = A⁻¹ * b = [-2 1 0
1 0 1
1/2 0 1] * [4 -3 1] = [-3 2 3/2]
to learn more about linear equations click here:
brainly.com/question/29739212
#SPJ11
Evaluate the expression for the given values.
a b-2 a if a=-2 and b=-3
Substituting a = -2 and b = -3 into the expression a(b-2a) results in -2. Therefore, the evaluated value of the expression is -2.
To evaluate the expression a(b-2a) for a = -2 and b = -3, we substitute the given values into the expression. Plugging in a = -2 and b = -3, we have -2((-3) – 2(-2)). To simplify the expression, we first simplify the inner brackets. The term -3 – 2(-2) can be rewritten as -3 + 4, which gives us 1.
Now, substituting this value back into the expression, we have -2(1). To find the result, we multiply -2 by 1. The product of -2 and 1 is -2. Therefore, when we evaluate the expression a(b-2a) for a = -2 and b = -3, we get -2 as the final answer.
Hence, by substituting the given values of a = -2 and b = -3 into the expression a(b-2a) and simplifying the resulting expression, we find that the evaluation yields -2 as the answer.
Learn more about Expression here: brainly.com/question/14083225
#SPJ11
you measure the period of a mass oscillating on a vertical spring ten times as follows: period (s): 1.36, 1.04, 1.22, 1.29, 1.48, 1.55, 0.97, 1.18, 1.13, 1.32 what are the mean and (sample) standard deviation?
The mean is 1.354 seconds and sample standard deviation is approximately 0.0164 seconds
Let us find the mean which is sum of all the observations by total number of observations.
Mean = (1.36 + 1.04 + 1.22 + 1.29 + 1.48 + 1.55 + 0.97 + 1.18 + 1.13 + 1.32) / 10
= 13.54 / 10
= 1.354
The mean of the data set is 1.354 seconds.
We will use the formula for the sample standard deviation, which involves finding the differences between each value and the mean, squaring those differences, summing them up, dividing by (n-1), and taking the square root.
Deviation = [(1.36 - 1.354)² + (1.04 - 1.354)² + (1.22 - 1.354)² + (1.29 - 1.354)² + (1.48 - 1.354)² + (1.55 - 1.354)² + (0.97 - 1.354)² + (1.18 - 1.354)² + (1.13 - 1.354)² + (1.32 - 1.354)²] / 9
= [0.000036 + 0.000088 + 0.000157 + 0.000068 + 0.000167 + 0.000167 + 0.001409 + 0.000136 + 0.000074 + 0.000073] / 9
= 0.002415 / 9
= 0.0002683
Standard Deviation = √(0.0002683)
= 0.0164
Hence, the sample standard deviation of the data set is 0.0164 seconds.
To learn more on Statistics click:
https://brainly.com/question/30218856
#SPJ4
A polynomial function P(x) with rational coefficients has the given roots. Find two additional roots of P(x)=0 .
-2 i and √10 .
To find two additional roots for the polynomial function P(x) = 0 with given roots -2i and √10, we consider the conjugate of -2i and the negative square root of 10.
The given roots are -2i and √10. Since the polynomial has rational coefficients, the additional roots must also be complex conjugates and negatives of the given roots, respectively.
The complex conjugate of -2i is 2i. Therefore, 2i is an additional root of P(x) = 0.
The negative square root of 10 is -√10. Hence, -√10 is the second additional root of P(x) = 0.
Therefore, the two additional roots for the polynomial function P(x) = 0, with given roots -2i and √10, are 2i and -√10.
Learn more about complex conjugate: brainly.com/question/29960316
#SPJ11
Name the remote interior angles of
B
EAC
D
The remove interior angles of angle BCD are given as follows:
<A and <C.
What are remote interior angles?Remote interior angles are defined as the angles of a triangle that do not share a vertex with a given exterior angle
The exterior angle for the triangle is angle C, hence angles <A and <B are the remote interior angles of the triangle relative to angel C.
More can be learned about remote interior angles at https://brainly.com/question/22759077
#SPJ1
A truck acquired at a cost of $175,000 has an estimated residual value of $11,500, has an estimated useful life of 30,000 miles, and was driven 2,400 miles during the year. Determine the following. If required, round your answer for the depreciation rate to two decimal places.
a.) calculate The units-of-activity depreciation for the year:
The units-of-activity depreciation method calculates depreciation based on the usage or activity level of an asset. So, the units-of-activity depreciation for the year is $13,080.
To calculate the units-of-activity depreciation for the year, we start by subtracting the estimated residual value from the initial cost to determine the depreciable amount: $175,000 - $11,500 = $163,500.
Next, we calculate the depreciation rate per mile by dividing the depreciable amount by the estimated useful life in miles: $163,500 / 30,000 miles = $5.45 per mile.
Finally, we multiply the depreciation rate per mile by the actual miles driven during the year (2,400 miles) to determine the units-of-activity depreciation: $5.45 per mile * 2,400 miles = $13,080.
Therefore, the units-of-activity depreciation for the year is $13,080. This method is suitable for assets whose wear and tear or usage is directly related to the number of units or activities performed. In this case, the truck's depreciation expense is based on the actual miles driven during the year, reflecting its usage and decreasing value based on that usage.
Learn more about depreciation more:
https://brainly.com/question/28161016
#SPJ11
Determine whether each equation is always, sometimes, or never true. 2 x+7-x=3+x+4
The equation 2x + 7 - x = 3 + x + 4 is sometimes true.To determine whether the equation is always, sometimes, or never true, we can simplify and analyze both sides of the equation.
To determine whether the equation is always, sometimes, or never true, we can simplify and analyze both sides of the equation.
Simplifying the equation:
2x + 7 - x = 3 + x + 4
x + 7 = 7 + x
We notice that both sides of the equation are identical. This means that no matter what value of x we substitute, both sides of the equation will always be equal. Therefore, the equation is sometimes true for any value of x.
In summary, the equation 2x + 7 - x = 3 + x + 4 is sometimes true.
Learn more about equation here
brainly.com/question/29538993
#SPJ11
What quantity should be added to both sides of this equation to complete the square?
x² -10 x=3
A -25
B -5
C 5
D 25
We need to add 25 to both sides of this equation to complete the square. Therefore, the correct option is option D.
The equation given to complete the square is;
[tex]x^2[/tex] - 10x = 3
We need to find out the quantity that we will add to both sides of the equation to complete the square.
[tex]x^2[/tex] - 10x - 3 = 0
([tex]x^2[/tex] - 10x + ) - 3 = 0
In this equation, a = 1, b = -10, and c = -3.
b = -10
b/2a = -10/(2 * 1) = -5
(b/2a[tex])^2[/tex] = [tex](-5)^2[/tex] = 25
([tex]x^2[/tex] - 10x + 25) - 3 - 25 = 0
(x - 5[tex])^2[/tex] - 28 = 0
(x - 5[tex])^2[/tex] = 28
Therefore, we need to add 25 to both sides of this equation to complete the square. The correct option is option D.
To learn more about completing the square;
https://brainly.com/question/13981588
#SPJ4
Read each question. Then write the letter of the correct answer on your paper.
The area of a rectangle is 6 x³-22x²+23 x-5 . The width is 3 x-5 . What is the length?
(F) 2x²-4 x+1 (G) 2x²+4 x-1
(H) 2x²+1 (I) 2x²-x-4
The length of the rectangle is , the correct option is F.
We are given that;
The area = [tex]6 x³-22x²+23 x-5 .[/tex]
Width= 3 x-5
Now,
The area of a rectangle is given by the formula `A = l*w`, where `l` is the length and `w` is the width.
We can substitute these values in the formula to get:
[tex]6x³-22x²+23x-5 = l * (3x-5)[/tex]
Simplifying this equation gives:
[tex]2x³ - 4x² + 3x + 1 = l[/tex]
Therefore, by the area answer will be [tex]2x²-4 x+1`.[/tex]
Learn more about the area;
https://brainly.com/question/1658516
#SPJ4
Find the period and amplitude of each function. Sketch each function from 0 to 2π . y=sin (2θ4)
The sketch of the function from 0 to 2π resembles one complete cycle of the sine function, with a period of 4π and an amplitude of 1.
To find the period and amplitude of the function y = sin(2θ/4), we can manipulate the given function to match the standard form of the sine function: y = A sin(Bθ + C), where A is the amplitude, B is the frequency (or the reciprocal of the period), and C is the phase shift.
Comparing the given function to the standard form, we have:
A = 1 (amplitude)
B = 2/4 = 1/2 (frequency)
The amplitude of the function is 1, which represents the maximum vertical distance the graph reaches from the midline.
To find the period, we use the formula T = 2π/B, where B is the frequency. In this case, the frequency is 1/2, so the period is:
T = 2π/(1/2) = 4π
Therefore, the period of the function is 4π, representing the length of one complete cycle of the sine function.
To sketch the function from 0 to 2π, we can plot points for several values of θ within that interval and connect them to form a smooth curve. Since the function is y = sin(2θ/4), we can simplify it to y = sin(θ/2) to make it easier to work with.
Using this simplified form, we can calculate the y-values for various values of θ:
θ = 0: y = sin(0/2) = sin(0) = 0
θ = π/2: y = sin((π/2)/2) = sin(π/4) = √2/2
θ = π: y = sin((π)/2) = sin(π/2) = 1
θ = 3π/2: y = sin((3π/2)/2) = sin(3π/4) = √2/2
θ = 2π: y = sin((2π)/2) = sin(π) = 0
Plotting these points on the graph and connecting them with a smooth curve, we get a graph that starts at 0, reaches a maximum value of 1, returns to 0, reaches a minimum value of -1, and returns to 0 again. The graph repeats this pattern every 4π, which matches the period we calculated.
The amplitude of the function, which is 1, represents the distance from the midline to the maximum or minimum value of the graph.
Therefore, the sketch of the function from 0 to 2π resembles one complete cycle of the sine function, with a period of 4π and an amplitude of 1.
Learn more about function from
https://brainly.com/question/11624077
#SPJ11
If MNPQ ≅ XYZW , find the scale factor of M N P Q to X Y Z W and the perimeter of each polygon.
The scale factor and the perimeters are = 1/2 and 34 and 17 units.
Given that are two polygons are similar MNPQ ~ XYZW, we need to find the scale factor and the perimeter of each polygon.
Scale factor = ratio of the lengths of the sides of the similar polygons.
Scale factor = MQ / WX = 8/4 = 2
Now,
The perimeter of the polygon XYZW = 10 + 9 + 8 + 7 = 34 units.
We know that the ratio of the perimeters of the similar polygons is equal to the scale factor,
So,
The perimeter of the polygon MNPQ = 34 / 2 = 17 units.
Hence the scale factor and the perimeters are = 1/2 and 34 and 17 units.
Learn more about Scale factor click;
https://brainly.com/question/29464385
#SPJ4
can somebody please help me?
Answer:
a₁=15 ; aₙ=aₙ₋₁ + 4
Step-by-step explanation:
In this image, you can see that for each step made, 4 is added to the previous number. a₁ should be 15 because it is the first number seen in the mix. The formula should come out to aₙ=aₙ₋₁+4. This is because the common difference is only 4, and that's essentially all you needed to plug in.
What decimal value does the 8-bit binary number 10011110 have if it is interpreted as an un-signed number? group of answer choices
The decimal value of the 8-bit binary number 10011110, when interpreted as an unsigned number, is 158.
To convert a binary number to decimal, you can assign each bit a weight based on its position and then calculate the sum. In an 8-bit number, the rightmost bit (bit 0) has a weight of 2^0 = 1, the next bit (bit 1) has a weight of 2^1 = 2, the next bit (bit 2) has a weight of 2^2 = 4, and so on.
In this case, we have:
1 * 2^7 + 0 * 2^6 + 0 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 0 * 2^0
= 128 + 0 + 0 + 16 + 8 + 4 + 2 + 0
= 158
So, the decimal value of the 8-bit binary number 10011110 is 158.
To know more about binary to decimal conversion, refer here:
https://brainly.com/question/24539025#
#SPJ11
Read the question. Then write the letter of the correct answer on your paper.Which describes the translation of y=|x-3|+5 ? a. y=|x| translated 3 units left and 5 units up b. y=|x| translated 3 units right and 5 units up c. y=|x| translated 5 units left and 3 units up d. y=|x| translated 5 units right and 3 units up
The correct answer is d. y=|x| translated 5 units right and 3 units up.
The equation y=|x-3|+5 represents a translation of the absolute value function y=|x| to the right by 3 units and up by 5 units.
The expression "x-3" inside the absolute value represents the horizontal translation of 3 units to the right.
The "+5" term outside the absolute value represents the vertical translation of 5 units up. Therefore, option d, y=|x| translated 5 units right and 3 units up, accurately describes the translation of the given equation.
To learn more about vertical click here
brainly.com/question/30105258
#SPJ11
the supermarket displays the unit price for the 15.3-ounce box in terms of cost per ounce, but displays the unit price for the 24-ounce box in terms of cost per pound. what are the unit prices, to the nearest cent, given by the supermarket? unit price for the 15.3-ounce box
The unit price for the 15.3-ounce box, given by the supermarket, can be determined by converting the unit price for the 24-ounce box from cost per pound to cost per ounce. The unit price for the 15.3-ounce box is approximately x cents per ounce (where x is the converted unit price per ounce).
To find the unit price for the 15.3-ounce box, we need to convert the unit price for the 24-ounce box from cost per pound to cost per ounce. Since there are 16 ounces in a pound, we can convert the cost per pound to cost per ounce by dividing it by 16.
Let's assume the unit price for the 24-ounce box, displayed by the supermarket, is y dollars per pound. To convert this to cost per ounce, we divide y by 16. The resulting value, y/16, represents the unit price in dollars per ounce.
Now, to express the unit price in cents per ounce (to the nearest cent), we multiply y/16 by 100 to convert it to cents. This gives us the converted unit price in cents per ounce, which is approximately x cents per ounce.
Therefore, the unit price for the 15.3-ounce box, given by the supermarket, is approximately x cents per ounce.
Learn more about supermarket here:
brainly.com/question/32798381
#SPJ11
Consider the following data set
5
6
7
15
22
Be careful with this question tick every correct option note that the 50 th percentile would be the middle numbe a. the mean is 11.00 b. the mean is 14.70 c. The median (the 50 th percentile) is 7.00 d. The median (the 50th percentile) is 10.75
a. The mean is 11.00 (correct)
b. The mean is 14.70 (incorrect)
c. The median (the 50th percentile) is 7.00 (correct)
d. The median (the 50th percentile) is 10.75 (incorrect)
5, 6, 7, 15, 22
The mean is calculated by adding up all the numbers and dividing by the total count:
Mean = (5 + 6 + 7 + 15 + 22) / 5 = 11
So option a. The mean is 11.00 is correct.
The median (the 50th percentile) is the middle number when the dataset is arranged in ascending order. Since we have an odd number of values, the median is the middle value itself.
So option d. The median (the 50th percentile) is 10.75 is incorrect.
The median of the dataset is 7 since it is the middle number when the dataset is arranged in ascending order.
So option c. The median (the 50th percentile) is 7.00 is correct.
learn more about median here:
https://brainly.com/question/300591
#SPJ11
Find the slope-intercept equation of the line that satisfies the given conditions. Passes through (−3,1) and is perpendicular to x−2y=8
y(x) = ____
The slope-intercept equation of the line that passes through (-3, 1) and is perpendicular to x - 2y = 8 is y = -2x - 5.
To find the slope-intercept equation of the line that passes through (-3, 1) and is perpendicular to the line x - 2y = 8, we need to determine the slope of the given line and then find the negative reciprocal of that slope to obtain the slope of the perpendicular line.
First, let's rearrange the equation x - 2y = 8 to the slope-intercept form (y = mx + b):
-2y = -x + 8
y = (1/2)x - 4
The slope of the given line is 1/2. The negative reciprocal of 1/2 is -2, which is the slope of the perpendicular line.
Now, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), with the point (-3, 1) and the slope -2:
y - 1 = -2(x - (-3))
y - 1 = -2(x + 3)
y - 1 = -2x - 6
y = -2x - 5
Therefore, the slope-intercept equation of the line that passes through (-3, 1) and is perpendicular to x - 2y = 8 is y = -2x - 5.
Learn more about slope-intercept equation here: https://brainly.com/question/29253302
#SPJ11
write a vector equation and parametric equations of a line given the following: line contains the point (2,7)
These parametric equations represent the x and y coordinates of points on the line as the parameter t varies.
To write the vector equation and parametric equations of a line that contains the point (2,7), we need an additional piece of information: either another point on the line or the direction vector of the line.
Let's say we have another point on the line, such as (4,9). With this information, we can proceed to write the vector equation and parametric equations.
Vector Equation: The vector equation of a line passing through points P(2,7) and Q(4,9) can be written as: r = p + t⋅d
Here, r represents the position vector of any point on the line, p represents the position vector of point P(2,7), t is a parameter that varies along the line, and d represents the direction vector of the line, which can be obtained by subtracting the position vectors of points P and Q:
d = Q - P = (4,9) - (2,7) = (2,2)
Therefore, the vector equation becomes:
r = (2,7) + t⋅(2,2)
Parametric Equations: The parametric equations express the x, y, and z coordinates of a point on the line in terms of the parameter t. In this case, since we are dealing with a 2D line, there will be only x and y coordinates.
x = 2 + 2t
y = 7 + 2t
These parametric equations represent the x and y coordinates of points on the line as the parameter t varies.
Please note that if you have a different point or specific direction vector in mind, the equations would be modified accordingly.
Learn more about equation from
https://brainly.com/question/29174899
#SPJ11
Write the indicated type of proof.
Two-column
Given: A B C H and D C G F are parallelograms.
Prove: ∠A ⊕ ∠F
The indicated type of proof for proving ∠A ⊕ ∠F is a Two-Column Proof. In a Two-Column Proof, we present the statements (or facts) on the left column and their corresponding justifications (or reasons) on the right column.
By systematically providing statements and their justifications, we demonstrate the logical progression of the proof, leading to the desired conclusion. To prove ∠A ⊕ ∠F, we would begin by listing the given information, such as "A B C H" and "D C G F are parallelograms," as the initial statements. Then, we would proceed with a series of logical deductions and theorems, referencing them as justifications. The goal is to establish the relationship or property that connects ∠A and ∠F, providing a step-by-step argument until we reach the desired conclusion.
Throughout the proof, we would use relevant geometric principles, definitions, postulates, and theorems to build a coherent and valid argument that supports the statement ∠A ⊕ ∠F. By following the structure of a Two-Column Proof, we can clearly present the logical progression of the proof and justify each step along the way, ultimately demonstrating the validity of the conclusion.
Learn more about parallelograms here: brainly.com/question/32441125
#SPJ11
Use the given information to find the missing side lengths in each 30°-60°-90° triangle. Rationalize any denominators.
shorter leg √3 cm
In a 30°-60°-90° triangle, the shorter leg is √3 cm, the longer leg is 2√3 cm, and the hypotenuse is 2 cm.
A 30°-60°-90° triangle is a special right triangle with specific angle measures. In this triangle, the sides are related by certain ratios. The shorter leg is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is opposite the 90° angle.
In a 30°-60°-90° triangle, the ratios of the side lengths are as follows:
The ratio of the shorter leg to the hypotenuse is 1:2, meaning the shorter leg is half the length of the hypotenuse.
The ratio of the longer leg to the hypotenuse is √3:2, meaning the longer leg is √3 times the length of the shorter leg.
The ratio of the longer leg to the shorter leg is √3:1, meaning the longer leg is √3 times the length of the shorter leg.
Given that the shorter leg is √3 cm, we can use these ratios to find the lengths of the other sides:
The longer leg is √3 * √3 = 3 cm.
The hypotenuse is 2 * √3 = 2√3 cm.
So, in this 30°-60°-90° triangle, the shorter leg is √3 cm, the longer leg is 3 cm, and the hypotenuse is 2√3 cm.
Learn more about right triangle here:
brainly.com/question/24220091
#SPJ11
Write an equation to solve the problem.
The length and width of a rectangle are in the ratio 5: 3 . The perimeter of the rectangle is 3cm . Find the length and width.
The length of the rectangle is 15/16 cm, and the width is 9/16 cm, maintaining the ratio of 5:3 and resulting in a perimeter of 3 cm.
Let's denote the length of the rectangle as L and the width as W. According to the problem, the ratio between the length and width is given as 5:3.
We can express this relationship using the equation:
L/W = 5/3
To find the length and width, we also need to consider the perimeter of the rectangle. The formula for the perimeter of a rectangle is given by:
Perimeter = 2(L + W)
In this case, the perimeter is given as 3 cm. Substituting the values into the equation, we have:
2(L + W) = 3
Now, we have a system of two equations:
Equation 1: L/W = 5/3
Equation 2: 2(L + W) = 3
We can solve this system of equations to find the values of L and W.
From Equation 1, we get:
L = (5/3)W
Substituting this value of L into Equation 2, we have:
2((5/3)W + W) = 3
(10/3)W + 2W = 3
(16/3)W = 3
W = (3 * 3) / 16
W = 9/16
Now, substituting this value of W back into Equation 1, we can find L:
L = (5/3)(9/16)
L = (45/48)
L = 15/16
Therefore, the length of the rectangle is 15/16 cm, and the width is 9/16 cm, maintaining the ratio of 5:3 and resulting in a perimeter of 3 cm.
Learn more about rectangular from
https://brainly.com/question/2607596
#SPJ11
Simplify each expression.
(8 - √-1) - (-3 + √-16)
The correct answer is 11-5i. The expression [tex](8 - \sqrt{-1}) - (-3 + \sqrt{-16})[/tex] can be -simplified as complex number 11 - 5i.
First, let's simplify the square roots:
[tex]\sqrt{-1}[/tex]is equal to the imaginary unit "i," which is defined as the square root of -1.
[tex]\sqrt{-16}[/tex] is equal to 4i because the square root of -16 is 4i.
Now let's substitute these values into the expression:
(8 - i) - (-3 + 4i)
To simplify, let's distribute the negative sign to both terms within the second set of parentheses:
(8 - i) + (3 - 4i)
Next, let's combine like terms:
8 + 3 = 11
-1i - 4i = -5i
Therefore, the simplified expression is 11 - 5i.
Learn more about complex numbers here:
https://brainly.com/question/29185603
#SPJ4
The start of a quadratic sequence is shown below.
Find the nth term rule for this sequence.
4, 22, 52,
52, 94, 148,…
Answer:
6n^2 - 5n + 3
Step-by-step explanation:
To find the nth term rule for the given quadratic sequence, we need to determine the pattern or relationship between the terms. Looking at the sequence:
4, 22, 52, 52, 94, 148,...
We can observe that the first term is 4, the second term is 22 (which is 18 more than the first term), and the third term is 52 (which is 30 more than the second term).
To find the nth term rule, we will first find the differences between consecutive terms:
1st difference: 18, 30, 0, 42, ...
We notice that the 2nd difference (the differences between the differences) is constant, which suggests that the sequence follows a quadratic pattern.
2nd difference: 12, -30, 42, ...
Now, to find the nth term rule, we can use the general form of a quadratic sequence:
an = dn^2 + en + f
By substituting the values of the terms into the equation, we can find the coefficients d, e, and f.
Let's use the first three terms to form three equations:
For the 1st term (n = 1):
4 = d(1)^2 + e(1) + f
4 = d + e + f ...(1)
For the 2nd term (n = 2):
22 = d(2)^2 + e(2) + f
22 = 4d + 2e + f ...(2)
For the 3rd term (n = 3):
52 = d(3)^2 + e(3) + f
52 = 9d + 3e + f ...(3)
Solving these three equations simultaneously will give us the values of d, e, and f.
Subtracting equation (1) from equation (2):
18 = 3d + e ...(4)
Subtracting equation (1) from equation (3):
48 = 8d + 2e ...(5)
Now, subtracting equation (4) from equation (5):
30 = 5d
d = 6
Substituting the value of d into equation (4):
18 = 3(6) + e
e = -5
Substituting the value of d into equation (1):
4 = 6 + (-5) + f
f = 3
Therefore, the nth term rule for this quadratic sequence is:
an = 6n^2 - 5n + 3
fifa is expected to make how much revenue from the world cup?
Answer:
Step-by-step explanation:
$4.7 billion ..
Solve the equation. 2/3x+1=5-2 x
After solving this equation we get, x = 1.714 or x = 12/7
To solve the given equation.
2/3x + 1 = 5 - 2x
Add 2x on both side.
2/3x + 1 + 2x= 5 - 2x + 2x
7x/3 + 1 = 5
subtract 1 on both side.
7x/3 = 5 - 1
7x/3 = 4
x = 12/7 or 1.714
Therefore, after solving this equation we get, x = 1.714.
Learn more about equation hare:
https://brainly.com/question/561757
#SPJ4
Solve each equation.
7|8-3 h|=21 h-49
After solving the compound equation with the modulus function, we obtain the solution h = 5/2.
To solve this question, we use the modulus function's properties and learn how to solve equations in their presence.
The modulus function returns the absolute value of the operand, number, or expression, regardless of the sign they carry. Denoted by |x|, it works in the following ways.
|x| = x, if x ≥ 0
|x| = -x, if x < 0
This function is beneficial in the field of mathematics and sciences, as in various cases, it is necessary for only the magnitude to be used, and the sign to be avoided.
Ex: Distance, Speed, etc.
In the given problem, 7|8 - 3h| = 21h - 49
The left-hand side can go through two possible cases.
Case 1:
8 - 3h ≥ 0
Then |8 - 3h| = 8 - 3h
So,
7(8 - 3h) = 21h - 49
56 - 21h = 21h - 49
56 + 49 = 21h + 21h
105 = 42h
h = 105/42
h = 21*5/21*2
h = 5/2 OR h = 2.5
Case 2:
8 - 3h < 0
Then |8 - 3h| = -(8 - 3h) = 3h - 8
So,
7(3h - 8) = 21h - 49
21h - 56 = 21h - 49
(21h - 21h) -56 + 49 = 0
-7 = 0
This is an absurd result.
Thus, we conclude that such a case is not possible.
Finally, we can say that Case 1 is true, and h = 2.5 is a solution for the compound equation.
For more on Modulus Function,
brainly.com/question/30012772
#SPJ4
determine whether the data described are qualitative or quantitative. the horsepower of motorcycles in a dealership.
The data described, specifically the horsepower of motorcycles in a dealership, is quantitative data. Quantitative data is numerical in nature and represents a measurable quantity or attribute. In this case, the horsepower values assigned to motorcycles can be measured and compared using numeric values.
Quantitative data represents numerical values that can be measured or counted. It provides a quantitative measurement or description of a particular attribute or characteristic. In the case of the horsepower of motorcycles in a dealership, the data is quantitative because it involves numerical values that quantify the power output of the motorcycles.
Horsepower is a unit of measurement used to indicate the power or performance of an engine, including that of motorcycles. It is typically measured using standardized tests or calculations. The horsepower values assigned to motorcycles in the dealership can be expressed as numerical quantities, such as 50 horsepower, 100 horsepower, or 150 horsepower.
Quantitative data allows for meaningful mathematical operations and comparisons. For example, you can calculate the average horsepower of all the motorcycles in the dealership, compare the horsepower of different models, or analyze the distribution of horsepower across the available motorcycles.
In summary, the horsepower of motorcycles in a dealership represents quantitative data because it involves numerical values that can be measured, compared, and analyzed.
Learn more about value from
https://brainly.com/question/24078844
#SPJ11
what is the gradient of this line? need help asap
Answer:
-2
Step-by-step explanation:
This is the steepness of the line.
Take 2 points (0,5) and (1,3). If you start at (0,5) you would move down 2 and right one to get to point (1,3)
-2/1 = -2
Helping in the name of Jesus.
Answer: Gradient = -2
Step-by-step explanation:
Gradient = [tex]\frac{y2-y1}{x2-x1}[/tex]
We take to point on the line (1, 3), (2, 1)
=> gradient = [tex]\frac{1-3}{2-1}[/tex] = -2
Write a conjecture that describes the pattern in the sequence. Then use your conjecture to find the next item in the sequence. 1, 1/2, 1/4, 1/8
Conjecture: The pattern in the sequence is that each term is the reciprocal of a power of 2, where the power increases by 1 for each subsequent term.
In the given sequence 1, 1/2, 1/4, 1/8, we can observe that each term is the reciprocal of a power of 2. The first term, 1, is equivalent to 2^0, and the second term, 1/2, is equivalent to 2^(-1), and so on. Therefore, the pattern suggests that each term is the reciprocal of 2 raised to the power of n, where n represents the position of the term in the sequence.
Using this conjecture, we can find the next item in the sequence. Since the last term in the given sequence is 1/8, which is equivalent to 2^(-3), the next term should be the reciprocal of 2 raised to the power of (-3 + 1), which simplifies to 2^(-2). Therefore, the next item in the sequence is 1/4, or 2^(-2).
To learn more about sequence.
brainly.com/question/30262438
#SPJ11
Find the doman of fog (x) where f(x) = 1/x−2 and y(x)= √x+4
The domain of the composition function f o g(x) can be expressed as (-∞, -4] ∪ (-4, 2) ∪ (2, +∞).
To find the domain of f o g(x), we need to consider two things: the domain of f(x) and the domain of g(x), and find their intersection.
The function f(x) = 1/(x-2) has a restricted domain because the denominator cannot be equal to zero. Thus, x-2 ≠ 0, which means x ≠ 2. So the domain of f(x) is all real numbers except x = 2.
The function g(x) = √(x+4) involves taking the square root of a real number. For the square root to be defined, the expression inside the radical (x+4) must be non-negative. Therefore, x+4 ≥ 0, which implies x ≥ -4. Hence, the domain of g(x) is all real numbers greater than or equal to -4.
To find the domain of f o g(x), we need to find the intersection of the domains of f(x) and g(x). Since f(x) cannot have x = 2 and g(x) must have x ≥ -4, the domain of f o g(x) is the set of real numbers greater than or equal to -4, excluding x = 2. In interval notation, the domain can be expressed as (-∞, -4] ∪ (-4, 2) ∪ (2, +∞).
Learn more about restricted domain here:
https://brainly.com/question/15091744
#SPJ11
State the property that justifies the statement.
If 4x-5=x+12, then 4x=x+17.
The property that justifies the statement is the addition property of equality.
Stating the property that justifies the statementFrom the question, we have the following parameters that can be used in our computation:
If 4x - 5 = x + 12, then 4x = x + 17.
From the above, we add 5 to both sides of the equation
So, we have
4x = x + 12 + 5
Evaluate
4x = x + 17
This means that the property is the addition property of equality.
Read more about expression at
https://brainly.com/question/31819389
#SPJ4
