Answers
Answer:
[tex]x=(-2,\frac{5}{3} )[/tex]
Step-by-step explanation:
1) We will use the matrix method to solve this problem.
[tex]\left[\begin{array}{ccc}-2/3&1&3\\1&0&-2\\\end{array}\right][/tex]
2) Swap Row₁ and Row₂ to make row reduction easier.
[tex]\left[\begin{array}{ccc}1&0&-2\\-2/3&1&3\\\end{array}\right][/tex]
3) Apply to Row₂ : Row₂ + [tex]\frac{2}{3}[/tex] Row₁.
[tex]\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\end{array}\right][/tex]
4) Simplify rows.
[tex]\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\\\end{array}\right][/tex]
Note: The matrix is now in row echelon form.
The steps below are for back substitution.
5) Apply Row₁ : Row₁ - 0 Row₂.
[tex]\left[\begin{array}{ccc}1&0&-2\0\\0&1&5/3\end{array}\right][/tex]
6) Simplify rows.
[tex]\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\\\end{array}\right][/tex]
Note: The matrix is now in reduced row echelon form.
7) Therefore,
[tex]x=-2\\x=\frac{5}{3}[/tex]
Related Questions
How can you find the coefficients of any row of Pascal’s triangle?
A) combinations
B) factorials
C) expansion
D) binomial expression
Answers
The coefficients of any row of Pascal’s triangle can be calculated using (A) combinations
How to determine the coefficients?A binomial expansion is represented as:
[tex](a + b)^n = ^nC_x a^xb^{n - x}[/tex]
Where:
x >= 0 and x <= n
In the above expression, the coefficient is:
[tex]^nC_x[/tex]
The above represents the xth term of a Pascal triangle and it is a combination expression
Hence, the coefficients of any row of Pascal’s triangle can be calculated using (A) combinations
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What is the solution to this system of equations? x + y = 2 and y - z = -3 and x + y - z = 0
Answers
Answer:
x = 3
y = -1
z = 2
Step-by-step explanation:
if x+y = 2, and x+y-z = 0, then we can substitute 2 for x+y. this means 2-z=0, meaning z=2. if y-z=-3, then y-2=-3, and y=-1. x+y=2 which means x-1=2 so x=3. plug in the values to check your answer.
Asap please!!!!!!! if jkl=rst, which congruences are true by cpctc? check all that apply.
a. l=r
b. jk=rs
c. k=s
d. j=s
e. kl=st
f. jl=rs
Answers
Answer:
b, c e
Step-by-step explanation:
A congruence statement lists corresponding parts in the same order. CPCTC says corresponding parts are congruent.
__
To see if any particular statement is consistent with CPCTC, identify the locations of the referenced parts in the congruence statement. If they match, the congruence is true
a. l = r ... jkl = rst . . . . not in the same place
b. jk = rs ... jkl = rst . . . . a match; true
c. k = s ... jkl = rst . . . . a match; true
d. j = s ... inconsistent with (c)
e. kl = st ... jkl = rst . . . . a match; true
f. jl = rs ... inconsistent with (b)
Statements b, c, e are consistent with the congruence statement, and are true by CPCTC.
Solve the inequality. –6 < 2 x – 4 < 4
Answers
Step-by-step explanation:
-6<2x-4<4
-2<2x<8
-1<x<4
x = (-1,4)
red was rotated to form blue
describe the rotation
Answers
Red was rotated to form blue as the figure was turned in different directions.
What is rotation?
A rotation simply means a transformation that turns a figure about a fixed point called the center of rotation.
An object and its rotation are simply the same shape and size, but the figures may be turned in different directions. In this case, red was rotated to form blue.
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Each x block shown on the scale has the same weight. See if you can answer the question. When you have your answer, enter it in the box below and select Submit to see if you are correct. How Much Does Each "x" Weight Weigh?
Answers
The value of x, given the data From the question is 2
Data obtained from the questionOn the left = 3 + 3xOn the right = 2x + 5Value of x =?How to determine the value of xLeft = Right (since the system is balanced)
3 + 3x = 2x + 5
Collect like terms
3x - 2x = 5 - 3
x = 2
Complete question
See attached photo
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Question 12 of 25
Which of the following values are in the range of the function graphed below?
Check all that apply.
A. -5
B. 3
C. 2
☐D. O
E. 1
F. -3
5
Answers
1 is the values are in the range of the function graphed below. Option E is corect.
What is the difference between domain and range?The domain denotes all potential x values, while the range denotes the domain's possible y values.
The domain is the value of x which lies between the -2 ≤ x ≤ 1.While the range shows the value of y which is equal to 1.
Hence, option E is correct
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Please help!! Consider the equation x/5 -2=11, where x represents the
number of basketball players that have signed up for a
new league. What is a possible scenario that would be
modeled by this equation? Consider how many teams in
the league and the number of players on each team this
equation could describe
Answers
Answer:
x=65
Each NBA team can have a maximum of 15 players, 13 of which can be active each game.
65/5=13 so it's safe to say tgat 5 team can be crated
Step-by-step explanation:
x/5-2=11-->transposing x/5=11+2---->x=13×5--->x=65
verification 65/5-2=11--->13-2=11
Shelby bought 2 cans of paint and 3/4 of a pint of special paint additive formulated to reduce mildew. Before painting her house, she divided the additive equally between the 2 cans of paint. How much additive did she put in each can?
Answers
A(n)______ is a number sentence that shows how two or more expressions are not equal
Answers
Answer:
Inequality is the answer
Answer: Inequality ✅
Step-by-step explanation:
Hii, do you need to know the answer to your question? No problem!
The answer to your question is "inequality".
An inequality is a number sentence that shows how two or more expressions are not equal.
An example of that is [tex]\sf 4x+4\geqslant3x-5[/tex].
So 4x+4 is greater than or equal to 3x-5, but they're not 100% equal (such is the case in equations).
--
Hope that this helped! Best wishes.
--
(5+4) +10=5+(4+10)
A. True
B. False
Answers
Answer:
A. True
Step-by-step explanation:
One of the ways to check this is solving each side of the equation.
(5+4)+10=5+(4+10)
Remember PEMDAS.
Parenthesis first.
(9)+10=5+(14)
Now, you can drop the parenthesis and add the numbers together.
9+10=19
5+14=19
19=19
This is a true statement.
Hope this helps!
If not, I am sorry.
Match each data set with its standard deviation.
Round your answer to the nearest tenth, if necessary.
Click on the link to use the GeoGebra graphing calculator to assist you.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
{74,76,77,77,78,82,130}
{8,74,76,77,77,78,82}
{74,74,76,77,77,78,82}
Answers
Answer:
don't know but please keep trying up
Figure it out..............................................
Find the midpoint of the segment with the following endpoints. (10, 6) and (4, 9)
Answers
Answer:
(7,7.5)
Step-by-step explanation:
midpoint formula:
(10+4)/2=7
(6+9)/2=7.5
(7,7.5)
Which equation can be used to solve for xxx in the following diagram?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
2x = 4x2x=4x2, x, equals, 4, x
(Choice B)
B
2x + 4x = 1802x+4x=1802, x, plus, 4, x, equals, 180
(Choice C)
C
2x + 4x = 902x+4x=902, x, plus, 4, x, equals, 90
(Choice D)
D
2x + 4x = 1502x+4x=1502, x, plus, 4, x, equals, 150
Answers
The equation that can be used to determine the value of x is Option B.
What is an Equation ?An equation is a mathematical statement formed when two algebraic expression are equated by an equal sign.
From the diagram ,
A straight line has an angle of 180 degree.
Therefore from the figure
To determine the value of x
2x + 4x = 180
6x = 180
x =30 degree
Thus the equation that can be used to determine the value of x is Option B.
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If it is already 110F degrees below zero, and the temperature drops another 40 F degrees, how cold is it now?
Answers
Answer:
-150
or 150 degrees below 0
Step-by-step explanation:
The temp is -110. Dropping another 40 degrees means subtracting 40.
-110 - 40 = -150
In the diagram below, AB is parallel to Co What is the value of y?
Answers
Answer:
D
Step-by-step explanation:
interior angles = 180
180-72
Factor: 117n + 90
Show your work don’t solve for n
Answers
To factor an expression, we can identify common factors between each terms, and take them out.
Solving the Question117n + 90
Both terms have the common factor of 9. Factor this out:
= 9(13n + 10)
13 and 10 do not have a common factor. Therefore, this is the final factored expression.
Answer9(13n + 10)
Which ordered pairs make both inequalities true? Check all that apply
Answers
Answer:.
Step-by-step explanation:
Match each inequality to the number line that represents its solution:
Answers
Step-by-step explanation:
I have solve all the questions and your work is to match with that option
Over a females lifetime, how many eggs will mature and travel to the uterus? 4 hundred thousand 5 hundred 4 hundred 3 hundred thousand
Answers
Over a female lifetime, about 300 hundred to 400 hundred will mature and travel to the uterus
How many eggs reach maturation and transfer to the uterus in a female lifetime?At birth, about 1 million eggs are present but by the period a person reaches adolescence, only about 300,000 are still there since a lot of follicles and oocytes would have been engaged to start the development and maturation process.
Only about three hundred to four hundred of them will ripe and ovulate over a woman's reproductive lifespan due to the decline in a woman's fertility as she matures.
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Examine the following graphs of two functions. Two functions. One is linear passing thru (1, 2), (3, 4), (6,7) and (8, 9). 2nd function is quadratic passing thru (3, 4), (5, 0), (7, 4) & (8, 9). © 2018 StrongMind. Created using GeoGebra. Which two values of x best represent where the two functions are equal? Enter your answer as two numbers, separated by a comma, like this: 1, 2
Answers
The two values of x best represent where the two functions are equal will be (12,11)
What is a graph?
A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
Given data;
Linear function passing through;
(1, 2), (3, 4), (6,7) and (8, 9)
Quadratic function passing through
(3, 4), (5, 0), (7, 4) & (8, 9)
Let x be two values of x best represent where the two functions are equal;
The value of the x is obtained from the graph where the two line meets.
The value of x willl be (12,11)
Hence, the two values of x best represent where the two functions are equal will be (12,11)
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On a piece of paper, graph y-5>2x-10. Then determine which answer
choice matches the graph you drew.
A
B
C
D
(21)
(0.5)
OA. Graph A
B. Graph B
C. Graph C
D. Graph D
(0.5)
((3.1)
(0.5)
(3.1).
(0.5)
Answers
Answer:
Graph B
Step-by-step explanation:
When graphing inequalities:
< or > : draw a dashed line≤ or ≥ : draw a solid line< or ≤ : shade under the line> or ≥ : shade above the lineGiven inequality:
[tex]y-5 > 2x-10[/tex]
Rearrange the given inequality to make y the subject:
[tex]\implies y-5+5 > 2x-10+5[/tex]
[tex]\implies y > 2x-5[/tex]
Therefore, we need to draw a dashed line and shade above it.
To draw the line:
Replace the > with = to find two points on the line:
[tex]\implies y=2x-5[/tex]
[tex]x=0 \implies y=2(0)-5=-5 \implies (0,-5)[/tex]
[tex]x=3 \implies y=2(3)-5=1 \implies (3,1)[/tex]
Plot the two found points: (0, -5) and (3, 1)
As the inequality is y > 2x - 5
Draw a dashed straight line through the two points.Shade above the line.The inequality equation is solved and the solution is plotted on the graph
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
y - 5 > 2x - 10
On simplifying , we get
Adding 5 on both sides , we get
y > 2x - 5
where 2 is the slope and 5 is the the intercept
Now , let the first point be P ( 0 , -5 )
when x = 0 and y = -5
-5 > -5
And , the graph of the inequality is plotted
Hence , the inequality is solved
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fill in the blank
83 x 391 - 83 x ____ = 83 x (391 - 15)
Answers
Answer:
83 x 391 - 83 x 15 = 83 x (391 - 15)
Step-by-step explanation:
BODMAS is stands for Bracket Of Division Multiplication Addition and Subtraction.
left hand side:
83 × 391 - 83 × ____ = 32453 - 83 × ____
right hand side:
83 × (391 - 15) = 83 × 376 = 31208
equating both sides
32453 - 83 × ____ = 31208
32453 - 31208 = 83 × ____
1245 ÷ 83 = 15
hence the answer is 15.
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Use the periodic compound interest formula to solve.
Suppose that $11,000 is invested at 5.8% compounded quarterly. Find the total amount of this investment after 6 years.
Answers
Answer:
$15,539.67
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $11,000r = 5.8% = 0.058n = 4 (quarterly)t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=11000\left(1+\frac{0.058}{4}\right)^{(4 \times 6)}[/tex]
[tex]\implies \sf A=11000(1.0145)^{24}[/tex]
[tex]\implies \sf A=15539.67451...[/tex]
Therefore, the value of the investment after 6 years will be $15,539.67 to the nearest cent.
choose the graph of the linear equation 30x+75y=300
Answers
Answer:
there ya go :)
factorise 3 squared+ 5x +12
Answers
factorise 3 squared+ 5x +12
A child designs a flag in the shape of a rhombus, as shown in the diagram below. Which expression can be used to determine the side length of the rhombus?
Answers
Using the cosine ratio, the expression that can be used to determine the side length of the given rhombus is: x = 10/cos 30.
What is the Cosine Ratio?The cosine ratio that can be used to solve a right triangle is, cos ∅ = adj/hyp.
x represents the side of the rhombus as shown in the image attached.
Hypotenuse = x Adjacent = 10 in.∅ = 30cos 30 = 10/x
x(cos 30) = 10
x = 10/cos 30
Thus, the equation that would be used to determine the side length is: x = 10/cos 30
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Answer:
A
Step-by-step explanation:
10/cos 30°
How to do proportional relationships in math 7th grade ?? Please explain ?!!
Answers
Answer:
Try searching online
Step-by-step explanation:
go to your browser then search up
How to do proportional relationships in math 7th grade ?? Please explain ?!!
What is the median of the following data set?
(3, 4, 2, 8, 5)
02
03
04
06
Answers
Answer:
4
Step-by-step explanation:
The median is the middle number when the list is sorted from least to greatest or greatest to least.
We make this list to get 2,3,4,5,8 or 8,5,4,3,2 and the middle number in both lists is 4.
Find the following, giving your answers
to 1 decimal place.
10 cm/
6 cm
8 cm
a) The volume of the cone.
b) The curved surface area of the cone.
Answers
Answer:
a) 301.6 cm³
b) 188.5 cm²
Step-by-step explanation:
The volume and lateral surface area of the cone can be found using the given dimensions with the given formulas. All that is needed is to substitute the appropriate values and do the arithmetic.
__
a) volumeThe volume is given by the formula ...
V = 1/3πr²h
The dimensions are given on the diagram: r = 6 cm, h = 8 cm. Using these values in the formula, we find the volume to be ...
V = 1/3π(6 cm)²(8 cm) = 96π cm³ ≈ 301.6 cm³
The volume of the cone is about 301.6 cm³.
__
b) areaThe lateral area of the cone is given by the formula ...
A = πrl
The dimensions are given on the diagram: r = 6 cm, l = 10 cm (the slant height). Using these values in the formula, we find the area to be ...
A = π(6 cm)(10 cm) = 60π cm² ≈ 188.5 cm²
The area of the curved surface is about 188.5 cm².