Answer:
The conjugate is 2+5i and the product is 29.
Step-by-step explanation:
The conjugate of a complex number [tex]a+bi[/tex] is [tex]a-bi[/tex]
Our complex number is 2-5i.
Here, a = 2 and b = -5
Thus, the conjugate of 2-5i is
[tex]2-(-5i)=2+5i[/tex]
Using this rule:
[tex](a+b)(a-b)=a^{2}-b^{2}[/tex]
And the fact that [tex]i^{2} = -1[/tex]
We can find the product of any complex number and its conjugate:
[tex](a+bi)(a-bi)=a^{2} - (bi)^{2}=a^{2} - b^{2} i^{2} = a^{2} + b^{2}[/tex]
As our complex number is [tex]2-5i[/tex], the product with its conjugate will be
[tex]2^{2} + (-5)^{2} =4+25=29[/tex]
HELP PLEASE ASAP. A video rental store keeps a list of their top 15 movie rentals each week. This week the list includes 6 action,
4 comedies, 3 dramas, and 2 mysteries. The store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to
show on the display monitors in the store. What is the probability that she selected 2 comedies and 1 action movie? EXPLAIN how the probability would
change if two more comedy movies were added to the list in place of the 2 mystery movies.
NOT SURE THE ANSWER IN THE PIC.
Answer:
the one selected, the one on top
Step-by-step explanation:
Explanation/Answer would be appreciated please
Answer: The solution for the system is (2, -7)
Step-by-step explanation:
Ok, here we have linear relationships.
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case, we have two lines:
ya, that passes through:
(-8, -5) and (-3, -6)
Then the slope is:
a = (-6 - (-5))/(-3 - (-8)) = (-6 + 5)/(-3 + 8) = -1/5
now, knowing one of the points like (-3, - 6) we can find the value of b.
y(x) = (-1/5)*x + b
y(-3) = -6 = (-1/5)*-3 + b
-6 = 3/5 + b
b = -6 - 3/5 = -33/5
then the first line is:
ya = (-1/5)*x -33/5
For the second line, we know that it passes through the points:
(-8, -15) and (-3, -11)
Then the slope is:
a = (-11 - (-15))/(-3 -(-8)) = (-11 + 15)/(-3 + 8) = 4/5
The our line is:
y(x) = (4/5)*x + b
and for b, we do the same as above, using one of the points, for example (-3, -11)
y(-3) = -11 = (4/5)*-3 + b
b = -11 + 12/5 = -(55 + 12)/5 = -43/5
then:
yb = (4/5)*x - 43/5.
Ok, our system of equations is:
ya = (-1/5)*x -33/5
yb = (4/5)*x - 43/5.
To solve this, we suppose ya = yb
then:
(-1/5)*x + -33/5 = (4/5)*x - 43/5.
-33/5 + 43/5 = (4/5)*x + (1/5)*x
10/5 = 2 = (4/5 + 1/5)*x = x
2 = x
now we evaluate x = 2 in one of the lines:
ya = (-1/5)*2 -33/5 = -2/5 - 33/5 = -35/5 = -7
Then the lines intersect at the point (2, - 7), which is the solution for the system.
Help ASAP please and thanks
PLEASE HELP!!! ASAP!!!
Answer:
28 units²
Step-by-step explanation:
→ Work out the size of the triangle if it was a full rectangle
Height = 4 and Base = 2
→ Work out area of triangle
0.5 × Height × Base ⇒ 0.5 × 4 × 2 ⇒ 2 × 2 ⇒ 4
→ Minus the area of the triangle from the "imaginary full' rectangle
Area of rectangle = Length × Width ⇒ 8 × 4 ⇒ 32
32 - 4 = 28
Answer:
[tex]\huge\boxed{28\ units^2}[/tex]
Step-by-step explanation:
The figure consists of a triangle, a square and a rectangle.
Area of Triangle:
[tex]\sf \frac{1}{2} (Base)(Height)\\Where \ Base = 2 , Height = 4 \\=> \frac{1}{2} (2)(4)\\=> 4\ units^2[/tex]
Area of Square:
[tex]\sf (Length)(Length)\\(4)(4)\\=> 16\ units^2[/tex]
Area of rectangle:
[tex]\sf (Length)(Width)\\Where \ Length = 4 , Width = 2\\=> (4)(2)\\=> 8 \ units^2[/tex]
Area of the whole figure:
=> 4 + 16 + 8
=> 28 units²
The health food store that you manage employs 7 clerks. Individual hourly wages are $8.10, $8.25, $8.45, $8.75, $9.00, $9.25, and $10.50. If each employee has 2 weeks unpaid vacation and works 8 hours a day , 5 days per week and is paid for all holidays , what the total annual payroll for the clerks ?
Answer:
16,848+17,160+17,576+18,200+18,720+19,240+21,840=
129,584
Step-by-step explanation:
[tex]$8.10, $8.25, $8.45, $8.75, $9.00, $9.25, and $10.50\\[/tex]
Annually= Yearly, A year has 365 days.
They work 40 hours a week, 8*5=40.
There are aprox, 10 holidays in a year. (You can change this in your work)
They have 2 weeks unpaid vacation, 14 days.
There are aprox, 52 weeks in a year. (You can change this in your work)
52 weeks - 2 weeks of unpaid vacation= 50 weeks.
Now Let's calculate the weekly income, for
$8.10*40=$324 per week.
$8.25*40=$330 per week.
$8.45*40=$338 per week.
$8.75*40=$350 per week.
$9.00*40=$360 per week.
$9.25*40=$370 per week.
$10.50*40=$420 per week.
Now Let's calculate the annually income, for each clerk.
324*50=16,200 + 648=16,848
330*50=16,500 + 660=17,160
338*50=16,900 + 676=17,576
350*50=17,500 + 700=18,200
360*50=18,000 + 720=18,720
370*50=18,500 + 740=19,240
420*50=21,000 + 840=21,840
Now the total annual payroll=
16,848+17,160+17,576+18,200+18,720+19,240+21,840=
129,584
PLEASE HELP!! I WILL GIVE BRAINLIEST AND 16 POINTS!!
Complete the equation of the line through (3,-1) and (4,7). Use exact numbers. What does "y" equal?
Answer:
lets start with finding the slope
m=7-(-1)/4-3
m=8
now we can choose either of the 2 points given and the slope and plug that into the point slope form
y-7=8(x-4)
y-7=8x-32
y=8x-25
and that is your equation
Answer:
y = 8x - 25
Step-by-step explanation:
The equation of a line is y = mx + b
To find the slope use y2-y1/x2-x1
When you plug it in it will be 7 + 1/4 - 3 (8)
Now it is y = 8x + b
Lastly you need to plug in a coordinate to the equation to find b
7 = 8(4) + b (-25)
Can someone please help me please and thanks.
Answer:
The probability of 3 students having blood type A is 1.23 , having blood type B is 0.3 and having blood type AB is 0.12
Step-by-step explanation:
Gracie, Mary, and Nancy each have a small collection of seashells. Gracie has 5 more than times the number of shells Mary has. Nancy has 1 more than times the number of shells Mary has. Gracie and Nancy have the same number of shells. If x is the number of shells Mary has, identify the equation that represents this situation and identify its solution.
Answer:
Answer is x = 24
Matches 3/2 x +1 = 4/5x-5
Step-by-step explanation:
We start with Mary 3/2x = 24 as 24/1.5 = 16 and 16 x 1/2 = 8
where 16 is 2/2 and 1/2 of 16 = 8
We find Nancy add 1 = 25 as 25/1.5 = 16.666.. and 1/2 = 8.333.
When 1 is added its done at end of both equations as multiplication occurs before hand.
Gracie has the same as Nancy = 5x+5 means 25 x 5 = 250+5 = 255 each.
50 x 5 = 250 + 5 +5= 510
510 + 24 + 1 = 535 seashells.
Because
24 + 1 = 25
matches
5/4 of 24 = 30
30 - 5 = 25
x=16 is the equation that represents this situation and identify its solution.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the number of shells Marry has.
Gracie has 5 more than times the number of shells Mary has.
Gracie = 1 1/4x + 5
Nancy = 1 1/2x+ 1
Now we have given that: Gracie =Nancy
[tex]1\frac{1}{4}[/tex] x + 5 = [tex]1\frac{1}{2}[/tex]x + 1
5/4x + 5 = 3/2x + 1
5x + 20 = 6x + 4
Subtract 6x and 20 on both sides
5x - 6x = 4 - 20
-x = - 16
x = 16.
Hence, x=16 is the equation that represents this situation.
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The ratio of boys to girls in the ninth grade is 7 to 9. there are 218 girls set up a proportion to model this information
Answer:
24.2
Step-by-step explanation:
Plssss answer this guys fastt Pleaseeee
Pleaseeeeeeeeeeeeeeeeeee
And when u make pls do it all and not half thanks u so much if u dooo
Answer:
You cant get someone to do all of this try doing a few or getting help from someone older that's what I did
Explanation:
I asked help for one problem and the explanation and now I understand how they did it so the other problems I can do now
It's better to make an effort and try doing some of them instead of asking someone to do all of it
Because when the test comes it won't be that easy so next time just try putting a few so that way you can try understanding it and you can apply it to similar problems.
I hope you can find this some what help to you in the future. Also this is a suggestion from my experience so you don't have to do it I'm just trying to help out.
A pantry contains 6 shelves each 42 inches long.
The shelves are to be relined with fresh paper.
The paper is sold in 1-yard rolls. The number
of 1-yard rolls needed is:
Answer:
7 1-yard rolls
Step-by-step explanation:
1 yard = 36 inches.
6(42 in) = 252 inches.
252 in/36 in = 7
Therefore, 7 1-yard rolls are needed.
The number of 1-yard rolls needed to sell 6 shelves each of 42 inches is 7.
Given,
A pantry contains 6 shelves.
Each shelves = 42 inches long.
The shelves are to be relined with fresh paper.
The paper is sold in 1-yard rolls.
We need to find the number of 1-yards rolls needed to sell 6 shelves.
How many inches is 1yards?1 yard = 36 inches.
We have,
6 shelves and each shelves is 42 inches.
1 shelves = 42 inches.
6 shelves = 6 x 42 inches
6 shelves = 252 inches.
And since,
36 inches = 1 yard
252 inches = (252/36) yard
252 inches = 7 yard
Thus the number of 1-yard rolls needed to sell 6 shelves each of 42 inches is 7 1-yard rolls.
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Figure B is a scaled copy of Figure A.
9
3.6
3.6
9
Figure A
1.2
3
1.2
3
Figure B
What is the scale factor from Figure A to Figure B?
Answer:
1/3
Step-by-step explanation:
We are going to a small shape from a big shape, so the scale factor must be less than 1.
3 (which is a side on the blue figure) and 9 (a side on the green figure)
3 and 9 are easy numbers (for me...) so 3:9 is smaller than 1.
3:9 simplified is 1:3 = 1/3
so 1/3 is the scale factor.
Let's make sure it's right....
9 * 1/3 (green figure to blue figure) is = 3.
3.6 * 1/3 = 1.2
you can check it yourself on a calculator if you don't believe me
I hope this helps have a great day!!!!
Calculate the area of the circle to the nearest hundredth of a square unit. Approximate as 3.14. a. 124.63 cm 2 b. 124.6 cm 2 c. 39.56 cm 2 d.19.78 cm 2
Answer:
[tex]124.63[/tex]
Step-by-step explanation:
[tex]a = \pi \times r {}^{2} = \pi \times (6.3) {}^{2} = \pi \times 39.69[/tex]
[tex]\pi \times 39.6 = 3.14 \times 39.69 = 124.63[/tex]
Hope this helps ;) ❤️❤️❤️
The area of circle will be;
⇒ 124.63 cm²
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The radius of circle = 6.3 cm
Now,
Since, The radius of circle = 6.3 cm
We know that;
Area of circle = π r²
Hence, We get;
⇒ Area of circle = 3.14 × 6.3²
= 3.14 × 39.69
= 124.63 cm²
Thus, The area of circle will be;
⇒ 124.63 cm²
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08
12.5%
The following items were bought on sale. Complete the missing information.
Amount Paid
Item Purchased
Video Game
Original Price
$80
Amount of Discount
20%
$14
$11.20
Movie Ticket
Laptop
$1,000
$750
Shoes
$55.00
10%
$49.5
Lumos Information Services 2020 LumosLearning.com
Answer:
1. $64
2. 20%
3. 25%
4. $65.50
Step-by-step explanation:
1. 80 x 20% = ?
method = 80 x 0.20 = 16 = $16 80-16 = 64 = $64
2. 14 x ? % = $11.20
method = We divide 11.20/14 = 0.8 = 0.80 = 80% inverse of 80% = 20%
proof 14 x 0.20 = 2.80 so; 14 -2.80 = $11.20
3. 1000 x ? = $750
method = 1000/750 = 0.75 0.75 = 75% inverse on original price = 25%
4. $55 x 10% = ?
method = 55 x 1.10 = 65.5 = $65.50
The net of a right rectangular prism is shown below: Find the volume of the prism with the given net (in cubic inches).
Answer:
240 inches cubed
Step-by-step explanation:
Volume equals length times width times height. Imagine the net is folded into its shape. The product of the base, 6 x 10 = 60, and the height, 4, equals 240. Remember that each square accounts for two inches. Hope this helps.
Any help will be nice...Dont answer for points >:( Correct equations for vertical line (7.5pt) Correct equations for horizontal lines (7.5pt) 1. In many cities and towns across the United States, the numbering system of the roads is based on a grid, similar to the latitude and longitude lines on a globe. Suppose the green lines in the following graph represent two east-west and two north-south running roads in a Midwestern town.
Answer:
See below.
Step-by-step explanation:
Horizontal lines have the equation:
[tex]y=n[/tex]
Where n is the value the horizontal line stays on.
Vertical lines have the equation:
[tex]x=n[/tex]
Where n is the value the vertical line stays on.
For the two north-south lines, one of them stays on -5 and the other stays on 8. Therefore, the two vertical line equations are:
[tex]x=-5 \text{ and } x=8[/tex]
For the two east-west lines, one of them stays on -7 and the other stays on 4.
Therefore, the two horizontal line equations are:
[tex]y=-7 \text{ and } y=4[/tex]
HELPPP
The diagram below represents a tower. Given the tower resembles a cone on top of a cylinder, which of
the measures below is the closest to the volume of the tower.
T
10 m
0
100
30 m
10 m
o
2600
2200
9400
10500
Previous
Answer:
the answer must be A as it is the closest, i think its a computer error
Answer:
if the answer wasn't A i would try B since its the next closest answer
Step-by-step explanation:
pLZZ i really need help my assignment past due and i just have one more question, please thankyou!!!!!!!!
Answer:
the answer is c
Step-by-step explanation:
convert the fractions to improper fractions 4/3 and 7/4 then multiply these fractions. youll get 28/ 12 and simplify to 2 1/3
Answer:
C
Step-by-step explanation:
So first, we should probably un-mix those fractions. So, we get:
4/3 x 7/4.
Multiplying this out, we get 28/12. Simplifying, we can get 2 1/3, which is C.
Let X, Y, and Z be points such that [tex]\frac{XZ}{XY} = \frac{ZY}{XY} = \frac{1}{2}.[/tex] If Y = (1, 7), Z = (-1, -7), then what is the sum of the coordinates of $X$?
Answer:
1
Step-by-step explanation:
1
Find the sine and cosine of each angle as a fraction and as a decimal. Round to the nearest hundredth.
Answer:
1st triangle:
sin(C): 0.64, [tex]\frac{16}{25}[/tex]
cos(C): 0.8, [tex]\frac{4}{5}[/tex]
Second triangle:
sin(C): 0.75, [tex]\frac{\sqrt{5} }{3}[/tex]
cos(C): 0.67, [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Using SOH CAH TOA, we know that to find the sin of an angle, it's Opposite/Hypotenuse.
To find the cos of an angle, it's adjacent/hypotenuse.
In the 1st triangle:
The adjacent to C is 16, the hypotenuse is 25.
[tex]\frac{16}{25} = 0.64[/tex] is the sin of C.
The adjacent to C is 20, and the hypotenuse is 25.
[tex]\frac{20}{25} = 0.8[/tex] is the cos of C.
In the second triangle:
The opposite to C is [tex]\sqrt{5}[/tex] and the hypotenuse is 2.
[tex]\frac{\sqrt{5} }{2} \approx0.75[/tex] is the sin of C.
The adjacent to C is 2 and the hypotenuse is 3.
[tex]\frac{2}{3} \approx 0.67[/tex] is the cos of C.
Hope this helped!
14+12= -15x+2x need help thanks
Answer:
x = -2
Step-by-step explanation:
Collect terms:
26 = -13x
Divide both sides of the equation by the coefficient of x:
26/-13 = x = -2
The solution is x = -2.
Answer:
-2
Step-by-step explanation:
14+12=-15x+2x
26=-13x
x=26/-13
x=-2
Let f(x) = 5x + 12. Find f−1(x).
Answer:
[tex]f(x)=5x+12\\\\ f^{-1}(x):\\ y=5x+12\ \ \ |Subtract\ 12\\ y-12=5x\ \ \ |Divide\ by\ 5\\ \frac{y-12}{5}=x\\\\ f{-1}(x)=\frac{x-12}{5}[/tex]
Step-by-step explanation:
Answer:
f^-1(x) = x/5 - 12/5
Step-by-step explanation:
f(x) = 5x + 12
y = 5x + 12
x = 5y + 12
5y = x - 12
y = x/5 - 12/5
f^-1(x) = x/5 - 12/5
Simplify the expression:
3(7r + 1) =
Answer:
21r +3
Step-by-step explanation:
3(7r + 1) =
Distribute
3*7r +3*1
21r +3
Answer:
21r+3
Step-by-step explanation:
3(7r + 1)
Use the distributive property.
This property is normally used when the 2 numbers inside of the parentheses can not be added easily.
3*7r+3*1
21r+3
One of the solutions of the system of equations shown in the graph has an x-value of -4. What is its corresponding integer y-value? -1 -3 0 3
Answer:
Solution: (-4,-3)
Step-by-step explanation:
We need to complete the solution set of given graph.
We are given two graph one straight line and one parabola. We can see in graph both intersect at two points.
At x=-4 and x=-1
We can easily find the value of y corresponding to the value of x using given graph.
At x=-4,
First we draw a vertical line at x=-4 and see where it cut graph. From that point draw a horizontal line and see where y-axis cut.
The value of at x=-4 would be -3
Please see the attachment and see the vertical and horizontal line.
Thus, The Solution is (-4,-3)
help me plz can i have help
Answer:
6×[tex]10^{-4}[/tex]
Step-by-step explanation:
Which inequality is shown on the number line below? ( the answers are in one image and the number line is shown in the other image) Please include ALL work!
Answer:
The inequality shown is p>-3
Explanation:
An open hole on the number line means that the inequality will be greater or less than a number. So far we have p <or> some number.
Since the line goes to the left then we know that p is greater than some number. Now we have, p> some number.
The inequality starts at -3 so we know that the equation must be p>-3.
The inequality shown is in the given number line will be p>-3.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
An open hole on the number line refers to that the inequality will be greater or less than a number.
So far we have p <or> some number.
Since the line goes to the left then we know that p is greater than few number on the line.
Now we have, p> some number.
Thus, The inequality starts at -3, so we know that the equation must be p>-3.
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PLS HELP ME WITH THIS I NEED IT QUICK!!!!!!!!!!!
Answer:
Below in bold.
Step-by-step explanation:
-6x + 3y = -7
The x intercepts occur when y = 0, so
-6x + 3(o) = -7
x = -7/-6
x = 7/6
So the x-intercept = (7/6, 0).
The y intercept:
-6(0) + 3y = -7
y = -7/3.
So the y-intercept = (0, -7/3.t).
Kate is arranging new furniture in her rectangular sitting room. She has mapped the arrangement on a coordinate plane. A, B, and C represent the sofas, V1 and V2 are decorative vases and AQ represents the aquarium. Find the distance between V1 and the aquarium. Question 4 options: A) 11 units B) 10 units C) 1 units D) units
Answer:
A
Step-by-step explanation:
To find the distance between V1 and AQ use the distance formula
[tex]d = \sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
First find the coordinates of both V1: (-6, 5) AQ: (5, 5)
Now plug it in and solve for d (11)
PLEASE HELP!!!!Create diagrams to represent the possible cases for common tangents between two
circles. Your diagram can be created using multimedia sources or drawn by hand. They
should not be copied and pasted from a website. Explain why your diagrams satisfy the
given criteria.
One common tangent a)diagram:
b): justification
Solve for x show work plz
Answer:
20
Step-by-step explanation:
We know that ΔBAC and ΔBED are similar becuase of the AA Postulate (they both have a right angle and they both share ∠B). Since AC is 15/3 = 5 times longer than ED, the scale factor is 5 which means AB is 5 times longer than EB. This makes EB = 25 / 5 = 5. Since AB = AE + EB and we know that AB = 25, AE = x and EB = 5, 25 = x + 5 which means x = 20.
