Evaluate:
log 64
1/16
Answer:
64
Step-by-step explanation:
Evaluate log64 1/16. Write an equation in logarithmic form. log64 1/16 = x. Convert the equation to exponential form 1/16 = 64
Which systems of linear equations have no solution?
x + y + z = 1,100
x - 2y - z = -500
2x + 3y + 2z = 2,600
x + y + z = 1,500
x - y -z = -500
2x + y + z = 2,000
x + y + z = 1,400
X-2y - Z = -500
2x + 2y + 2z = 2,700
x + y + z = 1,400
-0.5x - 0.5y - 0.5z = -900
2x + 3y + 2z = 3,000
x + y + z = 1,900
x - y - 2z = -2,000
2x + 2y + z = 1,100
x + y + z = 2,400
2x - 2y + 2z = 700
x + 3y + z = 2,400
Answer:
Step-by-step explanation:
The systems of linear equations that have no solution are:
a)
x + y + z = 1,100
x - 2y - z = -500
2x + 3y + 2z = 2,600
b)
x + y + z = 2,400
2x - 2y + 2z = 700
x + 3y + z = 2,400
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
To determine which systems of linear equations have no solution, we need to check whether the system is inconsistent, i.e., there are no values of x, y, and z that satisfy all the equations simultaneously.
One way to check this is to use row reduction to put the system into row echelon form or reduced row echelon form and see if we obtain any contradictory equations.
Another way is to use determinants, but we'll use row reduction here.
a)
| 1 1 1 | 1,100 |
| 1 -2 -1 | -500 |
| 2 3 2 | 2,600 |
R2 = R2 - R1 and R3 = R3 - 2R1:
| 1 1 1 | 1,100 |
| 0 -3 -2 | -1,600 |
| 0 1 -1 | -1,800 |
R2 = -1/3 R2 and R3 = R3 + R2:
| 1 1 1 | 1,100 |
| 0 1/3 2/3 | 533.33|
| 0 0 1/3 | -933.33|
Now, we can solve for z in the last equation:
z = -2800
Substituting into the second equation gives:
y = 2666.67
But substituting into the first equation gives:
x = -566.67
So, this system has no solution.
b)
| 1 1 1 | 1,500 |
| 1 -1 -1 | -500 |
| 2 1 1 | 2,000 |
R2 = R2 - R1 and R3 = R3 - 2R1:
| 1 1 1 | 1,500 |
| 0 -2 -2 | -2,000 |
| 0 -1 -1 | -1,000 |
R2 = -1/2 R2 and R3 = R3 - 1/2 R2:
| 1 1 1 | 1,500 |
| 0 1 1 | 1,000 |
| 0 0 -1 | -500 |
Now, we can solve for z in the last equation:
z = 500
Substituting into the second equation gives:
y = 500
But substituting into the first equation gives:
x = 500
So, this system has a unique solution.
c)
| 1 1 1 | 1,400 |
| 1 -2 -1 | -500 |
| 2 2 2 | 2,700 |
R2 = R2 - R1 and R3 = R3 - 2R1:
| 1 1 1 | 1,400 |
| 0 -3 -2 | -900 |
| 0 0 0 | 0 |
The last row of the augmented matrix corresponds to the equation 0x + 0y + 0z = 0, which is always true.
Therefore, this equation is not contradictory and doesn't add any new information to the system.
We can eliminate it and rewrite the system as:
| 1 1 1 | 1,400 |
| 0 -3 -2 | -900 |
R2 = -1/3 R2:
| 1 1 1 | 1,400 |
| 0 1 2/3 | 300 |
R1 = R1 - R2:
| 1 0 1/3 | 1,100 |
| 0 1 2/3 | 300 |
Now, we can solve for z in the first equation:
z = 3,300
Substituting into the second equation gives:
y = -1,200
But substituting into the first equation gives:
x = -2,200
So, this system has a unique solution.
d)
| 1 1 1 | 1,400 |
|-0.5 -0.5 -0.5 | -900 |
| 2 3 2 | 3,000 |
R2 = 2R1 + R2 and R3 = -4R1 + R3:
| 1 1 1 | 1,400 |
| 0 1/2 1/2 | -100 |
| 0 -1 -2 | -3,600 |
R3 = -2R2 + R3:
| 1 1 1 | 1,400 |
| 0 1/2 1/2 | -100 |
| 0 0 -3 | -3,400 |
Now, we can solve for z in the last equation:
z = 1,133.33
Substituting into the second equation gives:
y = -1,066.67
But substituting into the first equation gives:
x = 2,333.33
So, this system has a unique solution.
e)
| 1 1 1 | 1,900 |
| 1 -1 -2 | -2,000 |
| 2 2 1 | 1,100 |
R2 = R2 - R1 and R3 = R3 - 2R1:
| 1 1 1 | 1,900 |
| 0 -2 -3 | -3,900 |
| 0 0 -3 | -4,100 |
Now, we can solve for z in the last equation:
z = 1,366.67
Substituting into the second equation gives:
y = -1,033.33
But substituting into the first equation gives:
x = 1,667
So, this system has a unique solution.
f)
| 1 1 1 | 2,400 |
| 2 -2 2 | 700 |
| 1 3 1 | 2,400 |
R2 = R2 - 2R1 and R3 = R3 - R1:
| 1 1 1 | 2,400 |
| 0 -4 0 | -1,100 |
| 0 2 0 | 1,000 |
R2 = -1/4 R2 and R3 = 1/2 R3:
| 1 1 1 | 2,400 |
| 0 1 0 | 275 |
| 0 1 0 | 500 |
R3 = R3 - R2:
| 1 1 1 | 2,400 |
| 0 1 0 | 275 |
| 0 0 0 | 225 |
The last equation shows that 0x + 0y + 0z = 225, which is impossible. Therefore, this system has no solution.
Thus,
The systems of linear equations that have no solution are:
a)
x + y + z = 1,100
x - 2y - z = -500
2x + 3y + 2z = 2,600
b)
x + y + z = 2,400
2x - 2y + 2z = 700
x + 3y + z = 2,400
Learn more about solutions of equations here:
https://brainly.com/question/545403
#SPJ7
For what value of x must ABCD be a parallelogram ?
Answer:
x = 4
Step-by-step explanation:
as it is parallelogram opposite sides are equal
so14x -7= 10x-9
14x-7+9=10x
14x -16 = 10x
14x -10x = 16
4x =16
x = 16/4
x = 4
also u can put x = 4 in both expressions and u will get answer of both 49
This is my last ONE I HAVE TO ANSWER HELP ME
Answer:
A you multiply them all together
What is the best first step in solving -4x+ 10?
Add
5
to both sides.
O
Subtract į from both sides.
Multiply both sides by -4 and reverse the inequality symbol.
Divide both sides by 10 and reverse the inequality symbol.
What is the answer please help me out please 37 big tall fat points
Answer:
Step-by-step explanation:
The first step is usually to isolate the x term. You have -4x - ⅖ on the lefthand side of the equation. You want to remove the -⅖ so the -4x is alone.
Add ⅖ to both sides:
-4x > ⅖ + 5/10
What is the slope of the line through (-12, 1) and (-1, 1)?
Answer:
The equation is y = 1. Therefore, the slope is undefined.
You have a recipe that calls for 2 parts of milk for every 5 parts of flour You use 8 cups of milk How much flour do you need?
Answer:
20
Step-by-step explanation:
The equation of a line is given by y−3=4(x+5)
Find the y-intercept of the line.
Write only the value (number) of the y -intercept as your answer.
What is this answer whoever could solve it is super smart
Answer: 3.19 feet.
Step-by-step explanation: 319 divided by 100 is 3.19
What is the solution to the system of equations? -2x+y=-5 3x - 2y= 12 A) (3, 1) B) (6,3) C) (-2,-9) D) (-2,-1)
Answer: c
Step-by-step explanation:
Solution by substitution method
-2x+y=-5
2x-y=5
and 3x-2y=12
Suppose,
2x-y=5→(1)
and 3x-2y=12→(2)
Taking equation (1), we have
2x-y=5
⇒y=2x-5→(3)
Putting y=2x-5 in equation (2), we get
3x-2y=12
3x-2(2x-5)=12
⇒3x-4x+10=12
⇒-x+10=12
⇒-x=12-10
⇒-x=2
⇒x=-2→(4)
Now, Putting x=-2 in equation (3), we get
y=2x-5
⇒y=2(-2)-5
⇒y=-4-5
⇒y= -9
∴y=-9andx=-2
Como calcular el 15% de 300
Daniel has a bag with 9 shoes in it. 4 of the shoes are sport shoes. What is the relative frequency probability that a randomly selected shoe will be a sport shoes?
P
13 cm
Q
5 cm
12 cm
What is the length of diagonal PQ? Round to the nearest hundredth
A. 27.93 cm
B. 25.01 cm
C 17.69 cm
D 18.38 cm
PLEASE HELP FAST I NEED IT RN
but maybe b
Step-by-step explanation:
question in pic! answer asap! will give brainliest!
Answer:
I believe the answer is x + 3
Step-by-step explanation:
[tex]{ \large{ \sf{w = \dfrac {\cancel{(x + 5)}(x + 3)}{ \cancel{x + 5}} }}}[/tex]
width = ( x + 3 ) Answer. Option. ( B )The oven at pete's pizza place holds 8 pizzas. It takes 15 minutes to bake 8 pizza's. Pete needs to know the maximum numbers of pizzas he can bake in 2 hours
Answer:
64 pizzas
Step-by-step explanation:
If someone wants to help me
Answer:
x=8
Step-by-step explanation:
*ASAP*
Miracle Maid Service charges a $30 house visit fee plus $5 per room to clean a house. Which graph models this situation?
3a-7=4b+1 solve for b
Answer:
b = [tex]\frac{3a-8}{4}[/tex]
Step-by-step explanation:
Given
3a - 7 = 4b + 1 ( subtract 1 from both sides )
3a - 8 = 4b ( divide both sides by 4 )
[tex]\frac{3a-8}{4}[/tex] = b
please help, no need to show work, tysmmmm!!
Answer:
translation
Step-by-step explanation:
Alright have posted it now.
Given the function f(x) = 3x + 6 and g(x), which function has a greater slope?
Answer:
If both g(x) and f(x) are the same equation, then they will have the same slopes.
Answer: C
Step-by-step explanation:
you're welcome
A ball has a diameter of 8 inches. What is its surface area? (Use 3.14 for pie.) WILL give brainest wh ok answer correct and fast.
How many solutions does 7(x - 2) + 5 = 3 (2x - 1) + 1 have?
Answer:
one, x = 7
Step-by-step explanation:
7(x - 2) + 5 = 3 (2x - 1) + 1
reduce:
7x - 14 + 5 = 6x - 3 + 1
x = 7
Diego's age `d` is 5 more than 2 times his sister's age `s`. This situation is represented by the equation `d=2s+5`. If we know Diego's age, which equation will help us find his sister's age?
Answer: [tex]s=\dfrac{(d-5)}{2}[/tex].
Step-by-step explanation:
Given: d denotes Diego's age while s denotes his sister's age.
The situation is represented by the equation d=2s+5.
To find his sister's age we can write the above equation as [tex]s=\dfrac{(d-5)}{2}[/tex] [we first subtract 5 from both sides and then divide both sides by 2]
Hence, the required equation: [tex]s=\dfrac{(d-5)}{2}[/tex].
f(x)=x2+3x and g(x)=2x2, find (f ∘ g)(−1).???????????????????????????????
Answer: its false
Step-by-step explanation:
How many times will the lines intersect?
2x-4y=3
7y-5x=8
Answer:
What line
Step-by-step explanation:
Please take a picture of the line
A snack bar offers chili and/or cheese on its hot dogs for an additional fee.
The owner kept track of the hot dog orders over the course of a week. His
data are shown in a relative frequency table.
Cheese
No cheese
Total
Chili
0.1
0.3
0.4
No chili
0.2
0.4
0.6
Total
0.3
0.7
1.0
What does the 0.4 in the highlighted cell mean?
A. 40% of his customers ordered no chili on their hot dog.
O O
OB. 40% of his customers ordered no cheese on their hot dog.
C. 40% of the customers that ordered no chili ordered no cheese.
O
D. 40% of his customers ordered no chili and no cheese on their hot
dog
Answer:
D. 40% of his customers ordered no chili and no cheese on their hot dog
Step-by-step explanation:
If we look at what column/row 0.4 is in we can see that it's in the "No cheese" and "No chili"
so
that's why it's 40% of his customers ordered no chili and no cheese on their hot
What is the slope of the equation y - 3 = -4(x - 5)?
O-4
O-3
O 20
O 23
Answer0-4
Step-by-step explanation:
If It takes me 3 minutes per assignment and I have 36 hrs worth of assignments how many assignments do I need to do to get 20 hrs??
Answer:
[tex]400[/tex]
Step-by-step explanation:
1 hour = 60 minutes
20 hours × 60 = 1200 minutes
1200 minutes/ 3 minutes per assignment= 400 assignments
plz mark me brainliest. :)