Answers
Answer:
4.
[tex]$x=\frac{2}{3} \pm \frac{1}{6}i \sqrt{158}$[/tex]
Step-by-step explanation:
[tex]18x^2-24x+87=0[/tex]
Using Quadratic Formula
[tex]$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$[/tex]
[tex]$x=\frac{-\left(-24\right)\pm \sqrt{\left(-24\right)^2-4\cdot \:18\cdot \:87}}{2\cdot \:18}$[/tex]
Solving the discriminant:
[tex]\Delta = \left(-24\right)^2-4\cdot \:18\cdot \:87\\\Delta = 576-6264\\ \Delta=-5688[/tex]
[tex]$x= \frac{24 \pm \sqrt{-5688} }{36} $[/tex]
[tex]$x= \frac{24 \pm \sqrt{5688i} }{36} $[/tex]
Once [tex]\sqrt{5688} =\sqrt{2^3\cdot \:3^2\cdot \:79}=6\sqrt{158}[/tex]
[tex]$x=\frac{24\pm6\sqrt{158}i}{36}$[/tex]
Dividing the denominator and numerator by 6
[tex]$x=\frac{4\pm \sqrt{158}i}{6}$[/tex]
Now rewrite it:
[tex]$x=\frac{4}{6} \pm i\frac{\sqrt{158}}{6}$[/tex]
[tex]$x=\frac{2}{3} \pm i \frac{\sqrt{158}}{6}$[/tex]
or
[tex]$x=\frac{2}{3} \pm \frac{1}{6}i \sqrt{158}$[/tex]
Related Questions
What is the volume of the solid figure? A rectangular prism on top of another longer rectangular prism. The top prism measures 5 inches by 5 inches by 5 inches. The bottom prism measures 20 inches by 5 inches by 5 inches. 625 in3 750 in3 800 in3 1,250 in3
Answers
Answer:
A
Step-by-step explanation:
V=5^(3)+20*5*5
V=125+500
V=625 in^3
Answer:
it is c
Step-by-step explanation:
Hank’s age is 15 years less than twice his sister’ s age. If Hank’s sister is 22 years old, how old is Hank?
Answers
Answer:
29
Step-by-step explanation:
2s-15=h
2(22)-15=h
44-15=h
29=h
Answer:
29
Step-by-step explanation:
22 multiplied by 2 is equal to 44. Subtract 15 from 44 and you get 29.
Determine which equation below can be solved to find the value of Angle
A. *
Answers
Answer:
i believe the correct answer is x+90+63=180
Step-by-step explanation:
Answer:
x + 90 + 63 = 180
Step-by-step explanation:
We do not have the value for angle B so we have to assume that B plus the 45 is 90. using this info we can see that A + 90 + 63 is equal to the line, which is 180(as all lines are). We can then get the equation x + 90 + 63 = 180
Can u Please help me.
Answers
Answer:
-3 degrees celcius
Step-by-step explanation:
To find the temperature at midnight, simply subtract the temperature change from the temperature at noon:
17 - 20 = -3
Therefore, it was -3 degrees at midnight.
Hope this helps :) Feel free to ask any questions!
A probability experiment consists of rolling a fair 16 sided die. Find the probability of the event below, rolling a 12
Answers
Answer:
1/6
Step-by-step explanation:
I think that is the answer if not sorry, have a nice day!
Pls pick me as brainliest!
14 weeks is expressed as a percentage of 50 weeks is?
Answers
Answer:
28%
Step-by-step explanation:
Fraction= 14 out of 50 weeks
To find percentage multiply the fraction by 100
14/50 * 100
= 1400/50
= 28 percent
Answer:
28%
Step-by-step explanation:
50 ws ................ 100%
14 ws ......................x%
x = 14*100/50 = 14*2 = 28%
Sin (7pie/6)= ????????????
Answers
Answer: B -1/2
Step-by-step explanation
Which inequality is true?
5(−2)>10
3(13)<39
11+(−3)<9
5 + 12>18
Answers
Answer: 11 + (-3) < 9 is true.
Step-by-step explanation:
When there is a + in front of an expression in parentheses , the expression remains the same.
11 - 3 < 9
Now subtract.
8 < 9
If y varies directly with x and y = 20 when x = 2,
write the equation that represents this direct variation
relationship
Enter your answer in equation form without spaces.
Example: y = ?x
Answers
Answer: its 20 x 2
Step-by-step explanation: hope it helps idk if it right but did my best..
A calculator that is regularly priced $20 is on
sale for 40% off. What is the sale price of the
calculator?
Answers
Answer:
$12.00
Step-by-step explanation:
a product that normally costs $20 with a 40 percent discount will cost you $12.00, and you saved $8.00.
To make 1 batch of vegetable soup, Sam needs 16 ounces of water and 8 ounces of vegetables. How does the amount of water compare to the amount of vegetables?
Answers
Answer:
1x16
Ste divided by 16 p-by-step explanation:
What are the next two numbers in this pattern?
3,-9, 27, -81, ...
A 243, -729
B -135, 189
C-243, 729
D 135, -189
I really need your help if I get this right I’ll pass
Answers
The pattern of this is that they multiply each number by -3.
3*-3=-9
-9*-3=26
27*-3=-81
So you have to multiply -81 by -3. Then multiply that by -3 to get the second number
-81*-3=243
243*-3=-729
pls answer as quick as possible for brainliest!!
Answers
Answer:
15
Step-by-step explanation:
(2 1/2 + 1 1/2 + 3 1/2) = 7 1/2 * 2 = 15
Answer:
15
Step-by-step explanation:
2.5+1.5+3.5 = 7.5
7.5*2 = 15
Which statement is not true about these triangles?
Answers
Answer:
the answer is the second option.
Step-by-step explanation:
Answer:
the second option
Step-by-step explanation:
∠S corresponds to ∠V.
Which is the equation in point slope form for the line that passes through (3,7) and is perpendicular to 3x-5y=8?
Answers
Answer:
Step-by-step explanation:
eq. of line is 3x-5y=8
5y=3x-8
y=3/5 x-8/5
its slope=3/5
slope of line perpendicular to it=-5/3
eq of line with slope -5/3 and passing through (3,7) is
y-7=-5/3(x-3)
or 3y-21=-5x+15
or 5x+3y=15+21
or 5x+3y=36
Identify the parent function that can be used to graph the function f(x)=-6[1/2x+3]+2/3
Answers
Answer:
B
Step-by-step explanation:
2 Points
Which of the following is a geometric sequence?
O A. 2,5, 7, 12, 19
B. 2, 4, 8, 16, 32
C. 3, 6, 9, 15, 24
O D. 6, 13, 20, 27, 34
Answers
Answer:
b and d
Step-by-step explanation:
Find the equation of the line that contains the given point and is perpendicular to the given line. Write the equation in slope-intercept form, if possible.
(8,1); y=-8x-1
Answers
Answer:
y= ⅛x
Step-by-step explanation:
Slope-intercept form
y= mx +c, where m is the gradient and c is the y-intercept.
Let's find the value of m first.
The product if the gradients of 2 perpendicular lines is -1.
Gradient of given line= -8
m(-8)= -1
m= -1 ÷(-8)
m= ⅛
y=⅛x +c
To find the value of c, substitute a coordinate.
When x=8, y=1,
1= ⅛(8) +c
1= 1 +c
c= 1 -1
c= 0
Thus, the equation if the line is y= ⅛x.
Jasmine, Georgia, and Olivia are in boats on a lake. Their
relative locations are shown in the diagram.
What is the distance from Georgia's boat to Olivia's boat?
Enter your answer in the box. Round your final answer to the
nearest whole number.
ft
Answers
Answer:
52 feet
Step-by-step explanation:
Took the test
Simplify 8a + 4a + 2
Answers
Answer:
12a+2
Step-by-step explanation:
You can add 8a and 4a together to get 12a
Add 8a+4a then put the +2 back which would be 12a+2 (sorry if this doesn’t make really sense Idk how to explain it lol)
Solve all these math questions and brainliest is yours! First come first valid answer will be brainliest. Include the measurements like cm, ft, m, etc
Answers
Answer:
Step-by-step explanation:
trapezoid
A=(B1+B2)/2*h
kite
A=(pq)/2
1)((3+5)/2)*4
(4/2)*4
2*4
8 cm^2
2)
(10*10)/2
100/2
50 cm^2
3)
(14*8)/2
112/2
56m^2
4)
((10+15)/2)*6
(25/2)*6
25*3
75in^2
5)
(14*16)/2
224/2
112 ft^2
6)
((24+13)/2)*9
(37/2)*9
18.5*9
166.5 mm^2
7)
((36+60)/2)*30
(96/2)*30
96*15
1440 in^2
8)
(12*12)/2
144/2
72cm^2
9)
28=(14*2x)/2
28=7x
x=4m
10)
((8+4)/2)*4
(12/2)*4
6*4
24 ft^2
.A linear equation in one variable has
Only one solution
Two solutions
More than two solutions
No solution
Answers
Answer:
Only One Solution
Step-by-step explanation:
Every linear equation that is a conditional equation has one solution. However, not every linear equation in one variable has a single solution. There are two other cases: no solution and the solution set of all real numbers. resulting value on the right side will always be one greater than the value on the left side.
What is the distance between the coordinates (-6,5) and (-3, 2)? Round your
answer to the nearest tenth.
Answers
Answer:
The distance between the points is approximately 4.2 units.
Step-by-step explanation:
Use the distance formula. To calculate the distance between point (x1, y1) and (y1, y2), use the following formula:
[tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex]
[tex]\sqrt{(-3--6)^{2} + (2-5)^{2} }[/tex]
[tex]\sqrt{3^{2} + -3^{2} }[/tex]
[tex]\sqrt{9 + 9}[/tex]
[tex]\sqrt{18}[/tex]
≈ 4.2 units
Hope this helps :) Feel free to ask me any questions!
please help asap C: :D
Answers
Answer:
$997
Step-by-step explanation:
Base Salary: $150 (given)
Additional information on everything he sells: 14%
He sells $6050.00 last week, so then his commision would be 14% of the $6050.
x = 150 + ( 0.14 x 6050 )
OR
14/100 x 6050
would equal: $847
Total pay for last week would equal base salary and the additional pay.
$150 + $847
= $997
His total pay for last week would equal $997.
Hope helps! - Stargaze
Using the ruler postulate, find the distance between –9 and 2.
Answers
Answer:
11 units
Step-by-step explanation:
According to ruler postulate, if there are two points A with coordinate a
and point B with coordinate b, \
then distance ab is given by subtracting coordinate in any order i.e it can be (a-b) or (b-a) and then take the absolute value value of it.
mathematically it can be represented as
AB = |a-b| or |b-a|
_________________________________________
in the given problem points are -9 and 2
thus distance
distance between –9 and 2 = |-9 -2| = |-11| = 11
absolute value of -11 is 11
alternatively, distance can be calculated as
distance between –9 and 2 = |2 -(-9) | = |2 + 9 | = |-11| = 11
The side length of a square patio is 2.59 meters. Which is the best estimate for the perimeter of the patio, in meters?
Answers
Hey there! I'm happy to help!
The perimeter is all of the sides of a shape added up.
Since all of the sides on a square are the same and we know one side, we just multiply it by four.
2.59(4)=10.36
Therefore, the patio is about 10.56 meters.
I hope that this helps! :D
Answer:
The best estimate is 10. Trust me, I did this assessment too.
Step-by-step explanation:
2.59 x 4 = 10.36. So it's 10.
Your mom bought a new couch on sale for $840. If the sale was 30%, what was the Original Price?
Answers
Answer:
1200$
Step-by-step explanation:
(840/(100-30))*100
(840/70)*100
12*100
1200
Vector performed an experiment at a local farm to determine if the addition of bananas to his biomass cow manure recipes helps produce more or less energy. He collected random samples of manure and bananas from the farm, prepared 15 bottles of each of both mixtures, and placed a balloon on top of each bottle. After two weeks he measured the circumference of each balloon in centimeters; the bigger the balloon grew, the more energy that was produced. The results of the experiment are displayed in the box plots below.
Which description most accurately summarizes the sample results?
Answers
Answer:
For his balloon to grow bigger, more manure is needed to enhance more growth energy
The mean of cow manure with mashed bananas is always more than the mean of only cow manure in any country.
Then the correct option is B.
What is Mean?Mean is simply defined as the average of the given set of numbers. The mean is considered as one of the measures of central tendencies in statistics. The mean is said to be an arithmetic mean. It is the ratio of the sum of the observation to the total number of observations.
Vector performed an experiment at a local farm to determine if the addition of bananas to his biomass cow manure recipes helps produce more or less energy.
He collected random samples of manure and bananas from the farm, prepared 15 bottles of each of both mixtures, and placed a balloon on top of each bottle.
After two weeks he measured the circumference of each ballon in centimeters; the bigger the balloon grew, the more energy that was produced.
The mean of cow manure will be
Mean = 10+11 +13 +13 + 14 +15 + 15 + 15 + 18 + 18 + 19 + 20 +22+25+26/15
= 254/15
= 16.93
The mean of cow manure with mashed banana will be
Mean = 22+22+26+29+30+31+36+36+38+39+43+46+46+49+50/15
= 543/15
= 36.2
Thus, The mean of cow manure with mashed bananas is more than the mean of only cow manure.
Learn more about the mean link is given below.
brainly.com/question/521501
#SPJ7
Given that: 2√2−√5 / 3√2+2√5 = =
Answers
Answer:
7√10/2 - 11
Step-by-step explanation:
(2√2−√5) / (3√2+2√5)=
(3√2-2√5)(2√2−√5)/(3√2+2√5)(3√2+-2√5)=
(12+10-3√10-4√10)/(18-20)=
(22-7√10)/-2= 7√10/2 - 11
Assume the sample below is a perfectly random sample of students at a school. How much greater is the mean of the
reported heights at the school than the mean of the actual, measured heights at the school?
Number Reported height Measured Height Difference
Description
1
61
62
-1
Under reported
2
68
68
0
Accurately reported
3
57.5
56.5
1
Over reported
4
48.5
47
1.5
Over reported
07
75
72
3
Over reported
6
65
65
O
Accurately reported
7
80
78
2
Over reported
8
68
67
1
Over reported
9
69
69.5
-0.5
Under reported
10
63
62.5
0.5
Over reported
Answers
Answer:
0.75
Step-by-step explanation:
The table is not well presented (See Attachment)
There are at least two approaches to this question
Method 1:
Steps
1. Calculate the mean of reported heights
Mean of reported heights = (61+68+57.5+48.5+75+65+80+68+69+63)/10
Mean of reported heights = 655/10
Mean of reported heights = 65.5
2. Calculate the mean of measured heights
Mean of measured heights = (62 + 68 + 56.5 + 47 + 72 + 65 + 78 + 67 + 69.5 + 62.5)/10
Mean of measured heights = 647.5/10
Mean of measured heights = 64.75
3. Get their difference
Difference = Mean of reported heights - Mean of measured heights
Difference = 65.5 - 64.75
Difference = 0,75
Method 2: Calculate the mean of their difference
Mean of difference = Sum of difference / Number of observations
Mean of difference = (-1 + 0 + 1 + 1.5 + 3 + 0 + 2 + 1 – 0.5 + 0.5)/10
Mean of difference = 7.5/10
Mean of difference = 0.75
Note that in both cases, the result is 0,75.
Hence, the reported heights at the school is 0.75 greater than the actual measured height
It was hard to do because you wrote it out next time try attaching the file but if my calculations are correct its C.)0.75