The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system, if it exists.
The solution to the system of linear equations, would be :
x = -1 - zy = - 4 - 4 zz = zHow to find the solution ?We can rewrite the system of linear equations to be:
x + 0 y + z = - 1
0 x + y + 4 z = - 4
0x + 0y + 0z = 0
The simple version is:
x + z = -1
y + 4z = -4
0 = 0
Therefore, the solution can be written as:
x = -1 - z
y = -4 - 4z
z = z
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Mia hired a moving company. The company charged $500 or its services, and Mia gives the movers a 16% tip.
Answer:
The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580
Step-by-step explanation:
How many deciliters are in 12 decaliters?
1,200 deciliters
120 deciliters
0.12 deciliters
0.012 deciliters
cual va en los espacios
The function value of f(f(7)) is -13.
We have,
x 9 -11 7 11 -6 -13
f(x) 11 4 -6 -1 -15 -5
From the table,
Using the given table, we can see that:
f(93) is not in the list of x values, so we cannot find its inverse.
Therefore,
We cannot evaluate [tex]f^{-1}(f(93)).[/tex]
f(7) is in the list of x values, and its corresponding function value is f(7) = -6. Therefore,
We can evaluate f(f(7)) by finding the function value corresponding to -6.
i.e
f(-6) = -13
Now,
The function value of f(f(7)).
= f(-6)
= -13
Thus,
The function value of f(f(7)) is -13.
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3. When kx³ + x² - 5x -5 is divided by x + 1, its remainder is 0. Hence, the value of k is?
Answer:
k = 1
Step-by-step explanation:
given a polynomial f(x) divided by (x + h) with a remainder of 0 , then (x + h) is a factor of f(x) and f(- h) = 0
here the polynomial is divided by (x + 1)
then substitute x = - 1 into the polynomial and equate to zero
k(- 1)³ + (- 1)² - 5(- 1) - 5 = 0
- k + 1 + 5 - 5 = 0
- k + 1 = 0 ( subtract 1 from both sides )
- k = - 1 ( multiply both sides by - 1 )
k = 1
Help a girl out
Use your brain powers
Triangle GHI is similar to triangle SQR. Therefore, option A and E are correct answers.
Given that, in triangle GHI, ∠G=104°, ∠H=45° and ∠I=31°.
In triangle QRS, ∠Q=45°, ∠R=31° and ∠S=104°.
In triangle XYZ, ∠X=104°, ∠Y=45° and ∠Z=31°.
Consider triangle GHI and triangle QRS
∠G=∠S=104°
∠H=∠Q=45°
∠I=∠R=31°
ΔGHI is similar to ΔSQR
Consider triangle XYZ and triangle QRS
∠X=∠S=104°
∠Z=∠Q=45°
∠Y=∠R=31°
ΔXYZ is similar to ΔSRQ
Consider triangle XYZ and triangle GHI
∠X=∠G=104°
∠Z=∠H=45°
∠Y=∠I=31°
ΔXYZ is similar to ΔGIH
Therefore, option A and E are correct answers.
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Samantha stores all of her important paperwork in the file cabinet shown below.
A locker measurement at the bottom as 2 one by 6 ft 2, side as 1 and a half ft, and length as 2 2 by 3 ft.
*Picture not drawn to scale
What is the volume of the file cabinet?
A.
7 2/9
cu ft
B.
6 1/12
cu ft
C.
4 1/36
cu ft
D.
2 17/24
cu ft
The volume of the file cabinet in this problem is given as follows:
V = 8 and 7/10 cu ft.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The dimensions for this problem are given as follows:
2.167 ft, 1.5 ft and 2.67 ft.
Hence the volume of the prism is given as follows:
V = 2.167 x 1.5 x 2.67
V = 8.7 ft³.
As a mixed number, the volume is given as follows:
V = 8 and 7/10 cu ft.
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In ABC, AB = 24.1, AC = 15.7, and BC = 25.3. What is LA?
The measure of angle A in triangle ABC is approximately 113.8 degrees.
To find the measure of angle A (LA) in triangle ABC, we can use the Law of Cosines:
c² = a² + b² - 2ab*cos(C)
where c is the length of the side opposite to angle C, and a and b are the lengths of the other two sides.
In this case, we want to find LA, which is opposite to side a (BC). So we can rewrite the Law of Cosines as:
cos(A) = (b² + c² - a²) / 2bc
Plugging in the values we have:
cos(A) = (24.1² + 15.7² - 25.3²) / (2 * 24.1 * 15.7)
cos(A) = -0.3694
Now we need to find the inverse cosine (cos⁻¹) of -0.3694 to get the measure of angle A:
A = cos⁻¹(-0.3694)
Using a calculator, we get:
A ≈ 113.8 degrees
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Help pldssssssss………………..
The missing value for the quadratic function is given as follows:
y = -3.
How to obtain the quadratic function?As a function of it's roots x* and x**, the quadratic function is defined as follows:
y = a(x - x*)(x - x**)
In which a is the leading coefficient.
The roots of the function are the values of x when y = 0, hence:
x* = -4, x** = -2.
Thus:
y = a(x + 4)(x + 2)
y = a(x² + 6x + 8).
When x = 0, y = -8, hence the leading coefficient a of the function is given as follows:
8a = -8
a = -1.
Hence:
y = -x² - 6x - 8;
The missing value is the value of y when x = -1, hence:
y = -(-1)² - 6(-1) - 8
y = -3.
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When cooking rice, the grain is 1/2 of the part to water. Write the ratio that represents this.
• Rice:Water = 2:1
Water:Ratio = 1:2
Rice:Water = 1:2
I need assistance please.
Your Assignment
Mr. Paulsen challenges Olivia and Angelica to move figure ABCDE onto figure A"B"C"D"E" using a series of two different transformations. They give two different answers.
Answer the questions to investigate ways to transform ABCDE.
1. Olivia finds a combination of two different transformations that moves ABCDE onto A"B"C"D"E". What is one way she might have done this? (3 points)
2. Angelica reflects ABCDE over the y-axis and translates it up 8 units. Does her transformed figure match A"B"C"D"E"? If not, describe how her transformed figure compares to A"B"C"D"E". (3 points)
3. Michael says he can move ABCDE onto A"B"C"D"E" with one transformation by translating ABCDE diagonally so that it moves 8 units up and 10 units right. Is he correct? Explain why or why not. (4 points)
One way Olivia might have moved ABCDE onto A"B"C"D"E" is by first reflecting ABCDE over the x-axis, and then translating it 4 units to the left and 6 units down.
1) This would map point A to A", B to B", C to C", D to D", and E to E", creating A"B"C"D"E".
2) Angelica's transformation does not result in a figure that matches A"B"C"D"E". Reflecting ABCDE over the y-axis would map point A to A", B to E", C to D", D to C", and E to B", so the shape would be flipped horizontally. Translating it up 8 units would then shift the shape up, but it would still be horizontally flipped, so it would not match A"B"C"D"E".
3) Michael's claim is not correct. Translating ABCDE diagonally 8 units up and 10 units right would move point A to point J, which is not on A"B"C"D"E". The other points would also not be in their correct positions, so the resulting shape would not match A"B"C"D"E". To get to A"B"C"D"E" with one transformation, Michael would need to use a combination of translation, rotation, and/or reflection.
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Find the value of x
The value of x in the intersecting secants in a circle is 0.5
Finding the value of x in the intersecting secantsFrom the question, we have the following parameters that can be used in our computation:
intersecting secants
Using the theorem of intersecting secants, we have teh following equation
2 * (x + 2) = 1 * (1 + 4)
Evaluating the like terms
So, we have
2 * (x + 2) = 1 * 5
Divide both sides by 2
This gives
x + 2 = 2.5
Evaluating the like terms
So, we have
x = 0.5
Hence, the value of x is 0.5
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Solve the following differential equations:
The general solution to the differential equation based on the information is y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)
How to explain the equationBased on the information, dy/dx + 3y = 2x³ e^(-3x)
The integrating factor is e^(∫3 dx) = e^(3x),
e^(3x) dy/dx + 3e^(3x) y = 2x^3 e^(3x - 3x)
d/dx (e^(3x) y) = 2x^3
e^(3x) y = ∫2x^3 dx = (1/2)x^4 + C
C is an arbitrary constant of integration.
y = (1/2) x^4 e^(-3x) + C e^(-3x)
The equation will be y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)
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prove that the roots of x² + (1 - k)x + k - 3 = 0 are real for all real values of k
We can prove that the quadratic equation x² + (1 - k)x + k - 3 = 0 has two real roots for all real values of k.
How can we prove the quadratic equation?The discriminant of the quadratic equation ax² + bx + c = 0 is given by Δ = b² - 4ac.
If Δ is positive, the equation has two real roots. If Δ is zero, the equation has one real root. If Δ is negative, the equation has two complex roots.
For the given equation, x² + (1 - k)x + k - 3 = 0, we can find the discriminant:
Δ = (1 - k)² - 4(k - 3)
= 1 - 2k + k² - 4k + 12
= k² - 6k + 13
To show that the roots are real for all real values of k, we need to show that Δ ≥ 0 for all k.
Δ = k² - 6k + 13
= (k - 3)² + 4
Since the square of any real number is non-negative, we have (k - 3)² ≥ 0. Therefore, Δ = (k - 3)² + 4 ≥ 4 for all real values of k.
Since Δ is always positive or zero, the quadratic equation x² + (1 - k)x + k - 3 = 0 has two real roots for all real values of k.
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Freezer a has interior dimensions of 1‘ x 1‘ x 5‘ and sells for $499.99 freezer B has interior dimensions of 1.5‘ x 1.5‘ x 4‘ and sells for $149.99 which freezer is a better buy in terms of dollars per cubic foot.
Freezer B is better to buy in terms of dollars per cubic foot.
We have,
Dimensions of Freezer A = 1 ft x 1 ft x 5 ft
Sale price of Freezer A = $499.99
Dimensions of Freezer B = 1.5 ft x 1.5 ft x 4 ft
Sale price of Freezer B = $149.99
Now, Dollars per cubic foot for Freezer A
= (1 x 1 x 5)/ 499.99
= 0.01
and, Dollars per cubic foot for Freezer B
= (1.5 x 1.5 x 4)/ 149.99
= 0.06
Thus, Freezer B is better to buy in terms of dollars per cubic foot.
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GCM for 16 and 32 I- resdy
The Greatest common Factor of 16 and 32 is 16
What is greatest common factor?Greatest common factor is the largest factor that all the numbers share. For example, 12, and 18 have three common factors: 2, 3and 6 the greatest is 6.
Similarly the factors of 16 and 32 are shown below;
factors of 16 are : 2,4,8,16
factors of 32 are : 2,4,8,16,32
The common factors are: 2,4,8,16
and the largest number among the common factors is 16
Therefore the greatest common factor of 16 and 32 is 16
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Offering 100 points to the first person to answer correctly. Need asap - PLEASE!
Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 12x2 − 2xy + 3. The friends have already collected the following number of cans:
Jessa: 3x2
Tyree: 5x2 − 8
Ben: 2xy + 4
Part A: Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work. (5 points)
Part B: Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all your work. (5 points)
An expression that represents the amount of canned food collected so far by the three friends is 8x² + 2xy - 4.
An expression that represents the number of cans the friends still need to collect to meet their goal is 4x² - 4xy + 2.
How to write the required expressions?From the information provided above, we can logically deduce the following number of canned food collection expressions for each friend:
Jessa; 3x²
Tyree: 5x² - 8
Ben: 2xy + 4
Canned food collection goal: 12x² - 2xy - 2
Therefore, an expression that represents the total amount of canned food collected so far by the three friends can be calculated and written as follows;
Total amount collected so far = 3x² + 5x² - 8 + 2xy + 4
Total amount collected so far = 8x² + 2xy - 4
In order to meet the goal, they need to collect this amount:
Remaining canned foods = 12x² - 2xy - 2 - (8x² + 2xy - 4)
Remaining canned foods = 12x² - 2xy - 2 - 8x² - 2xy + 4
Remaining canned foods = 4x² - 4xy + 2
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Identify the pairs of supplementary angles.
Choose all that apply.
A. RQS and SQR
B. SQT and SQR
C. TQP and RQP
D. SQR and RQP
E. PQR and RQP
F. SQT and TQP
G. TQP and PQT
H. SQR and TQP
The pairs of angles that are supplementary angles include the following:
SQT and SQR = Option B
TQP and RQP = Option C
SQR and RQP = Option D
SQT and TQP = Option F
What are supplementary angles?A supplementary angle is the angle that makes up to 180° when both are summed up together.
The angles that are chosen above include the following:
<SQT = 165°
<SQR = 15°
The addition of the both angles = 180°, and therefore is an example of a supplementary angle.
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A store purchases mixing bowls from
the manufacturer for $8 each.
Calculate the sticker price for the
bowls in order to achieve a 60%
gross margin.
A. $13.33
C. $12.00
B. $15.50
D. $20.00
please help find the equations of the following lines
The line equations according to its features are, respectively:
Case C: y = - 2
Case D: x = - 7
Case E: y = - x + 1 / 2
Case F: y = - (1 / 3) · x + 20 / 3
Case G: y = 4 · x + 17
How to determine the equation of lines
In this question we must determine five line equations based on its features. The equation of the line can be found by understanding the following features:
A line can be found by knowing a slope and a point.Two lines are parallel when both lines have the same slope.Two lines are perpendicular when the product of the slopes of both lines is equal to - 1.There are two forms of the equation of the line:
Slope-intercept
y = m · x + k
Standard
a · x + b · y + c = 0
Where:
x - Independent variable.y - Depedent variable.m - Slopek - Intercepta, b, c - Standard coefficients.Now we proceed to determine the equation of each line:
Case C: m = 0, (x, y) = (- 7, - 2)
- 2 = 0 · (- 7) + k
k = - 2
y = - 2
Case D: m = 0, (x, y) = (- 7, - 2)
x = - 7
Case E: k = 1 / 2, m = - 1
y = - x + 1 / 2
Case F: Parallel to x - 3 · y = 9, (x, y) = (2, 6)
x - 3 · y = 9
3 · y = 9 - x
y = 3 - (1 / 3) · x
m = - 1 / 3
6 = - (1 / 3) · 2 + k
6 = - 2 / 3 + k
k = 20 / 3
y = - (1 / 3) · x + 20 / 3
Case G: Perpendicular to y + (1 / 4) · x - 5 = 0, (x, y) = (- 3, 5)
y + (1 / 4) · x - 5 = 0
y = - (1 / 4) · x + 5
m = - 1 / 4
m' = 4
5 = 4 · (- 3) + k
5 = - 12 + k
k = 17
y = 4 · x + 17
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Help!!!! Please
Asap
Answer:
events at A and B are independent because P(A)(B)≠P(A)
Help I need help with this now
The volume of the rectangular prism is 90 units³
We have,
The figure shown has the dimensions:
L = Length = 5 units
W = Width = 6 units
H = Height = 3 units
Now,
The volume of the rectangular prism.
= L x W x H
= 5 x 6 x 3
= 90 units³
Thus,
The volume of the rectangular prism is 90 units³
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PLEASE SOMEONE HELP ME!! ANSWER BELOW
A. The slope of the linear function is given as follows: m = 2.
B. The slope means that the number of races increases by two when the number of track meets increases by one.
C. The y-intercept of 5 means that when there are 5 races when there are 0 track races.
D. The slope-intercept definition of the linear function is given as follows: y = 2x + 5.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the intercept, representing the value of y when x assumes a value of zero.The input and output variables for this problem are given as follows:
Input x: number of track meets.Output y: number of races.Two points in the function are given as follows:
(0,5) and (1,7).
Hence the slope and the intercept are given as follows:
Slope of 2, as when x increases by one, y increases by two.Intercept of 5, as when x = 0, y = 5.Meaning that the function is defined as follows
y = 2x + 5.
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What is one of the stages in Cooley's looking-glass self theory?
O A.
OB.
O C.
O D.
We imagine how we look to other people.
We pretend to be someone else we admire.
We spend time looking at ourselves in the mirror.
We discard past patterns and adapt new ones.
One of the stages in Cooley's looking-glass self theory is A. We imagine how we look to other people.
What is Cooley's theory ?As per Cooley's theory, our self-concept is shaped through a social interchange in which we envision how others perceive us, evaluate that perception and then deliberate on how those assessments influence our self-esteem.
All these components are part of the "looking-glass self" process, consisting of three stages: 1) fantasising about how one appears to others 2) pondering over the judgments made based on appearance and 3) evolution of the self-image influenced by such judgements. Notably, imagining one's outward persona forms an integral element of this psychological principle.
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Helpppp
A desktop is shaped like a semicircle with a diameter of 28 inches. What is the area of the desktop? Round your answer to the nearest square inch, if necessary
The area of the desktop is 307.72 square inches.
What is the area of the desktop?Remember that the area of a semicircle of radius R is given by the formula:
A = (pi/2)*R²
Where pi = 3.14
Here we know that the diameter is 28 inches, then the radius is:
R = 28in/2 = 14 inches
Replacing that in the formula for the area we will get:
A= (3.14/2)*(14 in)²
A = 307.72 in²
That is the area of the desktop.
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An educational researcher devised a wooden toy assembly project to test learning in 6-year-olds. The time in seconds to assemble the project was noted, and the toy was disassembled out of the child's sight. Then the child was given the task to repeat. The researcher would conclude that learning occurred if the mean of the second assembly times was less than the mean of the first assembly times.
Find the 99% confidence interval for the difference in means.
Child
2
3
4
Trial 1
108 140
154
115
Trial 2
99
118 154
96
5
130
108
107
102
110
0 0.7
0-07<4-4 < 23.5
0-29
O 29
Offering 100 points to the first correct answer. Need ASAP - Please!!
The lengths of two sides of a triangle are shown.
Side 1: 8x2 − 5x − 2
Side 2: 7x − x2 + 3
The perimeter of the triangle is 4x3 − 3x2 + 2x − 6.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (4 points)
Part B: What is the length of the third side of the triangle? Show your work. (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)
Te polynomials are closed under addition and subtraction
What is the total length of the two sides, 1 and 2, of the triangle?This is calculated as
Length 1 and 2 = 8x^2 − 5x − 2 + 7x − x^2 + 3
Evaluate
Length 1 and 2 = 7x^2 + 2x + 1
What is the length of the third side of the triangle?This is calculated as
Third side = Perimeter - Length 1 and 2
So, we have
Third side = 4x^3 − 3x^2 + 2x − 6 - 7x^2 - 2x - 1
Evaluate
Third side = 4x^3 − 10x^2 − 7
Polynomials are closed under addition and subtraction?Yes, the answers for Part A and Part B show that the polynomials are closed under addition and subtraction
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Homework part2 need help asap
The key features of the given quadratic functions are listed below.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.
For the quadratic function y = 3x² - 5, the key features are as follows;
Axis of symmetry: x = 0.
Vertex: (0, -5).
Domain: [-∞, ∞]
Range: [-5, ∞]
For the quadratic function y = -2x² + 12x - 15, the key features are as follows;
Axis of symmetry: x = 3.
Vertex: (3, 3).
Domain: [-∞, ∞]
Range: [-∞, 3]
For the quadratic function y = -x² + 1, the key features are as follows;
Axis of symmetry: x = 0.
Vertex: (0, 1).
Domain: [-∞, ∞]
Range: [-∞, 1]
For the quadratic function y = 2x² - 16x + 30, the key features are as follows;
Axis of symmetry: x = 4.
Vertex: (4, -2).
Domain: [-∞, ∞]
Range: [-2, ∞]
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When cooking rice, the grain is 1/2 of the part to water. Write the ratio that represents this.
• Rice:Water = 2:1
Water:Ratio = 1:2
Rice:Water = 1:2
Answer:
Rice:Water = 1:2
Step-by-step explanation:
Someone help me do this ols
The values of the variables x and y for the cyclic quadrilateral are 9 and 17 respectively.
How to evaluate for the variables in the cyclic quadrilateralThe figure is a cyclic quadrilateral since it four side vertices lie on the circumference of the circle. The sum of the interior angles of a cyclic quadrilateral is also 360°. Also opposite angles of a cyclic quadrilateral add up to 180°
Thus;
11x + 8 + 8x + 1 = 180° {opposite angles of a cyclic quadrilateral}
19x + 9 = 180°
19x = 180° - 9 {collect like terms}
19x = 171
x = 171/19
x = 9
Also;
6y - 4 + 5y - 3 = 180°
11y - 7 = 180°
11y = 180 + 7
11y = 187
y = 187/11
y = 17
Therefore, the values of the variables x and y for the cyclic quadrilateral are 9 and 17 respectively.
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