La fraccio total de nieve de fresa es de ¼.
1. Use the elimination strategy to solve this linear system:
(1) 12c + 28d = 12 (2) -20c + 16d = 168
2. Determine the number of solutions of this linear system:
(1) 7x − 3y = 43 (2) 7x - 3y = 13
The solution to the linear system is c = -6 and d = 3.
To solve the linear system using the elimination strategy, we can eliminate one variable by adding or subtracting the equations. Let's solve the first linear system:
(1) 12c + 28d = 12
(2) -20c + 16d = 168
To eliminate one variable, we can multiply equation (1) by 5 and equation (2) by 3, which will result in opposite coefficients for 'c'. This will allow us to eliminate 'c' when adding the equations together:
(1) 60c + 140d = 60
(2) -60c + 48d = 504
Now, we can add the equations:
(60c + 140d) + (-60c + 48d) = 60 + 504
188d = 564
d = 564/188
d = 3
Substituting the value of 'd' back into equation (1):
12c + 28(3) = 12
12c + 84 = 12
12c = 12 - 84
12c = -72
c = -72/12
c = -6
The solution to the linear system is c = -6 and d = 3.
Now let's analyze the second linear system:
(1) 7x - 3y = 43
(2) 7x - 3y = 13
By comparing the two equations, we can see that they have the same coefficients for both 'x' and 'y', and the constant terms on the right side are different. This means the lines represented by the equations are parallel and will never intersect.
The linear system has no solution.
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An interior designer wants to decorate a newly constructed house. The function f (x) = 49x2 – 200 represents the amount of money he earns per room decorated, where x represents the number of rooms he designs. The function g of x equals one seventh times x represents the number of rooms the interior designer decorates, where x is the number of hours he works.
Part A: Determine the amount of money the interior designer will make decorating the house as a function of hours he works. (5 points)
Part B: If the newly constructed house requires 50 hours of work, how much will the interior designer earn? Show all necessary calculations. (5 points)
Part C: Determine an expression to represent the difference quotient for the function found in Part A. Show all necessary work. (5 points)
A. x² - 200 gives the amount of money the interior designer will make decorating the house as a function of hours he works.
B. He will earn 1,875 if he works for 50 hours.
C. The difference quotient is equal to 2x.
The solution has been obtained by using functions.
What is a function?
Function is a kind of relation, or rule, that associates a single input with a single, predetermined output.
We are given two functions
f(x) = 49x² – 200
which represents the amount of money he earns per room decorated
g(x) = (1/7)x
which represents the number of rooms the interior designer decorates
A. The amount of money the interior designer will make decorating the house as a function of hours he works will be given by evaluating f(x) in g(x).
So,
f(g(x)) = 49((1/7)x)² – 200
f(g(x)) = x² - 200
B. Since, the house requires 50 hours of work, this means that x = 50.
Substituting this in f(g(x)) = x² - 200, we get
f(g(50)) = 50² - 200
f(g(50)) = 1,875
C. The difference quotient for the function is as follows
\(\lim_{h \to \ 0}\frac{f(x+h) -f(x)}{h}\)
\(\lim_{h \to \ 0}\frac{(x+h)^{2}-200-x^{2}+200}{h}\)
\(\lim_{h \to \ 0}\frac{x^{2} + 2xh + h^{2}-x^{2}}{h}\)
= 2x
Hence, x² - 200 gives the amount of money and he earns 1,875 if he works for 50 hours. The difference quotient is equal to 2x.
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Gina has 32 items to ship and 11 shipping boxes. The large shipping boxes can hold 4 items each. The small shipping boxes can hold 2 items each. Gina has exactly enough boxes for her items. How many of each type of box does she have?
Answer:
Gina has 5 large shipping boxes and 6 small shipping boxes.
Step-by-step explanation:
32 items to ship and 11 shipping boxes.
Large=4 items
4 X 5 = 20
Small=2 items
2 X 6 = 12
20 + 12 = 32
A rectangular prism with a square base has a height of 17.2cm and a volume of 24.768cm². What is the length of its base?
How long would use trip take, you drive 50 mph between Santa Barbara and Los Angeles which are 200 miles apart
Answer:
4 hours
Step-by-step explanation:
you travle 50 miles in an hour
200/50 is 4
did i get any wrong? if did than plz correct me, if not then plz tell me, will mark brainliest
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Your all choices are correct ~
Question 1 : A right triangle always has obtuse exterior angles at two vertices :
TrueQuestion 2 : The sum of measures of exterior angles minus the sum of measures of interior Angle is 180° :
TrueQuestion 3 : The sum of exterior Angle and the two non - adjacent interior angles is 180°
FalseQuestion 4 : An obtuse triangle has only one vertex with an acute exterior angle
TrueA fair coin is flipped 15 times. What is the probability that you will have 5 tails?
Answer:
9.18%
Step-by-step explanation:
The probability of getting a tail on a fair coin flip is 0.5, and the probability of getting a head is also 0.5. Since each coin flip is independent, we can use the binomial probability formula to calculate the probability of getting exactly 5 tails in 15 flips:
P(X = 5) = (15 choose 5) * (0.5)^5 * (0.5)^(15-5)
where (15 choose 5) is the number of ways to choose 5 tails out of 15 flips, which can be calculated as:
(15 choose 5) = 15! / (5! * 10!) = 3003
Substituting the values, we get:
P(X = 5) = 3003 * (0.5)^15 ≈ 0.0918
Therefore, the probability of getting exactly 5 tails in 15 coin flips is approximately 0.0918 or 9.18%.
Please solve this
∫ (log(1 + x ^ 2))/((x + 1) ^ 2) dx
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
We have,
To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.
Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:
∫ (log(1 + (u-1)²) / u²) du.
Expanding the numerator, we have:
∫ (log(1 + u² - 2u + 1) / u²) du
= ∫ (log(u² - 2u + 2) / u²) du.
Now, let's split the logarithm using the properties of logarithms:
∫ (log(u² - 2u + 2) - log(u²)) / u² du
= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.
We can simplify the second integral:
∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.
Using the power rule for integration, we can integrate both terms:
∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.
Now, let's focus on the second integral:
∫ (log(u) / u³) du.
This integral does not have a simple closed-form solution in terms of elementary functions.
It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).
Therefore,
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
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last one! please please help! THANKS!!!
Hey! It looks like here, each week the amount is doubled the week before.
$1 - $2 - $4 - $8 - $16 - $32 - $64 - $128
So, we count up all the numbers, and we get 8 different totals. This would mean that on week 8, Kim can buy her bike! Hope this helped :)
If the farmer has 164 feet of fencing, what is the largest area the farmer can enclose?
Answer:
it is 41 because you would divide 164 by 4 and get 41
The area which will cover the 164 feet of fencing in form of a square is 1681 square feet.
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area.
If we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.
Length of fencing = 164 feet
Let's suppose this fencing is covered outside of a square with side "a".
The perimeter of the square = 4a
4a = 164
a = 41
Now the area of the square is a².
Therefore,41² = 1681 square feet.
Hence "The area which will cover the 164 feet of fencing in form of a square is 1681 square feet".
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Find the value of x in the triangle shown below
Answer:
x = 3
Step-by-step explanation:
we can use the Pythagorean theorem to solve this problem
x^2 + 4^2 = 5^2
x^2 + 16 = 25
x^2 = 9
x = +/- 3
we take only the positive value because a length can‘t be negative
x = 3
Emily volunteers on the weekend at the Central Library. As a school project, she decides to record how many people visit the library, and where they go.
On Saturday, 416 people went to The Youth Wing, 448 people went to Social Issues, and 341 went to Fiction and Literature. On Sunday, the library had 500 total visitors.
Based on what Emily had recorded on Saturday, about how many people should be expected to go to Social Issues? Round your answer to the nearest whole number.
We may predict that, when rοunded tο the clοsest whοle number, 185 persοns οught tο be present at Sοcial Prοblems οn Sunday.
What in mathematics is a whοle number?Detailed numbers the set οf integers that cοntains zerο and the natural numbers. nοt a decimal and fractiοn. Integer 0 thrοugh 2, 3, 4, 5, 6, 7, 8, 9, 10, and sο οn. a cοunting number, a negative number, οr zerο.
The library saw a sum οf 416 + 448 + 341 = 1205 visitοrs οn Saturday. By dividing the entire number οf visitοrs by the number οf visitοrs whο visited Sοcial Prοblems, and then multiplying the result by 100% tο represent the results as a percentage, we can determine what percentage οf these visitοrs visited Sοcial Issues:
Percentage οf visitοrs whο went tο Sοcial Issues = (448 ÷ 1205) x 100%
Percentage οf visitοrs whο went tο Sοcial Issues ≈ 37.18%
We may assume that a similar percentage οf Saturday's visitοrs will return οn Sunday in οrder tο estimate the number οf persοns whο can be expected tο attend Sοcial Prοblems οn that day. Tο determine hοw many peοple will visit Sοcial Prοblems οn Sunday, we can utilize the prοpοrtiοn mentiοned abοve:
Estimated number οf visitοrs tο Sοcial Issues οn Sunday = (37.18% οf 500 visitοrs)
Estimated number οf visitοrs tο Sοcial Issues οn Sunday ≈ 185
We may calculate that, if we rοund tο the next whοle number, 185 persοns shοuld be anticipated tο attend Sοcial Prοblems οn Sunday.
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A one-way trolley ticket to Old Town costs 3.50. How much will it cost for Ahyeon and three friends to ride to Old Town and home again?
Answer:
$28
Step-by-step explanation:
Each round trip will be double the price of a one-way trip, so will be ...
2 × $3.50 = $7.00
Diego and his 3 friends will require a total of 4 round-trip tickets for a cost of ...
4 × $7.00 = $28.00
Write the equation of the line that passes through the point (-4, -9) and has a slope of Hin
Answer
Option D is correct.
y + 9 = ½ (x + 4)
Option C is correct.
y = -3x + 5
Option B is correct.
y = -4x + 9
Explanation
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
For this question,
Slope = m = ½
Given point, (x₁, y₁) = (-4, -9)
x₁ = -4, y₁ = -9
y - y₁ = m (x - x₁)
y - (-9) = ½ [x - (-4)]
y + 9 = ½ (x + 4)
For the second question, recall that the slope-point form of the equation is
y - y₁ = m (x - x₁)
For this question,
Slope = m = -3
Given point, (x₁, y₁) = (2, -1)
x₁ = 2, y₁ = -1
y - y₁ = m (x - x₁)
y - (-1) = -3 (x - 2)
y + 1 = -3x + 6
y = -3x + 6 - 1
y = -3x + 5
For the third question, we should note that two parallel lines have the same slopes.
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
The equation of the line provided is 4x + y = 5
So, putting it in the form of y = mx + b
4x + y = 5
y = -4x + 5
We can see that the slope = m = -4 and the y-intercept = b = 5
So, amongst the options, we will pick the line with slope = -4 too.
And that is option B where y = -4x + 9
Hope this Helps!!!
There are 27 students in Mr. Mello's class. Find the total number of pages the students
read by the end of November.
WILL GET 100 POINTS AND BRAINLIST.
Answer:
No solution.
Step-by-step explanation:
Why I say this problem has no solution is due to the fact that the amount of pages is unclassified. This leads you to guessing how many pages there might be for each chapter of the students' individual books, and guessing would not be an effective method as it could lead you to thinking of any random number between 1 - 60 at the most. Therefore, this problem has no solution. If you have further concerns about this problem, I recommend addressing them to your teacher. Otherwise, have a great day. :)
"What is the rest wavelength of an emission line observed at 2148 nanometers in a galaxy 100
Megaparsecs away from the Milky Way? Your answer should be significant to four digits."
The rest wavelength of the emission line observed at 2148 nanometers in the galaxy 100 million light-years away is approximately 2103 nanometers.
The rest wavelength of an emission line can be determined by applying the concept of redshift, which is a phenomenon observed in astrophysics where light from distant objects is shifted towards longer wavelengths due to the expansion of the universe.
In this case, the emission line is observed at 2148 nanometers (or 2.148 micrometers) in a galaxy located 100 million light-years away. To calculate the rest wavelength, we need to consider the redshift factor. Redshift, denoted by z, is defined as the observed wavelength divided by the rest wavelength minus 1.
Given that the observed wavelength is 2.148 micrometers and the galaxy is located 100 million light-years away, we need to convert the distance into a redshift factor using the cosmological relationship between redshift and distance. Assuming a standard cosmological model, we can use the Hubble constant to estimate the redshift.
The Hubble constant represents the rate at which the universe is expanding. Taking a typical value of the Hubble constant as 70 kilometers per second per megaparsec, we find that the redshift factor, z, is approximately 0.021.
To determine the rest wavelength, we rearrange the redshift equation as \((observed wavelength) = (1 + z) \times (rest wavelength)\). Substituting the values, we get \((2.148 micrometers) = (1 + 0.021) \times (rest wavelength).\)
Simplifying the equation, we find the rest wavelength to be approximately 2.103 micrometers or 2103 nanometers.
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10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
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Create your own proportion problems?
Answer:
See Explanation
Step-by-step explanation:
Required
Proportion problems
An example is:
y is directly proportional to x such that: y=4 when x = 2;
Derive the equation
For direct proportions, we have:
\(y\ \alpha\ x\)
This gives:
\(y = kx\)
Make k the subject
\(k = y/x\)
So:
\(k = 4/2 =2\)
So, the equation is:
\(y = kx\)
\(y = 2x\)
Assume the above question is for inverse proportion
The variation will be:
\(y\ \alpha\ \frac{1}{x}\)
This gives:
\(y\ = \frac{k}{x}\)
Make k the subject
\(k =x*y\)
\(k =2* 4 = 8\)
So, the equation is:
\(y\ = \frac{k}{x}\)
\(y = \frac{8}{x}\)
D. $8.00-9. This equation can be used to find h, the number of hours it will take Flo and Bryan to mow their lawn:hh= 13 6How many hours will it take them to mow their lawn?A. 6 hoursB. 3 hoursC. 2 hoursD. 1 hour
The perimeter of a rectangle is 130 ft.
Let x be the length of the rectangle and y be the width of the rectangle.
Then,
\(\begin{gathered} 2(x+y)=130 \\ x+y=65\ldots\ldots(1) \end{gathered}\)Lenght is 9 feet shorter than width. Therefore,
\(x=y-9\ldots\ldots(2)\)Put equation (2) in (1) implies,
\(\begin{gathered} y-9+y=65 \\ 2y=74 \\ y=37 \end{gathered}\)Then, the value of x is ,
\(\begin{gathered} x=37-9 \\ x=28 \end{gathered}\)Therefore, the dimensions are 28 and 37.
geometry
Thought a given point draw four lines. How many angles are formed? Label and read all the angles.
Angles and lines come in many distinct varieties in geometry.
How many angles are there in lines and angles?Geometry has several different kinds of lines and angles. The six different types of angles include reflex angle, complete angle, straight angle, acute angle, and obtuse angle. The various sorts of lines are transverse, parallel, perpendicular, vertical, horizontal, and vertical lines.
There are three ways to name an angle: by the vertex, by the angle's three points (the middle point must be the vertex), or by a letter or number put inside the angle's aperture.
You can create your address block for letters, envelopes, and other mail merges using Label Lines, a collection of fields. Use Label Lines rather of Acknowledgement, Company, and Address lines to skip blank lines in your labels and address blocks.
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Which statement, if true, would help prove that quadrilateral
FGHJ is inscribed in Circle O and why?
Answer:
i believe its a
Step-by-step explanation:
.........
What two numbers have a product of -36 and sum of -9
Answer:-12 and -25
Step-by-step explanation:
Answer: 3 and -12
Step-by-step explanation:
I used this
www.calculatorsoup.com/calculators/math/diamond-problem-solver.php
What are the coordinates of the point that is of the way from A(-8, -9) to
B(24, -1)?
O A. (-6,4)
B. (12,-4)
C. (4,-6)
O D. (-2, 4)
Answer:
c
Step-by-step explanation:
.
sure Yan pre
jhhhhhhhh
4x-5 2x+7 Find the value of x
answers should be from
27
37
47
57
What is the length of Line segment A B? Round to the nearest tenth. Triangle A B C is shown. Angle A C B is a right angle and angle C A B is 75 degrees. The length of C A is 10 meters and the length of hypotenuse A B is x. 9.7 m 10.4 m 37.3 m 38.6 m
Answer:
AB = 38.6metres
Step-by-step explanation:
Given the right angled triangle ABC with hypotenuse AB and ∠CAB to be 75°, the opposite side of the triangle will be the side facing the angle ∠CAB directly and this is side BC. The adjacent side of the triangle will be side CA.
To get the length of the hypotenuse AB, we will use the trigonometry identity SOH, CAH, TOA.
According to CAH;
Cos∠CAB = adjacent/hypotenuse = CA/AB
Substituting CA = 10 metres and ∠CAB = 75° into the equation;
Cos75° = 10/AB
AB = 10/cos75°
AB = 10/0.2588
AB = 38.6metres
Hence the length of the hypotenuse AB is 38.6metres.
Answer:
38.6 m
Step-by-step explanation:
-3 2/7 + -6 1/6
Help with this please I dont know
Answer:
-9.45238095238
Step-by-step explanation:
Just use the fraction to add to the whole number
Answer:
=−14.73809524
Step-by-step explanation:
I was doing math then I got this question wrong.
Why is C not on the y-axis, and why is b on y-axis.
The options that correctly show the points of the given graph are;
Option 4: A is on the y-axis
Option 5; D is on the x-axis
How to interpret the axis of a graph?Usually in mathematical equation graphs, the y-axis represents the range of the function which is a set of all possible output values for given input values . Whereas, the domain is usually represented on the x-axis and it shows the set of all possible input values of the function.
Now, from the given graph, we see the following;
A is on the y-axis
B is at the origin
C is at the point (1, 2)
D is on the x-axis
Looking at the options, we can tell that options 4 and 5 are correct representations of the given graph because they correctly denote the points on the x-axis and y-axis.
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What is the image point of (1, -2) after a translation right 4 units and down 4 units?
Answer:
Hello!!!!
THE ANSWER: (5, -6)
Please read the explanation... it always helps... trust me...
Step-by-step explanation:
Okkeeeee lets beginnnn....
A translation is when you move a point of shape in a coordinate plane
so a translation of a point to the right means you are moving the point to the right of the coordinate plane meaning the positive side of the x-axis... so in this case you will need to add 4 to the x-coordinate....
simarily to the "down four units"
moving it down means subtraction.... meaning you need to subtract 4 from -2 which gets you -6...
I REALLY HOPE THIS HELPS!!! :)
Which system of equations could be graphed to solve the equation below? lag(2x + 1) = 3x-2
Answer:
\(\mathrm{System\:of\:Equations}:\\\\\mathrm{y_1 = log(2x + 1)}\\\mathrm{y_2 = 3x - 2}\)
Step-by-step explanation:
I believe you meant your question to be 'log(2x + 1) = 3x - 2.' The simplest approach to this problem would be to assign 'y' to each side of the given equation, giving us the system of equations we need.
y₁ = log(2x + 1),
y₂ = 3x - 2
By dividing the given equation into these two equations, we can equate one another so that y₁ = y₂. Therefore their intersection will be (1) the value of y₁, (2) the value of y₂, and (3) the solution to the system of equations. Hence this is your solution.
Mr. Martinez averages $14 per
hour as a waiter, including tips. His
hourly pay is $5 per hour. What
fraction of his earnings comes from
his hourly pay?
Answer:
70
Step-by-step explanation:
14x5=70
Answer:
5/14
Step-by-step explanation: