Answer:
Step-by-step explanation:
First, let's calculate the total water required per day for all the calves:
82 calves x 5 gal/head/day = 410 gallons/day
Next, we can calculate the volume of water that each tank can hold:
4' x 2' x 2' oval tank: (4 x 2 x 2) + (π x 2² x 0.5) = 16 + 6.28 = 22.28 cubic feet = 166.5 gallons
6' x 2' x 2' oval tank: (6 x 2 x 2) + (π x 2² x 0.5) = 24 + 6.28 = 30.28 cubic feet = 227 gallons
8' x 3' x 2' oval tank: (8 x 3 x 2) + (π x 3² x 0.5) = 48 + 14.14 = 62.14 cubic feet = 466 gallons
8' diameter x 2' tall round tank: (π x 4² x 2) / 3 = 100.53 cubic feet = 754 gallons
To determine which tank(s) to purchase, we need to make sure that the total volume of water they can hold is at least 410 gallons.
Option 1 (4' x 2' x 2' oval tank) holds 166.5 gallons, so we would need to purchase at least 3 of them to meet the total water requirement (3 x 166.5 = 499.5 gallons). This would cost $420.
Option 2 (6' x 2' x 2' oval tank) holds 227 gallons, so we would need to purchase at least 2 of them to meet the total water requirement (2 x 227 = 454 gallons). This would cost $420.
Option 3 (8' x 3' x 2' oval tank) holds 466 gallons, so one tank would be enough to meet the total water requirement. This would cost $390.
Option 4 (8' diameter x 2' tall round tank) holds 754 gallons, which is more than enough to meet the total water requirement. However, it is the most expensive option at $500.
Based on these calculations, the best option would be the 8' x 3' x 2' oval tank, which can hold enough water for all the calves and is also the most cost-effective option.
Ina works in a juice firm and has to develop the production plan for the lemon and the orange juice concentrates. The fruits (lemon and orange) that she needs to make the juice are not the bottleneck but Ina is concerned about the other main ingredients that go into making the juice: a water-based solution, sugar, and a vitamin mix. Checking with the ERP system tells her that she has 10.4 metric tons of the water solution, 2.94 metric tons of sugar, and 2000 kg of vitamin mix. The recipe tells her to use 51 kg of water solution to make a metric ton of lemon drink and 79 kg of water solution to make a metric ton of orange drink. For the lemon drink she also needs 21 kg of sugar and 17 kg of vitamin mix. The orange drink needs 19 kg of sugar and 5 kg of vitamin mix.From the sales department, Ina knows that the lemon soft drink sells at 59 SEK/ton and the orange drink sells at 71 SEK/ton. (SEK = Swedish krona).How much lemon drink should Ina produce to maximize revenue
Ina should produce 68.24 metric tons of lemon drink to maximize revenue.
To maximize revenue, Ina needs to determine the optimal production quantity of lemon and orange drinks. She can do this by calculating the contribution margin for each product, which is the difference between the selling price and the variable cost per unit.
In this case, the variable cost includes the amount of water solution, sugar, and vitamin mix used for each product. By dividing the available quantity of each ingredient by the amount used for each product, Ina can determine the maximum production quantity for each product.
Using these quantities and the contribution margin for each product, Ina can calculate the total revenue for each production scenario.
The production quantity that yields the highest revenue is the optimal production quantity. In this case, the optimal production quantity for lemon drink is 68.24 metric tons, which would yield a revenue of 4,026,143 SEK.
Hence, to maximize revenue, Ina should produce 68.24 metric tons of lemon drink.
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Find the unit rate.
30 orders in 3 days = orders per day
Answer:
10 orders per day
Step-by-step explanation:
evaluate the integral. (remember to use absolute values where appropriate. use c for the constant of integration.) ax x2 − px dx
The evaluated integral is: 1/2 ln |√(x^2 - px + p) + √p| - ln 2 + C
Assuming that "a" and "p" are constants, we can use integration by substitution to evaluate the integral:
Let u = x^2 - px, then du/dx = 2x - p and dx = du/(2x - p)
Substituting, we get:
∫a x^2 - px dx = ∫a u du/(2x - p)
Next, we need to express the denominator in terms of u:
2x - p = 2(sqrt(u + p) - sqrt(p))
Substituting this back into the integral, we get:
∫a u du/[2(sqrt(u + p) - sqrt(p))
= 1/2 ∫a du/[sqrt(u + p) - sqrt(p)]
Now, we can use a trigonometric substitution, let u + p = psec^2(θ), then du = psec^2(θ)tan(θ)dθ
Substituting, we get:
1/2 ∫a du/[sqrt(u + p) - sqrt(p)]
= 1/2 ∫θ sec(θ)tan(θ)dθ
= 1/2 ln |sec(θ) + tan(θ)| + C
= 1/2 ln |√(u + p)/√p + √(u + p)/√p| + C
= 1/2 ln |(√(u + p) + √p)/√p| + C
= 1/2 ln |√(u + p) + √p| - ln 2 + C
Substituting back for u, we get:
1/2 ln |√(x^2 - px + p) + √p| - ln 2 + C
Therefore, the evaluated integral is:
1/2 ln |√(x^2 - px + p) + √p| - ln 2 + C
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Giving Brainly 30 pounds = _ounces
O 1.875
O3.75
O240
O480
Answer:
because gddyureeyuuhgdetgdsrty=3.75
Explain how to find the cost of an item for $100 that is 8% off.
then solve to find the new price of the item.
Given:
Find the actual cost of an item that is at present $100 that is 8% off.
To find:
8% of x = $100
Solution:
Let the actual cost be x. [tex]8\% \: of \: x = 100[/tex][tex] \frac{8\%}{100} \times x = 100[/tex][tex]x = 100 \times \frac{100}{8} [/tex][tex]x = \frac{10000}{8} [/tex][tex]x = 1250[/tex]Therefore, the cost of the item was $125 or $1250.At what point on the surface z = 2 + x2 + y2 is its tangent plane parallel to the following planes?
(a) z = 6
(x, y, z) =
(b) z = 6 + 4x − 12y
(x, y, z) =
The point on the surface z = 2 + x² + y² at which the tangent plane is parallel to the plane z = 6 is (0,0,2), and parallel to the plane z = 6 + 4x − 12y is (2,-6,42).
Tangent plane is a plane that touches a surface at a point.
Normal vector to a plane is a vector that is perpendicular to the plane.
The normal vector to the tangent plane at any point on the surface is given by the gradient at that point.
To find the point at which the tangent plane of z = 2 + x² + y² is parallel to the given planes, we need to find the gradient of the surface at that point. The gradient of the surface is given by the partial derivatives of the function with respect to x and y.
dz/dx = 2x
dz/dy = 2y
Therefore, the normal vector to the tangent plane at the point (x,y,z) is (2x, 2y, -1).
(a) For the tangent plane to be parallel to the plane z = 6, the normal vectors of the two planes must be parallel.
The normal vector of the plane z = 6 is (0,0,1).
Therefore, we need to find the point (x,y,z) on the surface such that (2x, 2y, -1) is parallel to (0,0,1).
This is only possible if x = y = 0.
Then we plug these values into the equation:
z = 2 + x² + y²
= 2 + 0 +0
= 2
Therefore, the point on the surface at which the tangent plane is parallel to the plane z = 6 is (0,0,2).
(b) For the tangent plane to be parallel to the plane z = 6 + 4x − 12y, the normal vectors of the two planes must be parallel.
The normal vector of the plane z = 6 + 4x − 12y is (4,-12,1).
Therefore, we need to find the point (x,y,z) on the surface such that (2x, 2y, -1) is parallel to (4,-12,1).
This is only possible if x = 2 and y = -6.
Then we plug these values into the equation:
z = 2 + x² + y²
= 2 + 2² + (-6)²
= 42
Therefore, the point on the surface at which the tangent plane is parallel to the plane z = 6 + 4x − 12y is (2,-6,42).
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The reduced fraction of m/n is 1/4. The reduced fraction of m^2/n is 2. What is the value of m+n?
Answer:
40 or 0
Step-by-step explanation:
We have a system. m/n = 1/4 and m^2/n =2.
m/n= 1/4
We can isolate m
m = n/4
We can now plug this into the other equation:
m^2/n = 2
(n/4)^2/n = 2
(n/4)^2 = 2n
n^2/16 = 2n
n^2 = 32n
n^2 - 32n = 0
n(n-32) = 0
N = 0, 32
from these, we can get n.
m/n = 1/4
m/32 = 1/4
m = 8
m/0 = 1/4
m = 0
So for each case, we have m +n = 0 + 0 = 0
and m +n = 8+ 32 = 40
Find M such that (x-2) is a factor of x^4+2x^3-10x^2+Mx-8
Answer:
i never seen ts a day in my life hope u get it right though
Step-by-step explanation:
a restaurant is sold through an agent who charges 2% for the first rs 5,00,000 and 3% for the rest. if the agent receives rs. 32,500 find the price of the restaurant
Answer:
rs. 1250000
Step-by-step explanation:
First, we need to check what is the maximum amount the agent will receive if it reaches the full rs 500000 amount at the 2% agent rate.
[tex](0.02)(500000) = 10000[/tex]
Because, [tex]32500 > 10000[/tex], we can see that the amount will be at least rs 50000.
From here, we do [tex]32500-10000=22500[/tex].
Because the remaining rs 22500 is taxed at the 3% rate, we can do
[tex]\frac{22500}{0.03} = 750000[/tex].
Adding the two numbers, [tex]500000+750000=1250000[/tex], we can see that the price of the restaurant is rs. 1250000
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Look at the triangle ABC, drawn on a square grid. Here are some statements about triangle ABC. For each statement, decide whether it is true or false.
a) The triangle is isosceles.
b) The triangle has three lines of symmetry.
c) The triangle is right-angled.
d) The triangle is equilateral.
Therefore , the solution of the given problem of triangle comes out to be b) True. The triangle's symmetry line is represented by the dashed line.
What is a triangle exactly?A triangular is a polygon because it has two or even more additional parts. It has a straightforward rectangle shape. A parallelogram with only sides A, B, as well as C is a triangle. When the sides are not exactly collinear, Euclidean geometry produces a single plane as compared to a cube. If a shape has three edges and three angles, it is said to be triangular. The intersection of a quadrilateral's three edges is known as an angle. The sum of a triangle's edges is 180 degrees.
Here,
a) Incorrect. Triangle ABC is not scalene because its two longest sides (AB and AC) are equivalent in length.
b) True. The triangle's symmetry line is represented by the dashed line.
c) Untrue. Triangle ABC is not right-angled because none of its edges are right angles.
d) Untrue. Although sides AB and AC of the triangle ABC are identical in length, side BC has a different length, making the triangle ABC not isosceles.
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I need someone to explain this to me because I don’t understand this.
Answer:
In the expression 250(1/2)^t/4, the following meanings can be attributed to the numbers:
250: This is the initial amount of caffeine in milligrams present in the coffee when it was brewed.
(1/2): This is the decay factor or the rate at which the caffeine content decreases over time. In other words, it represents the fraction of caffeine that remains after each hour. Here, the expression (1/2)^t means that the caffeine content will decrease by a factor of 1/2 after each hour.
t: This represents the time elapsed in hours since the coffee was brewed.
4: This is a scaling factor or a unit conversion factor used to convert the expression into milligrams. The expression 250(1/2)^t/4 represents the amount of caffeine remaining in milligrams after t hours.
To summarize, the expression 250(1/2)^t/4 models the amount of caffeine remaining in a coffee after t hours, where 250 is the initial amount of caffeine in milligrams, (1/2) is the decay factor or the fraction of caffeine that remains after each hour, t is the time elapsed in hours, and 4 is the scaling factor used to convert the expression into milligrams.
Among the answer choices provided, the second one is the most accurate:
250 represents the amount of caffeine in a body. 1/2 represents the decay rate of the caffeine. 4 represents the amount of hours it takes for the caffeine to reach its half-life.
The given expression 250(1/2)^t/4 models the amount of caffeine remaining in a coffee after t hours, where 250 is the initial amount of caffeine in milligrams, (1/2) is the decay factor or the fraction of caffeine that remains after each hour, t is the time elapsed in hours, and 4 is the scaling factor used to convert the expression into milligrams. Therefore, the answer choices that mention coffee consumption or growth factor of coffee are not correct in this context.
In this expression, the fraction 1/2 represents the decay rate or the fraction of caffeine that remains after each hour. The number 4 is used to scale the expression into milligrams and does not represent the half-life of caffeine. The half-life of caffeine is the amount of time it takes for half of the initial caffeine amount to decay, and it can be calculated using the formula t1/2 = ln(2) / k, where k is the decay constant.
Prism P and prism Q are similar.
The ratio of the surface area of prism P to the surface area of prism Q is 1 : 3.
The volume of prism Q is 86cm^3
.
Calculate the volume of prism P.
The volume of prism P is 16.55 cm³.
What are Similar Figures?Similar figures are those figures which are having the same shape, but the sizes are different.
Given that,
Prism P and prism Q are similar.
Ratio of the surface area of the prism P to Q = 1 : 3
Also, we have,
Volume of prism Q = 86 cm³
Scale factor of height of the prism would be square root of surface area of the prism.
Scale factor of volume of the prism would be the cube of the height of the prism.
Let volume of prism P be V(P) and volume of the prism Q be V(Q).
V(P) / V(Q) = 1 / (√3)³
V(P) = V(Q) / (√3)³
= 86 / (√3)³
= 16.55 cm³
Hence the volume of prism P is 16.55 cm³.
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A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 20 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
The graph that shows the linear equation y = 20 + 10x is the first graph.
Which graph represents this situation?Here we want to see which of the graphs shows the linear equation:
y = 20 + 10x
Notice that the constant (the y-intercept) is 20, so the line should intercept the y-axis at y = 20.
Then we have a slope of 10, so the line should go upwards,with that we can conclude that the correct option is the first graph.
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I need help with this question please and thank you
Answer:
blue: 0.763orange: 0.767green: 0.770Step-by-step explanation:
You want to fill in a table of opposite side and hypotenuse from values given in the figure, then compute the ratio opposite/hypotenuse.
TableThe table values for "opposite" and "hypotenuse" are copied from the figure, so those are correct as shown in the problem statement.
The ratios can be expressed to 3 significant figures, since the dimensions are given to that precision. A calculator nicely provides those values.
The opposite/hypotenuse ratios are ...
blue: 0.763orange: 0.767green: 0.770__
Additional comment
If this were a well-designed problem, the ratios would be identical to sin(50°) ≈ 0.766.
12−(−85)+45+(−36)
This is integer question
Solve it
12-(-85)+45+(-36)
negative 1 multiply negative 85 will leave an positive 85 and positive 1 multiply negative36 will also leave negative answer then you simplify to get 106
Explain how you can use basic movies to transform the equation 6x+5y=15 into 2y=15-6x
We can use basic arithmetic operations to to transform the linear equation 6x+5y=15 into 5y=15-6x.
What is a linear equation, exactly?
A linear equation is an algebraic equation that represents a straight line on a graph. It is an equation of the form y = mx + b, where x and y are variables, m is the slope or gradient of the line, and b is the y-intercept.
In general, a linear equation can be written in the form ax + by = c, where a, b, and c are constants. However, this form can be converted into the slope-intercept form (y = mx + b) by solving for y and rearranging the terms.
Now,
To transform the equation 6x + 5y = 15 into the form 5y = 15 - 6x, we can use basic algebraic operations such as addition, subtraction, multiplication, and division to isolate the variable we want to solve for (in this case, y) on one side of the equation.
Start with the equation 6x + 5y = 15.
Subtract 6x from both sides of the equation to isolate the term with y. This gives:
5y = 15 - 6x
So, we can use basic algebraic operations such as subtraction.
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Right question:-
Explain how you can use basic movies to transform the equation 6x+5y=15 into 5y=15-6x
The line plot displays the cost of used books in dollars.
A horizontal line starting at 3 with tick marks every one unit up to 8. The line is labeled Cost in Dollars, and the graph is titled Cost of Used Books. There are two dots above 4, 5, and 7. There are four dots above 6.
Which measure of center is most appropriate to represent the data in the graph, and why?
The median is the best measure of center because there are no outliers present.
The mean is the best measure of center because there are no outliers present.
The median is the best measure of center because there are outliers present.
The mean is the best measure of center because there are outliers present.
Answer: The median is the best measure of center because there are no outliers present.
Step-by-step explanation:
Its way more easy to use the median because in this case there isnt any outliers meaning less work.
Iris is heading a recycling drive. The chart below gives the number of kilograms of each kind of recycling brought to the drive.
A recycling sign picture.
A recycling sign picture.
=
3
kilograms
=3kilogramsequals, 3, start text, k, i, l, o, g, r, a, m, s, end text
A picture graph shows the horizontal axis labeled Kilograms and the vertical axis labeled Kind of recycling. Each recycling kind is listed along the vertical axis from the bottom of the axis to the top of the axis as follows: aluminum, plastic, glass, and paper. The kilograms for each recycling kind are represented by the number of recycling sign pictures plotted on the graph. Aluminum is represented by 6 recycling sign pictures, plastic is represented by 4 recycling sign pictures, glass is represented by 2 recycling sign pictures, and paper is represented by 8 recycling sign pictures.
A picture graph shows the horizontal axis labeled Kilograms and the vertical axis labeled Kind of recycling. Each recycling kind is listed along the vertical axis from the bottom of the axis to the top of the axis as follows: aluminum, plastic, glass, and paper. The kilograms for each recycling kind are represented by the number of recycling sign pictures plotted on the graph. Aluminum is represented by 6 recycling sign pictures, plastic is represented by 4 recycling sign pictures, glass is represented by 2 recycling sign pictures, and paper is represented by 8 recycling sign pictures.
How many kilograms of recycling have been brought to the drive in all?
A total of 20 kilograms of recycling have been brought to the drive.
What is statistics ?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of quantitative methods to extract meaningful insights from data, which can be used to make informed decisions or draw conclusions about a particular population or phenomenon.
According to given information:To find the total kilograms of recycling brought to the drive, we need to add up the kilograms for each kind of recycling:
Total Kilograms = Kilograms of Aluminum + Kilograms of Plastic + Kilograms of Glass + Kilograms of Paper
From the graph, we can see that:
Kilograms of Aluminum = 6
Kilograms of Plastic = 4
Kilograms of Glass = 2
Kilograms of Paper = 8
Substituting these values into the formula, we get
Total Kilograms = 6 + 4 + 2 + 8 = 20
Therefore, a total of 20 kilograms of recycling have been brought to the drive.
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Mr. Rodriguez is making 2 different size wedding cakes
The small cake has a diameter of 8 Inches. The large has a diameter 24 inches.
If the pans have a depth that is the same at 3 Inches. How many times greater is the volume of the large cake to the small cake.
Answer:
9x
Step-by-step explanation:
Think of a cake as a very short cylinder. Volume of a cylinder=πr²h
small cake: V = π(8/2)²(3) = 151 in³
large cake: V= π(24/2)²(3) = 1357 in³
1357/151 ≈ 9
large cake is 9 time greater in volume than the small cake
shortcut solution: 24/8 = 3, 3² = 9
simon types 540 words in half and hour how many words can he type in 120 seconds
Answer:
36 words
Step-by-step explanation:
540 = 30 mins
? = 2 mins
then you criss cross it
30 mins = 1080 mins
you divide them both with 30
36
about 10% of people in the united states do not wear a seat belt. suppose we take a random sample of 180 U.S. residents and let X = The number of people who do not wear their seat belts.
calculate the mean and standard deviation of the sampling distribution of x
The mean of the sampling distribution of X is 18 and the standard deviation is approximately 3.00.
What is mean ?
Mean can be defined as ratio of number of favourable outcomes , total number of outcomes.
The population proportion of people who do not wear seat belts is 0.1 or 10%. We can assume that the sample is randomly selected and that the sample size is small enough relative to the population that we can use the binomial distribution to model the number of people who do not wear seat belts.
The mean of the sampling distribution of X is:
μ = np = 180 × 0.1 = 18
where n is the sample size and p is the population proportion.
The standard deviation of the sampling distribution of X is:
σ = sqrt(np(1-p)) = sqrt(180 × 0.1 × 0.9) ≈ 3.00
where sqrt() represents the square root function.
Therefore, the mean of the sampling distribution of X is 18 and the standard deviation is approximately 3.00.
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The image of the point (0, 7) under a translation is (-2,5). Find the coordinates of
the image of the point (5,-2) under the same translation.
Answer:
(3,-4)
Step-by-step explanation:
Point (0,7) moves 2 left to -2, and 2 down to 5. So (5,-2) left 2 and down 2 gets (3,-4).. Right?
How does the stem-and-leaf plot show the distribution of these data? O A. The lengths of the rows are similar to the widths of bars in a histogram; longer rows of data correspond to higher freque OB. The lengths of the rows are similar to the heights of bars in a histogram; longer rows of data correspond to higher freque OC. The lengths of the rows are similar to the widths of bars in a histogram; longer rows of data correspond to smaller freque O D. The lengths of the rows are similar to the heights of bars in a histogram; longer rows of data correspond to smaller freque
The stem-and-leaf plot shows that the lengths of the bars in a histogram are similar to the lengths of the rows, and long rows of data suggest higher frequency.
The stem-and-leaf plot is a type of graphical representation used to plot and display the collection of numbers. The leaf is used to represent the one's place of the digit. And the stem is used to represent the tens place of the digit. It is represented in tabular data organized into discrete numerical categories.
The main advantage of this plot is that it helps to organize a large set of data values. They are also used to determine the median and mode. But they are not very informative for a small set of data. When this plot is compared to the histogram, the length of the rows of this plot is similar to the height of the bars in the histogram. So that the longer row of this plot corresponds to the higher frequency. So the correct statement is option A.
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what is 200g as a percentage of 5kg
Answer: good morning the answer to your question is 4%
Step-by-step explanation:
200/5000*100= 4 %
hope this helps!
The diffusion equation can be written as R2=4Dt where R is the average displacement, D is the diffusion constant, and t is the time. What can you say about the relationship between average displacement squared (R2) and time (t)? (Is it linear, exponential, etc.?)
Question 10
For the analysis, we will include a trendline on our R2 vs. t graph. The trendline equation has the form y=mx+b. Which variable from the diffusion equation corresponds to y in the trendline equation? Which variable from the diffusion equation corresponds to x in the trendline equaton?
Question 11
Given your answer to question 10, how could you solve for the diffusion constant in terms of the slope and a constant?
Question 12
Suppose your trendline equation is y=1.24x+5.63 Solve for the diffusion constant.
The fοrmula D = m/4, we can calculate the diffusiοn cοnstant 'D' as:
D = 1.24/4 = 0.31
What is a Diffusiοn?Diffusiοn is the prοcess by which particles οf a substance mοve frοm an area οf high cοncentratiοn tο an area οf lοwer cοncentratiοn, resulting in a net mοvement οf particles dοwn their cοncentratiοn gradient.
This οccurs due tο the randοm mοtiοn οf individual particles, which leads tο a tendency fοr particles tο spread οut and becοme evenly distributed οver time.
Answer tο Questiοn 9:
The relatiοnship between average displacement squared (R²) and time (t) is linear.
Answer tο Questiοn 10:
The variable 'R2' in the diffusiοn equatiοn cοrrespοnds tο 'y' in the trendline equatiοn, and the variable 't' in the diffusiοn equatiοn cοrrespοnds tο 'x' in the trendline equatiοn.
Answer tο Questiοn 11:
We can sοlve fοr the diffusiοn cοnstant 'D' in terms οf the slοpe 'm' and a cοnstant 'c' by equating the diffusiοn equatiοn and the trendline equatiοn.
The diffusiοn equatiοn: R2 = 4Dt
The trendline equatiοn: y = mx + b
Substituting the cοrrespοnding variables, we get:
R2 = y, D = cοnstant, t = x, m = slοpe, b = cοnstant
Sο, we have:
R2 = 4Dt
y = mx + b
Equating the twο equatiοns, we get:
y = 4Dx + 0 (since b = 0)
Cοmparing this with the trendline equatiοn y = mx + b, we can see that:
m = 4D
Therefοre, we can sοlve fοr 'D' as:
D = m/4
Answer tο Questiοn 12:
Given the trendline equatiοn y = 1.24x + 5.63, we can see that the slοpe 'm' is 1.24.
Using the fοrmula D = m/4, we can calculate the diffusiοn cοnstant 'D' as:
D = 1.24/4 = 0.31
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PLEASE HELP ME PLEASE
Answer:
D
Step-by-step explanation:
The ends of the graph is approaching -∞, which means it is decreasing
how many solutions do the following system of equations have y=2x+7 y-2x=7
The given two equations represent the same line, and there are infinitely many solutions to this system of equations.
What is the solution to the equation?A solution to an equation is a number that can be substituted for the variable to provide a true number statement.
The system of equation is given as:
y = 2x+7 .....(i)
y-2x = 7 .....(ii)
We can solve this system of equations by substituting y = 2x + 7 from the first equation into the second equation:
y - 2x = 7
(2x + 7) - 2x = 7 (substituting y = 2x + 7)
7 = 7
As we can see, the equation simplifies to 7 = 7, which is always true.
This means that the two equations represent the same line, and there are infinitely many solutions to this system of equations.
Any point on the line y = 2x + 7 will satisfy both equations, so there is no unique solution to the system.
Learn more about the solution to the equation here:
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Since rugs will only be $6 per square foot, Katie is going to get a new rug for her apartment. The rug is shaped like a rectangle with a width of 8 feet and a diagonal length of 17 feet. How much will the rug cost?
Step-by-step explanation:
first we need to get the area of the rug she is going to get
since the rug is a rectangular shape with width and diagonal
using Pythagoras theorem to find the opposite
let
A: opposite. ,. B: adjacent,. C: hypotenuse
[tex] {c}^{2} = {a}^{2} + {b }^{2} [/tex]
[tex] {17}^{2} = {8}^{2} + {b}^{2} [/tex]
[tex] {b}^{2} = {17}^{2} - {8}^{2} [/tex]
[tex]b = \sqrt{ {17}^{2} - {8}^{2} } = 15[/tex]
now the area if the new rug is
length x width
[tex]15 \times 8 = 120 {feet}^{2} [/tex]
$6 for a square foot
for 120 square feet
120 x 6 = $720
final Answer
the rug will cost $720
How many solutions does this equation have?
–1 − m = 6 − 7 − m
Answer:
Step-by-step explanation:
Let's simplify the equation first:
-1 - m = -1 - m
Now, we can see that the equation has an infinite number of solutions.
To see why, let's isolate the variable "m" on one side:
-1 - m + m = -1
-1 = -1
As you can see, this is always true, regardless of the value of "m". Therefore, any value of "m" will satisfy this equation.
please someone help me with this question
Answer:
i) 104 °F
ii) 343 °K
Step-by-step explanation:
We have the relationship between temperature in degrees Fahrenheit(y) and degrees Kelvin(x) as:
[tex]y\:=\:\dfrac{9}{5}\left(x-273\right)+32[/tex]
i) When temperature in Kelvin is 313°K, the equivalent temperature in °F is:
[tex]\begin{aligned}y &= \dfrac{9}{5}(313-273) + 32\\& = \dfrac{9}{5}(40) + 32\\&= 9 \cdot 8 + 32\\\\&= 72 + 32\\\\& = 104^\circ F\end{aligned}\\[/tex]
So at 313°K, the equivalent temperature is 104°F
[tex]====================================[/tex]
ii) We are given the temperature in degrees Fahrenheit and asked to find the temperature in degrees Kelvin
We have the equation for temperature conversion from °K to °F as:
[tex]y\:=\:\dfrac{9}{5}\left(x-273\right)+32[/tex]
Let's manipulate this equation so that x is given in terms of y
Switch sides:Here x = degrees Kelvin and y = degrees Fahrenheit
Given y = 158°F, just plug in this value into the equation for x giving
[tex]\begin{aligned}x &= \dfrac{5}{9}(158 - 32) + 273\\& = \dfrac{5}{9}(126) + 273\\&= 70 + 273\\&= 343\end{aligned}[/tex]
Therefore temperature in °K for temperature 158°F = 342 °K
