When solving the following equations, multiply the first and second equation by a constant in order to eliminate the y terms.
2x + 2y = 7
6x + 3y = -2
What are the constants of both equations?
Answers
Answer:
multipliers: 3, 2 for subtraction; or 3, -2 for addition.solution: (x, y) = (-4 1/6, 7 2/3)Step-by-step explanation:
You want to solve the given system of equations by eliminating the y-term. You also want to know what constants are used in the process.
EliminationThe y-term can be eliminated from these equations by combining them in such a way as to may the coefficient of y be zero. This can be done an infinite number of ways.
One way that works reasonably well is to identify the coefficients of y, and multiply each equation by the y-coefficient in the other equation. The resulting equations can be subtracted one from the other to eliminate the y-terms, which now have identical coefficients. You can choose the equation with the smaller x-coefficient to subtract from the other one.
ApplicationThe y-term coefficients are 2 and 3.
Multiply the first equation by 3, and the second by 2.
3 × (2x +2y) = 3 × 7 ⇒ 6x +6y = 21
2 × (6x +3y) = 2 × (-2) ⇒ 12x +6y = -4
The x-coefficients are 6 and 12. We choose to subtract the first equation (with x-coefficient 6) from the second equation:
(12x +6y) -(6x +6y) = (-4) -(21)
6x = -25 . . . . . . . . simplified
x = -25/6 = -4 1/6 . . . . . divide by 6
Substituting for x in the first equation, we have ...
2(-25/6) +2y = 7
2y = 7 +25/3 . . . . . add 25/3
2y = 46/3 . . . . . . . .combine terms
y = 23/3 = 7 2/3 . . . . divide by 2
The solution to the equations is (x, y) = (-4 1/6, 7 2/3).
CheckSince these numbers are not integers, we choose to check them in the original equations. We used the first equation to find y, so we'll use the second equation for checking.
6(-4 1/6) +3(7 2/3) = -25 +23 = -2 . . . . . . as required
__
Additional comment
If you solve these by addition, rather than subtraction, you want to choose multipliers that result in opposite coefficients, so they add to zero. Essentially, you use the opposite coefficients, as described above, but you negate one of them.
Above, we chose the subtraction in a way that resulted in the x-coefficient being positive. If you arbitrarily choose the signs of the multipliers (always negating the second one, for example), the combined equations may make the x-coefficient negative. That works, too, but may require more mental effort to deal with the minus sign.
Of course, you can use the x-coefficients and eliminate the x-terms.
Or, you can use a single multiplier that corresponds to the ratio of the coefficients. For example the ratio of the 2nd y-coefficient to the first one is 3/2. Multiplying the first equation by this will give the y-term a coefficient of 3, matching the y-coefficient in the 2nd equation. Then the subtraction can proceed as already described.
(6x +3y) -3/2(2x +2y) = (-2) -3/2(7)
3x = -25/2 . . . . . simplified; y is gone.
Related Questions
HELP I NEED IN ONLY TEN MUINETS Checking Your Understanding
Quick
Check
Drag each rate into the box labeled Unit Rate or Not Unit Rate.
60 miles per hour
Unit Rate
Not a Unit Rate
168 hours in 7 days
34 miles for each gallon
$15 for 2 DVDs
$8 for every hour
22 words per minute
Answers
Answer:
The first thing to do is to find out which answer choices are similar and then it will be easier to find an answer.
Step-by-step explanation:
Answer:
Unit rate are
22 words per minute
34 miles for each gallon
60 miles per hour
$8 for every hour
Not a unit rate
168 hours in 7 days
$15 for 2 DVDS
PLEASE HELP!!!!!!!!!!!!!
Answers
Hope this helps!
On December 7, Toys R Fun purchased $1,000 of merchandise with terms of 2/10, n/30. If payment is made on December 30, demonstrate the required journal entry for Toys R Fun to record the payment under the perpetual inventory system.
Answers
The correct option b. Debit Accounts Payable $1,000; Credit Cash $980; Credit Merchandise Inventory $20, is the required journal entry for Toys R Fun.
Explain the term Credit Merchandise Inventory?Merchandise inventory serves as a holding account of inventory that is awaiting sale as a current asset. Since there is a typical debit balance, debit grows while credit shrinks.For the stated question;
Toys R Fun is offered a discount of two percent if he settles within 10 days as well as the payable is required in 30 days, as indicated by the terms "2/10,n/30."
$20 (2 percent of $1,000) is the result.
On the 17th, which falls inside the discount days, the payment for the journal entry for Toys R Fun is:
$1,000 - Dr. Accounts Payable
Cr money - $980
$20 worth of Cr inventory.
Let's say, however, that the payment is made by December 30 rather than that day.
The submission will be:
$1,000 Dr. Accounts Payable.
$1,000 cash in Cr.
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The complete question is-
On Dec. 7, Toys R Fun purchased $1,000 of merchandise with terms of 2/10,n/30. If payment is made on December 30, demonstrate the required journal entry for Toys R Fun to record the payment under the perpetual inventory system.
a. Debit Cash $1,000; Credit Accounts Payable $1,000
b. Debit Accounts Payable $1,000; credit Cash $980; credit Merchandise Inventory $20.
c. Debit Accounts Payable $1,000; credit Cash $1,000
i need help bc my dad got 18+ and i want him to give it to me so help me with this plz
5-8=
2-8+3=
6-17=
help nowwwww
Answers
Answer:
5-8= -3
2-8+3= -3
6-17= -11
Step-by-step explanation:
3
7
-11
About 3% of the population has a particular genetic mutation. 600 people are randomly selected.
Find the mean for the number of people with the genetic mutation in such groups of 600.
Answers
The mean for the number of people with the genetic mutation in such groups of 600 is 18.
Given that,
About 3% of the population has a particular genetic mutation.
This means that for any group of people, 3% of the people has a particular genetic mutation.
This is a binomial distribution.
Probability that people having genetic mutation = 3% = 0.03
Random sample size = 600
Mean for a binomial distribution can be calculated as,
Mean = n × p
= 600 × 0.03
= 18
Hence the mean number of people having genetic mutation is 18.
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Mrs. Liu is mixing glue and shaving cream to make snowman puff paint for her art class. The ounces of glue to ounces of shaving cream must have a ratio of 7:15. If she is mixing 56 ounces of glue, how much shaving cream does she need?
Answers
The ounces of shaving cream will be 230 ounces.
How to illustrate the ratio?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
In this case, Mrs. Liu is mixing glue and shaving cream to make snowman puff paint for her art class. The ounces of glue to ounces of shaving cream must have a ratio of 7:15. If she is mixing 56 ounces of glue ,the shaving cream will be:
= 56 ÷ 7/15
= 56 × 15/7
= 120
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NEED HELP!! I"LL GIVE YOU BRAINLIEST!! Find the value of b. a = 3 and c =12
Answers
Answer: b = 11.62
Step-by-step explanation:
We can use this formula to solve for b:
\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)
\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)
\(b^2= \sqrt{144-9}\)
= 11.61895004
We can round that to 11.62.
Hope this helped!
Please see screenshot
Answers
The graph of the feasible region is attached
How to determine the graph of the feasible regionFrom the question, we have the following parameters that can be used in our computation:
\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)
To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0
Using the above as a guide, the graph is attached
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Translate the triangle.
Then enter the new coordinates.
Answers
answer:
A' (-3,3) B' (-2,-1) C' (-6, -2)
Which of the following has imaginary solutions?
x ^ 2 + 3x - 5 = 0
x ^ 4 - 5x ^ 2 + 3 = 0
2x ^ 2 - 6x = - 7
- 3x ^ 2 = - 5
Answers
2x² - 6x = -7 equation has imaginary solutions
To determine if an equation has imaginary solutions, we can examine the discriminant of the quadratic equation
x² + 3x - 5 = 0
a = 1, b = 3, c = -5
Discriminant = (3)² - 4(1)(-5) = 9 + 20 = 29
The equation has two real solutions
x⁴ - 5x ^ 2 + 3 = 0
This equation is a quartic equation, not a quadratic equation. Quartic equations can have both real and imaginary solutions
2x² - 6x = -7
2x^2 - 6x + 7 = 0
a = 2, b = -6, c = 7
Discriminant = (-6)²- 4(2)(7) = 36 - 56 = -20
Since the discriminant (-20) is negative, the equation has two complex (imaginary) solutions.
-3x² = -5
Dividing both sides by -3, we get:
x²= 5
a = 1, b = 0, c = -5
Discriminant = 0² - 4(1)(-5) = 20
The equation has two real solutions.
Hence, 2x² - 6x = -7 equation has imaginary solutions
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What are the coordinates of the endpoints of the midsegment for A RST that is parallel TS? Enter your answer by filling in the boxes. (_ , _) and (_ , _)
Answers
Answer:
2,4 3,5
Step-by-step explanation:
An equation of a circle is given as (x + 6)2 + (y − 7)2 = 81. Find the center and radius of the circle.
Answers
The equation of a circle is written as (x – h)^2 + (y – k)^2 = r^2
h and k are the center point and r is the radius.
In the given equation h = -6 and k = 7 and r would be the square root of 81, which is 9.
Center (-6,7)
Radius = 9
The required center is \((-6,7)\) and the radius is 9 units.
Given equation is,
\((x + 6)^2 + (y-7)^2 = 81\)....(1)
Equation of the circle: The general equation of the circle with the center (a,b) and the radius r is represented by,
\((x-a)^2+(y-b)^2=r^2\)...(2)
We can write the given equation as,
\((x + 6)^2 + (y-7)^2 = (9)^2\)
Comparing equations (1) and (2) we get,
The Centre of the given circle is \((-6,7)\)
The radius of the given circle is 9 units.
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Which of these fractions is an improper fraction? 5/3 or 3/5
Answers
Answer:
5/3 is an improper fraction because 5 is higher then 3. So the correct way of writing it would be 1 2/3.
Step-by-step explanation:
Explanation:
5/3 is an improper fraction, and could be a mixed number, because the denominator is less than the numerator.
5/3 = 1 2/3
that the amount of heating oil used during a given month is inversely proportional to the outside temperature if Andrea's pet store uses 514 gallons of oil in a month that has an average temperature of 36°F, how much oil would she expect to use in a month (of the same length) with an average daily temperature of 35°F?______ gallons (type an integer or fraction)
Answers
The expected gallons oil to be used in a month with an average daily temperature of 35°f is 528 24/35 gallons
What is Inverse variation?Inverse variation is the relationships between variable. It states if the value of one quantity increases, then the value of the other quantity decreases.
It is in form of A=k/T
where k is the constant , A is the amount of oil and T is the average Temperature used daily
To find the value of k when A is 514 and T is 36
k =AT
= 514× 36=18504
to find the value of A when T is 35
A = K/T
= 18504/35
= 528 24/35 gallons.
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Which of the following is a true statement of the figure?
An image of a triangle ABC. The angle bisector of angle B is ray BD. Point D lies on side AC.
Question 1 options:
A
D
D
C
=
D
C
C
B
A
C
A
B
=
D
B
D
C
A
D
D
C
=
A
B
C
B
B
C
B
A
=
D
C
C
B
Answers
Angle ∠EBD is congruent to angle ∠DBA. Option D is the true statement.
What is an angle bisector?An angle bisector is the line segment that bisects the angle into two equal halves.
Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
Ray BE is a bisector of angle CBA,
∠CBE = ∠EBA = 60°
∠EBD = ∠EBA - ∠DBA
∠EBD = 60 - 30 = 30
So,
∠EBD = ∠DBA [DB becomes angle bisector of angle EBA]
Thus, ∠EBD is congruent with ∠DBA is the only correct answer among the option.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Which of the following statements is true if ray BE is a bisector of angle CBA?
A. Ray BD is a bisector of angle CBA.
B. ∠EBD is congruent to ∠CBE.
C. Ray BE is a bisector of angle ABE.
D. ∠EBD is congruent to ∠DBA.
A university is interested in determining the average statistics anxiety score for all undergraduate students in the U.S. For a random sample of 33 undergraduate students, it is found that the average average statistics anxiety score is 39.4 with a standard deviation of 0.9. Assume that the statistics anxiety scores for all undergraduate students in the U.S is normally distributed. A 98% confidence interval for the true mean statistics anxiety score μ is closest to.
Answers
The 98% confidence interval for the true mean statistics anxiety score (μ) is approximately (39.037, 39.763).
To calculate the 98% confidence interval for the true mean statistics anxiety score (μ) for all undergraduate students in the U.S., we can use the formula:
Confidence interval = sample mean ± (critical value * standard error)
First, we need to find the critical value associated with a 98% confidence level. Since we are assuming a normal distribution, we can use the Z-table or a statistical software to find this value. For a 98% confidence level, the critical value is approximately 2.33.
Next, we calculate the standard error (SE) using the formula:
SE = standard deviation / √sample size
In this case, the standard deviation is 0.9 and the sample size is 33. Plugging these values into the formula, we get: SE = 0.9 / √33 ≈ 0.156
Now, we can calculate the confidence interval:Confidence interval = 39.4 ± (2.33 * 0.156)
Simplifying the expression:Confidence interval ≈ 39.4 ± 0.363
This gives us the interval (39.037, 39.763). This means we are 98% confident that the true mean statistics anxiety score for all undergraduate students in the U.S. falls within this interval.
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20 points fast plzz!!! Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 feet. Use the perimeter formula to find the width of the rectangular yard in inches: P = 2L + 2W.
6 in.
12 in.
72 in.
144 in.
Answers
Answer:
The width of the rectangular yard is 72 inches
Step-by-step explanation:
Let
L -----> the length of the yard
W ----> the width of the yard
we know that
The perimeter is equal to
we have
substitute in the formula and solve for W
Divide by 2 both sides
Subtract 5 both sides
Convert feet to inches
Remember that
1 ft= 12 in
Step-by-step explanation:
The width of the rectangle is 6 feet or 72 inches if the perimeter of the yard is 22 feet, and the length of his yard is 5 feet.
What is rectangle?It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.
Perimeter of the rectangle :
P = 2L + 2W
L = 5 feet
22 = 2(5) + 2W
After calculating:
W = 6 feet
1 feet = 12 inches
6 feet = 72 inches
Thus, the width of the rectangle is 6 feet or 72 inches if the perimeter of the yard is 22 feet, and the length of his yard is 5 feet.
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Michael has a granola recipe that requires 1 4 pounds of oats to make one batch of granola. If Michael uses 4 5 pounds of oats while making granola, how many batches has he made?
Answers
Michael has made 3.21 batches of granola.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Michael has a granola recipe that requires 14 pounds of oats to make one batch of granola.
If Michael uses 45 pounds of oats while making granola,
then number of batches he made,
= 45 /14
= 3.21
Hence, he made 3.21 batches.
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Photo for the question I asked a few seconds ago please help
Answers
Answer:
9160.88
Step-by-step explanation:
Hope this helps and have a wonderful day!!!
Answer:
A≈9160.88
Step-by-step explanation:
A=πr^2=π·54^2≈9160.88418
Simplify
12 cm : 60 mm
Answers
Answer:
cm^3/5
Step-by-step explanation:
STEP 1: m
Simplify ——
60
Equation at the end of step 1: m
((12c • ——) • m) • m
60
STEP 2 :Multiplying exponential expressions : 2.1 m2 multiplied by m1 = m(2 + 1) = m3.
final result is cm^3/5
Answer:
3cm:15cm or to simplify it further 1cm:5cm
A circular flower bed is 20 m in diameter and has a circular sidewalk around it that is 2m wide. Find the area of the sidewalk in square meters. Use 3.14 for
Answers
According to the solving the area of the sidewalk is 138.16 square meters.
What is an area?Size of a location on a surface is expressed in terms of area. As opposed to surface area, which refers to the area of an open surface or the border of a three-dimensional object, plane region or plane size refers to the area of a shape or planar lamina.
According to the given information:The width of the circular sidewalk is 2 m, which means that the radius of the entire area, including the flower bed and the sidewalk, is 10 m + 2 m = 12 m.
To find the area of the sidewalk, we need to subtract the area of the flower bed from the area of the larger circle.
Area of larger circle = πr²
= 3.14 x 12²
= 452.16 square meters (rounded to two decimal places)
Area of flower bed = πr²
= 3.14 x 10²
= 314 square meters
Area of the sidewalk = Area of larger circle - Area of flower bed
= 452.16 - 314
= 138.16 square meters (rounded to two decimal places)
Therefore, the area of the sidewalk is 138.16 square meters.
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can you please help me with this
Answers
Sathish will be going to pay a total of $64.8 for the gas.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
The First 150 and last 150 km will cover by Satish only
Since 6 liters covers 100 km
So,
Cost of 300 km (18 liters) ⇒ 18×1.2 = 21.6
Now,
The journey 2100 - 300 = 1800 km has been covered by all three
Split 1800/3 = 600 km of money Satish will pay
So,
Cost of 600km(36 liters) ⇒ 36 × 1.2 = 43.2
Total paid = 21.6 + 43.2 = 64.8.
Hence "Satis will be going to pay a total of $64.8 for the gas".
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6. Sumio rotated the arrow below 270° clockwise.
↑
Which of the following shows the arrow after the 270° clockwise rot
0->
OK
O
Answers
The arrow after a 270° clockwise rotation will be pointing downward. Therefore, the correct answer is option C.
After a 270° clockwise rotation, the arrow will point downward. This rotation involves rotating the arrow in the clockwise direction by 270° from its original position. As a result, the arrow will change its orientation to face downward, opposite to its initial upward direction. This can be visualized as if the arrow has been flipped vertically, pointing towards the bottom. The other options, such as the right side arrow, left side arrow, or upward arrow, do not correspond to the direction of rotation specified in the question.Thus, the correct answer is option c.
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Without writing the equation x^2 + y^2 + 24x – 26y+ 277 = 0 in the standard form, state whether the graph of this equation is a
parabola, circle, ellipse, or hyperbola.
a. parabola
c. hyperbola
b. ellipse
d. circle
Answers
Answer:
circle
Step-by-step explanation:
You can see there is a x^2 and y^2 and 24 x and 26 y meaning if you do complete the square you can write it as a circle in standard form
Find the perimeter and area of the figure, 6 cm, 7 cm, 9.5 cm, and 6.5 cm
Answers
Answer:
Perimeter = 29 cm
Step-by-step explanation:
The perimeter is the sum of all sides of the geometric figure:
perimeter = 6 + 7 + 9.5 + 6.5
perimeter = 29 cm
5. Skylar got a manicure for $25. If she plans to
tip 20%, how much is her tip?
Answers
Answer:
$5.00
Step-by-step explanation:
All we have to do is multiply 25 x 1/5 or 20%
25 x 1/5 = $5.00
to check, $5 x 5 = 25
Please help me answer this question.
What is the vertex of the parabola?
Answers
Answer:
g
Step-by-step explanation:
the point at the intersection of the parabola and its line of symmetry
The number of lines that can be drawn perpendicular to a given line at a given point on that line in space is:
A. 3
B. 0
C. not enough information
D. infinitely many
Answers
Answer:
D. infinitely many
Step-by-step explanation:
Perpendicular lines can be drawn everywhere on the lone in infinitely different places, making the answer infinite.
The number of lines that can be drawn perpendicular to a given line at a given point on that line in space is infinite many.
The correct answer is an option (D)
What is perpendicular to line?"It is a straight line that makes an angle of 90° with another line. "For given question,
Lines are perpendicular to each other if their intersection with one another forms a right angle. Through any given line, there are an infinite number of perpendicular lines.Through a specific point on a line, there exists only one perpendicular line. Similarly, for a line and a point not on that line, there is only one perpendicular line through the point.We can draw infinite perpendicular lines to a
Therefore, the number of lines that can be drawn perpendicular to a given line at a given point on that line in space is infinite many.
The correct answer is an option (D)
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What’s the correct answer answer asap for brainlist
Answers
Answer:
your answer is B
Step-by-step explanation:
Germany, Austria-Hungary, Bulgaria, and the Ottoman Empire
The Hernandez family and the Cox family each used their sprinklers last summer. The Hernandez family’s sprinkler was used for 15 hours. The fox familys sprinkler was used for 30 hours. There was a combined total output of 1275 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 50 L per hour?
Answers
ANSWER
The output rate for the Hernandez family was 15 L/hr and for the Fox family was 35 L/hr.
EXPLANATION
To solve this problem, we have to create a system of two simultaneous equations.
Let the output rate of the Hernandez family sprinkler be h.
Let the output rate of the Fox family sprinkler be f.
The product of the rate and the time used is equal to the output:
\(\text{Rate}\cdot\text{time}=\text{output}\)We have that the combined total output for both sprinklers is 1275 L, which means that:
\(\begin{gathered} (15\cdot h)+(30\cdot f)=1275 \\ \Rightarrow15h+30f=1275 \end{gathered}\)The sum of the two rates is 50 L/hr, which means that:
\(h+f=50\)Now, we have a system of two simultaneous equations:
\(\begin{gathered} 15h+30f=1275 \\ h+f=50 \end{gathered}\)Solve the equations by substitution.
Make h the subject of the formula in the second equation:
\(h=50-f\)Substitute that into the first equation:
\(\begin{gathered} 15(50-f)+30f=1275 \\ 750-15f+30f=1275 \\ 750+15f=1275 \\ \Rightarrow15f=1275-750=525 \\ f=\frac{525}{15} \\ f=35\text{ L/hr} \end{gathered}\)Recall that:
\(h=50-f\)Therefore, we have that:
\(\begin{gathered} h=50-35 \\ h=15\text{ L/hr} \end{gathered}\)Hence, the output rate for the Hernandez family was 15 L/hr and for the Fox family was 35 L/hr.