[tex]\large\underline{\sf{Solution-}}[/tex]
Given complex number is
[tex]\rm \longmapsto\:\dfrac{1}{ {(2 + i)}^{2} } [/tex]
[tex]\rm \: = \: \dfrac{1}{4 + {i}^{2} + 2 \times 2 \times i} [/tex]
[tex]\rm \: = \: \dfrac{1}{4 - 1 + 4i} [/tex]
[tex]\rm \: = \: \dfrac{1}{3+ 4i} [/tex]
[tex]\rm \: = \: \dfrac{1}{3+ 4i} \times \dfrac{3 - 4i}{3 - 4i} [/tex]
[tex]\rm \: = \: \dfrac{3 - 4i}{ {3}^{2} - {(4i)}^{2} } [/tex]
[tex]\rm \: = \: \dfrac{3 - 4i}{9 -16 {i}^{2} } [/tex]
We know,
[tex] \rm \longmapsto\:\tt{ {i}^{2} \: = \: - \: 1 \: } \\ [/tex]
So, using this, we get
[tex]\rm \: = \: \dfrac{3 - 4i}{9 -16( - 1)} [/tex]
[tex]\rm \: = \: \dfrac{3 - 4i}{9 + 16} [/tex]
[tex]\rm \: = \: \dfrac{3 - 4i}{25} [/tex]
[tex]\rm \: = \: \dfrac{3}{25} - \dfrac{4}{25}i[/tex]
In which part of the graph is the distance from home constant?
Distance from home
Time
A. 4
B. 3
C. 1
D. 2
Step-by-step explanation:
the answer is A. 4
as a horizontal line
Mother bought 3 cans of sardines at ₱17.80 each, 5 cans of milk at ₱38.85 each, 3kg sugar at ₱60.50 each, and 2 cans of corn beef at ₱78.85 each. Find the total amount bought. If she paid ₱500 bill, find her change.
Step-by-step explanation:
Total amount is:
3*17.80 + 5*38.85 + 3*60.50 + 2*78.85 = 586.85If the numbers are correct ₱500 won't be enough as the total amount exceeds it.
Mother bought 3 cans of sardines at ₱17.80 each, 5 cans of milk at ₱38.85 each, 3kg sugar at ₱60.50 each, and 2 cans of corn beef at ₱78.85 each. Find the total amount bought. If she paid ₱500 bill, find her change.
Statement:Mother bought 3 cans of sardines at ₱17.80 each, 5 cans of milk at ₱38.85 each, 3kg sugar at ₱60.50 each, and 2 cans of corn beef at ₱78.85 each.
Solution:The total amount for which she had brought the items
= ₱ (3×17.80 + 5×38.85 + 3×60.50 + 2×78.85)
= ₱ (53.40 + 194.25 + 181.50 + 157.70)
= ₱ 586.85
Answer:The total amount for which she had brought the items is ₱ 586.85.
I cannot solve the second part of the sum because the amount exceeds ₱ 500.
Hope it helps
Shaq painted 600 portraits in 8 hours at that rate how many portraits would he paint in 4 minutes?
Answer: In 4 minutes he will make 5 portraits
Step-by-step explanation:
[tex]\large \boldsymbol{} 600p-8h=480 min \\\\ x \ p-4 min \\\\ x=\dfrac{600\cdot 4}{480} =\dfrac{2400}{480} =5 \ portraits \\\\ \rm Answer : 5[/tex]
Use the definition f(a) = lim x->a f(x) - f(a)/(x-a) to find the derivative of the given function at the indicated point.2) F(x) =-8 -×2, a = 2. A.) 2 B.) -2 c.) -4 d.)4
Answer:
B
Step-by-step explanation: HOPE IT HELP
c. Point B (-3, -4) is also on the circle. Verify algebraically whether triangle OAB is a
right-angle triangle.
Answer:
89
Step-by-step explanation:
don't use this awnser its wrong
HELP ME PLEASE PLEASE PLEASE
Answer:
#1) 3 different roots, total 6#2) 3 different roots, total 9#3) 3 different roots, total 4Step-by-step explanation:
#1The roots are:
x - 3 = 0 ⇒ x = 3, multiplicity 2x + 1 = 0 ⇒ x = -1, multiplicity 32x + 5 = 0 ⇒ x = -2.5#2The roots are:
x = 0, multiplicity 3x + 2 = 0 ⇒ x = -2x - 4 = 0 ⇒ x = 4, multiplicity 5#3The roots are:
x² - 1 = 0 ⇒ (x + 1)(x - 1) = 0 ⇒ x = -1, x = 1x² + 4x + 4 = 0 ⇒ (x + 2)² = 0 ⇒ x + 2 = 0 ⇒ x = -1, multiplicity 2Ed is 7 years older than Ted. Ed's age is also 3/2 times Ted's age. How old areTed and Ed.
Solve this equation. 3(x−9)>3x+6
Answer:
No solution
Step-by-step explanation:
There are no values of x that make the inequality true.
do 12,16, and 20 make a right triangle
Answer:
so yes it does :)
Step-by-step explanation:
There is a fourth category of triangles in which one of interior angles is of 90∘ . It is called right triangle. 1) 12,16,20 : 202=162+122 : True, hence right triangle
Which method used to determine numbers of bacteria in a sample involves the preparation of a series of dilutions of the sample in sterile water, adding measured volumes of each dilution to melted nutrient agar plates, making pour plates, incubating, counting colonies, and multiplying colony counts by dilution factors to determine the number of bacteria in the sample
Answer:To obtain a readily counted and statistically accurate number of bacteria. When performing a standard plate count using the pour plate method, the dilutions are first made, and then measured aliquots of each dilution are cultured.
Step-by-step explanation:
Solve for x.
2x/3 +1=3
O x =6
O x =3
O x = 1 1/3
O x = 2 2/3
Answer:
3......................
Answer:
X=3!
Let's solve your equation step-by-step.
Step 1: Simplify both sides of the equation.
Step 2: Subtract 1 from both sides.
Step 3: Multiply both sides by 3/2.
Answer:
x=3
The picture needs to be answered.
Answer:
if 3 children go to the water park, 4 adults can go: TRUE
if 6 children go to the water park 3 adjults can go: FALSE
no adults, 6 children: TRUE (even 9 children can go)
no children, 6 adults: TRUE
10x is indeed the cost of the children
15y is indeed the cost of the adults
what are the two possible names for the line between a reflection
Answer:
Line m, because if you put a mirror on m, one figure will be truly reflected in another
what is 2/4 added to 1/3?
Will give brainliest if correct
Find the slope:
15. (4, 3); (-1, 10)
16. (3, -5); (2, -5)
17. (-5, 2); (-5, 3)
Answer:
15) Slope (m) = -7/5
16) Slope (m) = 0
17) Slope (m) = 1/0 (It's an undefined slope, in other words it's just a vertical line)
Step-by-step explanation:
Use this formula for each, to find slope⤵⤵⤵
[tex] \frac{y {2} - y1}{x2 - x1} [/tex]
15) ⤵
[tex] \frac{10 - 3}{ - 1 - 4} = \frac{7}{ - 5} = - \frac{7}{5} [/tex]
16) ⤵
[tex]\frac{ - 5 - ( - 5)} {2 - 3} = \frac{0}{ - 1} = 0[/tex]
17) ⤵
[tex] \frac{ 3 - 2}{ - 5 - ( - 5)} = \frac{1}{0} [/tex]
Hope this helps :)
Hello! I need help with this question
i’m just stuck on #6, is it d or c???
Simplify
10-2
103
-100,000
*
1
10
1
10
100,000
RETRY
Answer:
100,000
Step-by-step explanation:
[tex] (\dfrac{10^{-2}}{10^3})^{-1} = [/tex]
When you divide powers with the same base, subtract the exponents.
[tex] = (10^{-2 - 3})^{-1} [/tex]
[tex] = (10^{-5})^{-1} [/tex]
To raise a power to a power, multiply the exponents.
[tex] = 10^{-5 \times (-1)} [/tex]
[tex] = 10^5 [/tex]
[tex] = 100,000 [/tex]
Isabella and her brother, Santiago, want to make their grandma's famous fruit salad, but they can't remember how to make the honey-lime dressing. They decide to make two versions with different amounts of sweet honey and tangy lime, then compare them. Isabella mixes 4 tablespoons of honey and 2 tablespoons of lime juice. Santiago mixes 5 tablespoons of honey and 4 tablespoons of lime juice. Whose dressing is sweeter?
Answer:
Isabella
Step-by-step explanation:
4:2, is Isabella's ratio of honey:lime.
5:4, is Santiagio's ratio of honey:lime.
Therefore, Isabella has 6 equal parts over all and 4/6 of those parts are honey.
Santiago, has 9 equal parts, so he has 5/9 parts of honey.
Next is to make the denominators the same:
That would make the denominators 54 and then you just multiply the opposite denominator to the numerator:
5/9=36/54
4/6=30/54.
This means that Isabella's dressing is sweeter.
find the product of
I need help y’all pls I will give brainliest
Answer: (-2,-2)
Step-by-step explanation:
Start at finding the y-intercept(-3) then do rise over run with -2x
Rise over run is count up/down then left/right
A 24 foot tall streetlight casts a shadow that is 18 feet long. How long of a shadow is cast by a nearby parking meter post that is 4 feet high?
WILL MARK BRAINLIEST for whoever answers in less than 5 minutes
Answer: A streetlight casts a shadow 15 feet long. At the same time, a 18-foot flag pole casts a shadow 10 feet long. How tall is the tree? | Socratic A tree casts a shadow 15 feet long.
Given g(x)=-x-2 find g(-3)
Answer:
g(-3)=1
Step-by-step explanation:
substitude x=-3
g(-3)=-(-3)-2
=1
Answer:
g(-3) = 1
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Functions
Function NotationStep-by-step explanation:
Step 1: Define
Identify
g(x) = -x - 2
Step 2: Evaluate
Substitute in x [Function g(x)]: g(-3) = -(-3) - 2Simplify: g(-3) = 3 - 2Subtract: g(-3) = 1The length of a rectangle is 2x + 6. Its width is 52. Find the value of ac if the perimeter is 138m².
Answer:
ac = 18.5
Step-by-step explanation:
perimeter of a rectangle = [tex]2(l+b)[/tex]
= 138m^2= 2(2x + 6 ) + 52
= 4x + 12 + 52 = 138
= 4x + 64 = 138
= 4x = 138 - 64
= 4x = 74
= x = 74/4
= x = 18.5
Please answer my question
12 points will be given
Who wants to be my friend?
Put all your names in the answers box or in the comments
Answer:
yes
Step-by-step explanation:
i like points lol
I really need help finding the solution!!
Answer:
-0.5 is not a solution
2 is a solution
Step-by-step explanation:
To check if something is a solution of the equation, you need to substitute the value in place of the variable
15 + 2y = -12 - 4y
15 + 2(-0.5) = -12 - 4(-0.5)
15 - 1 = -12 + 2
14 ≠ -10 ∴ -0.5 is not a solution
5 - 2(3x + 5) = 3 - 10x
5 - 2[3(2) + 5] = 3 - 10(2)
5 - 2(6 + 5) = 3 - 10(2)
5 - 12 - 10 = 3 - 120
-17 = -17 ∴ 2 is a solution
Help ASAP!!! ILL GOVE BRAINLIEST IF YOU GET IT RIGHT!
Step-by-step explanation:
I am not sure but i think it is D or E (last 2 choices)
Sorry if wrong
The Elsie Dairy uses a machine that fills 28 cartons of milk an hour. How many will be filled in 6.5 hours?
Answer:
About 182 cartons will be filled in 6.5 hours.
Step-by-step explanation:
Multiply 6.5 by 28 to get 182
Answer:
The answer is 182
Step-by-step explanation:
28 x 6.5 = 182. if the machine fills 28 cartoons in a hour and you leave it running for 6.5 or 6 hours and 30 minutes that will be 182 cartoons filled in that amount of time.
Please help me on this it’s due
================================================
Explanation:
Let's start off converting the mixed number 12 & 1/4 to an improper fraction.
[tex]a \frac{b}{c} = \frac{a*c+b}{c}\\\\12 \frac{1}{4} = \frac{12*4+1}{4}\\\\12 \frac{1}{4} = \frac{49}{4}\\\\[/tex]
Do the same for the other mixed number 2 & 1/3.
[tex]a \frac{b}{c} = \frac{a*c+b}{c}\\\\2 \frac{1}{3} = \frac{2*3+1}{3}\\\\2 \frac{1}{3} = \frac{7}{3}\\\\[/tex]
-----------------------
From here, we divide the two fractions. I converted them to improper fractions to make the division process easier.
[tex]\frac{49}{4} \div \frac{7}{3} = \frac{49}{4} \times \frac{3}{7}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{49\times 3}{4\times 7}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{7\times 7\times 3}{4\times 7}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{7\times 3}{4}\\\\\frac{49}{4} \div \frac{7}{3} = \frac{21}{4}\\\\[/tex]
The last step is to convert that result to a mixed number.
[tex]\frac{21}{4} = \frac{4*5+1}{4}\\\\\frac{21}{4} = \frac{4*5}{4}+\frac{1}{4}\\\\\frac{21}{4} = 4+\frac{1}{4}\\\\\frac{21}{4} = 5 \frac{1}{4}\\\\[/tex]
Note that 21/4 = 5.25 and 1/4 = 0.25 to help check the answer.
-----------------------
Therefore, she can make 5 cakes. The fractional portion 1/4 is ignored since we're only considering whole cakes rather than partial ones.
write each equation in slope-intercept form. underline the slope and circle the y-intercept in each equation 5x+3y=30
The slope - intercept form is: ___
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]y = \underline{-\frac{5}{3}}x + \boxed{10}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\text{Converting to Slope-Intercept Form:}\\5x + 3y = 30\\\rule{150}{0.5}\\\rightarrow 5x - 5x + 3y = 30 - 5x\\\\\rightarrow 3y = 30-5x\\\\\rightarrow\frac{3y=30-5x}{3}\\\\\rightarrow y = 10 -\frac{5}{3}x\\\\\rightarrow \boxed{y = -\frac{5}{3}x + 10}[/tex]
⸻⸻⸻⸻
[tex]\text{General Slope-Intercept Formula:}\\y = mx + b\\\rule{150}{0.5}\\$\bullet \text{ }m -\text{Slope}\\$\bullet \text{ }b -\text{Y-Intercept}\\\rule{150}{0.5}\\\text{In the given equation, the slope would be } -\frac{5}{3} \text{ and the y-intercept would be } 10.[/tex]
⸻⸻⸻⸻
[tex]y = \underline{-\frac{5}{3}}x + \boxed{10}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.