Select all the complex numbers in the given table
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]
3x - 2y = 3; 6x – 4y = 1
How many solutions ?
Answer:
It has no solution
Step-by-step explanation:
3x - 2y = 3
6x - 4y = 1
To fond the number of solutions, we will first of all solve this system of equation.
We can solve this system of equation by either substitution method or elimination method or both method
We will be using both method to solve this system of equation.
3x - 2y = 3 ------------------------------------(1)
6x - 4y = 1 ------------------------------------(2)
we will first eliminate y, to do that, lets multiply equation (1) by 4 and then multiply equation(2) by 2
12x - 8y = 12 ----------------------------------(3)
12x - 8y = 2 ------------------------------------(4)
Subtract equation (4) from equation (3)
0 = 10
But 0≠ 10
This system of equation has no solution
Answer:
No solution.
Step-by-step explanation:
3x-2y=3
6x-4y=1, or 2(3x-2y)=1, 2×3=1, 6=1
Since 6 cannot be equal to 1, this system of equations has no solution
Which expressions are equivalent? Check all that apply.
3^9 3^4 -9^2 9^9 81^1
Answer:
3^4 and 81^1
Step-by-step explanation:
Find the product of 2x2(6x + 3). 12x3 12x3 + 3 12x3 + 6x2 2x2 + 6x + 3
Answer:
C. 12x³ + 6x²
Step-by-step explanation:
I'm an FLVS kid and got the question right, so I wanted to explain my answer:
You just have to use the distributive property for this one. Multiply 2x² by each term in the brackets.
2x²(6x + 3) ← original question for ref.
2x²(6x) = 12x³
2 · 6 = 12x² · x = x³("x" techniqually has a placeholder exponent of 1. To multiply two exponents with the same base, you just add the exponents. So x2 + x1 = x3.)2x²(3) = 6x²
2 · 3 = 6Keep the variable and exponent the sameSo the new terms are 12x³ + 6x²
The answer is C.
Which situation can match the given inequality? 7x < 4x + 5
The cost of 7 journals is $5 greater than the cost of 4 journals.
The cost of 7 journals is less than the cost of 4 journals plus a $5 novel.
The cost of 7 journals is less than the cost of 4 journals with a $5 off coupon. The cost of 7 journals is greater than the cost of 4 journals plus a $5 novel.
Answer:
The cost of 7 journals is less than the cost of 4 journals plus a $5 novel.
Step-by-step explanation:
Let
x -----> the cost of a journal
Verify each case
case 1) The cost of 7 journals is $5 greater than the cost of 4 journals
In this case the equation would be
[tex]7x=4x+5[/tex]
case 2) The cost of 7 journals is less than the cost of 4 journals plus a $5 novel.
so
[tex]7x<4x+5[/tex]
solve for x
subtract 4x both sides
[tex]3x<5[/tex]
divide by 3 both sides
[tex]x<\$1.67[/tex]
so
The cost of one journal must be less than $1.67
case 3) The cost of 7 journals is less than the cost of 4 journals with a $5 off coupon.
so
The inequality would be
[tex]7x<4x-5[/tex]
case 4) The cost of 7 journals is greater than the cost of 4 journals plus a $5 novel.
so
The inequality would be
[tex]7x>4x-5[/tex]
If f(x) = 2x² + 5, then what is the remainder when f (x) is divided by x – 10?
Answer:
Step-by-step explanation:
x - 10 = 0
x = 10
f(10) = 2*10² + 5 = 2*100 + 5 = 200 + 5
= 205
Remainder = 205
Answer:
195 is the right answer
Step-by-step explanation:
195
please help I NEED HELP PLS SKDJLAK
Answer: -√6 + 1
Step-by-step explanation:
[tex]\dfrac{\tan\bigg(-\dfrac{2\pi}{3}\bigg)}{\sin\bigg(\dfrac{7\pi}{4}\bigg)}-\sec(-\pi)\\\\\\=\dfrac{\tan(240^o)}{\sin(315^o)}-\sec(180^o)\\\\\\=\dfrac{\sqrt3}{-\dfrac{\sqrt2}{2}}-(-1)\\\\\\=\dfrac{-2\sqrt3}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)+1\\\\\\=\large\boxed{-\sqrt6+1}[/tex]
2. On rectangle ABCD below, if A is located at
(3, 4) and B is located at (7,6), is the slope
of BC ?
Answer: The slope of BC is -2.
Step-by-step explanation:
We know that a rectangle has all opposite sides equal and parallel.
Each interior angle is a right angle.
Therefore , if rectangle ABCD is a rectangle then , AB should perpendicular to BC. [ ∵ Angle between AB and BC is 90° .] (1)
Also , slope of line passing through (a,b) and (c,d) : [tex]\dfrac{d-b}{c-a}[/tex]
If A is located at (3, 4) and B is located at (7,6) .
Then , The slope of AB = [tex]\dfrac{6-4}{7-3}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]
Also, the product of slopes of two perpendicular lines is -1.
Then , (Slope of AB) x (Slope of BC) = -1 [From (1)]
[tex]\Rightarrow\ \dfrac{1}{2}\times (\text{Slope of BC})= -1\\\\\Rightarrow\ \text{Slope of BC}=-2[/tex]
Hence, the slope of BC is -2.
Beverly is starting a new diet. Her current weight is 160 pounds. She expects to lose 4 pounds per month. If x represents the number of months Beverly is on the diet, which linear function models the situation?
$8 buys 40 ounces of ground turkey
We see here that $1 will buy 5 ounces of ground turkey.
To find out how much $1 will buy, we can set up a proportion using the given information.
We know that $8 buys 40 ounces of ground turkey. Let's set up the proportion:
$8/40 ounces = $1/x ounces
To solve the proportion, we can cross-multiply:
$8 × x ounces = 40 ounces * $1
Simplifying further:
$8x = $40
To isolate x (the number of ounces that $1 will buy), we can divide both sides of the equation by $8:
x = $40 / $8
x = 5 ounces
Therefore, $1 will buy 5 ounces of ground turkey.
Alternatively, we can set up a ratio using the given information:
$8 for 40 ounces
To find out how much $1 will buy, we can find the unit price:
Unit price = Total cost / Total quantity
Unit price = $8 / 40 ounce
Unit price = $0.20 per ounce
Since $1 is equal to 100 cents, we can divide $1 by the unit price:
$1 / $0.20 per ounce = 5 ounces
Therefore, $1 will buy 5 ounces of ground turkey.
Complete question:
$8 buys 40 ounces of ground turkey, how much will $1 buy?
A TV sells for 290$. If it's discounted at 15%, what is the discount
The discount is $43.50, making the price of the discounted TV $246.50.
15% = .15
.15 x 290 = 43.5
$290 - $43.50 = $246.50
3 1/25 into a decimal
Answer:
3.04
Step-by-step explanation:
If s represents speed write an inequality to represent how fast a person can legally dive a vehicle in a school zone with a speed limit of 25 mph ?
Solve the equation
-4(8+y)=9
Answer:
[tex]-\frac{41}{4}[/tex]
Step-by-step explanation:
-4(8+y)=9
Distribute:
-32-4y=9
Add 32 on both sides:
-4y=41
Divide -4 with 41:
y=-41/4
Answer:
[tex]y = - \frac{41}{4} = - 10 \frac{1}{4} \\ [/tex]
Step-by-step explanation:
[tex]-4(8+y)=9 \\ - 32 - 4y = 9 \\ - 4y = 9 + 32 \\ - 4y = 41 \\ \\ y = - \frac{41}{4} = - 10 \frac{1}{4} [/tex]
Isolate the identity
cos 2x - cos 8x
cos 2x + cos 8x
HELP PLS
Answer:
Cos 2x = Cos (5x-3x)
Cos(5x)Cos(3x) + Sin(5x)Sin(3x)
Cos 8x = Cos (5x + 3x)
Cos(5x)Cos(3x) - Sin(5x)Sin(3x)
Cos 2x - Cos 8x
= Cos(5x)Cos(3x) + Sin(5x)Sin(3x) -
[Cos(5x)Cos(3x) - Sin(5x)Sin(3x)]
= 2Sin(5x)Sin(3x)
Cos 2x + Cos 8x
= Cos(5x)Cos(3x) + Sin(5x)Sin(3x) +
[Cos(5x)Cos(3x) - Sin(5x)Sin(3x)]
= 2Cos(5x)Cos(3x)
= 2Sin(5x)Sin(3x) ÷ 2Cos(5x)Cos(3x)
2 gets cancelled out
Sin(5x)/Cos(5x) is Tan(5x)
Sin(3x)/Cos(3x) is Tan(3x)
Hence the fraction is identical to
Tan(5x)Tan(3x)
Find the slope of the line that passes through points (4,5) and (-1,3)
A.)5/2
B.) 1/6
C.)2/5
D.)-5/2
Answer:
C - 2/5
Step-by-step explanation:
Using the formula for slope
m = (y_2 - y_1) / (x_2 - x_1)
Given two points
( 4 , 5) (-1 , 3)
x_1 = 4
y_1 = 5
x_2 = -1
y_2 = 3
Insert the values into the equation
m = (y_2 - y_1) / (x_2 - x_1)
m = ( 3 - 5) / ( -1 - 4)
= -2 / -5
- $ - cancels out
m = 2/5
Slope = m = 2/5
There are (26)3⋅ 20 bacteria in a sample. What is the total number of bacteria in the sample
22
23
29
218
Answer:
29?
Step-by-step explanation:
Answer:it might be 29
Step-by-step explanation:
Suppose that h(x) varies directly with x and h(x) = 44 when x = 2.
What is h (2) when x = 1.5?
Ο 14.7
Ο
Ο 132
Ο
Ο 22
Ο
Ο 33
Value of h(1.5) is 33
Step-by-step explanation:
Step 1: Find the relation between h(x) and x. Given h(x) = 44 when x = 2. Then h(x) = 22 × x = 22xStep 2: Find h(x) when x = 1.5⇒ h(1.5) = 22 × 1.5 = 33
Final answer:
To find h(2) when x = 1.5, you first determine the constant of variation (k) using the given information h(x) = 44 when x = 2. This leads to k = 22. Plugging x = 1.5 into the direct variation equation h(x) = k*x, we get h(1.5) = (option D) 33.
Explanation:
If h(x) varies directly with x, then we can express this relationship as h(x) = k*x, where k is the constant of variation. We're given that h(2) = 44, so we can solve for k by plugging in the values:
44 = k*2 => k = 22.
Now that we have the value of k, we can find h(1.5) by multiplying k by 1.5:
h(1.5) = 22 * 1.5 = 33.
Therefore, the value of h(2) when x = 1.5 is (option D) 33.
Which lines best approximate the directrices of the ellipse? Round to the nearest tenth. x = −4.6 and x = 4.6 x = −3.5 and x = 3.5 y = −4.6 and y = 4.6 y = −3.5 and y = 3.5
Answer: c
Step-by-step explanation:
Answer:
C y = −4.6 and y = 4.6
Step-by-step explanation:
Edge 2023
degree of inverse tangent of 0.83
Answer:
39.69 degrees
Step-by-step explanation:
Let
x ----> the measure of the angle
we have that
[tex]tan(X)=0.83[/tex]
using a calculator
[tex]m\angle X=tan^{-1}(0.83)=39.69^o[/tex]
3.
Performance Task A person is planning a
weekly workout schedule of cardio and yoga.
He has at most 12 hours per week to work out.
The amounts of time he wants to spend on
cardio and yoga are shown.
Whrite a system of linear inequalities to represent this situation
Answer:
2/3 ≥ 3/6
Step-by-step explanation:
Cross Multiply
f/g=h/i
f×i=g×h
2×6> 3×3
12> 9
if you qre travelling @90 km/h how far will you travel in 42 mins? Can someone show me step by step solution pls on how to work it out.
Answer:
Distance = 63 km
Step-by-step explanation:
Speed = 90 km/h
Time = 42 mins
Time = 42 / 60 = 0.7 hrs
Distance = Speed × time
Distance = 90 km/h × 0.7 hr
Distance = 63 km
credit card customer owes $523.85. They
re only able to make a payment of $184.50. How
much money does the customer still owe?
Answer:
$339.25
Step-by-step explanation:
Since the credit card customer owes $523.85 and is only able to make a payment of $184.50
Amount still owed
= $523.85 - $184.60
= $339.25
The customer still owes $339.25
jack had 8 dogs each of them need them need a 30min walk how long will jack be walking his dogs.
Answer:
240 minutes or 4 hours
Step-by-step explanation:
Step 1: Multiply
8 * 30
240 min
If you want hours:
240 / 60
4 hours
Answer: 240 minutes or 4 hours
7. A school supply company packages the
erasers shown below in boxes of 12. How
many cubic inches does the package contain?
2 in
.5in
Find eraser )
Answer:
5 in
Step-by-step explanation:
I don't actually the ans
Select the expression that is equivalent to the given polynomial.
16r4 – 625
O A. (2x + 5)(2x - 5)(2x + 5i) (2x – 5i)
B. (2x - 5)(2x – 5)(2x – 5i)(2x – 5i)
C. (2x - 5)(2x – 5)(2x + 5i)(2x – 5i)
D. (2x + 5)(2x + 5)(2x + 5) (21 + 5i)
Observe that [tex]16r^4[/tex] is the square of [tex]4r^2[/tex], and 625 is the square of 25.
So, your expression is a difference of squares, and as such we can rewrite it as
[tex]16r^4-625=(4r^2+25)(4r^2-25)[/tex]
Now again, [tex]4r^2[/tex] is the square of [tex]2r[/tex], and 25 is the square of 5. So, we have a sum and a difference of squares.
But if we think of 25 as [tex]-(5i)^2[/tex], we have again the difference of two squares, so we have
[tex]4r^2+25=(2r+5i)(2r-5i)[/tex]
[tex]4r^2-25=(2r+5)(2r-5)[/tex]
Option A is the correct expression equivalent to 16r⁴-625.
The options in the question must have r in place of x.
What does the imaginary number i mean?The imaginary number 'i' is the solution of the algebraic equation x²+1.
Thus, x²+1=(x+i)(x-i).
How to factorize (a²+b²)?We can observe that (a+bi)(a-bi)=(a²+b²)+i(-ab+ba)=a²+b².
Hence the factorization of a²+b² is (a+bi)(a-bi)
How to factorize the given polynomial?16r⁴-625
=(4r²-25)(4r²+25)
=(2r-5)(2r+5)(2r+5i)(2r-5i)
So, option A is the correct expression equivalent to 16r⁴-625.
To learn more about factorization visit- https://brainly.com/question/20293447?referrer=searchResults
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two friends bought a $14 pizza. Each person bought their own drink. The total cost of the food can be represented by the expression $2x + $14. What expression represents the cost of food for one person
What is the answer to 7x=3x+24
Answer:
7x=3x+24
4x=24
x=6
Answer:
[tex]x=6\\[/tex]
Step-by-step explanation:
[tex]7x=3x+24[/tex]
[tex]7x-3x=3x-3x+24[/tex]
[tex]4x=24[/tex]
[tex]\frac{4x}{4} =\frac{24}{4}[/tex]
[tex]x=6[/tex]
M=-2 (-3,4) how do you write it into slope intercept
Answer:
y = -2x - 2
Plug the x- and y-values into the appropriate spaces in the slope-intercept form and see which value for b would make the equation true:
4 = -2(-3) +/- ?
4 = 6 - 2
4 = 4
I don't know if this makes sense, I'm sorry if it doesn't but the answer is correct because it goes through the point (-3,4)
The answer is y = -2x - 2
You have to first plug the x- and y-values into the correct spots in the slope-intercept form and see which value for b would make the equation true.
4 = -2(-3) +/- ?
4 = 6 - 2
4 = 4
Hope to help.
Describe an easy way to find the square root
when the number is not a perfect square?
The product of a rational number multiplied by itself is called as a perfect square.,we can easily find out the square root for a number which is a imperfect square
Step-by-step explanation:
using the following formula we can find a square root for a number which is a imperfect square
X = Non perfect square
√x = (square root of nearest lower perfect square +(x - perfect square)÷2×(√perfect square )
[tex]√x = (square root of nearest lower perfect square +(x - perfect square)÷2×(√perfect square )[/tex]Example
√38
the nearest perfect root is 36
36 (√36=6)
so √38 = √36 + (38-36)/2√36
= 6 + 2/12
=6 + 1/6 = 6.166 (answer)
[tex]√38 the nearest perfect root is 36 36 (√36=6)so √38 = √36 + (38-36)/2√36 = 6 + 2/12=6 + 1/6 = 6.166 (answer)[/tex]
To find the square root of a non-perfect square, use estimation techniques or the quadratic formula if in relation to an equation. Use the imaginary unit i for square roots of negative numbers, and simplify by removing perfect squares when adding or subtracting radicals.
Finding the square root of a number that is not a perfect square can be done using a few different methods. One simple non-calculator method is to use estimation and refinement; start with an approximate guess and improve it. When dealing with negative numbers, remember that we use the imaginary unit i to denote the square roots of negative numbers. For example, a₂ can be written as 2i. Adding and subtracting radicals involves simplifying each radical by removing perfect squares and combining like terms.
For equations where the square root is part of a quadratic equation, ax²+bx+c = 0, if a, b, and c are non-zero, we should use the quadratic formula to find solutions. Estimation also applies when dealing with cube roots or higher, where we can start with an initial guess and use methods like calculus to refine it.
To estimate a surd like a₃ without a calculator, consider its place on the number line between two integers, knowing that a₃ is about 1.732. This helps get an approximate value which is often sufficient for many applications.