The result of the product of the given complex numbers as required to be determined is; Choice C; -5 + 14i.
What is the product of the given complex numbers?It follows from the task content that the result of the product of the given complex numbers is to be determined.
On this note, since the required product to be evaluated is; (–4 + i) (2 – 3i).
We can therefore multiply as follows;
-8 + 12i + 2i - 3i².
However, it is noteworthy to know that; i² = -1.
Hence, we have that;
-8 + 14i + 3
= -5 + 14i
On this note, it follows that the result of the product of complex numbers as required is; -5 + 14i.
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PLEASE HELP!!
The equation of a circle is (x+10)2+(y−4)2=100.
What is the center and radius of the circle?
Responses
center: (10, −4); radius: 10,000
center: , begin ordered pair 10 comma negative 4 end ordered pair, ; radius: 10,000
center: (−10, 4); radius: 10,000
center: , begin ordered pair negative 10 comma 4 end ordered pair, ; radius: 10,000
center: (10, −4); radius: 10
center: , begin ordered pair 10 comma negative 4 end ordered pair, ; radius: 10
center: (−10, 4); radius: 10
The center of the circle is (-10,4) and the radius is 10.
What is a circle?The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the outer trace.
All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
The equation of the circle is,
( x - h )² + ( y - k )² = r²
(x+10)² + (y−4)² = 100
(x+10)² + (y−4)² = 10²
Compare the equations and find the center and radius,
Center = ( h,k) = ( -10,4)
Radius = r = 10
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The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)
What is expression ?
expression can be defined as with the minimum of two variables or numbers and at least one math operation.
Given expression,
= 4 1/3 / (-5/6 )
= (13/3 )/ (-5/6)
= 13*6 / -15
= -26/5
By evaluating the other expressions to find its equivalent,
(13 / 3) / (-5/6)
= 13 * 6 / -15
= -26/5
Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .
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The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)
What is expression ?expression can be defined as with the minimum of two variables or numbers and at least one math operation.
What is division?Division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. The division operation is represented by the symbol ÷ or /, and it is the inverse operation of multiplication.
Given expression,
= 4 1/3 / (-5/6 )
= (13/3 )/ (-5/6)
= 13*6 / -15
= -26/5
By evaluating the other expressions to find its equivalent,
(13 / 3) / (-5/6)
= 13 * 6 / -15
= -26/5
Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .
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In the diagram below, QR is parallel to NO. If NQ = 12, QR 20, and NO = 35, find the length of QP. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Note that in the attached Geometric Figure (Diagram) which features QR as parallel to NO, if NQ = 12, QR 20, and NO = 35, then the length of QP is equal to 16.
What is the rationale for the above result?[tex]\overline {QR}[/tex] is Parallel to [tex]\overline {NO}[/tex]; therefore
QR/NO = PQ/PN
⇒ 20/35 = PQ/PQ +12
This is because:
PN = PQ + NQ; which is also
PN = PQ +12
(PQ + 12) x 20 = 35PQ
20PQ + 240= 35PQ ; Collect like terms
240= 35 PQ - 20 PQ
240 = 15PQ; Divide both sides by 15
⇒ 240/15 = 15PQ/15
⇒ 16 = PQ
Therefore, QP = PQ which is equal to 16.
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Find the length of the missing side. It’s a written response
Answer:
the missing side is [tex]\sqrt{89}[/tex]
Step-by-step explanation:
We use Pythagoras theorem
[tex]8^{2} +5^{2} =x^{2} \\64 + 25 = x^{2} \\89=x^{2} \\\sqrt{89} =x[/tex]
Find X. Please show steps, thank you.
Answer:
C=10
Step-by-step explanation:
helpp pleasee! Actual help not fake people, you will be reported
Answer:
side AB
Step-by-step explanation:
The scatter plot shows the ages of drivers who attended a car show and the ages of their cars.
What is the age range of drivers who own an 8-year-old car?
The required range of drivers who own 8 years car is 23years.
Given that,
The scatter plot shows the ages of drivers who attended a car show and the ages of their cars.
We have to determine,
The age range of drivers who own an 8-year-old car.
According to the question,
The Range is the difference between the lowest and highest values.
Therefore,
The age range of drivers who own 8 years old car is 17,25 and 40 years.
Then,
Range of drivers who own 8 years car = highest value of range - lowest value of age.
Range of age of drivers who own 8 years car = 40 - 17 = 23years
Hence, The required range of drivers who own 8 years car is 23years.
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Find the zeros of the following function
Answer:
15 and -20
Step-by-step explanation:
The zeros/ roots are the x intercepts of the graph
Sandy programmed a website's checkout process with an equation to calculate the amount customers will be charged when they download so. The website offers a discount. If one song is brought at the full price of $1.29, then each additional song is 99 cent State an equation that represents the cost, f(×) and when X songs are downloaded
Answer:
f(x) = 0.99x + 0.3
Step-by-step explanation:
f(x) = 1.29 + 0.99(x - 1)
Distribute
f(x) = 1.29 + 0.99x - 0.99
Combine like terms
f(x) = 0.99x + 0.3
Find the inverse of the function.
y = -4x
Write your answer in the form ax + b. Simplify any fractions.
y =
Help please
Answer:
The inverse function is [tex]y = -\frac{x}{4}[/tex]
Step-by-step explanation:
Inverse of a function:
To find the inverse of a function, we exchange x by y, then we isolate y.
y = -4x
Finding the inverse:
[tex]x = -4y[/tex]
[tex]4y = -x[/tex]
[tex]y = -\frac{x}{4}[/tex]
So
The inverse function is [tex]y = -\frac{x}{4}[/tex]
Sally can paint a room in 3 hours while it takes Steve 6 hours to paint the same room. How long would it take them to paint the room if they worked together?
Answer:
2h
Step-by-step explanation:
You can solve this one by adding their rates, but you have to invert the numbers they give you to find the rate. Rate is measured in something per unit of time, and "per" indicates division. So the rates are: 1/3 of an hour (Sally) and 1/6 of an hour (Steve). So add the rates: 1/3 + 1/6 = 1/2. (1/3 is 2/6, and 2/6 + 1/6 = 3/6). Since their combined rate is 1/2 of a room in one hour, it takes them two hours to paint the room.
The difference of two numbers is 3. Their sum is 13.
Answer:
8 and 5
Step-by-step explanation:
This morning, Carmen car had 18.61 gallons of fuel. now, 3.9 gallons left. How much fuel did Carmen use
Two cars leave towns 360 kilometers apart at the same time and travel toward each other. One car’s rate is 10 kilometers per hour less than the others. If they meet in 2 hours what is the rate of the slower car
9514 1404 393
Answer:
85 km/h
Step-by-step explanation:
Let s represent the speed of the slower car. Then the travel time is ...
time = distance/speed
2 = 360/(s +(s+10))
4s +20 = 360 . . . . . multiply by 2s+10
4s = 340 . . . . . . . . . subtract 20
s = 85 . . . . . . . . . . . divide by 4
__
The rate of the slower car is 85 km/h.
Nina and Luca were told to draw a net for the three-dimensional figure shown below. Which statement
nets is true?
Three-dimensional Figure
Answer:
d
Step-by-step explanation:
5. Based on recent results, scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312. Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1. Assume that the two tests use different scales to measure the same aptitude. If someone gets an SAT score that is in the 95th percentile, find the actual SAT score and the equivalent ACT score.
Answer:
The actual SAT score is 2024.
The equivalent ACT score is 29.49.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
SAT score that is in the 95th percentile
Scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312, which means that [tex]\mu = 1511, \sigma = 312[/tex]
95th percentile is X when Z has a pvalue of 0.95, so X when Z = 1.645. The score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 1511}{312}[/tex]
[tex]X - 1511 = 1.645*312[/tex]
[tex]X = 2024[/tex]
The actual SAT score is 2024.
Equivalent ACT score:
The equivalent ACT score is the 95th percentile of ACT scores.
Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1, which means that [tex]\mu = 21.1, \sigma = 5.1[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 21.1}{5.1}[/tex]
[tex]X - 21.1 = 1.645*5.1[/tex]
[tex]X = 29.49[/tex]
The equivalent ACT score is 29.49.
The diameter of a circle has endpoints P(-6,-11 ) and Q(4, 7). Write an equation for the circle. Be sure to show and explain all work. Thank you!
Answer:
(x + 1)^2 + (y + 2)^2 = 106
Step-by-step explanation:
The formula for a circle is
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) is the center of the circle and r is the raadius
--------------------------------------
The center is the midpoint of the diameter end points
(h, k) = ( (-6 + 4)/2 , (-11 + 7)/2 )
(h, k) = (-1, -2)
The radius is the distance from the center to an endpoint
Using (h, k) and Q
r^2 = (4 - -1)^2 + (7 - -2)^2
r^2 = 5^2 + 9^2
r^2 = 106
-------------------------------
Plug into the circle formula
(x + 1)^2 + (y + 2)^2 = 106
WILL GIVE BRAINLIEST
There are 6.02 × 10^23 atoms in 1 gram of hydrogen. How many atoms are there in 400 grams of hydrogen? Write your answer in scientific notation. If necessary, round your answer to two decimal places.
If possible PLEASE write the answer in the form of 54x10^3
Answer: 2.403 × 10^3 atoms
Step-by-step explanation:
10^13 x 6.02 = 6.02^23 and 6.02^23 x 4 = 2,403 turned into 2.403 x 10^3 atoms.
A quadratic function and an exponential function are graphed below. Which graph most likely represents the quadratic function? (5 points)
graph of function g of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 8 and 5, 32 and 6, 64. Graph of function f of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 10 and 5, 26 and 6, 37
f(x), because an increasing exponential function will eventually exceed an increasing quadratic function
g(x), because an increasing quadratic function will eventually exceed an increasing exponential function
g(x), because an increasing exponential function will always exceed an increasing quadratic function until their graphs intersect
f(x), because an increasing quadratic function will always exceed an increasing exponential function until their graphs intersect
Answer:
It's A
Step-by-step explanation:
I just did the test and it is A
PLS HELP ME!!!
COSINE RULE I THINK!!
please explain in some detail and will mark brainliest
Answer:
Step-by-step explanation:
if there is any triangle ABC and a,b,c are sides opposite angles A,B,C respectively , then
[tex]cos~A=\frac{b^2+c^2-a^2}{2bc} \\cos~B=\frac{c^2+a^2-b^2}{2ca} \\cos~C=\frac{a^2+b^2-c^2}{2ab}[/tex]
B=101
a= 3 cm
b=y
c=1 cm
use formula for cos B
cos 101=cos(90+11)=sin 11
[tex]-sin~11=\frac{1^2+3^2-y^2}{2 \times 3 \times 1} \\-6 \times sin~11=1+9-y^2\\y^2=10+6~sin~11\\y^2\approx 10+6\times 0.1908\\y^2 \approx11.1448\\y\approx3.338[/tex]
Answer:
2.16
Step-by-step explanation:
To find the length y:
Since we have an angle with two sides next to it, it is 'cosy', so we can use the cosine rule to find y. Let's make y = a for the formula.
Using the cosine formula:
a^2 = b^2 + c^2 - 2bc cos(A)
where b=1, c=3 and A=101
substitute these values in the formula:
a ^2 = 1^2 + 3^2 - 2(1)(3) × cos(101)
a ^2 = 4.647970...
Square root to find a:
a = √4.647970...
a = 2.16
thus, y = 2.16 to 3sf
Math XL for School Practice X
Savvas Realize
Savvas Realize
X+
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со
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8-9; MathXL for School: Practice & Problem Solving
Due 05/11/21
X8.9.PS-14
Question Help
2 cm
A glass bead has the shape of a rectangular prism with a smaller rectangular
prism removed. What is the volume of the glass that forms the bead?
2am
6cm
7 cm
6 cm
(The figure is not to scale)
The volume of the glass that forms the bead is cm3,
Answer:
224 cm³Step-by-step explanation:
Required volume is:
6*6*7 - 2*2*7 = 224 cm³Any help pls. Question is : Find the equation of line B, which is perpendicular toy-2x=-8(x-8)and passes through the point (6,-6). Find the midpoint of the line segment AB in the following figure
Answer:
Perpendicular line ⇒ 2x + 9y + 42 = 0
midpoint: (-1,1)
Step-by-step explanation:
Let's find the coordinates of midpoint of AB
Here, from figure, A = (-3,-2), B = (1,4)
So midpoint:
[tex]P = (\frac{-3+1}{2},\frac{-2+4}{2})[/tex]
∴ P = (-1, 1)
Now, given straight line is x - 2y = -8(x-8)
⇒x - 2y = -8x+64
⇒9x - 2y - 64 = 0
Perpendicular line to 9x - 2y - 64 = 0 is 2x + 9y + k = 0
Perpendicular line passes though (6,-6)
Putting the values, we get
2(6) + 9(-6) + k = 0
⇒12 - 54 + k = 0
⇒k = 42
∴ Perpendicular line ⇒ 2x + 9y + 42 = 0
please help me thank you
Answer:
52 cm²
Step-by-step explanation:
There are 3 distinct faces:
one with sides 2 and 3
one with sides 2 and 4
one with sides 3 and 4
There are two of each distinct face (they are accros each other)
so we find their areas (we times by two as there are two of each face)
2×3×2=12
2×4×2=16
3×4×2=24
Finally we add the values:
12+16+24=52 cm²
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Answer:
1) draw a line from (2,4) to (6,4)
2) 27.5
3) 16
4) 43.5
5) $97.88
Step-by-step explanation:
1) draw a line from (2,4) to (6,4)
2) (7+4)/2=5.5x5=27.5
3) 4x4=16
4) 27.5+16=43.5
5) 43.5x2.25= 97.875 = $97.88
What is the pattern in this sequence? −3,1,5,9,13, ...
Answer:
Pattern is: +4
Step-by-step explanation:
an arithmetic series/ pattern since the next number is got by adding 4 to tge previous number
What is 3x?
I’m confused because I know x is the variable. So let’s say x=30. Do I multiply it like 3 • 30 = 90?
3x=90
Answer: 3 · 30= 90
Step-by-step explanation:
yes you are correct
anyone know this click to see links will get reported
Answer:
exponents, exponents, parenthesis, parenthesis/exponents, parenthesis.
Step-by-step explanation:
I meet a boy and asked about his age,he said he don't know his age but his age is half of the age of his mum and who is five years lest than his Father. The total age of the three is one hundred,now how old will each be the son,mother and the father if there overall age is hundred years?
Answer:
i had a stroke while reading this
Step-by-step explanation:
Answer:
son: 19
mother: 38
father: 43
Step-by-step explanation:
x + 2x + 2x+5 = 100
5x = 95
x = 19
Write an equation of the line that passes through (-3,3) and is perpendicular to the line 2y = 8x - 6
The equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6 is y = (-1/4)x + 9/4.
What is the equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the equation of the original line.
Write in slope intercept form
2y = 8x - 6
y = 8x/2 - 6/2
y = 4x - 3
Using the slope intercept, slope m is 3.
The equation of a perpendicular line to 2y = 8x - 6 must have a slope that is the negative reciprocal of the original slope.
Slope of perpendicular line = -1 / ( 4 )
Slope of perpendicular line = -1/4
Plug the slope m = -1/4 and point (-3,3) into point-slope formula and simplify.
( y - y₁ ) = m( x - x₁ )
( y - 3 ) = (-1/4)( x - (-3) )
( y - 3 ) = (-1/4)( x + 3 )
y - 3 = (-1/4)x - 3/4
y = (-1/4)x - 3/4 + 3
y = (-1/4)x + 9/4
Therefore, the equation of the perpendicular line is y = (-1/4)x + 9/4.
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