After solving by formula the second expression is y = [tex](x^2 + 1)[/tex].
We know that the product of the HCF and LCM of two numbers is equal to the product of the numbers themselves. In this case, we can apply the same principle to expressions:
HCF * LCM = (x + 1) * [tex](x^3+ x^2 - x - 1)[/tex]
the first number is [tex]x^{2} -1\\[/tex] and let the second number is y
Therefore, we can set up the equation:
(x + 1) * [tex](x^3+ x^2 - x - 1)[/tex] = [tex]x^{2} -1\\[/tex] * y
[tex]x^4 + x^3 + x^2 - x^3 - x^2 + x - x - 1 = x^2 - 1 * y[/tex]
Simplifying:
[tex]x^4 - 1 = (x^2 - 1) * y[/tex]
Now, we can divide both sides by [tex](x^2 - 1)[/tex]:
[tex](x^4 - 1) / (x^2 - 1) = y[/tex]
Notice that [tex](x^2 - 1)[/tex]can be factored as (x + 1)(x - 1). Therefore, we can simplify further:
[tex](x^4 - 1) / ((x + 1)(x - 1)) = y[/tex]
The expression [tex](x^4 - 1)[/tex] can be factored using the difference of squares:
[tex](x^4 - 1) = (x^2 + 1)(x^2 - 1)[/tex]
[tex][(x^2 + 1)(x^2 - 1)] / ((x + 1)(x - 1)) = y[/tex]
Now, we can cancel out the common factor [tex](x^2 - 1)[/tex] from the numerator and denominator:
[tex]y =(x^2 + 1)[/tex]
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Solve for x
000 о
10
07
0 5
6x + 8
K
U
N
122°
L
M
194°
The numerical value of x in the minor arc KU of the circle is 7.
What is the numerical value of x?The inscribed angle theorem states that an angle x inscribed in a circle is half of the central angle 2x that subtends the same arc on the circle.
It is expressed as:
Internal angle = 1/2 × ( major arc + minor arc )
From the diagram:
Internal angle = 122 degrees
Major arc = 194 degrees
Minor arc = ( 6x + 8 )
Plug these values into the above formula and solve for x:
Internal angle = 1/2 × ( major arc + minor arc )
122 = 1/2 × ( 194 + ( 6x + 8 ) )
Multiply both sides by 2:
122 × 2 = 2 × 1/2 × ( 194 + ( 6x + 8 ) )
122 × 2 =( 194 + ( 6x + 8 ) )
244 = 194 + 8 + 6x
244 = 202 + 6x
6x = 244 - 202
6x = 42
x = 42/6
x = 7
Therefore, the value of x is 7.
Option B) 7 is the correct answer,
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Answer:
x = - 2 , x = 4
Step-by-step explanation:
the x- intercepts are the points on the x- axis where the graph crosses
the graph crosses the x - axis at - 2 and 4 , then
x- intercepts are x = - 2 , x = 4
Which explains whether or not the graph represents a direct variation?
The graph has a constant of variation of 3, so it represents a direct variation.
The graph has a slope of 3, so it represents a direct variation.
The graph has a positive slope, so it does not represent a direct variation.
O The graph does not begin at the origin, so it does not represent a direct variation.
Save and
0
A normal distribution has a mean of 7 and a standard deviation of 2 . What percent of values are from 7 to 13?
49.87 because I searched it up
1. Replacement value: $270,000; coverage 80%
The insurance policy would cover up to $216,000 for the item or property.
If the replacement value of an item or property is $270,000 and your insurance policy provides coverage for 80% of the replacement value, it means that your insurance policy will cover up to 80% of the $270,000 in the event of a covered loss.
To calculate the coverage amount, you would multiply the replacement value by the coverage percentage:
Coverage Amount = Replacement Value * Coverage Percentage
In this case:
Coverage Amount = $270,000 * 0.80
Coverage Amount = $216,000
Therefore, your insurance policy would cover up to $216,000 for the item or property in question. Any losses exceeding this coverage amount would not be covered by your insurance policy.
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Pls help
Which statement is true?
A. As x increases, the rate of change of f(x) exceeds the rate of change of g(x).
B. As x increases, the rate of change of g(x) exceeds the rate of change of f(x).
C. On every interval of x-values, the average rate of change of g(x) exceeds the average rate of change of f(x).
D. On every interval of x-values,
the average rate of change of f(x) exceeds the average rate of change of g(x).
The statement that is true is as x increases, the rate of change of g(x) exceeds the rate of change of f(x). Option B
How to determine the statementFirst, let us determine the derivatives Let's first of the functions f(x) and g(x) to compare their rates of change:
The functions are given as;
f(x) = 1/50(3)
g(x) = 1/5(x²)
Since the derivative of a constant is zero, f'(x) = 0.
g'(x) = 2/5x
Then, we can say that the rate of change of g(x) increases faster than the rate of change of f(x) as x increases.
The rate of change of g(x) (2/5x) will grow as x increases, while the rate of change of f(x) stays constant.
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Work out the height, y, of the isosceles triangle shown below. Give your answer in metres to 2 d.p. 57° 11.5 m Not drawn accurately
The height of the isosceles triangle is approximately 9.70 meters.
To find the height (y) of an isosceles triangle given its slant height and two angles, we can use trigonometry. Here are the steps to solve this problem:
Start by drawing a sketch of the isosceles triangle. Label the base as "b," the height as "y," and the slant height as "s."
Since the triangle is isosceles, the two base angles are congruent, meaning each angle measures 57 degrees. Label one of these angles as "θ."
We know that the slant height (s) is given as 11.5 m.
Apply the sine function to relate the slant height (s) to the angle (θ) and the height (y) of the triangle. The sine of an angle is defined as the ratio of the opposite side (y) to the hypotenuse (s). So, we have sin(θ) = y/s.
Substitute the given values into the equation: sin(57 degrees) = y/11.5.
Solve the equation for y by multiplying both sides by 11.5: y = 11.5 * sin(57 degrees).
Use a calculator to find the value of sin(57 degrees) and multiply it by 11.5 to obtain the height (y) of the triangle.
Performing the calculation, y = 11.5 * sin(57 degrees) ≈ 9.70 meters (rounded to two decimal places).
Therefore, the height of the isosceles triangle is approximately 9.70 meters.
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at castleton university alex bought three mathematics textbook and four programming textbooks athe same school rick bought eight mathematic textbooks and a single programming textbook of alex spent 854.14 rick spend 1866.39 on textbooks what was the average cost of each book
Answer:
math = 227.98
programming = 42.55
Step-by-step explanation:
Answer:
math = 227.98
programming = 42.55
Step-by-step explanation:
We have
3m + 4p = 854.14 -eq(1)
8m + 1p = 1866.39 -eq(2)
rq(2) x 4: 32m + 4p = 7465.56 -eq(3)
eq(3)-eq(1):
32m + 4p = 7465.56
- ( 3m + 4p = 854.14)
--------------------------------
29m = 6611.42
--------------------------------
⇒ m = 6611.42/29
m = 227.98
sub in eq(1)
3(227.98) + 4p = 854.14
4p = 854.14 - 683.94
4p = 170.2
p = 170.2/4
p = 42.55
What is the range of the rational function
The range of the rational function in this problem is given as follows:
All real values. (fourth option).
How to obtain the domain and range of a function?The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is defined as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.From the graph of the function given by the image presented at the end of the answer, it assumes all values of y, hence the range is all real values.
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Suitable average for averaging the shoe sizes of children is
Select one:
a. Mean
b. Harmonic Mean
c. Geometric Mean
d. Percentile
e. Mode
state the extrema of the given function
Absolute minimum y= ____
x-intercept? ____
Continuous or discontinuous?
PLS HELP YALL I HAVE FINALS TMR AND IM STRESSED!!!
The extreme of the function is Absolute minimum
y = -2
x-intercept = 3
What is a discontinuous function?A discontinuous function is a mathematical function that has one or more points in its domain where the function fails to be continuous.
In other words, at these specific points, the function exhibits a discontinuity, indicating a break or jump in the graph.
In the graph, there was discontinuities at points
x = -2, and x = 2
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Question 1 of 35
Colleen is buying a $279,000 home with a 30-year mortgage at 4.5%. Because
she is not making a down payment, PMI in the amount of $134.25 per month
is required for the first 2 years of the loan. Based on this information, what is
the total cost of this loan?
OA. $475,415
OB. $512,136
OC. $508,914
OD.
$493,776
SUBMIT
Answer:
Step-by-step explanation:
add it then subtract the value
eight hundred twenty nine and six tenths as a decimal
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I can't really see the graph clearly but I think that the x-intercepts should be (-16/7, 0) and (32/7, 0).
Answer:
x-intercepts: -2, 4
Step-by-step explanation:
The given graph shows a parabola that opens downwards.
The y-intercept is the point at which the curve crosses the y-axis, so when x = 0. From inspection of the given graph, we can see that the parabola crosses the y-axis when y = 8. Therefore, the y-intercept is (0, 8).
The x-intercepts are the points at which the curve crosses the x-axis, so when y = 0. From inspection of the given graph, we can see that the parabola crosses the x-axis when x = -2 and x = 4. Therefore, the x-intercepts are (-2, 0) and (4, 0).
Does anybody know the answer i need. It quick!!!!!
The area of the triangle in this problem is given as follows:
34 ft².
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
The parameters for this problem are given as follows:
b = 10 ft, h = 6.8 ft.
Hence the area is given as follows:
A = 0.5 x 10 x 6.8
A = 34 ft².
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Find the measure of the indicated arc
Answer:
80
Step-by-step explanation:
a
35°
8
X
8
12
35⁰
For the two right triangles
above, explain why
X
12. What
trigonometric ratio is equal to
the two given ratios.
X = 4√6 because the tangent of 35 degrees is equal to X/8 in the first right triangle and 12/X in the second right triangle.
We have two right triangles with an angle of 35 degrees and side lengths of 8 units and 12 units.
To explain why X = 12, we can use the trigonometric ratio of tangent (tan). In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
In the first right triangle, the side opposite to the angle of 35 degrees is X, and the adjacent side is 8 units. So, we have:
tan(35 degrees) = X / 8
Similarly, in the second right triangle, the side opposite to the angle of 35 degrees is 12 units, and the adjacent side is X. So, we have:
tan(35 degrees) = 12 / X
Since the tangent of an angle is the same regardless of the orientation of the triangle, we can equate the two ratios:
X / 8 = 12 / X
To solve for X, we can cross-multiply:
X^2 = 8 * 12
X^2 = 96
Taking the square root of both sides, we get:
X = √96
Simplifying, we have:
X = 4√6
Therefore, X is equal to 4 times the square root of 6.
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The row operation on the matrix [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex] is [tex]\left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
How to perform the row operation on the matrixFrom the question, we have the following parameters that can be used in our computation:
[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
The row operation is given as
1/2R₁
This means that we divide the entries on the first row by 2
Using the above as a guide, we have the following:
[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
Hence, the row operation on the matrix is [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
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1. 20x + 14y +6z
2.6x + 2y
3. 1/2(6n - 12m)
Answer:
1. linear equation
2. linear equation
3. algebraic equation
Step-by-step explanation:
1. The expression 20x + 14y + 6z represents a linear equation with three variables: x, y, and z. It consists of three terms: 20x, 14y, and 6z. The coefficients of these terms are 20, 14, and 6 respectively. This equation represents a plane in a three-dimensional coordinate system, where the variables x, y, and z determine the position on the plane.
2. The expression 6x + 2y represents a linear equation with two variables: x and y. It consists of two terms: 6x and 2y. The coefficients of these terms are 6 and 2 respectively. This equation represents a straight line in a two-dimensional coordinate system, where the variables x and y determine the position on the line.
3. The expression 1/2(6n - 12m) represents an algebraic equation with two variables: n and m. It consists of one term: 6n - 12m. The coefficient of this term is 1/2. This equation represents a relationship between the variables n and m, where n and m could be any real numbers.
pls help !!!!!! geometry
Find the circumference and area of a circle with a diameter of 8 feet. Use 3.14 to approximate the value of
as needed. Include units of measure with proper exponents when applicable.
Answer:25.12
Step-by-step explanation:
Use the second equation
C = 8(3.14) = 25.12
Answer:
Area = 50.24 feet²
Circumference = 25.12 feet
Step-by-step explanation:
If the circle's diameter is 8 feet, then the radius will be 4 feet.
A=4²(3.14)
=16(3.14)
=50.24
C=2π(4)
C=8π
C≅25.12
simplify 9 1/2 x 9 1/2 using radical form
answers to choose from are
3, 9, 81 or 6561
Answer:
[tex] \sqrt{9} \sqrt{9} = 9[/tex]
(cosecx+2)(2cosx-1)=0
The solutions to the equation (cosec(x)+2)(2cos(x)-1) are x = -π/6 + 2πn, 7π/6 + 2πn, x = π/3 + 2πn, 5π/3 + 2πn.
To solve the given equation, we can make use of zero-product property. The zero-product property states that if the product of the two factors is equal to zero, then one of the factors has to be equal to zero. So, now we will equate each factor to zero to find the solution.
1. (cosec(x)+2) = 0
= cosec(x) = -2
Taking reciprocal on both the sides:
= 1/cosec(x) = -1/2
= sin(x) = -1/2
The solutions for sin(x) = -1/2 occur when x = -π/6 + 2πn and 7π/6 + 2πn, where 'n' is an integer.
2. (2cos(x)-1) = 0
= 2cos(x) = 1
= cos(x) = 1/2
The solutions for cos(x) = 1/2 occur when x = π/3 + 2πn and 5π/3 + 2πn, where 'n' is an integer.
Therefore, the solutions to the equation (cosec(x)+2)(2cos(x)-1) are x = -π/6 + 2πn, 7π/6 + 2πn, x = π/3 + 2πn, 5π/3 + 2πn.
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The complete question is: Find out the possible solutions of the equation (cosecx+2)(2cosx-1)=0.
Select the correct answer. Which function represents the inverse function of the function f(x)=x^2 +5
Answer:
f^(-1)(x) = ±√(x - 5).
Step-by-step explanation:
Replace f(x) with y: y = x^2 + 5.
Swap the x and y variables: x = y^2 + 5.
Solve the equation for y. To do this, we'll rearrange the equation:
x - 5 = y^2.
Take the square root of both sides (considering both positive and negative square roots):
±√(x - 5) = y.
Swap y and x again to express the inverse function:
f^(-1)(x) = ±√(x - 5).
David sold mugs at a crafts show. On the first day, he sold 10 mugs but lost $ 5.40 on each mug. On the second day, he raised his price and sold 7 mugs with a profit of $ 5.00 on each mug. What was his total profit or loss? Write a profit as a positive number and a loss as a negative number.
Answer:
Davis has a loss of $19
i.e -19
Step-by-step explanation:
On day 1, David lost 5.4 * 10 = $54
On day 2, David gained 5 * 7 = $35
Overall, his loss is greater than the profit
Total loss is $54 - $35 = $19
Pamela is buying a $242,000 home with a 30-year mortgage. She will make
an 8% down payment. Use the table below to find her monthly PMI payment.
Base-To-Loan %
95.01% to 97%
90.01% to 95%
85.01% to 90%
85% and Under
OA. $96.48
OB. $144.72
OC. $157.30
OD. $151.01
Fixed-Rate Loan
30 yrs. 15 yrs.
0.90% 0.79%
0.78% 0.26%
0.52% 0.23%
0.32% 0.19%
ARM 2% +1 Year Cap
30 yrs.
15 yrs.
n/a
0.92% 0.81%
0.65%
n/a
0.37%
0.54%
0.26%
15. AB2+ BC2 = AC²
O A.
OB.
O C.
OD.
2 BDC = LADB
LBCA
DCB
2 BAC = LBAD
2 DBC = LBAC
multipl
Rese
Answer:
Step-by-step explanation:
"Valeria and her family play the board game Parrots and Pirates on game night. Players who land on a cannon space roll a 6-sided weighted penalty die to determine how many gold doubloons they will lose. To see how the die is weighted, Valeria rolls it 15 times and records the results. Based on the data, what is the probability of rolling a 6 with this die.
The probability of rolling a 6 with this die would be = 1/15.
How determine the outcome of the given event?To determine the possibility of the given event, the formula for probability should be used and it's given below as follows:
Probability= Possible outcome/sample space
where;
possible outcome= 1
sample space= 15
Probability = 1/15
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Find measure of angle HFJ
Look at picture for reference
The measure of angle HFJ in the right triangle JFH is 43 degrees.
What is the measure of angle HFJ?In the right triangle FGJ, first, we determine the hypotenuse FJ.
Angle GFJ = 43 degrees
Opposite of angle GFJ = 6
Hypotenuse FJ = ?
Using the trigonometric ratio, we can find the hypotenuse FJ:
sine = opposite / hypotenuse
sin( 43 ) = 6 / FJ
FJ = 6 / sin( 43 )
FJ = 8.7977
Now, we can find angle HFJ,
Angle HFJ = ?
opposite = 6
Hypotenuse FJ = 8.7977
Using the trigonometric ratio:
sin ( HFJ ) = 6 / 8.7977
sin ( HFJ ) = 6 / 8.7977
HFJ = sin⁻¹( 6 / 8.7977 )
HFJ = 43°
Therefore, angle HFJ measure 43 degrees.
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Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 29, 31, 49, 37, 26, 28. Use a 0.025 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?
The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.
To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.
Step 1: Set up hypotheses
H₀: The outcomes of the die are equally likely.
H₁: The outcomes of the die are not equally likely.
Step 2: Select the significance level
The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.
Step 3: Compute the test statistic
We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.
Expected frequencies (fair die):
1: 200/6 = 33.33
2: 200/6 = 33.33
3: 200/6 = 33.33
4: 200/6 = 33.33
5: 200/6 = 33.33
6: 200/6 = 33.33
Applying the chi-square formula, we get the test statistic:
χ² = ∑((observed - expected)² / expected)
Calculating this value, we get χ² ≈ 13.97.
Step 4: Determine the critical value
Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.
Step 5: Make a decision
The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.
The loaded die appears to behave differently from a fair die.
In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.
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