Answer:
7 - 3 i
Step-by-step explanation:
Simplifying
(3 + -2i) + (4 + -5i) = 0
Remove parenthesis around (3 + -2i)
3 + -2i + (4 + -5i) = 0
Remove parenthesis around (4 + -5i)
3 + -2i + 4 + -5i = 0
Reorder the terms:
3 + 4 + -2i + -5i = 0
Combine like terms: 3 + 4 = 7
7 + -2i + -5i = 0
Combine like terms: -2i + -5i = -7i
7 + -7i = 0
Solving
7 + -7i = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + -7i = 0 + -7
Combine like terms: 7 + -7 = 0
0 + -7i = 0 + -7
-7i = 0 + -7
Combine like terms: 0 + -7 = -7
-7i = -7
Divide each side by '-7'.
i = 1
Simplifying
i = 1
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n2+n
Answer:
Perfect square trinomial: [tex]n^2+n+\dfrac{1}{4}[/tex]
Binomial squared: [tex]\left(n+\dfrac{1}{2}\right)^2[/tex].
Step-by-step explanation:
The given expression is [tex]n^2+n.[/tex]
Here coefficient of n is 1.
Now, find square of half of coefficient of n.
[tex]\left(\dfrac{1}{2}\times 1\right)^2=\dfrac{1}{4}[/tex]
Now, add [tex]\dfrac{1}{4}[/tex] in the expression to make it perfect square trinomial.
[tex]n^2+n+\dfrac{1}{4}[/tex]
[tex]\Rightarrow n^2+n+\left(\dfrac{1}{2}\right)^2[/tex]
[tex]\Rightarrow \left(n+\dfrac{1}{2}\right)^2[/tex] [tex]\because (a+b)^2=a^2+2ab+b^2[/tex]
Therefore, perfect square trinomial is [tex]n^2+n+\dfrac{1}{4}[/tex] and binomial squared is [tex]\left(n+\dfrac{1}{2}\right)^2[/tex].
The following equation:
C= 312 + 19900
gives the total cost, in dollars, to produce a units of a product at a factory. If the monthly operating
budget of the factor is $35400, how many units can be produced there in that month?
Answer: In that month,
units can be produced for $35400.
Enter an integer or decimal number (more..]
Question Help: D Video
Submit Question
Answer:
49.68
Step-by-step explanation:
you would just plug in 35400 for y so you get 35400=312x+19900 and then you would subtract 19900 from both sides so you get 15500 and then divide that by 312 which is 49.68
[tex](3+\sqrt{7})(3-\sqrt{7})[/tex]
Answer:
The answer should be 2 but it won't let me post it with less than twenty characters so yeah
Where is 50−−√+5√ located on a number line? A. between 7 and 8 B. between 8 and 9 C. between 9 and 10 D. between 10 and 11
Answer:
between 7 and 8
Step-by-step explanation:
Benito embroiders and sells T-shirts. The graph shows his profit as a function of the number of shirts sold. After selling a certain number of shirts, Benito uses some earnings to buy more materials and then increases the price of the shirts. Which of the following is true? a. The domain of the function is {x | x is a real number greater than or equal to 0}. b. Benito increases the price after selling 50 shirts. c. The x-intercept represents the shirts he has to sell before making a profit. d. The y-intercept represents the cost of one T-shirt.
Answer:
a. The domain of the function is {x | x is a real number greater than or equal to 0}.
Step-by-step explanation:
The graph shows
1) the domain of the function {x | x is a real number greater than or equal to 0}
The domain of the function of the graph is obtained by the x - values which range from 0-11 . Thus they are equal or greater than zero.
2) the y- intercept shows the profit that is made by selling a certain number of shirts.
3) the x- intercept shows the number of shirts sold
4) Benito increases the price at least after the profit of $25 is made because we see from the graph that there is a loss of $10 if one shirt is sold separately and the dot on the eight appears around $ 25.
Only option a is true.
Graphs are used to show the relationship between related quantities.
From the given options, the true statement is:
c. The x-intercept represents the shirts he has to sell before making a profit.
From the given graph, we have the following observations.
1. The domain of the graph is [tex]x \ge 2[/tex]
The corresponding y-values are negative for x = 0 and 1.
Because the graph represents the profit function, no value of x must correspond to a negative y-value.
Hence, (a) is false
2. It is impossible to say that his price increases, after selling 50 shirts
The y values show profit from shirts; not the price of shirts
Hence, (b) is false
3. The x-intercept indicates when he'll make a profit
The graph crosses the x-axis at x= 2.
This means that, he has to sell at least 2 shirts, before making a profit.
Hence, (c) is true
4. The y-intercept is the cost of 1 shirt
The y values show profit from shirts; not the price of shirts
Hence, (d) is false
Based on the above analysis, we can conclude that (c) is true
Read more about graphs at:
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Michael paid $16.40 for 20.5 centimeters of wire. Find the unit price in dollars per centimeter. If necessary round your answer to the nearest cent.
Answer:
$0.80
Step-by-step explanation:
$16.40 ÷ 20.5 = 0.80
You can check your work by doing :
20.5 cm of wire × $0.80 = $16.40
The unit price of the wire which Michael bought 20.5 cm for $16.40 is $0.8.
What is The Unit price?The price of a product offered in more or fewer than one unit is referred to as the unit price. The "unit pricing" of a food package informs you of the price per pound, quart, or another unit of weight or volume. Normally, it is displayed underneath the food on the shelf. The item price (total price) and unit price (unit price) for the food item are both displayed on the shelf tag. When shoppers are taught how to use unit price information in supermarkets, research reveals that they can save about 17–18%, but over time, this number decreases.
Given:
The price for the length of 20.5-centimeter wire, a = $16.40,
Calculate the price of 1 cm wire by dividing the total price by the length of the wire,
So unit price = 16.40 ÷ 20.5
Unit price = $0.8
Therefore, the unit price of the wire is $0.8.
To know more about unit price:
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Simplify each expression using the order of operations. Then, match the expression (term) on the left with its solution (definition) on the right. (4 points) Group of answer choices 42 + 3 − 2(3) [ Choose ] 22 ⋅ 8 ÷ 2 + 2 [ Choose ] (42 + 16) + 12 [ Choose ] 8 ⋅ 32 + 3 [ Choose ]
Answer:
39, 90, 70, 259
Step-by-step explanation:
1 ).................................................
42 + 3 − 2(3) = 42 + 3 - 6 = 45 - 6 = 392) .................................................
22 ⋅ 8 ÷ 2 + 2 = 176 ÷ 2 + 2 = 88 + 2 = 903) .................................................
(42 + 16) + 12 = 58 + 12 = 704) .................................................
8 ⋅ 32 + 3 = 256 + 3 = 259Which of the following expressions represents the width of the door?
a-(4x+5)- x-x
B-(4x+5)-(2x-3)
C-(4x+5)+(2x-3)
D-(2x-3)- x-x
Answer:
b
Step-by-step explanation:
Sarah and John are running clockwise around a circular track with radius 25 meters. They start at the same position, and Sarah runs at 2.7 m/s while John runs at 2.2 m/s. How far away from their starting point are they when Sarah catches up and passes John for the first time after the start?
Answer:
62.8 m
Step-by-step explanation:
The length of one lap is ...
C = 2πr = 2π(25 m) = 50π m ≈ 157.08 m
Sarah is gaining ground on John at the rate of 2.7 m/s -2.2 m/s = 0.5 m/s. So it will take Sarah ...
157.08 m/(0.5 m/s) = 314.16 s
to run 1 lap farther than John does.
It takes Sarah ...
157.08 m/(2.7 m/s) = 58.18 s
to run 1 lap, so in the time it takes her to catch John, she will have run ...
314.16 s/(58.18 s/lap) = 5.4 laps
She (and John) will be 0.4 laps from their start when they meet again. That distance is ...
(0.4)(157.08 m) = 62.8 m
Sarah will catch and pass John 62.8 meters from their starting position.
Yaneev thinks of a number y. He subtracts three from the number, then doubles it. Then he subtracts three again, and doubles the number again. The result is his original number y. What is y?
Answer: y=6
Step-by-step explanation:
The given number is y.
According to the question,
Step 1 . subtracts three from the number (y-3), then doubles it
i.e. Final number = 2(y-3)
Step 2 . subtracts three again i.e. (2(y-3)-3), and doubles the number again
i.e. Final result = 2(2(y-3)-3)
If the result is his original number y, then
2(2(y-3)-3) =y
⇒ 2(2y-6-3)=y [ using distributive property]
⇒ 2(2y-9)=y
⇒ 2(2y)-2(9)=y [ using distributive property]
⇒ 4y -18=y
⇒ 4y -y= 18
⇒ 3y= 18
⇒ y= 6 [Divide both sides by 3]
Hence, y=6
Answer:
y = 6
Step-by-step explanation:
here, lets plug it into the equation.
((y - 3)2) - 3)2 = y
((6-3)2) - 3)2 = 6
6-3 = 3 * 2 = 6 - 3 = 3 * 2 = 6
The graph of a quadratic function with vertex (-3,2) is shown in the figure below . Find the domain and the range
Answer:
domain: all realsrange: y ≥ 2Step-by-step explanation:
The domain of any polynomial function, quadratics included, is "all reals."
The graph opens upward, so the y-value of the vertex is the minimum value of the range: y ≥ 2.
write a sentence as an equation
the product of t and 15 , minus 94 is the same as 103
Answer:
15t-94=103
Step-by-step explanation:
hav a nice day
Answer:
You already wrote the sentence, so im guessing that you want the equation...
(15)(t) - 94 = 103
Convert the decimal below to a fraction in simplest form.
0.131
Answer:
Submit Answer
Answer:
131/100 is the fraction in the simplest form
Answer:
131/1000
Step-by-step explanation:
This is the simplest form as a fraction
Two cyclists, 40 miles apart, start riding toward each other at the same time. One cycles 3 times as fast
as the other. If they meet 2
hours later, what is the speed (in mi/h) of the faster cyclist?
Answer:
15 mph
Step-by-step explanation:
The cyclists will cover distance at a rate proportional to their speed. So, the distance ratio is ...
faster cyclist distance : slower cyclist distance = 3 : 1
Then the faster cyclist covers 3 : (3+1) = 3/4 of the total distance, or (3/4)(40 mi) = 30 mi.
That distance took 2 hours for the faster cyclist, so the speed was ...
speed = distance/time = 30 mi/(2 h) = 15 mi/h
The area of a rectangular wall of a barn is 16 square feet. Its length is 4 feet longer than twice its width. Find the length and width of the wall of the barn.
Answer:
width = 2 ft
length = 8 ft
Step-by-step explanation:
area = L x W
area = 16 ft^2
width = x
length = 2x+4
width = 2 ft
length = 2(2)+4
length = 4+4
length = 8 ft
area = 8 x 2 = 16 ft^2
a rescue company determined that 90 out of 100 calls they received were true emergencies. which describes the fraction of their calls that were true emergencies.
Step-by-step explanation:
It is given that,
A rescue company determined that 90 out of 100 calls rescue company determined that 90 out of 100 calls. We need to find the fraction of their calls that were true emergencies.
Fractions can be written as true value on the denominator and the part of it on the numerator.
The required value is : [tex]\dfrac{90}{100}=\dfrac{9}{10}[/tex]
So, (9/10) describes the fraction of their calls that were true emergencies.
Set up the equation for the area of a triangle in
you graphing calculator. Define the variables and
use the sliders to find the areas of the triangles
below.
Answer:
The person above me is right, and the answer for the second part is "somewhat similar".
Step-by-step explanation:
Edge 2021.
Help! Please! You can just give answers if want to make It faster.
Answer:
X' = (-3 , -5)
Y' = (-1, -1)
Z' = (4, -8)
General rule: (x,y) = (y, -x)
I am 1 brainly away from the next rank, your help would be appreciated
you live in the building on the left in the drawing, and a friend lives in the other building. the two of you are having a discussion about the heights of the buildings, and your friend claims that the height of his building is more than 1.50 times the height of yours. to resolve the issue you climb to the roof of your building and estimate that your line of sight to the top edge of the other building makes an angle of 21° above the horizontal, whereas your line of sight to the base of the other building makes an angle of 52° below the horizontal. determine the ratio of the height of the taller building to the height of the shorter building. state whether your friend is right or wrong.
Answer:
4
Step-by-step explanation:
which expression is equivalent to 23-5
Answer:
9+9
Step-by-step explanation:
9+9=18
23-5=18
Need some assistance lovely’s
Answer:
60
Step-by-step explanation:
The sum of the angles of a triangle is 180
x+x+x = 180
3x= 180
Divide by 3
3x/3=180/3
x = 60
Answer:
60
Step-by-step explanation:
sum of measure of interior angles of a triangle is 180
x+x+x=180
3x=180
x=180/3
x=60
Which equation correctly shows the multiplication of the means and extremes in the proportion 7.2∕9.6 = 21.6∕28.8?
Answer:
7.2 × 28.8 = 9. 6 × 21.6
Step-by-step explanation:
Given the equation:
7.2∕9.6 = 21.6∕28.8
The equation which provides the multiplication of the means and the extremes in the equation provided above can be obtained through cross multiplication of the two ratios or proportion.
(7.2 / 9.6) = (21.6 / 28.8)
L. H. S = R. H. S
(numerator of L. H. S * denominator of R. H. S) = (denominator of L. H. S * numerator of R. H. S)
Hence, we have ;
7.2 × 28.8 = 9. 6 × 21.6
Can you help me with this I’ll give you a brain list
Answer:
the answer is c or the third line
Step-by-step explanation:
lets see all choices by solving them
The first line 5+2-(-8) Now we should follow the bodmas rule 5 + 2 + 8 because - ( - ) become +so the answer is 13 means not negative
2. The second line 5-8-(-6)
Also now we should follow the bodmas rule
5 - 8 + 6 because - ( - ) become +- 3 + 6
3 the answer is 3 so it means not negative
3. The third line 6+6-17
Now it is simple we solve it
6 + 6 - 1712 - 17
-5 the answer is -5 means negative
4. The fourth line 6-4-(-8)
Again we need bodmas rule
6 - 4 + 8 because - ( - ) become +-2 + 8
6 the answer is 6 means not negative
I hope u like it
Anwser The First 4 For ___ Points
Answer:
1) -2/3
2) 7/60
3) -11/10
4) 37/24
Step-by-step explanation: calculator
Answer:
1.= -2/10 2.298143
step-by-step explanation:
ansver
Answer from: Quest
step-by-step explanation:
x^2 -12x + 36 + y^2 = 36
x^2 + y^2 = 12x
r^2 = 12rcos(theta)
r = 12 cos(theta)
Step-by-step explanation:
Find the sum of the measures of the interior angles of the polygon. 15-gon A. 2340° B. 2520° C. 2160° D. 1170°
Answer:
2340
Step-by-step explanation:
Formulae for sum of interior angles is 180(n-2)
Whereby n=number of sides
[tex]180(15 - 2) \\ 180(13) \\ = 2340degrees[/tex]
There are 6 fiction books and 8 nonfiction books on a reading list. Your teacher randomly assigns you 4 books to read over summer. What is the probability that you are assigned all nonfiction books?
Answer:
Step-by-step explanation:
A store sells paint sets. Each paint set costs the same amount. During a sale, the store reduces the price of each paint set by $1.50. Logan spends
$13.47 on 3 paint sets at the sale price.
What was the price of I paint set before the sale?
Answer:
the price of I paint set before the sale was $5.99
Step-by-step explanation:
Selling price of 3 paint sets = $13.47
To get selling price of 1 set
we divide both LHS and RHS by 3
Selling price of 3/3 = 1 paint sets = $13.47/3 = $4.49
Thus, selling price of 1 paint set after sale is $4.49
Given that
the store reduces the price of each paint set by $1.50
Let the price before sale be x
selling price of 1 paint set after sale = price before sale - $1.50
$4.49 = $x - $.150
$x = $4.49 + $1.50 = $5.99
Thus, the price of I paint set before the sale was $5.99
All of the following are equivalent except
O 4y
O (4)
04.y
O 4+ y
Answer:
I think it's 4y
Step-by-step explanation:
I think it's 4y is because if y = 0 they all work but 4y which is 0 while all the others are 4
Ellie takes her dog, Jack, for a 3 mile walk each day. On the first part of the walk, they go 2 mph. Then for the second part of their walk, they go 3 mph but for half the time that they went 2 mph. How long was their walk in hours?
Answer:
the entire walk is 9/7 hours i think
find the perimeter and area of each figure below.