Answer: a) The profit function can be written as:
P(x) = 5x - 400x + 600
To find the asymptotes, we can look at the denominator of the second term, which is (x - 3). This means that there is a vertical asymptote at x = 3. To find the intercepts, we can set P(x) = 0:
5x - 400x + 600 = 0
Solving for x, we get:
x = 1.5 and x = 2.5
Therefore, there are x-intercepts at (1.5, 0) and (2.5, 0). To sketch the graph, we can also note that the coefficient of x^2 is negative, which means that the graph is a downward-facing parabola.
b) The domain of the function is the set of all possible values of x, which in this context represents the amount of coffee sold. Since we cannot sell a negative amount of coffee, the domain is x ≥ 0.
The range of the function is the set of all possible values of P(x), which represents the profit. Since the coefficient of x^2 is negative, the maximum profit occurs at the vertex of the parabola. The vertex has x-coordinate:
x = -b/(2a) = -(-400)/(2(-200)) = 1
Therefore, the maximum profit occurs when x = 1. The vertex has y-coordinate:
P(1) = 5(1) - 400(1) + 600 = 205
Since the coefficient of x^2 is negative, the range is (-∞, 205].
c) The horizontal asymptote of the function is y = -400, which represents the long-term average profit per kilogram of coffee sold. This means that as x gets very large, the profit per kilogram approaches -400. This could happen, for example, if the cost of producing the coffee increased significantly while the price remained the same.
d) To find the amount of coffee that must be sold to make a profit of $4000, we can set P(x) = 4000 and solve for x:
5x - 400x + 600 = 4000
Simplifying, we get:
-395x = -3400
Dividing both sides by -395, we get:
x ≈ 8.61
Therefore, approximately 8.61 kg of coffee must be sold to make a profit of $4000.
Step-by-step explanation:
what are the x- and y- coordinates of point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B? x= [m/m+n](x2 -x1) +x1 y = [m/m+n](y2 - y1) +y1
Where m is the distance from A to P and n is the distance from P to B.
What is Length?Length is a measure of distance or size. It is the measurement of the longest dimension of an object, such as a line, segment, or plane. It is commonly used to measure the physical size of objects, as well as the space between them. Length can be measured in many different units, such as meters, feet, or inches. Length is also used to measure the amount of time it takes for something to occur, such as the length of a movie or a song.
Therefore, if the coordinates of A are (x1, y1) and the coordinates of B are (x2, y2), the x- and y- coordinates of point P would be:
x= [2/3(x2 -x1) +x1
y = [2/3](y2 - y1) +y1
This equation can be used to calculate the coordinates of any point P on a directed line segment from A to B such that P is a fraction of the length of the line segment from A to B. By setting the fraction equal to 2/3, we can calculate the coordinates of point P that is 2/3 the length of the line segment from A to B. This can be useful in a variety of applications, such as computer graphics, game design, and engineering. For example, this equation could be used to calculate the coordinates of a point on a line segment that is an exact distance from the two endpoints, or to calculate the coordinates of a point that is a certain percentage of the distance between the two endpoints.
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The coordinates of point P such that it is 2/3 the length of the line segment from A to B are (4, -2). Therefore, the correct option is d-(3,-2).
What is Length?Length is a measure of distance or size. It is the measurement of the longest dimension of an object, such as a line, segment, or plane. It is commonly used to measure the physical size of objects, as well as the space between them. Length can be measured in many different units, such as meters, feet, or inches.
Given the coordinates of the points A, B and P, we can calculate the x- and y- coordinates of point P such that it is 2/3 the length of the line segment from A to B.
To do this, we need to use the following formula: x = [m/m+n](x2 -x1) +x1, y = [m/m+n](y2 - y1) +y1, where m is 2/3, n is 1/3, x1 and y1 are the x- and y-coordinates of point A, and x2 and y2 are the x- and y-coordinates of point B.
In this case, m = 2/3, n = 1/3, x1 = 2, y1 = -1, x2 = 4, y2 = -3.
Therefore, plugging these values into the formula we get:
x = [2/3](4 -2) +2 = 4
y = [2/3](-3 - (-1)) + (-1) = -2
Therefore, the coordinates of point P such that it is 2/3 the length of the line segment from A to B are (4, -2). Therefore, the correct option is d-(3,-2).
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Which of the following is NOT a use of the perpendicular bisector?
A.Finding center of a circle given points on the circle.
B.Drawing a square.
C.Drawing a triangle with two equal sides lengths (isosceles triangle).
D.Finding the circumference ofthe a triangle.
Drawing a square is NOT a use of the perpendicular bisector.
What does perpendicular bisector mean?
A line that bisects another line segment into two equal-sized segments by crossing it perpendicularly might be said to be a perpendicular bisector. The midpoint of a line segment is traversed by a perpendicular bisector. A ruler and a compass are needed to build it. The line segment that is being divided is bisected at an angle of 90° on both sides.
What use serve perpendicular bisectors?
A line that cuts through the junction of two adjacent line segments at a right angle is known as a perpendicular bisector. With this in mind, we may state that a perpendicular bisector always splits a line segment in its middle. The word "bisect" itself refers to an even or uniform division.
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Your tank has a volume of 10 L at the surface (1 atm pressure). You reach a depth of 66 ft. What is the
pressure? What is the volume?
the pressure at a depth of 66 ft is 197,580 Pa, and the volume of the tank at this depth is 0.000505 L.
EquationsTo find the pressure at a depth of 66 ft in a liquid, we can use the formula:
pressure = density x gravity x depth
Assuming the liquid in the tank is water, the density is 1000 kg/m³, and gravity is 9.81 m/s².
First, we need to convert 66 ft to meters:
66 ft x 0.3048 m/ft = 20.1168 m
Then, we can find the pressure at this depth:
pressure = 1000 kg/m³ x 9.81 m/s² x 20.1168 m = 197,580 Pa
To find the volume of the tank at this depth, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume (1 atm and 10 L, respectively), and P₂ and V₂ are the final pressure and volume.
We can rearrange this equation to solve for V₂:
V₂ = (P₁ x V₁) / P₂
Substituting the values, we get:
V₂ = (1 atm x 10 L) / (197,580 Pa / 1 atm) = 0.000505 L
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A company is focus testing a new type of fruit drink. The focus group is 47% male. Of the responses, 40% of the males and 54% of the females said they would buy the fruit drink. Find the ratio of males who would buy the drink to females who would buy the drink. Round to the nearest ten thousandth if necessary.
Answer: the ratio of males who would buy the drink to females who would buy the drink is approximately 0.6560.
Step-by-step explanation:
Let's assume that there are 100 people in the focus group. Then, the number of males in the focus group is 47 and the number of females is 53.
Out of 47 males, 40% said they would buy the fruit drink, which is 0.4 x 47 = 18.8 males (rounded to the nearest whole number). Out of 53 females, 54% said they would buy the fruit drink, which is 0.54 x 53 = 28.62 females (rounded to the nearest whole number).
The ratio of males who would buy the drink to females who would buy the drink is:
18.8/28.62 = 0.6560 (rounded to the nearest ten-thousandth)
Therefore, the ratio of males who would buy the drink to females who would buy the drink is approximately 0.6560.
Orlando and Nancy are scuba diving. Orlando is at an elevation of -60 feet, and he is descending at a rate of 8 feet per minute. Nancy is at an elevation of -35 feet and she is descending at a rate of 12 feet each minute. The variable t represents the time in minutes. After how many minutes will Orlando and Nancy be at the same elevation? At what elevation will they be at that time?
Answer:
Orlando and Nancy will be at an elevation of -110 when they are at the same elevation.
Step-by-step explanation:
We can set up an equation to find the time it takes for Orlando and Nancy to be at the same elevation
We will use the variable T to represent the time in minutes
Orlando's elevation : -60 + 8t
Nancy's elevation : -35 + 12t
We will solve for t to see at what time the elevations were equal
-60 + 8t = -35 + 12t
-60 + 35 = 12t - 8t
-25 = 4t
4t = -25
t = -6.25
This means that both will be at the same elevation 6.25 minutes before Orlando goes down
To find the elevation they will be at that time, we will plug -6.25 into either expression.
-60 + 8t = -60 + 8(-6.25) = -110
Orlando and Nancy will be at an elevation of -110 when they are at the same elevation.
For what values of a are the following expressions true?
|a+5|=a+5
|a+5|=-5-a
Convert 1.374 to a percent. Do not add any additional values to the number.
Answer:
137.4%
Step-by-step explanation:
evaluate if r = 7. r - 12 =?
Answer:
if r is 7 then the answer is -5
if r is 7 then the answer is -5Step-by-step explanation:
if r is 7 then the answer is -5Step-by-step explanation:r-7=-5 because r is =to 7 so if you subtract 12 from 7 the answer you will get is -5
Parramore Corp has $15 million of sales, $2 million of inventories, $2 million of receivables, and $2.5 million of payables. Its cost of goods sold is 70% of sales, and it finances working capital with bank loans at a 7% rate. Assume 365 days in year for your calculations. What is Parramore's cash conversion cycle (CCC)? Do not round intermediate calculations. Round your answer to two decimal places. days If Parramore could lower its inventories and receivables by 11% each and increase its payables by 11%, all without affecting sales or cost of goods sold, what would be the new CCC? Do not round intermediate calculations. Round your answer to two decimal places. days How much cash would be freed up, if Parramore could lower its inventories and receivables by 11% each and increase its payables by 11%, all without affecting sales or cost of goods sold? Write out your answer completely. For Example, 13.2 million should be entered as 13,200,000. Do not round intermediate calculations. Round your answer to the nearest dollar. $ By how much would pretax profits change, if Parramore could lower its inventories and receivables by 11% each and increase its payables by 11%, all without affecting sales or cost of goods sold? Write out your answer completely. For Example, 13.2 million should be entered as 13,200,000. Do not round intermediate calculations. Round your answer to the nearest dollar. $
Answer:
copy paste it on gool then you will find the same thing but it has it done
Step-by-step explanation:
Please help. Deeply appreciated
By using the Pythagorean theorem we know that the given triangle is not a right triangle.
What is the Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2.
The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular.
The smallest and most well-known triplets are (3,4,5).
So, we have the values already,
Now, calculate as follows:
3² + 4² = 6²
9 + 16 = 36
25 ≠ 36
Hence, the given triangle is not a right triangle.
Therefore, by using the Pythagorean theorem we know that the given triangle is not a right triangle.
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the length of a rectangle is 9 centimeters less than its width. what are the rectangles dimension if its area is 90.
Length of rectangle in cm:
Width of rectangle in cm:
Let the width of the rectangle be "X". Then the length of the rectangle will be (X-9).
Formula to find the area of a rectangle is given by-
[tex] \small \underline{ \boxed{ \sf{ \pmb{Area_{(rectangle)} = Length\times Width }}}}\\[/tex]
On substituting the values-
[tex] \:\:\:\:\:\:\longrightarrow \sf {Area_{(rectangle)} = X \times \bigg(X-9\bigg)}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {90 = X^2 -9X}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-9X =90}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-9X -90=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-15X+6X -90=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X\bigg(X-15\bigg) +6\times \bigg(X-15\bigg)=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {\bigg(X-15\bigg) \times \bigg(X+6\bigg) =0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \boxed{ \tt{ \pmb{ \red{X = 15\: Or,\: -6}}}}\\[/tex]
Since,width cannot be (Negative) , so the width will be 15cm.And the length will be (X-9)= (15-9)=6cm.
5/12x6/15=30/180
How do I simplify?
Answer:
0.167
Step-by-step explanation:
if you divide 30/180 it will get you a decimal of 0.166666667 but if you were to divide 180 by 30 you will get 6
technecaly your answer would be 0.166666667 but you only take the first number in the decimal which is 0.1 then take six 0.16 then add the 7 0.167
that should end up being your answer if i did the math right
Answer:
Step-by-step explanation:
5/12 * 6/15 =30/180
1/6=1/6
which is true, Right-hand side is equal to left-hand side
Roselli's Machine Manufacturing Co reported its sales as R120 000, a gross profit of R50 000, and current liabilities of R25 000. If the current ratio is 2,5 and the quick ratio is 1,75, what is the inventory turnover for the company?
Answer:
Step-by-step explanation:
To find the inventory turnover for Roselli's Machine Manufacturing Co, we need to use the formula:
Inventory turnover = Cost of goods sold / Average inventory
First, we need to find the cost of goods sold (COGS):
COGS = Sales - Gross profit
COGS = R120 000 - R50 000
COGS = R70 000
Next, we need to find the average inventory. We can use the quick ratio formula to find the current assets:
Quick ratio = (Current assets - Inventory) / Current liabilities
Rearranging the formula to solve for inventory, we get:
Inventory = Current assets - (Quick ratio x Current liabilities)
Plugging in the values we know, we get:
1.75 = (Current assets - Inventory) / R25 000
Current assets - Inventory = 1.75 x R25 000
Current assets - Inventory = R43 750
Inventory = Current assets - R43 750
Since the current ratio is 2.5, we know that:
Current assets / Current liabilities = 2.5
Solving for current assets, we get:
Current assets = 2.5 x R25 000
Current assets = R62 500
Substituting the values we found for inventory and COGS into the inventory turnover formula, we get:
Inventory turnover = COGS / Average inventory
Inventory turnover = R70 000 / [(R62 500 - R43 750) / 2]
Inventory turnover = R70 000 / (R18 750 / 2)
Inventory turnover = R70 000 / R9 375
Inventory turnover = 7.47
Therefore, the inventory turnover for Roselli's Machine Manufacturing Co is 7.47.
Bruno bought a used car for $8,500 and had to pay 7.0% sales tax.
How much tax did he pay?
Answer:
Step-by-step explanation:
$8,500 -7.0%= $7,905
$8,500 - $7,905 = $595
Find the ratio of the perimeter of △ABC to the perimeter of △XYZ.
The ratio between the perimeter of triangle ABC and the perimeter of triangle XYZ is given as follows:
1/3.
What is the perimeter of a triangle?The perimeter of a triangle is the total length of its three sides. To find the perimeter of a triangle, you need to add up the lengths of all three sides.
The ratio between the side lengths of triangle ABC and triangle XYZ is given as follows:
5/15 = 1/3.
The perimeter of a triangle is measured in units, as area the side lengths, hence they have the same ratio, and thus the ratio between the perimeter of triangle ABC and the perimeter of triangle XYZ is given as follows:
1/3.
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another bank offers a different savings rate. if an account with $400 earns interest of $6, how much interest is earned by an account with $1800?
Answer:
$27
Step-by-step explanation:
$400 earns $6
$6÷$400= 0.015% interest
$1800 * 0.015% = $27
a telephone company makes up its monthly bills as follows: a fixed charge of 800 naira plus a charge proportional to the number of units of call on the telephone. if it charges 2 naira per unit of call, calculate the total charge on
a) 80units
b) 150units
c) 782 units
The total charge for 782 units of call is 2364 naira.
What is a total charge?
Total Charges refers to all payments made by the Customer and all amounts due under the Contract for products and services that the Council has actually provided, regardless of whether the Customer has received an invoice.
We can use the formula:
total charge = fixed charge + charge per unit x number of units
a) For 80 units of call:
total charge = 800 + 2 x 80
total charge = 800 + 160
total charge = 960 naira
Therefore, the total charge for 80 units of call is 960 naira.
b) For 150 units of call:
total charge = 800 + 2 x 150
total charge = 800 + 300
total charge = 1100 naira
Therefore, the total charge for 150 units of call is 1100 naira.
c) For 782 units of call:
total charge = 800 + 2 x 782
total charge = 800 + 1564
total charge = 2364 naira
Therefore, the total charge for 782 units of call is 2364 naira.
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What is the equation of the line thatt is parallel to the given line and passes through the point (12,-2)?
We want to write it in slope-intercept form:
y = mx + (b' = -12m - 2).
What is the parallel and perpendicular line equation?The slope of parallel lines is the same. The slopes of perpendicular lines are opposite reciprocals. To put it another way, if m=ab, then m=ba. To find the equation of a line, first determine the slope using the given information.
We can use the fact that parallel lines have the same slope to find the equation of a line that is parallel to a given line and passes through a given point.
Assume that the given line has the equation y = mx + b, where m represents the slope and b represents the y-intercept.
The slope of the line we are looking for is m because it is parallel to the given line. Because we don't know what the y-intercept of this line is, let's call it b'.
We now have two pieces of information regarding the new line:
It has the same slope as the given line (m).
It runs through the point (12,-2).
We can use this data to calculate the equation of the new line:
To begin, we can use the point-slope form of a line equation:
y - y1 = m(x - x1) (x - x1)
(x1, y1) denotes the point (12,-2) and m denotes the slope of the given line.
Substituting known values:
y - (-2) = m(x - 12) (x - 12)
Simplifying:
y + 2 = mx - 12m
We must now calculate the value of b' that makes this equation true for any point on the line. Because b' is the line's y-intercept, we can set x = 0 and solve for y:
y + 2 = m(0) - 12m
y = -12m - 2
As a result, the equation of the line parallel to the given line and passing through the point (12,-2) is:
y = mx - 12m - 2
Alternatively, we can write it in slope-intercept form:
y = mx + (b' = -12m - 2).
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Which of the following values of x makes this inequality true? Circle all that apply
5 + x > 5
A.1/2
B. -10
C. -5
D. 0.000003
E. 1.5
Answer:
A. 1/2
D. 0.000003
E. 1.5
Step-by-step explanation:
The inequality 5 + x > 5 can be simplified as follows:
5 + x > 5
x > 5 - 5
x > 0
True or false? the solution  Who’s system of equation is the point or points with a graph crosses the X axis 
answer: false
explanation: i took the test and got it right
As a result, the spot or points where the graph crosses the x-axis is not always the solution of a system of equations.
what is solution ?A solution in mathematics is the response to an issue or equation that meets specific requirements. The context of the issue or equation determines the kind of solution. For instance, in mathematics, the value of the variable(s) that makes an equation true is known as the solution. For instance, the answer to the equation 2x + 5 = 9 is x = 2, since the equation can be solved with x = 2.
given
False.
The values of the variables that fulfill every equation in a system of equations are represented by the system's solution.
A unique solution to a system of equations corresponds to the spot in the Cartesian plane where the equations' graphs intersect. This spot could be on the x-axis or not.
The graphs of the equations will be coincident or parallel lines that do not intersect and do not span the x-axis if a system of equations has an infinite number of solutions.
As a result, the spot or points where the graph crosses the x-axis is not always the solution of a system of equations.
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The perimeter of a rectangular garden is 30 ft. The length is 3 ft more than the width. Find the length and the width of the garden.
Step-by-step explanation:
the perimeter of a rectangle is
2×length + 2×width
in our case
length = width + 3
and
2×length + 2×width = 30
using the first equation in the second :
2×(width + 3) + 2×width = 30
width + 3 + width = 15
2×width + 3 = 15
2×width = 12
width = 12/2 = 6 ft
length = width + 3 = 6 + 3 = 9 ft
What is the effective interest rate of a simple discount note for $3,500 at a bank discount rate of 11%, for 24 months?
The effective interest rate of the simple discount note is 6%.
The effective interest rate (EIR) of a simple discount note can be calculated using the following formula:
EIR = (Discount ÷ Face Value) x (360 ÷ t)
Where Discount is the difference between the face value and the discounted value, t is the time in days from the issuance of the note until its maturity, and 360 is the number of days in a year used for interest rate calculations.
In this case, the face value is $3,500, the bank discount rate is 11%, and the time to maturity is 24 months or 720 days.
Discounted value = Face value x (1 - Bank discount rate x t ÷ 360)
Discounted value = $3,500 x (1 - 0.11 x 720 ÷ 360)
Discounted value = $3,080
Therefore, the discount is $420 ($3,500 - $3,080).
Using the formula for EIR, we get:
EIR = ($420 ÷ $3,500) x (360 ÷ 720)
EIR = 0.06 or 6%
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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 16 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
Step-by-step explanation:
Let x be the measure of the first angle.
According to the problem, we know that:
The sum of the angles of the triangle is 180: x + y + z = 180
The sum of the second and third angles is five times the measure of the first angle: y + z = 5x
The third angle is 16 more than the second: z = y + 16
We can substitute the third equation into the second equation to get:
y + (y + 16) = 5x
Simplifying this equation, we get:
2y + 16 = 5x
We can rearrange this equation to get:
y = (5/2)x - 8
Now we can substitute this equation and the equation z = y + 16 into the first equation to get:
x + (5/2)x - 8 + (5/2)x + 8 = 180
Simplifying this equation, we get:
6x = 360
Dividing both sides by 6, we get:
x = 60
Now we can use this value of x to find y and z:
y = (5/2)x - 8 = (5/2)(60) - 8 = 58
z = y + 16 = 58 + 16 = 74
Therefore, the measures of the three angles are x = 60, y = 58, and z = 74.
Type the correct answer in the box. Use numerals instead of words.
The cone and cylinder below both have a height of 11 feet.
The cone has a radius of 3 feet.
The cylinder has a volume of 310.86 cubic feet.
Complete the statements using 3.14 for pi. Any non-integer answers in this problem should be entered as decimals rounded to the nearest hundredth.
The volume of the cone is [?]
cubic feet.
The radius of the cylinder is [?]
feet.
The ratio of the volume of the cone to the volume of the cylinder is 1:[?]
.
Parts of similar triangles
Find x
In Δ PRQ, The value of the missing variable x is 4.8.
What is the triangle area formula?Calculating the area οf a triangle. Use the fοrmula area = 1/2 * base * height tο calculate the area οf a triangle. Select a side tο serve as the base and calculate the triangle's height frοm that pοint.
Cοrrespοnding sides in similar triangles are prοpοrtiοnal. As a result, using the infοrmatiοn prοvided, we can calculate the fοllοwing prοpοrtiοn:
As Δ PQS ≅ Δ PRQ
Then according to CPCT
PQ ≅ PR
and
PS ≅ PQ
Then we have
7 ≅ 5+ x
5 ≅ 7
Then
[tex]$ \frac{7}{5 + x} = \frac{5}{7}[/tex]
Cross multiply
[tex]$ \frac{7}{5 + x} = \frac{5}{7}[/tex]
7 × 7 = 5(5+ x)
49 = 25 + 5x
49 - 25 = 5x
24 = 5x
x = 24/5
x = 4.8
Thus, In Δ PRQ, The value of the missing variable x is 4.8.
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Complete question:
Parts of similar triangle are given as the Δ PQS ≅ Δ PRQ. Find the value of x.
logos to shop that sells two models of Radio 1 cost 3 times as much as the other in the to cost £72 wants to know the cost of the cheaper one if they're cheaper radio cost x pounds form an equation and X what should Laura's answer be
Laura's answer should be: The cost of the cheaper radio is £18.
What is equations ?
An equation is a statement that two expressions are equal. It typically involves one or more variables (represented by letters) and mathematical operations such as addition, subtraction, multiplication, and division.
Let's call the cost of the cheaper radio "x". Then, according to the problem, the cost of the more expensive radio is 3x.
We know that the total cost for both radios is £72, so we can set up an equation:
x + 3x = 72
Simplifying the equation, we get:
4x = 7
Dividing both sides by 4, we get:
x = 18
Therefore, the cost of the cheaper radio is £18.
Therefore, Laura's answer should be: The cost of the cheaper radio is £18.
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What is the length of side x?
Given:-
A right angled triangle with two angles 60° and 30° is given to us.Length of two shorter sides is x and √10 .To find:-
The value of x .Answer:-
Here since the given triangle is a right angled triangle, we may use the trigonometric ratios . We can see that perpendicular and base are involved in this question whose measures are "x" and "√10" respectively with respect to 60° angle. So here we may use the ratio of tangent as , in any right angled triangle,
[tex]\implies\tan\theta =\dfrac{p}{b} \\[/tex]
and here p = x , and b = √10 . So on substituting the respective values, we have;
[tex]\implies \tan\theta = \dfrac{x}{\sqrt{10}} \\[/tex]
Also the angle here is 60° , so that;
[tex]\implies\tan60^o =\dfrac{x}{\sqrt10} \\[/tex]
The value tan60° is √3 , so we have;
[tex]\implies \sqrt3 =\dfrac{x}{\sqrt10}\\[/tex]
[tex]\implies x =\sqrt{10}\cdot \sqrt{3}\\[/tex]
[tex]\implies x =\sqrt{10\cdot 3} \\[/tex]
[tex]\implies x =\sqrt{30} \\[/tex]
The value of √30 is approximately 5.48 , so that;
[tex]\implies \underline{\underline{\red{\quad x = 5.48\quad }}} \\[/tex]
Therefore the value of x is approximately 5.48 .
Answer:
The length of side x in simplest radical form is [tex]\sqrt{30}[/tex].
Step-by-step explanation:
From inspection of the given right triangle, we can see that the interior angles are 30°, 60° and 90°. Therefore, this triangle is a 30-60-90 triangle.
A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : √3 : 2. Therefore, the formula for the ratio of the sides is b: b√3 : 2b where:
b is the shortest side opposite the 30° angle.b√3 is the side opposite the 60° angle.2b is the longest side (hypotenuse) opposite the right angle.We have been given the side opposite the 30° angle, so:
[tex]\implies b=\sqrt{10}[/tex]
The side labelled "x" is the side opposite the 60° angle, so:
[tex]\implies x=b\sqrt{3}[/tex]
Substitute the found value of b into the equation for x:
[tex]\implies x=\sqrt{10}\sqrt{3}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}[/tex]
[tex]\implies x=\sqrt{10 \cdot3}[/tex]
[tex]\implies x=\sqrt{30}[/tex]
Therefore, the length of side x in simplest radical form is [tex]\sqrt{30}[/tex].
[tex]\hrulefill[/tex]
We can also calculate the length of side x using the tangent trigonometric ratio:
[tex]\boxed{\tan \theta=\sf \dfrac{O}{A}}[/tex]
where:
θ is the angle.O is the side opposite the angle.A is the side adjacent the angle.From inspection of the given right triangle:
θ = 30°O = √(10)A = xSubstitute these values into the formula:
[tex]\implies \tan 30^{\circ}=\dfrac{\sqrt{10}}{x}[/tex]
[tex]\implies \dfrac{\sqrt{3}}{3}=\dfrac{\sqrt{10}}{x}[/tex]
[tex]\implies x\sqrt{3}=3\sqrt{10}[/tex]
[tex]\implies x=\dfrac{3\sqrt{10}}{\sqrt{3}}[/tex]
Rationalise the denominator by multiplying the numerator and denominator by √3:
[tex]\implies x=\dfrac{3\sqrt{10}}{\sqrt{3}}\cdot \dfrac{\sqrt{3}}{\sqrt{3}}[/tex]
[tex]\implies x=\dfrac{3\sqrt{10}\sqrt{3}}{3}[/tex]
[tex]\implies x=\sqrt{10}\sqrt{3}[/tex]
[tex]\implies x=\sqrt{10\cdot3}[/tex]
[tex]\implies x=\sqrt{30}[/tex]
Therefore, the length of side x in simplest radical form is [tex]\sqrt{30}[/tex].
Hello,can yall help me with this
The area of Jade's rectangular wall is equal to 11⅓ yd² expressed as a mixed fraction
How to evaluate for the area of the rectangular wallGiven the formula for calculating area of rectangle as A = bh
b = 4¼ yd
h = 2⅔
so we can calculate the area of the rectangular wall as follows:
4¼ yd × 2⅔ yd
expressing the values of b and h as improper fractions;
17/4 yd × 8/3 yd
by simplification;
34/3 yd²
34/3 expressed as a mixed number is 11⅓.
Therefore, the area of Jade's rectangular wall is equal to 11⅓ yd² expressed as a mixed fraction.
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John drives to work each morning, and the trip takes an average of µ = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, what is the probability that John’s drive to work will take between 36 and 40 minutes?
The probability that John's drive to work will take between 36 and 40 minutes is 0.3413.
What is Probability?Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability is used in many areas of life, such as gambling, finance, and science. It is also used to make decisions in everyday life, such as estimating the likelihood of rain or the chance of winning a bet.
Using the normal distribution, the probability of John's drive taking between 36 and 40 minutes can be calculated using the standard normal distribution table. The formula for calculating the probability is: P(x<X<y) = P(y) - P(x).
For the given problem, the lower boundary is 36 minutes and the upper boundary is 40 minutes. Using the standard normal distribution table, the probability of John's drive taking between 36 and 40 minutes can be calculated by subtracting the probability of 36 minutes from the probability of 40 minutes. This gives us a probability of 0.3413.
Therefore, the probability that John's drive to work will take between 36 and 40 minutes is 0.3413.
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The probability that John's drive to work will take between 36 and 40 minutes is 0.3829.
What is Probability?Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability is used in many areas of life, such as gambling, finance, and science. It is also used to make decisions in everyday life, such as estimating the likelihood of rain or the chance of winning a bet.
The probability that John's drive to work will take between 36 and 40 minutes can be calculated using a normal distribution table. The mean of the distribution is µ = 38 minutes, and the standard deviation is σ = 5 minutes.
To calculate the probability, we need to convert the given range (36 minutes to 40 minutes) into standard normal scores. This is done by subtracting the mean (µ = 38 minutes) from the lower bound (36 minutes) and then dividing by the standard deviation (σ = 5 minutes). The result is a standard normal score of -0.4. The same calculation is carried out for the upper bound (40 minutes) and the result is a standard normal score of 0.4.
Using a normal distribution table, we can then determine the probability that John's drive to work will take between 36 and 40 minutes. This probability is equal to the area under the normal curve between the two standard normal scores of -0.4 and 0.4. The result is a probability of 0.3829.
Therefore, the probability that John's drive to work will take between 36 and 40 minutes is 0.3829.
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Parts of similar triangles
Find x
The measurement of the side EF in ΔDEF is 13 units.
What's the triangle formula?Tο determine the area οf a triangle, use the fοrmula area = 1/2 * base * height. Determine the height οf the triangle frοm a base side. Then enter the base and height measurements intο the fοrmula.
Because the twο in the figure are similar, we can set up an equatiοn and sοlve fοr the unknοwn value οf x using the prοpοrtiοnality οf cοrrespοnding sides:
As ΔDEF ≅ ΔJHI
Then EF ≅ IH
3x - 2 = x + 8
3x - x = 8 + 2
2x = 10
x = 10/5
x = 5
EF = x + 8
= 5 + 8
= 13
Thus, The measurement of the side EF in ΔDEF is 13 units.
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