Answer:
The answer is 123.
Step-by-step explanation:
Given that-
( [tex]x + \frac{1}{x}[/tex] ) = 3.....................(i)
To find -
( [tex]x^{5} + \frac{1 }{x^{5} }[/tex] ) = ?
Now squaring both sides of equation (i)-
( [tex]x^{2} + \frac{1}{x^{2} } + 2[/tex] ) = 9
( [tex]x^{2} + \frac{1}{x^{2} }[/tex] ) = 7....................(ii)
On cubing equation (i) both sides-
( [tex]x^{3} + \frac{1}{x^{3} } + 3 ( x + \frac{1}{x} )[/tex] ) = 27
( [tex]x^{3} + \frac{1}{x^{3} } + 3 * 3[/tex] ) = 27
( [tex]x^{3} + \frac{1}{x^{3} }[/tex] ) = 27 - 9
( [tex]x^{3} + \frac{1}{x^{3} }[/tex] ) = 18.....................(iii)
Multiply equation (i) and equation (ii)-
( [tex]x^{2} + \frac{1}{x^{2} }[/tex] ) ( [tex]x^{3} + \frac{1}{x^{3} }[/tex] ) = 7 × 18
( [tex]x^{5} + \frac{1}{x^{5} } )+ ( x + \frac{1}{x} )[/tex] = 126
( [tex]x^{5} + \frac{1}{x^{5} } ) = 126 - 3
( [tex]x^{5} + \frac{1}{x^{5} } ) = 123
A 20-ft-long wire is used to support a television antaans. The wire is connected to the
antenna 15 ft above the ground. How far away from the base of the tower will the other
end of the wire be located?
Answer:
The distance of base of wire to the base of tower is 13.27 ft
Step-by-step explanation:
Given as :
The measure of wire connected between base ad antenna top = 20 ft
The wire is connected to the antenna on tower at height h = 15 ft above the ground
Let The distance of base of wire to the base of tower = x ft
Let the angle drawn on ground = Ф
Now, According to question
In figure AOB
Sin angle = [tex]\dfrac{\textrm perpendicular}{\textrm hypotenuse}[/tex]
i.e SinФ = [tex]\dfrac{\textrm AB}{\textrm BO}[/tex]
Or, SinФ = [tex]\dfrac{\textrm h}{\textrm 20}[/tex]
Or, SinФ = [tex]\dfrac{\textrm 15}{\textrm 20}[/tex]
Or, SinФ = [tex]\dfrac{\textrm 3}{\textrm 4}[/tex]
or, Ф = [tex]sin^{-1}(\frac{3}{4})[/tex]
∴ Ф = 48.5°
Now, Again from figure
Tan angle = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]
i.e TanФ = [tex]\dfrac{\textrm AB}{\textrm OA}[/tex]
Or, Tan 48.5° = [tex]\dfrac{\textrm h}{\textrm x}[/tex]
Or, 1.13 = [tex]\dfrac{\textrm 15}{\textrm x}[/tex]
∴ x = [tex]\dfrac{\textrm 15}{\textrm 1.13}[/tex]
i.e x = 13.27 feet
So, The distance of base of wire to the base of tower = x = 13.27 ft
Hence, The distance of base of wire to the base of tower is 13.27 ft Answer
Final answer:
The other end of the wire will be located approximately √175 ft away from the base of the tower.
Explanation:
To find the distance from the base of the tower to the other end of the wire, we can use the Pythagorean theorem. The wire forms the hypotenuse of a right triangle, with one leg being the height of the antenna and the other leg being the distance from the base of the tower. Let's call this distance 'x'.
Using the Pythagorean theorem, we have:
x² + 15² = 20²
Simplifying this equation, we get:
x² = 20² - 15²
x² = 400 - 225
x² = 175
Taking the square root of both sides, we find:
x = √175
So the other end of the wire will be located approximately √175 ft away from the base of the tower.
what is the answer to this
Answer:
-81
Step-by-step explanation:
Answer:
1/81
Step-by-step explanation:
20% tip on a bill of 86.74
Answer:
$17.35
Step-by-step explanation:
86.74*.2
Put y=-2x+4 in a graph
Answer:
Step-by-step explanation:
construct the graph with the following points.
x=0
y= -2(0)+4
y= 4
(0,4)
x=2
y=-2(2)+4
y=0
(2,0)
join these two points with a straight line.
feel free to ask any questions
what is (-x+3)-(x-5)
Answer:
-2x+8
Step-by-step explanation:
Juan bought
two new tires for his bike. He also had the bike
tuned up. The total bill was $65. How much did
Juan spend on the 2 tires?
Answer:
$32.50
Step-by-step explanation:
Just divide $65 by 2 and you get $32.5(0).
Juan spent $32.50 on the 2 tires.
You are very welcome!
The cost of two tires = 65 - cots of tuned up.
And we need the cost of two tires.
What is subtraction?Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.
Given:
Juan bought two new tires for his bike.
He also had the bike tuned up.
The total bill was $65.
To find the cost of two tires:
The cost of two tires = 65 - cots of tuned up.
Therefore, we need the value of missing information.
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The complete question:
Draw a Conclusion: Juan bought two new tires for his bike. He also had the bikec tuned up. The total bill was $65. How much did Juan spend on the 2 tires?
Which system of linear inequalities has the point (2, 1) in its solution set?
y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded.
y less-than negative one-half x + 3. y less-than one-half x. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded.
y less-than-or-equal-to negative x + 3. y less-than-or-equal-to one-half x + 2 On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded.
y less-than one-half x. y less-than-or-equal-to negative one-half x + 2 On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 2) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 4, negative 2) and (0, 0). Everything below the line is shaded.
Answer:Its C
Step-by-step explanation:
ED 2023
The correct answer is provided by the third system.
To determine which system of linear inequalities includes the point (2, 1), we need to substitute this point into each inequality and check if the inequalities hold true. Let's evaluate each system step-by-step:
System 1
y < -x + 3y [tex]\leq[/tex] 0.5x + 3Evaluating at (2, 1):
1 < -2 + 3 → 1 < 1 (False)1 ≤ 0.5(2) + 3 → 1 ≤ 4 (True)The point (2, 1) does not satisfy the first inequality, so it is not in the solution set for the first system.
System 2
y < -0.5x + 3y < 0.5xEvaluating at (2, 1):
[tex]1 < -0.5(2) + 3 \rightarrow 1 < 2[/tex] (True)[tex]1 < 0.5(2) →\rightarrow 1 < 1[/tex] (False)The point (2, 1) does not satisfy the second inequality, so it is not in the solution set for this system either.
System 3
y [tex]\leq[/tex] -x + 3y [tex]\leq[/tex] 0.5x + 2Evaluating at (2, 1):
[tex]1 \leq -2 + 3 \rightarrow 1 \leq 1[/tex] (True)[tex]1 \leq 0.5(2) + 2 \rightarrow 1 \leq 3[/tex] (True)The point (2, 1) satisfies both inequalities, so it is in the solution set for the third system.
System 4
y < 0.5xy [tex]\leq[/tex] -0.5x + 2Evaluating at (2, 1):
[tex]1 < 0.5(2) \rightarrow 1 < 1[/tex](False)[tex]1 \leq -0.5(2) + 2 \rightarrow 1 \leq 1[/tex] (True)The point (2, 1) does not satisfy the first inequality, so it is not in the solution set for the fourth system.
The system of linear inequalities that includes the point (2, 1) is the third one: y [tex]\leq[/tex] -x + 3, and y [tex]\leq[/tex] 0.5x + 2.
Jaime drove from all groceries food store to get rich savings bank and then to AAA hardware. How far did Jaime drive?
Answer:
Jaime drove for 6.127 miles.
Step-by-step explanation:
See the attached diagram.
The length from All Groceries Food store to Get Rich Savings bank along Flower street is x miles (say) and the length from Get Rich Savings bank to AAA hardware along the Broad street is 4 miles.
Since, the Flower street and Broad street are perpendicular to each other, hence,
[tex]\tan 28 = \frac{x}{4}[/tex]
⇒ x = 4 tan 28 = 2.127 miles.
Therefore, Jaime drove for (4 + 2.127) = 6.127 miles ≈ 6.1 miles. (Answer)
Rewrite the function by completing the square.
h(x)= x^2+3x-18
Answer:
Step-by-step explanation:
Simplifying
h(x) = x2 + 3x + -18
Multiply h * x
hx = x2 + 3x + -18
Reorder the terms:
hx = -18 + 3x + x2
Solving
hx = -18 + 3x + x2
Solving for variable 'h'.
Move all terms containing h to the left, all other terms to the right.
Divide each side by 'x'.
h = -18x-1 + 3 + x
Simplifying
h = -18x-1 + 3 + x
Reorder the terms:
h = 3 + -18x-1 + x
Answer:
h(x)= (x+3/2 ) ^2 − 81/4
Step-by-step explanation:
Its correct :)
There are 12 female students and 18 male students in a class. Which of the following expresses the ratio of female students to male students in simplest form?
A.3/2
B.3 to 2
C.2/3
D.3:2
Answer:
C. 2/3
Step-by-step explanation:
12 female / 18 male
Dividing by 6 we get:
2 female / 3 male
or 2/3
Answer:
C.2/3
Step-by-step explanation:
In forensic anthropology, the length of the femur bone (the thigh bone) in the skeleton is used to estimate the height of the person when he or she was alive. The height of a person is estimated to be 4 times the length of the femur.22
(a)If the femur bone on a female skeleton measures 15.5 inches, approximately how tall was the
woman?
(b) If the femur bone on a male skeleton measures 17 inches, approximately how tall was the
man?
(C) Write an equation for the height, H. of a person with femur bone of length b.
(d) Graph the equation H with height on the y-axis and bone length on the z-axis. Your graph
should include heights up to 80 inches.
(e) What is the slope of your line? What does it mean in this context?
(f) Use your equation or the graph to estimate the length of your own femur bone. (Be sure to
indicate your height and how you figured out your estimated femur bone length.)
What are the 3 author's purposes?
Answer:
To persuade, inform and entertain.
Step-by-step explanation:
You can remember it as PIE, if that helps!
3/4n + 7 = 28 − n =
I need help ASAP please!
Which is the MOST REASONABLE approach for the company to take to lessen the number of latecomers to work?
A) Relocate the company to an area with less traffic.
B) Deduct the lost time for any reason from vacation time.
C) Delay the start time of work days when there is bad weather.
D) Implement better procedures at the security gate.
Answer:
D) Implement better procedures at the security gate.
Step-by-step explanation:
suppose you order two pizzas, 2 garlic breads, and one order of barbecue wings. how much change would you receive from $30?
Answer:
$6
The drawings will help
Mike had 2/3 of a cake. He cut 3/4 of the cake to wrap and store in the freezer.
He ate the remaining portion
How much of the cake did he eat
A. 3/4
B. 1/4
C. 1/2
D. 1/8
E. 1/6
E
The portion of cake Mike ate is 1/6.
The numbers given are expressed as fractions. Fractions are numbers that consist of numerators and denominators. For example, in the fraction 2/3, 2 is the numerator and 3 is the denominator.
The first step is to determine which portion of the cake that was stored in the freezer.
Portion kept in the freezer = 2/3 x 3/4 = 1/2
The second step is to determine the amount of cake Mike ate.
2/3 - 1/2
[tex]\frac{4 - 3}{6}[/tex] = [tex]\frac{1}{6}[/tex]
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The portion of the cake that Mike ate is [tex]\frac{1}{6}[/tex].
The given parameters:
Original fraction of cake Mike possessed = 2/3Fraction of the cake Mike stored = 3/4The portion of the cake that Mike wrapped and stored in the freezer is calculated as follows;
[tex]= \frac{3}{4} \times \frac{2}{3} \\\\= \frac{1}{2}[/tex]
The portion of the cake that Mike ate is calculated as follows;
[tex]remaining = original - portion \ stored\\\\remaining = \frac{2}{3} - \frac{1}{2} = \frac{4 - 3}{6} = \frac{1}{6}[/tex]
Thus, the portion of the cake that Mike ate is [tex]\frac{1}{6}[/tex].
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all numbers are divisible by
Answer:
one
Step-by-step explanation:
Answer:
All numbers are divisible by 1
Step-by-step explanation:
Which graph represents the function
-10 -3 -6 -4 -
I
4
6
8
10
x
1
0
-10
There are no illustrations, so it is impossible to answer this question. I apologise.
Find the area of the shape.
Either enter an exact answer in terms of
π
πpi or use
3.14
3.143, point, 14 for
π
πpi and enter your answer as a decimal.
Okay I will just keep it in terms of pi to make it more pretty.
area = 1/4π(8²) = 16π
answer: 16π
Answer : The area of the shape is, 50.24 unit square.
Step-by-step explanation :
To calculate the the area of shaded sector in the circle in degree, the formula used as:
[tex]A=\frac{\theta}{360}\times \pi r^2[/tex]
where,
A = area of sector
[tex]\theta[/tex] = angle = 90°
r = radius of circle = 8 unit
Now put all the given values in the above formula, we get:
[tex]A=\frac{90}{360}\times 3.14\times (8)^2[/tex]
[tex]A=50.24[/tex]
Therefore, the area of the shape is, 50.24 unit square.
I need the quadratic formula.
Answer:
ax^2+bx+c=0
Step-by-step explanation:
hope this helps
Answer:
[see picture]
Step-by-step explanation:
The formula shown in the picture is the quadratic formula.
When:
[tex]ax^2+bx+c=0[/tex]
a, b, c ≠ 0
x = unknown
A person kicks a 4.0-kilogram door with a 48-newton force causing the door to accelerate at 12 meters per second 2 . What is the magnitude of the force exerted by the door on the person? A. 48 N B. 24 N C. 12 N D. 4.0 N
According to Newton's Third Law of Motion, the force exerted by the door on the person who kicks it, is equal and opposite to the force the person exerts on the door, i.e., 48 Newtons.
Explanation:The question asks about the force exerted by a door on a person if the person kicks the door with a certain force. This scenario illustrates Newton's Third Law of Motion, which states: 'For every action, there is an equal and opposite reaction.' So, if the person exerts a force of 48 Newtons on the door, then the door will exert an equal and opposite force of 48 Newtons on the person. Therefore, the answer is A. 48 N.
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help plz ASAP graph the solution to the inequality on the number line : q < 69.5
Answer:
Step-by-step explanation:
Remember:
If something is:
-equal to a number
-equal to or less then a number
-euqal to or greater than a number
Then you you would use a closed mark with an arrow.
Note: Don't use the arrow for the "equal to" part
If something is greater/less than a number:
Then you would use an open mark with an arrow
So since you're using the inequality q < 69.5,
You would graph it with an open mark with a left arrow, and the open mark must be on the number 69.5
The graph the solution to the given inequality on the number line plotted below.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is q < 69.5.
The result can be shown in multiple forms.
Inequality Form:q<69.5
Interval Notation:(−∞,69.5)
Therefore, the graph the solution to the given inequality on the number line plotted below.
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Evaluate the function rule for the given value.
y = 6.4x for x = -3
Answer:
y=-19.2
Step-by-step explanation:
6.4(-3)=-19.2
A square pyramid is 6 feet on each side. The height of the pyramid is 6 feet. What is the total area of the pyramid?
(1215 +36)
(3675 +36) 2
1725 +36)
7252
Answer:
The Area of square pyramid is 36 + 36[tex]\sqrt{5}[/tex] .
Step-by-step explanation:
Given as :
For A square pyramid
The measure of each base side = b = 6 feet
The height of the pyramid = h = 6 feet
Let The Total area of pyramid = A square feet
Now, According to question
The area of square pyramid
Area = b² + 2 × b [tex]\sqrt{\frac{b^{2} }{4}+h^{2} }[/tex]
Where b is the square base edge
And h is the pyramid height
I.e A = 6² + 2 × 6 [tex]\sqrt{\frac{6^{2} }{4}+6^{2} }[/tex]
Or, A = 36 + 12 × [tex]\sqrt{\frac{36 }{4}+36 }[/tex]
Or, A = 36 + 12 × [tex]\sqrt{9+36}[/tex]
Or, A = 36 + 12 × [tex]\sqrt{45}[/tex]
Or, A = 36 + 12 × 3[tex]\sqrt{5}[/tex]
Or, A = 36 + 36[tex]\sqrt{5}[/tex]
So,The Area of square pyramid = A = 36 + 36[tex]\sqrt{5}[/tex]
Hence, The Area of square pyramid is 36 + 36[tex]\sqrt{5}[/tex] . Answer
What is the chemical formula for the molecule modeled?
A) CHO
B) C4H11O2
C) C6H12O2
D) C6H9O
Answer: C
Step-by-step explanation:
The molecule modeled is [tex]CH_3-CH_3-C-CH_3-CH_2-COOH[/tex] or [tex]{\text} C_6H_{12}O_6[/tex].
Thus, option (C) is correct.
A chemical formula is a concise representation of the composition of a chemical compound. It uses symbols and subscripts to denote the types and numbers of atoms present in the compound.
Chemical formulas are used to describe the ratio of elements in a compound and give valuable information about its constituents.
In the given compound,
Number of Hydrogen = 12
Number of Carbon= 6
Number of Oxygen = 2
Also, there is Carboxylic function group in chain "COOH".
Therefore, the compound name is [tex]CH_3-CH_3-C-CH_3-CH_2-COOH[/tex] or [tex]{\text} C_6H_{12}O_6[/tex].
Thus, option (C) is correct.
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In the expression ax+bx,a is a decimal and b is a fraction. How do you decide whether to write a as a fraction or b as a decimal?
To decide whether to write a as a fraction or b as a decimal in the expression ax+bx, consider the context of the problem. If dealing with measurements or real-life quantities, write a as a decimal. If dealing with parts of a whole or ratios, write b as a fraction.
Explanation:In the expression ax+bx, a is a decimal and b is a fraction. To decide whether to write a as a fraction or b as a decimal, you can consider the context of the problem or the specific instructions. If the problem involves measurements or real-life quantities, it is more appropriate to write a as a decimal. On the other hand, if the problem deals with parts of a whole or ratios, it is more appropriate to write b as a fraction.
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Whether you write 'a' as a fraction or 'b' as a decimal in the expression ax+bx depends on the context of the problem you're solving. 'a' can be converted to a fraction by expressing the decimal in fractional terms, whereas 'b' can be turned into a decimal by dividing the numerator by the denominator.
Explanation:In the expression ax+bx, where 'a' is a decimal and 'b' is a fraction, deciding whether to write 'a' as a fraction or 'b' as a decimal depends largely on the problem you're solving and what format is most convenient or understandable. To convert 'a' from a decimal to a fraction, you can write the decimal in fractional form. If the denominator is not 100, convert it to a fraction with a denominator of 100, which then allows you to present it as a percentage. On the other hand, to convert 'b' from a fraction to a decimal, you can simply divide the numerator of the fraction by the denominator.
A practical example could be if a=0.5 and b=3/4 in the expression. Here, you can write 'a' as 1/2 (a fraction) and 'b' as 0.75 (a decimal). Therefore, the expression becomes 1/2x + 0.75x.
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Simplify by combining like terms.
3(-2y-9)-2y
Answer: -8y-27
Step-by-step explanation: Simplify the expression.
Hope this helps you out.
Answer:
-8y-27.
Step-by-step explanation:
3(-2y-9)-2y
= 3*-2y+3*-9 -2y
= -6y-27-2y
= -8y-27.
Use the distributive property to write an equivalent expresión to 4(6x+5)
Answer: 6(4x + 5)
Step-by-step explanation: 4(6x + 5) 24x + 20
What would you earn in total commissions on the following sales of $5100 $4876 $5215 $6225 and $5235 if you if you earn a commission rate of 1.5%
Answer:
$5100 would be $76.50
$4876 would be $73.14
$5215 would be $78.23
$6225 would be $93.38
$5235 would be $78.53
Step-by-step explanation:
To find commissions take your sale price and multiply it by your percentage and divide by 100
Answer: $399.77
Step-by-step explanation:
5/4 square yards in 1/3 of an hour what is the unit rate
Answer:
[tex]3\frac{3}{4}\ \frac{yd^2}{h}[/tex]
or
[tex]3.75\ \frac{yd^2}{h}[/tex]
Step-by-step explanation:
we know that
To find out the unit rate, divide the total square yards by the total time in hours
so
[tex]\frac{(5/4)}{(1/3)}=\frac{15}{4}\ \frac{yd^2}{h}[/tex]
Convert to mixed number
[tex]\frac{15}{4}\ \frac{yd^2}{h}=\frac{12}{4}+\frac{3}{4}=3\frac{3}{4}\ \frac{yd^2}{h}[/tex]
or
[tex]3.75\ \frac{yd^2}{h}[/tex]