The missing reason in Step 8 is substitution
When a triangle is not a right triangle and when either the lengths of two sides and the measurement of the included angle are known (SAS) or the lengths of the three sides are known (SSS), the Law of Cosines is used to discover the remaining pieces of the triangle.
According to the law of cosine, if a, b, and c are any triangle's three sides, then a² = b² + c² - 2bcosa
The x in statement 5 of the preceding proof is changed to c cos A from statement 6 in statement 8 of the proof.
Option C, from the list of alternatives, is the one that best explains statement 8.
Hence missing reason in Step 8 is substitution
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Answer: OPTION C
Step-by-step explanation:
EDGE22
For the following function y = f(x) = 4x^3 - 5
I worked out this Calculus problem, but I keep getting 1/-432 for part c. Can anyone work out the problem step-by-step so I can understand what I’m doing wrong? It would be greatly appreciated.
The answer for each of the differentiation are; f'(-6) = 432; f⁻¹(y) = ∛((y + 5)/4); df⁻¹/dy = 1/432
How to differentiate functions?
1) f(x) = 4x³ - 5
We will differentiate it to get;
f'(x) = df/dx = 12x²
f'(-6) = 12(-6)²
f'(-6) = 432
2) We are given the formula;
x = f⁻¹(y)
Thus;
y = 4x³ - 5
4x³ = y + 5
x³ = (y + 5)/4
x = ∛((y + 5)/4)
f⁻¹(y) = ∛((y + 5)/4)
c) f⁻¹(y) = ∛((y + 5)/4)
df⁻¹/dy = -1/12y²
At f(-6), we have;
df⁻¹/dy = 1/432
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Polynomial of lowest degree with zeros of 3/4 (multiplicity 2) and 1/3 (multiplicity 1) and with f(0) = -81
The polynomial is given by f(x) = 9(4x − 3)² (3x - 1) .
What is a Polynomial ?A polynomial is an expression that consists of indeterminate , Coefficients , exponents and mathematical operations.
It is given that
The zero of the function is at 3/4 with multiplicity of 2 = (x - 3/4)²
The zero of the function is at 1/3 with multiplicity of 1 = (x - 1/3)
The polynomial can be written as
f(x) = a (4x − 3)² (3x - 1)
-81 = a (0 − 3)² (0 -1)
a = 9
f(x) = 9(4x − 3)² (3x - 1)
Therefore the polynomial is given by f(x) = 9(4x − 3)² (3x - 1) .
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The Math Club has 23 members and needs to elect officers. They will need a President, Vice President, Secretary, and Treasurer. How many ways can a 4-member committee be formed?
Answer:
212520 different committees
Step-by-step explanation:
Candidates
For a President: 23
For a Vice President: 22
For a Secretary: 21
For a Treasurer: 20
Number of ways: (23)(22)(21)(20) = 212520
Hope this helps
Answer:
To whom it may concern the answer to this problem would be 212,520.
Step-by-step explanation:
Many people think this problem to be a combination problem, but it is actually a permutation. Since there must be some specific semblance to the order of the equation. Now, to begin with, the work for this problem is...
[tex]_{n}_P_{r}=\frac{n!}{(n-r)!} \\_{23} _P_{4}=\frac{23!}{(23-4)!} \\_{23}_P_{4}=\frac{23!}{19!} \\_{23}_P_{4}=\frac{23*22*21*20*19!}{19!} \\_{23}_P_{4}=\frac{212,520}{1} \\_{23}_P_{4}=212,520[/tex]
Remember that the 19! cancel each other out. Hope this helps!
What are the domain and range of the function f of x equals the quantity of x squared minus 3 x minus 28, all over x plus 4?
Find and prove an inequality relating 100n and n^{3} .
An inequality relating 100n and n³ is 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.
What is inequality?An inequality is comparison of two values, showing if one is less than, greater than, or simply not equal to another value.
Since 100n and n³ for n = 1, 2, 3, . . . 9, 10, 11 are 100, 200, 300, . . . 900, 1000, 1100 and 1, 8, 27, . . . 729, 1000, 1331 respectively.
Therefore, an inequality relating 100n and n³ will be 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.
Induction hypothesis:
Suppose 100n ≤ k³ for some positive integer k ≥ 10.
We need to show that 100( k + 1 ) ≤ ( k + 1 )³ = k³ + 3k² +3k + 1.
Note 100( k + 1 ) = 100k + 100 ≤ k³ + 100
≤ k³ + 3k² (∵ k ≥ 10 )
≤ k³ + 3k² + 3k
≤ k³ + 3k²+3k + 1
So 100( k + 1 ) ≤ ( k + 1 )³, which is true.
Hence by the principle of mathematical induction, 100n ≤ k³ for every integer k ≥ 10.
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Determine the values of x and y.
Answer: x = 130, y = 130
Step-by-step explanation:
By the corresponding angles theorem, x = 130
Thus, by the vertical angles theorem, y = 130
Write 9.7 to one significant figure
9.7 to one significant figure is 10
How to approximate the number?We have:
9.7
To approximate to one significant figure, we have to estimate the number such that it is represented by a non zero digit.
When 9.7 is approximated, we have:
10
Hence, 9.7 to one significant figure is 10
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At school B, 108 year 8 students study French.
This is 60% of the year group.
How many students do not study French in year 8 in school B?
Step-by-step explanation:
108 = 60%
1% = 60%/60 = 108/60 = 1.8
100% = 1%×100 = 1.8×100 = 180
how many do not study French ?
the remainder of the students. that is 40% (100% - 60%) or 72 students (40×1.8 or simply 180-108).
Answer:
72 students do not study French.
Step-by-step explanation:
60% = 108 students
1. 108 ÷ 60 = 1.8 ( this is to find 1% of the students)
2. 1.8(1%) × 40 = 72
To check the answer:
108 + 72 = 180
180 × 60% = 108
The number of measles cases increased 36.5% to 193 cases this year. What was the number of cases prior to the increase? The number of measles cases increased 36.5 % to 193 cases this year . What was the number of cases prior to the increase ?
Answer:
70.445
Step-by-step explanation:
you have to subtract 36.5 by 193.
You damage your car and it will cost $2,700 to repair. You have a $500 deductible. How much will the insurance company pay? A.$500 b.$2,200 c.$2,700 D.$0 e.$1,000
Answer:
After finding the money we were short with, we find that Option-b, that is, $2200 is the correct option.
Step-by-step explanation:
Given that the cost to repair the damaged car is $2700. We have $500.
Insurance company is a company that gives the payment of someone's valuable items when they are lost or get damaged. For example, home insurance, car insurance, life insurance and much more.
Here we can see that we are short with $2700 - $500 = $2200.
So, to complete the payment, insurance company will pay $2200.
Clearly, the correct option is Option-b.
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Find the slope of a line perpendicular to a line through the given points. E(5, 7), F(3, 1)
Answer: -1/3
Step-by-step explanation:
The slope of the given line is [tex]\frac{7-1}{5-3}=\frac{6}{2}=3[/tex].
Thus, since perpendicular lines have slopes that are negative reciprocals of each other, the answer is -1/3
Simplify 2√2-√3
---------------
√2+√3
Step-by-step explanation:
[tex] = \frac{2 \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } [/tex]
[tex] = \frac{2 \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } [/tex]
[tex] = \frac{ 2( \sqrt{2} - \sqrt{3} )( \sqrt{2} - \sqrt{3} )}{ { \sqrt{2} }^{2} - { \sqrt{3} }^{2} }[/tex]
[tex] = \frac{2(2 - \sqrt{6} - \sqrt{6} - 3) }{2 - 3} [/tex]
[tex] = \frac{2( - 1 - 2 \sqrt{6} )}{ - 1} [/tex]
[tex] = \frac{ - 2(1 + 2 \sqrt{6} )}{ - 1} [/tex]
[tex] = 2(1 + 2 \sqrt{6} )[/tex]
[tex] = 2 + 4 \sqrt{6} [/tex]
Please help! Will give the brainliest!
The answer is J. [tex](x+4)(x-2)=x\cdot x[/tex]
There are 3 feet in 1 yard. This is equivalent to 12 feet in 4 yards. Which proportion can be used to represent this?
12
4
77-7/22
12
12
3
12
03-1/2/
4
The proportion that can be used to represent the given statement is [tex]\frac{3}{1} =\frac{12}{4}[/tex]
Given that there are 3 feet in 1 yard, which is equivalent to 12 feet in 4 yards.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.
We need to determine the proportion that can be used to represent this.
Now, 1 yard = 3 feet implies 4 yards = 12 feet.
The required proportion can be written as [tex]\frac{3}{1} =\frac{12}{4}[/tex].
Therefore, the proportion that can be used to represent the given statement is [tex]\frac{3}{1} =\frac{12}{4}[/tex].
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Which function is the inverse of f(x) = 2x + 3
y=2x+3
to find inverse swap x and y
x=2y+3
x-3=2y
y=(x-3)/2
y=(x/2)-(3/2)
The inverse is f^-1(x)=(x/2)-(3/2)
Hope it helps!
When treated with an antibiotic, 92% of all the dolphins are cured of an ear infection. If 7 dolphins are treated, find the probability that exactly 4 are cured.
The probability is
(Round your answer to 4 decimal places.)
The probability that exactly 4 are cured from 7 dolphins is 0.0128
What is Probability ?Probability is the likeliness of an event to occur and it has a range of 0 to 1, where 0 means unlikely and 1 indicates certainty of the event to happen.
It is given that the 92% of all the dolphins are cured of an ear infection ,When treated with an antibiotic
If there are total dolphins given as 7
On the basis of given data
The dolphin that cannot be cured is given by
1 - p = 1 - (92/100) = 0.08 = 8/100
q = (8/100)
n= 7
r = 4
Therefore by Binomial Distribution
[tex]P = ^nC_r p^r q^{n-r}[/tex]
Putting the values
[tex]P = ^7C_4 (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]
[tex]P = \dfrac{7!}{4! \;3!} (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]
P = 0.0128
Therefore the probability is 0.0128.
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What is the solution of
x²-1
2
x2 +5X+4
<0?
Answer:
Step-by-step explanation:
3x+6-2 = 6x-(7/2*9/0)
[tex]3x+6-2 = 6x-( \frac{7}{2} \times \frac{9}{0} ) \\ \\ 3x + 4 = 6x - \frac{63}{0} \\ \\ 3x + 4 = 6x - 0 \\ \\ 4 + 0 = 6x - 3x \\ \\ 3x = 4 \\ \\ x = \frac{4}{3} .[/tex]
The value of x is 4/3 .
Answer: No Solution
Why?
Any number divided by 0 is not defined, but we are given 9/0 in the question. Hence we cannot solve the equation for the value of ‘x’.
Determine algebraically whether the function is even, odd, or neither: f(x)=3x ³ +5
3
cky has a board that is 2 feet long. She needs to cut the board into 11 pieces of equal length. How long
ould each piece be?
0.223 feet
0.25 feet
0.5 feet
0.75 feet
ase select the best answer from the choices provided
A
В
C
D
Answer:
0.223 is the answers for the question but I got this answer 0.181
Step-by-step explanation:
please mark me as brainlest
Which x-value is in the domain of the function f (x) = 4cot(2x) + 3?
0
pi over 3
pi over 2
π
Answer: pi/3
Step-by-step explanation:
All of the other answers are asymptotes of the function, which by definition means they are not included in the domain, because they are undefined in the domain at that point. If you graph the function and graph all of those x values, you will see that (pi/3) is the only line that crosses the function.
Also, I took the test and got it right.
Only the value of x , [tex]\frac{\pi }{3}[/tex] is in the domain of the function.
What is domain of a function?The domain of a function is the set of values that we are allowed to plug into our function which makes the function defined.
What are the trigonometric functions?The trigonometric functions are also called the angle functions, which relates the angles and the ratios of the sides of a right angle triangle.
According to the given question.
We have a trigonomtery function.
[tex]f(x) = 4cot(2x)+3[/tex]
The above trigonometry function can be written as
[tex]f(x) = 4\frac{cos(2x)}{sin(2x)} + 3[/tex]
For the function to be defined the denominator can't be zero.
[tex]sin(2x) \neq 2n\pi ( n \in0, 1, 2, 3, ..)[/tex]
Therefore, from the given values for the x we can only put [tex]\frac{\pi }{3}[/tex] in the given function because [tex]\frac{\pi }{2}[/tex] makes the denominator o which makes the function undefined. Similarly for the π also.
Hence, only the value of x , [tex]\frac{\pi }{3}[/tex] is in the domain of the function.
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The ratio of apples to oranges is 1 to .
For every apples, there are 6 oranges.
For every 4 apples, there are oranges.
Apples are % of the total number of fruits.
meijun had some money. she used 1/3 of it on a watch and 1/9 of it on a gift. the watch and the gift cost $144 altogether. how much money did she have at first?
Answer:
$324
Step-by-step explanation:
let x be the amount of money she had at first , then
[tex]\frac{1}{3}[/tex] x + [tex]\frac{1}{9}[/tex] x = 144 ( multiply through by 9 to clear the fractions )
3x + x = 1296
4x = 1296 ( divide both sides by 4 )
x = 324
she had $324 at first
The function f(x) = x2 + 6x +7 is graphed below.
Drag the correct word and the the appropriate value to the box with each given interval to indicate whether the function is increasing or decreasing on that interval
The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the function f(x) = x² + 6x + 7. This is a quadratic equation,that is of degree two.
The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.
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In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°. Find m∠G. Round your answer to the nearest tenth.
The value of m∠G = 48.6° .
What is a Triangle ?A triangle is a polygon with three sides , angles and vertices.
It is given that
In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°
m∠G = ?
well, using the law of cosines,
GH ² = 9² + 11² - 2(9)(11) cos65°
f = 10.88 ft
now, using the law of sines,
sinG/9 = sin65°/10.88
m∠G = 48.6°
Therefore the value of m∠G = 48.6° .
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A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.1 years, and standard deviation of 0.6 years.
If you randomly purchase one item, what is the probability it will last longer than 2 years?
The probability will last longer than 2 years will be 3.3%.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
First let us calculate the z score using the formula:
[tex]z = \dfrac{(x- \mu)} { s}[/tex]
where x = 2, u is the mean = 3.1 years, and s is the standard deviation
[tex]z =\dfrac{ (2 - 3.1) }{ 0.6}[/tex]
z = -1.83
From the standard probability tables, the p-value at z = -1.83 is:
P = 0.033 = 3.3%
Therefore the probability that will last longer than 2 years will be 3.3%.
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Question 7 (2 points)
In the figure below, AABC and AADF are congruent equilateral triangles. Determine the values of x and y-
X =
B
2x+9
D
y=
A
C
6⁰
5x-12
F
2x + 9 = 5x - 12
2x - 5x = - 1- 9
- 3x = - 21
x = 21/3
x = 7
Y = 60°
find the slope of the line that passes through the points (2,1) and (-7,4)
Answer:
[tex]-\frac13[/tex]
Step-by-step explanation:
Just the slope, so we can simply apply the definition, as variation in y over the variation in x
[tex]m= \frac{\Delta y}{\Delta x} = \frac{1-4}{2-(-7)} = \frac {-3}{9} = -\frac13[/tex]
Answer:
0.222
Step-by-step explanation:
Y2-Y1 ÷ X2-X1
4-2 ÷ -7-2
2÷-9
0.222
If you are given the graph of a line in an xyplane and its corresponding equation, you can be sure that the coordinates of every point on that line will satisfy the equation.
If the graph of a line in an x y plane and its corresponding equation is given then , all the coordinates of every point on that line will satisfy the equation is a true statement.
What is the equation for a straight line ?An equation of a straight line is given by
y = mx+c
where m is the slope and c is the intercept on y axis.
If the graph of a line in an x y plane and its corresponding equation is given then , all the coordinates of every point on that line will satisfy the equation .
Even for a scatter plot the line of the best fit is drawn and every point on the line will satisfy the equation.
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La diferencia de las medidas de dos ángulos suplementarios es 20% determina el complemento del menor de dichos ángulos
Smaller angle = 50
Larger angle = 130
Let smaller angle be x degree
=> larger angle= [tex]3x - 20[/tex]
Since these angles are supplementary , So
[tex]= > x + 3x - 20 = 180\\= > 4x = 200\\= > x = 50\\= > 3x - 20\\ = > 150 - 20 = 130[/tex]
So smaller angle would be 50 deg & larger angle would be 130 deg.
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