Answer:
the concentration of sugar in the tank after 10 minutes is approximately 0.056 pounds per gallon.
Step-by-step explanation:
Let's first calculate the amount of sugar that will be added to the tank during the 10 minutes:Amount of sugar added = rate of sugar * time = 2 pounds/minute * 10 minutes = 20 poundsThe initial amount of water in the tank is 300 gallons, and 20 gallons per minute are being added, so after 10 minutes, the amount of water in the tank will be:Amount of water in the tank = initial amount of water + rate of water * time = 300 gallons + 20 gallons/minute * 10 minutes = 500 gallonsTherefore, after 10 minutes, the total volume of the mixture in the tank will be 500 gallons, and the total amount of sugar in the tank will be 8 + 20 = 28 pounds.To find the concentration of sugar in the tank, we divide the total amount of sugar by the total volume of the mixture:Concentration of sugar = total amount of sugar / total volume of mixture = 28 pounds / 500 gallons ≈ 0.056 pounds per gallon
We can use the formula:
concentration = (total sugar added in pounds) / (total water in gallons)
First, we need to find out how much sugar is added in 10 minutes. Since sugar is being added at a rate of 2 pounds per minute , in 10 minutes, we will have:
total sugar added = 2 pounds/minute * 10 minutes = 20 pounds
Next, we need to find out how much water is in the tank after 10 minutes. Since water is being added at a rate of 20 gallons per minute , in 10 minutes, we will have:
total water added = 20 gallons/minute * 10 minutes = 200 gallons
Therefore, the total amount of water in the tank after 10 minutes is:
total water = 300 gallons (initial water) + 200 gallons (water added) = 500 gallons
Finally, we can calculate the concentration of sugar in the tank by plugging in the values:
concentration = total sugar added / total water
concentration = 20 pounds / 500 gallons
concentration = 0.04 pounds/gallon
Therefore, after 10 minutes, the concentration of sugar in the tank is 0.04 pounds per gallon.
sherita is painting the hallway of her apartment she draws a graph illustrating the proportional relationship of the minutes she works x to the passes through the point(16,18)
Part A: which ordered pair on the line would display Sherita’s unit rate of square feet painted per minute.
Part B:select all of the points that lie on the line
(2,2.5)
(3.5,3.9375)
(4,5)
(32,36)
(10,11.5)
(0,0)
The answer of the given question based on graph is Part A: the unit rate of square feet painted per minute is 1.125, so the ordered pair that displays this unit rate is (1, 1.125) and Part B: the points that lie on the line are (3.5,3.9375), (4,5), and (32,36).
What is Slope?Slope refers to the steepness of a line or a surface. More specifically, slope is defined as the ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two points on a line or a surface. In other words, slope measures how much a line or a surface rises or falls as it moves horizontally.
Since the relationship between the minutes worked and the square feet painted is proportional, we can use the slope-intercept form of a linear equation to represent it:
To find the equation of the line, we can use the given point (16,18) and the fact that the relationship is proportional. If we let the unit rate be r (in square feet per minute), then we have:
18 = r(16)
r = 18/16
r = 1.125
So the equation of the line is:
y = 1.125x
Part A: The unit rate of square feet painted per minute is 1.125, so the ordered pair that displays this unit rate is (1, 1.125), since the slope represents the unit rate in a proportional relationship.
Part B: To determine which of the points lie on the line, we can plug in the x-values into the equation y = 1.125x and see if the resulting y-values match.
(y - 18) / (x - 16) = slope
Using the slope calculated above, we can simplify this equation to:
y = 1.125(x - 16) + 18
Now, we can plug in the x and y values for each point and check if they satisfy this equation:
(2,2.5): 2.5 = 1.125(2 - 16) + 18, not on the line
(3.5,3.9375): 3.9375 = 1.125(3.5 - 16) + 18, on the line
(4,5): 5 = 1.125(4 - 16) + 18, on the line
(32,36): 36 = 1.125(32 - 16) + 18, on the line
(10,11.5): 11.5 = 1.125(10 - 16) + 18, not on the line
(0,0): 0 = 1.125(0 - 16) + 18, not on the line
Therefore, the points that lie on the line are (3.5,3.9375), (4,5), and (32,36).
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Which function is increasing and has a domain of (1, ∞)?
The functiοn is increasing and has a dοmain οf (1, ∞) is οptiοn D f(x) = lοg (x - 1) + 1.
What is ratiοnal functiοn?Every equatiοn with οne οr mοre ratiοnal expressiοns is said tο be ratiοnal. A fractiοn whοse numeratοr and denοminatοr are pοlynοmials is knοwn as a ratiοnal expressiοn. A ratiο οf twο pοlynοmials is, in οther wοrds, a ratiοnal expressiοn.
The LCD (Least Cοmmοn Denοminatοr) οf the fractiοns, eliminatiοn οf the denοminatοrs, and simplificatiοn οf the resultant equatiοn are methοds fοr sοlving ratiοnal equatiοns. Sοlving the resultant equatiοn—which can require factοring, simplificatiοn, οr the use οf οther algebraic strategies—will prοvide the answers tο a ratiοnal equatiοn.
Fοr the given functiοn:
Optiοn A:
f(x) = -lοg(x - 1) + 2
Here, lοg is negative, hence fοr increasing value οf x f(x) will decrease.
Optiοn B:
f(x) = -lοg(x - 2) + 1
Here, lοg is negative, hence fοr increasing value οf x f(x) will decrease.
Optiοn C:
f(x) = lοg(x - 2) + 1
Here, (x - 2) > =
x > 2
The dοmain dοes nοt satisfy.
Optiοn D:
f(x) = lοg (x - 1) + 1
Here, (x - 1) > 0
x > 1 tο infinity.
Hence, the functiοn is increasing and has a dοmain οf (1, ∞) is οptiοn D f(x) = lοg (x - 1) + 1.
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The complete function is:
IM BEGGING U SOMEONE
The dilation of the black figure to blue figure is a reduction with a scale factor of 0.5
How to find the scale of dilation?A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.
It can either be an enlargement or a reduction.
An enlargement means a scale factor greater than 1 while a reduction is a scale factor less than 1.
Thus, this dilation is a reduction.
Coordinates of initial figure are:
(-8, 10), (10, 10), (8, -8), (2, -8)
Coordinates of dilated figure are:
(1, -4), (4, -4), (-4, 5), (5, 5)
Thus, it is clear that the scale factor is 0.5
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write an equation for the ellipse with vertices (-8, 5), (4, 5) and foci (-7,5),(3,5)
Answer:
Step-by-step explanation:
16
lbozo
help timed asap hurry
The value of y for the given quadrilateral is 5.
What is a quadrilateral?A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
The Latin words quadra, which means four, and latus, which means sides, are combined to form the English term quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides. As a result, depending on the sides and angles, we might have several sorts of quadrilaterals.
We know that the opposite sides of the quadrilateral have a sum of 180 degrees.
Thus,
23y + 13y = 180
36y = 180
y = 5
Hence, the value of y for the given quadrilateral is 5.
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1. Explain the difference between an in-text citation and the reference list.
Answer:
In-text citations are the short citations you include in the written text that help a reader to understand which sources you are quoting or referring to in your writing example(Field, 2022). Reference is the full details of the source you have cited in your writing.
The amount of money in a savings account increases by 0.2% every month.
Part A
Write a function for the amount of money in the account, B, after t months with an initial deposit of $100.
Part B
By what factor does the amount in the account increase every month? Every year? Every 5 years? Round answers to the nearest thousandth.
each month:
each year:
every five years:
HELPPP!!! ASAP SHOW WORK PLS
Therefore, only the points (4, 1) and (3, 8) can be used to find the distance between the points (4, 1) and (3, 8) using the Pythagorean theorem.
What is coordinate?In mathematics, a coordinate is a set of numbers that uniquely determines the position of a point or an object in space. The most common coordinate system is the Cartesian coordinate system, which uses two or three numerical values to locate points on a plane or in space.
Here,
To find the distance between the points (4, 1) and (3, 8) using the Pythagorean theorem, we need to use the coordinates of these two points to form a right-angled triangle, with the line segment connecting the two points as its hypotenuse. Therefore, the points that can be used to find the distance between the points (4, 1) and (3, 8) using the Pythagorean theorem are:
(4, 1) and (3, 8)
The point (0, 0) cannot be used to find the distance between the two given points using the Pythagorean theorem because it is not on the line segment connecting the two points.
The point (4, 8) cannot be used to find the distance between the two given points using the Pythagorean theorem because it is not on the line segment connecting the two points.
The point (4, 3) cannot be used to find the distance between the two given points using the Pythagorean theorem because it is not on the line segment connecting the two points.
The point (1, 8) cannot be used to find the distance between the two given points using the Pythagorean theorem because it is not on the line segment connecting the two points.
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A retiree invests $9,000 in a savings plan that pays 4% per year. What will the account balance be at the end of the first year?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$9000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &1 \end{cases} \\\\\\ A = 9000[1+(0.04)(1)] \implies A = 9360[/tex]
Find the value of J.
The value of j is equal to 9√3 meters.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the sides are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side).
Note: j is the side opposite to the 60° angle.
The side opposite to the 60° angle, j = 9 × √3
The side opposite to the 60° angle, c = 9√3 meters.
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a rectangular park has a length of (x + 5) and a width of (x - 2). What is the area of the park?
The area of a rectangle is given by the formula:
Area = length x width
In this case, the length of the park is x + 5 and the width is x - 2. So, we can substitute these expressions into the formula to get:
Area = (x + 5) x (x - 2)
Expanding the product, we get:
Area = x^2 + 5x - 2x - 10
Simplifying, we have:
Area = x^2 + 3x - 10
Therefore, the area of the rectangular park is given by the expression x^2 + 3x - 10.
Solve both triangles below, where A= 45 degrees, c= 4.2 degrees, C= 40 degrees, N= 45 degrees, and m= 2. Round to the nearest tenth.
Triangle 1:
A = 45 degrees, C = 40 degrees, c = 4.2
First, we need to find angle B.
B =[tex] 180 - (A + C) = 180 - (45 + 40) = 95[/tex] degrees
Now, we can use the Law of Sines to find side b.
[tex]b/sin(B) = c/sin(C)[/tex]
b =[tex] (c * sin(B)) / sin(C)[/tex]
b =[tex] (4.2 * sin(95)) / sin(40)[/tex]
b ≈ [tex]5.6[/tex]
Triangle 2:
N = 45 degrees, M = 180 - N = 135 degrees, m = 2
To find side n, we can use the Law of Sines again.
[tex]n/sin(N) = m/sin(M)[/tex]
n =[tex] (m * sin(N)) / sin(M)[/tex]
n =[tex] (2 * sin(45)) / sin(135)[/tex]
n ≈ [tex]1.4[/tex]
So, the solutions for the two triangles are:
Triangle 1: A = 45 degrees, B = 95 degrees, C = 40 degrees, b ≈ 5.6, c = 4.2
Triangle 2: N = 45 degrees, M = 135 degrees, n ≈ 1.4, m = 2
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I = E/R solve for R
pls help
Step-by-step explanation:
I = E/R multiply both sides of the equation by R
I R = E / R * R
I R = E Now divide both sides by I
R = E/ I
What is the surface area of the triangular prism shown if a = 20 units, b = 29 units, c = 22 units, w = 15 units, and h = 21 units?
Translateeachexpression. Words
Expression
1. 2. 3. 4.
“five more than a number” “the quotient of a number and -2” “twice a number”
“a number decreased by 7”
“the product of a number and twelve” “three subtracted from a number” “earning $15 per hour”
“$5 less than the cost of the ticket”
“the sum of a number and 24”
“50 markers divided among several students” “two-fifths of a number”
“half a number minus nineteen”
“11 less than the product of a number and -4”
“the total of eight times a number and five”
“the difference of a number squared and 14”
“three-fourths of a number plus17
Answer:
Step-by-step explanation:
5 + x (where x represents the number)
x / (-2)
2x
x - 7
12x
x - 3
$15h (where h represents the number of hours worked)
C - $5 (where C represents the cost of the ticket)
x + 24
50 / n (where n represents the number of students)
(2/5)x
(1/2)x - 19
-4x - 11
8x + 5
x^2 - 14
(3/4)x + 17
----------------------------------
Five added to a number
The result of dividing a number by -2
Two times a number
A number decreased by 7
The result of multiplying a number by 12
A number decreased by 3
Earning $15 per hour
The cost of the ticket minus $5
The sum of a number and 24
Dividing 50 markers among several students
Two-fifths times a number
Half of a number minus 19
The result of subtracting 11 from the product of a number and -4
The sum of eight times a number and five
The difference between the square of a number and 14
Three-fourths times a number plus 17
convert to slope-intercept form (y=mx+b)
A rectangular skating rink is 30 m by 20 m. It is to be doubled in area by adding a strip at one end and a strip of equal width along one side. Find the width of the strip.
The width of the added strip is 10 meters.
What is Area?
Area is a measure of the amount of surface enclosed by a two-dimensional shape or figure. It is usually expressed in square units, such as square meters or square inches, and is calculated by multiplying the length of a side or a diameter by itself or by using an appropriate formula for the shape.
If the area of the skating rink is doubled by adding a strip of equal width along one side and another strip at one end, then the new dimensions of the skating rink would be
=> (30 + x) × (20 + x),
where x is the width of the added strip.
According to the problem, the new area of the skating rink is double the original area, so we can set up the following equation:
=> (30 + x)(20 + x) = 2(30 ×20)
Expanding the left-hand side and simplifying, we get:
=> 600 + 50x + x² = 1200
Rearranging and solving for x, we get:
=> x² + 50x - 600 = 0
Factoring the left-hand side, we get:
=> (x + 60)(x - 10) = 0
Therefore, the possible values for x are x = -60 and x = 10. Since the width of the strip cannot be negative, we reject x = -60 and conclude that the width of the added strip is 10 meters.
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A television game show has 15 doors, of which the contestant must pick 3. Behind 3 of the doors are expensive cars,
and behind the other 12 doors are consolation prizes. The contestant gets to keep the items behind the 3 doors she
selects. Determine the probability that the contestant wins at least one car.
The probability that the contestant wins at least one car is 13/35.
How to calculate the probabilityA television game show has 15 doors, of which the contestant must pick 3. Behind 3 of the doors are expensive cars, and behind the other 12 doors are consolation prizes
probability of an event =total favorable outcome for event/total possible outcomes
P(contestant wins at least one car) will be:
= 1 - 12/15 × 11/14
=13/35
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we know that a confidence interval for a population proportion is (0.22,0.40), with a margin of error of 0.09.
What is the sample proportion, p ?
Part 1 of 3
O Points: 0 of 1
A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing
data are given in the table.
Labor-Hours per Ski
Trick Ski
9
1
Department
Fabricating
Finishing
Answer parts (A), (B), and (C) below.
Slalom Ski
6
1
Save
Maximum Labor-Hours
Available per Day
432
63
(A) If the profit on a trick ski is $60 and the profit on a slalom ski is $50, how many of each type of ski should be
manufactured each day to realize a maximum profit? What is the maximum profit?
The maximum profit is $. The maximum occurs when
trick skis and
slalom skis are produced.
The maximum profit of manufacturing company is = $3150
What do you mean by the term Linear Equation in one variable ?
If an equation is in ax + b = c and there is only one variable in the equation then it is called linear equation in one variable. a , b , c are real number and a is not equal to 0.
To maximize profit, we must determine the number of trick and slalom skis to produce each day, subject to the constraints of available labor hours.
Let x be the number of skis and y be the number of slalom skis produced per day.
The objective function to be maximized is:
Profit = 60x50 a
With the following limitations:
Production hours: 9x 6 a ≤ 432
Final hours: x y ≤ 63
Non-negativity constraints: x ≥ 0, y ≥ 0
We can solve this linear programming problem using graphical or algebraic methods. Here we use algebraic methods:
From the second limit, we get y ≤ 63 - x.
If this inequality is replaced by the first limit, we get:
9 x 6 (63 - x) ≤ 432
3x ≤ 54
x ≤ 18
This means that the maximum production rate is 18 pieces per day. Replacing x = 18 by the inequality y ≤ 63 - x, we get:
y ≤ 63 – 18 = 45
So the maximum production is 45 slalom skis per day.
To verify that this is the correct solution, we need to ensure that it satisfies the non-negativity constraints:
x ≥ 0 and y ≥ 0 are already given in the assignment statement.
Therefore, the maximum profit is:
Profit = 60(18) 50(45) = $3150
The biggest profit is when 18 trick skis and 45 slalom skis are made per day.
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Describe the graph of the equation x=4. Is the equation a function?
Answer:
x = 4 is a straight, vertical line at 4 on the x axis.
Last week, a candy store sold 6 1/3 pounds of white chocolate. It sold 4 times as much milk chocolate as white chocolate. DUE NOWW HELP ANSWER BOTH BRO
Question 1
How many pounds (in mixed number form) of milk chocolate did the candy store sell last week?
Responses
A 24 2/3
B. 25 2/3
C. 25 1/3
D. 24 1/3
Question 2
How many more pounds of milk chocolate were sold than white chocolate at the candy store last week?
Responses
A. 19 2/3
B. 18
C. 19
D. 18 2/3
Answer:
Question 1 C. 25 1/3
Question 2 C. 19
Step-by-step explanation:
brief :
1. 6 1/3 = 19/3
19/3 * 4 = 76/3
76/3 = 25 1/3
To solve this problem, we need to use the information provided and do some simple arithmetic.
Question 1:
The candy store sold 6 1/3 pounds of white chocolate. Since it sold 4 times as much milk chocolate as white chocolate, we can find the amount of milk chocolate sold by multiplying 6 1/3 by 4:
6 1/3 * 4 = 25 1/3
Therefore, the candy store sold 25 1/3 pounds of milk chocolate last week.
Answer: C. 25 1/3
Question 2:
To find the difference between the amount of milk chocolate and white chocolate sold, we can subtract the amount of white chocolate from the amount of milk chocolate:
25 1/3 - 6 1/3 = 19
Therefore, the candy store sold 19 more pounds of milk chocolate than white chocolate.
Answer: C. 19
chatgpt
A random sample of 11 observations from one population revealed a sample mean of 22 and a sample standard deviation of 4.3. A random sample of 8 observations from another population revealed a sample mean of 26 and a sample standard deviation of 4.4.
The test statistic is less than the critical value, so, we reject the null hypothesis and conclude that there is a statistically significant difference between the population means.
What is a two-sample t-test?A two-sample t-test is used to compare the means of two samples to determine if there is a statistically significant difference between them.
To answer this question, we must conduct a two-sample t-test.
In this case, the null hypothesis is that there is no difference between the population means, and the alternative hypothesis is that there is a difference between the population means.
The test statistic is calculated using the following formula:
t = (x₁ - x₂) / (√((s₁²/n₁) + (s₂²/n₂)))
Where x₁ and x₂ are the sample means of the two samples, s₁ and s₂ are the sample standard deviations, and n₁ and n₂ are the sample sizes.
Plugging in the sample data, we get:
t = (22 - 26) / (√((4.3²/11) + (4.4²/8)))
= -1.98
The critical value of t for a two-tailed test at the 0.01 significance level is 2.58.
Since the test statistic is less than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference between the population means.
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Question:
A random sample of 11 observations from one population revealed a sample mean of 22 and a sample standard deviation of 4.3. A random sample of 8 observations from another population revealed a sample mean of 26 and a sample standard deviation of 4.4. At the 0.01 significance level, is there a difference between the population means?
Please help thank you very much!
Hello!
Lets consider what the question asks for:
--> graphs of either line intersecting/parallel/identical
--> # of solutions the system has
The information given:
6x + y = 25
x + 3y = 3
Let's solve the FIRST problem
--> graphs of either line intersecting/parallel/identical
--> let's put both equations into slope-intercept form, where we
isolate the y-variable all by itself to one side
[tex]6x+3y=25\\3y=-6x+25\\\\y=-2x+\dfrac{25}{3}[/tex]
[tex]x+3y=3\\3y=-x+3\\y=-\dfrac{1}{3}x+1[/tex]
--> both equations AREN'T parallel as the slope (coefficient of x-
variable) aren't equal
--> both equations AREN'T identical as they don't look the same
--> both equations ARE INTERSECTING as they have different
slopes and aren't identical
Let's solve our second question:
--> how many solutions does the system have:
--> both lines intersect
-->both lines are linear as the highest power that the x-variable
has are 1
--> thus there is only ONE SOLUTION
Answer:
Intersecting
Has ONE SOLUTION
Find the value of x.
Answer:
x = 4,5
Step-by-step explanation:
These two triangles are similar (according to 3 sides):
The three sides of one triangle are proportional to the three sides of the other triangle:
[tex] \frac{7.5}{5} = \frac{6}{4} = \frac{x}{3} [/tex]
[tex] \frac{6}{4} = \frac{x}{3} [/tex]
Use the property of proportion to find x (cross-multiply):
[tex]4x = 6 \times 3[/tex]
[tex]4x = 18[/tex]
Divide both sides by 4 to make x the subject:
[tex]x = 4.5[/tex]
Jane won 9 out of the 10 video games she played. What percent of the video games did Jane win?
Convince Me!
When using an equivalent fraction to find a percent, why do you write 100 as the denominator?
Jane won 90% of the video games. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
The four fundamental operations, sometimes known as "arithmetic operations," are believed to adequately characterise all real numbers. Division, multiplication, addition, and subtraction are followed by the mathematical operations quotient, product, sum, and difference.
We are given that Jane won 9 out of the 10 video games she played.
Let the percentage be x.
Using the multiplication operation, we get,
⇒ 10 * x% = 9
⇒ 10 * [tex]\frac{x}{100}[/tex] = 9
⇒ [tex]\frac{x}{10}[/tex] = 9
⇒ x = 90
Hence, Jane won 90% of the video games.
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Since, there are multiple questions so, the question answered above is:
Question: Jane won 9 out of the 10 video games she played. What percent of the video games did Jane win?
A rectangular room is 2 times as long as it is wide, and its perimeter is 48 meters. Find the dimensions of the room.
Answer: Let's assume that the width of the rectangular room is "x" meters. Then, according to the problem, the length of the room is 2 times the width, which means the length is "2x" meters.
The perimeter of the room is the sum of all four sides, so we can write:
Perimeter = 2 × (length + width)
Substituting the values, we get:
48 = 2 × (2x + x)
Simplifying the expression, we get:
48 = 2 × 3x
Dividing both sides by 2, we get:
24 = 3x
Solving for "x", we get:
x = 8
Therefore, the width of the room is 8 meters and the length is 2 times the width, which is 2 × 8 = 16 meters.
So the dimensions of the room are 8 meters by 16 meters.
Step-by-step explanation:
if point A(a,b) lies on the line 3x-4y=26 and B(b,a) lies on the line 5x-3y+31=0. Find the equation and length of AB.
The equation of the line passing through points [tex]A(a,b)[/tex] and [tex]B(b,a)[/tex] is [tex]x + y = a + b[/tex] , and the length of [tex]AB[/tex] is [tex]\sqrt(2(a - b)^2).[/tex]
What is the slope of the line?To find the equation of the line passing through points A(a,b) and B(b,a), we can first find the slope of the line. using the two given points, and then use the point-slope form of a line equation.
The slope of a line passing through two points ([tex]x_{1} , y_{1}[/tex]) and ([tex]x_{2}, y_{2}[/tex]) is given by:
[tex]m = (y_{2} - y_{1} ) / (x_{2} - x_{1} )[/tex]
Applying this formula, we can find the slope of the line passing through points A(a,b) and B(b,a):
Slope [tex](m) = (a - b) / (b - a)[/tex]
Since a and b can take any real values, we can see that the slope of the line passing through points A and B is -1.
Now, let's find the equation of the line passing through points A and B using the point-slope form of a line equation:
Point-slope form: [tex]y - y_{1} = m(x - x_{1} )[/tex]
Substituting the slope (-1) and the coordinates of point A(a,b) into the point-slope form, we get:
[tex]y - b = -1(x - a)[/tex]
Expanding the equation, we get:
[tex]y - b = -x + a[/tex]
Rearranging the terms, we get the equation of the line passing through points A(a,b) and B(b,a):
[tex]x + y = a + b[/tex]
Now, let's find the length of AB using the distance formula:
The distance between two points [tex](x_{1} , y_{1} )[/tex] and [tex](x_{2} , y_{2} )[/tex] is given by:
[tex]d = \sqrt((x_{2} - x_{1} )^2 + (y_{2} - y_{1} )^2)[/tex]
Applying this formula, we can find the length of AB using the coordinates of points A(a,b) and B(b,a):
Length of [tex]AB (d) = \sqrt((b - a)^2 + (a - b)^2)[/tex]
Simplifying the expression, we get:
Length of [tex]AB (d) = \sqrt(2(a - b)^2)[/tex]
Therefore, The equation of the line passing through points [tex]A(a,b)[/tex] and [tex]B(b,a)[/tex] is [tex]x + y = a + b[/tex] , and the length of [tex]AB[/tex] is [tex]\sqrt(2(a - b)^2).[/tex]
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Need help, will give points.
The value of (f o g)(3) using composite function is 35
What is composite function?Composite function refers to the combining of functions in a manner where the output from one function becomes the input for the next function.
To calculate the composite function (f o g)(3), we use the techniques below.
From the question,
Given:
f(x) = 3x-1g(x) = x²+3Note that,
(f o g)(3) = f(g)(3)Step 1: Find g(3)
To find g(3) we suebtitute the value of x in g(x) by 3Therefore,
g(3) = 3²+3g(3) = 12Step 2: To find f(g)(3), we subetitute the value of x in f(x) by 12
f(g)(3) = 3(12)-1 f(g)(3) = 36-1f(g)(3) = 35Hence, (f o g)(3) is 35
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Multiply and write the fraction or mixed number in simplest form 2/5x6/7=
Answer:
[tex]\frac{12}{35}[/tex]
Step-by-step explanation:
[tex]\frac{2}{5}[/tex] x [tex]\frac{6}{7}[/tex] = [tex]\frac{12}{35}[/tex]
[tex]\frac{12}{35}[/tex] is already in simplest form, so the answer is [tex]\frac{12}{35}[/tex]