Solve the system of equations and choose the correct answer from the list of options.
x + y = 1
y = x −5
Label the ordered pair as (x, y). (4 points)
a
(0, 0)
b
(3, −2)
c
(−2, 3)
d
(−3, 0)
Answer:
b
Step-by-step explanation:
substitute y in x
x+x-5=1
2x=6
x=3
y=3-5
y= -2
please help asap tysm <3
Answer:
6
Step-by-step explanation:
if you use a= l x w substitute in what you know
54 = 9 x w
divide both sides by 9
b=6
The following steps are used to rewrite the polynomial expression, 3(x + 4y) + 5(2x - y).
Step 1: (3x + 12y) + (10x - 5y)
Step 2: (3x + 12y) + (-5y + 10x)
Step 3: 3x + (12y - 5y) + 10x
Step 4: 3x + 10x + (12y - 5y)
Step 5: 13x + 7y
Identify the property used in each of the steps:
Step 1:
Select a Value
i hope this helps! let me know if i got it wrong
Consider the graphed function.
What are the domain and the range of this function?
D: ?
E: ?
X:?
Y:?
Answer:
Domain: -5 ≤ x < 1
Range: -4 ≤ y < 5
Step-by-step explanation:
The graph is a line segment with a solid dot for an endpoint and an open dot for the other endpoint. The solid dot is included in the domain and range, and the open dot is not.
The domain is the set of x-coordinates.
The range is the set of y-coordinates.
Domain: -5 ≤ x < 1
Range: -4 ≤ y < 5
Determine whether the ratios are equivalent 8/7 and 9/8
A fraction is a way to describe a part of a whole. The two ratios are not equal.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
To check whether the two of the given ratios are equivalent or not, convert the denominator of the fraction equal, therefore, take the LCM of the fractions denominator.
8/7 = (8 × 8)/(7 × 8) = 64/56
9/8 = (9 × 7)/(8 × 7) = 63/56
Now, if compare the two fractions, it can be concluded that the two fractions are not equal.
Hence, the two ratios are not equal.
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In the equation Y=13X+38 where Y is a function of X a) Y is a constant. b) 38 is a variable. c) the slope of the line is 13. d) None of these. 13) If Kolin catches 25 fish and gathers 70 fruits it would be co a) an efficient combination b) an unattainable combination c) an inefficient combination d) the most efficient combination Use the figure on the left to answer qucstions 14. 14. What is the equilibrium price and quantify? a. $35 and 6 dozens of roses per day b. $10 and 2 dozens of roses per day? c. Sis and 14 dozens of roses per day d. $25 and 10 dozens of roses per day
1)The slope of the line is C) 13. 2)It would be inefficient since it is not the most optimal use of resources.the correct option is C. 3)The equilibrium price and quantity are D) $25 and 10 dozens of roses per day, respectively.
1) Y = 13X + 38, where Y is a function of X.
The slope of the line is 13.
Therefore, the correct option is C.
2) Kolin catches 25 fish and gathers 70 fruits. If we consider the combination, then it would be inefficient since it is not the most optimal use of resources.
Therefore, the correct option is C.
3) Using the given figure, we can see that the point where the demand and supply curves intersect is the equilibrium point. At this point, the equilibrium price is $25 and the equilibrium quantity is 10 dozens of roses per day.
Therefore, the correct option is D. The equilibrium price and quantity are $25 and 10 dozens of roses per day, respectively.
Note that this is the point of intersection between the demand and supply curves, which represents the market equilibrium.
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how many different ways can you arrange these 10 people in a circle? (two arrangements are considered the same, if one arrangement could be rotated to get the other arrangement.)
You can arrange 10 people in a circle in 362880 different ways if two arrangements are considered the same
What is a combination?In mathematics, a combination or combinations are all the possible groupings that can be made of a given number of elements, without repeating them and regardless of the order in which they are found.
Information about the problem:
As the table is round, the first person can take any seat, then the seat on the right can be taken by 1 of 9 people, then the next seat by 1 of 8 and so on until the 10th person has no choice of seats.
This is expressed by:
9*8*7*6*5*4*3*2
9!
362,880
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Each ordered pair is from an inverse variation. Find the constant of variation. (3/8, 2/3)
The constant of variation is 1/4 .
What is inverse variation ?The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity. That means if one value increases than another one will automatically decrease and vice versa.
Let say if x and y are two values and k is a constant value, then
According to inverse variation,
k = xy or y = k/x
In the given question,
Take the order pair \((\frac{3}{8} ,\frac{2}{3} )\)
As it is an inverse variation, we can substitute it
y=k/x or k = xy
put the values from order pair
k = \(\frac{3}{8}\) × \(\frac{2}{3}\)
k = \(\frac{1}{4}\)
Therefore, the constant of variation for order pair \((\frac{3}{8} ,\frac{2}{3} )\) is 1/4 .
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Pls help me guys I really need it, pls dont say anything random!!!
Answer:
sorry but you need to answer that in your own dont be lazy
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
The slope of the line shown in the graph is _____
and the y-intercept of the line is _____ .
The slope of the line shown in the graph is __2/3__
and the y-intercept of the line is __6___
How to find the slope and the y-intercept?The general linear equation is written as follows:
y = ax + b
Where a is the slope and b is the y-intercept.
On the graph we can see that the y-intercept is y = 6, then we can write the line as:
y = ax + 6
The line also passes through the point (-9, 0), replacing these values in the line we will get:
0 = a*-9 + 6
9a = 6
a = 6/9
a = 2/3
That is the slope.
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Please don’t answer just for points! Help is really needed~
i dont understand
what do we need to do?
24n³ + 30n² + 20n + 25
Answer:
(4n+5)(6n2+5)
Step-by-step explanation:
Add and subtract the second term to the expression and factor by grouping.
I factored it I don't know if that's what you wanted
A single tractor-trailer driver is starting a new shift, intending to travel 450 miles from Charlotte, NC to Pittsburgh, PA. Estimating an average speed of 50 mph and abiding by the current HOS rules, what is the minimum number of clock hours (not driving hours) it will take him?
It will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.
The current Hours of Service (HOS) rules for truck drivers stipulate that a truck driver cannot drive for more than 11 hours after 10 consecutive hours off duty.
Additionally, the driver is not allowed to drive beyond 14 hours after coming on duty.
The driver's shift includes both driving and non-driving time.
Therefore, it is necessary to consider the total amount of time spent on the job.
The truck driver will have to stop for rest breaks, refueling, or other reasons during the 450-mile journey to Pittsburgh, Pennsylvania. The driver is required to take a 30-minute break after eight hours of driving.
Therefore, the minimum number of clock hours (not driving hours) it will take the truck driver to travel the 450-mile distance from Charlotte, NC to Pittsburgh, PA is calculated as follows:
Time for the trip = (Distance ÷ Average Speed) + Breaks
Time for the trip = (450 ÷ 50) + (30 ÷ 60) × 2
Time for the trip = 9 + 1
Time for the trip = 10 clock hours
Therefore, it will take a minimum of 10 clock hours (not driving hours) for the truck driver to travel 450 miles from Charlotte, NC to Pittsburgh, PA.
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A building that is 50 feet tall casts a shadow 30 feet long. Nearby, a tree casts a 75-foot-long shadow. How tall is the tree?
The height that describes how tall the tree is is 37.5 feet.
How to determine how tall the tree isTo determine how tall the tree is, we need to apply the proportion formula to arrive at the right answer. We express the values this way:
\(\frac{x}{75} = \frac{50}{30}\)
Now we cross multiply to have
30x = 1125
x = 1125/30
= 37.5
So, the length of the tree is 37.5 feet.
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nuts cost $3.75 per pound. david paid a total of $45 for nuts. how many pounds of nuts did david buy? enter your answer in the box.
David bought 12 pounds of nuts.
Given, The cost of nuts per pound is $3.75.
David paid a total of $45 for nuts.
Let's assume the pounds of nuts that David bought be x.
Total cost of nuts bought = $45
Cost per pound of nuts = $3.75
Now we need to find how many pounds of nuts did David buy.
So, the equation that relates the cost of nuts and the pounds of nuts is as follows:
Total cost of nuts bought = Cost per pound of nuts * Pounds of nuts bought
$45 = $3.75x
Solving for x,
we get; x = $45 / $3.75x
= 12 pounds.
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Kirby is trying to hypnotize Chrissy by swinging a pendulum at an angle of 80°.the length of chain attached is 10 inches long. What is the total are length AB that the pendulum travels
The total arc length AB that the pendulum travels is approximately 13.96 inches.
To find the total arc length traveled by the pendulum, we can use the formula for the arc length of a pendulum given by:
Arc length (s) = θ × r
where θ is the angle in radians and r is the length of the pendulum.
However, in this case, we are given the angle in degrees, so we need to convert it to radians. The formula for converting degrees to radians is:
θ (in radians) = (π/180) × θ (in degrees)
Given that the angle is 80°, we can convert it to radians as follows:
θ (in radians) = (π/180) × 80° = (4π/9) radians
Now, we can calculate the arc length:
Arc length (s) = (4π/9) radians × 10 inches
The total arc length traveled by the pendulum is therefore:
Arc length (s) = (40π/9) inches
To approximate the answer, we can use the value of π as approximately 3.14:
Arc length (s) ≈ (40 × 3.14/9) inches
Arc length (s) ≈ 13.96 inches
Therefore, the total arc length AB that the pendulum travels is approximately 13.96 inches.
Please note that this calculation assumes that the pendulum swings in a perfect arc without any friction or external factors affecting its motion. In reality, there may be slight variations due to factors such as air resistance or imperfections in the pendulum's motion.
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Round 452,906 to the nearest hundred.
Answer : 500,000 450,000 453,000 452,900 452,910 step-by-step explanation:
look to the right one digit of the place they are asking to round . if it is either greater than or equal to5, then you round up the place they want. if it is not, then it says the same. then all he number to right of it becomes 0s.
I need help for this question real quick. Please help if you can
Answer:
183.6 \(cm^{2}\)
Step-by-step explanation:
Area = Area of trapezium - area of parallelogram-area of semicircle
= \(\frac{1}{2}(a+b)h-b*h-\frac{\pi r^{2} }{2\\}\)
=\(\frac{1}{2}(25+15)24-13*16-\frac{\pi (15/2)^{2} }{2\\}\)
= 183.6 \(cm^{2}\)
Rose is planning a surprise party for her father. She is inviting 94 people besides her father and herself. She can seat 8 people at each table. How many tables will Rose need?
4a=32
Fill in the blank:
a=___
Answer:
a = 8Step-by-step explanation:
Divide both sides by 4.a = 32 ÷ 4
a = 8
Find the seventh term of the sequence which has a first term of 1/2 and has a common ratio of three
The seventh term of the sequence is 364.5
Geometric progressionFrom the question, we are to determine the seventh term of the sequence
Using the formula,
\(a_{n} = ar^{n-1}\)
Where \(a_{n}\) is the nth term
a is the first term
and r is the common ratio
From the given information,
a = 1/2
r = 3
Thus,
\(a_{7} = (\frac{1}{2}) 3^{7-1}\)
\(a_{7} = (\frac{1}{2}) 3^{6}\)
\(a_{7} = \frac{1}{2} \times 729\)
\(a_{7} = 364\frac{1}{2} \ OR \ 364.5\)
Hence, the seventh term of the sequence is 364.5
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Determine P(c) using the remainder theorem.. (look at image)
Answer:
P(-5) = 109
Step-by-step explanation:
Remainder theorem:If the polynomial p(x) is divided by the linear polynomial (x-a), the remainder is p(a).
Dividend = divisor * quotient + remainder.
p(x) = (x-a) * q(x) + p(a)
Here, q(x) is the quotient and p(a) is the remainder.
P(x) = 4x² - x + 4
P(-5) = 4*(-5)² - 1*(-5) + 4
= 4*25 + 5 + 4
= 100 + 5 + 4
= 109
solve the equation: 5x -5
Answer: 5(x-1)
Step-by-step explanation:
On a test that has a normal distribution, a score of 47 falls one standard deviation below the mean, and a score of 65 falls two standard deviations above the mean. Determine the mean of this test.
The mean of the test is M = 53
Given data ,
On a test that has a normal distribution, a score of 47 falls one standard deviation below the mean, and a score of 65 falls two standard deviations above the mean.
Now , A score of 47 falls one standard deviation below the mean, so we have:
47 = μ - σ
A score of 65 falls two standard deviations above the mean, so we have:
65 = μ + 2σ
We now have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the mean (μ).
From the first equation, we can isolate μ:
μ = 47 + σ
Substituting this value into the second equation:
65 = (47 + σ) + 2σ
65 = 47 + 3σ
Rearranging the equation:
3σ = 65 - 47
3σ = 18
σ = 6
Substituting the value of σ back into the first equation to find μ:
47 = μ - 6
μ = 47 + 6
μ = 53
Hence , the mean of the test is 53
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Under his cell phone plan, Joseph pays a flat cost of $48 per month and $3 per gigabyte, or part of a gigabyte. (For example, if he used 2.3 gigabytes, he would have to pay for 3 whole gigabytes.) He wants to keep his bill under $55 per month. What is the maximum whole number of gigabytes of data he can use while staying within his budget?
Answer:
gigabytes
gigabytes
Answer: 2 is the maximum number of gigabytes
Step-by-step explanation:
diana had 41 stickers she put them in 7 equal groups she put as many possible in each group she gave the leftover stickers to her sister how many stickers did diana give to her sister
6 number of stickers diana given to her sister.
What is Division?A division is a process of splitting a specific amount into equal parts.
Diana had 41 stickers and she put them in 7 equal groups. To find out how many stickers she put in each group, we can divide 41 by 7:
41 ÷ 7 = 5 with a remainder of 6
This means that Diana put 5 stickers in each of the 7 groups, and she had 6 stickers leftover.
She gave the leftover stickers to her sister, so she gave her sister 6 stickers.
Hence, 6 number of stickers diana given to her sister.
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I need help...........
Answer: a
Step-by-step explanation:
The lineab bisects bi equally
Identify the expression as a polynomial or not a polynomial. For a polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these. 18a^(5)b^(4)+12a^(6)b^(7)-12b^(5)+10b^(6)
It has four terms, it is classified as a polynomial with four terms, which is neither a monomial, binomial, nor trinomial.
The given expression, 18a^5b^4 + 12a^6b^7 - 12b^5 + 10b^6, is a polynomial.
To determine the degree and classify it further, we need to identify the highest power of the variables involved. In this case, the variables are "a" and "b".
Degree of "a" = 6 (highest power of "a" is 6)
Degree of "b" = 7 (highest power of "b" is 7)
Since the degree is determined by the highest power of any variable, the degree of the polynomial is 7.
Now let's classify it based on the number of terms:
The expression has four terms:
18a^5b^4
12a^6b^7
-12b^5
10b^6
Since it has four terms, it is classified as a polynomial with four terms, which is neither a monomial, binomial, nor trinomial.
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Could someone please answer these 2
Answer:
A. 1/6
B. 1
Step-by-step explanation:
A. 9/j x j/54= 9/54 = 1/6
B. 6k/8m : 3k/4m = 6k/8m : 4m / 3k = 2/2 =1
Answer:
a. 3/2
b. 1
Step-by-step explanation:
A. To simplify the expression, we can cancel out the common factor of j:
9/j * j/54 = (9/1 * 1/6) = 3/2
Therefore, 9/j * j/54 simplifies to 3/2.
B. To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. That is,
(a/b) ÷ (c/d) = (a/b) x (d/c)
Using this rule, we can simplify the given expression as follows:
6k/8m ÷ 3k/4m = (6k/8m) x (4m/3k)
= (6/8) x (4/3)
= 2/2
= 1
7(n - m) for m = 4 and n = 15
Answer:
63
Step-by-step explanation:
7(15-4)
7(9)
63