[tex]\large\underline{\sf{Solution-}}[/tex]
Given complex number is
[tex]\rm \longmapsto\:\dfrac{3 + 2i}{ - 2 + i} [/tex]
So, on rationalizing the denominator, we get
[tex]\rm \: = \: \dfrac{3 + 2i}{ - 2 + i} \times \dfrac{ - 2 - i}{ - 2 - i} [/tex]
[tex]\rm \: = \: \dfrac{ - 6 - 3i - 4i - {2i}^{2} }{ {( - 2)}^{2} - {i}^{2} } [/tex]
We know,
[tex] \rm \red\longmapsto\:\tt{ {i}^{2} \: = \: - \: 1 \: } \\ [/tex]
So, using this, we get
[tex]\rm \: = \: \dfrac{ - 6 - 7i - 2( - 1) }{ 4 - ( - 1)} [/tex]
[tex]\rm \: = \: \dfrac{ - 6 - 7i + 2}{ 4 + 1} [/tex]
[tex]\rm \: = \: \dfrac{ - 4 - 7i }{5} [/tex]
[tex]\rm \: = \: - \dfrac{4}{5} - \dfrac{7}{5} i[/tex]
In this question, 5x squared +7, which one is the constant?
Answer:
7 would be the constant
Step-by-step explanation:
Constants are the values in an equation that never changed or are isolated. For instance, 5 would not be a constant because of the variable (x) being multiplied. Though, if it were 5+x square +7, 5 and 7 would be the constants.
Last year 2,315 people attended a game and this year 2,778 people attended. What is the percent increase in attendance?
Answer:
20 percent
Step-by-step explanation:
From the New Number deduct Old Number i.e. 2778-2315 = 463
Divide above number by Old Number i.e. 463/2315 = 0.2
Multiply the result by 100 i.e. 0.2*100 = 20%
List your questions you have down below so I can help you answer them I am really good at math :))
Theo used to drive 60 miles to work each day. His new home is now 20 miles away
from his job. What is the percent of
decrease in the distance Theo travels to
work? Round to the nearest tenth if
necessary.
Answer:
66.6% decrease in distance
Rounded 67%
He is traveling 1/3 of what he used to travel
Step-by-step explanation:
The percentage of decrease in the distance Theo travels to work is 66.7%.
Used concept of percentage;
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating the hundredth part of any quantity is called a percentage.
Given that;
Theo used to drive 60 miles to work each day.
And, His new home is now 20 miles away from his job.
Hence the percentage of decrease in the distance Theo travels to work is,
P = (60 - 20)/60 x 100
P = 40/60 x 100
P = 66.7%
So, The percentage of decrease in the distance Theo travels to work is 66.7%.
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30 points! (check image)
a. x = 15, y = 40
b. x = 30, y = 40
c. x = 15, y = 20
d. x = 30, y = 20
Answer: a. x = 15, y = 40
Step-by-step explanation:
So we already know that ΔABC and ΔFDE are congruent, which means their angles are equal. Based on this information, we could note that:
∠A = ∠F
∠C = ∠E
∠B = ∠D
Since we already know the measurement of ∠B, we could then conclude that ∠D, or y, is equal to 40°. This leaves us with two possible answers, a or b.
In order to find the value of x, we need to know the measurement of ∠F. And in order to find ∠F, we need to find the measurement of ∠A. We already know that the angles in a triangle sums up to 180°. So we would start as the following.
∠A + ∠B + ∠C = 180
We first substitute the known measurements.
∠A + 40 + 110 = 180
We then add up 40 with 110.
∠A + 150 = 180
We finally substract 150 on both sides of the equation. This gives us the measurement of ∠A.
∠A = 30°
Now that we know ∠A, we could start finding the value of x. So we already know this:
∠A = ∠F
We first substitute each angle with their known measurements.
30 = 2x
We now divide both sides by two. This gives the value of x.
x = 15
Magda's checking account has $42.45. She withdraws $60 from the account. Which equation shows the new balance, in dollars, of Magda's account?
Answer:
42.45 - 60 = - 17.55
Step-by-step explanation:
there is a 20 character limit so filler..
An equilateral triangle has a perimeter of
12
y
+
9
. What is the length of each side of the triangle?
Answer:
4y + 3
Step-by-step explanation:
Each side is equal to each other, since there are 3 sides, you divide the equation by 3.
hello pls fill in the question marks :) Multiply (x + 1)^3
(x + 1)^3= (x + 1)(x + 1)^2
= (x + 1)(x^2 + 2x + 1)
= x3 + ?x^2 + ?x + ?
Answer: 3, 3, 1
Step-by-step explanation:
(x+1)³= (x+1)(x+1)²
=(x+1)(x²+2x+1)
=x³+ 3x²+3x+1
which of the following straight line is parallel to y = 7 - 2x?
Answer:
Whichever line has a slope of -2
Step-by-step explanation:
rewrite in slope intercept
y=mx+b where m=slope
y=-2x+7
-2 is the slope of the original line
a parallel line will never intersect
the parallel line must have the same slope
If machine A makes a yoyo every five minutes and machine B makes a yoyo every 10 minutes
Answer:
Then machine A is twice as effiecent as machine B
Step-by-step explanation:
Your roommate asks to borrow $500 and agrees to pay it in 45 days with interest rate of 4%. How much interest will you earn?
Answer:
20
Step-by-step explanation:
BRAINLIEST to correct answer!!
They are equally spaced so all the circles share the same center point.
WILL GIVE BRAINLYEST!!!!!
What is the perimeter of kite WXYZ?
O 253 +2 units
0 2753 +5 units
O 2753 + 10 units
O 253 + 14 units
Answer:
+10 units
Step-by-step explanation:
The perimeter of the kite is: C. 2√53 + 10 units.
What is the Perimeter of a Kite?Perimeter = sum of all four sides that makes up the kite.
Find the length of each side of the kite:
WX = |-3 - 2| = 5 units
WZ = |-2 - 3)| = 5 units.
Using the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], find the length of XY and ZY:
[tex]XY = \sqrt{(4 - 2)^2 + (-4 - 3)^2} \\\\\mathbf{XY = \sqrt{53} }[/tex]
[tex]ZY = \sqrt{(-3 - 4)^2 + (-2 -(-4))^2} \\\\\mathbf{ZY = \sqrt{53} }[/tex]
Perimeter of the Kite = √53 + √53 + 5 + 5 = 2√53 + 10 units.
Perimeter of the Kite = 2√53 + 10 units.
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Which of the following represents the eighth root of x to the fifth power in exponential form? (6 points)
5x^8
8x^5
x to the five eighths power x^(5/8)
x to the eight fifths power x^(8/5)
Answer:
[tex]x^{\frac{5}{8}}[/tex]
Step-by-step explanation:
8th root of x to the power fifth. This means the power will be 5/8
[tex]x^{\frac{5}{8}}[/tex]Your choice is correct .
Someone Please help 2!!!!
Translate the sentence into an inequality.
Twice the difference of a number and 4 is at most - 18.
Use the variable x for the unknown number.
Let the no be x
Inequality given by
[tex]\\ \sf\longmapsto 2(x-4)\leqslant -18[/tex]
Let's solve
[tex]\\ \sf\longmapsto x-4\leqslant -9[/tex]
[tex]\\ \sf\longmapsto x\leqslant -5[/tex]
Answer:
the value of x => x≤-5
Step-by-step explanation:
2(x-4)≤-18
x-4≤-18/2
x≤-9+4
x≤-5
hope it's helpful to you
what is n? 2(n+5)=-2
Answer:
[tex]n=-6[/tex]
Step-by-step explanation:
Thanks!!!!!
Emily has 20 chocolate chip cookies in 48 sugar cookies she wants to make baskets with the same number of cookies in each basket what is the greatest number of baskets she can make
Answer: Take your pick, Emily.
Step-by-step explanation:
1) Assuming Emily wants both Chocolate Chip(CC) and Sugar Cookies(SC) in each basket, she could make 20 baskets having 1 CC and 2 SC in each basket. That would leave 8 SC (48-40) without any matching CC.
2) If Emily doesn't care about the makeup of each basket (e.g., some baskets may have any combination of cookies), she has a total of (20 + 48) or 68 cookies. She has the following choices:
1 cookie each: 68 baskets
2 cookies each: 34 baskets
3 cookies each: 22 baskets with 2 cookies left over
And so forth.
Unless Emily was given some other condition (e.g., a minimum of 5 cookies/basket), there are many possible answers.
help please! (will mark as brainliest)
please help me! correct answer will get brainliest!
Answer:
Step-by-step explanation:
any with a decimal number because ther is decimals and the x cordinates are in the middle the grpha line indicating o.5 or decimla number
solve for x 1/12=4x/3+5/3(x-7/4)
Answer:
x=1
Step-by-step explanation:
1) multiply the numbers
2) combine multiplied terms into a single fraction
3) distribute
4) combine fractions with common denominator
5) combine like terms
6) multiply all terms by the same value to eliminate fraction denominators
7) cancel multiplied terms that are in the denominator
8) multiply the numbers
9) add 35/4 to both sides of the equation
10) simplify
( add the numbers twice)
11) divide both sides of the equation by the same term
12) simplify
(divide the numbers, cancel terms that are in both the numerator and denominator, and last but not least move the variable to the left)
well and behold your answer is x=1
[tex]\frac{x}{2}[/tex]±4=8
HELP PLEASE ASAP GIVE AN EXPLANATION.
Jack is preparing a garden space. He has enough fertilizer to cover 121 square feet. He wants to make a square garden. What should be the length of each side?
Answer:
12 im pretty sure
Step-by-step explanation:
12x12=144
this was the question that was on my test
I’m only giving brainlyest to the right answer
Answer: c is the right answer
Step-by-step explanation: i just did it and i got it right.
a. In problem 3, figure PQRST is an image of figure VWXYZ.
Identify the corresponding angles.
2 Vand
and ZS
LZ and
Xand
and ZQ
Figure is not required .
Names of Pentagons are enough.
PQRSTVWXYZ[tex]\\ \sf\Rrightarrow <P\sim <V[/tex]
[tex]\\ \sf\Rrightarrow <Q\sim <W[/tex]
[tex]\\ \sf\Rrightarrow <R\sim <X[/tex]
[tex]\\ \sf\Rrightarrow <S\sim <Y[/tex]
[tex]\\ \sf\Rrightarrow <T\sim <Z[/tex]
Neee help wit these step 1-6
Answer:
what to do now
Step-by-step explanation:
neep help with iready
Answer:
I can help you.
Step-by-step explanation:
In the number 919,827, what is the nearest thousand?
Answer: 919,80
Step-by-step explanation:
Answer:
920,000
Step-by-step explanation:
9 hundred thousands
1 ten thousands
9 thousands
8 hundreds
2 tens
7 ones
Rounding: 5 and up round up, 4 and below round down.
8 is higher than 4 so you round 919,827 to 920,000.
Please help me. Please put correct answer
Mixed Number Form:
[tex] - 1 \frac1 2[/tex]
HELPPPPPPPPPPPPPPP PLSSSSSSS
Answer:
x = 85°
y = 85°
Step-by-step explanation:
The sum of angles in a triangle are 180°
So 29 + 66 + x = 180
Solve for x:
180 = 29 + 66 + x
Subtract 29 and 66 from both sides
85 = x
x = 85°
_______________________________________
x = y because they are vertical angles, and are congruent.
Since x is 85°, y = 85° as well
-Chetan K
Answer:
X= 85
Y= 85
Step-by-step explanation:
All angles in a triangle add up to 180.
Because we are given two of the angles of this triangle, we can solve for X.
180= 29+66+X
Therefore,
X= 180-29-66
X= 85
To solve for Y:
if two angles are diagonal from each other with no other lines intersecting the angle (as seen in this example), then the two diagonal angles are equal.
In this example, X is diagonal to Y
Therefore,
X=Y
X=85
Y=85