Answers
1. Definition of Congruence:∠ RSU ≅ ∠ VST
2. Definition of Congruence: m∠ RSU = m∠ VST
3. Angle Addition Postulate: m∠ RSU + m∠ USV = m/RSV
4. Angle Addition Postulate: m∠ VST + m∠ USV = m∠ UST
5. Transitive Property: m∠ RSU + m∠ USV = m∠ UST
6. Substitution Property: m∠ RSV = m∠ UST
7. Definition of Congruence: ∠ RSV ≅ ∠ UST
What is the transitive property?In mathematics, a relation R on a set X is said to have a transitive property if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c.
This is shown in the case of number 6 where :
m∠ RSU + m∠ USV = m∠ UST
The transitive property is also shown in equality states where all values of a, b, and c, if a = b, and b = c, then a = c.
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Related Questions
Find the surface area of water tower that is 40 feet tall and has a diameter of 30 feet. DO NOT ROUND YOUR ANSWER!
Answers
Answer: SA=5183.62788
Step-by-step explanation:
A=2πrh+2πr2=2·π·15·40+2·π·152≈ 5183.62788
~Find the radius- 30 divided by 2= 15 so radius =15
A box has a base area of 1.1 m2.
The box is placed on the ground and exerts a force of 4.5 kN.
What pressure is the force applied with?
Give your answer in kN/m2 and rounded to 2 dp.
Answers
Answer:
To find the pressure that the box exerts on the ground, we need to divide the force by the area of the base:
pressure = force / area
We are given that the force is 4.5 kN and the area is 1.1 m². However, we need to convert the force from kilonewtons to newtons before we can divide by the area:
force = 4.5 kN = 4,500 N
Now we can plug in the values:
pressure = 4,500 N / 1.1 m² = 4,090.91 N/m²
To express the pressure in kilonewtons per square meter, we need to divide by 1,000:
pressure = 4.09091 kN/m²
Rounding to 2 decimal places, we get:
pressure ≈ 4.09 kN/m²
Therefore, the pressure exerted by the box on the ground is approximately 4.09 kN/m².
2x+ 5y=7
solve for x and y
Answers
Answer:
x = 0 y = 7/5
Now imagine the quadrilateral is the base of a prism that has a height of h
units. What is the volume of this prism compared to the one with a height of 1
unit? The volume of the prism is Bh, which is h times the volume
V of the
original prism.
right prism
Answers
The volume of the prism with height h is h times the volume of the prism with height 1 unit.
If the original prism has a volume of V and a height of 1 unit, then the volume of the prism with height h is given by:
Bh = (V)(h)
where B is the area of the quadrilateral base.
The volume of the prism with height h is h times the volume of the original prism. So, we can compare the volume of the two prisms by looking at their volume ratios:
Volume ratio = Volume of prism with height h / Volume of original prism
= Bh / (V)(1)
= Bh / V
= h
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I NEED HELP!!! RN ASAP!
Write each decrease as a percent.
Illustrate each answer with a
number line.
a) The price of a book decreased from
$15.00 to $12.00.
b) The number of students who take
the bus to school decreased from 200 to 150
Answers
We can calculate the percentages according to the amounts provided in the prompt, and then make a number line to illustrate each percentage as follows:
a) The price of the book decreased by 20%.
$15.00 $12.00
|-----------------|------->
100% 80%
b) The percentage decrease in the number of students who take the bus to school is 25%.
200 150
|-----------------|------->
100% 75%
How to calculate percentagesCalculating percentages involves finding a portion of a whole expressed as a fraction of 100. To calculate a percentage, divide the part by the whole and then multiply the result by 100.
For example, if 20 out of 100 students are absent, the percentage of absent students is:
(20/100) x 100 = 20%.
With that in mind, we can conclude that we have correctly answered this question.
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A textbook store sold a combined total of 288 history and chemistry textbooks in a week. The number of chemistry textbooks sold was 72 less than the number of history textbooks sold. How many textbooks of each type were sold?
Answers
The number οf histοry bοοks is 180 that sοld in a week. The number οf chemistry textbοοks is 108 sοld in a week.
What is an equatiοn?There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical declaratiοn that illustrates the equality οf twο mathematical expressiοns.
Given that the tοtal number οf bοοks that sοld in a week is 288.
The number οf chemistry textbοοks sοld was 72 less than the number οf histοry textbοοks sοld.
Assume that the number οf histοry textbοοks sοld was x.
The number οf chemistry textbοοks sοld was (x-72)
The tοtal number οf bοοks sοld was x + (x-72) = 2x - 72.
Accοrding tο the questiοn:
2x - 72 = 288
Add 72 frοm bοth sides:
2x - 72 + 72 = 288 + 72
2x = 360
Divide bοth sides by 2:
x = 360/2
x = 180
The number οf histοry textbοοks sοld was 180.
The number οf chemistry textbοοks sοld was (180-72) = 108.
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The following items were bought on sale.Complete the missing information in the table.Be sure to specify which answer box you are answering.Also show how you got to these numbers.
Answers
How did we go about computing the above missing figures from the given table?
1) In the first line item - the Sales Price, Percent Saved and Percent Paid are given.
To work out the Original Price, we can state that: if 20% off the value of x = 800 what is x, (where x is the Original Price)?
If 20% is taken off the value of x, we need to find the original value of x before the discount was applied. We can set up the following equation:
x - 20% of x = 800
Simplifying by factoring out x on the left side, we get:
x * (1 - 20%) = 800
Converting 20% to a decimal, we get:
x * (1 - 0.20) = 800
Simplifying, we get:
x * 0.80 = 800
Dividing both sides by 0.80, we get:
x = 1000
Therefore, the original value of x before the 20% discount was applied is $1000.
Since the Original price is $1000, and the Sales price is $800, that means the Amount of Discount ($) is:
Original Price - Sales Price
= $1,000 - $800
= $200
Thus, the discount value for the Television is $200and the original price is $1000.
2) With regard to the sneakers, Original Price was $80 and the percent saved is 25%.The percentage saved is 75%.
Thus, the Sales Price = Original Price - (Original Price * Percent Saved)
Sales Price = 80 - (80 * 25%)
Sales Price = 80 - 20
Sales Price = $60
Since $20 was removed form the Original Price, that means the Amount of Discount ($) is $20.
3)
For the Video Game, we know the Sales Price and the Percent Paid, which is 90%.
That means $54 = 90% of x, where x is the Original Price.
To find x,
54 = 0.9x
x = 54/0.9
x (Original Price) = $60
Thus, the Original Price of the Video Game is $60.
Since Original Price = $60; and
Sales Price = $54
Amount discounted = Original Price - Sales Price
Amount discounted = 60-54
Amount discounted = $6
As a percentage of the Original Price $6 is: 6/60 * 100
= 10%
4) For the MP3 player, we know that that the Sales Price = $51.60 which is 60% (Percent Paid) of the Original Price. We also know that the Percent saved is 40% of the Original price.
Thus, if $51.6 is 60% of the original price, we can use the following proportion to find the original price:
60% = $51.6 / original price
To solve for the original price, we can isolate it by multiplying both sides by the reciprocal of 60%, which is 100% / 60%, or 5 / 3:
original price = $51.6 / (60%)
original price = $51.6 / (0.60)
original price = $86
Therefore, the original price before the 60% reduction was $86.
Amount of Discount = Original Price - Sales Price
= 86 - 51.6
= $34.4
Thus, Original Price and Amount of Discount for the MP3 Player are $86.00 and $34.40 respectively.
5)
For the book, we know that the Amount of Discount is $2.60 which is 80% (Percent Paid) of the Original Price.
If $2.6 is 20% of the original price, we can use the following proportion to find the original price:
20% = $2.6 / original price
To solve for the original price, we can isolate it by multiplying both sides by the reciprocal of 20%, which is 100% / 20%, or 5:
original price = $2.6 / (20%)
original price = $2.6 / (0.20)
original price = $13
Therefore, the original price before the 20% reduction was $13.
Since Original price = $13 and Discount given is $2.60, Thus,
Sales Price = Original Price - Discount Given
Sales Price = 13- 2.60
Sales Price = $ 10.40
Note that the percentage saved (discount) =
2.6/13 * 100
= 20%
Thus, the Percentage Saved = 20%.
6)
For the Snack Bar, we know that the Sales Price is $1.70 and the Amount of Discount is $0.30. This means that the Original Price =
Sales Price + Discount Given = 1.7 + 0.3
Original Price = $2.00
To find what percent 0.3 is of 2, we can use the following proportion:
x/100 = 0.3/2
where x is the percent we want to find.
To solve for x, we can cross-multiply and simplify:
2x = 30
x = 15
Therefore, $0.3 is 15% of $2 which is the percent saved.
If the percent saved is 15%, then the percent paid is:
100 - 15
= 85%
Thus, the percent paid is 85% of the Original Price.
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When the litres are 16 how many litres are 3/4 of the tank capacity?
Answers
Answer:
16 litres = 100% of the tank capacity
x litres = 75% of the tank capacity (since 3/4 is equivalent to 75%)
To solve for x, we can cross-multiply and simplify:
16 * 75 = 100x
1200 = 100x
x = 12
Therefore, 3/4 of the tank capacity when the tank holds 16 litres is 12 litres.
Answer:
= 12 liters.
Step-by-step explanation:
16*3/4 =48/4.
= 12
(-3+4)2 distributive property and it needs to have work shown
Answers
Answer:
2
Step-by-step explanation:
PEMDAS
(-3+4)2
(1)2
2x1=2
A carpet is placed in the middle of a room 15m long and 12m broad so that it leaves a uniform width of 1m around it . find the area and the cost of the carpet at Rupee 500 square meter
Answers
Answer:
[tex]130m^{2}[/tex] , [tex]65.000 rs[/tex]
Step-by-step explanation:
Given Length = 15m
Given Breadth = 12m
Since there is a 1m gap between the sides,
Actual Length = 15 - 2 = 13m
Actual Breadth = 12 - 2 = 10m
From here find the Area:
L * B = AR of a cuboid , so
13 x 10 = [tex]130m^{2}[/tex] is the Area
for every [tex]m^{2}[/tex] it is 500 rupees, so for [tex]130m^{2}[/tex] ,
130 * 500 = 65,000 rupees.
(d) Find the value of k for which the vertex of the parabola y=x2+kx+9 lies on the line x=−3. (e) Find the value of k for which the vertex of the parabola y=kx2+3x+4 lies on the line x=3
Answers
(d) The value of k for which the vertex of the parabola y=x2+kx+9 lies on the line x=−3 is 6. (e) The value of k for which the vertex of the parabola y=kx2+3x+4 lies on the line x=3 is -2.
(d) k=6 (e) k=-2
The vertex form of a quadratic function is given as;
f(x) = a(x-h)² + kf(x) = a(x−h)²+k, with vertex (h, k)
∴ for the quadratic equation y=x²+kx+9, the vertex is given by;
x = -b/2a = -k/2 ∴ k = -2x, using x=-3k = -2x = 6,
thus the vertex of the parabola y=x²+6x+9 lies on line x = -3
(e) Similarly, for the quadratic equation y=kx²+3x+4, the vertex is given by;
x = -b/2a = -3/2k ∴ k = -2x/3, using x=3k = -2x/3 = -2(3)/3 = -2,
thus the vertex of the parabola y=-2x²+3x+4 lies on the line x = 3
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Hence , write down the equation with y as the subject ( in terms of x ). The value of m and q must be indicated
Answers
The equation with y as the subject is y = x^m / (4x^n - 2)
To solve for y as the subject of the equation, we need to isolate y on one side of the equation. Here's how we can do it,
First, we can rearrange the equation to get all the y terms on one side:
4x^n y - 2y = x^m
Next, we can factor out y from the left-hand side,
y(4x^n - 2) = x^m
Finally, we can divide both sides by (4x^n - 2) to isolate y,
y = x^m / (4x^n - 2)
Therefore, the equation with y as the subject is:
y = x^m / (4x^n - 2)
where m and n are the constants given in the original equation.
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The given question is incomplete, the complete question is:
Hence , write down the equation with y as the subject ( in terms of x ). The value of m and q must be indicated. equation 4x^ny -2y - x^m = 0, m and n are constant
Speed, Velocity, and Acceleration Escape Room.
Enter the correct 4 digit code (no spaces level 4
Answers
Based on the information in the image, we can infer that the correct four-digit code is: 4321
How to find the four-digit secret code?To find the four-digit secret code we must observe the image carefully, especially the intertwined lines. What we must do is follow the direction of the lines in the order from A to D to identify which number the line of each letter matches.
According to the above we can infer that the lines of each letter coincide in the following way with the numbers:
A-4B-3C-2D-1So according to the image, the four-digit secret code would be 4321.
Note: This question is incomplete. Here is the complete information:
Attached image
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5. Diego is building a fence for a rectangular garden. It needs to be at least 10 feet
wide and at least 8 feet long. The fencing he uses costs $3 per foot. His budget is
$120. He wrote some inequalities to represent the constraints in this situation:
1) f = 2x + 2y
2) x ≥ 10
3) y ≥ 8
4) 3f ≤ 120
a. Explain what each equation or inequality represents.
Answers
x ≥ 10: This inequality represents the minimum width of the garden, which is at least 10 feet.
y ≥ 8: This inequality represents the minimum length of the garden, which is at least 8 feet.
3f ≤ 120: This inequality represents the budget constraint for Diego. The cost of fencing, which is equal to the length of the fencing multiplied by the cost per foot, must be less than or equal to $120. Since the cost per foot is $3, the total cost of fencing is equal to 3f. Therefore, 3f must be less than or equal to $120.
The population in the United States between 1930 and 1975 had parameters B = 0. 00004 and c = 1. 9. Use this information to determine an explicit formula for this period
Answers
The explicit formula for the population in the United States between 1930 and 1975 is [tex]P(t) = 0.00004t^1.9 + 1[/tex], where t is the number of years after 1930.
To calculate the population for any year between 1930 and 1975, we can simply substitute the corresponding year for t in the equation. For example, if we want to calculate the population in 1950, we can substitute t = 1950 in the equation.
Therefore, [tex]P(1950) = 0.00004(1950)^1.9 + 1 = 0.0035 + 1 = 1.0035[/tex].
This is the population in 1950. In conclusion, the explicit formula for the population in the United States between 1930 and 1975 is [tex]P(t) = 0.00004t^1.9 + 1[/tex], where t is the number of years after 1930.
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The quantity y varies directly with the square of x and inversely with z. When x is 9 and z is 27, y is 6. What is the constant of variation?
2
9
18
54
Answers
y varies directly as x means
[tex]y=kx[/tex]
y varies inversely with z means
[tex]y=k\div z[/tex]
therefore
[tex]y=(kx^2)\div z[/tex]
k=constant of variation
[tex]6=(k9^2)\div 27[/tex]
[tex]6=(k81)\div27[/tex]
[tex]6=3k[/tex]
divide both sides by 3
[tex]2=k[/tex]
the constant of variation is 2
If the quantity y varies directly with the square of x and inversely with z, then we can write the following equation:
What is equation ?
A assertion that two mathematical expressions are equal is known as an equation. It typically consists of variables, constants, and mathematical operations, and it may also include functions, exponents, and other mathematical symbols. Equations are used to represent relationships between quantities in mathematics and to solve problems in various fields such as physics, engineering, and economics.
y = k * (x^2) / z
where k is the constant of variation.
We are given that when x is 9, z is 27, and y is 6. Substituting these values into the equation, we get:
6 = k * (9^2) / 27
Simplifying, we get:
6 = k * 3
k = 6 / 3
k = 2
Therefore, the constant of variation is 2.
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Question 1 (1 point ) If y varies directly as x and y=15 when x=12 find y when x=32 a 40 b ,5 c ,-5 d -40
Answers
a is correct
Question 1 (1 point )If y varies directly as x and y = 15 when x = 12, find y when x = 32. The value of y when x = 32 is 40.How to solve direct variation problems?A direct variation is a function that can be expressed in the form y = kx, where k is a nonzero constant. Two quantities x and y are said to be in direct variation if they satisfy this relationship. To solve direct variation problems, you can use the following formula: y = kx, where k is the constant of variation.The solution to the problem is given below:Given:y varies directly as xx = 12, y = 15To find:y when x = 32Formula:Since y varies directly as x, we have:y = kxLet's substitute x and y values in the above equation:15 = k × 1215/12 = kk = 5/4Thus, the equation of the direct variation is: y = (5/4) xTo find the value of y when x = 32, substitute 32 for x:y = (5/4) × 32y = 40Therefore, y = 40 when x = 32. Hence, the option (a) is correct.
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Please follow the directions
Answers
Based on the information in the table, the graph shows a diagonal going down from left to right.
How to graph on a cartesian plane?To graph in a Cartesian plane we must be clear that it is a tool to graph the coordinates. The first number of the coordinate corresponds to the x-axis (horizontal) and the second number corresponds to the y-coordinate (vertical). According to the above, we can infer the graph would look like this (image attached). This graph corresponds to a function because it is a constant, in this case it is a diagonal line that descends from left to right.
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A+B=25, A^2+B^2= 225 FIND AB
Answers
Answer:200
Step-by-step explanation:
A+B=25
A^2+B^2= 225
we use short multiplication formulas:
(A+B)^2=A^2+B^2+2AB
and solve the equation
25^2=225+2AB
625=225+2AB
625-225=2AB
400=2AB
AB=200
Find the slope of the line that passes through the points (−6,5) and (2,5).
Answers
m= y2-y1/x2-x1
m= 5-5/2+6= 0
Answer: The slope is equal to zero
Step-by-step explanation:
Find the slope of (-6,5) and (2,5)
First subtract the x coordinates 2 and -6
which equals 8
Next subtract the y coordinates 5 and 5
which equals o
Then you get 8/0 and when you simplify you get 0, so the slope is zero.
Drag each tile to the correct box. Arrange the functions in decreasing order of their periods. Y=-3cos(x+2pi) y=2/3cot(pi/4)+6 y=1/2tan(5pi/6 + pi)
y=5csc(3x)+6 y=-10sin(pi/5 - 2pi)
Answers
Step-by-step explanation:
The correct order of the functions in decreasing order of their periods is:
y = -10sin(pi/5 - 2pi)
y = 2/3cot(pi/4)+6
y = 5csc(3x)+6
y = 1/2tan(5pi/6 + pi)
y = -3cos(x+2pi)
Note: The periods of trigonometric functions are determined by the coefficient of the independent variable (x in this case). The period of y = asin(bx + c) or y = acos(bx + c) is 2pi/b, and the period of y = atan(bx + c) or y = acot(bx + c) is pi/b. The period of y = acsc(bx + c) or y = asec(bx + c) is 2pi/|b|.
if you can help, please do
Answers
The equation that represents the variation is given by F = 42m/p
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.
F varies directly as m and inversely with p, hence:
F ∝ m/p
Let k represent the constant of proportion. Therefore:
F= k*m/p
F = 36 when m = 6 and p = 7. Hence:
36 = k*6 / 7
k = 36 * 7 / 6
k = 42
The equation is F = 42m/p
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Reggie ran for 180 yards during the last football game, which is 40 more yards than his previous personal best. Monte ran 50 more yards than Adrian during the same game. If Monte ran the same amount of yards Reggie ran in one game for his previous personal best, how many yards did Adrian run? Define your variables
Answers
We want to find the number of yards Adrian ran during the last game, which is represented by the variable a. Adrian ran 90 yards during the last football game.
Let's define the variables we will use in this problem:
r: the number of yards Reggie ran during his previous personal best.
m: the number of yards Monte ran during the last game.
a: the number of yards Adrian ran during the last game.
From the problem statement, we know that:
Reggie ran for 180 yards during the last game, which is 40 more yards than his previous personal best: r + 40 = 180.
Monte ran 50 more yards than Adrian during the same game: m = a + 50.
Monte ran the same amount of yards Reggie ran in one game for his previous personal best: m = r.
We want to find the number of yards Adrian ran during the last game, which is represented by the variable a. To solve for a, we need to use the information we have to create an equation that relates a to the other variables.
From the equation r + 40 = 180, we can solve for r by subtracting 40 from both sides: r = 180 - 40 = 140.
Substituting m = r into the equation m = a + 50, we get: r = a + 50.
Now we can substitute the value of r we found earlier into this equation: 140 = a + 50.
Solving for a, we subtract 50 from both sides: a = 90.
Therefore, Adrian ran 90 yards during the last football game.
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i was wondering if someone could help me with this problem I would appreciate it greatly
Answers
The median increases by 0.5 and the mean decreases by 4.375
What are median and mean?
Median and mean are measures of central tendency that are commonly used in statistics. The median is the middle value in a sorted list of numbers. To find the median, you need to arrange the numbers in order from lowest to highest (or highest to lowest) and then find the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers. The mean is the average of all the numbers in a list. To find the mean, you need to add up all the numbers in the list and then divide by the total number of values. It is calculated by summing up all the values and dividing the result by the total number of values. The mean is influenced by outliers and extreme values in the data.
(a) The median is the middle value in a sorted list of numbers. In the original list, the median is 547. If the number 605 is changed to 549, then the new list becomes:
381, 465, 496, 537, 547, 589, 604, 549
Now the median is the average of the two middle values, which are 547 and 549. Therefore, the median increases by:
(549 + 547)/2 - 547 = 0.5
So, the median increases by 0.5.
(b) The mean is the average of all the numbers in a list. In the original list, the mean is:
(381 + 465 + 496 + 537 + 547 + 589 + 604 + 605) / 8 = 527.5
If the number 605 is changed to 549, then the new list becomes:
381, 465, 496, 537, 547, 589, 604, 549
The mean of this new list is:
(381 + 465 + 496 + 537 + 547 + 589 + 604 + 549) / 8 = 523.125
Therefore, the mean decreases by:
527.5 - 523.125 = 4.375
So, the mean decreases by 4.375
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How to write the correct solution of 5a^2-25b^×
Answers
The correct solution of the expression 5a² -25bˣ is 5(a² - 5bˣ)
How to determine the correct solution of the expressionFrom the question, we have the following parameters that can be used in our computation:
5a² -25bˣ
The expression is already in its simplest form in terms of combining like terms.
However, we can still look into factoring the expression
To do this, we can factor out the greatest common factor of 5 and rewrite the expression as follows:
5a² -25bˣ = 5(a² - 5bˣ)
This is the factored form of the expression, where the greatest common factor of 5 has been factored out.
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Find the volume of the sphere. Either answer in terms of π or use 3.14 for π and round your final answer to the nearest hundredth.
Answers
Answer:
V = (4/3)π(4^3) = 256π/3 cubic units
Here is a diagram of a person standing next to a lorry.
The diagram shows two centimetre rulers.
The person and the lorry are drawn to the same scale.
The lorry is approximately 11.2 m in length.
Using the scale diagram, estimate the height of the person in metres.
Answers
By using the scale diagram, the height of this person in meters is equal to 1.6 meter.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)
Based on the information provided about the lorry, the lorry is approximately 11.2 m in length and 14 cm on a scale diagram. Therefore, the height of the person in meters can be calculated as follows;
1 centimeter = 11.2/14
1 centimeter = 0.8 meter.
Height of the person in meters = 0.8 meter × 2
Height of the person in meters = 1.6 meter.
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Please help me on this
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The criteria that we could use to prove the congruency that ΔABC ≅ ΔDEC is;
Vertical Angles are Congruent. We could then use AAS to prove that ΔABC ≅ ΔDEC
How to find the Triangle Congruence Postulate?There are different triangle congruency postulates namely:
SSS: Side Side Side Congruency Postulate
SAS: Side Angle Side Congruency Postulate
ASA: Angle Side Angle Congruency Postulate
AAS: Angle Angle Side Congruency Postulate
HL: Hypotenuse Leg Congruency Postulate
We want to prove that ΔABC ≅ ΔDEC
Now, from the given image, we see that we are given 2 congruent sides.
However, angle ECD is congruent to angle DCA because they are vertically opposite angles and vertical angles are congruent.
Thus, the triangles are congruent by AAS Congruency postulate.
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The range of values of x for which the inequality 0 less than or equal to x less than 6
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The range of values of x that satisfy the inequality 0 ≤ x < 6 is the set of all real numbers between 0 (inclusive) and 6 (exclusive), i.e., the interval [0, 6).
The inequality 0 ≤ x < 6 can be interpreted as follows: x can take on any value between 0 and 6, including 0 but not including 6. This means that x can be any number greater than or equal to 0 and less than 6. In other words, the range of values for x that satisfy this inequality is the set of all real numbers in the interval [0, 6), where the square bracket indicates that 0 is included in the interval (i.e., 0 is a valid value of x) and the round bracket indicates that 6 is excluded from the interval (i.e., 6 is not a valid value of x). This interval can be visualized as a number line with a closed circle at 0 and an open circle at 6, indicating that 0 is included in the range of values for x but 6 is not.
Therefore, any value of x between 0 and 6 (excluding 6) satisfies the inequality 0 ≤ x < 6.
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Monthly salary Is $2332. It is given an Increase of 6. 9%. After the first increase, It rece/ves a second increase of 15%. What Is the
new monthly salary after both increases? Round to the nearest dollar.
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The new monthly salary after two increases of 6.9% and 15% is 2867.
The new monthly salary after two increases is calculated as follows:
First Increase:
The initial salary of 2332 increases by 6.9%. This is calculated by multiplying the salary by the percentage increase, i.e. 2332 x 0.069 = 160.68. The new salary after the first increase is 2332 + 160.68 = 2492.68.
Second Increase:
The salary after the first increase of 2492.68 is further increased by 15%. This is calculated by multiplying the salary by the percentage increase, i.e. 2492.68 x 0.15 = 373.90. The new salary after both increases is 2492.68 + 373.90 = 2866.58.
Rounded to the nearest dollar, the new monthly salary after both increases is 2867.
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