Answers
3x+6y=27
x+2y=11
The idea of elimination is to eliminate (cancel out) a variable so that only one variable exists. For example, if x is eliminated, then y is being solved, and if y is eliminated, then x is being solved. We must pick a variable in the system (x or y) and find a LCM that is the additive inverse, meaning the variables cancel out. Some example of an additive inverse: -5+5=0 and 6-6=0; it is the inverse (opposite) of addition (so subtraction) in which undoes the operation to cancel it out to zero. Likewise for subtraction to addition. So, let’s choose a variable, identify the LCM of the two same variables in both equations, and either negate or add the variables together so they cancel out to 0.
Let’s choose x:
The LCM of 3 and 1 is 3, so we only need to multiply the second equation by a factor. 1•-3=-3, so we’ll multiply the entire second equation by 3, and 3-3=0:
3x+6y=27
-3(x+2y)=-3(11)
Distribute and multiply:
-3x-6y=-33
Here is the new set:
3x+6y=27
-3x-6y=11
Now, simply add or subtract the two equations:
(3x-3x)+(6-6)=27+11
Simplify:
0+0=38
0=38
This is a false statement, and thus the system does not have any solutions, meaning the lines are parallel.
So, the answer is: No Solutions
Related Questions
Which point(s) lie on the graph of the equation y = -5x - 3?
Answers
Explanation below in image
Plug in values of x to find corresponding values of y.
For example, replace x with 0 to find that...
y = -5x-3
y = -5*0 - 3
y = 0 - 3
y = -3
We have x = 0 lead to y = -3.
Therefore, the point (0, -3) is on this line. This is the y intercept.
Now try something like x = 1
y = -5x-3
y = -5*1 - 3
y = -5 - 3
y = -8
It shows the point (1,-8) is also on the line.
The straight line goes through (0,-3) and (1,-8)
We can repeat this process infinitely many times since there are infinitely many numbers to pick for x.
See the graph below. I used GeoGebra to make it, but you can use something like Desmos or similar.
2) Out of the 976 potatoes in the storeroom, 61 are rotten. What percentage of
the potatoes are rotten?
Answers
Answer:
The answer is 6.25%
Step-by-step explanation:
Given;Out of the 976 potatoes in the storeroom, 61 are rotten.So,
(61 ÷ 976) × 100%
0.0625 × 100% = 6.25%
Thus, 6.25% of potatoes are rotten.
Step-by-step explanation:
% of potatoes rotten = 61/976 × 100
=> 6100/976
=> 6.25%
Parallelogram ABCD has vertices at A (-3, 6.5), B (-1, -1.5), and C (4.5, 0). What are the coordinates of Point D?
Answers
The coordinates of Point D are (2.5, 8).
What is parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.
Given:
Parallelogram ABCD has vertices at A (-3, 6.5), B (-1, -1.5), and C (4.5, 0).
We have to find the coordinates of Point D.
Let its fourth vertex be D(a, b).
Join AC and BD. Let AC and BD intersect at point O.
We know that the diagonals of a parallelogram bisect each other.
So, O is the midpoint of AC as well as that of BD.
Using the midpoint formula,
Midpoint = [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
Here, ([tex](x_1, y_1) = (-3, 6.5), (x_2, y_2) = (4.5, 0)[/tex]
⇒ Midpoint of AC = [tex](\frac{-3 + 4.5}{2}, \frac{6.5 +0}{2}) = (\frac{1.5}{2}, \frac{6.5}{2}) = (0.75, 3.25)[/tex]
Now,
Midpoint of BD is = [tex](\frac{-1+a)}{2}, \frac{-1.5+b}{2})[/tex]
⇒
[tex]\frac{-1+a}{2} = 0.75, \frac{-1.5+b}{2} = 3.25 \\ -1 + a = 1.5, -1.5 + b = 6.50\\a = 2.5, b = 8[/tex]
Hence, the coordinates of Point D are (2.5, 8).
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if a tree is 105 metres tall in real life what would be the height of the diagram of the tree if the scale was 1: 1000
Answers
Answer:
1.05
Step-by-step explanation:
it is 105 divided by 1000
Answer:
0.105 metres
Step-by-step explanation:
105 divided by 1000
9+2+4+6+123=?
please help
Answers
Answer:
144
Step-by-step explanation:
9+2+4+6+123=
11+10+123
21+123
144
Your brother gave you $10 to help with a shoe purchase. This covered 8% of the cost. How much did the shoes cost? Write and solve an equation, let s represent the cost of the shoes.
Answers
The equation to represent the cost of shoes is 0.08s=10 and the cost of shoes is $125.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, your brother gave you $10 to help with a shoe purchase. This covered 8% of the cost.
Let s represent the cost of the shoes.
Now, equation is
8% of s=10
8/100 ×s=10
0.08s=10
s=10/0.08
s=$125
Therefore, the equation to represent the cost of shoes is 0.08s=10 and the cost of shoes is $125.
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Translate the sentence into an equation.
Five times the sum of a number and 9 equals 3.
Use the variable y for the unknown number.
Answers
Answer: To translate the given sentence into an equation, we can start by replacing the words "five times the sum" with the mathematical expression "5(x + 9)". Then, we can replace the word "number" with the variable y, to get:
5(y + 9) = 3
Next, we can distribute the 5 to obtain:
5y + 45 = 3
Finally, we can subtract 45 from both sides to solve for y:
5y = -42
y = -42/5
y = -8.4
Therefore, the equation that represents the given sentence is y = -8.4.
Step-by-step explanation:
consider the trinomial 15x² - 34x - 16.
List all the factor pairs for -240.
Answers
Answer: To find the factor pairs for -240, we can use the following steps:
Find the prime factorization of -240: -240 = (-2) * (-2) * (-2) * (-3) * (-5)
For each prime factor, there are two possible factor pairs: (-1) and (1), and (-n) and (n). For example, for the factor -2, the possible factor pairs are (-1) and (1), and (-2) and (2).
The factor pairs for -240 are: (-1) and (1), (-2) and (2), (-3) and (3), (-5) and (5), (-6) and (6), (-10) and (10), (-15) and (15), (-30) and (30).
Thus, the factor pairs for -240 are: (-1, 1), (-2, 2), (-3, 3), (-5, 5), (-6, 6), (-10, 10), (-15, 15), and (-30, 30).
Step-by-step explanation:
Give an example of Limit of a Polynomial Function.
Note; With explanation po sana.
Pa help po pls.. I'll mark as brainliest for the one who can answer.
Answers
An example of limit in polynomial will be the polynomial function f(x) = x³ + 2x² - 5. As x approaches 2, the value of the function approaches 11. So, the limit of f(x) as x approaches 2 is 11.
What is a polynomial?A polynomial simply means an expression which is composed of variables, constants and exponents, which are combined using mathematical operations such as addition, subtraction, multiplication and division
In mathematical notation, we can write it as: Here, lim x->2 (x³ + 2x² - 5)
= x³ + 2x² - 5
= 2³ + 2(2²) - 5
= 8 + 8 - 5
= 11
This means that as x gets arbitrarily close to 2, the values of the function gets arbitrarily close to 11.
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please help !!!!!!!!
Answers
8.96848786347
i think this should be right i did it with my 5th grade math skills and dont wory i have an a+
each day you do homework for m minutes and watch tv for 30 minutes. Which expression can you use to find how many minutes you do both activities.
Answers
Answer:
Let y be the expression for the minutes you do both activities.then
y=m+30 is the required expression
Helpp!! Solve the system by graphing.
Answers
Step by step
y = 2x +2
y = 2x -2
these two equations have the same slope (2) with different y intercepts (2 and -2) so they are parallel lines. Since the lines are parallel, the pair of equations have no solution.
During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes. Based on this relative frequency, how many pars or better could he be expected to make on the remaining 150 holes? Round to the nearest whole number if necessary.
70 pars or better
60 pars or better
65 pars or better
53 pars or better
Answers
Dirk will make 70 pars or better.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes.
Out of 90 holes, Dirk made par or better on 42 holes.
At this rate, Out of 1 hole, Dirk made par or better on (42/90) holes.
Then, Out of 150 holes, Dirk will make par or better on -
(42/90 x 150) holes
(42/90 x 150)
70
Therefore, Dirk will make 70 pars or better.
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Which of the binomials below is a factor of this trinomial? x^2 + x - 30
Answers
The binomials which correctly represent the factors of the given trinomial; x² + x - 30 as required in the task content are; ( x - 5 ) and ( x + 6 ).
Which binomials correctly represents the factors of the given trinomial?As evident in the task content; the given trinomial whose binomial factors are to be determined is; x² + x - 30.
By factorisation; the given trinomial expression can be written as;
x² + 6x - 5x - 30
x ( x + 6 ) -5 ( x + 6 )
( x - 5 ) ( x + 6 )
On this note, the required binomials which are factors of the given trinomial expression are; ( x - 5 ) and ( x + 6 ).
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Lenore rounds each factor to the nearest ten to estimate the product of 51 times 37 as 1,500.is Lenore’s estimate reasonable?Explain.
Answers
Answer:
yes
Step-by-step explanation:
51 to nearest ten is 50
37 to nearest ten is 40
50 * 40 = 2000
and it's an estimate so yes
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the perimeter of the right triangle shown
O 10 units
O 24 units
O 36 units
O 64 unitsl
Answers
Answer: 24 units.
Step-by-step explanation: To find the perimeter of a triangle, you need to add the length, width, and hypotenuse. The length and width are provided, but we need to find the hypotenuse of the triangle. To do this, we need to use the Pythagorean Theorem.
The Pythagorean Theorem is basically a^2 + b^2 = c^2 where a and b are the legs of the triangle and c is the hypotenuse (also known as the triangle's longest side). However, whatever answer you get needs to be square-rooted, which is your complete answer. Let's say that the side that's 6 units is leg a and the side that's 8 units is leg b.
6^2 + 8^2 = c^2
36 + 64 = 100
√100 = 10.
Now that we know the hypotenuse, we can add it to our other two sides.
6 + 8 + 10 = 24.
Therefore, 24 is your answer.
Let me know if this is right! :)
29. What is length of x?
Please explain this one too me since I did not understand it thanks
Answers
The value of x is 10 yards. The given shape is a trapezoid.
What are trigonometry ratios?
Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Draw a line parallel to the base.
Name the corner point of the shape.
Assume that ∠ADG = θ.
Consider △BDF:
BD = 6 + x
DF = 8 + 4.8 = 12.8 yrds.
The cosine of an angle is the ratio of the base to the hypotenuse of the right-angle triangle.
cos θ = DF/BD
cos θ = 12.8 /(6+x) .....(i)
Consider △CDE:
cos θ = DE/CD
cos θ = 8/x .....(ii)
Now equate equations (i) and (ii):
12.8 /(6+x) = 8/x
Cross multiply:
12.8 × x = 8(6+x)
12.8x = 48 + 8x
12.8x - 8x = 48
4.8x = 48
Divide both sides by 4.8:
x = 48/4.8
x = 10
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The value of x is 10 yards. The given shape is a trapezoid.
What are trigonometry ratios?Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Draw a line parallel to the base.
Name the corner point of the shape.
Assume that ∠ADG = θ.
Consider △BDF:
BD = 6 + x
DF = 8 + 4.8 = 12.8 yrds.
The cosine of an angle is the ratio of the base to the hypotenuse of the right-angle triangle.
cos θ = DF/BD
cos θ = 12.8 /(6+x) .....(i)
Consider △CDE:
cos θ = DE/CD
cos θ = 8/x .....(ii)
Now equate equations (i) and (ii):
12.8 /(6+x) = 8/x
Cross multiply:
12.8 × x = 8(6+x)
12.8x = 48 + 8x
12.8x - 8x = 48
4.8x = 48
Divide both sides by 4.8:
x = 48/4.8
x = 10
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each minute your heart pumps 1.5 gallons of blood around your body. How many pints of blood will your heart pump in a day?
Answers
The heart pumps around 17280 pints of blood in a day.
To find out how many pints of blood your heart pumps in a day, we need to determine the total volume of blood that your heart pumps in one day.
We know that your heart pumps 1.5 gallons of blood per minute. To find out how much blood your heart pumps in one day, we need to multiply that amount by the number of minutes in a day.
1 day = 24 hours
1 hour = 60 minutes
So, the number of minutes in one day is 24 hours x 60 minutes = 1440 minutes
Now, we can use this information to find out how many gallons of blood your heart pumps in a day.
Gallons of blood pumped per day = 1.5 gallons/minute x 1440 minutes/day
= 2160 gallons
1 gallon = 8 pints
So the number of pints of blood that your heart pumps in a day = 2160 gallons × 8 pints/gallon = 17280 pints.
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your heart pumps 2000 gallons of blood around your body each day.
if your body pumps around 1.5 gallons of blood each minute then a day is 24 hours so yu do that x together which is 20 but as its hours you do it for 2000 and just incase yu need some more info
(1.5 imperial gallons) x 24 hours = 589.173508 m3 s
SORRY IF THIS DONT ALL MAKE SO MUCH SENSE
two copies of one tenth
Answers
Answer:
0.2 or 1/5 or one fifth----------------------------------------
Two copies of one tenth translates as:
2*1/10 = 2*0.1 = 0.2 or 1/5Answer:
Two copies of 1/10 = 1/5
Step-by-step explanation:
Given statement,
→ two copies of one tenth.
Forming the expression,
→ 2 × (1/10)
Let's simplify the expression,
→ 2 × (1/10)
→ (2 × 1)/10
→ 2/10
→ 1/5
Hence, the answer is 1/5.
A bill of $3400 was paid with $20 notes and $100 notes. Ninety notes were used. How many $20 notes were used?
Answers
Answer:
70
Step-by-step explanation:
for every 5 $20 notes is $100 70 notes is $1400 and the other 20 is $2000 which makes 3400
3) At the grocery store, the bags of oranges weigh 4 1/3 pounds. How much would 2 1/2 bags of oranges weigh?
Answers
Answer:7 7/8. pounds.
Step-by-step explanation:
A recipe calls for 6 liters of oj, 3 liters of grape juice and 9.5 liters of ice water. How much grape juice and water will be used with 2 liters of Jo?
Answers
If we use 2 liters of OJ, you will need to change the recipe and use:
1 liter of grape juice.3.2 liters of water.How much grape juice and water it will need?We know that a recipe calls for 6 liters of OJ, 3 liters of grape juice and 9.5 liters of ice cream.
If instead we use 2 liters of OJ, then the ratio of the recipe that we use is given by the quotient below:
2L/6L = 1/3
So we will just use 1/3 of each of the amounts that the recipe calls, we will se:
(1/3)*3 liters of grape juice = 1 liter of grape juice.
(1/3)*9.5 liters of water = 3.2 liters of water.
These are the amounts that you need to use.
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Give the following number
in Base 10.
F16 = [? ]10
Answers
The next decimal number should be changed to hexadecimal. Your final response may contain up to six fractional digits. In decimal 386210, subscript 10 to F16.
How do you write a number in base 10?F16 is 001000011000.1111. 218. F716 is 001000011000.111101112. 710 = (h0)16 = 716 is how the hexadecimal number is represented. It is necessary to add a 1 to the left and modify the number for both to 0. In base-2, the numeral 15 is represented as 1111, and the number 16 is represented as 10000. The greatest value in base-16 is the letter F, in a similar vein. such that 10 is the new value.
Binary 10 equals 1010, thus. Dividing 10 by 2 successively until the quotient equals 0 will yield the decimal to binary equivalent. By writing the remainder in each division step from bottom to top, it is possible to determine the binary equivalent.Base-16 is the definition given to hexadecimal. There are many powers of 16 in each place value in the number. The hexadecimal numbers are: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. 10 through 15 are represented, accordingly, by the letters A through F.
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I need help with this, I need to simplify but I don't know how
Answers
Answer: solve the same variables
Step-by-step explanation:
1. 3y + 4.1
2. 4x +
3. 5x + 22½
4. 4y²
5. + 25
6. 0
Is a function that can be graphed
as a solid line discrete or continuous?
Answers
Linear function Is a function that can be graphed as a solid line discrete or continuous
What is a linear function?Linear functions are simply known as functions whose graph is a straight line.
They have one dependent variable and one independent variable.
These functions have either one or two variables without exponents.
Continuous graphs are used to represent functions that are continuous along their entire or whole domain.
Whereas, discrete graphs are used to represent values at specific points along the number line from different directions.
Types of the linear function;
Direct variationslope-intercept formstandard formpoint-slope formHence, it is a linear function
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a wall is 50cmx50cm how many 2cmx1cm tiles would you need to fill it
Answers
Answer: 1250
Step-by-step explanation: 50 x 50 = 2,500
2,500 divided by 2 is 1250
in a company, 60% of workers are women. if 800 people work on the company who aren't women, how many workers are there in all? use pencil and paper. show two different ways that you can solve this problem. how many workers in all?
Answers
Answer:
2000 workers
Step-by-step explanation:
All the workers: 100%
Women: 60%
Others: 40% = 800 workers
=> 1% of the workers: 800/40 = 20 workers
=> 100% = 20 x 100 = 2000 workers
(I can't think of another one)
A students wants to write an expression for, all of the elements which are not in set A. Which expression below matches the statement A. NA (B) B (C) -A (D) A’
Answers
The expression A' represents the statement for all of the elements which are not in set A.
What is Set?A set is a collection of well defined objects.
Given that A students wants to write an expression for all of the elements which are not in set A.
The elements within set A are denoted by A.
We have to find all of the elements which are not in set A.
U represents the universal set and A is the given set.
A'=U-A
Hence, the expression A' represents the statement for all of the elements which are not in set A.
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Ms.Metz had her students estimate the length and width of a math book. Dana's estimate was 40cm by 20cm. The book measured 24cm by 16cm. How far off was her estimate?
Answers
Dana's estimated length was 66.67% far off the actual length and her estimated width was 25% far off the actual width.
What is percent error?Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.
Percent Error Formula
The formula for percent error is:
PE = (|Estimated value-Actual value|/ Actual value) × 100
Given,
Actual length of the book = 24 cm
Actual width of the book = 16 cm
Dana's estimated length of the book = 40 cm
Dana's estimated width of the book = 20 cm
Error in measurement of length of the book =
(Measured Length - Actual Length/Actual length) × 100
= (40 - 24/24) ×100 = 66.67%
Error in measurement of width of the book =
(Measured width - Actual width/Actual width) × 100
= (20 - 16 / 16) × 100 = 25%
Hence, Dana's estimated length and breadth was 66.67% and 25% far off the actual length and width of the book respectively.
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Find the length of the model in the picture!!!Then find the scale factor.The length of an actual bird is shown on the picture.
Answers
We calculated length of model bird in the picture = 2 ¹⁵₁₆ inch and scale factor =1/2
what is scale factor?
It is expressed as the ratio of the dimension of a model object and dimension of an actual object.
A scale factor is a number which is multiplied by an object in order to form a proportional enlarged or reduced object.
What is the length of the model in the picture?Given, the length of an actual bird = 5⁷₈ inch = 47/8 inch
also given, 1 inch = 0.5 inch
1 inch = 1/2 inch
we need to determine the length of model bird by multiplying the above factor.
now, length of model bird = 47/8 × 0.5 inch = 47/16 inch = 2¹⁵₁₆ inch
scale factor = length of model bird/ length of actual bird = 47/16 /47/8
scale factor = 1/2
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