Answer: x^2+4
Work Shown:
x = -2i
x^2 = (-2i)^2
x^2 = 4i^2
x^2 = 4(-1)
x^2 = -4
x^2+4 = 0
Side note: Since -2i is one root, this means 2i is the other conjugate root.
[tex]\text{For quadratic equations, if one root is complex, the other root will be its conjugate.}\\\\\text{So, the roots of the second degree polynomial are}~ \alpha = -2i ~~ \text{and}~~ \beta =2i \\\\\text{The equation is,}\\\\~~~~~~~x^2-(\alpha + \beta) x +\alpha \beta = 0\\ \\\implies x^2 -(-2i+2i)x +(2i)(-2i)=0\\\\\implies x^2 -0\cdot x -4i^2 =0\\ \\\implies x^2 -4(-1)=0\\\\\implies x^2 +4=0[/tex]
Please help!!!! (07.05 LC)
How many solutions does the equation 3x + 6 = -1 - 3 + 4x have?
O Two
O None
One
O Infinitely many
Answer:
one
Step-by-step explanation:
3x + 6 = -1 - 3 + 4x
Combine like terms
3x+6 = -4 +4x
Subtract 3x from each side
3x+6-3x = -4+4x-3x
6 = -4+x
Add 4 to each side
4+6 = -4+x+4
10 =x
There is one solution
Only one it's 10
I am so confused please help and thank you.
Answer:
C. AC~= DF, FB~=CB
Step-by-step explanation:
In order use HL theorem you have to have two right triangles, which it's marked that you do. HL stands for Hypotenuse-Leg. So in order to use Hypotenuse-Leg you have to know that the hypotenuses are congruent on the two triangles and also a leg is the same on the two triangles. AC and DF are the two hypotenuse. And FB and CB are legs. You need those two congruent segment pairs in order to use HL theorem.
In science class you are filling a cylindrical beaker with a fluid. The beaker has a circular base with a diameter of 4 inches and a height of 8 inches. You are filling the fluid into a tank that is shaped like a rectangular prism and has a volume of 100 cubic inches. How many times will you have to fill up the cylindrical beaker before the tank is full? Round to the nearest tenth.
0.9947≅1 times you have to fill up the cylindrical beaker before the tank is full.
What is volume?Volume is defined as the space occupied by any body in the three-Dimenions. All three parameters are required for the volume like length,width and hieght of cube or cubied.
here we have a beaker of cylindrical shape the volume of the shape will be calculated as:
[tex]\rm V=\dfrac{\pi}{4}\times d^2\times l=\dfrac{\pi}{4}\times (4)^2\times 8=100.53\ cubc\ inch[/tex]
We have a volume of rectangular prism = 100 cubic inches
So number of times the beaker fill the fluid will be calculated as:
[tex]=\dfrac { Volume \ of\ Prism}{Volume\ of\ beaker}=\dfrac{100}{100.53}=0.9947[/tex]
hence 0.9947≅1 times you have to fill up the cylindrical beaker before the tank is full.
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How many sets of one eighths are in 3/4
Answer:
6
Divide the fractions.
3 / 1 = 3
4 / 8 = 2
Use the numerator as a multiplicand.
2 × 3 = 6
1. When selecting a sample for a survey, the way you choose your sample:
A:may lead to biased results.
B:is not important.
C:should always include people you can access conveniently.
D:will not change the results of the data.
Answer:
When selecting a sample for a survey, the way you choose your sample: A) may lead to biased results.
Step-by-step explanation:
The way you choose your sample matters a lot in order to help limit the bias in sampling data.
There are four types of random samples: simple, stratified, cluster, and systematic.
There are two types of non-random samples: voluntary response and convenience.
You always want to have a random sample in order to have accurate, non-biased results. Therefore, A) May lead to biased results is the best answer.
Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables r = 0.123 What is the value of the coefficient of determination ? r ^ 2 = (Round to four decimal places as needed.)
The coefficient of determination is the square of the correlation coefficient, and the value is 0.0151
How to determine the coefficient of determination?The given parameter is:
Correlation coefficient, r = 0.123
Rewrite as:
r = 0.123
Take the square of both sides
r² = 0.123²
Evaluate the square
r² = 0.015129
Approximate
r² = 0.0151
The coefficient of determination is represented by r²
Hence, the coefficient of determination is 0.0151
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Can any math experts please help me with this thank you so much
[tex]1.~\boxed{\sf0.55555555555}\boxed[/tex]
[tex]2.~\boxed{\sf 0.54545454545}\boxed[/tex]
Use the ordered pair (2, 4) to find which equation describes the graph below.
Answer:
the answer is b , sub 2for x in each equ then whatever answer you get , use it to check is that what y is on grph
What is the pair of fractions of 1/4 & 1/3
The pair of fractions 1/4 and 1/3 when evaluated is; 7/12.
What is the pair of fractions of 1/4 &1/3?From the task content;
The addition of the pair of fractions 1/4 and 1/3 is required.On this note, it follows that the common factor between the two fractions is used in evaluation.
This therefore follows that the pair of fractions is; 7/12.
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Try and challenge yourself with this question!
Answer:
216°..........................
A particular extension cord can support up to 8 amps. Martino has an iron whose label states 720 watts, and he wonders if the iron can be plugged into the extension cord. If watts are converted to amps by dividing by 144, how many amps does the iron use?
Answer:
Step-by-step explanation:
Remark
To convert watts to amps, divide the watts by the amps
Givens
720 watts
8 amps (maximum safety of extension chord)
144 conversion factor
Solution
Amps = 720 watts / 144
Amps = 5
Answer
The iron uses 5 amps of current.
The extension chord is safe to use since 5 is less than 8
Answer:
720÷144=5 AMPS
Step-by-step explanation:
5ANSWER
varies directly with the number of
The doliar amount d that Megan earns
hours h that she works. In her last paycheck, she earned $148.50 working
18 hours.
If her next paycheck is $90.75, how many hours did she work?
Step-by-step explanation:
Let p and h represent pay and hours worked respectively,
p = kh
k = p/h = 148.5/18 = 8.25
p= 8.25h
90.75 = 8.25h
h = 11 hours.
Hope it helps! :)
If the mean of nine values is 25, find the sum of the values
Answer:
Sum of nine values = 225
Step-by-step explanation:
mean=∑[tex](x_{1 } +x_{2} + ...x_{9})/9=25[/tex]
∑ = (25)(9) = 225
Hope this helps
Mr Thando wants to build a garage.he went to local store obstain a quotation for the building material.below is the quotation from phindanani dealer
The computation of the quotation when Thando wants to build a garage will be $1700.
How to compute the quotation?Your information is incomplete. An overview will be given based on the information. It should be noted that a quotation is given when one wants to construct a building.
Let's assume that the prices include:
Sand = $1000
Machinery work = $200
Building materials = $400
In this case, you simply have to add the values together.
= $1000 + $200 + $400
= $1700
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The sum of the solution x^2-6x+5=0
Answer:
X=5
X=1
Step-by-step explanation:
2−6+5=0x
a = 1
b = -6
c = 5
=−(−6)±(−6)2−4⋅1⋅5√2⋅1
Four friends went to a drive-in diner for milkshakes. They each paid $4.41 for their milkshake, including a 5% sales tax. What was the total cost of the milkshakes before tax was added?
Answer:
17.64 easy math
Step-by-step explanation:
Whoever helps me get the right answer gets 20 points
A triangle has side lengths 3.4 cm, 4 cm, and 5.2 cm. The angle measures are 40°, 50°, and 90°.
What type of triangle is this triangle?
acute isosceles
acute scalene
right isosceles
right scalene
Answer:
right scalene
How many different strings can be made from the letters in ORONO using some or all of the letters? (15 pts.)
The number of different strings that can be made from the letters in ORONO using some or all of the letters is 63
What is the number of permutations in which n things can be arranged such that some groups are identical?Suppose there are n items.
Suppose we have
[tex]i_1, i_2, ..., i_k[/tex]
sized groups of identical items.
Then the permutations of their arrangements is given as
[tex]\dfrac{n!}{i_1! \times i_2! \times ... \times i_k!}[/tex]
We're given the word ORONO.
Case 1: One letter string:3 ways: O, R, or N
Case 2: Two letter string:Subcase: Consists O:
5 ways: OR, RO, ON, NO, OO
Subcase: Doesn't consist O:
2 way: RN, NR
Total permutation under this case = 5+2 = 7
Case 3: Three letter string:Subcase: Consists 3 'O':
1 way: OOO
Subcase: Consists 2 'O':
6 ways: OOR, ROO, ORO, OON, NOO, ONO
Subcase: Consists 1 'O':
6 ways: ORN, ONR, RNO, RON, NOR, NRO (or that there are 3 distinct letters to be arranged, which can be done in 3! = 6 ways)
Subcase: Doesn't consist O:
0 ways as only R and N cannot form three letter string.
Total permutation under this case = 1+6+6= 13
Case 4: 4 letter string:Subcase: Consists 3 'O':
So, we've got {O,O,O,R,N}
3 'O's are mandatory, so fourth letter is either R or N:
O, O, O, R can arrange themselves in : [tex]4!/3! = 4 \: \rm ways[/tex] (as total 4 words but 3 are identical)
Similarly, O, O, O, N can arrange themselves in 4 ways,
So when 4 letter string from ORONO consists of 3 'O's, then total 4+4=8 distinct strings can be made.
Subcase: Consists 2 'O':
So, we've got {O,O,R,N}
The total permuations of these 4 letters, of which 2 are identital is:
[tex]\dfrac{4!}{2!} = 12[/tex]
Subcase: Consists 1 'O':
0 ways: Single 'O' and one-one R and N cannot form four letter string.
Subcase: Doesn't consist O:
0 ways as only R and N cannot form four letter string.
Total permutation under this case = 8+12 = 20
Case 5: Five lettered string:All 5 letters of ORONO would be used.
There are 3 identical objects, so total number of their permutation is:
5!/3! = 20
Thus, from all these cases, we conclude that:
Total permutations of string letters using some or all letters of ORONO is:
3+7+13+20+20 = 63
Thus, the number of different strings that can be made from the letters in ORONO using some or all of the letters is 63
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Pls help me!!!!!!!!!!’
Answer:
m<6 = 119°
Step-by-step explanation:
Two lines are parallel with each along a line.
m<4 and m<6 are supplementary angles which both angles add up to 180°.
m<4 + m<6 = 180°
61° + m<6 = 180°
m<6 = 180° - 61°
m<6 = 119°
Answer:
Step-by-step explanation:
m<6 + 61 = 180
m<6 = 139
ANSWER THIS CORRECTLY FOR BRAINLIEST (ALGEBRA)
Answer:
33.49 cubic inches
Step-by-step explanation:
Clive has $900 in his bank account at the beginning of the school semester, Clive is hoping
to have at least $300 in his bank account at the end of the semester (18 weeks). If Clive only withdraws $35 a week for food, gas, and entertainment, will Clive be able to reach his goal at the end of the semester? Write an inequality that models the situation, and justify
your response both in a written format and algebraically.
Solve for x.
50
39
6
7
Answer:
x = 6
Step-by-step explanation:
Interior angles of a triangle sum to 180°
⇒ (8x + 2)° + 70° + 60° = 180°
⇒ 8x + 132° = 180°
Subtract 132° from both sides:
⇒ 8x + 132° - 132° = 180° - 132°
⇒ 8x = 48°
Divide both sides by 8:
⇒ 8x ÷ 8 = 48° ÷ 8
⇒ x = 6
Therefore, the value of x is 6.
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Apply angle sum property
8x+2+70+60=1808x+132=1808x=180-1328x=48x=6Consider the problem: After charging for 1/3 of an hour, a phone is at 2/5 of its full power. How long will it take the phone to charge completely?
Base on the given ratio, it will take the phone 5/6 hours to charge completely
How to determine the time to charge completely?The given parameter can be represented as:
Ratio = Time : Proportion
So, we have:
Ratio = 1/3 : 2/5
To charge fully, we have:
Time : 1 = 1/3 : 2/5
Express as fraction
Time/1 = 1/3/ 2/5
Evaluate
Time = 5/6
Hence, it will take the phone 5/6 hours to charge completely
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List all the possible rational roots for the polynomial x^3+x^2 - 3x+12
Answer: Heyaa! ~
Your Answers are... ±1,±2,±3,±4,±6,±12
Step-by-step explanation:
Find every combination of ± p/q, where p is a factor of the constant and
q is a factor of the leading coefficient.
Hopefully this helps you! ^^
- Matthew
Congruent yes or no Congruent? ___________
If so, what property? ________
Answer:
Yes
Property: Scalene
Step-by-step explanation:
ask my friend
Jack Enough
Solve the following system by graphing and identify the point of intersection.
Answer: Option #1: ( -2 , -1 )
Step-by-step explanation:
5(-2) - (-1) = 9
(-2) - (-1) = -1
a line passing through the point (−2, −3) with a slope of −6.
y + 3 = −6(x + 2) A
y + 2 = 6(x + 3) B
y − 3 = −6(x − 2) C
y − 2 = 6(x − 3) D
Answer:
A
Step-by-step explanation:
y + 3 = -6(x + 2)
y + 3 = -6x - 12
y + 3 = -6x - 12
y = -6x - 15
FIND THE EXACT AREA OF THE SHADED PLEASE HELP ILL GIVE BRAINLIESTTTT
well, if we take the whole area of the circle, including the trapezoid in it, and then we get the area of the trapezoid and subtract it from that of the circle's, what's leftover is what we did not subtract, namely the shaded area. Let's notice the circle has a diameter of 20, thus a radius of half that, or 10.
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=12\\ b=20\\ h=8 \end{cases}\implies A=\cfrac{8(12+20)}{2}\implies A=128 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Areas}}{\stackrel{circle}{\pi (10)^2}~~ - ~~\stackrel{trapezoid}{128}}\implies 100\pi ~~ - ~~128~~\approx~~186.16[/tex]
Vistance Formula
Find the distance between the two points. Show all work!
AY
(5.-10). (-5, 4)
Answer:
2 sqrt 74
Step-by-step explanation:
d^2 = ( x1-x2)^2 + (y1-y2)^2
d^2 = ( 5 - -5 )^2 + ( -10 -4)^2
= 100 + 196
d^2 = 296
d = sqrt 296 = 2 sqrt (74)
Identify the maximum or minimum value, domain, and range of the graph of the quadratic function.
Answer:
See below ~
Step-by-step explanation:
Details of the graph of the quadratic equation
Minimum value = -1Domain : all real numbersRange : y ≥ -1