Answer:
see below
Step-by-step explanation:
To find the conjugate of a+bi take the opposite of bi so it would be a - bi
7-3i, the conjugate is 7 + 3i
8+2i the conjugate is 8 -2i
The product of a number and its conjugate is
(a+bi) (a-bi) = a^2 +abi-abi -b^2 i^2 = a^2 - b^2 (-1) = a^2 + b^2
( 4-i) ( 4+i) = 4^2 + 1^2 = 16+1 = 17
( 6+3i)(6-3i) = 6^2 + 3^2 = 36+9 = 45
#1
z=7-3i[tex]\\ \sf\longmapsto \overline{z}=7+3i[/tex]
#2
z=8+2i[tex]\\ \sf\longmapsto \overline{z}=8-2i[/tex]
#3
[tex]\boxed{\sf z\overline{z}=|z|^2}[/tex]
[tex]\\ \sf\longmapsto z=4-i[/tex]
[tex]\\ \sf\longmapsto |z|^2=4^2+(-1)^2[/tex]
[tex]\\ \sf\longmapsto 16+1=17[/tex]
#4
[tex]\\ \sf\longmapsto |z|^2[/tex]
[tex]\\ \sf\longmapsto 6^2+3^2[/tex]
[tex]\\ \sf\longmapsto 36+9[/tex]
[tex]\\ \sf\longmapsto 45[/tex]
I need help please .
The middle school band has 600 os members, 200 of the members were chosen for the highly selective All-State Band. What is the value of the ratio of the number of students who were chosen for the All-State Band to the number of students who were not chosen for the All-State Band?
Answer: For every three students in band, one will be selected for All-State band.
Step-by-step explanation: The easiest way to explain it is to reduce 600 and 200 by the same number until you can't anymore. I know it sounds like I'm coming up with this off the top of my head, but rest assured that I'm not.
What’s the midpoint of points a (6,-4) and b (2,-10) graphically
Answer:
here is ur midpoint
Step-by-step explanation:
(4, -7)
Please anything helps. Bisect each angle below
(Don’t know what I was doing on the first one)
Answer:
U are doing right but don't move ur compass when u are doing the line (i mean opposite line)otherwise ur line at not bisect
Determine whether each equation is always, sometimes, or never true.
2x + 7 - x = 3 + x + 4
Always
Sometimes
Never
Empty Set
I said never but I want see if thats right
Write each decimal number as a fraction or mixed number in simplest form?
You're letting x = 0.325325325…, which means
1000x = 325.325325325… (or 325.325, but pretend the underline is actually an overline)
Then the next box you'd fill in with 0.325325325… (or 0.325).
Subtracting these, you have
1000x - x = 325.325325325… - 0.325325325…
999x = 325
Finally, solving for x gives
x = 325/999
Choose the answer that has a value of -8.
A. 6 - (-2)
B. 12 + -4
C. 3 - 5
D. -4 - 4
Answer:
THE ANSWER IS D
PLEASE GIMME BRAINLIEST BESTIEEE (╥﹏╥)(╥﹏╥)
What is the equation of the line that passes through the point (2, -4) and has a
slope of 2
Answer:
y = 2x - 8 OR 4 - 2x = -4 - y
Step-by-step explanation:
Use the point-slope form m(x₁-x₂) = (y₁-y₂); m means slope
plug in your numbers:
2(2-x₂) = (-4-y₂)
4 - 2x = -4 - y
or to put it into Y=mx + b:
y = 2x + 8
Which equation can be solved for x in the following diagram?
Answer:
D
Step-by-step explanation:
opposite angles are equal
186 div by 20 because i am lost
Answer:
9.3
Step-by-step explanation:
186/20 = 18.6/2 = 9.3
[tex]Hello[/tex] [tex]There![/tex]
The answer is...
[tex]\frac{93}{10}.[/tex]
Hopefully, this helps you!!
[tex]AnimeVines[/tex]
i need help with 4=2/3(2x-9
Answer:
x=15/2
Hope it helps :)
Answer:
x = 7.5
Step-by-step explanation:
4 = 2/3 (2x - 9)
4 = 4/3x - 6
4 + 6 = 4/3x - 6 + 6
10 = 4/3x
10 x 3/4 = x
x = 7.5
Here's an easy question for points: 5 x 2/6 =
Q) 5 × (2/6) = ?
→ 5 × (2/6)
→ 10/6
→ 5/3 {final answer}
This one if to hard for me
Answer:
x=0 , x = 1/2
Step-by-step explanation:
(4x-1)=1 —> 4x-1=1—> 4x=1+1—> 4x=2 —> x=2/4 —> x= 1/2
-(4x-1)=1—>-4x+1=1—> 4x= 1-1 —> x=0
Hello there!
We are given the equation:
[tex] \displaystyle \large{ |4x - 1| = 1}[/tex]
Definition/Property
[tex] \displaystyle \large{ |a| = \sqrt{ {a}^{2} } } \\ \displaystyle \large{ |a| = b \longrightarrow a = \pm b} \\ \displaystyle \large{ |a| = \begin{cases} a \: \: (x \geqslant 0) \\ - a \: \: (a < 0) \end{cases}}[/tex]
First, cancel the absolute value sign and write plus-minus beside 1.
[tex] \displaystyle \large{ |4x - 1| = 1} \\ \displaystyle \large{ 4x - 1 = \pm 1} \\ [/tex]
Break in two cases.
[tex] \displaystyle \large{ 4x - 1 = \begin{cases} 1 \\ - 1 \end{cases}} \\ \displaystyle \large{ 4x = \begin{cases} 1 + 1 \\ - 1 + 1 \end{cases}} \\ \displaystyle \large{ 4x = \begin{cases} 2 \\ 0 \end{cases}} \\ \displaystyle \large{ x = \begin{cases} \frac{2}{4} \\ \frac{0}{4} \end{cases}}[/tex]
Therefore, x = 0 or 1/2
Let me know if you have any questions!
Topic: Absolute Value Function - Equations
True or false: (√2 + √3)^2 = 2 + 3 = 5
Explain:
Hi! I'm happy to help!
A square root, means:
√x=y
This means that:
x=y·y=√x·√x
When we have the square button, it causes everything to be multiplied by itself once.
√x²=x
Due to the fact that the squared symbol is outside of the parenthesis, it causes both the square toot of 2, and the square root of 3, to be squared.
Now that we know this, √2², and √3²= 2, and 3.
This is why we get 2+3.
2+3=5, which is pretty self explanatory.
I hope this was helpful, keep learning! :D
What is an equation of the line that passes through the points (1, 8) and (-1, -2)
Answer:
Step-by-step explanation:
(1,8) (-1,-2)
Slope: (-2-8)/(-1-1) = -10/-2 = 5
y -8 = 5 (x - 1)
y - 8 = 5x - 5
y = 5x +3
What is the slope of the line that passes through the points (7,9) and (15,-29)
Answer:
-4.75
Step-by-step explanation:
Slope = (y2-y1) / (x2-x1)
So applying the formula
(-29-9)/(15-7)
= -38/8 = -4.75
the base of a triangle is 13cm and its height is 5cm. what is the area of the triangle
Answer:
32.5cm
Step-by-step explanation:
Using the formula A=h_b*b/2
We get 5*13/2=32.5
Gonna post this one last time in hope that someone helps and explains this to me lol.
Answer: Y = 3500, X = 16
Step-by-step explanation:
Your maximum Y-value is 3000, or, the price of your car, so that could be the answer that's being looked for. However, it's always a good idea to leave a little extra space on the end of the graph so that you can show that your line ends instead of continuing onwards.
Your maximum X-value is 15, or, the number of months it would take to pay off the car (200 dollars per month, until you reach 3000 dollars), but again, it's always smart to leave a little buffer space so that you can see that the graph actually ends.
The answer your teacher wants is probably that the maximum Y-value should be 3000 and the maximum X-value should be 15, but if you have to actually graph this equation yourself and want it to be understood that your graph is a line segment and not a line (the difference being that a line is infinite and a line segment has two ends), you will want to show that by not ending the graph at the same spot as the line segment and instead extending it a little further.
A diver descends at a rate of 4 feet per minute. How far is the diver below sea level after 20 minutes?
Answer:
4 × 20 = 80 or just add 4 20 times
Solve the following using substitution
Y = 2X - 3
4X -3Y = 31
Answer:
Step-by-step explanation:
ax+by=c solving for y
Answer:
[tex]ax + by = c \\ by = c - ax \\ \\ y = \frac{c - ax}{b} \\ \\ y = \frac{c}{b} - \frac{ax}{b} [/tex]
I hope I helped you^_^
|x-3|<2
|4x+1|>0
|x-1|<5
Ayudaaaaaaa pleaseeeee
Recuerda que
• |x| = x si x ≥ 0
• |x| = -x si x < 0
Necesitas considerar dos casos:
• si x - 3 ≥ 0,
|x - 3| < 1 ⇒ x - 3 < 1 ⇒ x < 4
• si x - 3 < 0,
|x - 3| < 1 ⇒ -(x - 3) = 3 - x < 1 ⇒ -x < -2 ⇒ x > 2
Entonces la solución consta de todos los números reales x tales que x > 2 y x < 4, o simplemente 2 < x < 4.
El método para resolver las otras desigualdades es el mismo.
|4x + 1| > 0 ⇒ 4x + 1 > 0 o -(4x + 1) > 0
… ⇒ 4x + 1 > 0 o -4x - 1 > 0
… ⇒ 4x > -1 o -4x > 1
… ⇒ x > -1/4 o x < -1/4
⇒ x ≠ -1/4
|x - 1| < 5 ⇒ x - 1 < 5 o -(x - 1) < 5
… ⇒ x - 1 < 5 o -x + 1 < 5
… ⇒ x < 6 o -x < 4
… ⇒ x < 6 o x > -4
⇒ -4 < x < 6
Remove all perfect squares from inside the square root [tex]\sqrt{200}[/tex]
What are the name of these angles? Are
they congruent or supplementary?
-15=5(3q-10)-5q
Solve the equation
Answer:
q = 3.5
Step-by-step explanation:
Start by distributing the 5
-15 = 15q - 50 - 5q
Combine like terms
-15 = 10q - 50
Add 50 to both sides
35 = 10q
Divide by 10 to isolate q
35/10 = q
q = 3.5
Answer:
q=3.5 or 4
Step-by-step explanation:
-15=5(3q-10)-5q
-5=15q-50-5q
-15+50=15q-5q
35=10q
Divide both sides by 10.
35÷10=10q÷10
3.5=q
Therefore,q= 3.5
Round up=4
.
Find the distance between the two points rounding to the nearest tenth (if necessary).
(−5,−9) and (−8,0)
Write an equation for the following real life scenario.
Use "h" to represent your variable.
Diane worked to earn $48.50 babysitting her neighbors, she earns $6.00 per hour.
I don't understand the question
When 12 is added to half the sum of a number and 3 the result is 28. What is the number?
Answer:
29
Step-by-step explanation:
What is the solution to this equation?
2x + 3 (x - 10) = 45
A. x = 15
B. x = 3
C. x = 7
D. x = 11
ANSWER: A (x = 15)
Answer:
The value of x is 15
Step-by-step explanation:
2x + 3(x - 10) = 45
2x + 3x - 30 = 45
5x - 30 = 45
Now, Add 30 both sides we get,
5x - 30 + 30 = 45 + 30
5x = 75
Now, Divide 5 from both sides we get,
5x/5 = 75/5
x = 15
Thus, The value of x is 15
Hence, Option A is correct
-TheUnknownScientist
helppppppp pleaseeereee
Which number sentence has a product of 42?
7 × (-6)
-6 × 7
-7 × (-6)
-7 × 6
Answer:
-7 × (-6)
Step-by-step explanation:
7 × (-6) = -42
-6 × 7 = -42
-7 × (-6) = 42
-7 × 6 = -42
Answer:
[tex] - 7 + ( - 6) = 42[/tex]
I hope I helped you^_^