Answer:
Option D: x = 5 ± 10i
Step-by-step explanation:
Given the quadratic equation, y = x² - 10x + 125,
where:
a = 1, b = -10, and c = 125:
Use the following quadratic formula to solve for the roots:
[tex]\displaystyle\mathsf{x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]
[tex]\displaystyle\mathsf{x=\frac{10\pm\sqrt{(-10)^2-4(1)(125)}}{2(1)}}[/tex]
[tex]\displaystyle\mathsf{x=\frac{10\pm\sqrt{100-500}}{2}\:=\:\frac{10\pm\sqrt{-400}}{2}}[/tex]
Apply the imaginary unit rule, where it states that: [tex]\displaystyle\mathsf{\sqrt{-a}\:=\:i\sqrt{a}}[/tex] :
[tex]\displaystyle\mathsf{x=\frac{10\pm\:20i}{2}}[/tex]
[tex]\displaystyle\mathsf{x=\frac{10\:+\:20i}{2}\:=\frac{10(1\:+\:2i)}{2}\:=\:5(1+2i)}\:=5+10i}[/tex]
[tex]\displaystyle\mathsf{x=\frac{10\:-\:20i}{2}\:=\frac{10(1\:-\:2i)}{2}\:=\:5(1-2i)}\:=5-10i}[/tex]
Therefore, the correct answer is Option D: x = 5 ± 10i .
Out of a class of 150 students, two-fifths opted for German classes and one-third opted for Italian classes. The remaining opted for French. What fraction opted for French?
Fraction of students that opted for French = [tex]\frac{4}{15}[/tex]
The total number of students = 150
Fraction of students that opted for German = [tex]\frac{2}{5}[/tex]
Fraction of students that opted for Italian = [tex]\frac{1}{3}[/tex]
Fraction of students that opted for French = 1 - Fraction of students that opted for German - Fraction of students that opted for Italian
Fraction of students that opted for French = [tex]1-\frac{2}{5} - \frac{1}{3}[/tex]
Fraction of students that opted for French = [tex]\frac{15-6-5}{15}[/tex]
Fraction of students that opted for French = [tex]\frac{4}{15}[/tex]
Learn more here: https://brainly.com/question/18819021
An inverted conical water tank with a height of 12 ft and a radius of 3 ft is drained through a hole in the vertex. If the water level drops at a rate of 1 ft/min, at what rate is water (in ft3/min) draining from the tank when the water depth is 8 ft
Answer:
dhdt≃0.283ft3s
Step-by-step explanation:
dhdt≃0.283ft3s
The draining from the tank when the water depth is 8 ft will be negative 1/π feet per minute.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
An inverted conical water tank with a height of 12 ft and a radius of 3 ft is drained through a hole in the vertex. If the water level drops at a rate of 1 ft/min.
[tex]\rm \dfrac{dV}{dt} = -1 \ ft/min[/tex]
The volume of the cone is given as,
V = (1/3) πr²h
The relation between r and h is given as,
r / h = 3 / 12
r = h / 4
Then the volume is written as,
V = (1/3) π (h/4)² × h
V = (π / 48) h³
Differentiate the volume with respect to time. Then we have
(dV)/(dt) = (π/48) x 3h² x (dh / dt)
- 1 = (π/48) x 3(4)² (dh / dt)
- 1/π = dh / dt
The draining from the tank when the water depth is 8 ft will be negative 1/π feet per minute.
More about the differentiation link is given below.
https://brainly.com/question/24062595
#SPJ5
3. The volume of a book is 60 cubic inches. If a large
box holds about 12 books, estimate the volume of a
large box.
T
A. 5 cubic inches
B. 72 cubic inches
C. 600 cubic inches
D.720 cubic inchens
Answer:
720 in^3.
Step-by-step explanation:
12 * 60 = 720.
Answer:
D
Step-by-step explanation:
60 in³ * (12) = 720 in³
You and a group of friends are going to a five-day outdoor music festival during spring break. You hope it does not rain during
the festival, but the weather forecast says there is a 50% chance of rain on the first day, a 25% chance of rain on the second day, a
20% chance of rain on the third day, 5% chance of rain on the fourth day, and a 10% chance of rain on the fifth day.
Assume these probabilities are independent of whether it rained on the previous day or not.
What is the probability that it does not rain during the entire festival?
%
(Round to 2 decimal places)
Answer:
Below in bold
Step-by-step explanation:
The probability that it doesn't rain is 1 - probability it does ( Prob written as a fraction). So for the first day Probability of not raining = 1 - 0.50 = 0.50.
So the probability of it not raining the entire festival
= 0.5 * 0.75 * 0.80 * 0.95 * 0.90
= 0.2565
or 25.65%
Need help on my math! :)
Please help me! Step by Step answer... Formula is:
A=P+Prt
Answer:
B
Step-by-step explanation:
2. A group of activists wants to raise money for a good cause, so they decide to sponsor a bicycle race. It receives $60 per cyclist entry and $15,000 in donations, but it must spend $18 per entry to cover the cost of the race.
Write and solve an inequality to determine the number of cyclists the group needs to raise at least $57,000. Be sure to define a variable and explain what your answer means in the context of the problem.
Answer
Step-by-step explanation:
The number of cyclists the group needs to raise at least $57,000 must be at least 1000 cyclistsLet x represent the number of cyclists.Since, the activists receive $60 per cyclist entry and $15,000 in donations, hence:Revenue = 60x + 15000Also, the cost of the race is $18 per entry, hence:Cost = 18xThey need to raise at least $57,000, hence:Profit ≥ 57000Revenue - Cost ≥ 57000(60x + 15000) - 18x ≥ 5700042x ≥ 42000x ≥ 1000Therefore the number of cyclists the group needs to raise at least $57,000 must be at least 1000 cyclistsAlan has $700 in a savings account. The interest rate is 10% per year and is not
compounded. How much will he have in total in 1 year?
Answer:
$770
Step-by-step explanation:
700 + 10% of 700 = 700 + 70 = 770
What is the slope of the line passing through the points A and B, as shown on the graph below?
A)-3
B) -1/3
C) 1/3
D) 3
Answer:
-1/3
Step-by-step explanation:
We can start by finding the coordinates of 2 points, A and B. A is (-3, 8) and B is (3, 6). Now, we can use [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] to find the slope, and if you plug in those points you get (8 - 6)/(-3 - 3) = 2/(-6) = -1/3.
Use this information to write an equation and solve the following problem. When you count by ones from any integer, you are counting consecutive integers. Using variables, three consecutive integers are x, x + 1, and x + 2. The sum of three consecutive integers is 48. What are they? Write an equation to represent the situation and solve. Show all of your work.
Answer:
19
Step-by-step explanation:
divide
how can i answer 6x-3y=-6
Answer:
Step-by-step explanation:
Rewrite in slope-intercept form.
The slope-intercept form is
y = m x + b , where m is the slope and b is the y-intercept. y = m x + b
Reorder 2 and 2 x . y = 2 x + 2
Use the slope-intercept form to find the slope and y-intercept.
Slope:
2
y-intercept:
2
In a survey of 1003 people, 59% said that they have never hesitated to give a handshake because they had a fear of germs. If an independent pollster wanted to conduct another survey, how many people must be surveyed
Answer:
592 people must be surveyed
what is the slope of the line // will mark brainliest and give points
[tex]\\ \sf\longmapsto m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{-1+2}{2+1}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{1}{3}[/tex]
The area of a rectangle is 17 1/2 in squared and it's shorter side is 3 1/2 in. Draw a diagram that shows this information. What is the length of the longer side.
Use an equation to find the value of k
so that the line passing through (−4,k)
and (6,−7)
has a slope of −15
Answer: k=143
Step-by-step explanation:
Let's start with the standard form of a linear equation: y = mx + b, where m ios the slope and b is trhe y-intercept (the value of y when x=0). We know the slope, so:
y = -15x + b
We can find the y-intercept, b, by using the one given point (6,-7) in the equation and solve for b:
y = -15x + b
-7 = -15(6) + b
-7 = -90+b
b = 83
The equation is y = -15x + 83
Use the x value of (-4,k) to find y, which will be k.
y = -15x + 83
y = -15(-4) + 83
y = 60 + 93
y = 143
k is 143
what is the answer for 3² =
write an equation for the function that passes through the points (1,3/2) and (3/2,2)
Answer:
y = 1x + 1/2
Step-by-step explanation:
y2 - y1 / x2 - x1
2 - 3/2 / 3/2 - 1
= 1/2 / 1/2
= 1
y = 1x + b
3/2 = 1(1) + b
3/2 = 1 + b
1/2 = b
Can anyone help me ASAP!
The answer would be 82 miles :)
Question 1
1 point
Which of the following represents the range of the function shown in the graph below?
(1) (-4,5]
(2)[-4,5)
(3) (-2,3)
(4) (-2,3]
I'm in need of help please
Answer:
1. x+ 2/3= -1/4
x+ 8/12= -3/12
-8/12 -8/12
x= -11/12
2. 1/4x+ 2/5= 1/3
1/4x+ 6/15= 5/15
-6/15 -6/15
1/4x= -1/15
15/60x= -4/60
÷15/60. ÷15/60
x= -4/15
help whats the answer f0r this one
A floor measuring 2m by 1.5m is ro be covered with tiles measuring 25cm×25cm. find the numbee lf tiles required to cover the floor and the cost of the tiles at ruppees 420 per dozen
Answer:
a floor measuring 2m by 1.5m is to be covered with tiles measuring 25cm square how many tiles will be needed? answer is 48
Solve y = x - 5 if the domain is 5
Please help asap!!
Answer:
its x=5
Step-by-step explanation:
well the domain should be not real numbers so yeah
HELP ME PLEASE AND THANK YOU (BRAINLIEST)
Rick deposits $3 into his bank account. The following week, he deposits 3 times that amount. Each week after that, he deposits 3 times the amount he did the previous week.
How much does he deposit in all during the first 3 weeks?
1. Write an exponential expression that represents Rick’s deposit in the second week. Explain how you identified the base and the exponent.
3x3=9
9x3=27
3+9+27=39
$39
Exponent: 3³
Explanation: because he deposited three times as much three times, which would make for a cubed answer.
Question attached. Please answer.
9514 1404 393
Answer:
18 cm²
Step-by-step explanation:
All sides of a rhombus are the same length (as shown by the markings), so one side is 1/4 of the perimeter:
(24 cm)/4 = 6 cm . . . . side length
As with all parallelograms, the area is the product of the side length and the height perpendicular to that side:
A = (6 cm)(3 cm) = 18 cm²
It has an area of 18 cm².
a trader bought a stock of cabbage for 1200 rupees. after removing the spoiled stock, he had a loss of 8%. what is the amount he got by selling the cabbage
Your class takes a field trip to a local farm. While looking at the cows and ducks you count 11 heads and 30 feet. How many of each animal did you see?
4 cows and 7 ducks
i drew 11 circles and added 2 feet to each of them then added 2 moor feet to the circles and then i counted how many had 4 feet and how many had 2 and that gave me the answer.
An electrician cuts a 28 feet piece of wire into two pieces one piece is 4 feet longer than the other how long are the pieces
Step-by-step explanation:
perdon, no entiendo bien tu pregunta
what is 12x - 22 + 3x - 3
Answer:
15x - 25
Step-by-step explanation:
12x - 22 + 3x - 3
12x + 3x - 22 - 3
15x - 25
Hope this helps.
Answer:
15x-25
Step-by-step explanation:
Collect like terms and calculate.
What is the slope of the line that passes through the points (-4,-4) and (6,4)
Answer:
0.8
Step-by-step explanation:
The points entered are part of a linear, rising function.
y = 0.8x - 0.8 is the solution. Have a good day man! :)
