The complete question is:
Create a matrix for this linear system:
what is the solution of the system?
[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]
The solution straight from the matrix as
[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]
[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex]
and z = r
What is the solution of the system?A solution to a system of equations exists a set of values for the variable that satisfy all the equations simultaneously.
Given:
[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]
By applying two more row operations, we get
[tex]$&{\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\2 & 3 & -1 & -2\end{array}\right] R_{2}+(-2) R_{1} \rightarrow R_{2}} \\[/tex]
[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 5 & 3 & -4\end{array}\right] \frac{1}{5} R_{2} \rightarrow R_{2} \\[/tex]
simplifying the above matrix, we get
[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right] R_{1}+R_{2} \rightarrow R_{1} \\[/tex]
[tex]$&\equiv\left[\begin{array}{rrr|r}1 & 0 & -\frac{7}{5} & \frac{1}{5} \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right]$$[/tex]
The solution straight from the matrix as
[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]
[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex] and
z = r
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Please solve quickly
The degenerate conic that is formed when a double cone is sliced at the ap-ex by a plane parallel to the base of the cone is a Point.
What degenerate conic is formed?When a plane that is parallel to the base of a double cone is used to slice the ap-ex, the conic section formed is a circle.
Circles lead to a Point degenerate conic being formed because a single point will be formed on the double cone that separates the shape.
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Give the equation of a line that has
a. no x-intercept
b. one x-intercept and one y-intercept
c. an infinite number of x-intercepts.
d. a y-intercept of -7.
a. x=5
b. y=x
c. y=0
d. y=x-7
A solid right pyramid has a regular hexagonal base with an area of 5.2 cm2 and a height of h cm. a solid right pyramid has a regular hexagonal base with an area of 5.2 centimeters squared and a height of h centimeters. which expression represents the volume of the pyramid?
The calculations show that this pyramid's volume is equivalent to:
5.2h/3 cm3.
What is a pyramid?A polyhedron constructed by joining a polygonal base and a point, is called a pyramid. A lateral face is a triangle formed by the base edge and vertex of each base. Conic solid with a polygonal basis describes it. The number of vertices, faces, and edges on a pyramid with an n-sided base is n + 1.
Given information:Base area = 5.2 [tex]cm^2[/tex].
Height in centimeters is equal to h.
How can the volume of a pyramid be calculated?The following formula is used to determine a pyramid's volume mathematically:
Base area divided by height equals one-third of the volume.
When we enter the parameters into the formula, we get;
Volume = 1/3 *5.2* h
Volume = 5.2h/3 [tex]cm^3.[/tex]
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I understand that the question you are looking for is :
A solid right pyramid has a regular hexagonal base with an area of 5. 2 cm2 and a height of h cm. a solid right pyramid has a regular hexagonal base with an area of 5. 2 centimeters squared and a height of h centimeters. which expression represents the volume of the pyramid? one-fifth(5. 2)h cm3 start fraction 1 over 5 h infraction(5. 2)h cm3 one-third(5. 2)h cm3 start fraction 1 over 3 h infraction(5. 2)h cm3
A submarine is descending to examine the seafloor 2,100 feet below the surface. it takes the submarine 2 hours to make this descent. Write an equation to
represent the relationship between the submarine's elevation and time.
Answer:
Step-by-step explanation:
x = time
y = elevation
At x = 0 , y = 0
It takes the submarine 2 hours to make descent of 2100 ft
=> x = 2 , y = - 2100
Slope = ( -2100 - 0)/(2 - 0) = -1050
y - 0 = -1050 ( x -0)
=> y = -1050x
1050x + y = 0
represent the relationship between the submarine's elevation and time.
Help and get what you want.
Answer:
70°
Step-by-step explanation:
This is a question on angle properties.
Angle K + 35 + 75 = 180 (Sum of angles in a triangle)
Angle K + 110 = 180
Angle K = 180 - 110 = 70°
Answer:
angle k = [tex]\boxed {70}^\circ[/tex]
Step-by-step explanation:
The angles in a triangle add up to 180°.
∴ ∠k + 75° + 35° = 180°
⇒ ∠k + 110° = 180°
⇒ ∠k = 180° - 110°
⇒ ∠k = 70°
select the graph that correctly represents the following equation. 4x-3y=-1
The graph of the given equation is shown below
Graph of a straight lineFrom the question, we are to determine the graph that represents the given equation
The given equation is
4x - 3y = -1
The graph of the equation is shown below
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2x + 1 = 4x - 19
Solve for x
Answer:
x = 10Step-by-step explanation:
2x + 1 = 4x - 19
Solve for x
2x + 1 = 4x - 19
2x - 4x = -19 - 1
-2x = -20
x = 20 : 2
x = 10
----------------
check
2 * 10 + 1 = 4 * 10 - 19
21 = 21
the answer is good
Answer: [tex]\Large\boxed{x=10}[/tex]
Step-by-step explanation:
2x + 1 = 4x - 19
Add 19 on both sides
2x + 1 +19 = 4x - 19 + 19
2x + 20 = 4x
Subtract 2x on both sides
2x + 20 - 2x = 4x - 2x
20 = 2x
Divide 2 on both sides
20 / 2 = 2x / 2
[tex]\Large\boxed{x=10}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
write the following numbers in p by q form 2.015151515...
Answer:
[tex]\frac{133}{66}[/tex]
Step-by-step explanation:
we require 2 equations with the repeating digits placed after the decimal point.
let x = 2.01515... ( multiply both sides by 10 and 1000 )
10x = 20.1515.... (1)
1000x = 2015.1515... (2)
subtract (1) from (2) thus eliminating the repeating digits
990x = 1995 ( divide both sides by 990 )
x = [tex]\frac{1995}{990}[/tex] = [tex]\frac{133}{66}[/tex] ← in simplest form
can someone pls explain how to do this
The polynomial A is represented as x - 2, making option A the right choice.
In the question, we are asked to find the correct representation of A, when the algebraic expression (x² + x)/(x + 3) can be rewritten as the algebraic expression A + 6/(x + 3), where A is a polynomial.
Thus, we can write an equation,
A + 6/(x + 3) = (x² + x)/(x + 3),
or, A + 6/(x + 3) - 6/(x + 3) = (x² + x)/(x + 3) - 6/(x + 3) {Subtracting 6/(x + 3) from the both sides of the equation}
or, A = (x² + x)/(x + 3) - 6/(x + 3) {Simplifying},
or, A = (x² + x - 6)/(x + 3) {Subtracting the two fractions with the same denominator (x + 3)},
or, A = (x² + 3x - 2x - 6)/(x + 3) {Mid-term factorization},
or, A = {x(x + 3) - 2(x + 3)}/(x + 3) {Taking common},
or, A = {(x - 2)(x + 3)}/(x + 3) {Taking (x + 3) common},
or, A = x - 2 {Cancelling (x + 3) from the numerator and the denominator}.
Thus, the polynomial A is represented as x - 2, making option A the right choice.
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Which of the diagrams below represents the statement "If it is an triangle,
then it has three vertices?
The answer is Figure A.
What is in a triangle?Three sides, three angles, and three vertices make up a triangle. A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property.Triangles are three-sided shapes. The various kinds of triangles go by various names. The angles' size and the sides' length determine the type of triangle (corners). Equilateral, isosceles, and scalene triangles are the three varieties of triangles based on the length of the sides.A triangle is a closed, two-dimensional object with three sides, three angles, and three vertices. A polygon also includes a triangle. Triangle ABC is shown in the image above. Triangles can be found in a variety of everyday objects, such as sandwiches, traffic signs, clothes hangers, and billiards racks.
Given: "If it is an triangle, then it has three vertices.
To find which diagram represents the given statement.
From the first diagram
Triangles have three vertices because they are formed by the intersection of three triangles.
using the second diagram
Three vertices make up the triangle's intersection zone.
Therefore, we cannot infer from the second diagram that a triangle has three vertices.
As a result, figure A represents the stated assertion.
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Carlos went to PetSmart to get his hamster an exercise ball. There was a small one with a 5 inch diameter and a 13 inch ball. How much more space (volume) is in the larger than the smaller? Round to the nearest tenth. (PLEASE ANSWER ASAP)
Given: f(x) = 2x + 5 and g(x) = x² and h(x) = -2x
h(g(f(x))) =
RETRY
X² +
X +
Answer: [tex]-8x^2 -40x-50[/tex]
Step-by-step explanation:
[tex]h(g(f(x))\\\\=h(g(2x+5))\\\\=h((2x+5)^2)\\\\=h(4x^2 +20x+25)\\\\=-2(4x^2 +20x+25)\\\\=-8x^2 -40x-50[/tex]
The value of the composite function h(g(f(x))) = -8x² - 40x - 50.
We have,
To find the composition h(g(f(x))), we need to substitute the function g(f(x)) into h(x) and simplify.
Given:
f(x) = 2x + 5
g(x) = x²
h(x) = -2x
First, we find g(f(x)) by substituting f(x) into g(x):
g(f(x)) = g(2x + 5) = (2x + 5)² = (2x + 5)(2x + 5) = 4x² + 20x + 25
Now, we substitute g(f(x)) into h(x):
h(g(f(x))) = h(4x² + 20x + 25) = -2(4x² + 20x + 25) = -8x² - 40x - 50
Therefore,
The value of the composite function h(g(f(x))) = -8x² - 40x - 50.
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The square below has an area of 1+ 2x + x² square meters.
What expression represents the length of one side of the square?
Side length
1+2x+x²
Side length
www
meters
Answer:
1 + x meters.
Step-by-step explanation:
A square has 4 equal sides so each side will have a length equal to the square root of the area.
Side length = √(1 + 2x + x^2)
= √(1 + x)(1 + x)
= 1 + x.
Anne can make 6 headbands 3/5 from meters of cloth. Which expression shows the amount of cloth needed to make 1 headband? What is the solution to the expression?
The amount of cloth needed to make 1 headband is 10 meters.
Unit valueNumber of headbands Anne made = 6Total clothes used = 3/5 metersCloth needed to make 1 headband = Number of headbands Anne made / Total clothes used
= 6 ÷ 3/5
= 6 × 5/3
= (6 × 5) / 3
= 30/3
= 10 meters
Therefore, the amount of cloth needed to make 1 headband is 10 meters.
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9) In the standard co-ordinate system, which of the following points in the greatest distance from origin? A. (-4, -1) B. (-3, 3) C. (4,0) D. (2, 3)
The point with the greatest distance to the origin is given by:
B. (-3, 3).
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The origin is given by point (0,0), hence the distance of a point (x,y) to the origin is given by:
D = sqrt(x² + y²).
Hence the distances for each point given in the problem are:
A. Distance = sqrt((-4)² + (-1)²) = sqrt(17).B. Distance = sqrt((-3)² + (3)²) = sqrt(18).C. Distance = sqrt((4)² + 0²) = sqrt(16).D. Distance = sqrt((2)² + 3²) = sqrt(13).Hence option B has the greatest distance.
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PLS HELP ASAP.........
Answer:
Step-by-step explanation:
Because there is sound and a tune that plays again anytime people are shown having fun at the carnival, the Kit Kat commercial is effective. When the sound is silenced, the commercial's lyrics will come to the viewer's thoughts without any further thought.
Is the given point interior, exterior, or on the circle (x 2)2 (y - 3)2 = 81? p(8, 4) click on the graphic to choose the correct answer.
From the equation we see that the center of the circle is at (-2,3) and the radius is 9.
So using the distance formula we can see if the distance from the center to the point (8,4) is 9 units from the center of the circle...
d^2=(8--2)^2+(4-3)^2 and d^2=r^2=81 so
81=10^2+1^2
81=101 which is not true...
So the point (8,4) is √101≈10.05 units away from the center, which is greater than the radius of the circle.
Thus the point lies outside or on the exterior of the circle...
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5x + 1 over 2 y2
What is the value of the expression above when x = 3 and y = 2?
The table below shows the depth of water in a bathtub as it is being filled over time. The data can be modeled by a linear equation where x is the elapsed time in minutes and y is the depth of the water in inches. What does the y-intercept of the linear equation that models the data indicate?
In the linear equation, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.
What is the Y-intercept of a Linear equation?A linear equation is modelled in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept of the equation, which is the initial value of y when x is zero.
Using two pair of points from the table, say, (1, 3) and (2, 5), find the slope (m) of the linear equation:
Slope (m) = change in y / change in x = (5 - 3)/(2 - 1)
Slope (m) = 2/1
Slope (m) = 2
To find the y-intercept (b), substitute (x, y) = (1, 3) and m = 2 into y = mx + b
3 = 1(2) + b
3 = 2 + b
Subtract 2 from both sides
3 - 2 = 2 + b - 2
1 = b
b = 1
Thus, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.
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Kamden is a mind-reading alien. He had each friend draw and look at a card, then he guessed whether the card had a star on it.
The two-way frequency table below shows data on guess and true status of the cards the friends drew.
Complete the following two-way table of column relative frequencies.
The completed table will have values filled into it accordingly from left to right and the downwards.
What values are required to complete the table?The concept of relative frequencies involves expressing the frequency of occurrence of events as a fraction of a whole frequency.
Hence, it follows that the blank space on the top-leftmost corner of the table can be filled with the value; 4/5 = 0.8.
For the top-rightmost blank space in the table, the required value is; 2/754 = 0.0027.
For the bottom-leftmost blank space, the required value to fill the table is; 1/5 = 0.2.
For the bottom-rightmost blank space, the required value is; 752/754 = 0.9973.
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the titanic had about half as many plates as they did pieces of silverware . About how many plates did they have ?
Answer:
about 1800 im sorry if im wrong
Step-by-step explanation:
Sorry, I’m in kind of a rush, could you guys explain this to me? Thank you so much!!!
35. Lucas and Jacob can paint a house in 1 hour
working together. If Jacob works alone, he can
paint the house in 1.5 hours. How long would
it take Lucas to complete the job on his own?
E. 1 hour
F. 1.5 hours
G. 2 hours
H. 3 hours
The time it will take Lucas to paint the house using rate is 3 hours
How to find the how long it take Lucas to paint the house using rate?They both paint the same house.
Lucas and Jacob can paint a house in 1 hour working together.
Jacob works alone, he can paint the house in 1.5 hours.
Therefore, the time it will take Lucas to paint the house using rate is as follows:
let
x = time it will take Lucas to paint the house
1 / 1 = 1 / x + 1 / 1.5
1 = 1.5 + x / 1.5x
cross multiply
1.5x = 1.5 + x
1.5x - x = 1.5
0.5x = 1.5
divide both sides by 0.5
x = 1.5 / 0.5
x = 3
Therefore, the time it will take Lucas to pain the house is 3 hours.
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how does math connect to animation?
Answer:
Math allows the animator to find the unknowns from a set of equations and to work out the aspects of the geometric figures when dealing with the objects that move and change.
Step-by-step explanation:
To learn more:
weusemath.org/?career=animator
Hope this helps!
Solve the following question
Considering that a fraction is not defined when the denominator is zero, the equation is not defined for an angle of 90º.
When is a fraction not defined?A fraction is not defined when the denominator is zero.
In this problem, the expression is given by:
cos(θ)/(1 - sin(θ)) + cos(θ)/(1 + sin(θ)) = 4.
The denominators are zero in two cases:
1 - sin(θ) = 0 -> sin(θ) = 1 -> θ = 90º.1 + sin(θ) = 0 -> sin(θ) = -1 -> θ = 270º.Hence the equation is not defined for an angle of 90º.
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need some help, please
Answer:
c = 15
Step-by-step explanation:
expand the left side and compare with like terms on the right side
2x(4x + 5) + 3(4x + 5) ← distribute parenthesis
= 8x² + 10x + 12x + 15 ← collect like terms
= 8x² + 22x + 15
compare to ax² + bx + c
then c = 15
Design an experiment that you could conduct in any branch of earth science. identify the independent variable and dependent variable. what safety precautions would you have to take?
Earth science is made of many branches of knowledge concerning all aspects of the Earth system. The main branches are geology, meteorology, climatology, oceanography, and environmental science. Astronomy uses principles understood from Earth to learn about the solar system, galaxy, and universe.
Overview of Earth Science:Only recently have humans begun to understand the complexity of our planet Earth. We have only known for a few hundred years that Earth is just a tiny part of an enormous galaxy, which in turn is a tiny part of an even greater universe.
An important component of experiments is the different variables involved. A variable is any parameter in the experiment that can change. This could be a parameter like temperature, weight or height, or it could be more complex, such as life expectancy or growth rate. Depending on how you set up your experiment, you will use different kinds of variables. There are three basic types to be familiar with.
Independent variable:The first type is the independent variable. This is the variable that is manipulated during an experiment. For example, when experimenting with how fertilisers affects plant growth, the fertiliser is the independent variable because this is the variable that you change. It might help to think of the independent variable as the cause of change in the experiment.
Dependent variable:In contrast to this, the dependent variable is the variable that is affected during an experiment. In our experiment, our dependent variable would be plant growth since this is affected by the amount of fertiliser applied. If you think of the independent variable as the cause, then the dependent variable is the effect.
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Can someone help me? And possibley tell me how to solve this as well? I'm totally clueless haha
Answer:
3
Step-by-step explanation:
-2 * 3= -6
-1 * 3= -3
0 *3= 0
1 *3 = 3
2* 3 = 6
3 * 3 =9
Answer:
? = 3
Step-by-step explanation:
To find the value of ?, substitute one of the ordered pairs from the table [except (0, 0)] into the given formula and solve for ?.
Given formula:
[tex]\sf y=\boxed{?} \:x[/tex]
Substitute x = 1 and y = 3 into the formula:
[tex]\sf 3=\boxed{?} \:1[/tex]
To isolate ? divide both sides by 1:
[tex]\implies \sf \dfrac{3}{1}=\dfrac{\boxed{?} \:1}{1}[/tex]
[tex]\implies \sf 3=\boxed{?}[/tex]
Therefore, ? = 3:
[tex]\implies \sf y=3x[/tex]
Check by inputting another value of x from the table into the found formula and comparing the calculated y-value:
[tex]\sf x=-2 \implies y=3(-2)=-6 \quad \boxed{\sf correct}[/tex]
[tex]\sf x=3 \implies y=3(3)=9 \quad \boxed{\sf correct}[/tex]
A circle's diameter has endpoints at
(-4,-7) and (5,-2).
a) What is the length of the diameter?
b) What is the length of the radius?
Part (a)
We'll use the distance formula.
[tex](x_1,y_1) = (-4,-7) \text{ and } (x_2, y_2) = (5,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-5)^2 + (-7-(-2))^2}\\\\d = \sqrt{(-4-5)^2 + (-7+2)^2}\\\\d = \sqrt{(-9)^2 + (-5)^2}\\\\d = \sqrt{81 + 25}\\\\d = \sqrt{106}\\\\d \approx 10.2956\\\\[/tex]
The diameter is exactly [tex]\sqrt{106}[/tex] units long which approximates to roughly 10.2956 units. Round that decimal value however your teacher instructs.
========================================================
Part (b)
We divide the diameter in half to get the radius.
Therefore, the radius is exactly [tex]\frac{\sqrt{106}}{2}[/tex] units long which is approximately 5.1478 units.
Aakash has a fever. His body temperature during the day was 99.2°F. By evening, his body temperature has increased by 3.4°F.
His body temperature in the evening is
°F.
Given that, Aakash has a fever, if his body temperature during the day was 99.2°F and by evening his body temperature has increased by 3.4°F, Aakash's body temperature in the evening is 102.6° Fahrenheit.
What is Aakash body temperature in the evening?The body temperature is simply a measure of how well a human body can produce and get rid of heat. the normal body temperature is or 37 degrees Celsius or 98.6 degrees Fahrenheit.
Given the data in the question;
Body temperature during the day = 99.2° FahrenheitTemperature Increase = 3.4° Fahrenheit Body temperature in the evening = ?To get Aakash body temperature in the evening, we simply add the initial body temperature and the the temperature increase.
Temperature in the evening = 99.2° Fahrenheit + 3.4° Fahrenheit
Temperature in the evening = 102.6° Fahrenheit
Given that, Aakash has a fever, if his body temperature during the day was 99.2°F and by evening his body temperature has increased by 3.4°F, Aakash's body temperature in the evening is 102.6° Fahrenheit.
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Graph. (Shade. Dashed line. Solid line?)
x+3y≥3
Answer:
Since the graph looks like this, I would say solid line