DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027
DY^2 = 170 * 169^2 / (135^2 + 50 -
In the given figure, we have a triangle DEF, where EF is a transversal intersecting DE and DF at points X and Y, respectively, such that XY || DE.
D
/ \
/ \
/ \
E-------F
Given that XF = 10, YF = 5, and EF = 13, we need to find DY.
We can start by using the property of similar triangles. Since XY || DE, we have the following similarity ratios:
EF / ED = EY / EJ (where J is the intersection of XY and DF)
EF / DF = EJ / EY
Substituting the given values, we get:
13 / ED = EY / EJ
13 / DF = EJ / (13 - EY)
Multiplying the above two equations, we get:
13 / ED * 13 / DF = EY / EJ * EJ / (13 - EY)
169 / (ED * DF) = EY / (13 - EY)
Substituting the values of XF = 10 and YF = 5, we get:
169 / (ED * DF) = 5 / 8
ED / DF = 135 / 169
Using the Pythagorean theorem on triangles DEX and DFY, we get:
ED^2 = EX^2 + DX^2
DF^2 = FY^2 + DY^2
Since EX + DX = EF = 13, we have DX = 13 - EX. Substituting this in the first equation and simplifying, we get:
ED^2 = EX^2 + (13 - EX)^2
ED^2 = 2EX^2 - 26EX + 170
Similarly, substituting FY = 13 - EY in the second equation and simplifying, we get:
DF^2 = FY^2 + DY^2
DF^2 = 170 - 26EY + EY^2 + DY^2
Now, using the fact that ED/DF = 135/169, we can substitute ED^2 = (135/169)^2 * DF^2 in the above equation for ED^2, and simplify to get:
(135/169)^2 * DF^2 = 2EX^2 - 26EX + 170
DF^2 = 170 * 169^2 / (135^2 + 2EX^2 - 26EX)
DF^2 = 170 * 169^2 / (135^2 + 2(10^2) - 26EX) (Substituting XF = 10)
Similarly, we can substitute EY = 5 in the above equation for DF^2 and simplify to get:
FY^2 + DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY) (Substituting YF = 5)
DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY) - FY^2
Substituting the given values, we get:
DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027
DY^2 = 170 * 169^2 / (135^2 + 50 -
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When students asked their teacher how old her children were, she said, "I have three children. The product of their ages is 72 and the sum of their ages is the number of this room. " The children then asked for the door to be opened to verify the room number. Then Carly told the teacher she needed more information to solve the problem. The teacher said, "My oldest child is good at math. " Then Carly announced the correct ages of her teacher's children. What are the ages of the teacher's children?
The ages of the teacher's three children whose product is 72 will be 3,3,8.
Let the age of three children be x, y, z
x × y × z = 72
x + y + z = No. of rooms
Now possible answers can be three numbers whose product is 72
There are two possible answers in which the product of the number is 72 and the sum of the number is also same
1) 2 × 6 × 6 = 72 and 2 + 6 + 6 = 14
2) 3 × 3 × 8 = 72 and 3 + 3 + 8 = 14
Now teacher gave a hint that his oldest child is good at math
Oldest means one of the three child is oldest so the only possible answer could be 3,3,8
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En una serie de razones geométricas iguales,los antecedentes son 2, 3 y 5. si el producto de los consecuentes es 810. halle la suma del mayor y menor consecuente.
As per the given geometric sequence, the sum of the greater and lesser consequents is 51.
We are given that the antecedents (which are just the first three terms) of a geometric sequence are 2, 3, and 5. Let's call the common ratio of this sequence r. Using the definition of a geometric sequence, we can write the terms of this sequence as 2, 2r, 2r² (since the first term is 2 and the common ratio is r), 3, 3r, 3r², 5, 5r, 5r².
Next, we are told that the product of the consequents (which are just the terms after the first three) is 810. To find the product of the consequents, we just multiply all the terms after the first three together. So we have:
(2r³) * (3r²) * (5r) = 30r⁶
We know that this product is equal to 810, so we can set up the equation:
30*r⁶ = 810
Solving for r, we get:
r⁶ = 27
r = 3 (since 3⁶ = 729)
Now that we know the common ratio is 3, we can find the terms of the sequence by multiplying each antecedent by 3. So the terms of the sequence are:
2, 6, 18, 3, 9, 27, 5, 15, 45
The greater and lesser consequents are 45 and 6, respectively. So the sum of the greater and lesser consequents is:
45 + 6 = 51
Therefore, the answer to the problem is 51.
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Complete Question:
In a series of equal geometric ratios, the antecedents are 2, 3, and 5. If the product of the consequents is 810, find the sum of the greater and lesser consequents.
15,10,20/3,... find the 9th term
Answer:
9th term is
[tex]a_9 = \dfrac{1280}{2187}\\[/tex]
Step-by-step explanation:
This sequence is clearly a geometric progression where the ratio of any term to the previous term is constant and known as common ratio
The 3 terms given are:
15, 10 and 20/3
10 ÷ 15 = 2/3
20/3 ÷ 10 = 2/3
So the common ratio is 2/3
For a geometric sequence with common ratio r and first term a₁, the nth term is given by the equation
aₙ = a₁ · rⁿ⁻¹
Here a₁ = first term = 15
r = 2/3
So the general equation for the nth term of this equation is
aₙ = 15 · (2/3)ⁿ⁻¹
The 9th term would be
[tex]a_9 = 15 \cdot \left(\dfrac{2}{3}\right)^{9-1}\\\\a_9 = 15 \cdot \left(\dfrac{2}{3}\right)^{8}\\\\a_9 = 15 \cdot \left(\dfrac{256}{6561}\right)\\\\a_9 = 15 \cdot \left(\dfrac{256}{6561}\right)\\[/tex]
15 is divisible by 3 giving 5
6561 is divisible by 3 giving 2187
So the above expression simplifies to
[tex]a_9 = 5 \cdot \dfrac{256}{2187}\\\\a_9 = \dfrac{1280}{2187}\\[/tex]
what is an equation of the line perpendicular to y= -3x + 4 that contains (-6,2)
The equation of the perpendicular line to y = -3x + 4 and passing through (-6, 2) is y = (1/3)x + 4.
What does a perpendicular line look like?
There are a lot of perpendicular lines that we may see in reality. The corners of a chalkboard, a window, the sides of a set square, and the Red Cross symbol are a few examples.
Knowing that the slopes of perpendicular lines are the negative reciprocals of one another is necessary to determine the equation of a line perpendicular to a given line.
The given line has a slope of -3, so the slope of a line perpendicular to it would be the negative reciprocal of -3, which is 1/3.
We also know that the line passes through the point (-6, 2).
The equation of the line passing through (-6, 2) and perpendicular to y = -3x + 4 can be found using the point-slope form of a line:
y - 2 = (1/3)(x + 6)
Simplifying this equation, we get:
y = (1/3)x + 4
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Can you explain what is the horizontal tangent plane and how
should I use the tangent plane equation to answer this question,
thanks.
equation: f(a,b) + f(1)(x-a) + f(2)(y-b) = z
The value of the function at that point is equal to the z-coordinate of the point on the plane.
How to use the tangent plane equation to find the equation of a tangent plane?A horizontal tangent plane is a plane that is parallel to the x-y plane and tangent to a surface at a point where the slope in the horizontal direction is zero.
To use the tangent plane equation to find a horizontal tangent plane, we need to find the partial derivatives of the function with respect to x and y, evaluate them at the point of interest, and check if they are both zero.
If they are both zero, then the tangent plane is horizontal and the equation simplifies to f(a,b) = z.
The tangent plane equation is given by:
f(a,b) + f(1)(x-a) + f(2)(y-b) = z
where (a,b) is the point where the tangent plane intersects the surface, and f(1) and f(2) are the partial derivatives of the function with respect to x and y, evaluated at (a,b).
To use this equation to find the horizontal tangent plane, we first find the partial derivatives f(1) and f(2), and evaluate them at the point where we want to find the tangent plane. If f(1) and f(2) are both zero at that point, then the tangent plane is horizontal and the equation simplifies to:
f(a,b) = z
This means that the value of the function at that point is equal to the z-coordinate of the point on the plane.
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Catherine talks on the phone for 3/4 of an hour every night. How many hours dose she talk on the phone is one week. No decimals pls!
Answer: 5 1/4
Step-by-step explanation: 3/4 times 7/1 equals 5.25
Turn the decimal to a fraction and get 5 1/4
1. deagan is painting a mural of a triangle for a lwhs conference room. the
triangular-shaped mural will be a total of 289 square feet; the height is 25
feet. what is the measure ofthe base?
question involving a mural painted by Deagan, which features a triangle, for a conference room at LWHS. You'd like to know the measure of the base.
Unfortunately, it seems that some essential information is missing from your question, such as the dimensions or other properties of the triangle. In order to accurately answer your question and calculate the measure of the base, please provide more information about the triangle or any related information given in the problem.
Once you provide the necessary information, I'd be happy to help you find the measure of the base and explain the process step-by-step!
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-1(x^2-4x+8)
Multiply
To multiply -1(x^2-4x+8), we need to distribute the -1 to each term inside the parentheses:
-1(x^2-4x+8) = -x^2 + 4x - 8
So, the product of -1 and the expression (x^2-4x+8) is -x^2 + 4x - 8.
Find m/STR.
186
T
m/STR=
112
R
degrees
Describe at least two advantages to using stem plots rather than frequency distributions
Stem plots (also known as stem-and-leaf plots) have several advantages over frequency distributions, including:
1. Stem plots show individual data points: Unlike frequency distributions, which group data into intervals, stem plots show each individual data point. This makes it easier to see the distribution of the data, including the shape, the range, and any outliers or gaps. Stem plots can also reveal patterns and trends in the data that may not be apparent from a frequency distribution.
2. Stem plots are easy to construct: Constructing a stem plot requires minimal computation and is relatively simple to create by hand. It involves only sorting the data and then splitting each data point into a stem (the leading digits) and a leaf (the trailing digit). This makes stem plots a convenient tool for quick exploratory data analysis, especially when dealing with small to moderate-sized datasets. In contrast, constructing a frequency distribution can be more time-consuming, as it requires choosing appropriate intervals and counting the number of data points in each interval.
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17/3 yd = how many ft
Answer:
w
Step-by-step explanation:
w
a restaurant meal cost $90 and there was a 6% meals tax on the price of the meal hey a)how much was the mail tax b) what was the total price of the meal with a meal tax
A restaurant meal cost $90 and there was a 6% meals tax on the price of the meal. The meal tax was $5.40 and the total price of the meal with the meal tax was $95.40.
Find the meal tax, you need to calculate 6% of the $90 meal cost.
Convert the percentage to a decimal by dividing by 100, so 6% = 0.06.
Multiply the meal cost by the decimal. In this case, $90 × 0.06 = $5.40.
So, the meal tax was $5.40.
Find the total price of the meal with the meal tax, you need to add the meal tax to the original cost of the meal.
Add the meal tax to the original cost, so $90 + $5.40 = $95.40.
The total price of the meal with the meal tax was $95.40.
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What is the local rate of change on this parabola at the point , (-6,8)?
To find the local rate of change on a curve at a specific point, we need to find the slope of the tangent line at that point. The tangent line represents the instantaneous rate of change or the rate of change at that particular point.
To find the slope of the tangent line at (-6,8) on the parabola, we need to take the derivative of the function at that point.
Assuming that the parabola is defined by the equation [tex]y = ax^2 + bx + c,[/tex]
where a, b, and c are constants, we can find the derivative of the function as follows:
[tex]dy/dx = 2ax + b[/tex]
Substituting [tex]x = -6,[/tex] we get:
[tex]dy/dx = 2a(-6) + b[/tex]
To find the values of a and b, we need more information about the parabola.
If we have the equation of the parabola or another point on the curve, we can use it to find the values of a and b.
Once we have the values of a and b, we can substitute them into the derivative equation and evaluate it at [tex]x = -6[/tex] to find the slope of the tangent line at (-[tex]6,8[/tex]), which is the local rate of change at that point.
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Drag each set of dots to the correct location on the dot plot. Each set of dots can be used more than once. Not all sets of dots will be used Tricia recorded the number of pets owned by each of her classmates. These data points represent the results of her survey 032. 41. 2. 1. 2. 1. 1. 3,4,2,0,0. 1. 1. 1. 0. 3 Create a dot plot that represents the data 1 Number of Students 2 Numbers of Pets
To create a dot plot that represents the given data, we need to place each data point on a number line and then represent it with a dot above its corresponding value. The number line should range from 0 to the maximum number of pets owned by any student, which in this case is 4.
First, we place a dot above the value 0, which occurs twice in the data set. Then, we place three dots above the value 1, which occurs five times in the data set. Next, we place two dots above the value 2, which occurs twice in the data set. Finally, we place one dot above the value 3 and one dot above the value 4.
In summary, the dot plot will have one dot above 3 and one dot above 4 for the number of pets axis, and for the number of students axis, we will have two dots above 0, five dots above 1, two dots above 2, and no dots above 3 or 4. This represents the distribution of the data in a visual way.
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In triangle ABC, angle B is a right angle. Give me measures of side BC and hypotenuse AC so that the measure of Angle A is greater than 75 degrees
In triangle ABC with angle B as a right angle, if the measure of angle A is greater than 75 degrees (e.g., 80 degrees), side BC can be approximately 9.848 units, and the hypotenuse AC can be 10 units.
In triangle ABC with angle B as a right angle, to find measures of side BC and hypotenuse AC such that the measure of angle A is greater than 75 degrees, we can use the sine function.
Determine the sine of angle A. Since angle A needs to be greater than 75 degrees, let's choose 80 degrees as an example.
sin(80°) = opposite side (BC) / hypotenuse (AC)
Choose a convenient value for the hypotenuse (AC). Let's choose AC = 10 units.
Solve for the opposite side (BC).
sin(80°) = BC / 10
BC = 10 * sin(80°)
BC ≈ 9.848
If the measure of angle A is more than 75 degrees (for example, 80 degrees), side BC and the hypotenuse AC in the triangle ABC with a right angle can both be 10 units.
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PLEASE HELP ME (sorry I couldn’t put the picture in)
The triangular prism is 1 foot high. The triangle that forms the base of the prism has a base of 6 inches and a height of 4 inches. The two remaining sides of the triangular bases are each 5 inches long. What is the surface area and volume of the triangular prism?
S= ___________ in^ 2
V= ___________ in^3
The surface area and volume of the triangular prism are:
S = [tex]204 in^2[/tex]
V = [tex]144 in^3[/tex]
How to solveThe area= 12 inches
The volume = 144 cubic inches
The area of each triangular face is already calculated (A = 12 square inches). The three rectangular faces have dimensions 5 x 12, 6 x 12, and 4 x 12.
Calculate the area of each rectangular face:
5 * 12 = 60 square inches
6 * 12 = 72 square inches
4 * 12 = 48 square inches
Now, sum the areas of all faces to get the surface area (S):
S = (2 * 12) + 60 + 72 + 48 = 204 square inches.
So, the surface area and volume of the triangular prism are:
S = [tex]204 in^2[/tex]
V = [tex]144 in^3[/tex]
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I am wondering what’s 75% of 188
I know 50% of 188 is 94 and 25% is 47
Answer: 141
Step-by-step explanation: 188 x 75% = 141
Answer:
141
Step-by-step explanation:
I looked it up.
Which scale factors produce an expansion under a dilation of the original image?
Select each correct answer.
0. 1
0. 9
2
7. 5
Tamekia and Marsha mow lawns during the summer to earn money. Tamekia determined that she can earn between $6. 00 and $6. 25 per hour. Marsha estimates that she earns between $7. 50 and $8. 00 per hour. About how much more money will Marsha earn than Tamekia if they each work 22 hours?
If Tamekia and Marsha work for 22 hours, Marsha will earn $27.50 more than Tamekia.
To determine the amount of money each person can earn, we need to know the hourly rate and the number of hours worked. Tamekia estimates that she can earn between $6.00 and $6.25 per hour. Let's assume that she can earn $6.25 per hour. If Tamekia works for 22 hours, her total earnings will be:
Total earnings for Tamekia = Hourly rate x Number of hours worked = $6.25 x 22 = $137.50
Now let's look at Marsha's earnings. Marsha estimates that she can earn between $7.50 and $8.00 per hour. Let's assume that she can earn $7.50 per hour. If Marsha works for 22 hours, her total earnings will be:
Total earnings for Marsha = Hourly rate x Number of hours worked = $7.50 x 22 = $165.00
To determine how much more money Marsha will earn than Tamekia, we need to subtract Tamekia's total earnings from Marsha's total earnings:
Difference in earnings = Total earnings for Marsha - Total earnings for Tamekia = $165.00 - $137.50 = $27.50
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The table displays data collected, in meters, from a track meet.
14
3
624
What is the median of the data collected?
2 19
332
2.5
02
4.5
03
€
To find the median of the data, we first need to arrange the numbers in order from smallest to largest:
3, 14, 624
Since we have an odd number of data points, the median is the middle number. In this case, the median is 14.
Therefore, the median of the data collected is 14 meters.
The circumference of a circle is 12.56 millimeters. What is the circle's radius?
C=12.56 mm
Use 3.14 for .
The radius of the circle is 2mm
How to determine the circumferenceIt is important to note that the formula that is used for calculating the circumference of a circle is expressed with the equation.
The equation is written as;
C = 2πr
Such that the parameters are;
C is the cicumference of the circle.r is the radius of the circle.πtakes the constant value of 22/7From the information given, we have thatt;
The radius of the circle = r
The circumference = 12.56mm
Substitute the values, we have;
12. 56 = 2×3.14r
Multiply the values
r = 12. 56/6. 28
divide the values
r = 2mm
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A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totaled $327. 50. The second order was for 6 bushes and 2 trees, and totaled $142. 96. Sam tried to use system of equation to solve the problem. If "b" represents bushes and "t" represents trees which system can Sam use?
System of equation Sam can use is 13b + 4t = 327.50 and 6b + 2t = 142.47 where "b" represents bushes and "t" represents trees.
Let the cost of bushes represented by b
cost of trees represented by t
First order is 13 buses and 4 trees and total is $327.50
By using the data equation form will be
13b + 4t = 327.50
Second order is 6 bushes and 2 trees and total is $142. 96
By using data the equation form will be
6b + 2t = 142.96
These set of equation will for and can be used.
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Let C = {factors of 12}
Work out n(C)
The value or n(C) based on the information will be 6.
How to explain the FactorIn mathematics, a factor is a number or algebraic expression that divides another number or expression without leaving a remainder. More formally, if a is a factor of b, then b can be expressed as a product of a and some other number or expression.
For example, in the expression 12 = 2 x 2 x 3, the numbers 2 and 3 are factors of 12. Similarly, in the expression x² - 4, (x - 2) and (x + 2) are factors because if we multiply them together we get x² - 4.
The factors of 12 are 1, 2, 3, 4, 6, and 12. Therefore, the set C contains six elements. Hence, n(C) = 6.
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Consider functions f and g. What is the approximate solution to the equation after three iterations of successive approximations? Use the graph as a starting point. 3x^2 - 6x - 4 = 2/x+3 +1
The required values on the graph, the solution is approximate x = -0.33.
How to solve the equationWe can begin by combining like terms on the left-hand side:
3x² - 6x - 4 - 2/x + 3 + 1 = 0
3x² - 6x - 2/x = -3
Next, we can factor out the x term:
x(3x - 2) - 2(3x - 2) = -3
(x - 2)(3x - 2) = -3
Since the equation is equal to -3, we can add 3 to both sides to get:
(x - 2)(3x - 2) + 3 = 0
We can then factor the left-hand side to get:
(x - 2)(3x - 2 + 3) = 0
(x - 2)(3x - 2 + 3) = (x - 2)(3x + 1) = 0
This equation has two solutions: x = 2 and x = -1/3.
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Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
Clue 1: The R stamps total 24 cents. R1 + R2 + R3 = 24 Clue 2: The R stamps with animals total 16 cents. R1 + R2 = 16 Combining this with Clue 1, we know R3 = 8 Clue 3: The stamps with animals total 20 cents. R1+ Combining this with Clue 2, we know S2 = 4 Clue 4: The stamps with two animals total 13 cents. S2 + R2 = Combining this with what we learned from Clue 3, we know R2 = +72 = 22 Clue 5: The two stamps with a person total 22 cents. Combing this with what we learned from Clue 2, we know I? Clue 6: The triangle stamps total 24 cents. I+ Combining this with what we learned from Clue 5, we know +52 = 20 Clue 7: The stamps with mechanical devices total 20 cents. 71+ R3 51 Combining this with what we learned from Clue 2 and Clue 6. we know Sl SA The S stamps total 11 cents. S1 + $2+ Combining this with what we learned from Clue 3 and Clue 7, we know 5
Using the combine clues method:
[tex]R_1=7\\\\R_2=9\\\\R_3=8\\\\S_1=2\\\\S_2=4\\\\S_3=5\\\\T_1=10\\\\T_2=14[/tex]
How to combine clues?Certain items that must be worn, used, or accessed in order to access particular clues. The maximum skill level needed to solve each master clue is shown.
Clue 1: [tex]R_1 + R_2 + R_3 = 24[/tex]
Clue 2: [tex]R_1 + R_2 =16[/tex]
Since, [tex]R_1 + R_2 + R_3 = 24[/tex] (from clue 1)
[tex]R_1 + R_2 + R_3 = 24\\\\16 + R_3 = 24[/tex]
Subtract both the sides by 16,
[tex]R_3=8[/tex]
Clue 3:
We need to find the blank [tex]R_1 +[/tex] __ [tex]+S_2=20[/tex] and [tex]S_2=4[/tex]
Since, [tex]R_1 + R_2 = 16[/tex] (from clue 2)
So,
[tex]R_1 + R_2 + S_2 = 20\\\\16 + S_2 = 20[/tex]
Subtract 16 from both sides.
[tex]16 + S_2 - 16 = 20 -16\\\\S_2 = 4[/tex]
So,
[tex]R_1 + R_2 + S_2 = 20[/tex]
Clue 4:
We need to find the blank [tex]R_2[/tex] = __
[tex]S_2 + R_2 = 13[/tex]
Since, [tex]S_2 = 4[/tex]
[tex]S_2 + R_2 = 13\\\\4 + R_2 = 13[/tex]
Subtract 4 from both sides.
[tex]R_2 = 9[/tex]
So, [tex]R_2 = 9[/tex]
Clue 5:
We need to find the blank ___ [tex]+ T_2 = 22[/tex] and [tex]T_2=[/tex] ___
[tex]R_3 + T_2 = 22[/tex]
Since, [tex]R_3 =8[/tex] (from the Clue 2)
[tex]R_3 + T_2 = 22[/tex]
[tex]8 + T_2 = 22[/tex]
Subtract both the sides by 8,
[tex]T_2 = 14[/tex]
So, [tex]R_3 + T_2 = 22[/tex]
Clue 6:
We need to find the blank [tex]T_1 +[/tex] ___ = 24 and ___ = 10
Since, [tex]T_1 + T_2 = 24[/tex] (from the Clue 5)
[tex]T_1 + 14 = 24[/tex]
Subtract both the sides by 14,
[tex]T_1 = 10[/tex]
Clue 7:
We need to find the value of [tex]S_1[/tex],
Given [tex]T_1 + R_3 + S_1 =20[/tex]
Since, [tex]T_1=10[/tex] and [tex]R_3=8[/tex]
[tex]10+ 8 + S_1 = 20\\\\18 + S_1 = 20[/tex]
Subtract both the sides by 18,
so, [tex]S_1=2[/tex]
Combining this with what we learned from Clue 2 and Clue 6, we know
[tex]S_1=2[/tex]
Now, we need to find the blank, [tex]S_1 + S_2 +[/tex] ___ = 11
Combining this with what we learned from Clue 3 and Clue 7, we know:
___ = 5
[tex]S_1 + S_2 + S_3 = 11\\\\2 + 4 + S_3 = 11\\\\6 + S_3 = 11[/tex]
Subtract both the sides by 6,
[tex]S_3 = 5[/tex]
For [tex]R_1[/tex]
Since,
[tex]R_1 + R_2 + R_3 = 24\\\\R_1 + 9 + 8 = 24\\\\R_1 + 17 = 24[/tex]
Subtract both the sides by 17,
[tex]R_1 = 17[/tex]
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What is amplitude in Trig.
Answer:
It the distance from mid line to top of wave.
Step-by-step explanation:
Answer:
Height of a wave (from mid line to max.
Step-by-step explanation:
A small printing company launched an online ordering system to expand its business. The equation с. 400-(1. 03)" represents the number of customers c it has in terms of the number of months m since it launched the ordering system. 1. By what factor does the number of customers grow in one year? Write your answer as an expression and a numerical value.
2. If y is the time in years write an equation for the numbers of costumers c as a function of the numbers of years y after the introduction of the ordering system.
1. The growth factor for the number of customers over a year is approximately 1.4266.
2. the growth factor in customers over a decade period is approximately 5.927.
Factors that affect how many consumers there are in a year are
c(12)/c(0) = (400 x (1.03)¹²) / (400 x (1.03)⁰)
= (1.03)¹²
= 1.4266....
Therefore, the growth factor for the number of customers over a year is approximately 1.4266.
2. To write an equation for the number of customers c as a function of the number of years y, we can substitute m = 12y into the original equation
[tex]c(y) = 400 x (1.03)^{12y}[/tex]
one decade = 10 years
= 120 months
We must calculate the value of the equation at m=120 and divide it by the equation's value at m=0.
c(120) / c(0) = [400 x (1.03)¹²⁰] / [400 x (1.03)⁰]
= (1.03)¹²⁰
= 5.927...
Therefore, the growth factor in customers over a ten-year period is approximately 5.927.
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Given Question is incomplete, complete question is given below:
A small printing company launched an online ordering system to expand its business. The equation [tex]c=400(1. 03)^m[/tex] represents the number of customers c it has in terms of the number of months m since it launched the ordering system.
1. By what factor does the number of customers grow in one year? Write your answer as an expression and a numerical value
2. If y is time in years, write an equation for the number of customers c as a function of the number of years y after the introduction of the ordering system. If this model continues to apply for a decade, by what factor will the number of customers grow in one decade?
How can you solve x3-2=2?
Answer: x=4/3
Step-by-step explanation:
3x-2=2
3x=2+2
3x=4
x=4/3
How many times of rs. 1300 is the value including 13% vat on rs. 13000?
There would be of 11.3 times rs. 1300 is the value including 13% vat on rs. 13000
To find out how many times Rs. 1300 is contained in the value including 13% VAT on Rs. 13000, we need to first calculate the total value including VAT.
VAT is a tax that is added to the net price of a product or service. In this case, the net price is Rs. 13000 and the VAT is 13% of the net price, which is:
VAT = 13% of Rs. 13000
= 0.13 x 13000
= Rs. 1690
So, the total value including VAT is:
Total value = Net price + VAT
= Rs. 13000 + Rs. 1690
= Rs. 14690
Now, to find out how many times Rs. 1300 is contained in this value, we divide the total value by Rs. 1300:
Number of times = Total value / Rs. 1300
= Rs. 14690 / Rs. 1300
= 11.3 (approx)
Therefore, the value including 13% VAT on Rs. 13000 is about 11.3 times the value of Rs. 1300.
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Solve the equation 2^(x-2)+2^3-x=3. Also prove that the roots also satisfies 4^(x)-6*2^(x+1)+32=0
The roots of the given equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3[/tex]also satisfy the equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]
How to find the roots of equation?To find the roots of equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3,[/tex] we can substitute [tex]y = 2^(^x^-^2^)[/tex]to get:
[tex]y + 2^(^5^-^x^)^/^y = 3[/tex]
Multiplying both sides by y, we get:
[tex]y^2 + 2^(^5^-^x^) = 3y[/tex]
Substituting y = 2^(x-2), we get:
[tex]2^(^2^x^-^8^) + 2^(^5^-^x^) = 3 * 2^(^x^-^2^)[/tex]
Multiplying both sides by 2^8, we get:
[tex]4(2^x) + 32 = 768(2^(^2^-^x^))[/tex]
Simplifying, we get:
[tex]4(2^x) - 768(2^-^x) + 32 = 0[/tex]
Dividing both sides by 4, we get:
[tex]2^x - 192(2^-^x) + 8 = 0[/tex]
Multiplying both sides by [tex]2^x[/tex], we get:
[tex]4^x - 192 + 2^x = 0[/tex]
Adding 192 to both sides, we get:
[tex]4^x + 2^x - 192 = 0[/tex]
This is the same as the given equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]
Therefore, we have shown that the roots of the given equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3[/tex] also satisfy the equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]
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