No, It is not possible to have a complex number in the form of a + bi when b = 0.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Complex number.
It is in the form of a + ib.
Where a and b are real numbers.
Now,
If b = 0 then we can not have a complex number.
Example:
a + bi
a = 1 and b = 0
1 + 0i = 1 which is not a complex number.
In order to have a complex number a can be any real number and 0 but b can not be a zero.
Thus,
It is not possible to have a complex number in the form of a + bi when
b = 0.
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All numbered streets runs parallel to each other. Both 3rd and 4th streets are intersected by king ave. As shown
Answer:
(a)
∠(a) = 105°
(b) ∠(b) = 75°
(c)
∠(c) = 105°
Step-by-step explanation:
Complete Question
1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown:
(a) Suppose a car is traveling west on 4th Street and turns onto King Avenue heading south. What is the measure of the angle created by the car's turning? Explain your answer.
(b) Suppose a car is traveling southwest on King Avenue and turns right onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.
(c) Suppose a car is traveling northeast on King Avenue and turns right onto 4th Street. What is the measure of the angle created by the car's turning? Explain your answer
Also find the attachment
Solution
(a)
∠(a) + 75° = 180°
∠(a) = 180° - 75°
∠(a) = 105°
(b) As we can see the 3rd and 4th street are parallel thus the corresponding angle will be equal
Thus, ∠(b) = 75°
(c)
∠(c) + 75° = 180°
∠(c) = 180° - 75°
∠(c) = 105°
Please answer the question below
The admission fee to the carnival is $4. 50 for children and $7. 25 for adults. If a large group purchased 28 tickets and paid $159 how many adult tickets did they purchase?
The number of adult tickets purchased is 12.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Let no. of adult = x
No. of children = 28 -x
So, 7. 25 * x + (28 - x) *4. 50 = 159
⇒2.75x +126=159
⇒2.75x =33
⇒x=33/2.75
x=12
Hence, the number of adult tickets purchased is 12.
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A square rug has an area 44ft. Power of 2Write the side length as a square root. Then decide if the side length is a rational number.
Answer: [tex]2\sqrt{11}\ ft[/tex], Irrational number
Step-by-step explanation:
Given
The square rug has an area of [tex]44\ ft^2[/tex]
The area of the square rug is [tex]\left( \text{Side length}\right)^2[/tex]
Suppose the side length is [tex]x[/tex]
[tex]\therefore x^2=44\\\Rightarrow x=\sqrt{44}\\\Rightarrow x=2\sqrt{11}\ ft[/tex]
As [tex]\sqrt{11}[/tex] is irrational, therefore, [tex]2\sqrt{11}[/tex] is not a rational number.
please help me with this!!
Answer: The answer is no, they are not proportional
Step-by-step explanation:
Let, third proportional is x 0.8 : 0.2 : : 0.2 : x = 0.8/0.2 = 0.2/x = x = 0.2 × 0.2/0.8 × 10 = 1/20 = 0.05 Hence, here third proportional is 0.05
Solve.
7 Jordan shoots 100 3-point shots per basketball practice.
She makes 44 of these shots. What decimal represents the
number of shots she makes?
8 At a county fair, 9 people out of 1,000 earned a perfect score
in a carnival game. What decimal represents the number of
people who earned a perfect score?
Answer:
7. .44
8. .009
Step-by-step explanation:
7. 44 ÷ 100 = .44
8. 9 ÷ 1000 = .009
How is a right triangle used to find the sine and cosine of an acute angle is there a unique right triangle that must be used?
We find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.
What is the tangent of the angle?
The ratio of the right-angle triangle's base or perpendicular is known as the tangent of the angle.
The ratio of two of the right-angled triangle's three sides is used to define the sine, cosine, and tangent of an acute angle.
Here,
We have to find out how is a right triangle used to find the sine and cosine of an acute angle is there a unique right triangle that must be used.
We concluded that a right triangle can be used to determine the tangent of any acute angle, by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.
Hence, we find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.
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Pl help it’s for a grade
Answer:
The initial fee
Step-by-step explanation:
Thats the fee to sort of set up the membership, the 15 is the monthly cost, and m is the months you use the membership. Make sense?
In March 2012, film director James Cameron climbed inside the Challenger Deep and descended into the deepest part of the Pacific Ocean, the Mariana Trench. After 12hour, the craft was approximately 2,750 meters beneath the ocean surface. Which equation describes the depth of the Challenger Deep in relation to sea level after 1 hour if they continue to descend at the same rate?
Answer:
hey guys!! answer is B!!
Step-by-step explanation
hope this helps!
Answer:
b give brainest
Step-by-step explanation:
Find the missing length of the right triangle.
which of the following require that you have parallel sides
The requirement of the parallel sides is Alternate interior angles.
What is the alternate interior angle?The angle formed by the line intersecting two parallel lines is called the alternate interior angle. This two angles are equal in magnitude.
The alternate interior angles require two parallel lines to be formed. Therefore the requirement of the parallel sides is Alternate interior angles.
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Does 4 5 6 make a right triangle?
The side lengths measuring 4 units , 5 units and 6 units does not make a Right Triangle as they do not satisfy the condition of the Pythagoras Theorem that the square of the longest side is equal to the sum of square of other two side .
The Pythagoras Theorem states that the square of the lonest side (hypotnuse) is equal to the sum of the square of the other two sides ,.
The side lengths of the triangle are given as 4 units , 5 units and 6 units ,
According to the condition , [tex]6^{2} = 4^{2} + 5^{2}[/tex]
On simplifying ;
we get ;
[tex]36 = 16 + 25[/tex] ;
[tex]36 \neq 41[/tex]
that means the given side do not form a right triangle .
Therefore , the side 4 units , 5 units and 6 units do not make a right triangle .
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6x + 5y = 4 5. and 6x – 7y = –20 what does x and y equal?
Answer:
x=-1 y=2
Step-by-step explanation:
Use Elimination or Substitution (Elimination shown below)
6x+5y=4
6x-7y =-20 <- Multiply by -1
-6x+7y=20
12y = 24
y=2
Plug back into either of the equations and solve for x.
6x + 10= 4
6x = -6
x = -1
Double check work:
-6+10 = 4
Help please I don't really understand
Answer:i need to know what youre trying to find first
Step-by-step explanation:
1/3 + 9/2 simple math
What is the range of the function on the graph
Answer:
All real numbers greater than or equal 2.
Step-by-step explanation:
There is a closed circle on the number 2,which means that it is included in the range. The line is increasing, meaning that all real numbers greater than or equal to 2 is the range.
Help pls this test is timed and I have been doing it sine 8:00 Florida time!!!!!!!!! It’s the m and q question thanks
Answer: A.
Step-by-step explanation: Because a solid can go from a liquid to a gas and if you think of ice, Ice starts as a solid then when it melts it turns into a liquid the when the liquid evaporates it turns to a gas. Hope this helped
5. 4 friends have a $20 coupon to help pay for their dinner. The total bill
including tax and tip comes to $84. Write AND solve an equation to
determine how much each friend will have to pay for the bill.
The nth term of a sequence is 3n squared -1. The nth term of a different sequence is 30 - n squared. Find the only number that is in both of these sequences
The number that belongs to both sequences is 26.
The formula known as the nth term allows us to locate any term in a series. The letter "n" stands for "number."
By changing the term number's value, we can create a series that uses the nth term (n).
To find the 10th term we would follow the formula for the sequence but substitute 10 instead of ‘n‘; to find the 50th term we would substitute 50 instead of n.
We have two sequences, let's call one as A and the other as B.
The n-th term of sequence A is written as:
aₙ = 3*n^2 - 1
the nth term of sequence B is written as:
bₙ = 30 - n^2
We want to find a term that belongs to both sequences, (it can be for different integers, we can use n for sequence A and x for sequence B)
Then we want to find:
aₙ = bₓ
where n and x are integer numbers.
Then we will heave:
3*n^2 - 1 = 30 - x^2
To find the pair, we could isolate one of the variables, then input different integers in the other variable and see if the outcome is also an integer.
Let's isolate n.
3*n^2 = 30 - x^2 + 1
3*n^2 = 31 - x^2
n^2 = (31 - x^2)/3
n = √( (31 - x^2)/3)
Now let's input different values for x, and see if the outcome is also an integer, notice that x is in a negative term inside a square root, then we have only a few values of x such that the equation can be true.
Then let's start with x = 1.
n(1) = √( (31 - 1^2)/3) = √(30/3) = √10
We know that √10 is not an integer.
now with x = 2,
n(2) = √( (31 - 2^2)/3) = √( (31 - 4)/3) = √(27/3) = √9 = 3
then if x = 2, we have n = 3.
Both of them are integers, then we get:
a₂ = 3*(3)^2 - 1 = 27 - 1 = 26
b₃ = 30 - 2^2 = 30 - 4 = 26
Therefore, The number that belongs to both sequences is 26.
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What does ∧ and ∨ mean in math?
The ^ operator in logical mathematics means the OR operation . Therefore , the statement ∧ and ∠means that a or the negation of a is joined by the or operation .
These are known as logical operations as they are based upon logic.The meaning of the term logic is reasoning which means to resonate. The reasoning may be a legal opinion or mathematical confirmation.
We apply logic on expression to check whether they are true of false . Some of the mathematical logics are a negation, conjunction, and disjunction logical operations. The symbols used for them in mathematical logic is, ‘~’ for negation ‘^’ for conjunction and ‘ v ‘ for disjunction.
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5. Refer to the figure below. (show work)
Given: UVWX is a parallelogram, m
A. Find m
B. Find UV.
C. Find m
D. Find YW.
Answer:
see explanation
Step-by-step explanation:
A
∠ UVX and ∠ WXV are alternate angles and are congruent , then
∠ UVX = ∠ WXV = 15°
∠ WVU = ∠ WVX + ∠ UVX = 24° + 15° = 39°
B
opposite sides of a parallelogram are congruent , then
UV = XW = 36
C
consecutive angles are supplementary , sum to 180° , then
∠ XUV + ∠ WVU = 180° , so
∠ XUV + 39° = 180° ( subtract 39° from both sides )
∠ XUV = 141°
D
diagonals bisect each other , so
YW = UY = 10
simplify 3a - 2(8 +4a)
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Answer:
Let's simplify step-by-step.
3a − 2 ( 8 + 4a )
Distribute:
= 3a + ( −2 ) ( 8 ) + ( −2 ) ( 4a )
= 3a + −16 + −8a
Combine Like Terms:
= 3a + −16 + −8a
= ( 3a + −8a ) + ( −16 )
Answer:
= −5a − 16
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
pls help ;-;
A spinner has 8 equal spaces numbered 1 through 8.
After 48 spins, about how many times would you expect it to land on
1, 2, or 3?
Answer:
The answer to this is 14%
Step-by-step explanation:
sorry if im wrong
(hope this helps can i plz have brainlist :D hehe)
Adrian,bobby, and chandler are assigned a random order during a three-person batting competition. What is the probability that bobby is assigned to go first, chandler is assigned to go second and Adrian is assigned to go last.
Answer:I think 1/3
Step-by-step explanation:
Answer:
1/6
Step-by-step explanation:
The process of each individual getting chosen is a sequence of events, meaning we need to multiply each individual probability separately in order to get the probability of this happening. For the first choice, the probability is 1/3 since there can only be one chosen to go first and there are three options. For the second choic,e the probability is 1/2 because only one can be chosen but there are now only 2 options since someone got chosen to be first. This leaves the last probability which is 1/1 since only one person is left. Therefore, to get the probability of this event happening we need to multiply all of these probabilities together...
1/3 * 1/2 * 1/1 = x
[tex]\frac{1 * 1 * 1}{3 * 2 * 1} =[/tex] [tex]\frac{1}{6}[/tex]
Therefore the probability of Bobby going first, Chandler going second, and Adrian going last is 1/6
Pls help. Find the surface area of the solid. Round to the nearest tenth if necessary
Answer:
850 m²
Step-by-step explanation:
There are 3 different pairs of rectangles—the side rectangles, the rectangles on the top and bottom, and the other side rectangles.
10x11=110
110x2=220
15x10=150
150x2=300
15x11=165
165x2=330
330+300+220=850 m².
The base of an open rectangular box is of length (2x + 5) cm and width x cm.
The area of this base is 58 cm².
The height of the open box is (x - 2) cm.
I have attached a pic
(I already did part (a) and (bi) and you may use the answers to help you do the (bii) question)
+ the answer for (bi) if you can’t see it, it is 4.28 and -6.78
This is the question:
b) (ii) Hence calculate the volume of the box, stating the units of your answer.
The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.
What is volume?Volume is the measure of the amount of 3-dimensional space occupied by an object or substance. It is usually measured in cubic units, such as cubic centimeters (cm3) or cubic meters (m3). Volume is an important concept in mathematics, physics, chemistry, and engineering, and is used to calculate the amount of material needed for a given project.
The volume of the box can be calculated by multiplying the area of the base with the height of the box. The area of the base is 58 cm² and the height of the box is x - 2 cm. Therefore, the volume of the box can be expressed as:
Volume = 58 cm² x (x - 2 cm)
= 58 cm³
The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.
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Which of the following terms correctly describe the object below?
Check all that apply.
A. Square
B. Solid
C. Cube
D. Polygon
E. Prism
F. Pyramid
Its a solid and a cube
You were wrong with square because a square only has one face while a cube has 6.
You were also wrong with polygon because while polygons are 1-dimensional a cube is 3-dimensional
The following terms correctly describe the given object Square, Solid, Cube, Polygon.
Options A, B, C, D are correct.
What is a cube?A cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.
Square is a figure in which all four sides are equal.
Solid is a three dimensional figure.
A Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Polygon is two dimensional figure with straight lines.
The following terms correctly describe the given object Square, Solid, Cube, Polygon.
Options A, B, C, D are correct.
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When Khadija stands at a distance of 18 m from the base of a tree, she forms
an angle of 57° with the top of the tree. What is the height of the tree to the
nearest tenth?
A 27.7 m
B 28.5 m
C 29.2 m
D 301 m
Rent-A-Car charges $50 to rent a car plus $0.25 per mile. Save-To-Rent charges $25 to rent a car plus $0.41 per
After how many miles will the cost be the same to rent a car?
miles
y = 0.25x + 50 and y = 0.3x + 40 will be the equation to find the cost to rent a car.
Define cost function.A mathematical formula known as a cost function is used to visualize how manufacturing costs will vary depending on the output level. In other words, given a specified quantity produced, it calculates the entire cost of production.
Define cost.Costs are the dollar amount spent on materials, labor, services, goods, equipment, and other items for use by a company or other accounting organization.
y = 0.25x + 50
y = 0.3x + 40
The equations will be written as y = mx + b, or slope-intercept form. You must determine what you have in order to determine what belongs where.
They receive $50 per day plus $0.25 per mile from Rent-A-Wreck. This indicates that the $0.25 per mile is the number that changes daily. Thus, y = 0.25x + 50 will be the equation.
They receive $40 per day with $0.30 per mile from Drive-A-Lemon. This indicates that the $0.30 per mile is the number that changes daily. y = 0.3x + 40 will be the formula.
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Please help thank you
Answer:
True
True
False