solve system by elimination
9x-3y=3
3x+8y=-17
Final answer:
The system of equations 9x - 3y = 3 and 3x + 8y = -17 is solved using elimination. By multiplying the second equation by 3 and subtracting the first from the resulting equation, y is eliminated and found to be -2. Substituting y into one of the original equations then gives x as -1/3.
Explanation:
Solving a System of Equations by Elimination
To solve the system by elimination, we aim to eliminate one of the variables by combining the equations. We have the equations 9x - 3y = 3 and 3x + 8y = -17. Let's multiply the second equation by 3 to align the coefficients of x.
After multiplication, our system looks like this:
9x - 3y = 3 (Equation 1)9x + 24y = -51 (Equation 2 multiplied by 3)
Now, subtract Equation 1 from Equation 2, which eliminates the x variable:
-3y - 24y = 3 - (-51)
-27y = 54
To find the value of y, divide both sides by -27:
y = -2
Now that we have y, we can substitute it back into one of the original equations to find x:
3x + 8(-2) = -17
3x - 16 = -17
3x = -1
x = -1/3
So the solution to the system is x = -1/3 and y = -2.
david's mass is 5kg less than john's,who in turn is 8kg lighter than paul.if their total mass is 197kg.how heavy is each person.
Answer:
Paul is 70 kg, John is 62 kg and David is 65 kg.
Step-by-step explanation:
Let x the mass for each person.
Paul = x
John is lighter than Paul, so John = x-8
David's mass is 5 kg less than John's, so David = x-5
Solution:
Make an equation.
x + (x-8) + (x-5) = 197
3x -13 = 197
3x = 197 + 13
3x= 210, then divide both side by 3, to get 70.
Do substitution to get a correct answer.
70+62+65= 197
197= 197
The domain of the following relation: R: {(−4, 3), (3, 6), (−2, 1), (3, 6)} is
1, 3, 6}.
{–4, 3, −2, 3}.
{–4, −2, 3}.
No domain exists.
...?
The domain of the given relation includes the set of all x-values in the relation, which is: {–4, −2, 3}.
What is the Domain of a Relation?The domain of a relation is the set of all possible x-values (input), while the y-values are the range.
Given the relation, {(−4, 3), (3, 6), (−2, 1), (3, 6)}:
Domain of the relation is: {–4, −2, 3}.
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A right prism has a base in the shape of an octagon. The side length of the octagon is 4 inches. The length of the apothem is 4.83 inches. The height of the prism is 12 inches. What is the volume of the prism? Round your answer to the nearest whole number.
cubic inches
The volume of the prism is 927 cubic Inches.
What is Volume?This is defined as the measure of how much space there is within a three-dimensional object.
Area of Octagon A = 1/2 x apothem x perimeter
A= 1/2 x 4.83 x 4(8) = 77.28
Volume = Area of the base × height
= 77.28 x 12 = 927 cubic inches.
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11/12 - 5/8 Write your answer as a fraction in simplest form.
To subtract[tex]\(\frac{11}{12} - \frac{5}{8}\), find a common denominator (24), then subtract numerators: \(\frac{11}{12} - \frac{5}{8} = \frac{7}{24}\)[/tex] in simplest form.
To subtract the fractions [tex]\(\frac{11}{12} - \frac{5}{8}\[/tex]), we need to find a common denominator.
The least common multiple (LCM) of 12 and 8 is 24.
Now, rewrite both fractions with the denominator 24:
[tex]\[\frac{11}{12} \times \frac{2}{2} = \frac{22}{24}\]\[\frac{5}{8} \times \frac{3}{3} = \frac{15}{24}\][/tex]
Now, subtract:
[tex]\[\frac{22}{24} - \frac{15}{24} = \frac{22 - 15}{24} = \frac{7}{24}\]So, \(\frac{11}{12} - \frac{5}{8} = \frac{7}{24}\)[/tex]
I need some help with this It is given that 2(3 + x) = 6 + 2x. This is an example of the ___________ property.
A) associative B) commutative C) distributive D) identity plz type the answer asap like by 7:50 or else I'm a dead man.
Vanessa has scored 45, 32, and 37 on her three math quizzes. She will take one more quiz and wants a quiz average of at least 40. What is the minimum score Vanessa needs to earn on her fourth quiz?
Answer:
46
Step-by-step explanation:
A costumer bought a car and paid $1808 in sales tax. the sales tax rate is 6% what was the price of the car before sales tax?
Convert 1.835 × 10−4 to standard notation.
Suppose one bottle of paint can cover 20 tiles. you have 348 tiles. how many bottles of paint do you need to buy to cover all 348 tiles? explain.
To cover 348 tiles when one bottle can cover 20 tiles, you divide 348 by 20 which equals 17.4, and then round up to 18 bottles since you can't buy a fraction of a bottle.
To determine how many bottles of paint are needed to cover 348 tiles when one bottle covers 20 tiles, you should divide the total number of tiles by the number of tiles that can be covered by one bottle. The calculation is as follows:
Divide 348 (the total number of tiles) by 20 (the number of tiles one bottle of paint can cover).
348 \/ 20 = 17.4
Since you can't buy a fraction of a bottle, you would need to round up to the next whole number. Therefore, you need 18 bottles of paint to cover all 348 tiles.
Write the expression as either the sine, cosine, or tangent of a single angle.
sin 48° cos 15° - cos 48° sin 15°
A. cos 33°
B. cos 63°
C. sin 63°
D. sin 33°
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
sin 48° cos 15° - cos 48° sin 15°
As we know that,
[tex]\sin A\cos B-\cos A\sin B=\sin(A-B)[/tex]
So, we get that
[tex]A=48\textdegree\\B=15\textdegree[/tex]
Now, put it in the above expression.
[tex]\sin (A-B)=\sin(48-15)=\sin 33\textdegree[/tex]
Hence, Option 'D' is correct.
the costs of two sound systems were decreased by $10. the original costs of the systems were $90 and $60. without calculating, which had a greater percent decrease? explain
A local hamburger shop sold a combined total of 510 hamburgers and cheeseburgers on Saturday. There were 60 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?
On Saturday, 285 hamburgers were sold.
What is the system of equation?A simultaneous equation is anyone or more equations that can have the same number of unknowns and be solved concurrently. And an equation system is a simultaneous equation.
Given, a local hamburger shop sold a combined total of 510 hamburgers and cheeseburgers on Saturday.
Let x represents the number of hamburgers sold and y represents the number of cheeseburgers sold.
So, x + y = 510 {equation 1}
According to the question,
there were 60 more cheeseburgers sold than hamburgers.
x = y+ 60
We have a system of equations,
Substituting the value of x to the equation 1,
y+60+ y = 510
2y = 510 - 60
y = 450 / 2
y = 225
Then, x = 285
Therefore, 285 hamburgers were sold on Saturday.
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Desert cover about 1/7 of all land on earth.about what percent of earth's land is made up of desert
calculate the length of the line segment Round answer to the nearest tenth.
Carter can swim 25 yards of freestyle in 19 seconds. what is his speed in yards per second? at this rate,what is his speed in yards per minute
Which algebraic expression is a polynomial with a degree of 2?
Y=mx 6. can you solve for m
The value of 'm' in the equation y=mx represents the slope of the line. However, without specific 'x' or 'y' values or a complete equation like y=mx+b, it is impossible to determine the value of 'm'.
Explanation:The formula y=mx is the slope-intercept form of a linear equation where y is the dependent variable, m is the slope, and x is the independent variable. However, in this particular case, the equation provided is not complete in this form because there is no specific 'x' or 'y' value provided, and so it's not possible to calculate 'm' directly from this equation. Instead, in a more complete example, like y = 3x, you could identify 'm' as 3 by simply looking at the coefficient of 'x'. In order to clarify your equation, please provide either specific values of 'x' and 'y', or a complete equation in the format y = mx + b, where b is the y-intercept.
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In desperate need of help with long division with variables and exponents!!!
find the width, ans height and area of 26'' TV screen that has an aspect ratio of 4:3. round to the nearest whole number.
erform a simple calculation to match the screen size of a standard TV to that of a widescreen TV. If you currently have a 4:3 TV and you want to continue watching 4:3 on a widescreen TV, multiply the diagonal length of the older TV model by 1.22. The result would be the diagonal screen size that the widescreen TV would have to be to match the old model.
Say you have a 40 inch (102 cm) TV with a 4:3 aspect ratio, but you're thinking about upgrading and you don't want your screen size to get smaller. You'd need to get at least a 50 inch (127 cm) screen to view in 4:3 without your picture getting smaller. That's because 1.22 x 40 = 49. Since 49 inch TVs are generally not made, you'd need to go up to 50 inches (127 cm).how was percent used to solve real-world problems
show that the following set of functions are subspaces of F(-infinity,infinity)
a) all everywhere differentiable function that satisfy f'+2f=0 ...?
To show that the set of functions satisfying f' + 2f = 0 is a subspace of F(-∞,∞), we prove closure under addition and scalar multiplication.
Differentiable functions: To prove that the set of functions satisfying f' + 2f = 0 is a subspace of F(-∞,∞), we need to show that the set is closed under addition and scalar multiplication. This involves demonstrating that if two functions f1 and f2 satisfy the given differential equation, then any linear combination c1f1 + c2f2 also satisfies it.
Proof:
Let f1, f2 be solutions of f' + 2f = 0, then (c1f1 + c2f2)' + 2(c1f1 + c2f2) = c1(f1' + 2f1) + c2(f2' + 2f2) = c1(0) + c2(0) = 0. Therefore, any linear combination of solutions is also a solution.
The graph shows the mass of a radioactive substance as a function of time.
Enter the initial mass of the substance in the box
?? = g
Numbers that are easy to compute using mentally are called?
Please tell me what is a Noun? Help me..
A jet flies 600 kilometers in 3/4 of an hour.how far can this jet fly n 1/ hour
Which of the following is the graph of y = 4x + 2?
The line y = 4x + 2 is graphed and attached with the answer.
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written to express proportional relationship as -
y = kx {k is constant}
We have a equation that represents a line as -
y = 4x + 2
We can graph the given equation as shown in the figure attached.
Therefore, the line y = 4x + 2 is graphed and attached with the answer.
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Stephanie can type around 70 words per minute. She has less than a week to type her final research paper. If the paper has to be at least 15 pages long and each page has about 350 words, how many hours should Stephanie set aside to type her assignment?Show your work to receive full credit.
3x + 2y = 2
-2x + y = 8
Solve the system of equations.
Answer:
A: (-2,4)
Step-by-step explanation:
i did it on usatestprep
Penny sells knitted scarves for $12 each. The cost of the supplies to make each scarf x dollars. How much profit will Penny make if she sells y scarves? A) y(12-x) B) 12(x-y) C) y(x-12) D) x(12-y)
Answer:
A
Step-by-step explanation: