Answer:
- 4
Step-by-step explanation:
The conjugate of - 2 + i is - 2 - i, thus
- 2 + i + (- 2) - i
= - 2 + i - 2 - i ← collect like terms
= - 4 ← in the form a + bi with b = 0
The sum of -2 + i and its complex conjugate is:
w = -4 + 0i
How to find the sum?
The complex conjugate of a number z = a + bi is:
z' = a - bi.
Then the complex conjugate of -2 + i is -2 - i.
The sum will give:
w = -2 + i + (-2 - i) = -4 + 0
Writing it in the wanted form we get:
w = -4 + 0i
If you want to learn more about complex numbers, you can read:
https://brainly.com/question/10662770
#SPJ2
Question 3
Round to the nearest tenth.
8.001 - (-3.4062) =
verbal expression for each algebraic expression 23f
Solve the following systems using the substitution method.
Answer:
Step-by-step explanation:
Step-by-step explanation:
1).2x + 8y = 12 ......... Equation 1
x - 2y = 0 .............. Equation 2
Make x the subject in equation 2 and substitute it into equation 1
That's
x = 2y
We have
2(2y) + 8y = 12
4y + 8y = 12
12y = 12
Divide both sides by 12
y = 1
Substitute y = 1 into x = 2y
That's
x = 2(1)
x = 2
The answers are
x = 2 , y = 12.)x + y = 7......... Equation 1
2x + y = 5 ......... Equation 2
Make y the subject in equation 1 and substitute it into equation 2
We have
y = x - 7
2x + x - 7 = 5
3x = 7 + 5
3x = 12
Divide both sides by 3
x = 4
Substitute x = 4 into y = x - 7
y = 4 - 7
y = - 3
We have the answers as
x = 4 , y = - 33).y = -1/2 + 1 ......... Equation 1
2x + 3y = 6 ........ Equation 2
From equation 1
y = 1/2
Substitute y = 1/2 into Equation 2
So we have
2x + 3(1/2) = 6
2x + 3/2 = 6
2x = 6 - 3/2
2x = 9/2
Divide both sides by 2
x = 9/4
The answers are
x = 9/4 , y = 1/24).2x - 1/3y = - 9.......... Equation 1
-3x + y = 15 ........... Equation 2
Make y the subject in equation 2 and substitute it into equation 1
That's
y = 15 + 3x
2x - 1/3( 15 + 3x) = - 9
2x - 5 - x = - 9
x = - 9 + 5
x = - 4
Substitute x = - 4 into y = 15 + 3x
That's
y = 15 + 3(-4)
y = 15 - 12
y = 3
The answers are
x = - 4 , y = 3Hope this helps you
A car is traveling at 60 mph and is tailgating another car at distance of only 30 ft. If the reaction time of the tailgater is 0.5 seconds ( time between seeing the brake lights of the car ahead flash and hitting the brake ), how far will his car travel during his reaction time ?
Answer:
44 ft
Step-by-step explanation:
We are given that;
Speed; v = 60 mph
Reaction time;t = 0.5 s
Now, we know that;
Distance = speed x time
Since time is in seconds, let's convert speed to mph to ft/s
From conversion,
1 mph = 1.46667 ft/s
So, 60 mph would give;
60 × 1.46667 ≈ 88 ft/s
Thus, distance his car travels during his reaction time is;
Distance = 88 × 0.5 = 44 ft
The length of a rectangle is 8 cm longer than twice the width. If the perimeter is 34 cm, find the dimensions of the rectangle.
Answer:
length = 14 cmwidth = 3 cmStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
where
l is the length
w is the width
From the question
Perimeter = 34 cm
The statement
The length of a rectangle is 8 cm longer than twice the width is written as
l = 8 + 2w
Substitute this expression into the above formula and solve for the width
That's
34 = 2( 8 + 2w) + 2w
34 = 16 + 4w + 2w
6w = 18
Divide both sides by 6
w = 3
Substitute this value into l = 8 + 2w
That's
l = 8 + 2(3)
= 8 + 6
l = 14
The dimensions are
length = 14 cm
width = 3 cm
Hope this helps you
Evaluate j/k-0.2k when j=25 and k=5
Answer:
[tex]4[/tex]
Step-by-step explanation:
[tex] \frac{j}{k} - 0.2k = \frac{25}{5} - 0.2(5) = 5 - 1 = 4[/tex]
Simplify the Expression *
Answer:
16√3
Step-by-step explanation:
(4√6)(2√2)
4*2√6*2
8√12=8√4*3=8*2√3
16√3
Between which two consecutive whole numbers does
[tex] \sqrt{75} [/tex]
lie? Fill out the sentence below to justify your answer and use your mouse to drag
[tex] \sqrt{75} [/tex]
to an approximately correct location on the number line.
y = -x + 2 on a graph
Identify the coefficient in the expression x + 4.
A x
B 1
C 0
D 4
Answer:
1
Step-by-step explanation:
The coefficient is the number in front of the variable. Since there is not a number written, there is an implied 1
x+4
1x+4
The coefficient is 1
PLZZZ HELP!!! Why is it helpful to break down the total amount you would need to save on a monthly, weekly, or daily basis?
Answer:
it makes the goals easier to reach
Step-by-step explanation:
you dont want to say you need 1,000 dollars.. you would want to say you are going to save 5 dollars a week till you reach it.
5 benefits of breaking down ones periodic savings have been listed below.
Breaking down the amount one will need to save on a daily, weekly or monthly basis is simply called budgeting.
Now, budgeting is very important because it helps to do the following;
- Helps to ensure you spend money appropriately on things that you really need and not just wants.
- Helps you to effectively monitor your spending habits/patterns.
- Helps you to meet your financial goals.
- Helps you to make good decisions on things that involve finance.
- Helps you to monitor your progress in savings or interest as the case may be.
Read more at; brainly.com/question/22532334
How does scientific idea become a theory ?
Answer:
A scientific idea can become a theory when you have enough prove to back it up and when it is supported by other scientists.
If 8f + 7 - 2f = 16, what
is the value of 12 f + 1?
I need help
[tex]8f+7-2f=16\\6f=16-7\\6f=9\\f=\frac{9}{6}[/tex]
We know f, now we want the 12f+1
Therefore, Substitute f = 9/6 in 12f+1
[tex]12(\frac{9}{6})+1\\ = 2*9+1\\=18+1\\=19[/tex]
If you are wondering where 2*9 comes from, it comes from the 12(9/6) and 12 is divided by 6 then we get 2 and multiply the 9 as we get 2*9.
How to study Math by yourself at home efficiently?
Answer:
Just do what you did in school
Step-by-step explanation:
Like example you did algebra exercise 1 2 and 3
do the same at home by yourself
i need help ! someone plz help me, thank you.
Answer: I think it's C
Step-by-step explanation: hope it helps
Solve the equation for x.
3(6x - 1) = 12
Answer:
soln
18x-3=12
18x=15
so,x=5/6
Which of the following statements is false?
-|-5| = -5
-(-5) = 5
-|5| = -5
|-5| = -5
The marked price of an article is Rs.2080. After allowing d% discount and levying
(d-2)% VAT the cost of the article becomes Rs.1997.84. Find the rate of VAT?
Answer:
13%
Step-by-step explanation:
Given:
MP = 2080Discount = d%VAT = (d-2)%Cost = 1997.84Apply discount:
2080 - d% = 2080*(1 - 0.01d)Add VAT:
2080*(1 - 0.01d) + (d - 2)% 2080*(1 - 0.01d) * (1 + (d -2)/100)2080*(1 - 0.01d) * (0.98 + 0.01d) = 1997.84(1 - 0.01d)(0.98 + 0.01d) = 1997.84/20800.98 + 0.01d - 0.0098d - 0.0001d² = 0.9605 - 0.0001d² + 0.0002d + 0.98- 0.9605 = 00.0001d²- 0.0002d - 0.0195 = 0d² - 2d + 195 = 0Solving the quadratic equation we get:
d = 15Then
VAT rate = 15 - 2 = 13%A bowl contained 28.2 grams of salt. Christine poured in another 57.04 grams. How much salt does the bowl contain now?
Answer:
85.24 grams
Step-by-step explanation:
28.2 + 57.04 = 85.24
If 10-6 is 4, what is 14-9?
Answer:
14-9 would be 5.
The sum of three intergers is 242. The 2nd number is 3 more than twice the first and the 3rd number is 9 less than 5 times the first. Find the numbers
Answer:
31, 65, 146
Step-by-step explanation:
math
What are the factors for x(5x+4)-(5x+4)
Answer:
(5 x + 4) (x - 1)
Step-by-step explanation:
Factor the following:
x (5 x + 4) - (5 x + 4)
Hint: | Pull a common factor out of x (5 x + 4) - (5 x + 4).
Factor 5 x + 4 out of x (5 x + 4) - (5 x + 4), resulting in (5 x + 4) (x - 1):
Answer: (5 x + 4) (x - 1)
100 POINTS PLEASE PLEASE HELP I NEED THE ANSWER ASAPP ;(
Answer:
y < -1/4 x +1
Step-by-step explanation:
Find two points on the dotted line
( 0,1) and (4,0)
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= (0-1)/(4-0)
= -1/4
The slope is -1/4
The y intercept is where it crosses the y axis or 1
The equation of the line, using slope intercept form
y = mx+b
y = -1/4x +1
The line is dotted which means there is no equals, just greater than or less than. It is shaded below which means less than
y < -1/4 x +1
Answer:
[tex]y<-\frac{1}{4}x+1[/tex]
Step-by-step explanation:
First, let's find the equation of the line.
From the graph, we can pick out two points to use: (0,1) (the y-intercept) and (4,0) (the x-intercept).
Find the slope. Let (0,1) be x₁ and y₁ and let (4,0) be x₂ and y₂
Find the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\frac{0-1}{4-0}\\m=-1/4[/tex]
Use the slope-intercept form:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
We already know the slope is -1/4 and the y-intercept is 1. So, substitute:
[tex]y=-\frac{1}{4}x+1[/tex]
Now, replace the equal sign with an inequality. Note that the line is dotted, so we won't use "or equal to." Also note that the blue, shaded area is below the line. Thus, we will use less than. Therefore:
[tex]y<-\frac{1}{4}x+1[/tex]
The sentences:
First, we picked out two points from the graph. Next, we used those two points to find the slope. We used the slope and one of the points to write our slope-intercept equation. Afterwards, we can determine from the graph that since the shaded area is below the dotted line, the equation must have a less than.
P and Q have coordinates (-2,3) and (5,4) respectively. Reflect P inthe X-axis to P' and Q in tha Y-axis to Q' .Find the distance between P'Q'.
Step-by-step explanation:
Hey, there!!
Let's simply work with it,
The given coordinates are, P(-2,3) and Q(5,4).
Now, finding the P' and Q'.
Reflection on x- axis .
P(x,y)---------> P' (x,-y)
P (-2,3)----------> P'(-2,-3)
Now, let's find Q'
Reflection on y-axis.
Q(x,y)----------> Q'(-x,y)
Q(5,4)---------> Q'(-5,4)
Now, The points are P'(-2,-3) and Q'(-5,4)
By distance formulae,
[tex]P'Q' = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]
Putting their values,
[tex]P'Q' = \sqrt{( { - 5 + 2)}^{2}( {4 + 3)}^{2} } [/tex]
[tex]P'Q' = \sqrt{( { - 3)}^{2} + ( {7)}^{2} } [/tex]
Simplifying them we get,
[tex]pq = \sqrt{58} [/tex]
Therefore, the distance between P'and Q' is root under 58 units.
Hope it helps...
Divide $700 in the ratio 5:3:2 (S
Answer:
350:210:140
Step-by-step explanation:
5+3+2=10, so we need 10 equal parts
700÷10=70
5x70=350
3x70=210
2x70=140
350:210:140
Answer:
Explanation: 5:3:2 means 5+ 3+ 2 = $10 is devided into $5,$3,$2. Therefore $700 is divided in ratio (5:3:2) as 700 10 ⋅5 = $350, 700 10 ⋅ 3 = $210 and 700 10 ⋅ 2 = $140
how do I solve this?
Answer:
17
Step-by-step explanation:
x^2 + 2y^2
Let x=3 and y =2
3^2 + 2 ( 2)^2
Exponents first
9 + 2* 4
Then multiply
9+8
Then add
17
Answer:
17
Step-by-step explanation:
● x^2 + 2y^2
Replace x by 3 and y by 2
● (3)^2 + 2×(2)^2
● 9 + 2 × 4
● 9 + 8
● 17
WY bisects UV at Y. If
UY = 2x +1 and YV = x+7, find
UV.
Answer:
3x + 8
Step-by-step explanation:
Since, WY bisects UV at Y.
Therefore,
UV = UY + YV
UV = 2x + 1 + x + 7
UV = 2x + x + 1 + 7
UV = 3x + 8
The measure of length UV given that UY = 2x +1 and YV = x+7 is 3x + 8
To bisect a given line means to divide the line into two equal parts.
If WY bisects UV at Y, then:
UY + YV = UV and UY = YV
Given the following parameters:
UY = 2x +1
YV = x+7
Required
UV
Substitute the given parameters into the formula shown above:
2x + 1 + x + 7 = UV
Collect the like terms
2x + x + 1 + 7 UV
3x + 8 = UV
Swap
UV = 3x + 8
Hence the measure of length UV is 3x + 8
Learn more here: https://brainly.com/question/17430417
find the slope of the line through (-4, 2) and (5,8) on a coordinate plane
Answer: m = 2/3
Step-by-step explanation: Use the slope formula to find the slope m.
: m = slope :
: slope of a line : m = rise/run = y2-y1/x2-x1 :
: (x1,y1) : coordinates of first point in the line :
: (x2,y2) : coordinates of second point in the line :
I hope this helps you out.
Answer:
Slope = 2 / 3
Step-by-step explanation:
Slope = (y2-y1) / (x2-x1)
y2 is the y coordinate of the second ordered pair and y1 is the y coordinate of the first ordered pair. x2 is the x coordinate of the second ordered pair and x1 is the x coordinate of the first ordered pair.
=(8-2) / (5+4)
= 6 / 9
Slope = 2 / 3
alex is 61 inches tall. what is her height in feet ?
may you please show the equation that goes with it
Answer:
5 feet 1 inches
Step-by-step explanation:
if 1 foot is 12 inches.
Then, 60 ÷ 12
= 5
So, 61 inches tall = 5 feet 1 inches.
The answer is 5 feet 1 inches.
The Height of Alex in feet is 5.0833 feet.
To convert inches to feet, we divide the number of inches by 12 since there are 12 inches in 1 foot.
Let's denote the height of Alex in inches as H in and her height in feet as H ft.
H in = 61 inches
H ft = ?
The equation to convert inches to feet is:
H ft = H_ in / 12
Substituting the value of H in into the equation, we have:
H = 61/12
H ft ≈ 5.0833 feet
Therefore, Alex's height is 5.0833 feet.
Learn more about Unit Conversion here:
https://brainly.com/question/28600662
#SPJ6
Bags of sugar come in 3 sizes. Small bag: A 175 g bag costs 45p. Medium bag: A 420 g bag costs £1.13. Large bag: A 1.2 kg bag costs £2.99. Find the cost per gram for each bag of sugar. Round your answers to 3dp.
Answer:
a 3.889
b 3.735
c 4.013
Step-by-step explanation:
a. 45p is 0 175/45=3.889
b 420/113= 3.735
c1.2kg= 1200g /299 =4.013
/ means divide