Classify the system and identify the number of solutions.
4x + 3y + 6z = 25
x + 5y + 7z = 13
2x + 9y + z = 1
Answers
Answer:
consistent, independent; one
Step-by-step explanation:
The solution is (4, −1, 2). Because the system has one solution, it is consistent and independent.
The system of equation is consistent and have unique solution.
What is Matrix?Rows and columns of numbers are arranged in a matrix.
A rectangular matrix is a grouping of numbers into rows and columns. The matrix A, for instance, has two rows and three columns.
Given:
4x + 3y + 6z = 25
x + 5y + 7z = 13
2x + 9y + z = 1
Writing the into matrix form
A= [tex]\left[\begin{array}{ccc}4&3&6\\1&5&7\\2&9&1\end{array}\right][/tex] and B= [tex]\left[\begin{array}{ccc}25\\13\\1\end{array}\right][/tex]
Now, find the determinant we get
[tex]D_x[/tex] = -796, [tex]D_y[/tex]= 199, [tex]D_z[/tex] = -398
and Determinant of matrix A= -199
So, x= -796/-199= 4
y= 199/-199 =-1
z= -398/-199 = 2
hence, the system of equation is consistent and have unique solution.
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Related Questions
An apprentice baker made 40 liters of 60% sugar syrup instead of 40 liters of 45% sugar syrup. How much syrup should she drain and replace with distilled water so that the resulting solution is 40 liters of 45% syrup?
Answers
Answer:
10 lStep-by-step explanation:
40 l of 60% sugar syrup becomes 40 l of 45% sugar syrup if x l is drained and replaced with distilled water. Sugar content is then:
(40 - x)*0.6 = 40*0.4524 - 0.6x = 180.6x = 24 - 180.6x = 6x = 6/0.6x = 10 l10 liters solution was replaced with distilled water
1 point
2). The ordered pairs all lie on the same line. Using the ordered pairs, write
an equation of the line in the form y = mx + b.*
(0, 3) (2, 7) (-1, 1) (5, 13)
Answers
Answer:
y = 2x + 3
Step-by-step explanation:
First things first we have to find the slope. To do so you simply choose two of the ordered pairs and use the formula:
y2 - y1 / x2 - x1
I will use (0, 3) and (2, 7).
7 - 3 / 2 - 0
4 / 2
2
let’s double check by using the other set of ordered pairs.
(-1, 1) and (5,13)
13-1 / 5 + 1
12 / 6
2
Our slope is 2!
Next we will use the point-slope formula:
y - y1 = m (x - x1)
we will do this with one of the ordered pairs, since they all lie on the same line the answer will be the same each time.
I will use (2, 7).
y - 7 = 2(x - 2)
distribute:
y - 7 = 2x - 4
add 7 to both sides:
y = 2x + 3
Just to be sure that i didn’t make any mistakes i will double check by using another ordered pair.
I will use (-1, 1)
y - 1 = 2 (x + 1)
distribute:
y - 1 = 2x + 2
add 1 to both sides
y =2x + 3
There we have it! The answer is:
y = 2x+ 3
What is true of triangle FGH? It is a right triangle. It is an obtuse triangle. It has exactly 2 congruent sides. It has exactly 3 congruent sides.
Answers
Answer:
D
Step-by-step explanation:
I just did it on edginuty
Answer:
D
explanation:
If you do it on ed then you should get the question right. : )
solve -x=9x by graphing
Answers
Answer:
the answer would be 0.
Step-by-step explanation:
the line would go straight down the middle.
Answer:
just plot that on the type of graph you are supposed to be dojng and solve it. I would do it but i dont have graph paper
Step-by-step explanation:
Find the area of Show your work and use appropriate units.
Answers
Answer:
30.42 in²Step-by-step explanation:
Refer to attached
Area of the triangle formula:
A = 1/2bhb is given: AB = 9 in
Line CD is added for h, finding its value:
CD/BC = sin 75°h/7 = 0.9659h = 7*0.966h = 6.76 inThen finding the area:
A = 1/2*6.76*9 = 30.42 in²2x-Y (5y X -6) 3^6y what is that as an expression
Answers
Answer:
The answer is:
2x + 30y^2 × 729^y
i would like sone help please. I said it was 96 but it marked it wrong.
Answers
Answer:
The lowest grade was 48
Step-by-step explanation:
Martha’s Grandfather at 63 years of age is 6 more than 3 times as old as Martha. What is Martha’s age?
Answers
Answer:
18
Step-by-step explanation:
6x3=18 beacause of the given number
Answer:
19 yrs old
Step-by-step explanation:
subtract 6 from 63 and you get 57
then you divide 57 by 3 and you get
therefore martha is 19
A package of 3 pairs of insulated costs $15.57. What is the unit price of the pairs of ?
Answers
Answer:
-3 pairs cost $15.57
15.57 divided by 3
$5.19 per pair unit rate
help! i need help on this math
Answers
Answer:
4
10
25
-1
-4
Step-by-step explanation:
Your answers are correct.
The coefficient of -x^2 is -1 since -x^2 is the same as -1x^2.
The coefficient of -4x is -4.
Would you rather be bitten by 15% of 120 mosquitoes or 8% of 250 mosquitoes explain why
Answers
Answer:
15% of 120 mosquitoes
Step-by-step explanation:
15% of 120 is 18 while 8% of 250 is 20. 15% of 120 is less mosquitoes
generate a frequency table using 3,12,25,2,3,6,17,17,15,13,20,12,21,18,19
Answers
Answer:
A frequency table is given below.
Step-by-step explanation:
Given the data
3,12,25,2,3,6,17,17,15,13,20,12,21,18,19
The frequency distribution table provides us a general snapshot of the data using which we may be able to find certain patterns.A frequency table is given by:
Class Count Percentage
0 - 6 4 26.7
7 - 13 3 20
14 - 20 6 40
21 - 27 2 13.3
Total 15 100
I need help please just give me the answer ..
Answers
Answer:
5x+10y+5z
Step-by-step explanation:
helpppppppppppppp pleaseeeeeeeeeeeeeeee
Answers
Answer:
Step-by-step explanation:
1. X=11
Answer:
First page
x=11
y=-15
Second page
x=26
x=10
Third page
x=36
x=88
fourth page
x=81
n=36
fifth page
x=10
x=2
Step-by-step explanation:
Hope this helps
can you mark brainliest it would really help me thank you
A package of 6 pairs of insulated gloves costs $51.54. What is the unit price of the pairs of gloves ?
Answers
Answer:
$8.59
Step-by-step explanation:
The unit price is just asking for what one pair of gloves cost.
[tex]\$ 51.54 \div6=\$8.59[/tex]
∴The unit price of the pairs of gloves is $8.59
Hope this helps!
Answer:
8.59
Step-by-step explanation:
A website sells sweaters. The amount of sales p(c) varies directly with the number of customers c. Eight customers bought a total of $335 worth of sweaters. Which equation can be used to find the sales for c customers? p(c) = 41.88c p(c) = 4188c p(c) = 41.88c p(c) = 4188c
Answers
Answer: p(c) = 41.88c
Step-by-step explanation:
From the question, we are informed that a website sells sweaters and that the amount of sales p(c) varies directly with the number of customers c.
We are further told that eight customers bought a total of $335 worth of sweaters.
The equation that can be used to find the sales for c customers will be:
= 335/8
Therefore, the answer is p(c) = 41.88c
= 41.88
An airplane flew across the Pacific Ocean. The table shows the amount of time and the distance traveled when the airplane was traveling at a constant speed. Complete the table with the missing values.
Answers
Answer:
SEE THE GRAPH
Step-by-step explanation:
2/7+x=17/5
please solve this
Answers
Step-by-step explanation:
x=17/5 - 2/7
LCM is 7*5=35
x= (17*7-2*5)/35=109/35
Suppose sin(x) = -3/5 and cos(x) < 0. What the value of cos(2x)?
A) -16/25
B) -7/25
C) 7/25
D) 16/25
Answers
Answer:
The value of cos(2x) = 7/25
Hence, option C is true.
Step-by-step explanation:
Using the trigonometric identity
cos 2x = 1 - 2sin²x
Given
sin(x) = -3/5cos(x) < 0so substituting the values
cos 2x = 1 - 2sin²x
= 1 - 2 (-3/5)²
= 1 - 2 (9/25)
= 1 - 18/25
= 7/25
Therefore,
The value of cos(2x) = 7/25
Hence, option C is true.
Answer:it’s C
Step-by-step explanation:
I just took it
it was -5 in Memphis and -12 in Nashville . which city was colder
Answers
Answer: nashville
Step-by-step explanation: its a lower degree
What kind of symmetry does Equation x^2 + (y+2)^2 = 4 have?(y-axis, x-axis, or origin)
Answers
Answer:
y-axis
Step-by-step explanation:
Since the equation is identical to the original equation, it is symmetric to the y-axis.
x^2 = 49, then x = 7. What would be a counterexample?
Answers
4. If you saved $2.00 on January 1, $4.00 on February 1, $8.00
on March 1. $16.00 on April 1, and so on. How much money
would you save in one year?
Answers
Answer:
$8190
Step-by-step explanation:
$8190
Mrs. Rodriguez wants to pay her restaurant bill which is $24.00. If Mrs. Rodriguez wants to leave a 20% tip on the total, how much should she pay?
$20.35
$26.40
$28.80
$33.60
Answers
Answer:
28.80
Step-by-step explanation:
I took the test on edge 2020
Answer:
28.80
Step-by-step explanation:
I took the test on edge 2020
Using the information given, select the statement that can deduce the line segments to be parallel. If there are
then select none.
When m_1= m_D
O AB II DC
AD || BC
none
Answers
Answer:
it is AD l l DC so ots B
Step-by-step explanation:
Answer
If the line segment AB is parallel to the line segment DC then, m∠1=m∠D by corresponding angles.
What is corresponding angle?Congruence and similarity tests in geometry involve comparing corresponding sides and angles of polygons.
Each side and angle in one polygon is paired with a side or angle in the second polygon, with the order of adjacency preserved.
One is an exterior angle (beyond the parallel lines), while the other is an interior angle (inside the parallel lines).
Corresponding angles and transversal lines are defined. Corresponding angles are a subset of angle pairs. Angles on the opposite side of the transversal are referred to as alternate angles.
If line segment AB is parallel to line segment DC,
m∠1=m∠D, by corresponding angles
If line segment AD is parallel to line segment BC,
m∠3=m∠B, by corresponding angles
Thus, this can be concluded regarding the given scenario.
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Which of the following represents the lowest speed in miles per hour?
A. 6 miles in 18 hour
B. 11 miles in 14 hour
C. 16 miles in 38 hour
D. 20 miles in 12 hour
Answers
Answer:
D
Step-by-step explanation:
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Answers
Answer:
Step-by-step explanation:
35% means 35 per hundred. 35/100. simplify and write as 7/20.
0.64 means its 2 zeros left of regular number. 64/100.
82% means 82 per hundred. 82/100. move decimal 2 spaces to left (division is left, multiplication is right). 0.82.
4/5. try to make denominator 100. multiply both numerator and denominator by 20. 80/100. move decimal 2 spaces to the left. 0.8.
14/50. try to make denominator 100. multiply both numerator and denominator by 2. 28/100. 28%
0.19 can be written as 19/100. 19%
Answer: 35%=7/20 0.64=64/100. 82%=82/100. 4/5=0.8 14/50=0.28 0.19=19%
Step-by-step explanation:
PLEASE PLEASE HELP GIVING BRAINALIST AND EXTRA POINTS FOR FIRST PERSON
Answers
Answer:
answers are below
Step-by-step explanation:
1. k = -12
2. x = 14
3. y = -18
4. x = 34/3 or 11.3333333
5. x = -10
6. b = 17
7. x = 1/7
8. y = -2
Hope this heps!! Tell me if you need any explanations :)
Answer:
1. -12
2. 14
3. -18
4. 11 1/3
5. -1 3/5
6. -17
7. 1/7
8. 7 1/3
Step-by-step explanation:
Most of them should be right but sorry if wrong
Which situation can be modeled by the inequality X ≥ 18?
OChildren go to school more that 18 days during a month.
O The map showed that the school was less than 18 blocks from her house.
O 18 eggs will fill an egg carton
O People 18 and over are considered adults
Answers
Answer:
Answer: People 18 and over are considered adults
Because more than or equal to 18
Good Luck!
Answer:
O#4, People 18 and over are considered adults.
Step-by-step explanation:
Since there is a line under it, it means greater than or equal to.
100 x 500 x 250 x 600 x 900 x 10 000 x 0 x 500 x 60 x 70 x 50 x 90 + 1 x 50 =
Answers
Answer:
50
Step-by-step explanation: