Answer:
Echelon form of augmented matrix [tex]\left[\begin{matrix} 2&3&-5&b_1\\0&\frac{47}{2} &\frac{101}{2} &b_2-\frac{17}{2}b_1 \\0&0&\frac{-10}{3} &b_3-2\frac{b_1}{6} \end{matrix}\right][/tex]
Step-by-step explanation:
We have, linear systems
[tex]2x_1+3x_2-5x_3=b_1[/tex]
[tex]17x_1+2x_2+8x_3=b_2[/tex]
[tex]-x_1+x_2-5x_3=b_3[/tex]
[tex](a)[/tex] Find the echelon form of the augmented matrix.
Firstly we find the augmented matrix (A) of the given linear system
[tex]A=\left[\begin{matrix} 2&3&-5&b_1\\17&2&8&b_2\\-1&1&-5&b_3\end{matrix}\right][/tex]
Now find the echelon form
[tex]=\left[\begin{matrix} 2&3&-5&b_1\\0&\frac{47}{2} &\frac{101}{2} &b_2-\frac{17}{2}b_1 \\0&\frac{5}{2} &\frac{-15}{2} &b_3+\frac{b_1}{2} \end{matrix}\right]^{R_2\rightarrow \frac{17}{2}R_1, R_3\rightarrow R_3+\frac{1}{2}R_1 }[/tex]
[tex]=\left[\begin{matrix} 2&3&-5&b_1\\0&\frac{47}{2} &\frac{101}{2} &b_2-\frac{17}{2}b_1 \\0&0&\frac{-10}{3} &b_3-2\frac{b_1}{6} \end{matrix}\right]^{R_2\rightarrow R_3-\frac{5}{6}R_1 }[/tex]
[tex](b)[/tex] From above echelon form of augmented matrix system is consistent .
So, system has always a solution exist for every condition of [tex]b_1,b_2, b_3[/tex]
[tex](c)[/tex] Yes, If we take point [tex](0,1,1)[/tex] then system of linear equation has exist a solution.
[tex](d)[/tex] yes, if pick randomly [tex]b_1,b_2, b_3[/tex] then always exist a solution of given system of linear equation.
A file that is 228 megabytes is being downloaded. If the download is 12.4% complete, how many megabytes have been downloaded? Round your answer to the
nearest tenth.
Help find the answer
Answer:
1218
(14x25)x3=1050
because you have three sides
14x12=168 then 168+168=336
then add al together 1050+336=1 386
please help me i will help you if you help me
Answer:
4/115
64/62
Step-by-step explanation:
Since you dont have to simplify, just find the number of each animal then put it over whatever other animal the questions said was treated
Find the supplement of 2/3of a right angle
Answer: supplement is 126 degrees 7
Step-by-step explanation: 2/3 of a right angle = (2/3 * 90) degrees = 60 degrees and its complement is 30 degrees 3/5 of a right angle = (3/5 * 90) degrees = 54 degrees and its is
supplement is 126 degrees 7
Solve.
z + 17 = 9
−9
−8
8
9
eight
Step-by-step explanation:
1. subract 17 -9 and you get
z= -8
-8+17=9
sry about that
Answer: -8
Step-by-step explanation:
To solve this, you would just plug the answers in the equation for Z and see which one makes sense and is accurate.
-8+17=9 is correct
702 miles is how many hours flight
Answer:
It depends on the speed and acceleration of the plane.
But it's approximately 2 hr
Which athletes, if any, would qualify for the finals if the length of a jump that qualifies for the finals were at least 20 feet?
Answer:
Amir and ryan would qualifiey
Step-by-step explanation:
What type of exponential function is f(x)=0.6(2.4)^x?
What is the function's percent rate of change?
Select from the drop-down menus to correctly complete each statement.
The function is an exponential CHOOSE function.
The percent rate of change of the function is CHOOSE%.
Answer:
growth
140%
Step-by-step explanation:
The function f(x) is an exponential growth function as f(x) increases when x increases.
The percent rate of change of the function f(x) is 201.6%.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 0.6 [tex](2.4)^x[/tex]
For x = 1,
f(1) = 0.6 x 2.4 = 1.44
For x = 2,
f(2) = 0.6 x 2.4² = 0.6 x 5.76 = 3.456
For x = 3,
f(3) = 0.6 x 2.4³ = 0.6 x 18.824 = 8.2944
We see that,
As the value of x increases, the value of f(x) increases.
f(x) is an exponential growth function.
Now,
The percentage rate of change of function f(x).
= (f(2) - f(1)) / (2 - 1) x 100
= (3.456 - 1.44) x 100
= 2.016 x 100
= 201.6 %
Thus,
f(x) is an exponential growth function.
f(x) percent rate of change is 201.6%
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If f(x) = 3x – 7 and g(x) = x2 – 5x + 5, then f(x) = g(x) for
what values of x?
a. x = 3 and x = 4
b. X = 6 and x = 2
c. x = -6 and x = -2
d. x = -3 and x = -4
Answer:
b
Step-by-step explanation:
3x - 7 = x² - 5x + 5
x² - 5x + 5 - 3x + 7 = 0
x² - 8x + 12 = 0
(x-6)(x-2)=0
x = 6
x = 2
Suppose x has a distribution with µ = 74 and σ = 8. If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means?
Options :
No, the sample size is too small.
Yes, the x distribution is normal with mean μ x = 66 and σ x = 1.5.
Yes, the x distribution is normal with mean μ x = 66 and σ x = 6.
Yes, the x distribution is normal with mean μ x = 66 and σ x = 0.4.
Answer:
No, the sample size is too small.
Step-by-step explanation:
Given that:
Mean, μ = 74
Standard deviation, σ = 8
Sample size, n = 16
Based on the information given, in other to be able to make inference on the x distribution of sample means, then the size of the sample of utmost importance in statistic. Large sample sizes (usually > 30) gives are always required as sampling distribution conform to the population distribution Inn terms of mean as the sample size grows larger as the distributon becomes approximately normal.
However, the sample size given above is well below 30.hence, making it difficult to say anything about the distribution of sample means
The Johnson family decides to take a trip to the theater over the holiday break. Theater tickets for adults cost $22. Children's tickets cost $15. 11 people went to see the play and the total cost was $228.
Let x= # of adults
Let y = # of children
Part A
Which equation represents the total number of people who went to see the play?
a.11x + 22 = 228
b.y = 15x + 11
c.22x + 15y = 228
d.x + y = 11
Part B
Which equation represents the total cost of the trip to the theater?
a.11x + 22 = 228
b.x + y = 11
c.y = 15x + 11
d.22x + 15y = 228
Answer:
a. 11 people went to see the play. the equation for the number of people who went is x + y = 11 because we don't know how many adults or children.
b. 22 dollars per adult, 15 dollars per child. since we don't know how many kids or how many adults, they're represented by x and y (as shown in part a)
the equation to represent the total cost is 22x + 15y =228 because the total cost to go was 228 and that's the only equation that has both variables and the total cost
Step-by-step explanation:
I hope this helps :))
A robot can complete 3 tasks in 2/5 hour. Each task takes the same amount of time.how long does it take the robot to completely one task?how many tasks can the robot complete in one hour
Answer:
part 1) It takes 2/15 hour to complete 1 task
Part 2) The robot can only complete 7 tasks in an hour (the remaining doens’t count)
Step-by-step explanation:
So first divide to find unit rate
2/5 ÷ 3
2/5 * 1/3
2/15
For part 2
Just put the unit rate in an equation
2/15x=1
Where 1 is the single hour and x is the task
solve
you’ll get 7 1/2
Due to only requesting for tasks in an Hour
its only 7 task
Help ASAP.. Find the measure of each missing angle .. M<1? M<2? M<3? M<4? M<5?
Answer:
m<1=62°
m<2=23°
m<3=157°
m<4=23°
m<5=62°
Step-by-step explanation:
m<1= 180-118=62
m<2=180-95-62=23
m<3=180-23=157
m<4=m<2=23
m<5=m<1=62
Measures of the missing angles
m∠1 = 62° , m∠2 = 23°, m∠3 = 157° , m∠4 = 23° , m∠5= 62°
What is an angle?An angle is the figure formed by two rays called sides of the angle sharing a common endpoint called the vertex of the angle.
Given,
In the figure
sum of angles on a straight line is 180° .
m∠1 + 118° = 180°
m∠1 = 180° - 118°
m∠1 = 62°
In a triangle, measurement of all interior angles is 180°
m∠1 + m∠2 + 95° = 180°
62° + m∠2 + 95° = 180°
m∠2 + 157° = 180°
m∠2 = 180° - 157°
m∠2 = 23°
Sum of angles on a straight line is 180°
m∠2 + m∠3 = 180°
23° + m∠3 = 180
m∠3 = 180° - 23°
m∠3 = 157°
Since ∠2 and ∠4 are supplementary angles
m∠4 = m∠2
m∠4 = 23°
Sum of all interior angles of a quadrilateral is 360°
m∠3 + m∠4 + m∠5 + 118° = 360°
157 + 23 + m∠5 +118 = 360
m∠5 + 298 = 360
m∠5 = 360 - 298
m∠5 = 62°
Hence, m∠1 = 62°, m∠2 = 23°, m∠3 = 157°, m∠4 = 23°, m∠5= 62° are the measures of the missing angles.
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What is $4.14/9$9.20 ?
Answer:
4.14
Step-by-step explanation:
_7787$&((&+_¶©=©=®÷^¶°
For an experiment, a scientist needs 1/2 cup baking soda for 4/5 liter of water. Using this ratio, how much baking soda is needed for one liter of water?
Answer choices-
4/10 cup
5/8 cup
8/5 cups
10/4 cups
Answer:
5/8 cup of baking powder.
Step-by-step explanation:
Hence, using the ration given in the above question:
4/5 liter of water = 1/2 cup of baking soda
1 liter of water = x cup of baking powder
Cross Multiply
4/5 liter of water × x cup of baking powder = 1 liter of water × 1/2cup of baking powder
x cup of baking powder = 1 liter of water × 1/2cup of baking powder/4/5 liter of water
x cup of baking powder = 1/2 ÷ 4/5
x cup of baking powder = 1/2 × 5/4
x cup of baking powder = 5/8 cup of baking powder.
Therefore,
5/8 cup of baking soda is needed for one liter of water.
What point appears to be the solution to the system of
equations shown in the graph?
Answer: (-2, -5)
Explanation:
The solution to the system is where the lines intersect. The point (-2,-5) is on both the blue and orange line simultaneously.
The point (-2, -5) means x = -2 and y = -5 pair up together to form the full solution.
-2, -5
got it right on edge
A man is running through a train tunnel. When he is 2 5 of the way through, he hears a train approaching the tunnel from behind him at a speed of 60 kilometers per hour. Whether he runs ahead or he runs back, he will reach an end of the tunnel at the same time the train reaches that end. At what rate, in kilometers per hour, is he running
Answer:
I think if he keeps running at the speed he is running about 25 mph
Step-by-step explanation:
honestly this one was very hard I do not know
Please help its due today
Jody wants to build a rectangular garden that has dimensions 16 feet by 24 feet. Fence post must be placed 4 feet apart.
Create a diagram that locates each post.
How many post will Jody need?
Answer:
8 posts total on both the 16 ft. sides(there are 4 sides to a rectangle), 12 posts on both the 24 ft. sides(there are 4 sides to a rectangle)
Step-by-step explanation:
they are spaced 4 ft apart. Jody will need 20 total posts.
In a survey of 2,900 people who owned a certain type of car, 1,740 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car
Answer:
60%
Step-by-step explanation:
1740 / 2900 = 0.6
Will give brainliest
Answer:
C
Step-by-step explanation:
Answer:
D = 4
Step-by-step explanation:
The side lengths of a triangle are 5, 3, and 4. Is this a right triangle?
A. Yes, because 32 +
*#2352
B. Yes, because 32 + 42 = 52,
O C. No, because 32 +42 + 52.
D. No, because 3+ 4+5.
Step-by-step explanation:
Given that,
The side lengths of a triangle are 5,3 and 4.
For a right triangle, the Pythagoras theorem is applicable. We know that, for a right triangle,
[tex]H^2=b^2+h^2[/tex]
Where
H is Hypotenuse
b is base
h is perpendicular height
If we put b = 3. h = 4, then
[tex]H^2=3^2+4^2\\\\H^2=9+16\\\\H=5[/tex]
Hence, it will form a right triangle.
Use the equation: y = 5x - 4 Write an equation in any form) of a line that passes through the point (-1,7) and is parallel to the original line.
Answer:
y = 5x + 12
Step-by-step explanation:
Use the formula: y - y1 = m(x - x1)
Plug in all numbers into your equation: y - 7 = 5(x - -1)
Minus with a minus becomes a positive: y - 7 = 5(x + 1)
Distribute: y - 7 = 5x + 5
Add 7 to both sides: +7 +7
Answer: y = 5x + 12
A football player kicks a ball with a mass of .55 kg. The average acceleration of the football was 14.9 m/s2
. How much force did the kicker supply to the football?
Question 2 options:
35.24 N
8.2 m/s2
35.24 m/s2
8.2 N
By Newton's second law, the average force exerted on the ball is
F = (0.55 kg) (14.9 m/s²) = 8.195 N ≈ 8.2 N
Answer:
8.2 N
Step-by-step explanation:
I took a test in school and I had this question I got a hundred, so pls trust me.
Also, brainliest pls. :)
Select the correct answer.
What is the zero of the function represented by this graph?
8
6
2-
- 2
2
6
2
-4
-6
-8
OA I = 5
OB. 1 = 1
OC. I = -1
OD. I = -5
The zero of the function represented by this graph is at x = -5.
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The zero of a function is a value of the independent variable (usually denoted as x) for which the value of the function (denoted as f(x)) is equal to zero.
In other words, the zero of a function is the value of x that makes the function equal to zero.
It is also known as a root or a solution of the function.
Geometrically, the zero of a function is the x-intercept of its graph, which is the point where the function crosses the x-axis.
Now,
From the function graph,
The graph has f(x) = y = 0 at the x = -5.
Thus,
The zero of the function represented by this graph is at x = -5.
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An 8% decrease from $5 per hour is ?
Answer:
$4.60
Step-by-step explanation:
8% = 0.08 as a decimal
0.08 x 5 = 0.40
8% of $5.00 is 40 cents
take 40 cents from 5 dollars
5.00 - 0.40 = 4.60
In a batch of 440 water purifiers, 8 were found to be defective. What is the probability that a water purifier chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary!
please help
Answer:
1.8% or 1.818181%
Step-by-step explanation:
If in a batch of 440 water purifiers, we find 8 to be defective.
Then the probability of the next purifier being defective is 8/440
In percentage = 8/440 * 100
=> 8/44 * 10
=> 8/22 * 5
=> 40/22
=> 20 / 11
20/11 is roughly 1.8181818
Rounding it to the nearest tenth, we get 1.8%
If my answer helped, kindly mark me as the brainliest!!
Thank You!!
A nursery owner buys 8 panes of glass to fix some damage to his greenhouse. The 8 panes cost $17.20. Unfortunately, he breaks 3 more panes while repairing the damage. What is the cost of another 3 panes of glass? Another 3 panes of glass cost $
q ?????????????
Answer:
$6.45
Step-by-step explanation:
y=4, -4y + 5 evaluate it please
Answer:
Step-by-step explanation:
=
4
−
4
+
5
=
9
−
4
[6] Jessica sold one third of her records and then bought 84 more. She now has 178 records. How many records did Jessica begin with?
Answer:
141 recordsStep-by-step explanation:
Let the initial number be x
Sold 1/3x, and now has:
x - 1/3x = 2/3xBought 84 more and now got 178:
2/3x + 84 = 1782/3x = 94x = 94 ÷ 2/3x = 94 × 3/2x = 141Jessica had 141 records initially
Marvel use 864 beads to make necklaces for the art Club she made 24 necklaces with the beads if each necklace has the same amount of beads how many babies did Markle used to make each necklace
Answer:
I think the answer is 20736 beads?
Step-by-step explanation:
If the last sentence is supposed to say beads instead of babies, the answer is 20736 beads. This is because if u multiply the amount of beads used in one bracelet by the amount of bracelets, you should get the total amount of beads. So the two quantities are 864 and 24. If you multiply the two, then you get the total amount of 20736 beads.