Answer:
45
Step-by-step explanation:
(6 + 3i)(6 − 3i) =6 (6 − 3i)+ 3i(6 − 3i)
= 36 -18i +18i-9[tex]i^{2}[/tex]
if [tex]i^{2} =-1[/tex]
36 -18i +18i-9[tex]i^{2}[/tex] = 36-9(-1)
=36+9
=45
=36-9i^2
=6^2 - (3i)^2
Answer:
[tex]\displaystyle 45[/tex]
Step-by-step explanation:
[tex]\displaystyle (6 + 3i)(6 - 3i) = 36 - 9i^2 = 36 - 9[-1] = 36 + 9 = 45[/tex]
Extended Information on the Complex Number System
[tex]\displaystyle \sqrt{-1} = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = 4\:[Any\:multiple\:of\:four][/tex]
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13. A point is ___
from two objects if it is the same distance from the objects.
Equidistant
When a point is equal between two objects, this is know as a equidistant. In geometry, an equidistant is a locus between two points in a perpendicular bisector.
______
Best Regards,
Wolfyy :)
Final answer:
A point is equidistant from two objects if it lies at the same distance from each object. This concept is framed within the realm of geometry, where theorems and corollaries help describe the spatial relationships between points and lines. Equidistance is a fundamental concept for understanding geometrical constructions and relationships.
Explanation:
A point is equidistant from two objects if it is the same distance from the objects. This can be understood through theorems and corollaries in geometry. For instance, a theorem states that if two lines are perpendicular to a third line, then points that are equidistant from the third line will also be equidistant from each other.
A corollary stemming from this theorem would be that two points that are equidistant from the ends of a straight line will determine a perpendicular bisector of that line. This signifies the point of intersection of both equidistant points with the line, which is also the midpoint of the straight line.
When it comes to determining if a point (x, y) is equidistant from two given lines represented by equations, we can use algebra to evaluate the relationships and find the solution that satisfies the distance criteria for the point in question.
In geometry, a point in space is considered the fundamental unit, which has no dimensions but can have a position that is described relative to other points. For example, to say that a point is equidistant from two other points or objects means that a rigid scale, if used, would measure the same distance from the point in question to each of the two objects.
0.03542 as a percent
Answer:
3.542 or 3/271/500
Step-by-step explanation:
0.03542×100
= 1771/50000 ×100
=1771/500
=3.542 or 3/271/500
It is the morning of the community-wide yard sale that Joe has been anticipating. According to The Weather Channel there is a 10% probability of snow in his area today.
Which of the following best describes the most likely way the probability was determined? (2 points)
Select one:
a. Historically, in this area, it has snowed 10% of the time on days with similar meteorological conditions as today.
b. It snows 10% of the time on this date each year.
c. Historically, in the United States, it has snowed 10% of the time on days with similar meteorological conditions as today.
d. Historically, it snows 10% of the days during this month.
Answer:
A
Step-by-step explanation:
United states is too broad and too many different conditions for the land. You do not base weather on the date either.
Historically, in this area, it has snowed 10% of the time on days with similar meteorological conditions as today best describes the most likely way the probability was determined. Thus option A is correct.
What is probability?The mathematical discipline known as probability specializes with determining the possibility of an event occurring. Composite reliabilities vary from 0 to 1, with 1 representing certainty and 0 representing hesitation.
Probability, which expresses the probability of a risk, is calculated by dividing the total possible combinations by the frequency of favorable events. Mornings with weather levels comparable to today's, precipitation has fallen 10% of the time. The Weather Forecast estimates there remains a 10% chance of snowfall around his region today.
Therefore, option A is the correct option.
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Roy buys a coat for $86.40 which includes An 8% sales tax which equation could you use to find the cost of the coat, c, without the Sales tax
Answer:
86.40 = c + 0.08 c is the equation which can be used to find the cost of the coat, c, without the Sales tax
Step-by-step explanation:
Let us assume the cost of the coat = c
Selling price of coat = $86.40
The sale tax on the coat = 8%
⇒ The sale tax = 8% of c
Calculating the sales tax, we get:
[tex]\frac{8}{100} \times = 0.08 c[/tex]
or, the sales tax amount on the cost price of coat = 0.08 c
Now, the Sales Price of coat =Cost Price of Coat + sales Tax Amount
⇒ $86.40 = c + 0.08 c
Hence, 86.40 = c + 0.08 c is the equation which can be used to find the cost of the coat, c, without the Sales tax.
2. For numbers 2a-2d, choose Yes or No to indicate whether
the product is correct.
O No
22. 0.48 X 10 = 4.8
2b. 0.76 x 10 = 76
26. 0.01 x 100 = 0.1
2d. 0.50 X 1,000 = 500
o Yes
o Yes
o Yes
o Yes
O No
o No
O No
One number is four times another number. The sum of their reciprocals is 1/4 . What are the numbers?
No, the numbers are not 4/5 and 16/5
Answer:
x=2, y=8
Step-by-step explanation:
Set up the equations:
4x=y
1/4x+1/y=1/4
---------------------
1/y+1/y=1/4
2/y=1/4
cross product
y*1=2*4
y=8
4x=8
x=8/4=2
The required numbers are given as 5 and 20, as of the given conditions.
Given that,
One number is four times another number. The sum of their reciprocals is 1/4.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Let the number be x,
According to the question,
y = 4x - - - - -{1}
and
1 / y + 1/ x = 1/4
1 / 4x + 1/x = 1/4
x = 5
Now,
y = 4 [5] = 20
Thus, the required numbers are given as 5 and 20, as of the given conditions.
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The circumference of a circle is 113 pi. What is the radius?
Answer:
R=18 (17.98)
Step-by-step explanation:
Since c=dπ
113=dπ
SOlve for d
113=dπ
/π /π
36=d (35.96)
Divide by 2, since the radius is the half of diameter
r=18 (17.98)
Please answer asap with an explanation
Answer:
The area of the given figure is [tex]66.5\ cm^2[/tex].
Step-by-step explanation:
To find out the area we should have to redraw the figure having nomenclature ABCDE and join BD. Thus we have a rectangle ABDE and a triangle BCD.
The new figure is in the attachment.
Given,
Length of AE = 7 cm
Length of DE = 8 cm
Length of CF = 11 cm
Solution,
Area of rectangle ABDE = [tex]length\times breadth=length\ of AE\timeslength\ of DE[/tex]
Area of ABDE = [tex]7\times8=56\ cm^2[/tex]
Now for triangle BCD,
Length of BD = length of AE = 7 cm
Length of GF = Length of DE = 8 cm
∴ Length of CG = Length of CF-Length of GF = [tex]11-8=3\ cm[/tex]
Area of triangle BCD = [tex]\frac{1}{2}\times base\times height}=\frac{1}{2}\times length\ of\ BD\times length\ of\ GF[/tex]
Area of BCD = [tex]\frac{1}{2}\times7\times3=\frac{21}{2}=10.5\ cm^2[/tex]
Area of ABCDE = Area of ABDE + Area of BCD = [tex]56+10.5=66.5\ cm^2[/tex]
Thus the area of the given figure is [tex]66.5\ cm^2[/tex].
When a window is open, the temperature in a room falls 5°F every 15 minutes. Before the window is opened, the temperature was 70°F . Pls Help Me! Will mark Brainliest
Use the Ray tool to make a graph that shows the temperature of the room, T, after the window has been open for m minutes.
Answer:
See attached graph
Step-by-step explanation:
Let m be the number of minutes passed and T be the temperature (in F°)
Before the window is opened, the temperature was 70°F, then at m = 0 minutes, T = 70°F
When a window is open, the temperature in a room falls 5°F every 15 minutes. This means
at m = 15, T = 70°F - 5°F = 65°F
at m = 30, T = 70°F - 10°F = 60°F
at m = 45, T = 70°F - 15°F = 55°F
and so on.
Plot points (0,70), (15,65), (30, 60), (45, 55) and connect them with a straight line. This is the graph that shows the temperature of the room, T, after the window has been open for m minutes.
Simplify (-8)(-2) + 11
Answer:
27
Step-by-step explanation:
-8 * -2 = 16
16 + 11 = 27
Solve the inequality. Graph the solution.
6n < 90
Answer:
[tex]\displaystyle 15 > n[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{6n}{6} < \frac{90}{6} → n < 15[/tex]
Whenever you divide\multiply by a negative, you reverse the inequality symbol.
** The above answer is written in reverse, which is the exact same result.
≥, ≤ → Solid Circle [●]
>, < → Blank Circle [○]
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sveltanas hair is 4 cm long her hair grows 1.5cm per month she wants her hair to be at least 16cm long
Answer:
8 months
Step-by-step explanation:
The question asks for the minimum number of months it would take her to grow her hair ATLEAST 16 cm.
Lets solve this!
Her hair is ALREADY 4 cm
She needs to make it 16 cm or greater
That is:
16 - 4 = 12 cm MORE
Per month growth rate = 1.5 cm
So we will divide the amount she needs to grow (atleast) by the growth rate per month:
12/1.5
= 8
Thus, in 8 months, her hair will grow:
8 * 1.5 = 12 cm
and 4 cm from before, so
12 + 4 = 16 cm
So, it will take a minimum of 8 months
Rearrange y=x2 (squared) to make x the subject.
Answer:
x = ±√y
Step-by-step explanation:
y = x²
±√y=√x²
±√y = x
slope intercept form slope:⅖ y-intercept:-2
Answer:
y= ⅖x - 2
Step-by-step explanation:
Formula: y = mx + b (m is the slope and b is the y intercept)
Info given:
m= 2/5
b= -2
Plug the info given into the formula, you get (2/5)x -2
Thomas rents a car for his vacation. the mileage included with the rental is 54 miles. For every mile he drives over 54 miles, he needs to pay $1 4/5. If he drives 69 miles, how much extra does he need to pay?
Answer:
Thomas needs to pay additional US$ 27 for the 15 extra miles not included in the mileage.
Step-by-step explanation:
1. Let's review the information given to us for solving the question:
Mileage included with the rental = 54 miles
Additional mile over 54 miles = US$ 1 4/5
Distance finally driven by Thomas = 69 miles
2. Let's calculate how much additional money Thomas needs to pay.
Extra miles driven by Thomas = Distance finally driven - Mileage included
Extra miles driven by Thomas = 69 - 54
Extra miles driven by Thomas = 15
Cost of the additional miles = 15 * 1 4/5
Cost of the additional miles = 15 * 1.80 ⇒ 4/5 = 0.80
Cost of the additional miles = 27
Thomas needs to pay additional US$ 27 for the 15 extra miles not included in the mileage.
9 candies cost less than $10 while 10 cost more than $11 how much does each candy cost
Answer:
this threw me off ,i got the same question:(
Step-by-step explanation:
(03.06 LC)
The functions f(x) = (x+4)2+2 and g(x) = (x - 2)2-2 have been rewritten using the completing the
square method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for
each function (10 points)
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BIVA - A - TEE 3 1 1 x x, E E
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-
Answer:
both are a minimum
Step-by-step explanation:
Given a quadratic function in vertex form
y = a(x - h)² + k
• If a > 0 then vertex is a minimum
• If a < 0 then vertex is a maximum
Here
f(x) = (x + 4)² + 2 ← with a = 1 > 0 ⇒ minimum vertex
g(x) = (x - 2)² - 2 ← with a = 1 > 0 ⇒ minimum vertex
Using the formula v= s/t , express s in terms of v and t; express t in terms of v and s.
Answer:
Express s in terms of v and t
s= v/t, multiplying both sides of the equation by t
Express t in terms of v and s
t= s/v ( from s=vt)
Step-by-step explanation:
Final answer:
To express s in terms of v and t, the formula is rearranged to s = vt. To express t in terms of v and s, the formula becomes t = s/v after rearranging.
Explanation:
To express s in terms of v and t using the formula v = s/t, we can rearrange the equation by multiplying both sides by t to get s = vt. Similarly, to express t in terms of v and s, we rearrange the formula to solve for t by dividing both sides by v, which gives us t = s/v.
To further clarify these transformations:
Expressing s: Start with v = s/t → Multiply both sides by t → vt = s.Expressing t: Start with v = s/t → Multiply both sides by t and then divide by v → s = vt → s/v = t.Mr. lee drive 8 miles from his house to Parkside Parkside is 4 miles south of Springfield from Parkside he drove 3 miles to Springdale then he drove 20 miles from Springdale to Brookville how far did Mr. Lee Drive in all
Mr Lee drive 31 miles from his house to Brookville
Solution:Given that
Mr. Lee drove 8 miles from his house to park side .
Parkside is 4 miles south of springfield.
From Parkside he drove 3 miles to springdale
Then he drove 20 miles from springdale to brookville.
Need to determine how far Mr Lee drive in all, from his house to Brookville.
Complete drive of Mr Lee from his house to Brookville is equal to 8 miles from his house to park side then 3 miles from Parkside to springdale , then 20 miles from springdale to brookville.
=> Complete drive of Mr Lee from his house to Brookville in miles = 8 + 3 + 20 = 31 miles
「14+ (-4) +6+(-16) = _
Answer:
0
Step-by-step explanation:
14+ (-4) +6+(-16) = _
10+6+(-16) =
16+(-16) = 0
Answer:
0
Step-by-step explanation:
14 + (-4) + 6 + (-16) =
10 + 6 + (-16) =
16 + (-16) =
0
solve this system of equations.
x-y=2
2.5x + y =5
Answer:
x=2, y=0. (2, 0).
Step-by-step explanation:
x-y=2
2.5x+y=5
---------------
x=y+2
2.5(y+2)+y=5
2.5y+5+y=5
3.5y=5-5
3.5y=0
y=0/3.5
y=0
x=0+2=2
Rewrite each fraction with a denominator of 24
2/3=
5/8=
Answer:
2/3=16/24
5/8=15/24
Step-by-step explanation:
2/3= 16/24
5/8= 15/24
because if you multiply across 2/3 by 8/8 equal 16/24
and if you multiply across 5/8 by 3/3 equal 15/24
The equivalent fraction for 2/3 and 5/8 are 16/24 and 15/24 respectively.
Given the following fractions
2/3
5/8
We are to rewrite the fractions as a denominator of 24.
For 2/3:
We will multiply both the numerator and denominator by 8 to have:
2/3 * 8/8 = 16/24
Similarly:
For 5/8:
We will multiply both the numerator and denominator by 3 to have:
5/8 * 3/3 = 15/24
Hence the equivalent fraction for 2/3 and 5/8 are 16/24 and 15/24 respectively.
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PLEASE HELP with this problem!!!
Answer:
vavavagagavavava
Step-by-step explanation:
zvvsvwgsgsgsgsgsgsgshsgshs
svavavvavavavavavavagagagaa8uevqvdbdgeuwgesgdushsstsvcvsvwgcr AA ctqqfcexrcagscc2vsvgagsggGgwgdvvasvvevavsvdbbdaggsgwgagsgagagagagytsswdtt a tgzggaaccscscscscfsfsfsfsfsfsffsfscfsfsffsfsfsffffsfsfsfsbebwvwvwgwgsgwgsgsagwvwansnsb✨shh da jhhhshehqjqjjjjdjdjjdjsjsjsjsj. sorry
need help solving with working much appreciated
Answer:
i. g = 70°
ii. x = 85°
Step-by-step explanation:
Given:
Let first we name the triangle
i. ) Δ PQR , m∠ PRQ = 40°
ii. ) Δ ABC is a right angle at B and a line B- D-C
m∠ DAC = 25°
m∠ ACD = 60°
m∠ BDA = x°
To Find:
i. g = ?
ii. x = ?
Solution:
i.
In Δ PQR , PR ≅ QR ...........{Given]
∴ Δ PQR is an Isosceles Triangle.
c.........{ Base angles of Isosceles triangle are equal }
∴ m∠ PQR = m∠ RPQ = g
Now sum of all the angles in a triangle is 180°
∴ m∠ PQR + m∠ RPQ + m∠ PRQ = 180°....{Angle sum property of Triangle}
[tex]g + g + 40 = 180\\2g=180-40\\2g=140\\g=\frac{140}{2} \\g=70\°[/tex]
∴ g = 70°
ii.
We know sum of all the angles in a triangle is 180°
In Δ DAC
m∠ DAC + m∠ ACD + m∠ ADC = 180°.....{Angle sum property of Triangle}
[tex]25+60+ \angle ADC = 180\\[/tex]
[tex]\angle ADC = 180-85\\\angle ADC =95\\[/tex]
Now By Linear Pair Angle Property
m∠ ADB + m∠ ADC = 180° ........{Linear Pair Angle Property}
[tex]x+95=180\\x=180-95\\x=85[/tex]
∴ x = 85°
Multiply the binomials (6a^3-5) (4a^3-11a)
For this case we must multiply the following expression:
[tex](6a ^ 3-5) (4a ^ 3-11a) =[/tex]
We apply distributive property considering that:
[tex]+ * + = +\\+ * - = -\\- * - = +[/tex]
So:
[tex]6a ^ 3 * 4a ^ 3-6a ^ 3 * 11a-5 * 4a ^ 3 + 5 * 11a =[/tex]
To multiply powers of the same base, we place the same base and add the exponents.
[tex]24a^ {3 + 3} -66a^ {3 + 1} -20a ^ 3 + 55a =\\24a ^ 6-66a ^ 4-20a ^ 3 + 55a[/tex]
Answer:
[tex]24a ^ 6-66a ^ 4-20a ^ 3 + 55a[/tex]
Which set of equations could be parametric equations?
y= x and y= 3x
y= x + 1 and y= 3x2
x= t and y=3t
x= 3y and y= x+1
The set of equations x = t and y = 3t could be parametric equations ⇒ 3rd answer
Step-by-step explanation:
Lets explain the meaning of parametric equations
A parametric equation is where the x and y coordinates are both written in terms of another letter
Examples:
x = 2t and y = 2 - t²x = 0.5 Ф and y = 2Ф, where Ф is measured from the positive x-axisLet us find the set of the parametric equations from the answer
Fist answer:
∵ y = x and y = 3x
∴ It is a set of linear equations
Second answer:
∵ y = x + 1 and y = 3x²
∴ It is a set of linear and quadratic equations
Third answer:
∵ x = t and y = 3t
∵ x and y are represented in terms of t
∴ It is a set of parametric equations
Fourth answer:
∵ x = 3y and y = x + 1
∴ It is a set of linear equations
The set of equations x = t and y = 3t could be parametric equations
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Which of the following correlation coefficients would correspond to a strong linear relationship in a data set?
A. 0
B. 0.5
C. 0.9
D. 100
Answer:
The correct answer is C.
Final answer:
The correlation coefficient of 0.9 indicates the strongest linear relationship among the provided options, and the weakest relationship is indicated when the coefficient is closest to 0.
Explanation:
The correlation coefficient that corresponds to a strong linear relationship in a data set is typically close to either -1 or +1. Based on the given options, the correlation coefficient of 0.9 (Option C) would indicate the strongest linear relationship, suggesting a very strong positive linear relationship between the two variables. Correlation coefficients close to 0 indicate weak relationships, and a value of exactly 0 implies no linear relationship at all. A perfect positive linear relationship has a correlation coefficient of +1, whereas a perfect negative linear relationship has a correlation coefficient of -1. Therefore, even negative coefficients such as -0.90 can also indicate a strong, but negative, linear relationship.
Hence, for the second part (Q4), the weakest relationship would be when the correlation coefficient is closest to 0 (Option A).
Each side of a square courtyard is 8 meters long. It costs $31.00 per meter to replace the brick wall around the courtyard. How much would it cost to replace the brick wall? $
Answer:
Step-by-step explanation:
31 times 8
Answer:
It would cost 992.
Step-by-step explanation:
8 meters X 4 sides=32
32X$31.00=992.
A bag contains 13 pieces of candy. In how many ways can five pieces be selected?
Five pieces can be selected in 1287 ways
Step-by-step explanation:
When the selection has to be made without considering the order of selection, combinations are used.
The formula for combination is:
[tex]C(n,r) = \frac{n!}{r!(n-r)!}[/tex]
Here
Total candies = n = 13
Candies to be selected = r = 5
Putting the values in the formula
[tex]C(13,5) = \frac{13!}{5!(13-5)!}\\=\frac{13!}{5!8!}\\=1287\ ways[/tex]
Five pieces can be selected in 1287 ways
Keywords: Combinations, selection
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There are 1,287 ways to select five pieces of candy from a bag of 13.
Explanation:To find the number of ways to select five pieces of candy from a bag of 13, we can use the concept of combinations.
The formula for combinations is C(n, r) = n! / (r!(n-r)!),
where n is the total number of items and r is the number of items to be selected.
Substituting the values, we get C(13, 5) = 13! / (5!(13-5)!).
Simplifying this expression, we find that there are 1,287 ways to select five pieces of candy from the bag.
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Jeremy and Justine work for a company that receives $45 for each unit of output sold. The company has a variable cost of $25 per item and a fixed cost of $1600.
Based on this information, Jeremy and Justine make some projections about potential profit.
• Jeremy states that for every 100 units of output sold, the company will make $3,600 in profit.
• Justine states that for every 300 units of output sold, the company will make $4,400 in profit.
The subject of this question is Business and the grade level is High School. Jeremy's projection is incorrect, while Justine's projection is correct.
Explanation:The subject of this question is Business and the grade level is High School.
Jeremy and Justine work for a company that receives $45 for each unit of output sold. The company has a variable cost of $25 per item and a fixed cost of $1600. To calculate profit, you subtract the total cost (fixed cost + variable cost) from the total revenue (45 * number of units sold).
Jeremy's projection states that for every 100 units of output sold, the company will make $3,600 in profit. Let's calculate this to verify if it's accurate. Justine's projection states that for every 300 units of output sold, the company will make $4,400 in profit. Let's calculate this to verify if it's accurate.
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