Final answer:
The system of linear equations x + y = 75 and 10x + y = 48 is solved using the elimination method, resulting in the solution x = 3 and y = 72.
Explanation:
The student is given a system of two linear equations:
x + y = 7510x + y = 48To solve this system, we can use the method of elimination or substitution. Here, elimination appears to be the more straightforward method. We'll subtract the second equation from the first to eliminate the variable y, as they both have the same coefficient in y. Subtracting the second equation from the first gives us:
9x = 27
Solving for x, we find:
x = 27 / 9 = 3
Now that we have the value for x, we can substitute it back into either of the original equations to find the value for y. Substituting into the first equation:
3 + y = 75 => y = 75 - 3 => y = 72
So the solution to the system is x = 3 and y = 72. This method remains effective even with the advent of computer algebra methods and Mathcad.
Please help! The question is in the picture.
Answer:B
Step-by-step explanation:
A scale has a percent error of 5%. The actual mass of a rock is 258 g.
Select from the drop-down menus to correctly complete the statement.
The scale is likely to show the mass is either [Choose...] g or [Choose...] g.
Please help, I have an F in math and the semesters almost over. Im doing over due so I can try to bring my grade up to a C. Please help, Ill give brainlyest.
Multiply the weight by 5%, then subtract that from the weight for the lower value and add it for the higher value:
258 x 0.05 = 12.9g
Lower value: 258 - 12.9 = 245.1g
Higher value: 258 + 12.9 = 270.9g
Y''+Y'+Y=1
solve ordinary differential equation
Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.
Identify which is NOT a Pythagorean triple.
A)5, 12, 13B)7, 24, 25C)8, 15, 16D)11, 60, 61E)12, 35, 37
Answer:
C) 8, 15, 16 is NOT Pythagorean TRIPLET.
Step-by-step explanation:
There numbers a, b and c are said to be a PYTHAGORAS TRIPLET if
[tex](a) ^2 + (b)^2 = (c) ^2[/tex]
Now, here in the given options:
A)5, 12, 13
[tex](5)^2 + (12)^2 = 25 + 144 = 169 = (13)^2\\\implies (5) ^2 + (12)^2 = (13) ^2[/tex]
Hence, 5, 12, 13 is a Pythagorean TRIPLET.
B)7, 24, 25
[tex](7)^2 + (24)^2 = 49 + 576= 625 = (25)^2\\\implies (7) ^2 + (24)^2 = (25) ^2[/tex]
Hence, 7, 24, 25 is a Pythagorean TRIPLET.
C)8, 15, 16
[tex](8)^2 + (15)^2 = 64 + 225= 289 \neq (16)^2 = 256\\\implies (8) ^2 + (15)^2 \neq (16) ^2[/tex]
Hence, 8, 15, 16 is NOT Pythagorean TRIPLET.
D)11, 60, 61
[tex](11)^2 + (60)^2 = 121 + 3600 = 3721 = (61)^2\\\implies (11) ^2 + (60)^2 = (61) ^2[/tex]
Hence, 11, 60, 61 is a Pythagorean TRIPLET.
E)12, 35, 37
[tex](12)^2 + (35)^2 = 144 + 1225 = 3721 = (37)^2\\\implies (12) ^2 + (35)^2 = (37) ^2[/tex]
Hence, 12,35 , 37 is a Pythagorean TRIPLET.
Jacob has a 20 gallon fish tank. He could only find a quart size pitcher to fill his tank. How many times will Jacob have to fill the pitcher to get 19 gallons of water in his tank?
A
38
B
76
C
80
D
152
Answer:
B.76
Step-by-step explanation:
4 quarts = 1 gallon
so 4 * 19=76
How do you determine the slope of a line
Answer:
To calculate the slope of a line you need only two points from that line, (x1, y1) and (x2, y2). There are three steps in calculating the slope of a straight line when you are not given its equation.
Step-by-step explanation:
Step One: Identify two points on the line. Step Two: Select one to be (x1, y1) and the other to be (x2, y2).
an old building has 48 big windows the building has 12 small windows thare are 9 broken windows how many windows are not broken
Answer:
51
Step-by-step explanation
12-9 = 3
48+ 3 = 51
Total number of not broken windows is 51 windows
Given that;Number of big window = 48
Number of small window = 12
Number of broken window = 9
Find:Total number of not broken windows
Computation:Total number of not broken windows = Number of big window + Number of small window - Number of broken window
Total number of not broken windows = 48+ 12 - 9
Total number of not broken windows = 60 - 9
Total number of not broken windows = 51 windows
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add the following complex numbers (2-8)+(5-i)
Answer:
-1-i
Step-by-step explanation:
(2-8)+(5-i)=-6+5-i=-1-i
What is the value of x in the equation? 4 3/7 x − 3 1/2 = 12
A) 3 2/5
B) 3 1/2
C) 3 3/4
D) 3 6/7
Answer:
B) 3 1/2 or 7/2
Step-by-step explanation:
4 3/7=31/7
3 1/2=7/2
---------------
31/7x-7/2=12
31/7x=12+7/2
31/7x=24/2+7/2
31/7x=31/2
x=(31/2)/(31/7)
x=(31/2)(7/31)
x=7/2
Answer:
The answer is B.) 3 1/2
Step-by-step explanation:
4
3
7
x − 3
1
2
= 12
31
7
x −
7
2
= 12
31
7
x · 14 −
7
2
· 14 = 12 · 14
62x − 49 = 168
62x = 217
x =
217
62
=
7
2
= 3
1
2
there are two green Skittles out of every five what percent are green
Answer:
40%Step-by-step explanation:
2 green of every 5:
[tex]\dfrac{2}{5}[/tex]
Convert to the percent:
[tex]\dfrac{2}{5}\cdot100\%=\dfrac{200}{5}\%=40\%[/tex]
14.
-2(y – 4) + 8y +2 < 16
Answer:
y<1
Step-by-step explanation:
-2(y-4)+8y+2<16
-2y+8+8y+2<16
6y+10<16
6y<16-10
6y<6
y<6/6
y<1
John was born in 1980 for his grandmother was born in 1928 of the year is 2014 how old are both John and his grandmother
John is 34, Grandmother is 86.
2014 - 1980 = 34.
2014 - 1928 = 86.
:)
What is the median of this set of data values? 11, 13, 14, 15, 18, 20, 23, 26
Step-by-step explanation:
= (11+13+14+15+18+20+23+26)/8
= 140/8
= 17.5
Answer:
16.5
Step-by-step explanation:
what is the slope for (12,5) (9,8)
We can use the points (12, 5) and (9, 8) to solve.
Slope formula: y2-y1/x2-x1
= 8-5/9-12
= 3/-3
= -1
______
Best Regards,
Wolfyy :)
determine the number of solutions for the systems
x+y=2 and 2x+2y=8
Answer:
The number of solutions of the system is zero
Step-by-step explanation:
we have
a) [tex]x+y=2[/tex]
Isolate the variable y
[tex]y=-x+2[/tex] ----> equation A
This is the equation of the line in slope intercept form
where
The slope is m=-1
The y-intercept is b=2
b) [tex]2x+2y=8[/tex]
Isolate the variable y
[tex]2y=-2x+8[/tex]
[tex]y=-x+4[/tex] ----> equation B
This is the equation of the line in slope intercept form
where
The slope is m=-1
The y-intercept is b=4
Remember that
If two lines are parallel, then their slopes are the same
In this problem the lines A and B are parallel lines with different y-intercept
so
The lines don't intersect
therefore
The system has no solution
Sasha research the size of zoos in her State. she found that the zoo in the north part of the state is almost twice as large as the zoo in the South. she also found that the zoo in the South part of the state has 200 fewer than twice the number of animals as the northern Zoo. how many animals per acres does each Zoo have?
acers - number of animals
North : 64 - ?
South : 35 - 3800
What is a non-example of unit rate
Answer:
60 calories per day
Step-by-step explanation:
example: 60 calories per serving so obviously the non example is the opposite
In the box, type in the number that will correctly complete the sentence.
Jane has a debt of $63. She owes equal amounts to seven different people. Her debt to each person can be expressed as Answer
dollars.
Answer:
$9 to each person
Step-by-step explanation:
63/7=9
Answer: 9
Step-by-step explanation:
$63 divided by 7 people = $9 debt per person
the total cost of c ounces of cinnamon if each ounce costs$.79
The total cost of c ounces of cinnamon would be $0.79c
Since each ounce costs $0.79, just multiply this number by the number of ounces to get the cost.
If one inch represents 18 feet, what dimensions would you use to make a scale drawing of a building 630 feet by 450 feet?
Answer:
35 by 25 inches
Step-by-step explanation:
1 inch = 18 feet
each 18 feet in the scale model is one inch, which means that there is one inch per 18 feet, so all you need to do is divide 630 by 18 and 450 by 18.
630/18 = 35
450/18 = 25
so the dimensions of the scale model are 35 by 25 inches
Cara is 14 years old . This is twice as old as her brother . How old is her brother
Cara's brother is 7 years old.
14 is twice as much as 7 (7 * 2 = 14).
Answer:
7
Step-by-step explanation:
If Cara is twice the age of her brother,
divide 14/2
7, her brother is 7
25. A company spends $34,000 annually on product payment costs. Its
total annual expenses are $296,000. About what percentage of the
total annual expenses is for product payment costs? Round to the
nearest hundredth of a percent.
Answer:
The percentage of the total annual expenses for product payment costs is 11.49% .
Step-by-step explanation:
Given:
Annually costs on product company spends = $34000 and total annual expenses = $296000.
Now, to get the percentage of the total annual expenses for product payment costs. We will calculate the percentage, $34000 by $296000:
According to question:
[tex]\frac{34000}{296000} \times 100[/tex]
[tex]=0.11486\times 100[/tex]
[tex]=11.486[/tex]
Now, rounding to the nearest hundredth of a percent to 11.486 will be 11.49. As we see 6 in the thousandth place and 8 in hundredth place so rounding to decimal in hundredth place will change 8 into 9.
Therefore, the percentage of the total annual expenses for product payment costs is 11.49% .
A manufacturer of tennis rackets makes a profit of $15 on each oversized racket and $8 on each standard racket. To meet dealer demand, daily production of standard rackets should be between 30 and 80, and production of oversized rackets should be between 10 and 30. To maintain high quality, the total number of rackets produced should not exceed 80 per day. How many of each type should be manufactured daily to maximize profit?
Answer:
30 oversized rackets and 50 standard rackets
Step-by-step explanation:
To maximize profit, it is very essential she strikes a balance between the two type of rackets. It is important to note that the profit on oversized racket is twice that of standard racket. Hence, she must make as many oversized rackets as possible.
The highest number of oversized racket she can make is 30. Subtracting 30 from the total number of rackets give 50 standard racket
To maximize profit, represent the constraints as a system of inequalities, graph these to find a feasible region, and evaluate the profit function at each vertex of this region.
Explanation:Maximizing Profit with Production ConstraintsTo determine how many of each type of tennis racket a manufacturer should produce daily to maximize profit, we can set up a system of inequalities based on the given constraints and then use linear programming. The constraints are that the daily production of standard rackets (S) should be between 30 and 80, and production of oversized rackets (O) should be between 10 and 30. Additionally, the total number of rackets produced (S + O) should not exceed 80 per day.
The profit function to be maximized is P = 15O + 8S. The optimization process involves graphing the inequalities to form a feasible region, then evaluating the profit function at each vertex of this region to find the maximum profit point.
The constraints can be written as:
We look for the corner points of the feasible region that satisfies all the constraints and calculate the profit at each of these points. The highest profit among these calculated values will give us the optimal number of each type of racket to produce.
By systematically evaluating the profit P at the corner points of the feasible region, the manufacturer can identify the production levels of standard and oversized rackets that will maximize profit within the given constraints.
This approach ensures that the manufacturer can meet dealer demand, maintain high quality through production limits, and optimize profit based on the profit margins of each racket type.
g(x) = x - 6
If the opposite of g(x) is-g(x),
then--g(x) =
Answer:
--g(x) = g(x) = x - 6
Step-by-step explanation:
The opposite of the opposite is the original.
the answer is 0
Step-by-step explanation:
on edge
20.
0/1 points
Previous Answers
GHColAlg12 5.1.094.MI.
An account now contains $11,680 and has been accumulating interest at a 8% annual rate, compounded continuously, for 5 years. Find the initi
$ 3,3839
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Answer:
The initial investment was $7945.58.
Step-by-step explanation:
Use the compound interest formula: A = P(1 + r)^t
A is the ending amount, in this case 11,680.
P is the starting amount, which is unknown.
r is the interest rate in decimal form, in that case 8% is 0.08.
t is the time in years, in this case 5.
Substitute known values into the equation
A = P(1 + r)^t
11,680 = P(1.08)^5
11,680 = 1.47P
P = 11,680/1.47
P = 7945.58
The initial investment was $7945.58.
6% of what number is 2.36
Answer:
39.3
Step-by-step explanation:
100 / 6 is about 16, 16.66667 to be exact:
2.36 * 16.66667 = approx. 39.3
Final answer:
To determine 6% of what number is 2.36, divide 2.36 by 0.06, resulting in an answer of approximately 39.33.
Explanation:
To find 6% of what number equals 2.36, we set up an equation where 6% (or 0.06) multiplied by a number 'x' equals 2.36. The equation looks like this: 0.06x = 2.36. To solve for 'x', you divide both sides of the equation by 0.06, which yields x = 2.36 ÷ 0.06. After calculating, you get that x equals 39.33. Therefore, 6% of 39.33 is 2.36.
What is the solution to the equation
1+1
Answer:
2
Step-by-step explanation:
but I would personally say FISH
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The Ambitious of Brainly And The Role of The TDSB And WHCI Student of The High School.
Write the quadratic equation whose roots are -5 -4 and whose leading coefficient is 4
Answer:
y = 4x² + 36x + 80
Step-by-step explanation:
Since the roots are x = - 5 and x = - 4 then the factors are
(x + 5) and (x + 4)
The equation is the product of the factors
y = (x + 5)(x + 4) and with leading coefficient of 4 is
y = 4(x + 5)(x + 4) ← expand factors
= 4(x² + 9x + 20)
= 4x² + 36x + 80
write the algebraic expression representing the length and width of marliens house
Answer:
You have to show us the shape for us to write down the expression.
If t stands for the number of years since 2000 write an equation for the deer population p as a function of t
To write an equation for the deer population p as a function of t, we can assume a constant growth rate and use the equation p = 80 + rt, where r is the growth rate per year.
Explanation:To write an equation for the deer population p as a function of t, we can use the information given. Let's assume that the population grows at a constant rate. If t represents the number of years since 2000, then we can write the equation as:
p = 80 + rt
where r is the growth rate per year. This equation assumes that there were 80 deer in the population in 2000, and the population has been growing at a constant rate since then.
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