7 Tyler sells popcorn at the movies. He arrives at work and sees there are some
kernels in the popcorn bin. He pours in 4 more cups of kernels to fill the bin.
Then he removes 1.5 cups of kernels-Now there are 6 cups of kernels in the
bin. Write and solve an equation to find out how many cups of kernels were
in the bin when Tyler arrived. Show your work.
Answer:
1.5 * 7 that is the answer of the question
The point P(1,1/2) lies on the curve y=x/(1+x)
(a) If Q is the point (x,x/(1+x)), find the slope of the secant line PQ
correct to four decimal places for the following values of x
(1) .5 (2) .9
(3) .99 (4) .999
(5) 1.5 (6) 1.1
(7) 1.01 (8) 1.001
Using the slope of curve,
1. If x=0.5, then the slope is: 0.3333.
2. If x=0.9, then the slope is: 0.2632
3. If x=0.99, then the slope is: 0.2513
4. If x=0.999, then the slope is: 0.2501
5. If x=1.5, then the slope is: 0.2
6. If x=1.1, then the slope is: 0.2381
7. If x=1.01, then the slope is: 0.2488
8. If x=1.001, then the slope is: 0.2499
Define a curve?
Three easy procedures can be used to compute the area under the curve. The curve's equation (y = f(x)), the boundaries within which the area is to be determined, and the axis encompassing the area must first be known.
The curve is given as:
y = x/1+x
Point, P = (1, 1/2) lies on the curve.
Point, Q = (x, x/1+x) is an arbitrary point on the curve.
The slope of the secant line PQ is:
y2-y1/x2-x1
= x-1/2(x+1) × 1/(x-1)
=1/2(x+1)
1. If x=0.5, then the slope is:
1/2(0.5+1)
= 1/3
= 0.3333
2. If x=0.9, then the slope is:
1/2(0.9+1)
= 1/3.8
= 0.2632
3. If x=0.99, then the slope is:
1/2(0.99+1)
= 1/3.98
= 0.2513
4. If x=0.999, then the slope is:
1/2(0.999+1)
= 1/3.998
= 0.2501
5. If x=1.5, then the slope is:
1/2(1.5+1)
= 1/5
= 0.2
6. If x=1.1, then the slope is:
1/2(1.1+1)
= 1/4.2
= 0.2381
7. If x=1.01, then the slope is:
1/2(1.01+1)
= 1/4.02
= 0.2488
8. If x=1.001, then the slope is:
1/2(1.001+1)
= 1/4.002
= 0.2499
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The demand of boxes of chocolates per week for a store is given by x^2 + p^2 = 2450 where p is the price in dollars and x is the quantity of boxes demanded. Find the rate of change of the quantity demanded when the price increases at a rate of $0.10 per week per box of chocolates at the point where the price is $7.
In linear equation, $-0.0143 is the rate of change of the quantity demanded when the price increases .
What in mathematics is a linear equation?
An mathematical equation with only a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
the demand function:
x² + p² = 2450
Differentiating both sides of the demand function with respect to time t using the chain rule, we get:
2x * dx/dt + 2p * dp/dt = 0
We also know that at the point where the price is $7, p = 7 and x satisfies:
x² + p² = 2450
Substituting p = 7 into the demand function, we get:
x² + 7² = 2450
x² = 2450 - 49x²
x = 49
substitute x = 49, p = 7, and dp/dt = $0.10 into the differentiated demand function and solve for dx/dp
2x * dx/dp + 2p * dp/dx = 0
2(49) * dx/dp + 2(7) * 0.10 = 0
98 dx/dp + 1.40 = 0
dx/dp = $-0.0143
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For a 30-day month, 15 days were sunny, 8 days fell on a weekend and 5 of the sunny days fell on a weekend. If S is the event that a day is sunny and W is the event that the day fell on a weekend, find P(W|S) and identify its meaning.
Group of answer choices
five eighths semicolon the probability that a day fell on a weekend given that it is sunny
one third semicolon the probability that a day is sunny given that it fell on a weekend
five eighths semicolon the probability that a day is sunny given that it fell on a weekend
one third semicolon the probability that a day fell on a weekend given that it is sunny
The answer is "a. five eighths; the probability that a day fell on a weekend given that it is sunny".
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how probable it is.
We can use Bayes' theorem to find P(W|S), the probability that a day fell on a weekend given that it is sunny:
P(W|S) = P(S|W) * P(W) / P(S)
We are given that 15 days were sunny out of a 30-day month, so P(S) = 15/30 = 1/2.
Out of the 30 days, 8 fell on a weekend, so P(W) = 8/30 = 4/15.
We are also given that 5 of the sunny days fell on a weekend, so P(S|W) = 5/8.
Substituting these values, we get:
P(W|S) = (5/8) * (4/15) / (1/2) = 5/12
Therefore, the answer is "a. five eighths; the probability that a day fell on a weekend given that it is sunny".
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A rancher is interested in the average age that a cow begins producing milk. Match the vocabulary word with its corresponding example.
-
The average age for the 62 observed milk cows as they first produced milk
-
The list of the 62 ages
-
All milk cows
-
The age when a milk cow first produced milk
-
The average age that all milk cows are when they first produce milk
-
The 62 milk cows that were observed by the rancher
Statistic
Parameter
Data
Variable
Sample
Population
1. Statistic, 2. Data, 3. Pοpulatiοn, 4. Variable, 5. Parameter, 6. Sample
Statistic:
A statistic is a numerical value that describes a characteristic οf a sample.
Parameter: A parameter is a numerical value that describes a characteristic οf a pοpulatiοn.
Data: Data refers tο the infοrmatiοn cοllected in a study οr experiment. This can include numbers, text, οr οther fοrms οf infοrmatiοn that can be analyzed.
Variable: A variable is any characteristic οr attribute that can take οn different values in a study οr experiment.
Sample: A sample is a grοup οf individuals οr οbjects selected frοm a larger pοpulatiοn fοr the purpοse οf cοnducting a study οr experiment. The characteristics οf the sample are used tο make inferences abοut the larger pοpulatiοn.
Pοpulatiοn: A pοpulatiοn is the entire grοup οf individuals οr οbjects that a study οr experiment is cοncerned with. The characteristics οf the pοpulatiοn are οften οf interest, but it is usually nοt feasible tο cοllect data frοm every member οf the pοpulatiοn, sο a sample is used instead.
Here we have
A rancher is interested in the average age that a cοw begins prοducing milk.
The fοllοwing vοcabulary can be matched as fοllοws
1. The average age fοr the 62 milk cοws as they first prοduced milk - Statistic
2. The list οf the 62 ages - Data
3. All milk cοws - Pοpulatiοn
4. The age when a milk cοw first prοduced milk - Variable
5. The average age that all milk cοws are when they first prοduce milk - Parameter
6. The 62 milk cοws that were οbserved by the rancher: Sample
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I need HELP!!! ASAP THIS IS DUE IN MINUTES PLEASE
The true statement about the value of a in comparison to 0 and 1 is that it is a real number between 0 and 1.
A graph of y = f⁻¹(x) is shown below.
An equation for f⁻¹(x) is [tex]y=\frac{1}{a^x}[/tex].
What is a decreasing function?For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.
By critically observing the graph of f(x), we can logically deduce that [tex]a^x[/tex] is positive for all values of x and as such, all values of a must also be positive:
0 < a
Additionally, the exponential function [tex]a^x[/tex] represent a decreasing function, so for any values of x, we have:
[tex]a^x > a^{x+1}[/tex]
1 > a
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what is the answer to? -12∣x−6∣−9=5∣x−6∣+7
50 points for whoever answers it
Answer: A
Step-by-step explanation:
(b) If you put $8350 in the ATM each day, what percent of the days in a month should you expect to run out of cash?
You can expect to run out of cash on approximately 39.45% of the days in a month when withdrawing $8,350 every day.
To determine the percentage of days in a month where you can expect to run out of cash, we'll need to consider the following terms: daily withdrawal, monthly cash usage, and average days in a month.
1. Daily withdrawal: This is the amount of money you withdraw from the ATM each day. In this case, you withdraw $8,350 every day.
2. Monthly cash usage: This is the total amount of money you will withdraw in a month. To calculate this, multiply the daily withdrawal by the number of days in a month. Since the average number of days in a month is approximately 30.42 (365 days in a year / 12 months), the monthly cash usage would be $8,350 x 30.42 ≈ $253,507.
3. Average days in a month: As mentioned earlier, this is approximately 30.42 days.
Now, we need to determine the number of days you would run out of cash. To do this, divide your monthly budget by the daily withdrawal amount. Let's assume you have a budget of $100,000:
Days without cash = $100,000 / $8,350 ≈ 11.98 days.
Since you can't have a fraction of a day, round it up to 12 days.
4. Calculate the percentage: To find the percentage of days you would run out of cash, divide the number of days without cash by the average number of days in a month and multiply by 100:
Percentage = (12 days / 30.42 days) x 100 ≈ 39.45%.
So, you can expect to run out of cash on approximately 39.45% of the days in a month when withdrawing $8,350 every day.
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Please help solve problem
The index form is solved to give 1/z^13/12
What are index forms?Index forms are described as mathematical forms used to represent numbers too large or small in more proper ways.
Other names for index forms are scientific notations and standard forms.
They are represented as numbers raised to a variable or an exponent.
The rules of index forms are;
Add the exponents when the bases are same and are multiplyingSubtract the exponents when the bases are same and dividingFrom the information given, we have;
z^-1/4/ z1/2 z1/3
Add the exponents
z^-1/4 / z 5/6
Subtract the exponents
z^ -6 - 20 /24
z^-26/24
1/z^13/12
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PLEASE HELP PLEASEEEEEEEEEEEEEE!!! SHOW WORK!
Answer:
C
Step-by-step explanation:
9x+2+4x+10+x=180
14x=180-2-10
14x=168
x=168/14=12
m∠Q=9x+2=9×12+2=108+2=110°
state the five number summary of the data used to construct the box and whisker plot i’ll give you brainlist
Answer:
Min: 85
Q1: 95
Median: 110
Q3: 120
Max: 125
i need help which answer
The list that shows the side lengths, in inches, of the triangle Riley drew is: 59/5, 57/5, 3/2
What is Triangle ?
A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is commonly used in various fields such as engineering, physics, and architecture. The sum of the angles of a triangle always adds up to 180 degrees.
To find the side lengths of the triangle Riley drew, we need to multiply each of Jim's side lengths by the scale factor of ‡, which means multiplying by 3.
The side lengths of Jim's triangle, when written with common denominators, are:
3¼ = 13/4
4.9 = 38/10
5/10 = 1/2
Multiplying each of these by 3 gives:
13/4 * 3 = 39/4
38/10 * 3 = 114/10 = 57/5
1/2 * 3 = 3/2
So, the side lengths of the triangle Riley drew are:
39/4, 57/5, 3/2
We can simplify these fractions by finding a common denominator:
39/4 = 236/20
57/5 = 228/20
3/2 = 30/20
So, the side lengths of the triangle Riley drew, in inches, are:
236/20, 228/20, 30/20
Simplifying further by dividing each numerator by 4, we get:
59/5, 57/5, 15/10
Therefore, the list that shows the side lengths, in inches, of the triangle Riley drew is:
59/5, 57/5, 3/2
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PLEASE HELP ILL RANK YOU WHATEVER YOU WANT
The triangle proportionality theorem indicates that Maria and Juan properly divides the plot of land
What is the triangle proportionality theorem?The triangle proportionality theorem which is known as Thales Theorem states that the segment drawn joining two of the sides of a triangle and parallel to the third side divides the other two sides proportionately.
The parallel lines with which Maria and Juan uses to divide the 300 feet long side into six sides of the same length, indicates that length of each division on the Shady Lane is 50 feet, therefore, the length of each division on the Oak Creek will also be the same.
The slope of the the divisions on Maria's Plan is steeper than the slopes on the division on Juan's Plan such that the length of each division on Oak Lane is longer for Juan, than for Maria.
However, the triangle proportionality theorem, and the width of each division on Shady Lane indicates that the width of each division is 50 feet.
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The slope of a curve is _____.
the change in y divided by the change in x
the difference quotient
the slope of a line tangent to the curve at a given point
none of the above
Answer:
Slope curve is the gradiient
Step-by-step explanation:
Gradient equation is m = change in y over change in x
Therefore the first answer is correct
You are running an obstacle course. As part of the course, you must climb up a diagonal rope net to a platform. The rope net starts 35 feet from the platform base, and the platform is 20 feet high. About how long is the rope net?
By using the Pythagorean theorem we conclude that the rope net is about 40.31 feet long.
What is Pythagorean theorem?The Pythagorean Theorem is a fundamental theorem in mathematics that describes the relationship between the sides of a right triangle.
We can use the Pythagorean theorem to solve this problem.
Let's consider the rope net as the hypotenuse of a right triangle, and the horizontal distance from the base of the platform to the starting point of the rope net as one leg of the triangle.
The other leg of the triangle is the vertical height of the platform.
Using the Pythagorean theorem, we have:
length of rope net = √(horizontal distance² + vertical height²)
Substituting the given values, we get:
length of rope net = √(35² + 20²)
= √(1225 + 400)
= √1625
= 40.31 feet (rounded to two decimal places)
Therefore, the rope net starts 35 feet from the platform base, and the platform is 20 feet high and the rope net is about 40.31 feet long.
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The table below shows the 10 most popular destinations for college students from Country X studying abroad for the 2008-2009 school year. If a student were selected at random from those who studied abroad in 2008-2009 at one of the destinations in the table, determine the empirical probability that the student studied in E,B, and F
Country E.- 14,012
Country B.-27,731
Country F.-11,011
The empirical probability that the student studied in E, B, and F is approximately 0.635.
The total number of students who studied abroad in the 2008-2009 school year is not given, so we cannot calculate the empirical probability directly. However, we can assume that the sample size is very large, and therefore the empirical probability of selecting a student who studied in each of the destinations listed is approximately equal to the relative frequency of students who studied in each of the destinations.
The total number of students who studied abroad in these 10 destinations is:
14,012 + 27,731 + 11,011 + 10,722 + 10,650 + 8,311 + 6,407 + 6,222 + 5,779 + 5,274 = 106,939
Therefore, the empirical probability of selecting a student who studied in E, B, and F is approximately:
≈ (14,012 + 27,731 + 11,011) / 106,939 ≈ 0.635
So, the empirical probability that the student studied in E, B, and F is approximately 0.635.
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A group of students stand at the door of the school and asked every 10th student who they would vote for in the upcoming class elections and why?
This is an example of a survey or sampling technique called systematic sampling. The students are selecting every 10th student from the population (in this case, the population is the entire student body) to survey.
This technique can be useful when the population is too large to survey everyone or when a random sample is difficult to obtain. By using systematic sampling, the students can obtain a representative sample of the student body without having to survey every single student.
However, it's important to note that systematic sampling can introduce bias if there is a pattern or structure in the population that is related to the sampling interval. For example, if every 10th student is in a particular grade level or section of the school, this could skew the results of the survey. To mitigate this potential bias, researchers should ensure that the sampling interval is random and that they are not selecting every nth person based on any identifiable characteristics.
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Need help
40 points!!
1. The diagonal of the base of the box is shorter than the length of the wind chime. 2. The interior diagonal of the box shorter than the length of the wind chime. 3. The wind chime will not fit in the box.
What is diagonal?A diagonal is a line segment that connects two polygonal corners (vertexes), although it is not an edge (side). In other words, it connects any two polygonal vertices that are not neighboring. So, when we directly link any two vertices that are not connected by any sides, we may draw the diagonals in a polygon. A diagonal is a line that runs straight across the vertices of a polygon and joins its opposing corners. In other terms, a line segment connecting any two non-adjacent corners is a polygon's diagonal. Depending on how many sides a polygon has, distinct polygons may have a variable number of diagonals.
Given that the length of the wind chime is 16 inches thus,
1. diagonal of base of the box = √10²+8² = √164 = 12.8
Hence, the diagonal of the base of the box is shorter than the length of the wind chime.
2. interior diagonal of the box = √6²+8²+10² = √200 = 14.14
The interior diagonal of the box shorter than the length of the wind chime
3. The wind chime will not fit in the box
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please help with this! giving brainliest and 20 points
Jake tossed a paper cup 50 times and recorded how it landed. The table shows the results:
Position Open Side Up Closed Side Up Landing on Side
Number of Times Landed in Position 2 6 42
Based on the table, determine the experimental probability of each outcome (landing open side up, landing closed side up, and landing on its side). Show your work
Step-by-step explanation:
50 tries experimentalprobabilities:
open : 2/50 = 1/25
closed 6/50 = 3/25
side : 42/50 = 21/25
Answer:
Open Side Up: 2/50 = 1/25 = 4%
Closed Side Up: 6/50 = 3/25 = 12%
Landing on Side: 42/50 = 21/25 = 84%
Find x round to the nearest 100th. (Please try to show work if you can) :)
length of side AB is approximately 5.74 units when rounded to the nearest hundredth
how to find value of x?To find the value of x in triangle ABC,
Applying the law of sines in triangle ABC, we have:
sin(A)/AB = sin(B)/AC
where AB is the length of side AB, and sin(A) and sin(B) are the sines of angles A and B, respectively.
Substituting the given values, we get:
sin(36)/AB = sin(180-36- angle C)/7
simplifying the equation, we get:
AB = 7sin(36)/sin(C)
To find the angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees:
angle C = 180 - angle A - angle B
Substituting the given values, we get:
angle C = 180 - 36 - 90 = 54 degrees
Substituting the values of sin(36) and sin(54) into the equation for AB, we get:
AB = 7sin(36)/sin(54) = 5.74 (rounded to the nearest hundredth)
Therefore, the length of side AB is approximately 5.74 units when rounded to the nearest hundredth.
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PLEASE HELP AND SHOW WORK FOR BRAINLIST
2. In the diagram below, trapezoid ABCD, with
bases AB and DC, is inscribed in circle O, with
diameter DC. If mAB = 80, what is mBC?
D
80
B
C
DAR?
Since trapezoid ABCD is inscribed in circle O, we know that angles A and D are right angles. We also know that the measure of angle ABD is equal to half the measure of arc AC. Since DC is a diameter of the circle, arc AC is a semicircle and thus has a measure of 180 degrees. Therefore, angle ABD has a measure of 90 degrees.
We also know that the sum of the measures of the angles in a trapezoid is equal to 360 degrees. Therefore, we can set up the following equation:
mAB + mBC + mCD + mDA = 360
Substituting the given values, we get:
80 + mBC + 90 + 90 = 360
Simplifying, we get:
mBC = 100
Therefore, mBC is equal to 100 degrees.
find volume of a cube with side length of 7 in.
Step-by-step explanation:
The volume of a cube is similar to that of a rectangular prism, the volume equals the length times width times height, however because it’s a cube all the measurements are the same, in this case 7 inches. So volume equals 7^3, thus equaling 343 inches cubed. Hope this helps!
Please help me with this question.
The correct option is (b) i.e. area of rectangle is [tex]x^{3} y^{4}[/tex].
What is rectangle?
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. the two sides come together at a straight angle at each corner ,The rectangle differs from a square because its two opposite sides are of equal length.
Given : width of rectangle : xy
length of rectangle : [tex]x^{2} y^{3}[/tex]
we know that, area of rectangle = length × breadth
= x²y³ × xy
Now, adding power of terms which has same base.
we get, [tex]x^{3} y^{4}[/tex]
so, the correct option is (b).
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movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer
Bernice received the following scores on five science tests: 96, 77, 82, 96, and 89. Which of the following statements is true?
O The mean of the set is greater than the median.
O The mean and median of the set of scores are the same.
O The mode of the set of scores is 96.
The median of the set of scores is 82.
The true statement is that the mode of the set of scores is 96. The solution has been obtained by using measures of central tendency.
What are measures of central tendency?
A summary measure called a measure of central tendency, also known as a measure of centre or a measure of central placement, aims to characterise the entirety of a set of data with a single number that corresponds to the centre or centre of its distribution.
We are given scores as 96, 77, 82, 96, and 89.
So, from this we get
⇒ Mean = (96 + 77 + 82 + 96 + 89) ÷ 5
⇒ Mean = 440 ÷ 5
⇒ Mean = 88
Similarly,
Arranging the numbers, we get 77, 82, 89, 96, 96.
So, the median is 89.
Mode is 96 as it is appearing two times.
Hence, the third statement is the true statement.
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the possible answers are
- GPS
- PSG
- GSP
- SGP
Answer:
AA Similarity
i hope this helps :)
help , it’s important, I’ll give brainliest if the answer is correct,
Answer:
value of ∅ = 67.5°
Step-by-step explanation:
cos135° = [tex]-\frac{1}{\sqrt{2} }[/tex]
so 2Ф = 135
Ф = [tex]\frac{135}{2} = 67.5[/tex]°
please help me with this question
A summer camp took a survey of the favorite book genres. Eighteen campers said that their favorite book genre is nonfiction.
What is the total number of campers that were surveyed?
Enter your answer in the box.
__ Campers
Answer:
360
Step-by-step explanation:
.05n = 18
n = 360 campers
Binaya has fixed a water tank in the shape of cylinder surmounted by a hemisphere on the roof of his house. The tank has its internal radius 90 cm and total height 3.8 m.
1) Find the cost of filling the tank with water at the rate of 20 paisa per litre.
Answer:
To find the cost of filling Binaya's water tank, we need to calculate the volume of the tank first. The tank is in the shape of a cylinder surmounted by a hemisphere, so we can find the volume by calculating the volumes of the cylinder and hemisphere separately and adding them together.
The formula for the volume of a cylinder is V_cyl = πr^2h, where r is the radius and h is the height.
Given that the internal radius of the tank is 90 cm and the total height is 3.8 m, we convert the height to cm to match the radius unit and get 380 cm in height.
So, the volume of the cylinder part of the tank will be V_cyl = π(90)^2(380) = 9147600 cm^3.
The formula for the volume of a hemisphere is V_hem = (2/3)πr^3, where r is the radius of the hemisphere. By halving the internal radius of the cylinder, we get the radius of the hemisphere as 45 cm.
So, the volume of the hemisphere part of the tank will be V_hem = (2/3)π(45)^3 = 95325π cm^3.
The total volume of the tank will be the sum of the volumes of the cylinder and hemisphere:
V_total = V_cyl + V_hem = 9147600 + 95325π = 9457589.25 cm^3.
To convert this volume to litres, we divide by 1000:
V_total_l = 9457.59 l.
The cost of filling the tank with water at the rate of 20 paisa per litre will be:
Cost = 9457.59 x 0.20 = 1891.52 paisa = 18.92 rupees (rounded to two decimal places).
Therefore, it will cost Binaya 18.92 rupees to fill his water tank with water at the given rate.
Three students are working to find the solution set of this system of equations y=3x-4 2y=6x-8
Answer:
x=1
Step-by-step explanation:
To solve this equation, you must substitute. The equation for y is given. To use substitution, you have to put the y equation into the second one. In this case it would look something like this:
2(3x-4)=6x-8
(distribute)
6x-8=6x-8
(add 8)
6x=6x
(divide by 6)
x=x
In this circumstance, x is equal to 1.
i need answer please
Answer:
We do not know if the triangles are congruent because we have no information about congruent sides.