The solution of the system of the equations are; x = -2/3, y = -1/2 and z = 1.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The system of equation is given by;
3x − 4y + z = 2 ---- (1)
−9x + 12y − 3z = − 6 -------(2)
4x − 2y − z = -16 -----(3)
Now we add equations 1 from equation 3;
(3x − 4y + z ) + (4x − 2y − z ) = 2 -16
7x - 6y = -14 -----(4)
Further we multiply equation 3 by 3 and subtract from equation 2;
3(4x − 2y − z) - (−9x + 12y − 3z ) = -48 + 6
12x - 6y - 3z + 9x - 12y + 3z = 42
21x - 18y = 42-----(5)
Now we multiply equation 4 by 3 and add it to equation 4
3(-3x + 3z) + (9x + 4z) = 5×3 - 2
-9x + 9z + 9x + 4z = 15 -2
13z = 13
z = 1
Now we put z = 1 in equation number 5
-3x + 3×1 = 5
-3x + 3 = 5
-3x = 5 - 3
-3x = 2
x = -2/3
y = -1/2
Therefore, the solution of the system of the equations are; x = -2/3, y = -1/2 and z = 1.
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Pls help me thank u very much
Answer: y= (7a+9b)/8
Step-by-step explanation:
I can only provide the answer now, If you want more explanations reply this
Step-by-step explanation:
(2y - a)/3 = (a + 3b)/4
first we get rid of the fractions by multiplying everything first by 3 and then also by 4 ;
(2y - a) = 3(a + 3b)/4
4(2y - a) = 3(a + 3b)/4
8y - 4a = 3a + 9b
8y = 7a + 9b
y = (7a + 9b)/8
Which is greater 10*4mg or 13g
Answer: 13g
Step-by-step explanation: because each gram is 1000 milligrams
5(x+10)+x
please help with explanation Q^Q
Answer:
Solution
=5(X+10)+X
=5×x+5×10+x
=5x+50+X
=6x+50
Step-by-step explanation:
Your answer is 6x+50.
I need help please!!!
Answer:
slope = - [tex]\frac{7}{13}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, - 10 ) and (x₂, y₂ ) = (- 4, - 3 )
m = [tex]\frac{-3-(- 10)}{-4-9}[/tex] = [tex]\frac{-3+10}{-13}[/tex] = [tex]\frac{7}{-13}[/tex] = - [tex]\frac{7}{13}[/tex]
betty can mow a lawn in 120 minutes. bullwinkle can mow the same lawn in 40 minutes. how long does it take for both betty and bullwinkle to mow the lawn if they are working together?
Using the Work time problem solving technic, Betty and Bullwinkle to mow the entire lawn in 30 minutes if they are working together.
As we know that if A is complete the work of z in x days and B is complete the same work (z) in y days then both of can do complete work together then Equation of both A and B are completing work (z) together in
( 1/x + 1/y = 1/z ) days
Since Betty can mow a lawn is 120 minutes, then
Betty's mowing rate is 1/120th of a lanw per minute.
Since Bullwinkle can mow a lawn is 40 minutes, then Bullwinkle mowing rate is 1/40th of a lawn per minute.
Suppose working together they can a lawn in x minutes.
both together they can mow a lawn is x minutes, then their combined mowing rate is 1/x th of a lawn per minute.
To get the equation,
the sum of their mowing rates must equal their combined mowing rate,
1/40 + 1/120 = 1/x
Solve that by multiplying through by LCD of 40 and 120 is 120 then 4x = 120 => x = 30
Hence, when both are working together they complete the work together in 30 minutes .
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can someone help me really quick
Answer:
1/2 teaspoon of salt per 1 teaspoon of baking soda.
Step-by-step explanation:
If you're starting with 1/2 tsp of baking soda and 1/4 tsp of salt, you can multiply that by two and still have the same ratio of salt to baking soda.
:)
5.375 divided by 0.25 explained
The division of 5.375 divided by 0.25 results to 21.5
What is Division?One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. How many groups will be created,
for instance, if 30 students need to be separated into groups of five for a sporting event?
In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome.
Given:
5.375 divided by 0.25
Now, dividing the above decimal
= 5.375/ 0.25
= 5375 x 100 / 25 x 1000
= 215 / 10
= 21.5
Hence, the division results to 21.5
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Please help me out with this question which graph shows a line with a slope of -2/3 passing through (-1,0)
Answer:
Step-by-step explanation:
Correct Answer: C.
First we can see that the slope is negative, meaning the graph is decreasing.
Then we go to the point (-1,0) and go down 2 and 3 right. if that point is on the line, then we know it's correct.
When analyzing two quantitative variables, what is the first thing that should be done?.
Using the theories of quantitative variables, we got that Graphical display is the first thing that should be done when we are analyzing two quantitative variables.
Comparing the Two Quantitative Variables As we did when considering only one variable, we begin with the graphical display. A scatterplot is the most useful display technique for comparing the two quantitative variables. We plot on the y-axis the variable we consider for the response variable and on the x-axis we place the explanatory or the predictor variable.
Hence, When analyzing two quantitative variables, the first thing that should be done is Graphical display.
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Tomas drives 75 km at an average speed of 110 km/h and then 7 km at 40 km/h without stopping. What is the average speed for the whole journey to 1 dp?
The average speed for the whole journey is 95.3km/hour
What is average speed?The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity. It is represented by the magnitude and does not have direction.
Average speed = Total distance/total time taken
The distance covered in the first journey is 75km and the time spent is calculated as Distance/speed
= 75/110 = 0.68hour
The time used for the second journey is
= distance/speed
= 7/40 = 0.18 hour
The total time spent = 0.68+0.18 = 0.86 hour
The total distance traveled = 75+7 = 82km
Therefore the average speed = 82/0.86 = 95.3 km/hour.
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It costs $2 to download a song and $12 to download an entire album. Jorge has $50 to spend on downloading music. Create an inequality that represents the number of songs (s ) and albums (a ) that Jorge could download.
The inequality that represents the number of songs and albums that Jorge could download is:
$2*s + $12*a ≤ $50
How to write the inequality?Here we have the variables:
s = number of songs.
a = number of albums.
Then the total cost can be written as:
$2*s + $12*a
And we know that Jorge has a maximum of $50 to spend, so the total cost can be equal to or smaller than $50, so the inequality is:
$2*s + $12*a ≤ $50
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30 Points!!
Thank you!
30 MINS PLS HELP ASAP
The values of m<4 and m<6 are 160° and 20° respectively
How to find the value of m<4 and m<6?
To solve this problem, we need some angle geometry knowledge:
Given that: m<6 = 1/8 m<4
Since m<6 = 1/8 m<4. Thus, m<4 = 8.m<6
m<6+ m<4 = m<6 + 8.m<6 = 9.m<6 (Algebra)
m<6+ 8.m<__ = 180° will be:
m<6+ 8.m<6 = 180°
Note: m<6 + m<5 = 180° (angles on a straight line) and m<5 = m<6 (alternate angles)
m<6+ 8.m<6 = 180°
9.m<6 = 180°
m<6 = 180/9 = 20°
m<4 = 8 x m<6
m<4 = 8 x 20° = 160°
Therefore, the values of m<4 = 160° and m<6 = 20°
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Bernie has decided to purchase a new car with a list price of $18,575. Sales tax in bernie’s state is 7. 40%, and he will be responsible for a $795 vehicle registration fee and a $110 documentation fee. Bernie plans to trade in his existing car, a 1999 buick riviera in good condition, and finance the rest of the cost for five years at an interest rate of 12. 77%, compounded monthly. Assuming that the dealer gives bernie the listed trade-in price for his car, what will his monthly payment be? round all dollar values to the nearest cent. Buick cars in good condition model/year 1998 1999 2000 2001 2002 century $929 $1,086 $1,150 $1,488 $1,595 lesabre $2,075 $2,282 $2,690 $2,935 $3,374 regal $1,676 $1,794 $2,030 $2,214 $2,566 riviera $1,291 $1,455 $1,520 $1,814 $1,959 a. $472. 05 b. $439. 12 c. $438. 20 d. $518. 23.
If the dealer gives Bernie the listed trade- in price for his car, he will pay $391.97 monthly.
Given that,
Bernie has decided to purchase a new car of $ 18,575.
The sales tax is 7.40%
Now,
18,575 x 7.40% = 1,374.55
Now, summing up the result of sales tax and purchase price, we get,
18,575 + 1,374.55 = 19,949.55
Bernie will give registration fees of $795
and, a documentation fees: $110
Now , we will sum up all the above information, i.e.,
= 19,949.55 + 795 + 110
= 20,854.55
Now, divide the result of documentation fees and registration fees by 5
20,854.55 ÷ 5 = 4,170.91
Dividing the above result by 12,
4,170.91 ÷ 12 = 347.58
Now, the finance the rest of the cost for five years at an interest rate 12.77%.
347.58 x 12.77% = 44.39
And,
347.58 + 44.39 = 391.97
Therefore, If the dealer gives Bernie the listed trade - in price for his car, he will pay $391.97 monthly.
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147,21,3 Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
The sequence is geometric and the common ratio is 1/7
How to determine if the sequence is arithmetic or geometric?An arithmetic sequence is a sequence of numbers in which each differs from the preceding one by a constant value e.g 2, 4, 6, etc. That is: 6-4 = 4-2 = 2
A geometric sequence is a sequence of numbers with a constant ratio between each number and the one before e.g. 9, 27, 81, etc. That is: 81/27 = 27/9 = 3
Given: 147, 21, 3
This sequence does not have a common difference. Thus, it is not arithmetic
This sequence has a common ratio. Thus, it is geometric
common ratio = 21/147 = 1/7 or 3/21 = 1/7
Therefore, the sequence is geometric and has a common ratio of 1/7
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In a sale , all prices are reduced by 30 %.
Calculate the marked price (original price) of an article which is sold for Rs 4200 in the sale
Answer:
$2940
Step-by-step explanation:
30 percent *4200 =
(30:100)*4200 =
(30*4200):100 =
126000:100 = $1260
4200-1260=$2940
Square root 42 as a decimal
Answer:
6.481.
Square Root of 42 in Decimal Form: 6.481.
question is in the picture.
The set of ordered pairs that represent 90 degrees counter clockwise rotation about he origin is
3) A' (-6, 1) B' (-6, 6) C' (-2, 1)
How to find the coordinates of the imageRotation is a from of transformation that involves circular movement about an axis.
There two types of rotation
clockwise anticlockwiseThe transformation rule for 90 degrees clockwise rotation is as follows
(x, y) for a scale factor of r → (-y, x)
From the graph the coordinates are read and following the given transformation rule we have
preimage image
A (1, 6) → A' (-6, 1)
B (6, 6) → B' (-6, 6)
C (1, 2) → C' (-2, 1)
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56 women make up an all female choir in a church. Two women are choen to ing together for a duet. How many poible pair could be choen for the duet?
The number of possible pair that could be chosen for duet is 1540 .
In the question ,
it is given that ,
total number of females in the choir group = 56 women
for duet the number of females that are required = 2 ,
the number of possible pair that can be chosen for the duet = ⁵⁶C₂ ,
⁵⁶C₂ = (56 × 55 × 54!)/2! × (56 - 2)!
= (56 × 55 × 54!)/2! × 54!
cancelling out the common factor 54! , we get
= (56 × 55)/2 .... because 2!= 2
= 28 × 55
= 1540
Therefore , The number of possible pair that could be chosen for duet is 1540 .
The given question is incomplete , the complete question is
56 women makes up an all female choir in a church. Two women are chosen to sing together for a duet. How many possible pair could be chosen for the duet ?
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the sum of two numbers is 61, if the larger number is seven less than three times the smaller number, find both numbers
Answer:
The two numbers are 17 and 44.
Step-by-step explanation:
x --> smaller number
y --> larger number
x + y = 61
y = 3x - 7
x + 3x - 7 = 61
4x - 7 = 61
4x = 68
x = 17
y = 3(17) - 7
y = 51 - 7
y = 44
Write a rule to describe this translation. (photo attached)
The rule for given translation is (x,y)→(x + 3, y - 4).
What is Transformation?In mathematics, the phrases translation, rotation, and reflection are all used to describe the change of forms. This refers to a form moving beyond a mirror line or a fixed point. While being translated, rotated, or reflected, the shape doesn't change. The constant rotation of a shape around a fixed point or across the mirror line is known as translation. Rotation defines the way a form moves about a central axis. Shapes can be rotated by a specific number of degrees either clockwise or counterclockwise.
The rule for translation of given figure will be,
We need to move x for 3 units to left and y for 4 units downwards to get the translation, so the rule is:
(x,y)→(x + 3, y - 4).
Therefore, the rule for given translation is (x,y)→(x + 3, y - 4).
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15= x/6 -1
please respond quick
Answer:
The answer to your questions is 96.
( 1/2 )² - 6 ( 2- 2/3 ) as a fraction in the simplest form?
Answer:
the answer is-7
Step-by-step explanation:
Answer:
Exact form: -31/4
Decimal form: -7.75
Mixed number form: -7 3/4
Joel earns a commission of 5% on the audio equipment he sells, and the store keeps the rest. He sells a $750 amplifier.
(b) How much does the store keep?
Answer:
$712.50
Step-by-step explanation:
.95(750) = 712.5 If they give 5% to the seller, they get to keep 95%
Find the distance between the two points.
(-2, 5) and (4, -1)
Answer:
Step-by-step explanation: the distance is 6 but if you're talking decimal then the distance is 1.4142
Write each number in expanded notation, first without and then with exponents 20,304
The value of 20,304 using exponents will be 2.0304 × 10⁴.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.
For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the value of 20,304 will be:
= 2.0304 × 10000
= 2.0304 × 10⁴.
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HELP ME ASAP!! PLEASEEE I GOTTA SUBMIT THIS IN 10 MINUTES
Answer:the last option
Step-by-step explanation:
The price of a used car is discounted $200 each week.
If the price of a used car is discounted $200 each week then the grapg will be linearly decreasing in nature
A linear graph can be either increasing, decreasing or constant.
Here the price of the car is being discounted $200 every week, so as the number of weeks increase, the price of the car decreases
So, the graph for this situation will be linearly decreasing.
The slope of this kind of graph is negative/
Therefore, If the price of a used car is discounted $200 each week then the grapg will be linearly decreasing in nature
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Consider the equation Y=x^2-3 a) using the given input, complete the table by entering the corresponding ordered pairs separated commas x, -2, -1, 0,1,2 y,_,_,_,_,_ b) Graph the equation by plotting the vertex and one other point
Answer: I don't know
Step-by-step explanation:
The wholesale price for a chair is $160. A certain furniture store marks up the wholesale price by 21%. Find the price of the chair in the furniture store.
Round your answer to the nearest cent, as necessary.
Answer:
$193.60
Step-by-step explanation:
160x1.21=$193.60
160+21%=$193.60