The answers of the shapes are: (10) 12cm²² and 12cm² (11) 15m² and 308m² (4) 308cm² (9) 896m² and 516m²
What is a triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry
The area of a triangle is given as
10. Area = 1/2 bh
Area of triangle A is 1/2 * 4*6 = 24/2
Area = 12cm²
If triangle a and b are similar
There areas are similar too
This implies that
Area of A = Area of B
1/2 * 5 * 2+x = 12
This implies that 2 + x = 12
Making x the subject,
x = 12-2 = 10cm²
11) Area of the shaded portion of the triangle on the right hand side
A= 1/2bh
A= 1/2*6*5
=1/2*30 = 15m²
Area of triangle at the left hand side is A= 1/2*5*2 = 5m²
Area of the rectangle is l*w
A= 9*5 = 45m²
The unshaded portion is = 45 - (15+5) = 45-20
Area = 25m²
4) Area of parallelogram = bh
A= = 22*14 = 308cm²
9)i. Area of triangle at right hand side
A = 1/2bh
Area = 1/2*28*28 = 784/2
Area = 392m² = Area of triangle at left too
Area of rectangle = l*w
Area = 60*28 = 1680m²
shaded portion = 1680-(2*392)
area = 1680-784 = 896m²
ii Area of rectangle = l*w
area = 22*38 = 836m²
area of parallelograms = (8*16) + (16*12)
Area of shaded portion = 836 - 320 = 516m²
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Emma bought a pair of earrings, a dress and a coat. The dress cost 6 times as much as the earrings, and the coat cost 13 times as much as the earrings. If the three items cost a total of $3200, how much did each of them cost?
Answer:cost of earring=$160
cost of dress= $960
cost of coat =$2,080
Step-by-step explanation:
Let cost of earring be represented as x
so that the cost of dress =6x
And the cost of coat =13x
Since the three items cost a total of $3200, we can develop an equation which can be represented as
cost of earring+cost of dress +cost of coat =3200
x +6x+13x=3200
20x =3200
x=3200/20=160
THerefore cost of earring=$160
cost of dress= 6x =$160 x 6=$960
cost of coat = 13x = $160 x 13=$2,080
Nonstop trains leave Toronto and Montreal at the same time each day going to the other city along the main line. One train travels at 120 km/h and the other at 90 km/h. Assuming the track is straight, how far apart are they one hour before they meet?
pls help ( ˘︹˘ )
Assuming the track is straight, the distance at which they are apart one hour before they meet is; 30 km
How to find the distance from speed and time?We are told that a Nonstop trains leave Toronto and Montreal at the same time each day going to the other city along the main line.
Speed of Train 1 = 120 km/h
Speed of Train 2 = 90 km/h
Time spent by train 1 = 1 hour
Time spent train 2 = 1 hour
Formula for distance is;
Distance = Speed * time
If they leave the same time each day, it means that;
Distance of train 1 = 120 * 1 = 120 km
Distance of train 2 = 90 * 1 = 90 km
Thus, distance at which they will be apart before meeting each other is;
Distance apart = 120 - 90
Distance apart = 30 km
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if the sum of the measures of the interior angles of a polygon is 1980°, how many sides does the polygon have?
Answer:
The polygon has 13 sides.
Step-by-step explanation:
The sum of the interior angles of a polygon is (n - 2) * 180, where n is the number of sides. This formula can be set equal to the sum of the interior angles to determine how many sides it has.
(n - 2) * 180 = 1980
180n - 360 = 1980
180n = 2340
n = 13
Help 30 POINTS, Please reply to the following prompt. Provide a well-thought out answer using complete sentences. Click in the box to begin typing your answer.
Prompt: Explain how you would find the area of the figure below
Note that the above is a complex 2 dimensional geometrical shape. To begin solving this you must deconstruct it into more regular shapes as shown in the attached.
How is this so?In the simplified version, it is clear that the complex shape is made up of
Two rectanglesTwo TrianglesOne semi-circle.In a case where the dimensions were given, we could solve for the area of the individual parts then sum all the areas up to get the Total Area of the complex shape.
Recall that the Area of a Rectangle is given by:
L x W
Where L = Length
W = Width
Triangle:
(b x h) /2
Where
B = Base
H = Height
Semi circle
1/2(πr2 )
Where
r = radius
π = 3.14
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6th grade math !!!!!!!!!!!!!!
Answer: It's the second option
Step-by-step explanation:
0x1.5=0
1x1.5=1.5
2x1.5=3
3x1.5=4.5
4x1.5=6
It's simple math
Hope this helped
Help someone that’s good at math need your help 15 points !
Answer:
4x-4+3
Step-by-step explanation:
Answer:
-4+4x=3
Step-by-step explanation:
So the first step is to derive an equation from the model.
There are 4 positive x and 4 negative 1 which equal 3 positive 1 which should look like:
4x-4=3
which could be rewritten as:
-4+4x=3
Combine like terms: m + 11g - 7g + 7m
Answer:
4g+8m
Step-by-step explanation:
7m+m=8m 11g-7g=4g
Three brothers share a 5 gigabyte (gb) family data plan on their cell phones. One month. Aaron used. 2.3gb, Brian
used 1.1gb, and Caleb used 1.6gb. If the total bill for the
month $110, how should they split up the bill so they pay the
same fraction of the bill as the data they used?
Step-by-step explanation:
\( \frac{5gb}{110} = \frac{2.3gb}{x} \)
→ x = 2.3 ×110÷5 = 50.6 $ Aaron pay
→Brian = 1.1 × 110 ÷5=24.2$
Caleb = 110 - ( 24.2 + 50.6 ) = 110 -74.8 = 35.2$
Aaron should pay $50.60, Brian should pay $24.20, and Caleb should pay $35.20 to split the bill in proportion to the data they used.
How to determine the way to split up the billTo split the bill among the three brothers in proportion to the data they used, we need to calculate the fraction of the total data used by each brother and allocate the bill accordingly.
The total data used by the three brothers is 2.3gb + 1.1gb + 1.6gb = 5gb.
Now, let's calculate the fraction of the bill that each brother should pay based on their data usage:
Aaron's fraction = 2.3gb / 5gb = 0.46
Brian's fraction = 1.1gb / 5gb = 0.22
Caleb's fraction = 1.6gb / 5gb = 0.32
The sum of these fractions should equal 1, representing the entire bill.
To allocate the bill, we multiply each brother's fraction by the total bill amount:
Aaron's payment = 0.46 * $110 = $50.60
Brian's payment = 0.22 * $110 = $24.20
Caleb's payment = 0.32 * $110 = $35.20
Therefore, Aaron should pay $50.60, Brian should pay $24.20, and Caleb should pay $35.20 to split the bill in proportion to the data they used.
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PLEAAAAAASEEEE HELPPPP ASAAPPPP 95 POINTS JUST FOR THIS
use the following arithmetic sequence and the formula an=a1+(n-1)d to answer the questions below 123,116,1099,102,95.
part 1. find the value of each of the following
part 2/ find the explicit formula, show work. part 3.
part 3. use the explicit formula you found from part 2 to find the value of the 100th term in the sequence show your work!
Answer:
see below
Step-by-step explanation:
123,116,109,102,95.
First find the common difference
d = 116 - 123 = -7
We are subtracting 7 each time
Using the formula
a1 = 123
d=-7
an = 123+ (n-1)(-7)
We need to find the 100th term
Let n = 100
a100 = 123 +(100-1) (-7)
= 123+(99)(-7)
= 123-693
= -570
Three tennis balls are stored in a cylindrical container with a height of 8.2 inches and a radius of 1.32 inches. The circumference of a tennis ball is 8 inches. Find the amount of space within the cylinder not taken up by the tennis balls. Round your answer to the nearest hundredth.
The amount of space within the cylinder not taken up by the tennis balls is 18.9 \(inches^3\)
The volume of a tennis ball:
The circumference of the tennis ball is 8 inches.
The tennis ball is the form of sphere whose circumference is given by formula \(2\pi r\), where r is the radius.
Thus, if r is the radius then according to condition,
\(2\pi r\) = 8 or
r = 8/2\(\pi\) inches.
Now, the volume of the sphere of radius r is \(\frac{4}{3}\pi r^3\) hence, find the volume of the given tennis ball by substituting r = 8/2\(\pi\) inches in \(\frac{4}{3}\pi r^3\) and simplify:
Volume = \(\frac{4}{3}\pi\) × \((\frac{8}{2\pi } )^3\)
Volume = 8.65\(inches^3\)
Hence the required volume of the tennis ball is 8.65\(inches^3\)
The volume of three tennis balls is (3 × 8.65) \(inches^3\) = 25.96 \(inches^3\)
Find the volume of the cylinder:
The volume of the cylinder with radius r units and height h units is given by \(\pi r^2h\) Hence the volume of the given cylinder with radius 1.32 inches , 8.2 height inches is:
\(\pi (1.32)^2\) × 8.2
= 3.14 × \((1.32)^2\) × 8.2
= 44.86 \(inches^3\)
Hence the volume of the cylinder is 44.86 \(inches^3\)
Find the amount of space within the cylinder not taken up by the tennis balls.
The required volume can be obtained by subtracting the volume three tennis balls from the volume of the cylinder as follows:
Volume of cylinder - volume of three tennis balls = (44.86 - 25.96) = 18.9 \(inches^3\)
Hence, the amount of space within the cylinder not taken up by the tennis balls is 18.9 \(inches^3\)
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Determine if triangle GHI and triangle JKL are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
Answer:
Given triangles are similar
Step-by-step explanation:
We can tell that given triangles are similar by comparing their side lengths.
HG is proportional to KJ
GI is proportional to JL
IH is proportional to LK
we can see the proportion better if we write it like this:
25/75 = 1/3
30/90 = 1/3
19/57 = 1/3
there are two ducks in front of a duck, two ducks behind a duck and a duck in the middle. how many ducks are there?
Answer:
3 Ducks
Step-by-step explanation:
Two ducks are in front of the last duck; the first duck has two
ducks behind; one duck is between the other two
Hence , there are 3 ducks
Hope it is correct
Answer: I think 7
Step-by-step explanation: Sorry if its wrong.
choose the best definition of hypothesis in the context of statistical analysis.
In statistical analysis, a hypothesis refers to a tentative explanation or prediction that is based on limited evidence and is subject to further investigation and testing. It is a statement that can be either true or false, and is typically formulated in such a way that it can be tested using statistical methods.
The hypothesis is often used to guide the research process, to help identify potential patterns or relationships in the data, and to evaluate the significance of the results.
Overall, the hypothesis plays a critical role in statistical analysis, as it provides a framework for understanding and interpreting data, and helps to ensure that research findings are reliable and valid.
A hypothesis in the context of statistical analysis is a tentative explanation or prediction about the relationship between two or more variables, which is subject to testing and empirical evaluation using statistical methods.
It is a statement that can be either true or false, and it is usually formulated in terms of the expected direction and strength of the relationship between the variables of interest.
The hypothesis is typically derived from existing theory, prior research, or common sense, and it serves as a guide for the collection, analysis, and interpretation of data in a scientific study.
The process of testing a hypothesis involves setting up null and alternative hypotheses, selecting an appropriate statistical test, collecting and analyzing data, and drawing conclusions based on the results of the analysis.
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Raw material purchases: $100,000 percentage of raw material purchases transferred to work in process: 50% direct labor: $200,000 overhead: $300,000 total depreciation: $30,000 which 80% is for inventory production and 20% for sg&a work in process completed: 70% finish goods that is sold: 90% as of december 31, 20xx how much raw materials are left in the balance sheet as of december 31, 20xx how much work-in-process inventory is left in the balance sheet as of december 31, 20xx how much finished goods are left in the balance sheet
As of December 31, 20XX, the balance sheet shows that the ending balance of raw materials is $76,000, the ending balance of work-in-process inventory is $52,600, and the ending balance of finished goods is $52,600.
In order to solve this problem, we need to follow a few steps. The steps are as follows:
1. Calculate the raw material transferred to work in process by multiplying the raw material purchases with the percentage transferred to the work in process.
2. Calculate the cost of goods manufactured (COGM) by adding the costs of raw material transferred to the work in process, direct labor, and overhead, and then subtracting the total depreciation.
3. Calculate the cost of goods sold (COGS) by multiplying the cost of goods manufactured with the percentage of finished goods that is sold.
4. Calculate the ending balance of raw materials by subtracting the COGM from the sum of raw material purchases and the beginning balance of raw materials.
5. Calculate the ending balance of work-in-process inventory by subtracting the COGS from the COGM.
6. Calculate the ending balance of finished goods by subtracting the COGS from the sum of the beginning balance of finished goods and the cost of goods manufactured.
Now, let's use the above method to solve the given problem.
Balance sheet for raw material purchases, transferred to work in process, direct labor, overhead, total depreciation, inventory production, and SG&A are given.
- Raw material purchases: $100,000
- Percentage of raw material purchases transferred to work in process: 50%
- Direct labor: $200,000
- Overhead: $300,000
- Total depreciation: $30,000, of which 80% is for inventory production and 20% for SG&A
- Work in process completed: 70%
- Finished goods that is sold: 90%
As of December 31, 20XX, we need to calculate how much raw materials are left on the balance sheet, how much work-in-process inventory is left on the balance sheet, and how much finished goods are left on the balance sheet. The problem is solved below.
1. Calculate the raw material transferred to work in process:
Raw material transferred to work in process = 50% of $100,000
= 0.50 × $100,000
= $50,000
2. Calculate the cost of goods manufactured (COGM):
Raw material purchases transferred to work in process = $50,000
Direct labor = $200,000
Overhead = $300,000
Total depreciation = $30,000, of which 80% is for inventory production and 20% for SG&A
COGM = ($50,000 + $200,000 + $300,000) - (80% × $30,000)
= $50,000 + $200,000 + $300,000 - $24,000
= $526,000
3. Calculate the cost of goods sold (COGS):
COGS = 90% × $526,000
= 0.90 × $526,000
= $473,400
4. Calculate the ending balance of raw materials:
Beginning balance of raw materials = $0
Raw material purchases = $100,000
Raw material transferred to work in process = $50,000
COGM = $526,000
Ending balance of raw materials = ($100,000 + $0) - $526,000 + $50,000
= $76,000
5. Calculate the ending balance of work-in-process inventory:
Beginning balance of work-in-process inventory = $0
COGM = $526,000
COGS = $473,400
Ending balance of work-in-process inventory = $526,000 - $473,400 + $0
= $52,600
6. Calculate the ending balance of finished goods:
Beginning balance of finished goods = $0
COGM = $526,000
COGS = $473,400
Ending balance of finished goods = ($0 + $526,000) - $473,400
= $52,600
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if a triangle has two angles that measures 46 and 102 degrees, what is the measure of the third angle?
Answer:
All triangles need to have 180 degrees
subtract the angles you already know
180 - 102 - 46 = 180 - 148 = 32
There is 32 degrees left so 32 is the answer
Step-by-step explanation:
Answer:
32°
Step-by-step explanation:
The triangle sum theorem states that the measures of the angles of a triangle is 180°
Given that TR(x)=20x and TC(x)=120+10x what is the break-even point?
The break-even point is the level of output at which total revenue (TR) equals total cost (TC). In this case, with TR(x) = 20x and TC(x) = 120 + 10x, we need to find the value of x where TR(x) = TC(x).
To find the break-even point, we set TR(x) equal to TC(x) and solve for x.
TR(x) = TC(x) can be expressed as:
20x = 120 + 10x
Simplifying the equation, we combine like terms:
20x - 10x = 120
10x = 120
To isolate x, we divide both sides of the equation by 10:
x = 12
Therefore, the break-even point occurs when x is equal to 12. At this level of output, the total revenue is equal to the total cost.
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SOMEONE PLS HELP ME ASAP PLSPLSpslpls omggg pls
Answer:
MATHPAPA.COM
Step-by-step explanation:
Go to MATHPAPA.Com and use the Algebraic Calculator
In a certain investigation: 460 persons were involved in the study: and based on an enquiry on their age. it was known that 75% of them were 22 or more years. The following frequency distribution shows the age composition of the persons under study. Find the mean and modal life of condensers_ Mid; age in years No. of persons 18 f; 23 28 33 90 122 ; 38 56 48 24 20 33'
Therefore , the solution of the given problem of percentage comes out to be 38 years old is the median age.
What does a percentage actually mean?In statistics, a "a%" is a figure or statistic that is expressed as a percentage of 100. The words "pct," "pct," but instead "pc" are also not frequently used. However, the sign "%" is frequently used to represent it. The percentage sum is flat; there are no dimensions. Percentages are truly integers because their numerator almost always equals 100. Either the % symbol (%) or the additional term "fraction" must come before a number to denote that it is a percentage.
Here,
The following algorithm must be used to determine the mean age:
=> mean = (all years added together) / (total number of persons)
The representative age for each age group is the age that falls in the middle of the range. With this approach, we can determine the total age as follows:
=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)
=> 162 + 644 + 924 + 2970 + 4636 + 2688 + 1152 + 1520 + 272.25
=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)
According to the information provided, there are 460 people in total.
=> mean = 17745.25 / 460
=> mean = 17745.25 / 460
As a result, the average lifespan is roughly 38.552 years.
The age category in this instance with the highest frequency has a midpoint of 38 and a frequency of 122. As a result, 38 years old is the median age.
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Jesse wanted a stamp collection his grandfather gave him 48 stamps to start it then his parents gave him 23 stamps and his aunt gave him 17 stamps how many stamps does Jesse have in his collection
Answer:88
Step-by-step explanation:
Choose the property illustrated by the following(9•y)•4=9•(y•4)
Answer:
y = 36
Step-by-step explanation:
(9×y)×4 = 9× (y × 4)
36 × 4y = 9y × 36
36 × 36 = 4y × 9y
1296 = 36y
36 = y
Which are possible?
If you could move the black shape up and down, and
left and right (but without spinning, stretching or flipping
it), which of these shapes could you match exactly?
(Select all that apply)
DA
B
с
original
1
Mrs. Murphy by balloons garlands paper lanterns and banners to decorate a school party she got three times as many bags of balloons as paper lanterns seven more garlands than paper lanterns and for banners she paid $5. 25 for each banner $6. 50 for each paper lantern five dollars for each bag of balloons and $3. 50 for each garland how many of each kind of decoration did she purchase if she paid $145. 50
She purchased 4 Paper Lanterns, 12 Bags of Balloons, 11 Garlands, and 4 Banners if she paid $145. 50.
The cost of lanterns is $6.50
Mrs Murphy bought 4 lanterns
Multiply the cost of one lantern ($6.50) by the number of lanterns bought (4) 6.50 multiplied by 4 equals 26
The cost of banners is $5.25
Mrs Murphy bought 4 banners
Multiply the cost of one banner ($5.25) by the number of banners bought (4) 5.25 multiplied by 4 equals 21
Mrs Murphy bought 3 times as many balloons as she did lanterns
So, you multiply the number of lanterns bought (4) by 3
This gives 12
We then multiply the cost of each balloon ($5.00) by the number of balloons bought (12)
5.00 multiplied by 12 equals 60
Mrs Murphy bought 7 more garlands as she did lanterns
So, we add 7 to the number of lanterns bought (4)
7 plus 4 equals 11
To find the cost of the total garlands bought
We multiply the cost of each garland ($3.50) by the number of garlands bought (11)
3.50 multiplied by 11 equals 38.5
Now we can add up the costs of all the items
26+21+60+38.5=145.50
145.50 was the total amount she spent so we know it is the correct answer.
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Dawson simplifies the equation 4y-3=4(y + 1) and says it has no solution. Is dawson correct?
Let's start by substituting the right-hand side of the equation into the left-hand side:
What does the math equation mean?
Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.
4y - 3 = 4(y + 1)
4y - 3 = 4y + 4
Now, we can isolate y by subtracting 4y from both sides:
0 = y + 4
-4 = y
So, there is a solution to the equation: y = -4. This means that Dawson is incorrect in saying that the equation has no solution.
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if two variables are correlated to each other, which two of the following are characteristics of the dependent variable? multiple select question. it is usually shown on the horizontal axis of a scatter diagram. in a cause and effect relationship, it is the effect. in a cause and effect relationship, it is the cause. it is usually shown on the vertical axis of a scatter diagram. need help? review these concept resources.
Therefore, the options "it is usually shown on the horizontal axis of a scatter diagram" and "it is usually shown on the vertical axis of a scatter diagram" could both be true, depending on the preference of the researcher or the convention used in a particular field or context.
Neither of the variables is considered as the dependent variable in a correlation analysis. Correlation refers to the strength of the relationship between two variables, without implying a cause-and-effect relationship or assigning one variable as the independent or dependent variable. Therefore, the options "in a cause and effect relationship, it is the effect" and "in a cause and effect relationship, it is the cause" are not applicable.
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What is the area of a picture of a silent that are 12 inches? Use The formula A=s^2, where is the length of one side
Answer:
144 in²
Step-by-step explanation:
Area of square: \(s^2\)
Here s is 12 inches.
Using the formula:
area: \(s^2\)
area: 12²
area: 12 * 12
→ 144 in²
The formula to find area of square is:
\( \tt \: area = {s}^{2} \)
Where,
s is sideIn our case,
s = 12 inchesSo,
\( \sf \: area = {12}^{2} \)
\( \boxed{ \bf \: area = 144 \: {in}^{2}}\)
What is the length of the rectangular plot of land shown? Use pencil and paper. How are the lengths of the legs of a right triangle related to the lengths of the sides of a rectangle?
The length of the rectangular plot of land is 168 ft.
To find the length of the rectangular plot of land, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In the given diagram, we can see that the plot of land forms a right triangle, where the length of one leg is 874 ft and the length of the diagonal is 890 ft. Therefore, the length of the rectangular plot can be found as follows:
\(h^2 = a^2 +b^2\\b^2 = h^2 - a^2\\b = \sqrt{h^2-a^2} \\b= \sqrt{(890)^2- (874)^2}\\ b= \sqrt{792100- 763876}\\ b= \sqrt{28224}\\ b= 168\)
So, the length of the rectangular plot of land is 168 ft.
The lengths of the legs of a right triangle are related to the lengths of the sides of a rectangle in the following way:
If we draw a rectangle with sides of length "a" and "b", then the diagonal of the rectangle (which is the hypotenuse of the right triangle formed by the sides of the rectangle) will have a length equal to the square root of (\(a^2 + b^2\)).
Conversely, if we have a right triangle with legs of length "a" and "b", then we can form a rectangle by making the legs of the triangle the sides of the rectangle. The length of one side of the rectangle will be "a" and the length of the other side will be "b".
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PLEASE HELP!! Which of the following are considered skew lines?
A- AC and CD
B- DH and BF
C- EG and FH
D- AE and GH
Answer:
A
Step-by-step explanation:
Hope this helps hope you get it right
Which quadratic equation models the situation correctly? y = 27(x â€"" 7)2 105 y = 27(x â€"" 105)2 7 y = 0.0018(x â€"" 7)2 105 y = 0.0018(x â€"" 105)2 7
The quadratic equation that correctly models the situation is y = 0.0018(x - 105)² + 7.
Quadratic equations are mathematical models used to represent situations that involve a squared variable. In this case, we are given four options: y = 27(x - 7)² + 105, y = 27(x - 105)² + 7, y = 0.0018(x - 7)² + 105, and y = 0.0018(x - 105)² + 7. We need to determine which equation accurately represents the given situation.
Analyzing the options, we notice that the quadratic term, (x - a)², represents a horizontal shift of the parabola. In the first two equations, the value of 'a' is 7 and 105, respectively. However, the situation requires a parabola that is shifted to the right, so the correct equation must have a value of 'a' greater than 7.
Next, we examine the coefficients in front of the quadratic term. The coefficient determines the vertical stretch or compression of the parabola. The options have coefficients of 27 and 0.0018. Since the situation does not mention any vertical scaling, a coefficient of 0.0018 seems more appropriate.
Finally, we consider the constant term, which determines the vertical translation of the parabola. The situation mentions a value of 7, so the correct equation should have a constant term of 7.
Based on this analysis, the quadratic equation that accurately models the situation is y = 0.0018(x - 105)² + 7. This equation represents a parabola shifted to the right by 105 units, with a slight vertical compression and a vertical translation of 7 units.
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7 (4x -2) is my question im confused on
Answer:
28x-14
Step-by-step explanation:
7(4x-2)
to solve this you have to expand the brackets
7×4x=28x
7×-2=-14
then we put these together to get the expanded expression
28x-14
Answer:
28x -14
Explanation:
7 (4x-2)
First, you need to apply the distributive property to the function which is multiplying the 7 by 4x and -2.
(7 * 4x) + (7 * -2)
Next, you do the multiplication of the 2 numbers.
(7 * 4x) = 28x
(7 * -2) = -14
Lastly, you add them together.
28x + (-14) = 28x -14
Express the following as a linear combination of
u = (3, 1, 7), v = (1, -1, 6)
and w = (7, 5, 5).
(14,10,14)
To express (14, 10, 14) as a linear combination of u = (3, 1, 7), v = (1, -1, 6), and w = (7, 5, 5), we need to find values for a, b, and c such that:
(14, 10, 14) = a(3, 1, 7) + b(1, -1, 6) + c(7, 5, 5)
This can be written as a system of equations:
14 = 3a + b + 7c
10 = a - b + 5c
14 = 7a + 6b + 5c
We can solve this system of equations using any method we prefer, such as substitution or elimination. One possible solution is:
a = 1
b = 2
c = 1
Therefore, the linear combination of u, v, and w that gives us (14, 10, 14) is:
(14, 10, 14) = 1(3, 1, 7) + 2(1, -1, 6) + 1(7, 5, 5)
= (3, 1, 7) + (2, -2, 12) + (7, 5, 5)
= (14, 10, 14)
So, the linear combination is 1u + 2v + 1w.
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