The augmented matrix is,
[tex]\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)[/tex]
We have given system of linear equation is,
[tex]x - y - 4z = 5,2x + 2z = 0 ,4x +y +z = 3.[/tex]
What is the meaning of augmented matrix?In an augmented matrix, each row represents one equation in the system and each column represents coefficients (with signs) of variables or the constant terms.
So, the first row is
[tex]1\ -1\ -4\ 5[/tex]
the second row is
[tex]2\ 0\ 2\ 0[/tex]
and the third row is
[tex]4\ 1\ 1\ 3[/tex]
Therefore the augmented matrix for this linear system is,
[tex]\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)[/tex]
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The augmented matrix for the given linear equations will be constructed as follows
[tex]\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right][/tex]
What will be the augmented matrix of the given linear equations?The augmented matrix is generally a matrix form of the given linear equations and the coefficient of the variables are arranged in the form of a matrix.
The given equation has three variables so the matrix form will be of [tex]3\times3[/tex]
The given linear equations are
[tex]x-y-4z=5\\2x+0y+2z=0\\4x+y+z=3[/tex]
From the above equations, we will make an augmented matrix.
[tex]\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right][/tex]
The first equation will be followed by the first row of the matrix and the rest will be followed the same.
Thus the augmented matrix for the given linear equations will be constructed as follows
[tex]\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right][/tex]
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Which transformation would make the quadratic parent function narrower and shift it down 5?
g(x) = 3x² - 5
g(x) = 10x² + 5
g(x) = 1/2x² - 5
g(x) = 1/3x² + 5
Answer:
(a) 3x² -5
Step-by-step explanation:
The shift down is accomplished by subtracting 5 from the function value. (Eliminates choices B and D.) The function graph is made narrower by a vertical expansion or a horizontal compression. Either way, the coefficient of the x² term will be greater than 1. (Eliminates choice C.)
The transformed function g(x) = 3x² -5 will be narrower and shifted down from the parent function.
Which method is the best way to solve the system shown below? 3x + 4y = 12 3x - 4y = 5
Answer:
[tex]3x + 4y = 12 \\ 3x - 4y = 5 \\ 6x = 17 \\ x = \frac{17}{6} \\ 3 \times \frac{17}{5} - 4y = 5 \\ 51 \div 5 - 4y = 5 \\ \\ 10.2 - 5 = 4y \\ y = \frac{5.2}{4} [/tex]
Helllp X _____ X
What Is : The Smallest Perfect number
Answer : 6
Explanation : 6 Is The Smallest Number Which Is The Sum Of 1, 2, And 3. Other Perfect Numbers Are 28, 496, And 8,128.
Answer: 6
Step-by-step explanation: is A Perfect Number
_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Mitchell’s cell phone provider’s phone line is busy 80% of the time. In 12 calls, what is the probability that it will be busy at least 10 times?
Answer:
Step-by-step explanation:
Binomial distribution: [tex]X \sim B(n,p)[/tex]
where n is the number and p is the probability
Given:
n = 12p = 0.8[tex]X \sim B(12,0.8)[/tex]
P(X ≥ 10) = 1 - P(X ≤ 9)
= 1 - 0.4416542515...
= 0.5583 (4 dp)
Given the circle with the equation (X - 32 + y2 = 49, determine the location of each point with respect to the graph of the
circle. In your final answer, state whether each point is on the Interior, exterior, or circumference of the circle. Include
your calculations as proof of each point's location.
A. (-1,1)
B. (10,0)
C. (4, -8)
Answer:
To find out if a point is inside, on, or outside a circle, we need to substitute the ordered pair into the equation of the circle:
(x-xc)^2+(y-yc)^2=r^2
where (xc,yc) is the centre of the circle, and r=radius of the circle.
If the left-hand side [(x-xc)^2+(y-yc)^2] is less than r^2, then point (x,y) is INSIDE the circle. If the left-hand side is equal to r^2, the point is ON the circle.
Finally, if the left-hand side is greater than r^2, the point is OUTSIDE the circle.
For the given problem, we have xc=3, yc=0, or centre at (3,0), r=sqrt(49)=7
(x-xc)^2+(y-yc)^2=r^2 => (x-3)^2+y^2=7^2
A. (-1,1),
(x-3)^2+y^2=7^2 => (-1-3)^2+1^2=16+1=17 <49 [inside circle]
B. (10,0)
(x-3)^2+y^2=7^2 => (10-3)^2+0^2=49+0=49 [on circle]
C. (4,-8)
(x-3)^2+y^2=7^2 => (4-3)^2+(-8)^2=1+64=65 > 49 [outside circle]
Step-by-step explanation:
A town doubles its size every 60 years. If the population is currently 1,100, what will the population be in 180 years ?
Answer: The population would be a total of 8,800 people.
Step-by-step explanation: Currently speaking, a town's population is 1,100 people in total. Since it doubles every 60 years, it would double 3 times in total, because 180 / 60 equals 3. 2 x 1,100, then 2 x 2,200, and then 2x 4,400, gives you 8,800.
Have a great day! :)
The graphs of y=f(x) and y=g(x) are shown.
indicate whether each statement about these graphs is true or false
Answer:
i think it it false, true, false
hope that's right lol
Step-by-step explanation:
PLEAS HELP ILL GIVE YOU 100 POINTSS!! NEED BY SUNDAY
1) Which of the following methods would be the easiest to use to solve x^2−6=0?
All three methods would be easy and effective.
A. factoring
B. using the quadratic formula
C. isolating the x2 term and finding the square root of both sides
2)Which of the following methods would be the easiest to use to solve x^2−11=0?
A. factoring
B. All three methods would be easy and effective.
C. using the quadratic formula
D. isolating the x2 term and finding the square root of both sides
3) Which of the following methods would be the easiest to use to solve x^2−11=0?
A. factoring
B. All three methods would be easy and effective.
C. using the quadratic formula
D. isolating the x2 term and finding the square root of both sides
4)Which equation would be the best to solve by completing the square?
A. 3x^2+4x=−2
B. x^2 + 11x = 40
C. x^2 = 49
D. x^2 + 10x = 75
Which of the following methods would be the easiest to use to solve x²−6=0?
C. isolating the x² term and finding the square root of both sides.Solution ⤵️[tex] \tt \: {x}^{2} - 6 = 0 \\ \tt {x}^{2} = 6 \\ \tt \: x = \pm \sqrt{6} \\ \tt \: x = - \sqrt{6} , x = \sqrt{6} [/tex]
And done, Solved!
[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
Which of the following methods would be the easiest to use to solve x²−11=0?
D. isolating the x² term and finding the square root of both sides[tex] \tt {x}^{2} - 11 = 0 \\ \tt \: {x}^{2} = 11 \\ \tt \: x = \pm \sqrt{11} \\ \tt \: x = - \sqrt{11} , x = \sqrt{11} [/tex]
[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
Which equation would be the best to solve by completing the square?
The equation in option C will be the best because the constant in the equation is a perfect square root...[tex] \tt {x}^{2} = 49 \\ \tt \: x = \pm7 \\ \tt \: x = - 7, x = 7[/tex]
Which graph represents the function f(x) = 2/x-1 +3
Answer:
Bottom left
Step-by-step explanation:
The limit as x approaches infinity is 3, so there is a horizontal asymptote at 3. So eliminate top left and bottom right.
Also, the fraction 2/(x-1) is undefined when x=1 (since the denominator is 0), so there is a vertical asymptote at x=1. Eliminate top right
So, your answer is the bottom left graph.
evatuate expreeion of the valube 5 (9+d) - 6
Answer:
39 + 5d
Step-by-step explanation:
First multiply 5 by 9 and 5 by d then subtract 6 from 45 (which you get from multiplying 5 by 9) and you get 39 and multiply 5 by d so you get 39 + 5d
let's solve:-
[tex]⇒5(9 + d) - 6(given \: equation) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ⇒by \: bodmas \: rule \: distribute \: 5 \: with \: 9 \: nd \: d \\ \\⇒ 45 + 5d - 6 (subtracting \: like \: terms) \: \: \: \: \: \: \: \: \\ \\⇒ 39 + 5d \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
Angle Pairs (Lines cut by a Transversal)
What are pair relation exists between angle 7 and angle 4? Use the picture as a reference.
_ Alternate Interior Angles
_ Alternate Exterior Angles
_ Same-Side Interior Angles
_ Same-Side Exterior Angles
_ Corresponding Angles
Answer:
same side interior angles
3. What are pair relation exists between angle 7 and angle 4?
Corresponding angles.Explanation :
A pair of angles in which one arm of each angle of a pair is on the same of the transversal and the other arm of the angles of the pair are directed in the same direction are known as Corresponding angles.⠀
From a hot-air balloon, Madison measures a 36^{\circ}
∘
angle of depression to a landmark that’s 785 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.
The balloon’s vertical distance above the ground is 570.3 feet
Angle of elevation and depressionGiven the following parameters
The angle of depression = 36 degrees
Base distance = 785 feet
Requiredvertical distance above the ground (H)
Using the SOH CAH TOA identity
tan 36 = H/785
H = 785tan36
H = 570.3 feet
Hence the balloon’s vertical distance above the ground is 570.3 feet
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At the start of 2014 Lucy's house was worth £200 000
The value of the house increased by 5% every year.
Work out the value of her house at the start of 2017.
Answer:
200000 x 1.05^3=231525
Step-by-step explanation:
X 1.05 because the price is increasing by 5% and ^3 because there are three years between 2014 and 2017
The graph of y = square root of x has been translated to the right 3 units and down 9 units. What is the equation of the translated graph?
A. y = 3 + +9
B. y = 9-3+3
C. y=3-√9 - x
D. y = -9+VT - 3
The translated function is:
g(x) = √(x - 3) - 9
How to find the translation?
The transformations used here are:
Horizontal translation:
For a general function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N).
If N is positive, the shift is to the left.If N is negative, the shift is to the right.Vertical translation:
For a general function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N.
If N is positive, the shift is upwards.If N is negative, the shift is downwards.So, if we have a translation of 3 units right and 9 units down, this would be written as:
g(x) = f(x - 3) - 9
Replacing f(x) by the actual function we get:
g(x) = √(x - 3) - 9
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3 x 107 + 2 x 104 + 1 x 102 + 8 x 10 =
Cuanto es?
doy corona y 11 pts
Answer:
Es 711
Hope this helps!
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Select the point on the number line that best approximates the location of √14
Answer:
between 3 and 4 around 3[tex]\frac{3\\}{4}[/tex]
Answer: 3.5
Step-by-step explanation:
You want to choose two numbers that have perfect roots. One above 14, and one below 14. The nearest two perfect roots to 14 is 9 and 16. We have the following inequality:
[tex]\sqrt{9} < \sqrt{14} < \sqrt{16}[/tex]
[tex]3 < \sqrt{14} < 4[/tex]
This means the square root of 14 is somewhere between 3 and 4. A good estimate would be 3.5
The measurements of two sides of a triangular playground are 24 feet and 30 feet. Which length could be the measurement of the third side of the triangular playground?
Answer: 7 feet
Step-by-step explanation: I did it trust
The length measurement of the third side of the triangular playground whose two sides are 24 ft and 30 ft long should be more than 6 but less than 54.
What is triangle inequality theorem?
Triangle inequality theorem of a triangle says that the sum of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
(a+b)>c
(b+c)>a
(c+a)>b
There is a triangular playground. The measurements of two sides of a triangular playground are 24 feet and 30 feet.
Suppose the length of the measurement of the third side of the triangular playground is c meters.
As the two sides are 24 ft and 30 ft long. Thus, by the triangle inequality theorem,
[tex]24+30 > c\\54 > c[/tex]
For the sides 24 ft and c ft,
[tex]24+c > 30\\c > 30-24\\c > 6[/tex]
Thus, the length measurement of the third side of the triangular playground whose two sides are 24 ft and 30 ft long should be more than 6 but less than 54.
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15. Which of the following is a composite number?
O A. 1
O B. 63
O C. 19
O D.O
Answer:
The answer is B.63
Explanation:
63 is a composite number because a composite numbers is any positive number which is not a "prime number"
(will mark brainliest to whoever responds!) PLEASE HELP ME OUT :)
Answer:
Step 3 is wrong
Step-by-step explanation:
[tex]x_1=\frac{-\left(-6\right)+14}{2\cdot \:5},\:x_2=\frac{-\left(-6\right)-14}{2\cdot \:5}[/tex]
is how she shouldve put it in
what is -12/5+|- 13/6| + (-3 2/3)
Answer: -39/10 alternative forms : -3 9/10, -3.9
Step-by-step explanation:
Which choice gives a reasonable explanation why Mona bought an item using credit .
A.Mona wants to pay interest on her purchase,
B.Mona wanted to earn interest on her purchase
C.The item cost more than Mona was able to pay
D.Mo
na had more money than she needed. i will give brainliest
Answer:
C The Item cost more than mona was able to pay
Step-by-step explanation:
I took the test
13. Rearrange this formula to make x the subject.
Y=2x/5
Step-by-step explanation:
[tex]y = \frac{2x}{5} [/tex]
crossmultiply
[tex]5y = 2x[/tex]
divide both side by 2, to make x alone
x = 5y / 2
pls give brainliest
Moesha needs 79.50 for a class trip. She already has 22.35 and she can earn the rest by babysitting for 8 hours. write an equation that can be solved to find h, moesha;s hourly earnings
Answer:
79-22=8h
Step-by-step explanation:
hope this helps!
If a trapezoid has an area of 60 m² and bases of 2 m and 6 m, what's its height?
Given :
Base = 2 m and 6 m.Area = 60 m².⠀
To find :
The height.⠀
Solution :
⠀
We know,
[tex]{ \longrightarrow{\qquad \sf{ \pmb {\dfrac{1}{2 } \times (b_{1} + b_{2}) \times h = {Area_{(Trapezoid)} } }}}}[/tex]
⠀
Now, Substituting the values :
⠀
[tex]{ \longrightarrow{\qquad \sf{ {\dfrac{1}{2 } \times (2 + 6) \times h = {60 } }}}}[/tex]
⠀
[tex]{ \longrightarrow{\qquad \sf{ {\dfrac{1}{2 } \times 8 \times h = {60 } }}}}[/tex]
⠀
[tex]{ \longrightarrow{\qquad \sf{ {\dfrac{8}{2 } \times h = {60 } }}}}[/tex]
⠀
[tex]{ \longrightarrow{\qquad \sf{ 4 \times h = {60 } }}}[/tex]
⠀
[tex]{ \longrightarrow{\qquad \sf{ h = { \dfrac{60}{4} } }}}[/tex]
⠀
[tex]{ \longrightarrow{\qquad \sf{ \pmb { h = {15} } }}}[/tex]
⠀
Therefore,
The height of the trapezoid is 15 m .PLEASE HELP ASAP ILL GIVE BRAINLIEST IF YOU SHOW THE STEPS!! You have to look at the picture for the questions!!
Answer:
3. f = gh
4. r = 1/s³
5. y = x[tex]\sqrt{z}[/tex]
6. m = n²/p
7. Inverse variation, s is constant
8. Direct Variation, x is constant
9. joint variation, q and r are both constants
10. Direct variation, r is constant
11. Joint variation, r and h are both constants
12. Inverse variation, x is constant
13. y = kx
17.5 = 21k
k = 21/17.5
y= (21/17.5)*39
y = 46.8
14.
m = kn
209 = 22k
k = 209/22
361 = (209/22)n
n = (361*22)/209
n = 38
Evaluate the expression for the given value of x.
4x + 6 for x = 7
The solution is
The distance from the earth to the moon is 3.84 x 105 km
a) Find this distance in metres.
b) How long would it take a spaceship to travel to the moon from earth if its average speed was 400 ms l?
Part (a)
Answer: [tex]3.84 \times 10^8 \text{ meters}[/tex]---------------------
Explanation:
Multiply by 1000 to go from km to meters.
This is because 1000 m = 1 km.
Multiplying by 1000 in scientific notation means we add 3 to the exponent 5. The 3 is because 1000 = 10^3.
So the [tex]3.84 \times 10^5 \text{ km}[/tex] becomes [tex]3.84 \times 10^8 \text{ meters}[/tex]
===========================================================
Part (b)
Answer in standard form: 960,000 seconds
Answer in scientific notation: [tex]9.6\times10^{5} \text{ seconds}[/tex]
---------------------
Work Shown:
[tex]\text{distance} = \text{rate}*\text{time}\\\\\text{time} = \frac{\text{distance}}{\text{time}}\\\\\text{time} = \frac{3.84 \times 10^8 \text{ meters}}{400 \ \text{ m}/\text{s}}\\\\\text{time} = \frac{3.84 \times 10^8}{4 \times 10^2} \text{ seconds}\\\\\text{time} = \frac{3.84}{4}*\frac{10^{8}}{10^2} \text{ seconds}\\\\\text{time} = 0.96 \times 10^{8-2} \text{ seconds}\\\\\text{time} = 0.96\times 10^{6} \text{ seconds}\\\\[/tex]
[tex]\text{time} = (9.6\times10^{-1})\times10^{6} \text{ seconds}\\\\\text{time} = 9.6\times(10^{-1}*10^{6}) \text{ seconds}\\\\\text{time} = 9.6\times10^{-1+6} \text{ seconds}\\\\\text{time} = 9.6\times10^{5} \text{ seconds}\\\\\text{time} = 960,000 \text{ seconds}\\\\[/tex]
To go from the scientific notation to standard form, move the decimal point 5 spaces to the right. The 5 is from the exponent.
In ABC, the measures of the angles A, B, and C, respectively, are in the ratio 1:6:8. Find the measure of each angle.
Answer:
180/15=12 12x6=72 12x8=96... 12, 72, 96?
What was your dream job as a kid?
Mine was to be a ballerina. Please tell me, I am making a survey for school.
Answer:
Mine was a fashion designer or a model. The model part died out because of my insecurities. But Fashion design is still something I am interested in,
Step-by-step explanation: