tìm m để phương trình có 1 nghiệm duy nhất
x+2y-2z=2
3x+7y-z=5
2x+4y+mz=7
Rewrite the system of equations in matrix form.
[tex]\begin{bmatrix}1&2&-2\\3&7&-1\\2&4&m\end{bmatrix} \mathbf x = \mathbf b[/tex]
This system has a unique solution [tex]\mathbf x = \mathbf A^{-1}\mathbf b[/tex] so long as the inverse of the coefficient matrix [tex]\mathbf A[/tex] exists. This is the case if the determinant is not zero.
We have
[tex]\det(\mathbf A) = m+4[/tex]
so the inverse, and hence a unique solution to the system of equations, exists as long as m ≠ -4.
The angle measure of a triangle is shown in the diagram.
what is the value of x?
A. 13
B. 20
C. 5
D. 12
Answer:C.5
Step-by-step explanation:
Tp 3 Work Backwards
1. Bowser, Abby, and Chuckles are 3 dogs with a
combined age of 44. Bowser is 6 years older than
Abby. Abby is 2 years younger than Chuckles, c.
Which expression could be used to find the age of
Chuckles?
Answer:
Your equation option is possibly in here somewhere.
Step-by-step explanation:
A = C - 2
B = A + 6 → A = B - 6
C - 2 = A = B - 6 → B = C + 4
44 = C + B + A
44 = C + (C + 4) + (C - 2)
44 = 3C + 2
42 = 3C
C = 7
Can someone explain it step by step ?
Answer:
1. (x - 1) × (x + 3)
2. x = 3 and y = -2
Step-by-step explanation:
x² + 2x - 32x + 3y = 0; y = 3x - 11rewrite the equation:
y = 3x - 11; 2x + 3y = 0
solve y = 3x - 11 for the y:
y = 3x - 11
substitute 3x - 11 for y in 2x + 3y = 0;
2x + 3y = 0;
2x + 3y = 0
2x + 3 (3x - 11) = 0
11x - 33 = 0 (simplify both sides of the equation)
11x - 33 + 33 = 0 + 33 (add 33 to both sides)
11x = 33
11x/11 = 33/11 (divide both sides by 11)
x = 3
subtitute 3 for x in y = 3x - 11
y = 3x - 11
y = (3)×(3) - 11
y = -2
I showed one equation because the other is self explanatory, hope this helps.
which of the following are perfect cubes 1)3375 2)8000 3)6859
Answer:
all are perfect cubes
Step-by-step explanation:
you can just cube root the numbers and bom if it aint decimal its a perfect cube
4m 10m - - The accompanying figure is a water tank whose radmis is 4m and height 10m. 4.1 Determine the total surface area of the tank. (3)
Answer:
45789932
Step-by-step explanation:
3456899954433222222344577890009
Need help with geometry problem
Answer:
y = [tex]6\sqrt{5}[/tex]
Step-by-step explanation:
x^2 + z^2 = 29^2
x^2 = y^2 + 9^2
y^2 + 20^2 = z^2
29^2 - z^2 = y^2 + 81 (equating for x^2 from eqn 1 and 2)
substitute 3rd eqn in 4th
29^2 - (y^2 + 20^2) = y^2 + 81
841 - y^2 - 400 = y^2 + 81
441 = 2y^2 + 81
360 = 2y^2
y^2 = 180
y = [tex]\sqrt{180}[/tex]
= [tex]\sqrt{36*5} \\[/tex]
y = [tex]6\sqrt{5}[/tex]
Which table of ordered pairs represents a proportional relationship?
CS
Х
-2
-4
-6
у
4
16
36
х
-4
-6
-8
y
-8
-12
-18
Х
-3
-5
-7
y
5
3
1
X
-3
6
_9
у
12
24
36
Answer: A 2-column table with 3 rows.
Step-by-step explanation:
O A woman's store sells the following categories of clothing for the following prices. blouses : Ghc14 each, skirt : Ghc 16 each, dress: Ghc 25 each, pantyhose:2 pairs for Ghc 3, socks: Ghc7. A lady goes to the store in a day when the store has a 20% off sale on all skirts. if ya buys 2 skirks, 1 dress and 4 pairs of pantyhose, how much money does lady have to pay?
Answer:
$4
Step-by-step explanation:
i know this because i passed collage last year
Given 4(3x-8)=52 prove x=7
Please help me
Answer:
4(3x-8)=52
divide both sides by 4
4/4(3x-8)=52/4
3x-8=13
add both sides by 8
3x-8+8=13+8
3x=21
divide both sides by 3
3x/3=21/3
x=7
Step-by-step explanation:
Step-by-step explanation:
4( 3x-8) = 52
12x - 32 = 52
Group all like terms
12x = 52 + 32
12x = 84
Divide both sides by 12
12/12x = 84/12
x = 7
Therefore, x = 7.
Hope it helps. Please mark me brainliest.
Round 0.00359 to the nearest ten-thousandth.
Answer:
0.0036 !
Step-by-step explanation:
Give brainliest please :)
0.00359, when rounded to nearest thousandth results in 0.0036.
What is Rounding Off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc. Rounding off numbers is done to preserve the significant figures.
Given, value to be rounded is : 0.00359
Since, 1 ten thousands = 10000 (104). So, 1 ten thousandth = 0.0001 (10-4)
Therefore, while rounding to nearest ten thousandth, we round the fractional part(or decimal part) upto 4 digits.
Here, In 0.00359, the digit after ten thousandth place is 9, which is (equal to or greater) than 5. So, 5 can be rounded to 6.
Hence, finally, 0.00359, when rounded to nearest thousandth results in 0.0036
Learn more about rounding off rules here:
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One integer is 8 less than another integer. The sum of the two integers is 72. Find the two integers. Step 2 of 2: What are the two integers? Separate values with a comma.
Answer:
40 and 32
Step-by-step explanation:
This is a linear systems equation problem.
a + b = 72
a = b - 8
Use substitution. Substitute b-8 for a in a+b=72
b-8+b=72
2b-8=72
add 8 to both sides
2b=80 (divide both sides by 2)
b = 40
Plug the value of b into the a=b-8
a=40-8
a=32
Check: 40 + 32 = 72 So the two integers are 40 and 32
A football team needs £465 to buy a new kit.
They raise £52.45 by holding a cake sale.
How much more money do they need to raise?
Solve: (4x^2-3x+7)-(x^2+8x-5)
Given polynomial:
(4x²-3x+7) - (x²+8x-5)
⇛ 4x²-3x+7-x²-8x+5
⇛ (4x²-x²) +(-3x-8x)+(7+5)
⇛ (4-1)x²+(-3-8)x+12
⇛ 3x²+(-11)x+12
⇛ 3x²-11x+12
(4x²-3x+7) - (x²+8x-5) = 3x²-11x+12Note:-
When subtracting two polynomials,change the symbols of the each term in the second polynomial which is subtracted from the first polynomial.
Read more:
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Answer:
[tex]3x^2-11x+12[/tex]
Step-by-step explanation:
First, distribute the negative:
[tex]4x^2-3x+7-x^2-8x+5[/tex]
Then combine like terms:
[tex]3x^2-11x+12[/tex]
Which is a recursive formula for this geometric sequence? -320, -80, -20, -5, . . .
The recursive formula for the geometric sequence is:
[tex]f(n) = \frac{1}{4}f(n - 1), f(1) = -320[/tex]
What is a geometric sequence?A geometric sequence is a sequence in which the coefficient of consecutive terms is always the same, called common ratio q.The recursive equation for a geometric sequence is:
[tex]f(n) = qf(n - 1)[/tex]
With f(1) as the first term.In this problem, the sequence is: {-320, -80, -20, -5, . . .}
The first term is [tex]f(1) = -320[/tex].The common ratio is [tex]q = \frac{-80}{-320} = \frac{1}{4}[/tex]Hence, the recursive equation is:
[tex]f(n) = \frac{1}{4}f(n - 1), f(1) = -320[/tex]
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The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]
Geometric progressionThe required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]
n the following sequence -320, -80, -20, -5,...
The The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]is given as:
r = -80/-320 = -20/-80 = 1/4The first term = -320The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]
Learn more on geometric functions here: https://brainly.com/question/222209
Due Tomorrow: answer question 3 using steps
Answer:
Step-by-step explanation:
Picture is quite fuzzy so I will ASSUME that the triangle has inner angles of 100° and 34° (now I'm told it's 38)
This means the unlabeled angle is 180 - 100 - 34 = 46°
180 - 100 - 38 = 42°
Using law of sines.
a/sin46 = 12/sin34
a/sin42 = 12/sin38
a = 12sin46/sin34 = 15.17415...
a = 12sin42/sin38 = 13.04217...
round as appropriate. I think it my say to the hundredths
a = 15.17
a = 13.04
If I did not guess the numbers in the photo correctly, just use the same technique to arrive at a better solution.
Owen paid $15 to download some of his favorite songs. He paid $2.50 per song. How many songs did he download?
The first step is to by a power of ten, so the divisor is a whole number.
The next step is to by figuring out how many times 250 goes into 1500.
Please help!!
Determine whether the inverse of F(x) is a function.
Answer:
Two crates, A and B, are connected with a rope of negligible mass over a frictionless pulley as represented in the diagram shown on the left. The crates are at rest.
Crate A has an unknown mass and hangs vertically to the right of the slope and crate B, with mass 14 kg, hangs on the slope to the left. The slope makes and angle of 68° with the horizontal.
The coefficient of static friction between crate B and the surface of the slope is 0.3. The direction of the frictional force is up the slope. Calculate the mass of crate A.
Which of the following correctly factors the expression −20x+4y−2?
A
4(−5x+4y+2)
B
2(−10x+2y−1)
C
−2(10x+2y+1)
D
−20(x−4y+2)
9514 1404 393
Answer:
B 2(−10x+2y−1)
Step-by-step explanation:
The greatest common factor is 2. Factoring that out gives the factorization shown in choice B.
2(-10x +2y -1)
__
You could factor out -2. Doing that would give ...
-2(10x -2y +1) . . . . . . . doesn't match choice C
Graph the linear equation. X = - 4y
find the prime factorization of each number. 52, and 41
Step-by-step explanation:
We will first find the prime factorization of 41 and 52. After we will calculate the factors of 41 and 52 and find the biggest common factor number .
Step-1: Prime Factorization of 41
Prime factors of 41 are 41. Prime factorization of 41 in exponential form is:
41 = 411
Step-2: Prime Factorization of 52
Prime factors of 52 are 2, 13. Prime factorization of 52 in exponential form is:
52 = 22 × 131
An isolates right triangle has a hypotenuse of 6. Find the length of the leg. Round to the nearest tenth.
Answer:
The length of the leg is 4.2 units.
Hope you could get an idea from it.
Doubt clarification - use comment section.
What is the amplitude and period of the function shown below?
The features of the sine function in this problem are given as follows:
Amplitude: 2.
Midline: y = -4.
Period: 3 units.
What is trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here, we have,
The equation is given as follows:
y = 2sin(2πx/3) - 4.
we have to define the sine function:
The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.
B: the period is 2π/B.
C: phase shift.
D: vertical shift.
The function has a minimum value of -6 and a maximum value of -2, for a difference of 4, hence the amplitude is given as follows:
2A = 4.
A = 2.
Without vertical shift, a function with amplitude of 2 would oscillate between -2 and 2, while this one oscillates between -6 and -2, hence the vertical shift is given as follows:
D = -4.
The shortest distance between repetitions can be given by 2 - (-1) = 3, hence the period is of 3 units and the coefficient B is given as follows:
2π/B = 3
B = 2π/3.
The function is at it's midline at the origin, hence it has no phase shift, and thus the equation is given as follows:
y = 2sin(2πx/3) - 4.
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The weight of an adult standard poodle was found to follow a normal distribution with a mean of 50 pounds and a standard deviation of 15 pounds. If represents the mean weight of a random sample of 7 adult standard poodles, what is (round off to second decimal place)
Using the Central Limit Theorem, it is found that the distribution of the sample means of the weights of the 7 adult standard poodles is normal, with mean of 50 pounds and standard deviation of 5.67 pounds.
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, for the population, [tex]\mu = 50, \sigma = 15[/tex].
Sample of 7, hence [tex]n = 7, s = \frac{15}{\sqrt{7}} = 5.67[/tex]The distribution of the sample means of the weights of the 7 adult standard poodles is normal, with mean of 50 pounds and standard deviation of 5.67 pounds.
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6/4 on a number line
Answer:
Here plz leave review thx
Step-by-step explanation:
HELP 100 points for these.
PLZZZ HELP also brainliest :)
Answer:
1) GCF is 1 in this case
2) GCF is 36
3) GCF is 3
4) GCF is 2
Step-by-step explanation:
Well GCF is greatest common factor, with that it Has to be the greatest and a common factor between 2 numbers. You can always list them out for example GCF of 3 and 12
THe factors of 3 are
1-3
The factors of 12 are
1-2-3-4-6-12
The greatest common one is 3.
Answer:
GCF = 1
GCF = 36
GCF = 3
GCF = 2
Step-by-step explanation:
45 & 16
The factors of 16 are: 1, 2, 4, 8, 16
The factors of 45 are: 1, 3, 5, 9, 15, 45
Then the greatest common factor is 1.
36 & 36
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
Then the greatest common factor is 36.
45 & 6
The factors of 6 are: 1, 2, 3, 6
The factors of 45 are: 1, 3, 5, 9, 15, 45
Then the greatest common factor is 3.
30 & 16
The factors of 16 are: 1, 2, 4, 8, 16
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
Then the greatest common factor is 2.
Can I have brainliest?
Create (or find) mathematical examples of the following;
1. Equation
2. Expression
3. Slope-Intercept Form
4. Slope Formula
5. Scientific Notation
6. Point-Slope Form
Answer:
Equation
2+5=9
Other i don't know
2
Select the correct answer.
Which statement is true about this equation?
-412p+5) + Bp=-11
A. The equation has one solution, p=2.
B. The equation has one solution, p=-2.
C. The equation has no solution.
D. The equation has infinitely many solutions.
Step-by-step explanation:
The equation has infinite solution p=2 that's tour variable
I need help ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
4
Step-by-step explanation:
Find the odds for and the odds against the event rolling a fair die and getting a 1,a4,a3 or 5
Answer:
Step-by-step explanation:
Assuming we're rolling a cube die with 6 sides.
Odds for rolling any of 1, 4, 3, or 5 has four possible successes
4/6 = 2/3
Odds for NOT rolling any of 1, 4, 3, or 5 has two possible successes, 2 and 6
2/6 = 1/3