The following linear system has [[12], [11], [4]] matrix of constants,
x + y + z = 12
x - y = 11
x - y + z = 4
(Option D)
Verification of the Choice:
The given linear system is,
x + y + z = 12
x - y = 11
x - y + z = 4
This can be written in the form of matrix as follows,
[tex]\left[\begin{array}{ccc}1&1&1\\1&-1&0\\1&-1&1\end{array}\right][/tex] [tex]\left[\begin{array}{}x&y&z\end{array}\right][/tex] = [tex]\left[\begin{array}{}12&11&4\end{array}\right][/tex]
Hence, option D is the correct linear system as it contains the desired matrix.
About the Other Options:
The RHS matrix in option A would be,
[tex]\left[\begin{array}{}26&17&23\end{array}\right][/tex] which is not the desired matrix.
Similarly, the linear systems in the options B and C contain the matrix [tex]\left[\begin{array}{}23&17&26\end{array}\right][/tex] and the matrix [tex]\left[\begin{array}{}4&11&12\end{array}\right][/tex] on the RHS of the equality, which are not desired.
Thus, option D is correct.
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The table shows the cost of birdseed at the Feed n Seed store. What is the constant of proportionality between the cost and the number of pounds?
A table titled Feed n Seed Bird Seed. The table has 2 columns, Pounds and Cost. Row 1 says 5, 2 dollars and ninety-five cents. Row 2 says ten, five dollars and ninety cents. Row 3 says fifteen, 8 dollars and eighty-five cents.
A
0.59
B
0.60
C
1.18
D
2.95
The constant of proportionality between the cost and the number of pounds is: A. 0.59.
What is Constant of Proportionality?The constant of proportionality of a relationship between two variables X and Y can be defined as the ratio between of X and Y at a constant value. This means that the ratio or product of X and Y will give us a constant if both are in a proportional relationship.
Thus, the constant of proportionality for the relationship between two variables X and Y would be calculated as:
Constant of proportionality (k) = Y/X. [this is the proportional between the two quantities, X and Y].
Given the table of values, using a pair of points on the table, say, (5, 2.95), we can calculate the constant of proportionality as:
X = 5
Y = 2.95
Constant of proportionality (k) = Y/X = 2.95/5
Constant of proportionality (k) = 0.59 pounds per dollar.
Therefore, the constant of proportionality between the cost and the number of pounds is: A. 0.59.
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Solve for t.......
[tex]4 (t + \cfrac{1}{4} \: ) = 3[/tex]
Answer:
[tex]t = \cfrac{1}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]4(t+\cfrac{1}{4})=3[/tex]
Divide both sides by 4:
[tex]t+\cfrac{1}{4}=\cfrac{3}{4}[/tex]
Subtract 1/4 from both sides:
[tex]t = \cfrac{3}{4}- \cfrac{1}{4}[/tex]
[tex]t = \cfrac{2}{4}[/tex]
Simplify:
[tex]t = \cfrac{1}{2}[/tex]
Answer:
[tex]t = \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]4(t + \frac{1}{4} ) = 3[/tex]
Divid the whole equation by 4.
[tex] \frac{4(t + \frac{1}{4} )}{4} = \frac{3}{4} [/tex]
[tex](t + \frac{1}{4} ) = \frac{3}{4} [/tex]
[tex]t + \frac{1}{4} = \frac{3}{4} [/tex]
Take 1/4 to right side.
[tex]t = \frac{ 3}{4} - \frac{1}{4} [/tex]
[tex]t= \frac{2}{4} [/tex]
To simplify the answer more divide the numerator and denominator by 2.
[tex]t = \frac{1}{2} [/tex]
Helpppppp What’s the prime factorization of 36 and 22
Show Work Please Thank You
The angles in degrees to radian is as follows:
-54 degrees = -3π / 10 radian
How to convert from degree to radian?The measurement is in degrees. Let's convert it to radian with respect to π.
Therefore,
180 degrees = π radian
-54 degrees = ?
cross multiply
Hence,
angle in radian = -54 × π / 180
angle in radian = - 54π / 180
angle in radian = - 6π / 20
angle in radian = -3π / 10 radian
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Which expression could represent the length of a rectangle that has an area equal to 4x2+12x?
there are two expressions that can represent the length of the rectangle, these two expressions are:
L = x
or
L = (4x + 12)
Which expression could represent the length of the rectangle?
Remember that for a rectangle of length L and width W, the area is given by:
A = L*W
In this case, we know that the area is:
[tex]A = 4x^2 + 12x[/tex]
We can factorize that expression into:
[tex]A = x*(4x + 12)[/tex]
So there are two expressions that can represent the length of the rectangle, these two expressions are:
L = x
or
L = (4x + 12)
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y=3x-4 and y= -x+2 to find the system of equations
Answer:
x=3/2 y=1/2
Step-by-step explanation:
If the measure of WZX is 262 what is the measure of XWY?
Answer:
49°
Step-by-step explanation:
The circumference of a circle measures 360 degrees, so arc XW is 98°.
So, angle XWY is 49°.
Please i need help for this calculus
Step-by-step explanation:
First thing first, let find the x value of where P and Q both meet y=5, we know that y=5, and y=2x^2+7x-4, so using transitive law,
[tex]5 = 2 {x}^{2} + 7x - 4[/tex]
[tex]2 {x}^{2} + 7x - 9[/tex]
[tex]2 {x}^{2} - 2x + 9x - 9[/tex]
[tex]2x(x - 1) + 9(x - 1)[/tex]
[tex](2x + 9)(x - 1) = 0[/tex]
[tex]x = 1[/tex]
[tex]2x + 9 = 0[/tex]
[tex]x = - \frac{9}{2} [/tex]
Now, to find the gradient of the curve let take the derivative of both sides
[tex]5 = 2 {x}^{2} + 7x - 4[/tex]
[tex]0 = 4x + 7[/tex]
[tex]4x + 7[/tex]
Plug in -9/2, let call that point P
[tex]4( \frac{ - 9}{2} ) + 7 = - 11[/tex]
Plug in 1, let call that point Q
[tex]4(1) + 7 = 11[/tex]
So the gradient of the curve at point P (-9/2,5) is -11
The gradient of the curve at point Q (1,5) is 11.
4(6)^x 864 for x answer for x
Answer:
x = 3
Step-by-step explanation:
Maybe you want the value of x such that ...
4(6^x) = 864
SolutionDividing by 4 gives ...
6^x = 216
You may know that 216 = 6^3. Using that, we can equate exponents:
6^x = 6^3
x = 3
Alternatively, we can use logarithms to find x. Taking logs gives ...
x·log(6) = log(216)
x = log(216)/log(6) = 3
A lender requires PMI that is 0.8% of the loan amount of $470,000. How much (in dollars) will this add to the borrower's monthly payments? (Round your answer to the nearest cent.)
$
The amount add to the borrower's monthly payment is $313.33.
Given that lender requires PMI that is 0.8% of the loan amount of $470,000.
A loan's PMI, or personal mortgage insurance, is a type of mortgage insurance used by lenders when making traditional loans such as home loans. A PMI helps cover the loss to the lender (bank) if the borrower stops making monthly mortgage payments on their home loan. Therefore, the PMI can be described as a kind of risk mitigation tool for the bank when the borrower defaults on their EMIs (monthly mortgage payments). So, PMI for a borrower is an additional cost or payment for the borrower on top of his monthly payments i.e. EMI.
Thus, the additional amount of dollars that the borrower has to pay for the PMI on his loan along with his monthly mortgage payments
= Principal Loan amount × (PMI/12)
= $470,000 × (0.8%/12)
= $470,000 × (0.008/12)
= $470,000 × 0.0006666667
=$313.333349
Hence, the additional monthly payment for PMI where lender requires PMI that is 0.8% of the loan amount of $470,000 is $313.33.
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Solve rs + t = u for the variable s
Answer:
[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]
Step-by-step explanation:
You have to move the variables (r and t) with u to isolate s.
[tex]rs+t=u[/tex]
[tex]-t[/tex] [tex]-t[/tex]
------------------------
[tex]rs=u-t[/tex]
÷ [tex]r[/tex] ÷ [tex]r[/tex]
------------------------
[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]
Which sequence has a common difference of -8?
{63, 71, 79, 87, 95, …}
{800, 8, 12.5, 1.5625, …}
{536, 528, 520, 512, 504, …}
{1, -8, 64, -512, 4,096, …}
8 ABC please trig assignment
Using equivalent angles, the solutions are given as follows:
a) [tex]x = \frac{15\pi}{23}[/tex].
b) [tex]x = \frac{9\pi}{62}, x = \frac{53\pi}{62}[/tex].
c) [tex]x = \frac{3\pi}{8}, \frac{11\pi}{8}[/tex]
What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
For item a, we have to find the equivalent angle on the 2nd quadrant, where the sine is also positive.
Hence:
[tex]\pi - \frac{8\pi}{23} = \frac{23\pi}{23} - \frac{8\pi}{23} = \frac{15\pi}{23}[/tex]
Hence [tex]x = \frac{15\pi}{23}[/tex].
For item b, if two angles are complementary, the sine of one is the cosine of the other.
Complementary angles add to 90º = 0.5pi, hence:
[tex]x + \frac{11\pi}{31} = \frac{\pi}{2}[/tex]
[tex]x = \frac{31\pi}{62} - \frac{22\pi}{62}[/tex]
[tex]x = \frac{9\pi}{62}[/tex]
The equivalent angle on the second quadrant is:
[tex]\pi - \frac{9\pi}{62} = \frac{62\pi}{62} - \frac{9\pi}{62} = \frac{53\pi}{62}[/tex]
Hence the solutions are:
[tex]x = \frac{9\pi}{62}, x = \frac{53\pi}{62}[/tex]
For item c, the angles are also complementary, hence:
[tex]x + \frac{\pi}{8} = \frac{\pi}{2}[/tex]
[tex]x = \frac{4\pi}{8} - \frac{\pi}{8}[/tex]
[tex]x = \frac{3\pi}{8}[/tex]
The tangent is also positive on the third quadrant, hence the equivalent angle is:
[tex]x = \pi + \frac{3\pi}{8} = \frac{8\pi}{8} + \frac{3\pi}{8} = \frac{11\pi}{8}[/tex]
Hence the solutions are:
[tex]x = \frac{3\pi}{8}, \frac{11\pi}{8}[/tex]
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How many solutions does the system have?
Y= 4x8
4y = 4x - 8
The number of solutions to the system is 1
What is a linear equation?A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the number of solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
y = 4x + 8
4y = 4x - 8
Substitute y = 4x + 8 in 4y = 4x - 8
4(4x + 8) = 4x - 8
Expand the equation
16x + 32 = 4x - 8
Evaluate the like terms
12x = - 40
Divide by 12
x = -10/3
The above means that the number of solutions to the system is 1
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B) Using the two point above find the slope using the formula m =
y/₁y₁
x₂-1
C) Plug in your slope and one of the two points above into point-slope formy - y₁ = m(x-x₁)
D) Change above equation into slope-intercept form y = mx + b. (See page 5 in lesson 5.06).
16+20
The linear equations are y - 25 = 0.89(x - 20) and y = 0.89x + 7.2
The slope of the lineThe complete question is added as an attachment
The two points from the graph are (20, 25) and (38, 41)
The slope of the line is calculated using
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (41 - 25)/(38 - 20)
Evaluate
m =0.89
The linear equation in point slope formThis is calculated as:
y - y1 = m(x - x1)
Substitute the known values in the above equation
y - 25 = 0.89 * (x - 20)
Evaluate
y - 25 = 0.89(x - 20)
The linear equation in slope-intercept formWe have:
y - 25 = 0.89(x - 20)
Expand
y - 25 = 0.89x - 17.8
Add 25 to both sides
y = 0.89x + 7.2
Hence, the linear equations are y - 25 = 0.89(x - 20) and y = 0.89x + 7.2
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Leila bought 3 gallons of milk in one-gallon containers. She paid $9.75. QUESTION: What is the unit rate?
Hello and Good morning/afternoon:
Let's take this problem step-by-step:
What does the problem want:
⇒ unit rate ⇒ price per gallon
What does the problem give us:
⇒ price of all three milk
⇒ number of gallons of milk bought
Therefore
[tex]\hookrightarrow \text {unit rate} = \text{total amount of money spent} / \text {total amount of milk bought}\\\\\hookrightarrow\text{unit rate} = 9.75 / 3 = 3.25 _. \text {dollar per gallon}[/tex]
Answer: 3.25 dollars per gallon
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03* For which one of the following functions is (-1,-1) a relative minimum?
f(x,y)=xy + 1/x + 1/y
f(x,y)=x^2 +2x
f(x,y)=xy-y^2
f(x,y)=xy-1/x-1/y
If (-1, -1) is an extremum of [tex]f[/tex], then both partial derivatives vanish at this point.
Compute the gradients and evaluate them at the given point.
[tex]f(x,y)=xy+\frac1x +\frac1y[/tex][tex]\nabla f = \left\langle y - \dfrac1{x^2}, x - \dfrac1{y^2}\right\rangle \implies \nabla f (-1,-1) = \langle-2,-2\rangle \neq \langle0,0,\rangle[/tex]
[tex]f(x,y) = x^2+2x[/tex][tex]\nabla f = \langle 2x+2,0\rangle \implies \nabla f(-1,-1) = \langle0,0\rangle[/tex]
[tex]f(x,y)=xy-y^2[/tex][tex]\nabla f = \langle y, x-2y\rangle \implies \nabla f(-1,1) = \langle-1,1\rangle \neq\langle0,0\rangle[/tex]
[tex]f(x,y) = xy-\frac1x-\frac1y[/tex][tex]\nabla f = \left\langle y + \frac1{x^2}, x + \frac1{y^2}\right\rangle \implies \nabla f(-1,1) = \langle0,0\rangle[/tex]
The first and third functions drop out.
The second function depends only on [tex]x[/tex]. Compute the second derivative and evaluate it at the critical point [tex]x=-1[/tex].
[tex]f(x,y) = x^2+2x \implies f'(x) = 2x + 2 \implies f''(x) = 2 > 0[/tex]
This indicates a minimum when [tex]x=-1[/tex]. In fact, since this function is independent of [tex]y[/tex], every point with this [tex]x[/tex] coordinate is a minimum. However,
[tex]x^2 + 2x = (x + 1)^2 - 1 \ge -1[/tex]
for all [tex]x[/tex], so (-1, 1) and all the other points [tex](-1,y)[/tex] are actually global minima.
For the fourth function, check the sign of the Hessian determinant at (-1, 1).
[tex]H(x,y) = \begin{bmatrix} f_{xx} & f_{xy} \\ f_{yx} & f_{yy} \end{bmatrix} = \begin{bmatrix} -2/x^3 & 1 \\ 1 & -2/y^3 \end{bmatrix} \implies \det H(-1,-1) = 3 > 0[/tex]
The second derivative with respect to [tex]x[/tex] is -2/(-1) = 2 > 0, so (-1, -1) is indeed a local minimum.
The correct choice is the fourth function.
WILL GIVE BRAINLIEST
Note * Use the d=rt formula (distance = rate * time). NOTE: You may not be able to solve for the variable. If you do not have enough information to solve for the variable then write the equation.
1) 50 mph
2) 70 mph
3) x mph
4) (x+10)mph
5) (x-5)mph
The length of the trip at a distance of 300 miles and the given times are
6 hours30/7 hours300/x hours300/x + 10 hours300/x - 5 hoursHow to determine the length of the trip?The distance is given as:
d = 300
The formula is represented as:
d = r * t
Make t the subject
t = d/r
Substitute 300 for d
t = 300/r
When r = 50 mph,
t = 300/50
Evaluate
t = 60
When r= 70 mph, we have
t = 300/70
Evaluate
t = 30/7
When r = x, we have
t = 300/x
When r = x + 10, we have
t = 300/x + 10
When r = x - 5, we have
t = 300/x - 5
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Complete question
A train traveled 300 miles. How long did the trip take if the train was traveling at a rate of:
Note * Use the d=rt formula (distance = rate * time). NOTE: You may not be able to solve for the variable. If you do not have enough information to solve for the variable then write the equation.
Please help, will mark brainliest.
Divide the interval [3, 5] into [tex]n[/tex] subintervals of equal length [tex]\Delta x=\frac{5-3}n = \frac2n[/tex].
[tex][3,5] = \left[3+\dfrac0n,3+\dfrac2n\right] \cup \left[3+\dfrac2n,3+\dfrac4n\right]\cup\left[3+\dfrac4n,3+\dfrac6n\right]\cup\cdots\cup\left[3+\dfrac{2(n-1)}n, 3+\dfrac{2n}n\right][/tex]
The right endpoint of the [tex]i[/tex]-th subinterval is
[tex]r_i = 3 + \dfrac{2i}n[/tex]
where [tex]1\le i\le n[/tex].
Then the definite integral is given by the Riemann sum
[tex]\displaystyle \int_3^5 \sqrt{8+x^2} \, dx = \lim_{n\to\infty} \sum_{i=1}^n \sqrt{8+{r_i}^2} \Delta x = \boxed{\lim_{n\to\infty} \frac2n \sum_{i=1}^n \sqrt{17 + \frac{12i}n + \frac{4i^2}{n^2}}}[/tex]
Which statement is true?
1-31 = 3 and -1-4| = -4
1-31 = 3 and 1-4| = -4
-131 = 3 and 14| = 4
1-31 = 3 and -14| = 4
Answer:
|-3| = 3 and -|-4| = -4
Step-by-step explanation:
The absolute value function changes the sign to positive, if it isn't already. The usual rules of arithmetic and logic apply to these statements.
|-3| = 3 (true) and -|-4| = -4 (true) ⇒ this statement is true
|-3| = 3 (true) and |-4| = -4 (false) ⇒ this statement is false
-|3| = 3 (false) and |4| = 4 (true) ⇒ this statement is false
|-3| = 3 (true) and -|4| = 4 (false) ⇒ this statement is false
__
Additional comment
A compound "and" statement is only true if all of the parts of it are true.
If s(x) = x - 7 and f(x) = 4x²-x + 3, which expression is equivalent to (t*s) (x)?
Answer: [tex]4x^3 -29x^2 +10x-21[/tex]
Step-by-step explanation:
[tex](4x^2 -x+3)(x-7)\\\\=4x^3 -28x^2 -x^2 +7x+3x-21\\\\=4x^3 -29x^2 +10x-21[/tex]
Let f(x)=x^2 and g(x)=(x+3)^2. Describe the transformation from f(x) to g(x).
Select one:
Shift right 3
Shift up 3
Shift down 3
Shift left 3
Answer:
shift left 3
Step-by-step explanation:
(x+3)²
x = -3
therefore translation by (-3,0)
The negative number shows it move to the left
I need help with this question
The cost of goods sold using LIFO is $99.
Cost of goods sold using LIFOUsing this formula
Cost of goods sold=(March 3 Purchased units × March 3 Purchase price)+ [(March 3 Purchased units -March 9 sold units)×March 1 Beginning inventory cost]
Let plug in the formula
Cost of goods sold=(15 units×$3.90)+[(22 units-15 units)×$5.80]
Cost of goods sold=$58.5+(7 units×$5.80)
Cost of goods sold=$58.5+$40.6
Cost of goods sold=$99.1
Cost of goods sold=$99 (Approximately)
Therefore the cost of goods sold using LIFO is $99.
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Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X ≥ 5), n=6, p=0.3
The probability of obtaining a success is 0.010935.
Given that the probability of obtaining success is P(X>=5),n=6,p=0.3.
We are required to find the probability of obtaining a success if the probability is P(X>=5).
Probability is basically likeliness of happening an event among all the events possible.
Binomial distribution is basically the discrete probability distribution of the number of successes in a sequence of n independent experiments.
[tex](a+b)^{n} =nC_{0}p^{0} (1-p)^{n-0}+-----------nC_{n} p^{n} (1-p)^{0}[/tex]
We have to just put n=6 anr r=6 and 5 one by one to get the probability.
P(X>=5)=[tex]6C_{5}(0.3)^{5} (0.7)^{1} +6C_{6}(0.3)^{6} (0.7)^{0}[/tex]
=6!/5!1!8*0.00243*0.7+0.000729
=6*0.00243*0.7+0.000729
=0.010206+0.000729
=0.010935
Hence the probability of obtaining a success if the probability is P(X>=5) is 0.010935.
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Help me with this question please. ASAP!
Answer:
Step-by-step explanation:
I am going to be honest here. I know the answer is 22 but I cant really explain it you kinda just have to trust I'm right.
FIND THE INDICATED PROBABILITY FOR THE FOLLOWING:
IF P(A OR B) = 0.9, P(A) = 0.5, AND P(B) = 0.6, FIND P(A AND B)
The value of the probability P(A and B) is 0.20
How to determine the probability?The given parameters about the probability are
P(A or B) = 0.9
P(A) = 0.5
P(B) = 0.6
To calculate the probability P(A and B), we use the following formula
P(A and B) = P(A) + P(B) - P(A or B)
Substitute the known values in the above equation
P(A and B) = 0.5 + 0.6 - 0.9
Evaluate the expression
P(A and B) = 0.2
Hence, the value of the probability P(A and B) is 0.20
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ASAP help me with this question PLEAZE
Answer:
38°
Step-by-step explanation:
EFGH is an isosceles trapezoid (a trapezoid with two congruent legs is isosceles)
∠HGF=70° (base angles of an isosceles trapezoid are congruent)
∠EGH=32° (angles in a triangle add to 180°)
∠FGE=38° (angle subtraction postulate)
Can someone please help meee<3
Answer:
36
Step-by-step explanation:
[tex]\sqrt{24a}=12\sqrt{6} \\ \\ 24a=864 \\ \\ a=36[/tex]
The Bureau of Alcohol, Tobacco, and Firearms (BATF) has been concerned about lead levels in California wines. In a previous testing of wine specimens, lead levels ranging from 47 to 660 parts per billion were recorded. How many wine specimens should be tested if the BATF wishes to estimate the true mean lead level for California wines to within 10 parts per billion with 95% confidence? (Round your answer up to the nearest whole number.)
The number of specimens should be tested is 1352.
According to the statement
we have to given that the in testing of wine specimens, lead levels ranging from 47 to 660 parts per billion were recorded. and we have to find the number specimen should be tested.
so,
Using the uniform and the z-distribution, it is found that 1353 specimens should be tested.
For an uniform distribution of bounds a and b, the standard deviation is given by:
σ = [tex]\sqrt{\frac{(b-a^{2})}{12} }[/tex]
and put the values a= 50 and b= 700 then the
standard deviation is 187.64
And here the critical value become 1.6 then
We want the sample for a margin of error of 10, thus, we have to solve for n with the help of value of m is 100.
Then n is 1352.
So, The number of specimens should be tested is 1352.
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6. Dacă a + 2b = 18 şi b+3c=17, calculaţi 3a+8b+6c.
Answer:
Răspuns: 88=>rezultatul
Explicație pas cu pas:
a+2b =18/×3
b+3c=17/×2
3a+6b =54 ^
2b+6c=34 | +
3a+(6b+2b)+6c=54+34
3a+8b+6c=88
Step-by-step explanation: