Answer:
No
Step-by-step explanation:
In order for a triangle to be a right angle, the sum of the squares of the two legs (a and b) must be equal the square of the longest side, known as the hypotenuse (c):
[tex]a^2+b^2=c^2[/tex]
The square root of 155 is the longest side as it is approximately 12.45. Thus, if the triangle is a right triangle, the square root of 155 must be the hypotenuse.
We can now check to see whether the sum of the squares of 7 and 9 equal the square of the square root of 155:
[tex]7^2+9^2=(\sqrt{155})^2\\ 49+81=155\\130=155[/tex]
The equation is not true since 130 is less than and not equal to 155. Therefore, a triangle with side lengths 7, 9, and the square root of 155 cannot be a right triangle.
Find f(-1).
Provide your answer below:
f(t)=-3t²-2t+1
Answer:
f(-1)=0
Step-by-step explanation:
To evaluate the function f(t) = -3t² - 2t + 1, we will start by plugging in -1 everywhere t occurs in the function :
[tex]\star \phantom{t-u} f(-1)=-3(-1)^2-2(-1)+1\\\\\\\star\phantom{t-u} f(-1)=-3*1+2+1\\\\\star\phantom{t-u} f(-1)=-3+3\\\\\underline{\star\phantom{t-u}f(-1)=0}[/tex]
[tex]\bigstar[/tex] Therefore the answer is f(-1) = 0
ACTIVITY 1: Find f−1 in each of the following.
The [tex]f^{-1}[/tex] inverse of f of each
1) (x + 1)/2
2) [tex]\sqrt{\frac{x+1}{4} } \\[/tex]
3) 3 - 4x
4) [tex](x+5)^{1/3}[/tex]
5) [tex]\sqrt{x + 4}[/tex]
1) function f(x) = 3x + 1
let f(x) = y
y = 3x + 1
y - 1 = 3x
(y - 1)/3 = x
x obtained is [tex]f^{-1}[/tex]
and y will be x
[tex]f^{-1}[/tex] = (x-1)/3
2) equation f(x) = 4x² - 1
let f(x) = y
y = 4x² - 1
y + 1 = 4x²
(y + 1 )/4 = x²
x = [tex]\sqrt{\frac{x + 1}{4} }[/tex]
x obtained is [tex]f^{-1}[/tex]
and y will be x
[tex]f^{-1}[/tex] = [tex]\sqrt{\frac{x + 1}{4} }[/tex]
similarly,
3) f(x) = 3-x/4
y = 3-x/4
4y = 3 - x
x = 3 - 4x
[tex]f^{-1}[/tex] = 3- 4x
4) y = x³ - 5
y + 5 = x³
x = [tex](y + 5)^{1/3}[/tex]
[tex]f^{-1}[/tex] = [tex](x+5)^{1/3}[/tex]
5) y = x² - 4
y + 4 = x²
x = √y + 4
[tex]f^{-1} = \sqrt{x + 4}[/tex]
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2010 2008
$971 $812
$977 $943
$900 $873
$1071 $1023
$501 $486
3. Identify whether the mean or median is a more accurate reflection of the data.
Explain why.
The median is the accurate reflection of the data
How to solve for the mean501, 900, 971, 977, 1071
The mean would be
summation of the values
mean = 884
The median is the value that occurs in the middle = 971
The median would be more accurate reflection of the data. 501 is an outler. This is what caused us to have a mean that is c loser to 884. Hence we have 971 the median to be more accurate reflection of the data
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I really need help, I’m struggling with 5 and 6
Answer:
5)
The inverse of the function f(x) = x^7 can be found by following these steps:
Step 1: Replace f(x) with y. The equation becomes y = x^7.
Step 2: Interchange x and y in the equation, so it becomes x = y^7.
Step 3: Solve the equation for y by taking the seventh root of both sides. This yields y = x^(1/7).
Therefore, the inverse function of f(x) = x^7 is g(x) = x^(1/7), which maps any given value of x to its seventh root.
It's important to note that the domain and range of the inverse function are the opposite of those of the original function. The domain of the inverse function is all real numbers, while the range is only positive real numbers. The domain of the original function is all real numbers, while the range is also all real numbers.
6)
To find the inverse of the function f(x) = (-2/5)x^3, we can follow these steps:
Step 1: Replace f(x) with y. The equation becomes y = (-2/5)x^3.
Step 2: Solve the equation for x in terms of y.
Multiply both sides by -5/2:
(-5/2) y = x^3
Take the cube root of both sides:
x = [(-5/2) y]^(1/3)
Step 3: Replace x with f^-1(y) to obtain the inverse function.
f^-1(y) = [(-5/2) y]^(1/3)
Therefore, the inverse function of f(x) = (-2/5)x^3 is f^-1(y) = [(-5/2) y]^(1/3).
It is important to note that the domain and range of the inverse function are the opposite of those of the original function. The domain of the inverse function is all real numbers, while the range is also all real numbers. The domain of the original function is all real numbers, while the range is only negative real numbers if x is negative and only positive real numbers if x is positive.
What is the perimeter and area of the Rhombus?
Z
6.2,
W
Y
7.4
9.7 cm
X
Answer:
Perimeter of rhombus = 4(9.7) = 38.8 cm
Area of rhombus = 4(1/2)(6.2)(7.4)
= 91.76 cm^2
Help I have to turn this in tmw!!
Answer:
[tex]\large\boxed{\tt Area = Length \times Width}[/tex]
[tex]\large\boxed{\tt Area = 8.6 \ cm. \times 3 \ cm.}[/tex]
[tex]\large\boxed{\tt Area = 25.8 \ cm.^{2}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked for the area of a 2D Rectangle.}[/tex]
[tex]\large\underline{\textsf{What is Area?}}[/tex]
[tex]\textsf{Area for 2D shapes is how much space is inside between edges. Consider edges}[/tex]
[tex]\textsf{as the sides of a shape.}[/tex]
[tex]\underline{\textsf{How are we able to find Area?}}[/tex]
[tex]\textsf{Many shapes require different formulas to find the area. Some have the same}[/tex]
[tex]\textsf{formulas however it depends on how many sides the shape has, and the number of}[/tex]
[tex]\textsf{dimensions shown in the shape. For a Rectangle it's simple. Because a Rectangle}[/tex]
[tex]\textsf{has 2 Dimensions (Length and Width), to find the area we should multiply}[/tex]
[tex]\textsf{the dimensions together, hence resulting in the amount of space inside the shape.}[/tex]
[tex]\large\underline{\textsf{Formula;}}[/tex]
[tex]\large\boxed{\tt Area = Length \times Width}[/tex]
[tex]\large\underline{\textsf{Plug in Values;}}[/tex]
[tex]\textsf{The Length and Width aren't mentioned in the question, but it doesn't matter}[/tex]
[tex]\textsf{since we're still going to get the same answer no matter which place they're in.}[/tex]
[tex]\large\boxed{\tt Area = 8.6 \ cm. \times 3 \ cm.}[/tex]
[tex]\large\underline{\textsf{Solving for the Area;}}[/tex]
[tex]\textsf{We have our formula, now multiply the dimensions together.}[/tex]
[tex]\large\boxed{\tt Area = 25.8 \ cm.^{2}}[/tex]
please help for this question
The single transformation that maps shape P onto shape Q is given as follows:
Reflection over the line y = 1.
What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Lateral or vertical movements.Reflections: A reflection is either over one of the axis on the graph or over a line.Rotations: A rotation is over a degree measure, either clockwise or counterclockwise.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, which can either enlarge or reduce the figure.The orientation of the figure changed, hence it underwent a reflection.
The intercepts are given as follows:
y = 4 and y = -2.
The line of reflection is the mean of the coordinates of the intercepts, hence:
(4 - 2)/2 -> y = 1.
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a. Use the graph to approximate the value of the car after 4 years.
b. Use the graph to approximate the value of the car after 5 years.
c. Use the graph to approximate when the car will be worth half its original value. (Determine the number of years.)
The car will be worth half its original value after 4 years
How to solveA graph for straight-line depreciation for a car is given.
a
The number of years the car totally depreciates is 8 years as seen in the graph which is x -intercept.
Step 3/7
The model makes straight-line depreciation. In a straight line depreciation equation, the intercepts are
(0, maximum car value) and (maximum lifespan,0)
Let y represent the value of the car at any time during its lifetime. The minimum y -value is zero dollars and the maximum y -value is the purchase price of $25,600
The intercepts are (0, 25, 600) and (8,0)
Determine the slope of the equation.
Two points determine a line, so only two points are needed to determine the slope of a line.
Let the coordinates of the -intercept be the first point. That is, (xi,yi) = (0, 25, 600)
Let the coordinates of the -intercept be the second point. That is (x2, y2)= (8,0)
Use the slope ratio as shown below;
The slope of the depreciation equation is.
-3200
The general form for the equation of a straight line is:
y = mx + b
Where m represents the slope of the line and b represents the y-intercept.
The slope is -3,200 and the -intercept is 25,600 as obtained.
Therefore, the straight line depreciation equation is:
y = -3,200x + 25,600
Therefore, the value of the car after 4 years is $12,800
b.
Use the depreciation equation and substitute x=5 years to find the car worth after 5 years.
Therefore, the value of the car after 5 years is $9,600
c.
The half value of the car is half of $25,600 which is $12,800
The car will be worth half its original value after 4 years
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Drag numbers to the table so it shows a proportional relationship between x and y.
The table is completed as follows:
x = 0.6, y = 6.x = 1.8, y = 18.What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
From the first row, when x = 0.2, y = 2, hence the constant is given as follows:
k = y/x
k = 2/0.2
k = 10.
Hence the equation is:
y = 10x.
Then the numeric values are given as follows:
x = 0.6, y = 10 x 0.6 = 6.x = 1.8, y = 10 x 1.8 = 18.More can be learned about proportional relationships at https://brainly.com/question/7723640
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Solve for x. Round to the nearest tenth of a degree, if necessary.
The value of x it the nearest tenth of degree is 25.6°
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Sin(tetha) = opp/ hyp
cos( tetha) = adj/ hyp
tan( tetha) = opp/ adj
Here, the hypotenuse is 92 and adjascent to the to the angle x is 63
therefore to calculate x we use cosine function
cos x = 83/92
cos x = 0.902
x = cos^-1( 0.902)
x = 25.6° ( nearest tenth)
therefore the value of x is 25.6°
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A restaurant manager tracks the number of people in every party to sit at a specific table every day for a week, then compiles the results into a probability distribution as shown in the table:
a.) There is a 25% chance that a party will contain 5 or more people. b.) There is a 50% chance that a party will contain 4 or more people. c.) There is a 50% chance that a party will contain 2 or fewer people.
d.) There is a 75% chance that a party will contain 3 or more people.
There are 25% chance of 5 more people in the party.
Hence option (a) is correct.
Relative frequency = (number of times of occurrence of an event )/ (number of trials)
For the given table
relative frequency for 1 people = 0.05 = 5%
relative frequency for 2 people = 0.46 = 46%
relative frequency for 3 people = 0.18 = 18%
relative frequency for 4 people = 0.22 = 22%
relative frequency for 5 people = 0.06 = 6%
relative frequency for 6 people = 0.03 = 3%
Since relative frequency for 1 people is 5%
Therefore,
Relative frequency for 5 people is = 5x5%
= 25 %
Hence,
Relative frequency of 5 more people 25%.
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In a large school, it was found that 79% of students are taking a math class, 70% of student are taking an English class, and 67% of students are taking both.
Find the probability that a randomly selected student is taking a math class or an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.
Find the probability that a randomly selected student is taking neither a math class nor an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.
a) The probability that a randomly selected student is taking a Math class or an English class is 0.82.
b) The probability that a randomly selected student is taking neither a math class nor an English class is 0.18.
What is the probability?Probability refers to the chance or likelihood that an expected success, event, or outcome occurs from many possible successes, events, or outcomes.
Probability is represented as a fractional value using decimals, fractions, or percentages.
The percentage of students taking a math class =79%
The percentage of students taking an English class = 70%
The percentage of students taking both classes = 67%
Let the event that a student is taking a math class = m
Let the event that a student is taking an English class = e
The probability of m is p(m) = 0.79
The probability of e is p(e) = 0.70
The probability of m and e is p(m and e) = 0.67
The probability that a randomly selected student is taking a math class or an English class = 0.82 (0.79 + 0.70 - 0.67)
The probability that a randomly selected student is taking neither a math class nor an English class = 0.18 (1 - 0.82)
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A 45-year-old man puts $2500 in a retirement account at the end of each quarter until he reaches the age of 66, then makes no further deposits. If the account pays 4% interest compounded quarterly, how much will be in the account when the man retires at age 71? There will be $ in the account.
Answer: The man will make deposits for 66 - 45 = 21 years, or 21 x 4 = 84 quarters.
The quarterly interest rate is 4% / 4 = 1%.
Let's use the formula for the future value of an annuity:
FV = PMT x ((1 + r)^n - 1) / r
where FV is the future value of the annuity, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.
In this case, PMT = $2500, r = 1%, and n = 84. Substituting these values into the formula, we get:
FV = $2500 x ((1 + 0.01)^84 - 1) / 0.01
FV = $2500 x (5.409 - 1) / 0.01
FV = $2500 x 540.9
FV = $1,352,250
Therefore, there will be $1,352,250 in the account when the man retires at age 71.
Each state sets its own state income tax rate. Table 1 shows 3 individuals'
incomes and taxes owed. Table 2 shows the income tax rates for several
states.
Table 1:
Name Income Taxes Owed
Beatrice $35,000
Gregory $55,000
Melinda $72,000
O $4,602.50
O $19,725
$2,450
$4,400
$3,600
O $46,025
O $61,147.50
Table 2:
State
Alabama
Georgia
Maine
If Anthony lives in Georgia and has an income of $65, 750, how much money
will he have left after he pays state income taxes?
Income Tax Rate
5%
7%
8%
From Table 2, we can see that Georgia's income tax rate is 7%.
To find the amount of state income taxes Anthony will owe, we can multiply his income by the tax rate:
State income tax = (Anthony's income) x (Georgia's tax rate)
State income tax = $65,750 x 0.07
State income tax = $4,602.50
Therefore, Anthony will owe $4,602.50 in state income taxes. To find out how much money he will have left after he pays these taxes, we can subtract the tax amount from his income:
Money left after paying state income taxes = Anthony's income - State income tax
Money left after paying state income taxes = $65,750 - $4,602.50
Money left after paying state income taxes = $61,147.50
Therefore, Anthony will have $61,147.50 left after he pays state income taxes.
Malden go company has a balance and its accounts payable control count of $10,500 on January 1, 2021. The subsidiary ledger contains three accounts Smith Company balance of $3000 white company balance of tMalden go company has a balance and it’s accounts payable control count of $10,500 on January 1, 2021. The subsidiary ledger contains three accounts Smith Company balance of $3000 white company balance of $2500 and Marina company during the January the following payable related transactions occurred
Answer:
6
Step-by-step explanation:
bc
Unit seven geometry and measurement homework to perimeter area of rectangles and parallelograms answer key
The required maximum area of the rectangle is 17.5m
How to explain the perimeterThe perimeter of a rectangle is = 70m.
We have to find The maximum area of rectangle .
A rectangle will have the maximum possible area for a given perimeter when all the sides are the same length. Since every rectangle has four sides, if you know the perimeter, divide it by four.
Maximum area of rectangle is = 70 / 4
= 17.5
The required value of maximum area of the rectangle is 17.5m.
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the perimeter of a rectangle is 70m. What are the dimensions that will produce the maximum area of such a rectangle
two decimal places. A discounted loan of R4 670,00 at a simple discount rate of 14% per year is offered to Mr Mothapo. The actual amount of money that Mr Mothapo receives is R3 852,75. This is represented by the following timeline: R3 852,75 ? months 14% simple discount R4670,00 The amount of R4 670,00 is due to be paid back after
The value of amount of R4 670,00 is due to be paid back after 1.47 years.
We have to given that;
A discounted loan of R4 670,00 at a simple discount rate of 14% per year is offered to Mr. Mothapo.
And, The actual amount of money that Mr. Mothapo receives is R3 852,75.
Now, Let n be the loan period.
Hence, We get;
4670,00 = 385275 (1 + 0.14)ⁿ
1.212121 = (1.14)ⁿ
n log 1.14 = log 1.2121
n = 1.47
Thus, The value of amount of R4 670,00 is due to be paid back after 1.47 years.
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PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
A. The expression that represents the total amount of canned food they have collected so far is: 4x² + 2xy + 3
B. Number of canned food still remaining to be collected is: 2x² - 4xy + 5
How to Solve Polynomial Expressions?A polynomial expression is a mathematical expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication of non-negative integer exponents.
Part A: To find the expression that represents the total amount of canned food they have collected so far, add the expression for each person given together.
3x² - 2 + x² + 2xy + 5
Combine like terms:
4x² + 2xy + 3
Part B: Number of canned food still remaining to be collected is calculated below.
(6x² - 2xy + 8) - (4x² + 2xy + 3)
Open bracket:
6x² - 2xy + 8 - 4x² - 2xy - 3
Combine like terms:
2x² - 4xy + 5
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Describe how the following functions are transformed from the parent function
f(x)=|x|-3
f(x)= - |x - 4|
f(x)= 1/3 |x|
f(x)= -2 |x-1|
Answer:
Each of these functions is a transformation of the parent function f(x) = |x|. The transformations include shifting the graph up or down, stretching or compressing the graph vertically, reflecting the graph across the x-axis, and shifting the graph left or right. The vertex of each graph is located at a different point.
Step-by-step explanation:
- The function f(x) = |x| - 3 is a transformation of the parent function f(x) = |x|. The "-3" at the end of the function shifts the graph 3 units down. This means that the vertex, or lowest point, of the graph is at (0, -3) instead of (0, 0).
- The function f(x) = -|x - 4| is also a transformation of the parent function f(x) = |x|. The negative sign in front of the absolute value function reflects the graph across the x-axis. The "-4" inside the absolute value function shifts the graph 4 units to the right. This means that the vertex of the graph is at (4, 0) instead of (0, 0).
- The function f(x) = (1/3)|x| is a transformation of the parent function f(x) = |x|. The "1/3" in front of the absolute value function stretches the graph vertically by a factor of 1/3. This means that the graph is narrower and closer to the x-axis than the parent function. However, because the absolute value function is symmetrical, the graph is still centered at (0, 0).
- The function f(x) = -2|x - 1| is also a transformation of the parent function f(x) = |x|. The negative sign in front of the absolute value function reflects the graph across the x-axis. The "-1" inside the absolute value function shifts the graph 1 unit to the right. The "2" in front of the absolute value function stretches the graph vertically by a factor of 2. This means that the graph is narrower and closer to the x-axis than the parent function, and it is also reflected across the x-axis. The vertex of the graph is at (1, 0).
wing Lines Parallel
Solve for x to make A||B.
B
3x
A
X = = [?]
7x
Enter
If line A is parallel to line B then the value of x is 18.
Given that a line A is parallel to line B
We have to find the value of x
3x+7x=180
Combine the like terms
10x=180
Divide both sides by 10
value x=18
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HELP PLS 65.1 + WHAT = 100 !!!
Answer: 34.9
Step-by-step explanation: 100 - 65.1
Given that a function, g, has a domain of -20 s × s 5 and a range of -5 s g(x) s 45 and that g(0) = -2 and g(-9) = 6, select the statement that could true for g.
A. g(-4)= -11
B. g(-13)= 20
C. g(0) = 2
D. g(7) = -1
The statement that could be true for the domain of g is g(-4) = -11.
option A.
Which statement is true for domain of g?
The function g has a domain of -20 s × s 5 and a range of -5 s g(x) s 45 and that g(0) = -2 and g(-9) = 6.
The given statements that could be true for g is calculated as follows;
Option A: g(-4) = -11
Since the range of g is -5 s g(x) s 45, it is possible for g(-4) to be -11.
Therefore, this could be true.
Option B: g(-13) = 20
Since the domain of g is -20 s × s 5, it is not possible for g(-13) to be defined. Therefore, option B is not true.
Option C: g(0) = 2
We are given that g(0) = -2, so option C is not true.
Option D: g(7) = -1
Since the domain of g is -20 s × s 5, it is not possible for g(7) to be defined. Therefore, option D is not true.
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The Problem Rodeos have long been a part of the culture in the southernmost part of the country and the growing popularity of the annual Easter event across South America prompted the Rupununi Development Corporation to construct a luxury resort with 60 two-bedroom suites for the visiting cultural troupes (troupe leaders and artistes). Capacity is ten troupe leaders and fifty artistes. Each suite is equipped with a small kitchenette, which contains a 7.3 cu ft. refrigerator, a microwave, and a coffee maker. A Drystan 6-piece bedroom set and the Ashley stationary sofa and love seat (all imported from Manaus at considerable cost) are also part of the furnishings. Each accommodation also has an excellent view if the Kanuku Mountains and nearby savannahs. The facility cost the Corporation $1,920,000 to build and equip and depreciation $160,000 per year (a fixed cost). Other operating costs include: Labor $320,000 per year plus $5 per suite per day Utilities $158,000 per year plus $1 per suite per day Miscellaneous $100,000 per year plus $6 per suite per day In addition to these costs, costs are also incurred on food and beverage for each guest. These costs are strictly variable, and (on average), are $40 per day for troupe leaders and $15 per day for artistes. Required Part A Assuming that the facility can maintain an average annual occupancy of 80% in both troupe leader and artistes suites (based on a 360 -day year), calculate the following: i. the annual fixed costs ii. the variable cost per guest by type of guest iii. the annual number of guest days by type of guest
Please answer correctly and explain reasoning for brainliest (If correct) and thanks!
Therefore, the correct answer is option C that is LM is reflected over the y-axis to L'M.
What is transformation?In mathematics, a transformation refers to a change in the position, shape, or size of a geometric figure. Transformations can be classified into four types: translation, rotation, reflection, and dilation.
Here,
The transformation of LM to L'M' involves both translation and reflection. To see the translation, we can compare the x- and y-coordinates of L and L', as well as M and M':
The x-coordinate of L' is 5 units more than the x-coordinate of L: -2 = -7 + 5.
The y-coordinate of L' is 2 units less than the y-coordinate of L: -4 = -2 - 2.
The x-coordinate of M' is 5 units more than the x-coordinate of M: 5 = 0 + 5.
The y-coordinate of M' is 2 units less than the y-coordinate of M: 3 = 5 - 2.
Therefore, we can conclude that LM is translated 5 units right and 2 units down to L'M'. This eliminates options OB and OD. To see the reflection, we can compare the x-coordinates of L and M, and their respective x-coordinates in L' and M':
The x-coordinate of L is negative and the x-coordinate of M is positive.
The x-coordinate of L' is negative and the x-coordinate of M' is positive.
Therefore, we can conclude that LM is reflected over the y-axis to L'M'. This eliminates option OA. Therefore, the correct answer is option OC.
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Use synthetic division to rewrite the following fraction in the form q(x)+r(x)d(x)
, where d(x) is the denominator of the original fraction, q(x)is the quotient, and r(x) is the remainder.
The result of the synthetic division is:4x⁵+17x⁴+14x³-3x²+2 = (4x⁴ + 5x³ - x²) (x + 3) + 56
what is synthetic division ?
Synthetic division is a simplified method of dividing a polynomial by a linear factor. It is commonly used in algebra to find the quotient and remainder when dividing a polynomial by a linear factor of the form (x-a).
In the given question,
To use synthetic division to rewrite the fraction, we first set up the problem like this:
-3 | 4 17 14 -3 0 2
| -12 -15 3 0
+----------------------------------
4 5 -1 0 0 2
The coefficients of the polynomial are written in descending order of powers of x, with any missing terms replaced by zeros. The divisor, x + 3, is written on the left, and the first coefficient of the polynomial is written on the top of the vertical line.
We then proceed to perform synthetic division as follows:
Bring down the first coefficient, which is 4, and write it under the horizontal line.
Multiply the divisor, -3, by the number we just brought down, which gives -12. Write this number under the next coefficient, 17.
Add the two numbers, 17 and -12, to get 5. Write this number under the next coefficient, 14.
Multiply the divisor, -3, by 5, which gives -15. Write this number under the next coefficient, -3.
Add the two numbers, -3 and -15, to get -18. Write this number under the next coefficient, 0.
Multiply the divisor, -3, by -18, which gives 54. Write this number under the next coefficient, 2.
Add the two numbers, 2 and 54, to get 56. This is the remainder, which we write above the divisor.
The result of the synthetic division is:
4x⁵+17x⁴+14x³-3x²+2 = (4x^4 + 5x³ - x²) (x + 3) + 56
Therefore, we have rewritten the fraction in the desired form:
4x⁵+17x⁴+14x³-3x²+2
---------------------- = 4x⁴ + 5x³ - x² + 56/(x+3)
x+3
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Find the perimeter of each figure
The perimeter of the composite figure is 46 metres.
How to find the perimeter of a figure?The perimeter of a figure is the sum of the whole sides of the 2 dimensional figure. Therefore, the perimeter of the composite figure is the sum of the whole sides.
Therefore, the perimeter of the figure can be found as follows:
perimeter of the shape = 5 + 6 + 9 + 11 + 3 + 12
perimeter of the shape = 11 + 9 + 11 + 15
perimeter of the shape =20 + 11 + 15
perimeter of the shape = 31 + 15
perimeter of the shape = 46 metres
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Factor the polynomial completely. If the polynomial is prime, so state.
15y2 - 19y + 6
Answer: 15y2 - 19y + 6 = 0
Step-by-step explanation:
The first term is, 15y2 its coefficient is 15 .The middle term is, -19y its coefficient is -19 .The last term, "the constant", is +6 Step-1 : Multiply the coefficient of the first term by the constant 15 • 6 = 90 Step-2 : Find two factors of 90 whose sum equals the coefficient of the middle term, which is -19 .
. Evaluate
11! 11!
24!
.
The evaluations are:
i. 11! = 39916800
ii. 24! = 2.045 x 10^37
What is expansion by factorial?Expansion by factorial is a method of expanding a given number from 1 to the number given. An example is given thus;
5! = 5 x 4 x 3 x 2 x 1!
= 120
To evaluate the given expressions;
a. 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1!
= 39916800
Also,
b. 24! = 24 x 23 x 22 x 20 x ........ x 5 x 4 x 3 x 2 x 1!
= 204484017332398 x 10 ^23
= 2.045 x 10^37
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Please help me with this
There is higher variability of y with large values of x.
There is a non linear relation between x and y.
How to explain the variabilityWe observe from figure b that for lower values of x the residuals are negative and as the values of x increases the residuals become positive but are distributed very close to the zero line.
Again for the extremely high values of x the residuals become negative following a decreasing non linear trend. Hence, from the residual plot we can conclude that the relation between x and y is a non linear one. Hence, the correct option is fourth option i.e, There is a non linear relation between x and y.
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I need to find both of the solutions to the equation 100+(n-2)^ = 149
The solutions to the equation 100+ (n - 2)² = 149 are n = 9 and n = -5
Finding the solutions to the equation 100+ (n - 2)² = 149From the question, we have the following parameters that can be used in our computation:
The equation 100+ (n - 2)² = 149
Express as
100+ (n - 2)² = 149
Subtract 100 from both sides of the equation
So, we have the following representation
(n - 2)² = 49
Take the square root of both sides
n - 2 = 7 and n - 2 = -7
Add 2 to both sides
n = 9 and n = -5
Hence, the solutions to the equation 100+ (n - 2)² = 149 are n = 9 and n = -5
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