Answers
1.
(a) 2π - 9
= 2 x 3.142 - 9 = 6.284 - 9
= -2.716
This will be closest to the letter C on the number line.
(b) [tex]\sqrt{3}[/tex]
= 1.732
This will be closest to the letter T on the number line.
(c) [tex]\sqrt[3]{9}[/tex] - 8
= 3-8
= -5
This will be closest to the letter S on the number line.
What are Real numbers?In the number system, real numbers are only the fusion of rational and irrational numbers. These numbers can generally be used for all arithmetic operations and can also be expressed on a number line. Imaginary numbers, which are often known as unreal numbers since they cannot be stated on a number line, are frequently used to symbolize complex numbers. Real numbers include things like 23, -12, 6.99, 5/2, and so on.Most physical constants, like the universal gravitational constant, and physical variables, including position, mass, speed, and electric charge, are represented using real numbers in the physical sciences.Although the Zermelo-Fraenkel axiomatization of set theory is the method most frequently used to formalize the real numbers, other mathematicians also explore the real numbers using other logical mathematical foundations. Electronic calculators and computers, with a few notable exceptions, do not work with real numbers. Instead, they frequently use floating-point numbers, which are finite-precision approximations that resemble scientific notation.To learn more about Real numbers, refer to:
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Related Questions
Which of the following is a polynomial?
(a) 2−6√+2 (b) 52−3+1
(c)√+1√ (d) None of these
Answers
The true statement about the expressions is (d) None of these
What are polynomial expressions?Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the polynomial expression?From the list of options, the given parameters are
(a) 2 − √6 + 2 (b) 52 − 3 + 1 (c)√1
For an expression to be a polynomial, the expression must have variables, coefficients and operators
None of the given expressions have variables, coefficients and operators.
This means that the expressions are not polynomial
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Question 1)
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles ..
♦ Note:
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Answers
Answer:
The height of pole is 20√3 m each and distance of pole from the point on road is 60 m and 20 m respectively.
Step-by-step explanation:
Given:
Two poles of equal heights are standing on opposite side of the road which is 80 m wide facing each other. From a point on the road the angle of elevation of poles are 60° and 30° respectively.To Find:
The height of poles and the distance of that point on the road from the pole.Formula used:
tan60° = √3 tan30° = 1/√3Let the height of each pole be H metres.
Also, let's assume that distance of the point from one pole (as shown in figure) be x m.
According to question, we have
tan60° = H/(80-x)
H = (80-x)√3.... (1)
Also, tan30° = H/x
H = x/√3... (2)
Putting value of eq(2) in eq(1), we get
x/√3 = (80-x)√3
x = 3(80-x)
x = 240 - 3x
4x = 240
x = 60 m
Putting value of x in eq(2), we get
H = 60/√3 = 20√3 m
So, the height of pole is 20√3 m each and distance of pole from the point on road is 60 m and 20 m respectively.
Answer:
Height of Pole: 20√3 m
Distance Of Point From Poles: 20m and 60m
Step-by-step explanation:
The attached graph may help you understand my explanation better
The two poles are Ab and CD and are 80m apart
O is the point between them
The angle of elevation from O to A is 60°
The angle of elevation from O to D is 30°
Since the two poles are given to be of equal height,
AB = CD
In ΔAOB using the law of tangents
tan 60° = AB/BO
tan 60° = √3 and AB = x
So we get
√3 = x/BO
Multiplying both sides by BO we get
√3 · BO = x
or BO = x/√3
Looking at ΔCOD
tan 30° = DC/OC
tan 30° = 1/√3
1/√3 = x/OC
OC · ( 1/√3) = x
OC = x ÷ 1/√3
= x · √3/1
OC = √3x
We also know that BO + OC = 80
Plugging this information with values computed gives us
x/√3 + √3x = 80
Multiply by √3 on both sides
(x/√3) · √3 + (√3x) √3 = 80√3
(x/√3) · √3 = x since the √3 terms cancel out
(√3x) √3 = 3x
So we get
(x/√3) · √3 + (√3x) √3 = 80√3
=>
x + 3x = 80√3
4x = 80√3
x = (80√3)/4
x =20√ 3
So the height of each pole = 20√ 3 m ≈ 34.64 m
The distance OC can be found from the previous equation
OC = √3x
=> OC = √3 x 20√3 = 20 x 3 = 60m
Since BO + OC = 80 m
BO = 80 - 60 = 20 m
Answer:
Height of each pole = 20√3 m
The point is located 20 m from one pole and 60 m from the other pole
f(x) = 4x^5 - x g(x) = x^3 – 2 (f / g)(x) =
Answers
The value of the function (f/g)(x) when f(x) = 4x^5 - x and g(x) = x^3 – 2 is
(f/g)(x) = (4x⁵- x)/(x³- 2)
Functions - It is defined as expressions, rules or laws that explains the relationship between two variables.
These variables are
Independent variableDependent variablesIt is important to note that composite functions are determined when the output of a given function is used as the input of another or different variable.
Given the functions;
f(x) = 4x^5 - x
and
g(x) = x^3 – 2
(f/g)(x) = f (x) / g(x)
(4x⁵- x)/(x³- 2)
The value of the function (f/g)(x) when f(x) = 4x^5 - x and g(x) = x^3 – 2 is
(f/g)(x) = (4x⁵- x)/(x³- 2)
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James is solving a number puzzple that involves three integers, a,b, and c, where, c is a positive integer.The product of a and b is 6.The product of a and c is -4.The product of b and cis -6.
Answers
Answer:
a = -2
b = -3
c = 2
Step-by-step explanation:
a*b = 6 {The product of a and b is 6]
a*c = -4 [The product of a and c is -4]
b*c = -6 [The product of b and c is -6]
- Rearrange:
1) a*c = -4 to a = (-4/c)
2) b*c = -6 to b = (-6/c)
Now substitute:
a*b = 6
(-4/c)*(-6/c) = 6
(24/c^2) = 6
c^2 = (24/6)
c^2 = 4
c = 2
use this value of c to find a and b:
a = (-4/c)
a = (-4/2)
a = -2
b = (-6/c)
b = (-6/2)
b = -3
For the four-digit number: 3040, what
must the value of the be so that
this four-digit number is divisible by
5?
Answers
The value which the four digit number is divisible by 5 is 608
What is Divisibility?
By looking at the digits of an integer, a divisibility rule can be used to quickly and conveniently determine if it can be divided by a specific number.
The given four-digit number is divisible by 5:
3040
To find the value from which the four digit number is divisible by 5
3040 ÷ 5
= 3040/5
= 608
Hence, The value of the be so that this four-digit number is divisible by 5 is 608
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2. How many subsets with 3 elements of the set
A = {a, b, c, d, e} contain a?
A) 6
B) 8
C) 10
D) 15
E) 20
Answers
Answer:
They are 6 sunsets
Step-by-step explanation:
the sets are
(abc),(abd),(ade),(acd),(ace),(ade)
For each pair of images, describe which of these transformations are translation, reflection, or rotation.
Answers
Answer:
A is translation because it's being moved to the right to get a'b'
b is reflection because you would reflect over the x-axis \
C is rotation
Picture A represents the translation, the picture represents the reflection, and picture C represents the rotation.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The lines are shown in the picture.
As we know from the definition of the geometric transformation, geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
From the picture,
Picture A, which is being moved to the right to obtain A'B', serves as a representation of the translation.
Because you would reflect over the x-axis, Picture A represents reflection.
Image A illustrates rotation.
Thus, picture A represents the translation, the picture represents the reflection, and picture C represents the rotation.
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0.4% as a decimal
ITS DUE AT MIDNIGHT
Answers
Answer: 0.004
Step-by-step explanation:
Several years ago, Melissa bought some gold at a price of $1,430 per ounce. When she
went to sell it, the gold was worth 30% more than it was when she purchased it. What
was the new value of the gold?
Answers
The new value of gold was $1859 per ounce.
How to calculate profit amount?
Finding profit is simple using this formula: Total Revenue - Total Expenses = Profit.
Price in which Melissa bought gold per ounce = $1,430
Given that, Melissa sell it when the gold price is 30% more than when she purchased it.
Price in which Melissa sell gold per ounce = $ 1,430 + 1,430×30%
= $ 1,430 + 1,430×[tex]\frac{30}{100}[/tex]
= $ 1,430 + 429
= $ 1,859
Hence, the new value of gold was $1859 per ounce.
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Answer in graph form. Find <0 if sin0= 7/10 and cot0 is positive.
Answers
Sin(0)=-7/10
To get the right triangle's known sides, use the sine definition. Each value's sign is determined by the quadrant.
sin(0)=opposite/hypotenuse
Find the triangle formed by the unit circle's neighboring side. Use the Pythagorean theorem to determine the remaining side since the hypotenuse and opposite sides are known.
Adjacent=√hypotenuse²−opposite²
Change the equation's known values with new ones.
Adjacent=√(10)²−(7)²
Inside the radical, simplify.
Raise10the strength of2.
Adjacent=√100−(7)²
Raise−7the strength of2.
Adjacent=√100-49
Multiply −1 by 49.
Adjacent=√100−49
Subtract49 from 100.
Adjacent=√51
Find the cosine value.
Find the value of using the cosine definition.
cos(0).
cos(0)=adj/hyp
Replace with the known values.
cos(0)=√51/10.
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To get the right triangle's known sides, use the sine definition. The quadrant determines each value's sign.
The value of cos(0) exists √51/10.
What is meant by trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous unique trigonometric identities that relate a triangle's side length and angle.
To get the right triangle's known sides, use the sine definition. The quadrant determines each value's sign.
sin(0) = opposite/hypotenuse
To find the triangle formed by the unit circle's neighboring side. Use the Pythagorean theorem to determine the remaining side since the hypotenuse and opposite sides are known.
Adjacent = √hypotenuse² − opposite²
substitute the values in the above equation, we get
Adjacent = √(10)² − (7)²
Adjacent = √100 - 49
simplifying the above equation, we get
Adjacent = √51
To find the cosine value.
cos(0) = adjacent/hypotenuse
Replace with the known values.
cos(0) = √51/10.
Therefore, the value of cos(0) = √51/10.
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Round the number shown on the calculator to 1 decimal place (1 d.p.).
Answers
Answer:
Step-by-step explanation:
As you see the picture the number is 1.249
step 1
As you know before decimal the digits are said to be ones,tens, hundred so on and starts from left to right.
But after decimal it goes right to left and they are said ones,tenth,hundredth
step 2
so here it says 1 decimal place means ones means one digit after dot or point so its 2
The number rounded off to 1 decimal place is 1.2
what is rounding off a decimal number?Rounding is a process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up. Rounding decimals refer to the rounding of decimal numbers to a certain degree of accuracy.
Given here, the number is 1.249 and thus the number rounded upto 2 decimal place is 1.25 and further rounding up the number to one decimal place we get 1.2
Hence, the number rounded upto one decimal place is 1.2
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Houa took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.20 plus $1.25 per mile. The total fare was $29.95, not including the tip. Which equation or tape diagram could be used to represent the context if x represents the number of miles in the taxi ride?
Answers
The equation or tape diagram could be used to represent the context if x represents the number of miles in the taxi ride is A. 29.95 - 1.2 / 1.25 = x
How to illustrate the information?From the information, Houa took a taxi from her house to the airport and the taxi company charged a pick-up fee of $1.20 plus $1.25 per mile. The total fare was $29.95,
Let the number of miles be represented by x.
Therefore, the information will be illustrated by:
1.20 + 1.25(x) = 29.95
1.20 + 1.25x = 29.25
Make x the subject
1.25x = 29.25 - 1.20
x = 29.25 - 1.20 / 1.25
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A rectangular sheet of paper is 12 and 1/2 cm long and 10and 2/3 cm wide
Find the perimeter
Answers
Explanation:
First, turn the mixed numbers into improper fractions:
12 and 1/2 is 25/2
25/2 + 25/2 = 50/2
10 and 2/3 is 32/3
32/3 + 32/3 = 64/3
Next, change the fractions so there is a common denominator:
50/2 = 150/6
64/3 = 128/6
Add the two fractions together:
150/6 + 128/6 = 278/6
Turn this back into a mixed number:
278/6 = 46 and 2/6
why do we draw a median
Answers
Find the perimeter and total area of the polygon shape shown below.
8
10
10
18
12
12
8
10
10
8
O Perimeter = 96 inches, Area = 192 square inches
O Perimeter = 56 inches, Area = 192 square inches
O Perimeter 56 inches, Area = 288
288 square inches
O Perimeter = 96 inches, Area =
144 square inches
Answers
Perimeter of polygon is 96 inches
Area is 192 square inch.
What is area and perimeter?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
Given,
Perimeter = sum of all sides
Perimeter = 8 + 10 + 10 + 18 + 12 +12 +8+ 10 + 10+8 + 10
Perimeter = 86
Perimeter of polygon is 96 inches
Area = Triangle ABC + Rectangle BCED + Triangle DEF
Area = [tex]\frac{1}{2}[/tex] × 12× 8 + 12×8 + [tex]\frac{1}{2}[/tex] ×12 × 8
Area = 192
Area is 192 square inch.
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Six student government officers want to go to the state convention. It will cost them $100 for registration, $380 for transportation and food, and $54 per person for the hotel. There is $500 budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge $5 per car, how many cars must they wash in order to have enough money to pay for the trip?
Answers
Answer:
61
Step-by-step explanation:
100+380+6(54)=804
804-500=304
304/5=60.8
Round answer to 61 because 60 is too little and will not meet the budget
factor out the coefficient of 1.1x + 9.9
Answers
Answer:
1.1(x + 9)
Step-by-step explanation:
1.1x + 9.9 ← factor out 1.1 from each term
= 1.1(x + 9)
To get x alone, divide both terms by 1.1
Jayden had pizza delivered. Jayden tips $5 for deliveries or 10% of the purchase, whichever is higher. The pizza delivered cost $29.50.
How much will Jayden tip?
Answers
Answer:
Five dollars?
Step-by-step explanation:
I don’t fully understand the question, so apologies if I am incorrect!
Find the probability of pulling a red card out of a standard deck of cards
Answers
Answer:
Find the probability of pulling a red card out of a standard deck of cards
Step-by-step explanation:
So, the probability of drawing a red-faced card is 6 out of 52 cards. Thus, the probability of drawing a red face card from a deck of cards is 6/52 = 3/26.
A standard deck of playing card consists 52 cards.
Cards is splitted into 4 suit i.e. Hearts, Spades, Diamond and Clubs.
Each suits consists of 13 cards - the Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, King and Queen.
Hearts & Diamond are red cards and Spades and Clubs are black cards.
Probably = Number of favourable/Possible outcomes/ Total outcomes.
Probability of pulling a red card = 26/ 52 = 0.5
Thus, probability of pulling a red card is 0.5.
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The peak of a mountain is 197.35 feet above sea level. The bottom of a lake is 131.38 feet below the sea level. What is the difference in elevations between the top of the mountain and the bottom of the mountain lake?
Answers
Answer: 65.97
Step-by-step explanation:
Given that log 2 = 0.3010 and log 3 = 0.4771, find log √30 without using a calculator.
Answers
Answer:
0.73855.
Step-by-step explanation:
log √30
log 30^1/2
= 1/2 log 30
30 = 2 * 3 * 5
= 3 * 10
So, log 30
= log (3*10) = log 3 + log 10
= 0.4771 + 1
= 1.4771
and log √30
= 1/2 log 30
= 1/2 * 1.4771
= 0.73855
what is
-6(4-t)=12t ?
Answers
[tex] - 6(4 - t) = 12t \\ - 6(4) - 6( - t) = 12t \\ - 24 +6 t = 12t \\ 6t - 12t = 24 \\ - 6t = 24 \\ \frac{ - 6t}{ - 6} = \frac{24}{ - 6} \\ t = - 4[/tex]
ATTACHED IS THE SOLUTION
Please answer this with an explannation. Thank You.
Answers
The value of x in the triangle is 46.40° .
How to find the angle of a triangle?The angle of a triangle can be found using sine rule.
Therefore, applying sine rule,
a / sin A = b / sin B = c / sin C
Hence,
5 / sin x = 6.9 / sin 88°
cross multiply
5 sin 88° = 6.9 sin x
5 × 0.99939082701 = 6.9 sin x
4.9969541351 = 6.9 sin x
divide both sides by 6.9
sin x = 4.9969541351 / 6.9
sin x = 0.72419625146
x = sin⁻¹ 0.72419625146
x = 46.4020264383
Therefore,
x = 46.40°
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Please help me with this ASAP!
Answers
Answer:
[tex] \frac{ {a}^{3} }{14 {b}^{2} {c}^{4} } [/tex]
Step-by-step explanation:
[tex] {14}^{ - 1} = \frac{1}{14} [/tex]
[tex] {b}^{ - 2} = \frac{1}{ {b}^{2} } [/tex]
[tex] \frac{ {14}^{ - 1} {a}^{3} {b}^{ - 2} }{ {c}^{4} } = \frac{ {a}^{3} }{14 {b}^{2} {c}^{4} } [/tex]
Point C is on line segment BD. Given
CD = 2 and BC = 8, determine the
length BD.
Answers
An element of a line known as a line segment joins two places that are thought of as line's ends. Point C is on line segment BD, Given CD = 2 and BC = 8, the length BD is 10.
What is line segment?A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of points on the line that lie inside those endpoints. The Euclidean distance between the two ends of a line segment determines its length. Half-open line segments contain exactly one of endpoints, while closed line segments have both of the endpoints. Open the line segments do not contain either of the endpoints. A line drawn above the symbols for the two endpoints is frequently used in geometry to indicate a line segment.
An element of a line known as a line segment joins two places that are thought of as line's ends. It is possible to measure the separation between two places. Given that line segments have a defined length, they can form the sides of any polygon.
Point C is on line segment BD.
CD+BC=2+8=10
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Answer:�
�
=
BC=
15
15
Step-by-step explanation:
List square numbers 50 to 80
Answers
7^2=49 so not correct
8^2=64 so correct
9^2=81 so not correct
Is this statement true or false?
0 x 5 = 5 x 0
Answers
The statement is true. Multiplication is commutative, which means that the order of multiplication does not affect the result.
The statement "0 x 5 = 5 x 0" is true because of the commutative property of multiplication. In multiplication, the order of factors does not change the result.
When we multiply 0 by 5, it equals 0 since anything multiplied by 0 is 0. Similarly, when we multiply 5 by 0, the result is still 0. Both expressions are equal to 0, confirming the commutative property.
In summary, 0 x 5 and 5 x 0 are interchangeable and yield the same result, proving the truth of the statement based on the fundamental property of multiplication.
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Please answer the question in the photo
Answers
The value of z in this convex polygon is equal to 66°
What is a polygon?A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides.
Note: The number of sides (n) of a pentagon is 5.
In Geometry, the sum of all the interior angles of a polygon with "n" sides is given by this formula:
Interior angle = 180 × (n - 2)
Interior angle = 180 × (5 - 2)
Interior angle = 180 × 3
Interior angle = 540°.
Now, we can determine the value of z as follows:
(180° - 2z) + (180° - z) + 130° + 108° + 140° = 540°
3z - 378° = 540° - 360°
3z = 378° - 180°
3z = 198°
z = 198°/3
z = 66°
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1.5x+ 4.5y=18 solve for x
Answers
Answer: x=12-3y
Step-by-step explanation:
• first we can see this is a linear equation since there are no terms alike.
(Meaning we won’t have just a number as our answer)
• if we are trying to find X then we must do everything else around it.
• first we have inverse operation meaning we have to subtract 4.5y from 18.
This gives us 1.5x = 18 - 4.5y
• now to get X alone we must do inverse operation again, but since it is multiplication this time we must divide.
1.5x = 18 - 4.5y
——- —————
1.5 1.5
• we now can cross off the 1.5 to give us X alone.
X = 18 - 4.5y
—————
1.5
•If we didn’t have like terms we would leave the answer like this but since we do we can simply.
The 18 and 1.5 are alike so this allows us to divide.
18 divided by 1.5 = 12
So this gives us our answer
X = 12 - 4.5y
can someone help me with the second 2
Answers
Answer:
Step-by-step explanation:
5?
Answer:
1. AM = 10
2. x = 21;
AM = 14
Step-by-step explanation:
5x = 3x + 4
-3x -3x
-----------------
2x = 4
÷2 ÷2
-------------
x = 2
AM = 5x
5(2) = 10
AM = 10
----------------------------------------------------------------------------------------------------------
|-------------x--------------|
*----|----*----|----*----|----*
A H M S
|---7---|
(assuming AH = HM = MS)
7 + 7 +7 = x
21 = x
AM = 14
I hope this helps!