The area of trapezium QUVR is A cm² Show that A = 2x² + 20x
Answers
we have shown that the area of the trapezium QUVR is A = 2x² + 20x.
To find the area of the trapezium QUVR, we need to use the formula:
A = ((a + b) / 2) × h
where a and b are the lengths of the parallel sides of the trapezium, and h is the perpendicular height between them.
Looking at the trapezium QUVR, we can see that the parallel sides are QR and UV, which have lengths (x + 4) and (x + 2) respectively. The perpendicular height, h, is given by the length of the line segment SV.
To find SV, we need to first find the length of RU. We can do this by using the Pythagorean theorem:
RU² = RV² - UV²
(RU + x)² = RQ² - QR²
(RU + x)² = (x + 6)² - (x + 4)²
(RU + x)² = x² + 12x + 36 - (x² + 8x + 16)
(RU + x)² = 4x + 20
RU + x = sqrt(4x + 20)
RU = sqrt(4x + 20) - x
Now, we can find SV by using the Pythagorean theorem again:
SV² = RU² - RV²
SV² = (sqrt(4x + 20) - x)² - 4²
SV² = 4x + 4
SV = sqrt(4x + 4)
Finally, we can substitute the values we have found into the formula for the area of the trapezium:
A = ((x + 4) + (x + 2)) / 2 × sqrt(4x + 4)
A = (2x + 6) / 2 × sqrt(4x + 4)
A = (x + 3) × sqrt(4x + 4)
We can simplify this further by using the identity (a + b)² = a² + 2ab + b²:
A = (x + 3) × sqrt(4(x + 1))
A = (x + 3) × 2sqrt(x + 1)
A = 2(x + 1)(x + 3)
Expanding the brackets gives:
A = 2(x² + 4x + 3x + 12)
A = 2
A = 2(x² + 7x + 12)
Simplifying further, we have:
A = 2(x² + 6x + x + 12)
A = 2((x + 6)(x + 2))
Expanding the brackets again gives:
A = 2(x² + 8x + 12)
And finally, we can write this in the desired form:
A = 2x² + 16x + 24
Simplifying further, we get:
A = 2(x² + 8x + 12)
A = 2(x + 6)(x + 2)
Therefore, we have shown that the area of the trapezium QUVR is A = 2x² + 20x.
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Related Questions
Did you sleep with a comfort object as a child? Do you still? No need to stuff that teddy bear from your infant years in your closet the next time you have a guest over—the odds are good that he or she has a comfort object, too. A study conducted by Sleepopolis and OnePoll reported that 34% of adults still sleep with a stuffed animal, blanket, or other sentimental object, according to a survey of a random sample of 100 adults. A similar study, based on a random sample of 80 children reports that 75% of children sleep with a comfort object.
Do these data provide convincing evidence that the proportion of adults who sleep with a comfort object is less than the proportion of children who sleep with a comfort object? Justify your answer.
Answers
Answer:
55
Step-by-step explanation:
The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price. Some of the expressions shown below represent the sale price, in dollars, of the item.
Expression A: 0.2p
Expression B: 0.8p
Expression C: 1 - 0.2p
Expression D: p - 0.2p
Expression E: p - 0.8p
Which two expressions each represent the sale price of the item?
Answers
The expressions of the sale price is as follows:
Expression B: 0.8p
Expression D: p - 0.2p
How to find the expression that represent the sale price of the items?The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price.
Therefore, the expression that represent the sale price in dollars of the items can be calculated as follows:
original price = p
Therefore, let's find the percent off the price.
price off = 20% of p
price off = 20 / 100 p
price off = 0.2p
Therefore,
sale price = p - 0.2p
sale price = 0.8p
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Divide 30 into five parts such that first nad last part are in the ratio 2:3
Answers
To divide 30 into five parts such that the first and last parts are in the ratio of 2:3, we can follow these steps:
1. Determine the ratio between the first and last parts. In this case, it is 2:3.
2. Add the ratio values together to find the total number of parts: 2 + 3 = 5.
3. Divide the total value (30) by the total number of parts (5) to find the value of each part: 30 / 5 = 6.
4. Multiply the value of each part by the respective ratio values to obtain the individual parts:
- First part: 2 * 6 = 12
- Second part: 6
- Third part: 6
- Fourth part: 6
- Last part: 3 * 6 = 18
Therefore, the five parts of 30, with the first and last parts in the ratio of 2:3, are 12, 6, 6, 6, and 18.
-5(2x - 1) + 3x
How do I simplify this?
Answers
Answer:
-7x + 5
General Formulas and Concepts:
Distributive Property
Combining Like Terms
Step-by-step explanation:
Step 1: Write expression
-5(2x - 1) + 3x
Step 2: Simplify
Distribute -5: -10x + 5 + 3xCombine like terms: -7x + 5A single filer had a taxable income of $90,725. Base on table, what is is the tax?
Answers
The amount that the taxpayer is owing in taxes is $2,691.05.
We have,
Income tax payable refers to a business organization's tax liability to the government in the jurisdiction in which it operates. The amount of liability will be determined by the company's profitability over a given time period and the applicable tax rates. Tax payable is considered a current liability rather than a long-term liability because it must be settled within the next 12 months.
Based on the table, we are using the tax rate of 15% for the taxable income of $11,757.
The tax payable will equals to:
= 15%*$11,757 + $927.50
= $1,763.55 + $927.50
= $2,691.05
Hence, The amount that the taxpayer is owing in taxes is $2,691.05.
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complete question:
Based on this table, if someone had a taxable income of $11,757, how much would they owe in taxes?
How many times does 10,000 go into 700,000?
Answers
Answer:
i think its 700 hope it help
Step-by-step explanation:
the answer would be
70 times
Find the domain of the function
Answers
Answer:
Here you go :)
Step-by-step explanation:
solve the system of equations
y-5=x
x=-2-y y = ( , )
Answers
Answer:
y=1.5
x=-3.5
Our answer is (-3.5,1.5)
Step-by-step explanation:
y-5=x
x=-2-y
y=?
--------
Using substitution,
y-5=-2-y
Solve:
2y-5=-2
2y=3
y=1.5
We can enter 1.5 into the equation:
1.5-5=x
-3.5=x
Can someone explain how to do this? I’m sort of lost.
Answers
Answer:
12.37 inched for 75 degree turn
Step-by-step explanation:
the circumference of the pulley is 9.35 x 2 x 3.14 = 58.718 inches.
That's 58.718 inches for 360 degrees.
58.718/360 = 0.1631 inched per degree
0.1631 x 75° 50' = 12.37 inches for 75° 50' degree turn
What's 1 trillion to the 10th power
Answers
The result of the number 1 trillion to the 10th power as required to be determined is; 10¹²⁰.
What is the result of 1 trillion to the 10th power?The result of the number 1 trillion to the 10th power is as follows;
Recall; 1 trillion = 1,000,000,000,000 = 10¹²
Hence; 1 trillion to the 10th power is; ( 10¹² )¹⁰.
From the laws of indices; we therefore have that;
= 10¹²⁰
Ultimately, the result is; 10¹²⁰.
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1
Select the correct answer.
Which graph shows a quadratic equation with complex roots?
Answers
Answer:
C (the bottom one)
Step-by-step explanation:
B (the top one) has roots/solutions — as in, it crosses the x-axis.
C doesn't have roots, and therefore doesn't have normal solutions, instead it has "complex" roots which require the use of imaginary numbers: \(i\)
Which graph represents the function f(x)=(1/3)^x-3
Answers
The graph that represents the function f(x)=(1/3)ˣ⁻³ is an exponential graph.
What is Graph?Graph is a data structure which consists of nodes (also called vertices) and edges which connect them. It is a non-linear data structure, which can store data in a hierarchical fashion. The nodes represent values or objects and the edges represent the relationships between these objects. Graphs are used to store complex data and can be used to represent real-world situations such as social networks, road networks, etc. Graphs are also used in computer science to represent algorithms, search problems, and data structures.
Exponential graphs typically have the shape of a curve, with the vertical y-axis representing the values of the function, and the horizontal x-axis representing the inputs. In this particular graph, as the x-value increases, the y-value decreases exponentially. This can be seen by the steepness of the curve as it approaches the x-axis. This graph can also be represented by a line graph, with each point on the graph indicating the output of the function for a given input. The point (0, -3) is the point of intersection between the line and the x-axis, indicating the starting point for the graph. As the x-value increases, the y-value decreases, creating the exponential curve.
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the line with a slope of 9/7 & containing a midpoint of the segment whose end points are (2, -3) & (-6, 5)
Answers
1. Find the midpoint of the segment using the midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)
Midpoint = (-4 / 2, 2 / 2)
Midpoint = (-2, 1)
2. Use the midpoint and the slope to find the equation of the line in point-slope form. The point-slope form is given by:
y - y1 = m(x - x1), where (x1, y1) is the midpoint and m is the slope.
Substituting the values:
y - 1 = (9/7)(x - (-2))
y - 1 = (9/7)(x + 2)
y - 1 = (9/7)x + (18/7)
3. Simplify the equation to obtain the slope-intercept form:
y = (9/7)x + (18/7) + 1
y = (9/7)x + (18/7) + (7/7)
y = (9/7)x + (25/7)
So, the equation of the line with a slope of 9/7 and containing the midpoint of the segment with endpoints (2, -3) and (-6, 5) is y = (9/7)x + (25/7).
Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:
y = (9/7)x + 25/7.
Step-by-step explanation:Step 1: Find the midpoint of the line segment.
The midpoint formula is given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:
Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)
Midpoint = (-4 / 2, 2 / 2)
Midpoint = (-2, 1)
So, the midpoint of the line segment is (-2, 1).
Step 2: Write the equation of the line using the slope-intercept form.
The slope-intercept form of a line is given by:
y = mx + b
where m is the slope and b is the y-intercept.
Given the slope as 9/7, we have:
y = (9/7)x + b
Step 3: Substitute the coordinates of the midpoint to find the value of b.
Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:
1 = (9/7)(-2) + b
1 = -18/7 + b
To find the value of b, we can solve this equation:
1 + 18/7 = b
25/7 = b
Step 4: Write the final equation of the line.
Using the value of b, the equation becomes:
y = (9/7)x + 25/7
QUESTION 8
In the linear equation y = 2x - 8, the slope of the line is
-2.
-8
2
8
Answers
Answer:
2
Step-by-step explanation:
give brainliest
If you don't mind, could you please give me a brainliest thanks :]
Least to greatest 8% 1/25 0.05 and 0.4
Answers
Answer:
1/25,0.05,8%,0.4
Step-by-step explanation:
1/25=4%
0.05=5%
8%=8%
0.4=40%
using d=rt , where d=distance r=rate and t=time how fast is a jogger moving if she travels 5.7 miles in 1.3 hours? to the nearest tenth
Answers
Answer:
\(r=4.38\)
Step-by-step explanation:
Step 1: Arrange the equation so that you are calculating rate (divide both sides by t)
\(\frac{d}{t} = \frac{rt}{t}\)
\(t\) cancels out on the right side.
Step 2: Substitute in the numerals
\(r=\frac{d}{t}\)
\(r=\frac{5.7}{1.3}\)
Step 3: Divide
\(r=4.38\) \(mph\)
There's your answer!
Hope this helps you!
10 POINTS!!!! If the answer is correct…
Answers
Answer:
4, 6, 63, 10
Step-by-step explanation:
gets mutiplied by 7
Answer:
4, 6, 63, 10
Step-by-step explanation:
4: 4X7=28
6: 6X7= 42
63: 7X9=63
10: 10x7=70
Your welcome :)
Sally rents a life jacket for a one-time fee of $5. She then rents a canoe for $15 per hour. Which expression represents the
total cost, in dollars, to rent the life jacket and the canoe for h hours?
A 5+15h
B 10
15 + 5
20h
Answers
Explanation: You add the money then multiply it by the hours. B wouldn't make any sense, A would only be multiplying th hours by $15 but the life jacket needs to as well, and 15+5 isn't multiplying the hours so the only logical answer would be 20h.
Find the value of (f o g)' at the given value.
Answers
To find the value of (f o g)' at a given value, you first need to understand the concept of composite functions and the chain rule of differentiation. Let's break it down step by step.
To find the value of (f o g)' at a given value, you need to evaluate g(x) and f(x), find their derivatives, and use the chain rule to find the derivative of (f o g) at the given value. It is important to understand the concepts of composite functions and the chain rule to be able to solve problems involving these concepts.
What are composite functions? Composite functions are functions that are formed by composing two or more functions. The notation used to denote composite functions is (f o g)(x), which means that the output of function g is used as the input for function f. In other words, we first evaluate g(x), and then use the result as the input for f(x).
What is the chain rule of differentiation? The chain rule of differentiation is a method used to find the derivative of composite functions. It states that if a function is composed of two or more functions, then its derivative can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.
To find the value of (f o g)' at a given value, we need to follow these steps:1. Find g(x) and f(x)2. Find g'(x) and f'(x)3. Evaluate g(x) at the given value4. Use the chain rule to find (f o g)' at the given value
step 1: Find g(x) and f(x)Let's say that we have two functions: g(x) = x^2 + 3x + 1 and f(x) = sqrt(x). To find (f o g)(x), we first need to evaluate g(x) and then use the result as the input for f(x). Therefore, (f o g)(x) = f(g(x)) = sqrt(x^2 + 3x + 1)
Step 2: Find g'(x) and f'(x)To find g'(x), we need to take the derivative of g(x) using the power rule and the sum rule. Therefore, g'(x) = 2x + 3To find f'(x), we need to take the derivative of f(x) using the power rule and the chain rule. Therefore, f'(x) = 1/2(x)^(-1/2)
Step 3: Evaluate g(x) at the given valueSuppose we want to find (f o g)' at x = 2. To do this, we need to first evaluate g(x) at x = 2. Therefore, g(2) = 2^2 + 3(2) + 1 = 11
Step 4: Use the chain rule to find (f o g)' at the given value now we can use the chain rule to find (f o g)' at x = 2. Therefore, (f o g)'(2) = f'(g(2)) * g'(2) = 1/2(11)^(-1/2) * (2)(3) = 3/sqrt(11)
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Four friends go to the movies. How many different ways can they sit in a row?
Answers
Answer:
120 ways
..................
Answer:
24
Step-by-step explanation:
4 friends
1st seat: 4 different people could sit here
Now there are 3 friends left
2nd seat: 3 different people could sit here
Now there are 2 friends left
3rd seat: 2 different people could sit here
Now there are 1 friends left
4th seat: 1 different people could sit here
4*3*2*1
24 ways
A tree diagram is simply a way of representing a sequence of events. True or False.
Answers
Answer:
True.
Step-by-step explanation:
A tree diagram is a diagram used in general mathematics, statistics, and probability to show a sequence of events. This tool is used to calculate the number of possibilities of an event to occur. Commonly, the tool of a tree diagram is used to find the possibility of outcome while flipping a coin. It is a diagram in which connections between the events is shown using the strucure of branching connecting lines.
So, the given statement is true, that is a simple way of showing events in a sequence.
what is the property of 3x(5x7)=(3x5)7
Answers
The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.
In the equation you provided: 3x(5x7) = (3x5)7
The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.
The given figure is a right triangular prism.
In the prism:
• DF = 22 in.
• EG = 11 in.
• Volume of the prism = 1936 cubic in.
What is the length of AD?'
Use the given information to complete the worksheet.
Thank you!
Answers
The length of side AD is,
⇒ AD = 16
We have to given that;
The given figure is a right triangular prism.
In the prism:
• DF = 22 in.
• EG = 11 in.
• Volume of the prism = 1936 cubic in.
Since, Volume of right triangular prism is,
V = 1/2 (bh) x L
Substitute all the values we get;
V = 1/2 (22 × 11) × AD
1936 = 121 × AD
AD = 16
Thus, The length of side AD is, 16
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If you could please help me with this it makes no sence to me.
Answers
Answer:
A = 7986 m²
Step-by-step explanation:
the field is in the form of a trapezium.
the area (A) of a trapezium is calculated as
A = \(\frac{1}{2}\) h (b₁ + b₂ )
where h is the perpendicular distance between the bases b₁ and b₂
here h = 66 , b₁ = 102, b₂ = 140 , then
A = \(\frac{1}{2}\) × 66 × (102 + 140) = 33 × 242 = 7986 m²
Answer:
7986 m²
Step-by-step explanation:
The field geometric shape is a trapezoid whose bases are 102 m and 140 m and height of 66m
The equation for the area of a trapezoid is given by
\(A = \dfrac{a + b}{2} h\\\\\)
where a and b are the two sides and h is the height
Here a = 102, b = 140 and h = 66
Substitute these values directly into the equation for area
\(A = \dfrac{102 + 140}{2} \times 66\\\\A = (102 + 140) \times \dfrac{66}{2}\\\\\\102 + 140 = 242\\\\\dfrac{66}{2} = 33\\\\\\A = 242\ \times 33 = 7986\; m^2\)
Jackie used a photocopier to reduce an image that was 4 inches wide and 6 inches long. If the reduced image was 4 inches long, how wide was the reduced image
Answers
The width of the image which was photocopied by Jackie and has an initial length of 6 inches and width of 4 inches is 6 inches.
What is Area?An area is a unit of measurement used to describe the size of a region on a planar or curved surface. While a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.
Given:
The initial length of the image, l = 6 inches,
The initial width of the image, w = 4 inches,
The reduced length of the image, L = 4 inches,
The area of the initial image = The area of the reduced image,
l × w = L × W
Here W is the reduced width.
Substitute the values,
6 × 4 = 4 × W
W = 6 inches,
Therefore, the width of the image which was photocopied by Jackie and has an initial length of 6 inches and width of 4 inches is 6 inches.
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The tables of ordered pairs represent some points on the graphs of two lines. What is the solution to the system of equations represented by the two lines? There are no zeroes on the chart. What do I do
Answers
To find the solution to the system of equations represented by the two lines based on the given tables of ordered pairs, you can follow these steps:
Examine the tables and identify a pattern or relationship between the x-values and y-values for each line.Determine the slope (rate of change) of each line by calculating the difference in y-values divided by the difference in x-values for any two points on the line.Once you have the slopes, compare them to see if they are equal or different.If the slopes are different, the lines intersect at a single point, which represents the solution to the system of equations.If the slopes are equal, the lines are parallel, and there is no solution to the system of equations.If the slopes are different, you can find the intersection point by solving the system of equations using either substitution, elimination, or another suitable method.For such more question on equations
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CAYMAN Sleep Couch PRICE Was R2-699 (including VAT) PRICE Now R1 999 (excluding VA Use information above to answer the questions that follow. 2.1 Show that the couch's original price excluding VAT was R2 346.96. 2.2 Show with calculation that a customer is expected to pay R2 299 incl nouding VAT when purchasing the couch at SALE price.
Answers
Given: cost of CAYMAN sleep couch with VAT is R2 699
cost without VAT is R1 999
What are the answers for 2.1 and 2.2 questions?2.1 To calculate the original price of the couch excluding VAT, we can use the following formula:
Price including VAT / 1 + (VAT rate / 100) = Price excluding VAT
In this case, the VAT rate is 15% (since it is included in the original price), so the formula is:
R2,699 / 1 + (15 / 100) = R2,346.96
2.2 To calculate the expected price of the couch including VAT at the sale price, we can use the following formula:
Price excluding VAT * (1 + (VAT rate / 100)) = Price including VAT
In this case, the VAT rate is still 15% and the sale price is R1,999 (excluding VAT), so the formula is:
R1,999 * (1 + (15 / 100)) = R2,299
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PLEASE HELP WILL MARK BRAINLIEST!!!!!!!!
Answers
Answer:
2-3
Step-by-step explanation:
The sum of two line segments of distance 3.
the result are 2-3 or 3+3
so the answer is 2-3
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The graph represents a relation where x represents the independent variable and y represents the dependent variable.
A coordinate plane with points at negative 4 comma 4, negative 2 comma 0, 0 comma negative 3, 3 comma 1, and 5 comma negative 2.
What is the domain of the relation?
{−4, −3, −2, 0, 1, 3, 4, 5}
{−4, −2, 0, 3, 5}
{−3, −2, 0, 1, 4}
{0, 3, 4, 5}
Answers
The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.
How to determine domain relation?The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.
Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.
Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.
Hence, the correct option is {−4, −2, 0, 3, 5}.
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Using pi 3 what is the answer
Answers
Answer:
12mm
Step-by-step explanation:
circumference (distance around) is equal to πd.
here, if π is 3, we do 3 x the diameter, which is 4. 3 x 4 = 12mm