Answer:
The correct option is;
12.3 + 0i
Step-by-step explanation:
The form a + b·i is the complex number form where the variables a and b are real numbers and i is the square root of -1, √(-1) that is i² = -1. As the answer to √(-1), cannot be found among the real numbers, i, is known as an imaginary number.
As such a given complex number of the form a + b·i, has a real, part or component, a, and an imaginary part, b.
The number 12.3, is a real number, therefore, representing the number in a complex number format, the imaginary part, b, would be zero, as follows;
12.3 + 0·i
Help with this find the image of (1 ,2) after a reflection about y=x followed by a reflection about y=-x
Answer: (-1, -2)
Step-by-step explanation:
so at first you have (1, 2)
then you were asked to reflect about y=x which is (x, y) = (y, -x)
(1, 2) = (2, -1)
then followed by y=-x which is (x, y) = (-y, -x)
(2, -1) = (-1, -2)
I hope this helps!
EXTRA POINTS If x = 2.5, 5x = ____. (Only input decimals such as 12.7 as the answer.)
Answer:
12.5
Step-by-step explanation:
2.5 * 5 = 12.5
Can someone please help me?
Answer:
The equation of the perpendicular line (PR) to line PQ is; y = -0.5x - 1.5
Step-by-step explanation:
The line is perpendicular to line adjoined by points P(-3,0) and Q(0,6)
The slope of line PQ is;
Slope = change in y ÷ change in x = [tex]\frac{6 - 0}{0 -- 3}[/tex] = 2
The product of slopes of two perpendicular lines = -1
Hence the slope of line PR = -1 ÷ slope of line PQ = -1/2
Taking another point (x,y) and point P(-3,0) the equation of line PR is;
Slope = [tex]\frac{y - 0}{x - -3} = -\frac{1}{2}[/tex]
Cross-multiplying gives;
2y = -x - 3 , y = -x/2 - 3/2 , y = -0.5x - 1.5
Factories (x+2y)^3+(x-2y)^3
With full explanation
Answer:
[tex]\boxed{=2x(x^2+6y^2)}[/tex]
Step-by-step explanation:
Remember:
[tex](a+b)(a-b)=a^2-b^2\\\\a^3+b^3=(a+b)(a^2-ab+b^2)\\\\\\(x+2y)^3+(x-2y)^3\\\\=(x+2y+x-2y)((x+2y)^2-(x+2y)(x-2y)+(x-2y)^2)\\\\=2x(x^2+4xy+4y^2-(x^2-4y^2)+x^2-4xy+4y^2)\\\\=2x(x^2+6y^2)\\[/tex]
I need help with #7 I got no clue what to do
Given = 1/(−3), what is ((+ℎ)−())/ℎ ?
Answer:
-(1/(x+h-3)(x-3))
Step-by-step explanation:
y=1/(x-3)
(f(x+h)-f(x))/h=(1/(x+h-3)-1/(x-3))/h=-(1/(x+h-3)(x-3))
PLEASE HELP! THANK U
Answer:
-26!!!! :))))
Step-by-step explanation:
Which theorem or postulate proves the two triangles are similar?
AA Postulate
SSS Theorem
AS Postulate
SAS Theorem
Answer:
AA Postulate
Step-by-step explanation:
The bottom lines are parallel. In this case they are also congruent. Combined with the top angle this makes in AA postulate
Graph a rectangle on the coordinate plane with an area of 250 ft^2. Pretend 1 unit=10 feet.
Answer:
turn the 10 to 5 and divide 250 by 2 which will give you your l and w subract 2 from your l and add 2 to your your w
Step-by-step explanation:
Answer:
Step-by-step explanation:
If the area is to be 250 ft^2, one possible set of dimensions would be
25 ft by 10 ft.
If 1 unit on the coordinate plane represents 10 feet, then the dimensions of the drawing would be 2.5 units by 1 unit.
Consider the formula 4(h-3k)= h+7.
(a) Make k the subject of the above formula.
(b) If the value of h is decreased by 8, write down the change in the value of k.
guys I really need help
plzzzzzz
Answer:
=k=0.25h-7/12
Step-by-step explanation:
4(h-3k)=h+7
=4h-12k=h+7
collecting like terms and leaving characters with k on 1 side, we get;
12k=3h-7
=k=0.25h-7/12
PLEASE HELP the vertex form of the equation of a parabola is y = (x - 3)2 + 36. what is the standard form of the equation?
Answer:
[tex]\large \boxed{\sf \bf \ \ x^2-6x+45 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
You need to develop the expression.
[tex]y=(x-3)^2+36\\\\=x^2-2 * 3 * x +3^2+36\\\\=x^2-6x+9+36\\\\=x^2-6x+45[/tex]
Thank you.
Answer:
D
Step-by-step explanation:
(-root3a-a)²
please solve this send answer quickly
As soon as possible
Answer:
The expression (-root3·a - a)², can be simplified into the form a² × (4 + 2·√3)
Step-by-step explanation:
The given expression can be written as follows;
(-root3·a - a)² = (-√3·a - a)²
Which can be expanded to give;
(-√3·a - a) × (-√3·a - a) = 3·a² + 2·√3·a² +a²
We collect like terms to get;
3·a² + 2·√3·a² +a² = 3·a² +a²+ 2·√3·a² = 4·a² + 2·√3·a²
We factorize out the common coefficients of the terms to have;
4·a² + 2·√3·a² = a² × (4 + 2·√3)
Which gives the initial expression (-root3·a - a)², to presented in the form a² × (4 + 2·√3).
In Exercises 22 describe how the change affects
the surface area of the right prism or right cylinder. Thank you!!
Step-by-step explanation:
Total Surface Area of original cylinder
= (2×(22/7)×9)(9+24)
=18×22/7×33
=1,866.8
Total Surface Area of new cylinder
=(2×(22/7)×9/3)(9/3+24/3)
=(2×(22/7)×3)(3+8)
=6×22/7×11
=207.4
Change or Ratio of org. cylinder to new cylinder
=1,866.8/207.4
=9.0009
59,8x60,2 bằng bao nhiêu ạ
Answer:
3,6
Step-by-step explanation:
Clarissa and Shawna, working together, can paint the exterior of a house in 6 days. Clarissa by herself can complete this in 5 days less than Shawna. how long will it take Clarissa to complete the job by herself?
Answer:
Clarissa will take 10 hours by herself
Step-by-step explanation:
Let s = time for shawna
s-5 = time for clarissa
The formula for determining the time is
1/a + 1/b = 1/c where a and b are the times alone and c is the time together
1/s + 1/(s-5) = 1/6
Multiply each side by 6s(s-5) to clear the fractions
6s(s-5) ( 1/s + 1/(s-5)) = 1/6 *6s(s-5)
Distribute
6(s-5) + 6s = s(s-5)
Distribute
6s -30 +6s = s^2 -5s
Combine like terms
12s -30 = s^2 -5s
Move everything to the right
0 = s^2 -5s -12s +30
0 = s^2 -17s +30
Factor
0 = ( s-15) (s-2)
Using the zero product property
s-15 =0 s-2 =0
s =15 s=2 ( This is not a reasonable answer since it is less than the time together)
s=15
s-5 = 10
Clarissa will take 10 hours by herself
I Need Help With This One :/
Answer:
(-5) ^ 11
Step-by-step explanation:
(-5) ^5 / (-5) ^ -6
We know that a^ b / a^ c = a^ ( b-c)
(-5)^ (5 - -6)
(-5) ^ (5+6)
(-5) ^ 11
Answer:
-5
Step-by-step explanation:
Mathaway
1. In a group of 500 students, 280 like bananas, 310 like apples, and 55 dislike both the fruits.
i) Find the number of students who like both the fruits.
ii) Find the number of students who like only one fruits.
iii) Show the result in venn-diagram
Answer:
Please see the attached images
Step-by-step explanation:
help pleasseeeee ! 15 points
the answers are
(-1,-5)
(0,-3)
(4,5)
(9,15)
Answer:
(0,-3)
Step-by-step explanation:
2x-y = 3
x+2y = -6
Multiply the first equation by 2 so we can eliminate y
2(2x-y =3)
4x -2y = 6
Add this to the second equation
4x -2y = 6
x+2y = -6
-----------------
5x +0y = 0
x = 0
Now find t
x+2y = -6
0+2y = -6
2y =-6
Divide by 2
y = -3
Answer:
Step-by-step explanation:
Let's try to eliminate y.
First we multiply the first equation by 2,
4x - 2y = 6
x + 2y = -6
Then we add them together
5x = 0
x = 0
Now we plug x into the first equation,
4(0) - 2y = 6
-2y = 6
y= -3
Now we plug x into the second equation,
0 + 2y = -6
2y = -6
y = -3
So our answer is,
(0,-3)
489
X
96°
x =
degrees
Answer:
x=144°
Step-by-step explanation:
To work out x, you have to find the other angle in the triangle.
Angles in triangles always add up to 180°, so you would have to add up the 2 angles you have and take it away from 180°.
48+96=144°
180-144=36°
Then, to find x, you have to do 180-36 because angles on a straight line always add up to 180°.
180-36=144°
x=144°
Hope this helps :)
An exterior angle of a triangle is equal to the sum of its interior opposite angles.
So,[tex]\large\bf{{\red{ \longrightarrow \:\large\rm \: x \: = \: 96 \degree \: + \: 48 \degree }}} \\ [/tex]
[tex]\large\bf{{\red{ \longrightarrow \:\large\rm \: x \: = \: 144 \degree }}} \\ [/tex]
For what values of the variable does the following expression make sense:
(squareroot) 1+3a/25
Answer:
a ≥ -1/3
Step-by-step explanation:
The square root must be greater than or equal to zero
sqrt(1+3a /25) ≥ 0
Square each side
(1+3a)/25≥ 0
Multiply each side by 25
1+3a≥0
Subtract 1
3a ≥ -1
Divide by 3
a ≥ -1/3
Simplify 7 to the 6th power ⋅ 7 to the fifth power.
49 to the 11th power
49 to the 35th power
7 to the 11th power
7 to the 35th power
Answer:
7 to the 11th power
Step-by-step explanation:
7⁶×7⁵=7¹¹
because a¹×a¹=a¹+¹
Please help
Maths....
6 cm from what im seeing
Answer: 7 cm
Step-by-step explanation:
Can someone pls help and explain it
Answer:
(7,-4) ; 12
Step-by-step explanation:
Basically, three corners of a rectangle are already on the graph. If you put a dot at (7,-4), that is the last corner(vertex) that finishes the rectangle
Then to find base of the rectangle, you find the length of the longer side, (the distance between the x coordinates). So you would subtract -5 from 7 and get 12, and 12 is the length of your base.
10 points to the person who answers this question.
Answer:
your answer is
2 X l+b
2 X 6x + 3x
8x + 10...
"All the religions are equal,the difference is their name ".Justify.
Evaluate the expression using the values in the left column to complete the table
Answer/Step-by-step explanation:
A. [tex] 4b + 3b [/tex]
Using b = 2
[tex] 4(2) + 3(2) = 8 + 6 = 14 [/tex]
Using b = 4
[tex] 4(4) + 3(4) = 16 + 12 = 28 [/tex]
Using b = 6
[tex] 4(6) + 3(6) = 24 + 18 = 42 [/tex]
Using b = 8
[tex] 4(8) + 3(8) = 32 + 24 = 56 [/tex]
Using b = 10
[tex] 4(10) + 3(10) = 40 + 30 = 70 [/tex]
Using b = 2
[tex] 4(12) + 3(12) = 48 + 36 = 84 [/tex]
B. [tex] 3(x - 2) [/tex]
Using x = 3
[tex] 3(3 - 2) = 3(1) = 3 [/tex]
Using x = 5
[tex] 3(5 - 2) = 3(3) = 9 [/tex]
Using x = 7
[tex] 3(7 - 2) = 3(5) = 15 [/tex]
Using x = 9
[tex] 3(9 - 2) = 3(7) = 21 [/tex]
Using x = 11
[tex] 3(11 - 2) = 3(9) = 27 [/tex]
Using x = 13
[tex] 3(13 - 2) = 3(11) = 33 [/tex]
C. [tex] 5(4a - 1) [/tex]
Using a = 2
[tex] 5(4(2) - 1) = 5(8 - 1) = 5(7) = 35 [/tex]
Using a = 3
[tex] 5(4(3) - 1) = 5(12 - 1) = 5(11) = 55 [/tex]
Using a = 4
[tex] 5(4(4) - 1) = 5(16 - 1) = 5(15) = 75 [/tex]
Using a = 5
[tex] 5(4(5) - 1) = 5(20 - 1) = 5(19) = 95 [/tex]
Using a = 6
[tex] 5(4(6) - 1) = 5(24 - 1) = 5(23) = 115 [/tex]
Using a = 7
[tex] 5(4(7) - 1) = 5(28 - 1) = 5(27) = 135 [/tex]
D. [tex] 6y - 2y + 4 [/tex]
Using y = 2
[tex] 6(2) - 2(2) + 4 = 12 - 4 + 4 = 12 [/tex]
Using y = 3
[tex] 6(3) - 2(3) + 4 = 18 - 6 + 4 = 18 - 2 = 16 [/tex]
Using y = 5
[tex] 6(5) - 2(5) + 4 = 30 - 10 + 4 = 30 - 6 = 24 [/tex]
Using y = 10
[tex] 6(10) - 2(10) + 4 = 60 - 20 + 4 = 60 - 16 = 44 [/tex]
Using y = 8
[tex] 6(8) - 2(8) + 4 = 48 - 16 + 4 = 48 - 12 = 36 [/tex]
Using y = 6
[tex] 6(6) - 2(6) + 4 = 36 - 12 + 4 = 36 - 8 = 28 [/tex]
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 8 N acts on a certain object, the acceleration of the object is 4 m/s?. If the acceleration of the object becomes 3 m/s?, what is the force?
Here Mass is constant
F1=8Na_1=4m/s^2a_2=3m/s^2F_2=?Using Newtons s law
[tex]\\ \sf \longmapsto F=ma[/tex]
[tex]\\ \sf \longmapsto \dfrac{F}{a}=m[/tex]
[tex]\\ \sf \longmapsto \dfrac{F_1}{a_1}=\dfrac{F_2}{a_2}[/tex]
[tex]\\ \sf \longmapsto \dfrac{8}{4}=\dfrac{F_2}{3}[/tex]
[tex]\\ \sf \longmapsto F_2=\dfrac{24}{4}[/tex]
[tex]\\ \sf \longmapsto F_2=6N[/tex]
Answer:
F = 6N
Step-by-step explanation:
Equation
F = ka
F - force
k - constant of proportionality
a - acceleration
Step 1 - find k
8N=k*4m/s^2
k=2
Step 2 - find F
F=2*3m/s^s
F=6
I need a written response to solve all 4 steps
a. Find the slope of the line that passes through the points (2,-5) and (-2,3).
b. What are the slope and y-intercept of the equation 2x - 5y = -10?
c. Find the x value so that the line through the points (x,-9) and (0,1) has a slope of -4.
d. Write the equation of a line that passes through the point (-1,5) and has a slope of -7. Your answer should be given in the form y = mx + b.
Answer:
a. -2
b. s = 2 and y = -5
c. (2.5, -9)
d. -7x - 2
Step-by-step explanation:
a. In the image, I have used rise over run, which is -8/4 or -2.
b. slope formula is mx + b = y, where m is slope and b is the y-intercept. In the equation 2x - 5y = -10, 2 is the slope and -5 is the y-intercept.
c. Plug in all given numbers into an equation and the ones you do not have will be in the points you need it to be. Once you graph the equation you will receive (2.5, -9).
d. y = mx + b
5 = (-7)(-1) + b
5 = 7 + b
-2 = b
y = -7x - 2
Plz HELP !!!!! I would appreciate it!!!
Answer/Step-by-step explanation:
a. The sides of ∆ABC can be labelled as follows, taking θ as the reference point.
Adjacent = side AB
Opposite = side BC
Hypotenuse = side AC
b. I. "<B is an acute angle" => FALSE. It is a right angle (90°)
II. "The side opposite to <C is BC" => FALSE. The side opposite to <C is AB.
III. The side adjacent to <A is AB => TRUE
IV. The side opposite to <B is not the longest. => FALSE. It is the hypotenuse and the longest side.
c. Cos θ = [tex] \frac{adjacent}{hypotenuse} = \frac{AB}{AC} [/tex]
Tan θ = [tex] \frac{opposite}{adjacent} = \frac{BC}{AB} [/tex]
d. Sin C = [tex] \frac{opp}{hypo} = \frac{AB}{AC} [/tex]
Cos C = [tex] \frac{adjacent}{hypotenuse} = \frac{BC}{AC} [/tex]
Tan C = [tex] \frac{opp}{adjacent} = \frac{AB}{BC} [/tex]
the sum of 5 consecutive even numbers is 130. find the numbers.
Answer:
22, 24, 26, 28, 30
Step-by-step explanation:
If the sum of 5 numbers is 130, that means the average of these numbers is 26.
If it is the average then it is the middle, or the third number. The two numbers before it would then be 22 and 24 by subtracting twos, and the two numbers after it would be 28 and 30 by adding twos.
22, 24, 26, 28, 30
Answer:
22,24,26,28,30
Step-by-step explanation:
I call the unknown number x
I write consecutive numbers in terms of x.
x+ (x+2) + (x+4) + (x+6) + (x+8) = 130
5x + 20 = 130
5x = (130 - 20)
5x = 110
x = 22 = smallest even number
x + 2 = 24 = second even number
x +4 = 26
x + 6 = 28
x + 8 = 30