Answers
The complex number from the table are
[tex]1+\sqrt{-3}, \ 4-3 \sqrt{-16}, \ \frac{3+2 \sqrt{-9}}{7}, \ 9 \sqrt{-\frac{7}{5}}[/tex]
Solution:
Let us solve and identify the complex number.
(A) [tex]5-\sqrt{\frac{9}{4}}[/tex]
[tex]5-\sqrt{\frac{9}{4}}= 5-\sqrt{\frac{3^2}{2^2}}[/tex]
[tex]= 5-\frac{3}{2}[/tex]
= 3.5
This is not a complex number.
(B) [tex]1+\sqrt{-3}[/tex]
[tex]1+\sqrt{-3}=1+\sqrt{-1\times 3}[/tex]
We know that [tex]\sqrt{-1} =i[/tex].
[tex]1+\sqrt{-3}=1+\sqrt{3}i[/tex]
This is a complex number.
(C) [tex]4-3 \sqrt{-16}[/tex]
[tex]4-3 \sqrt{-16}=4-3 \sqrt{-1\times 4^2}[/tex]
[tex]4-3 \sqrt{-16}=4-3\times4 \sqrt{-1}[/tex]
We know that [tex]\sqrt{-1} =i[/tex].
[tex]4-3 \sqrt{-16}=4-12i[/tex]
This is a complex number.
(D) [tex]\frac{2-\sqrt{12}}{5}[/tex]
[tex]\frac{2-\sqrt{12}}{5}=\frac{2-2\sqrt{3}}{5}[/tex]
There is no –1 in the root.
This is not a complex number.
(E) [tex]\frac{3+2 \sqrt{-9}}{7}[/tex]
[tex]\frac{3+2 \sqrt{-9}}{7}=\frac{3+2 \sqrt{-1\times 3^2}}{7}[/tex]
We know that [tex]\sqrt{-1} =i[/tex].
[tex]=\frac{3+6i}{7}[/tex]
This is a complex number.
(F) [tex]9 \sqrt{-\frac{7}{5}}[/tex]
[tex]9 \sqrt{-\frac{7}{5}}=9 \sqrt{-1 \times \frac{7}{5}}[/tex]
We know that [tex]\sqrt{-1} =i[/tex].
[tex]9 \sqrt{-\frac{7}{5}}=9 \sqrt{ \frac{7}{5}}i[/tex]
This is a complex number.
Hence the complex number from the table are
[tex]1+\sqrt{-3}, \ 4-3 \sqrt{-16}, \ \frac{3+2 \sqrt{-9}}{7}, \ 9 \sqrt{-\frac{7}{5}}[/tex]
Related Questions
Four CDs and 4 DVDs cost $164. The cost of the 4 CDs is half the cost of the
4 DVDs. What is the cost of each CD?
Which of the following problems would help you solve the problem above?
Answers
Answer:
Each CD cost $20.50
Step-by-step explanation:
You would divide the cost of the DVDs by 4: 164÷4=41
Now the CDs are half the cost of the DVDs so you would divide 41 by 2: 41÷2=20.50
Your answer would be $20.50
Find the area of the isosceles triangle with legs 12 and base 17. Simplify all radicals
a2+b2=c2
Answers
Answer:
[tex]Area= \frac{17 \sqrt{865} }{4} \: {units}^{2} [/tex]
Step-by-step explanation:
From Pythagoras theorem,
[tex] {h}^{2} = {12}^{2} + { (\frac{17}{2} )}^{2} [/tex]
[tex]{h}^{2} = \frac{865}{4} [/tex]
[tex]h = \frac{ \sqrt{865} }{2} [/tex]
The area of the isosceles triangle is
[tex]Area= \frac{1}{2} bh[/tex]
[tex]Area= \frac{1}{2} \times 17 \times \frac{ \sqrt{865} }{2} = \frac{17 \sqrt{865} }{4} [/tex]
How would I solve this ?
Answers
1. Use the Multiplication Distributive Property: (xy)^a = x^a y^a
3√6 3√x √y^2
2. Use this rule: (x^a)^b = x^ab
3√6 3√xy^2/3
Answer please i will give 10 points and mark brainiest
Answers
Answer: 320 , 112, 432
Step-by-step explanation:
Volume of Rectangular Prism= 4 * 8 * 10
= 32*10
= 320 ft cubed
Volume of triangular prism= 4 * 7 * 8
= 28 * 8
= 224
= 224 divided by 2
= 112
Volume of composite= 112 + 320
= 432
What is the median house price?
o $750,000
$764,000
$880,000
0 $1,200,000
Submit
Skip
ch
OB W M -
Answers
Answer: $822,000
Step-by-step explanation:
Median of even numbers is the average of the two middle numbers
Median = $764,000 + $880,000 ÷ 2
= $1,644,000/2
= $822,000
From the elements Li,K,Mg,C,Al,S identify the (a) element belonging to the same group
(b) element which has the tendency to lose two electrons.
(c) element which prefers sharing of electrons to complete its octet
(d) most metallic element
(e) element that forms acidic oxide
(f) element that belongs to group 13
Answers
Answer:
(a) Li and K belongs to the same group.
(b) Mg has the tendency to lose two electrons.
(c) C prefers sharing of electrons to complete its octet.
(d) K is the most metallic element.
(e) S forms acidic oxide.
(f) Al belongs to group 13.
_______________________
(a) Li and K belongs to the same group. (Group 1)
(b) Mg has the tendency to lose two electrons because it has 2 ions in it's outermost shell
(c) C prefers sharing of electrons to complete its octet because it has 6 ions in it's outermost shell need 2 ions to complete octet
(d) K is the most metallic element.
(e) S forms acidic oxide.
(f) Al belongs to group 13.
A. Quotient
B. Difference
C. Product
D. Sum
Answers
Answer: product
Step-by-step explanation:
product means that you are multiplying
[tex]\pi r * r = \pi r^{2}[/tex]
what two perfect squares are the closest to 175
Answers
Answer:
Perfect squares are whole numbers that are squared, so the two that are closest to 175 would be:
13*13=169 and
14*14=196
The two perfect squares closest to 175 are (13*13) and (14*14)
Hope this helps ;)
There are 25 students who answered a survey about sports. Four-fifths of them like football. How many students like football.
Answers
A fifth of 25 students would be 5 (25/5).
Four-fifths of the students would be the result of (25/5) multiplied by 4.
(25/5)*4
5*4
= 20; 20 students like football.
Answer:
20
Step-by-step explanation:
25 divided by 5 equals 5 then 5 times 4 to get 4/5 which is 20
Ruby read 0.85. Of a book what fraction of the book does ruby have left to read? Write in simplest form
Answers
Answer: 17/20
Happy to help!!!
Order the numbers from least to greatest. -1/20, -5/8, -1 , and -3/4
Answers
Answer:
The answer is: -1, -3/4, -5/8, -1/20
(−3x − 6)(3x2 − 6x + 3)????
Answers
Answer:
-216
Step-by-step explanation:
(−3x − 6)(3x2 − 6x + 3)
=(18)(6 − 6x + 3)
=(18)(6 − 18)
=(18)(− 12)
= -216
Answer:
-9 • (x + 2) • (x - 1)2
Step-by-step explanation:
(-3x-6)(3x2-6x+3)
Final result :
-9 • (x + 2) • (x - 1)2
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(-3x - 6) • ((3x2 - 6x) + 3)
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
-3x - 6 = -3 • (x + 2)
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
(3x2 - 6x + 3) = 3 • (x2 - 2x + 1)
Trying to factor by splitting the middle term
4.2 Factoring x2 - 2x + 1
The first term is, x2 its coefficient is 1 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 1 • 1 = 1
Step-2 : Find two factors of 1 whose sum equals the coefficient of the middle term, which is -2 .
-1 + -1 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and -1
x2 - 1x - 1x - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-1)
Add up the last 2 terms, pulling out common factors :
1 • (x-1)
Step-5 : Add up the four terms of step 4 :
(x-1) • (x-1)
Which is the desired factorization
Multiplying Exponential Expressions :
4.3 Multiply (x-1) by (x-1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x-1) and the exponents are :
1 , as (x-1) is the same number as (x-1)1
and 1 , as (x-1) is the same number as (x-1)1
The product is therefore, (x-1)(1+1) = (x-1)2
Final result :
-9 • (x + 2) • (x - 1)2
Find the rate of change of the function
15x - 5y=20
Answers
Answer:
3
Step-by-step explanation:
⇒15x-20=5y
⇒(15x-20)/5=y
⇒3x
The rate of change of the function is 3
m = 3how to find the rate of change of the functionTo find the rate of change of the function 15x - 5y = 20, we need to solve for y in terms of x and then determine the coefficient of x, which represents the rate of change.
Let's solve the equation for y:
15x - 5y = 20
Subtract 15x from both sides:
-5y = -15x + 20
Divide both sides by -5:
y = (15/5)x - 4
Simplifying the equation:
y = 3x - 4
Now we can observe that the coefficient of x is 3. Therefore, the rate of change of the function is 3. This means that for every unit increase in x, the corresponding y-value increases by 3.
Learn more about rate of change at
https://brainly.com/question/8728504
#SPJ2
Another unit cube with the same length, width, and height as the unit cube shown would have the same volume.
Answers
Answer: Yes, if both are the same length width and height, then they would have the same volume.
what is x
x - 3 = -5
Answers
Answer: x = -2.
Step-by-step explanation:
Answer: x= -2
Step-by-step explanation: Add three to both sides
Use the slope formula to find the slope that passes through the points : (-4, 10) and (2,-8)
Answers
Answer:
slope is 9
Step-by-step explanation:
y2-y1 over x2-x1 so you would do -8-10 over 2-4 which would be -18 over -2 and the you devide -18 devided by -2 and you get your answer and it is 9
The ordered pairs below represent a relationship between x and y.
Answers
Answer:
Step-by-step explanation:
Which expression is equivalent to 9/10
Answers
Answer:
The equivalent expression to 9(15) is 9(10+5).
Step-by-step explanation:
this is equivalent to 910 because 27 x 10 = 30 x 9 = 270.
this is also equal to 9(15) to 9(10+5)
An expression is defined as a set of numbers, variables, and mathematical operations. The expression that is equivalent to 9/10÷2/3 is (9×3)/(10×2).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression is equivalent to 9/10÷2/3, can be written as,
[tex]\dfrac9{10} \div \dfrac23\\\\\\= \dfrac{\frac{9}{10}}{\frac23}\\\\\\= \dfrac{9\times 3}{10 \times 2}[/tex]
Thus, the expression that is equivalent to 9/10÷2/3 is (9×3)/(10×2).
Learn more about Expression:
https://brainly.com/question/13947055
Rasie 2 to the 4th power then find the difference
Answers
3 halves times the product of 3 1 fifth
Answers
Answer: 48/10 , if you need it simpflity then its 4 and four fifths ( 4 4/5 )
how do i write this decimals 56.01 in expanded form
Answers
Answer: sowwy if im wrong
Expanded Numbers Form:
50
+6
+0
+0.01
Step-by-step explanation:
Expanded Numbers Form:
50
+6
+0
+0.01
Expanded Factors Form:
5*10
+6*1
+0*0.1
+1*0.01
Expanded Exponential Form:
5*101
+6*100
+0*10-1
+1*10-2
The expanded form of 56.01 is 50 + 6 + 0.01.
To write the decimal 56.01 in expanded form, we break down each digit's place value.
56.01 can be expressed in expanded form as follows:
50 + 6 + 0.01
The place values are as follows:
50 (50 is in the tens place, and we can also write it as 5 * 10)
6 (6 is in the ones place, and it is just 6)
0.01 (0.01 is in the hundredths place, and we can also write it as 1/100)
So, the expanded form of 56.01 is 50 + 6 + 0.01.
To know more about decimals here
https://brainly.com/question/28393353
#SPJ2
What is s in 2m+4s=16 if m=-2
Answers
Answer:
s = 5
Step-by-step explanation:
2m + 4s = 16
Step 1: Plug in -2 for m
2(-2) + 4s = 16
-4 + 4s = 16
Step 2: Solve for s
-4 + 4s + 4 = 16 + 4
4s / 4 = 20 / 4
s = 5
Answer: s = 5
Answer:
s= 5
Step-by-step explanation:
s= 5
m= - 2
2m + 4s= 16
Replace the m with the value it is in brackets. Remember brackets mean to multiply.
2(-2) + 4s= 16
-4 + 4s= 16
Carry over the -4 and make s the subject.
4s= 16 - - 4
4s= 16 + 4
4s= 20
s= 20/4
s= 5
Therefore s= 5
To check if the answer was correct, replace the s and m with the value it is in brackets. s= 5; m= 2
2(-2) + 4(5)= 16
-4 + 20 = 16
Therefore s= 5 and the answer is correct!
What is the equation of a circle with center (2,-8) and radius 9?
Answers
Answer:
9^2= (x+2)^2+(y+8)^2
Step-by-step explanation:
The equation is r^2=(x+h)^2+(y-k)^2
Answer:
x2+y2-4x+16y-13
Step-by-step explanation:
center (h,k)=2,-8
radius(r)=9
we know
(x-h)2+(y-k)2=r2
now insert above given information
(x-2)2+(y+8)2=9×9
eveuinup: 08%
Use simple interest to find the ending balance.
17) $26,000 at 3% for 2 years
Answers
Answer: $27,560
Step-by-step explanation:
Formular for simple interest = PRT
P= 26,000
R=3% = 3/100 = 0.03
T= 2
26,000 x 0.03× 2
= 1,560
Ending balance will be 26,000 + 1,560
= $27,560
ANSWER TO BE NAMED BRAINLIEST GET A THANK YOU AND 5 STAR VOTE FOR YOUR ANSWER
PLZ HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ALSO I WILL FRIEND REQUEST U
Find the area of trapezoid ABCD.
A) 80 cm2
B) 96 cm2
C) 104 cm2
D) 112 cm2
Answers
So you gotta break the trapezoid into 2 shapes, square and triangle.
Area of the square: 8 x 10 = 80 cm^2
Area of the triangle : 1/2 x base x height
base: 6
height: 8
therefore, 1/2 x 6 x 8 = 24 cm^2
24+80 = 104 cm^2
Therefore your answer is C
The area of the trapezoid ABCD should be option c [tex]104\ cm^2[/tex]
Calculation of the area of the trapezoid ABCD:Since
We know that
Area of the square= [tex]8 \times 10 = 80\ cm^2[/tex]
And,
Area of the triangle: [tex]1/2 \times base \times height[/tex]
Here
base = 6
height = 8
So, the area should be
[tex]= 1/2 \times 6 \times 8 \\\\= 24\ cm^2[/tex]
Now the area of trapezoid is
= 24+80
= 104
Hence, The area of the trapezoid ABCD should be option c [tex]104\ cm^2[/tex]
Learn more about area here: https://brainly.com/question/24608799
An item was increased by 20% but then decreased by 25%. Calculate the percentage change and state if it was an increase or decrease.
Answers
Answer:
10% Decrease
Step-by-step explanation:
Let the number is 100.
Now, if we increase the number by 20%, the new number will be -
100 + (100 × 20%) = 100 + 20 = 120
The new number is 120.
Again, if we decrease the new number by 25%, the number will be -
120 - (120 × 25%) = 120 - 30 = 90
The new number is 90.
The change will be decreased by = (100 - 90) = 10
Percentage change = (10 ÷ 100) × 100 = 10%
Between x = 0 and x = 1, which function has the same average rate of change as y = 3x ? A) y = 8x + 2 B) y = 3x + 2 C) y = 2x D) y = 1 3 -x
Answers
Answer: .
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
I did the usatestprep
Rishi is making a map of a remote village. In this village, each hut has a rectangular base measuring
4
m
4 m4, start text, space, m, end text by
6
m
6 m6, start text, space, m, end text.
Move the points on the grid below to draw the base of one of the huts described above.
Answers
The required dimensions of the hut base will be 8 by 12 m.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
The perimeter of a rectangle = 2(L+W)
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that Rishi is making a map of a remote village. In this village, each hut has a rectangular base measuring 4 m by 6 m.
Move the points on the grid below to draw the base of one of the huts described above.
As shown in the above figure, just move the top two points down two spaces. Two sides take up four, and the other two take up six. we can find that the length of the hut base is 12 m and the width 8 m.
Therefore, the required dimensions of the hut base will be 8 by 12 m.
Learn more about the Perimeter of the rectangle here:
brainly.com/question/15287805
#SPJ5
2. Doug paid $39.95 for dinner. He left a 15% tip for the server. Which of the following is closest to
the tip left by Doug? *
Answers
Answer:
$5.99
Step-by-step explanation:
In this problem, Doug paid the following amount for the dinner:
[tex]p=\$39.95[/tex]
He also left a 15% tip.
Here we want to calculate what is the amount correspondant to the tip.
In order to find this value, we have to calculate the 15% of the value of the dinner, therefore we want to find
the 15% of 39.95$
The percentage (15%) can be rewritten as fraction:
[tex]15\% =\frac{15}{100}[/tex]
Therefore, the amount of the tip is
[tex]t=\frac{15}{100}p[/tex]
And substituting p, we find:
[tex]t=\frac{15}{100}(\$39.95)=\$5.99[/tex]
So, the tip is $5.99.
Answer: 5.99
Step-by-step explanation:
Change % to decimal
Then multiply
15% =.15
39.95 x .15 = 5.99
If you were calculating the volume of a cube that has a side length of 8 inches, how would you write the calculations in exponential form? What are 2 more ways to read the exponent verbally
Answers
Answer:
[tex] {8}^{3} \: \: eight \: exponent \: 3 \: or \: eight \: raised \: to \: the \: power \: 3[/tex]
Step-by-step explanation:
[tex] {8}^{3} \: \: eight \: exponent \: 3 \: or \: eight \: raised \: to \: the \: power \: 3[/tex]