The two points on the line are (5, -9/5) and (-5/3, 3).
The other point on the line is (0, -12/7).
What is system of equations?The equation [tex]\frac{m}{5} +\frac{n}{3} =0[/tex] can be rewritten as:
3m + 5n = 0
When m=5:
3m + 5n = 0
3(5) + 5n = 0
n = -9/5
Simplify the above equation,
When n=3:
3m + 5n = 0
3m + 5(3) = 0
m = -5/3
the two points on the line are (5, -9/5) and (-5/3, 3)
The equation [tex]\frac{m}{10} -\frac{7n}{6} =4[/tex] can be simplified as follows:
m/10 - 7n/6 = 4
m/10 = 7n/6 + 4
m = 70n/6 + 40
m = 35n/3 + 20
When n=0:
m = 35n/3 + 20
m = 20
So, the point on the line is (20, 0).
When m=0:
35n/3 + 20 = 0
35n/3 = -20
n = -12/7
So, the other point on the line is (0, -12/7).
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If the difference of two numbers is less than the sum of the numbers, which of the following must be true.
F. Neither number is positive
G. At least one of the number is positive
H. Exactly one of the number is positive
J. Both numbers are positive
K. None of these statement must be true
True, option (G) is which is - at least one of the numbers is positive.
Define term positive integer number?A positive integer is a whole number greater than zero, i.e., any number that can be expressed without fractions or decimals, and is greater than zero.
If the difference of two numbers is less than the sum of the numbers, it is always true that at least one of the numbers is positive. As a result, "At least one of the numbers is positive" is the response, which is (G).
Here we assume that x and y are two numbers. The difference between the two numbers is |x - y|, which is always positive.
Now, according to the given condition:
|x - y| < x + y
Simplifying this inequality, we get:
-x + y < x + y
2y > 0
Dividing both sides by 2, we get:
y > 0
Therefore, we can conclude that at least one of the numbers (y) is positive. Note that it is possible for both numbers to be positive or for one number to be positive and the other to be zero.
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sqrt y^6 where y is greater than or equal to 0
Simplifying the expression √y⁶ for y is y³
Simplifying the expression for yFrom the question, we have the following parameters that can be used in our computation:
sqrt y^6
Rewrite the expression using numbers and mathematical symbol
So, we have
√y⁶
Take the square root of both sides
So, we have
√y⁶ = y³
Hence, the solution to the expression √y⁶ is y³
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Show that each equation is true. ( 1 - 3 )
Find the exact value of x. ( 4 - 6 )
The lengths of x of the right angle triangle using pythagoras theorem are:
x = 5
x = 3
x = 10
How to use Pythagoras Theorem?Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
4) Applying Pythagoras theorem, we can find x as:
x = √(13² - 12²)
x = √(169 - 144)
x = √25
x = 5
5) Applying Pythagoras theorem, we can find x as:
x = √(5² - 4²)
x = √9
x = 3
6) Applying Pythagoras theorem, we can find x as:
x = √(8² - 6²)
x = √100
x = 10
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Given that a line has a slope of 1/2 and
its y-intercept is the point (0, 7), write
the equation of the line in slope-
intercept form, y = mx + b.
A. y= (1/2)x
B. 7 = (1/2)x+ 0
C. y= (1/2)x+ 7
D. y= 7x+ ½
Sonic Corporation purchased and installed electronic payment equipment at its drive-in restaurants in San Marcos, TX, at a cost of $37,800. The equipment has an estimated residual value of $2,400. The equipment is expected to process 261,000 payments over its three-year useful life. Per year, expected payment transactions are 62,640, year 1; 143,550, year 2; and 54,810, year 3.
Complete a depreciation schedule for each of the alternative methods.
1. Straight-line.
2. Units-of-production.
3. Double-declining-balance.
Annual depreciation = ($37,800 - $2,400) / 3 years = $11,800 per year
Depreciation per unit = ($37,800 - $2,400) / 261,000 = $0.139 per unit
Depreciation rate = 2 / 3 = 0.667 or 66.7%
Complete a depreciation schedule for each of the alternative methods.Method of the straight line:
Annual depreciation = (Cost - Residual value) / Useful life
Annual depreciation = ($37,800 - $2,400) / 3 years = $11,800 per year
Schedule of depreciation: shown in the below table
Units-of-production method:
Depreciation per unit = (Cost - Residual value) / Total units of production
Depreciation per unit = ($37,800 - $2,400) / 261,000 = $0.139 per unit
Depreciation schedule:
Double-declining-balance method:
Depreciation rate = 2 / Useful life
Depreciation rate = 2 / 3 = 0.667 or 66.7%
Depreciation schedule: shown in the below table
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Given the functions f(x)=1x+2 and g(x)=x2−2x, what is the domain of the composition (f∘g)(x)?
Responses
x≠−2 and x≠0
x is not equal to negative 2, and , x is not equal to 0
x≠0
x is not equal to 0
all real numbers
all real numbers
x≠−2
x is not equal to negative 2
Considering both functions, there are no restrictions or exclusions for any real number values in the domain. Therefore, the domain of the composition (f∘g)(x) is all real numbers.
To determine the domain of the composition (f∘g)(x), we need to consider the domains of both functions f(x) and g(x) and determine any restrictions.
The function f(x) =[tex]1x + 2[/tex] does not have any explicit restrictions on its domain. It is defined for all real numbers.
The function g(x) = [tex]x^2 - 2x[/tex] is a quadratic function. Quadratic functions are defined for all real numbers, so there are no restrictions on the domain of g(x).
When we compose functions, we need to ensure that the output of the inner function is within the domain of the outer function. In this case, the composition (f∘g)(x) means we substitute g(x) into f(x), resulting in f(g(x)).
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Write an expression in factored form for the polynomial of least possible degree graphed below.
An expression in factored form for the polynomial of least possible degree is y(x) = (x-2)(x+2).
What is polynomial?
Polynomials can be represented in various forms, including standard form, factored form, and expanded form. Standard form is where the polynomial is written with the terms in descending order of degree, with coefficients in front of each term. Factored form is where the polynomial is written as a product of linear factors, and expanded form is where the polynomial is written out in full, with all the terms multiplied together.
A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using addition, subtraction, and multiplication operations. The variables are raised to non-negative integer powers, and the highest power of the variable is called the degree of the polynomial.
For example, the polynomial 2x³ + 3x³ - 4x + 1 has degree 3, as the highest power of x is 3. The coefficients in this polynomial are 2, 3, -4, and 1.
Here, the curve touch two points (-2,0) and (2,0).
So, we can say (-2) and 2 are the root of the polynomial.
We know of a and b are two root of any polynomial then the polynomial will be (x-a)(x-b).
So, the expression is y(x) = (x-2)(x+2).
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help help help help
A kite flying in the air has a 75-foot string attached to it, and the string is pulled taut. The angle of elevation of the kite is 41 degrees. Find the height of the kite. Round your answer to the nearest tenth.
The height of the kite is 49.2 foot.
We have,
A kite is flying in the air has a 41 ft string attached to it.
The angle of elevation of the kite is 47 degrees.
Using Trigonometry
sin 41 = P/H
sin 41 = P/ 75
0.6560 = P / 75
P = 49.2 foot
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What is 16 g as a fraction of 2 kg?
Give your answer in its simplest form.
00
Answer: 1/125 in it's simplest form
Step-by-step explanation:
can someone help please it’s due at 12
angle 1 = 180 - 74 the angle on a straight line is given as 180
= 106 degrees
What are alternate angles?Alternate angles are a pair of angles formed by a transversal intersecting two parallel lines. These angles are located on opposite sides of the transversal and on opposite sides of the parallel lines.
The alternate angles are congruent, which means they have the same measure or degree. In other words, if one alternate angle measures x degrees, then its corresponding alternate angle will also measure x degrees.
angle 2 = angle 1
They are vertical angles hence they are equal
angle 3 = 74 degrees
They are vertical angles as well
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The cost that a recycling company charges is directly proportional to the number of recycling bins collected. The cost is $33 for each bin.
A: Write a direct variation equation to represent the cost.
B: How many bins can a customer pay the company to collect the bins for $500? Write and solve the equation.
C: Suppose the customer plans to tip the recycling company $30, how many bins can the customer get removed for $500 now? Write and solve the equation.
a) The direct variation equation is y = 33x.
b) The customer can pay the company to collect 15 bins.
c) The customer can get approximately 16 bins (rounded to the nearest whole number) removed for $500 with a $30 tip included.
A) The direct variation equation to represent the cost would be y = kx, where y represents the cost, x represents the number of bins collected, and k is the constant of proportionality. In this case, since the cost is $33 for each bin collected, the value of k is 33. Therefore, the direct variation equation is y = 33x.
B) To find the number of bins a customer can pay the company to collect for $500, we can set the cost (y) equal to $500 and solve for x (the number of bins). Thus, we have:
y = 33x
500 = 33x
x = 500/33
x ≈ 15.15
Therefore, the customer can pay the company to collect 15 bins (rounded to the nearest whole number) for $500.
C) If the customer plans to tip the recycling company $30, the total cost would be $500 + $30 = $530. We can set the cost (y) equal to $530 and solve for x:
y = 33x + 30
530 = 33x + 30
500 = 33x
x ≈ 15.91
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a group of students was to clean up to two areas in their school. area a was 1 1 2 times of area b. in the morning (half of a day), the number of students cleaning area a was 3 times that of the number of students in area b. in the afternoon (another half of a day), 7 12 of the students worked in area a while the rest of them in area b. at the end of the day, area a was done, but area b still needed 4 students to work one more day before it was done. how many were there in this group of students?
the total number of students in the group is (5/17)12B. We don't have a specific value for B, so we can't give a specific answer for the number of students,
How to solve the problem?
Let's use the following variables to represent the unknowns in the problem:
Let A be the area of area A
Let B be the area of area B
Let x be the number of students working in area B in the morning
Let 3x be the number of students working in area A in the morning
Let y be the total number of students in the group
From the problem statement, we know that A = 1.5B (since area A is 1.5 times area B). We also know that in the morning, the number of students working in area A is 3 times the number of students working in area B. This can be expressed as:
3x = y/2 (since half of the students work in the morning)
In the afternoon, 7/12 of the students work in area A, so the number of students working in area B is:
(1-7/12)y = 5/12y
At the end of the day, area A is done and area B still needs 4 more students to work for another day. This means that the amount of work done by the students in area B is (y/2 - 3x) + (5/12y - 4B) = B, since the total work needed to be done in area B is B and the amount of work done by the students in area A is y/2 - 3x.
Substituting A = 1.5B and 3x = y/2, we can solve for y:
(y/2 - 3x) + (5/12y - 4B) = B
y/2 - 3(y/2)/3 + 5/12y - 4B = B
y/2 - y/2 + 5/12y = 5B
17/12y = 5B
y = (5/17)12B
Therefore, the total number of students in the group is (5/17)12B. We don't have a specific value for B, so we can't give a specific answer for the number of students, but we can say that the number of students is proportional to the area of area B. If we know the area of area B, we can use the equation above to find the total number of students in the group.
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Tom and Philip were given the graph of a linear function and asked to find the slope. Tom says that the slope is 12 while Philip says that the slope is 2.
Which reason correctly justifies Tom's answer?
The accompanying data represent women's median earnings as a percentage of men's median earnings for recent years beginning with 1989. Is there a trend? How does it appear to affect women? Construct a time-series graph. Median Earnings Year Median Earnings 1989 1990 1991 1992 1993 1994 1995 1996 1997 59.2 60.1 62.3 61.7 62.5 61.7 61.7 65.0 67.0 Year 1998 1999 2000 2001 2002 2003 2004 2005 Median Earnings 65.6 62.9 63.3 61.5 65.2 63.9 66.7 68.8 Full data set 0 www X C. Median Earnings 70- 64- 584 1989 1997 Year 2005 Clear all Final check
Time Series Graph: Plot A
Based on the above plot, earnings first rise till 1997, and then start falling till 2001. After 2001, earnings start rising again. So overall there is an upward trend.
Why is option A the answer?Based on these observations, the answer is Option A, which says:
Option A: There is a general upward trend though there have benn some down years. An upward trend would be helpful to women so that their earnings become equal to those of men.
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Find the area of parallelogram WXYZ. Round your answer to the nearest tenth if
necessary.
21 in
18 in
21 in
23.2 in
23.2 in
Answer:
area of parallelogram=
base x height
21 in x 18 in
378 in
rounded to nearest ten
380 inches square.
What is the solution to the system of equations graphed below?
3
2
68 x
The solution of the system of equations is given by the point of intersection of all the equations that compose the graph.
How to obtain the solution to the system of equations?In this problem, the graph of the system of equations is given, hence we use it to obtain the solution.
The solution of the system of equations is given by the point of intersection of all the equations that compose the graph, that is, the point where all the curves cross each other.
The point of intersection represents the solution of the system of equations as it is the input values for which all the equations have the same output value.
Missing InformationThe problem is incomplete, hence the procedure to obtain the solution of the system of equations from the graph is presented.
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Probability problem pls help me
The probability that the number generated is:
1). 94 = 1/4, (2). even = 1/4, (3). odd = 0, (4). less than 32 = 1/25, and (5). greater than 74 = 1/25.
What is probabilityThe probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.
The total possible outcome = 10
probability of generating 94 = 5/10 × 5/10 = 1/4
probability of generating an even number = 5/10 × 5/10 = 1/4 {all numbers ending with 0,2,4,6, and 8 must be even}
probability of generating an odd number = 0 {since the second digit must be from 0,2,4,6, and 8, hence no odd number can be generated}
probability of generating less than 32 = 2/10 × 2/10 = 1/25 {since the first digit must either be 1 or 3, while the second digit must be either 0 or 2}
probability of generating greater than 72 = 2/10 × 2/10 = 1/25 {since the first digit must either be 7 or 9, while the second digit must be either 6 or 8}.
Therefore, the probability that the number generated is:
1). 94 = 1/4, (2). even = 1/4, (3). odd = 0, (4). less than 32 = 1/25, and (5). greater than 74 = 1/25.
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The hypotenuse of a right triangle measures 13 cm and one of its legs measures 12 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
5 cm
Step-by-step explanation:
Given two sides of a right triangle, we can find the other side using the Pythagorean theorem, which is
[tex]a^2+b^2=c^2[/tex], where a and b are any of the two legs (e.g., you can set 12 can be a or b) and c is the hypotenuse.
If we allow 12 to b a and 13 to be c, we can solve for b, which is the measure of the other side:
[tex]12^2+b^2=13^2\\144+b^2=169\\b^2=25\\b=5\\b=-5[/tex]
When taking the square root of a number, you always get a negative number and a positive number, since squaring a negative gives a positive answer (e.g. 5^2 = 25 and (-5)^2 = 25). However, because you can't have a negative answer, the answer is simply b = 5 cm
We can even check our answer by making sure that the sum of the square of the two legs equals the square of the hypotenuse:
[tex]12^2+5^2=13^2\\144+25=169\\169=169[/tex]
Triangle D has been dilated to create triangle D′. Use the image to answer the question. image of a triangle labeled D with side lengths of 6, 8, 10 and a second triangle labeled D prime with side lengths of 18, 24, 30 Determine the scale factor used. one half 2 3 one third
Dilating a shape will proportionately affect its side lengths.
To find the scale factor between the given triangles, take one side on the larger triangle and divide it by the corresponding side on the smaller triangle. I will divide the triangles' top sides (24 and 8).
[tex]\text{scale factor}=\dfrac{24}{8} =3[/tex]
So, the scale factor used was 3.
Answer: 3
Step-by-step explanation:
I took the quiz so you do not have to!
simplify 7(x-2y)-5(x-3y)
[A] x+2y
[B] x+y
[C] 2x+y
[D] 2x-y
Answer:
The answer is **C. 2x+y**
* Expand the parentheses: 7x-14y - 5x+15y
* Combine like terms: 2x+y
Here is the step-by-step solution:
1. Expand the parentheses:
```
7(x-2y)-5(x-3y)
= 7x-14y - 5x+15y
```
2. Combine like terms:
```
= (7x-5x) + (-14y+15y)
= 2x + y
```
Step-by-step explanation:
Answer:
Let's simplify the expression step by step:
7(x - 2y) - 5(x - 3y)
= 7x - 14y - 5x + 15y (distributing the 7 and -5)
= 2x + y (combining like terms)
Therefore, the simplified expression is 2x + y, which corresponds to option [C].
Step-by-step explanation:
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Enter the correct answer.
DONE
The equation of this graphed line is equal to y = x/2 - 5.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-1 + 5)/(8 - 0)
Slope (m) = 4/8
Slope (m) = 1/2.
At data point (0, -5) and a slope of 1/2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-5) = 1/2(x - 0)
y + 5 = x/2
y = x/2 - 5
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please help i dont know what it is i think 324 but someone let me know how to do it
Answer: 3
Step-by-step explanation:
A = 3 × (1ft)²
A = 3 × 1 ft²
A = 3ft²
trell is working in a lab testing bacteria populations. After starting out with a population of 404 bacteria, he observes the change in population and notices that the The population doubles every 36 minutes. tep 1 of 2: Find the equation for the population P in terms of time t in minutes.
We can actually see here that the equation for the population P in terms of time t in minutes will be: P = 404 × 2^(t/36).
How we arrived at the solution?We can see here that looking at the change in population, we can use the following:
P = P₀ × 2^(t/Δt).
Where:
P₀ = initial population = 404 bacterias
t = time elapsed (in minutes).
Δt = time it takes for the population to double (36 minutes).
Thus, we see that substituting this, we have:
P = 404 × 2^(t/36).
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Probability problem pls help me
Where is the question?
Jeremiah needed dog food for his new puppy. He compared the prices and sizes of three types of dog food.
Canine Cakes Bark Bits Woofy Waffles
Size (pounds) 30 40 28
Cost $54 $70 $42
Part A: Calculate the corresponding unit rate for each package. (9 points)
Part B: Determine the best buy using the unit rates found in Part A. Explain your answer.
------------------------------------------------------------------
The table shows the grading scale for Ms. Gray's social studies class.
A 90%–100%
B 80%–89%
C 70%–79%
Part A: Pick a number between 21 and 29. This number will represent how many points you earned. If you have a pop quiz worth a total of 30 points, using the number you selected, calculate the percentage you earned on the test. Show each step of your work. (8 points)
Part B: Based on the percentage found in Part A, would you earn a grade of A, B, or C using the grading scale provided? Explain your answer.
Answer:
see explanation
Step-by-step explanation:
Part A:
54$ for 30 pounds = 54/30 = 9/5 dollars per pound
70$ for 40 pounds = 70/40 = 7/4 dollars per pound
42$ for 28 pounds = 42/28 = 3/2 dollars per pound
Part B:
3/2 = 1.5 ($/lb)
7/4 = 1.75 ($/lb)
9/5= 1.8 ($/lb)
The best buy is Woofy Waffles for 1.5 $ per pound
Lisa will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $55 and costs an additional $0.13 per mile driven. The second plan has an initial fee of $48 and costs an additional $0.15 per mile driven.
For what amount of driving do the two plans cost the same?
What is the cost when the two planes cost the same?
Answer:
Step-by-step explanation:
To find the point at which the two plans cost the same, we can set their total costs equal to each other:
55 + 0.13x = 48 + 0.15x
Simplifying and solving for x, we get:
0.02x = 7
x = 350
Therefore, the plans will cost the same when Lisa drives 350 miles.
To find the cost at this point, we can substitute x=350 into either equation. Let's use the first plan:
Total cost = 55 + 0.13(350) = $97.50
Therefore, if Lisa drives 350 miles, the cost for either plan will be $97.50.
Help please if you can.
Answer:
24/91
Step-by-step explanation:
We can see that the square on the right has a side length of 24 and the square on the left has a side length of 91.
The scale factor = square on right/square on left = 24/91
matrix A = 2 -7 matrix B = -9 5
6 1 1 -1
If X - A = B, what is X?
If your claim is in the alternative hypothesis and you reject the null hypothesis, then your conclusion would be:
O The sample data support the original claim
O There is sufficient evidence to warrant rejection of the original claim
O There is not sufficient evidence to warrant rejection of the original claim
O There is not sufficient sample evidence to support the original claim
The value of your conclusion would be:
⇒ There is sufficient evidence to warrant rejection of the original claim
We have to given that;
For your claim is in the alternative hypothesis and you reject the null hypothesis.
Hence, We know that;
If your claim is in the alternative hypothesis and you reject the null hypothesis, There is sufficient evidence to warrant rejection of the original claim
Thus, The correct option is, B.
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What is the solution of log(f-3)-log(17-40)?
04
05
O 15
O 20
The solution of the given logarithm function log(f-3)-log(17-40) is
f < 3.
So no option is correct.
What is a logarithm function?A logarithm function is a mathematical function that describes the relationship between a given number (called the argument or input) and a specified base. The logarithm of a number x with respect to a base b is the power to which b must be raised to give x.
In other words, if we have the equation y = log_b(x), then y represents the power to which the base b must be raised to get x. For example, if b=2, then log_2(8) = 3 because 2 raised to the power of 3 equals 8.
According to the given informationThe given expression is:
log(f-3)-log(17-40)
We can simplify this expression using the property of logarithms:
log(a) - log(b) = log(a/b)
So, we get:
log((f-3)/(17-40))
Now, for this expression to have a real solution, the argument of the logarithm must be positive, so we have:
(f-3)/(17-40) > 0
Solving for f, we get:
f - 3 < 0 (since 17-40 is negative)
f < 3
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