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
Ritz can eat 6 apples in 15 minutes. How long does it take Ritz to eat 16
apples at the same rate? *
Answers
Hey there! I'm happy to help!
We see that it takes 15 minutes to eat 6 apples. But, we want to find how long it takes to get to sixteen apples. We need to multiply this by something to get our six apples to sixteen. Let's divide 16 by 6 to find what we need to multiply by.
16/6= 2 2/3
So, if we need to multiply our number of apples by 2 2/3 to get to sixteen, we also need to multiply our minutes by 2 2/3.
15(2 2/3)= 40
Therefore, it takes Ritz 40 minutes to eat sixteen apples at this rate.
One trick to solve problems like this fast is to multiply the two different things you see (minutes and apples) and then divide by the other thing you see (apples in this case). Then, you get the minutes.
15(16)=240
240/6=40
I hope that this helps! Have a wonderful day!
Answer:
40 minutes
Step-by-step explanation:
using the converstion factor
15min 15min times16 240
16ap. times = = = 40
6 apples 6 6
Which is greater 8/25 or 0.32
Answers
[tex]\frac{8}{25} = 0.32\\[/tex] when simplified into decimals.
This means that these two are equal. hope this helps!
8/25 is equal to 0.32
let me know if u need explanation
Help me pleaseeee. Which equation represents the graphed function?
Answers
Answer:
D
Step-by-step explanation:
Can someone please tell me what the slope of the line in this graph is!!!!!!
Answers
Answer:
-1/3 I think
Step-by-step explanation:
I find the slope by finding 2 points where the line hits. I then just count up and across. Could be wrong :/
Hope this helps though :)
Answer:
slope = y2-y1
x2- x1
= 4-2 = 2
6-0. 6
= 1/3
Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces?
Answers
Answer:
The answer is "(0,0)"
Step-by-step explanation:
In the given some information is missing that is point so, the correct answer to this question can be described as follows:
book Number = x
overall Book weight = y
Neither x nor y can be negative. We have to be positive values, then.
Since x indicates the number of books, that must be a positive integer. It can not be a decimal number or fractional number.
So the only viable solution from the given options is (0, 0).
Answer:
6 ounces. Which ordered pair is a viable solution if x represents the number of books he orders
Step-by-s6 ounces.
need help asap!
15 points
Answers
Answer:
D
Step-by-step explanation:
8*320=2560
(2560)^1/3=8*5^1/3
Answer:
It's D (8[tex]\sqrt[3]{5}[/tex])
I won't do step-by-step because it's multiple choice.
Goodluck :)
Find the cardinal number for the set. Α = {3, 6, 9, . . . , 36}
Answers
Hey mate!!
Answer:
n(A)=12
Solution,
A={3,6,9,12,15,18,21,24,27,30,33,36}
Just count the elements,
There are 12 elements in the set.
So the cardinal number of the set is 12.
Hope it helps...Answer:
[tex]12[/tex]
Step-by-step explanation:
A = {3,6,9,12,15,18,21,24,27,30,33,36}
To find the cardinal number,
just count the numbersSo, according to that,
there are 12 numbers in this set.
So, it's clear for us that, the cardinal number of this set is 12
n (A)= 12
hope this helps
brainliest appreciated
good luck! have a nice day!
Sophia wants to find out whether people like a new airport .she surveyed 20 people who work at the airport one morning in March to find their opinion of the airport . Write down two ways Sophia could improve her data collection method.
Answers
Answer:
By asking a larger quantity of people.
Changing the time/date of when she went and asked the questions
Answer:
by asking more people because then she can get a more diverse answer
Step-by-step explanation:
The quantities x and y are proportional.
pls help plsssss this work is due 20 min plsss helppp
Answers
Answer: 2.5
Step-by-step explanation:
y = rx
substitute numbers in and solve for r
if
y = 10
x = 4
then
10 = r4
r = 10/4 = 2.5
this works for all the other numbers and always gives r = 2.5
Jordan invested $8,500 in an account paying an interest rate of 4.1% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $13,070?
Answers
Answer:
52 days
Step-by-step explanation:
if compounding daily we can see what 1 year accumulates using the function
360 / interest rate = 360/4.1 = 87.8048780488 = 87.80 per day
We can use inverse of the balance profit to use the exact amount difference to then divide into the date of withdrawal
$13070- 8500 = 4570
4570/ 87.8048780488 = 52.04 = 52 days.
Find the areas of the trapezoids.
Answers
Answer:
30 square units
Step-by-step explanation:
i did this problem before.
Solve and work out the value of a
Answers
Step-by-step explanation:
Since these angles are supplementary (meaning they have a sum of 180 degrees) we get 3a + 2a + 4a = 180° which simplifies to 9a = 180 and then a = 20°
Answer:
a = 20
Step-by-step explanation:
The angles form a straight line, which is 180 degrees
3a + 2a + 4a = 180
Combine like terms
9a = 180
Divide by 9
9a/9 =180/9
a = 20
The sum of the numbers 120. The third number is 4 times the second. The first number is 6 less than the second. What are the numbers?
Answers
Answer:
First number: 15
Second number: 21
Third number: 84
Step-by-step explanation:
Which of these statements is true for f(x) =
- (3)
A. The range of (x) is y to
B. The domain of fx) is x > 0.
C. It is always increasing
D. The graph contains
Answers
Help pleasseee •-•
1. The dot plot below shows the vertical jump of some NBA players. A vertical jump
is how high a player can jump from a standstill. Draw a box plot of the heights for the
vertical jumps of the NBA players above the dot plot.
Answers
Jordan invested $8,500 in an account paying an interest rate of 4.1% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $13,070?
Answers
Answer:
11 years
Step-by-step explanation:
Answer:
Its actually 10 years
Step-by-step explanation:
Its about 10.4 but it says nearest year and 10 is closer than 11
How should the decimal point in 6.8 be moved to determine the product of 6.8
and 100?
()) two places to the left
1)) three places to the right
<)) three places to the left
()) two places to the right
Answers
The correct answer is two places to the right
The following information should be considered:
For each and every 0 you have to move the decimal one place. And since the 100 is positive you move the decimal to the right.Learn more: https://brainly.com/question/17429689?referrer=searchResults
The chemicals in my swimming pool use a ratio of 2 tablets of chlorine for every 5 days. Which ratio shows the number of chlorine tablets needed for 20 days? A. 5 to 20 B. 8 to 20 C. 7 to 20 D. 3 to 20
Answers
Answer:
The answer would be B. 8 to 20
Step-by-step explanation:
You use 2 tablets per 5 days and there are 20 days 5/20=4 4 times you need to add tablets 4 times 2 is 8 which would make the ratio 8 to 20. Hope this helped. :)
Answer:
B
Step-by-step explanation:
Works on edge 2021
Please answer need help
Answers
-3.5, -3, -2 1/2, -2, 2.5
Subtract.
5 3/4 - 2 7/8 HELLLLLLLPPPPPPPPPPP
Answers
Answer: HI, Hope this helps you dear!
Step-by-step explanation:
3/4 - 2 7/8 = 2.8755
Answer:
2 7/8
Step-by-step explanation:
5 3/4 = 23/4
2 7/8 = 23/8
23×2=46
4×2=8
46/8-23/8= 2 7/8
a) write a formula for the perimeter p of the figure.
b) calculate the value of x if p=64
Answers
Answer:
[tex]x-2+x+10+x+11=64\\\\3x+19=64\\3x=64-19\\3x=45\\x=15\\[/tex]
I need help with this question get brailiest
Answers
Answer:
Mini golf: $10.00, batting cage: $2.50
Step-by-step explanation:
We have that 5 mini golf + 4 batting = 60, and 3 mini golf + 6 batting = 45.
Let m=mini golf price, and b=batting cage price.
Then 5m+4b=60 and 3m+6b=45.
We can multiply the first equation by 3 and second by 5 to get
15m+12b=180
15m+30b=225
Subtract the two to get -18b=-45, so b=45/18=$2.50
Then m=$10 if you substitute b back in the first equation.
Hope that helped,
-sirswagger21
Answer:
mini golf10:00 batting cage 2:50
Step-by-step explanation:
A triangle on a coordinate plane is translated according to the rule T-8,4(x, y). Which is another way to write this rule?
A (x,y) - (x + 4, y - 8)
B (x,y) - (x - 4, y - 8)
C (x, y) - (x - 8, y + 4)
D (x,y) - (x + 8, y - 4)
Answers
Answer:
CStep-by-step explanation:
(x, y) → (x – 8, y + 4)A triangle on a coordinate plane translated according to the rule [tex]T_{-8,4}(x,y)[/tex]can also be written as [tex](x,y)[/tex] → [tex](x-8,y+4)[/tex] according to the translation rule.
What is translation rule ?According to translation rule [tex]T_{a,b}(x,y)[/tex] tells that translation of a point (x,y)
by (a,b) is given by [tex](x,y)[/tex]→[tex](x+a,y+b)[/tex].
How to use translation rule to find the answer?Given that [tex]T_{-8,4}(x,y)[/tex], a=-8 and b=4
Putting in the values given in the question to the translation rule we get
[tex](x,y)[/tex]→[tex](x+(-8),y+(4))[/tex]
[tex](x,y)[/tex]→[tex](x-8,y+4)[/tex]
Hence we get triangle on a coordinate plane translated according to the rule [tex]T_{-8,4}(x,y)[/tex]can also be written as [tex](x,y)[/tex] → [tex](x-8,y+4)[/tex]. Answer C is correct.
Learn more about translation rule here:
brainly.com/question/1678275
#SPJ2
Can someone please help me I am almost done with this
Answers
Hey!!
{12,13,25} is not a Pythagorean triple
please see the attached picture for full solution
hope it helps
A.75/1 dollars per daythe cost $75 for each day.
B.1/25 dollars per day; the cost is $25 for each day.
C.1/150 dollars per daythe costs $1 for 150 days
D.25/1 dollars per daythe cost is $25 for each day
Answers
Answer:
D
Step-by-step explanation:
Count by 25. Its a no-brainer honestly.
The ratio of the number of Mays necklaces to the number of Helen's necklace is 25:9. May has 100 necklaces. How many necklaces does Helen have.
Answers
Answer:
36
Step-by-step explanation:
25:9
25*4 = 100
9*4 = 36
A fruit basket contains seven apples, four bananas, and eight pears. If a piece of fruit is picked at random from the basket, which of the following is closest to the probability that it is not a banana?
1) 0.21
2) 0.68
3) 0.79
4) 0.32
Answers
Answer:
1) 0.21
Step-by-step explanation:
This is because there are 4 bananas out of all 19 fruits. 4/19 is equal to 0.21052631578.
This tennis ball has an diameter of 2.7 inches. What is the volume of this tennis ball? Use 3.14 for π and round your answer to a whole number.
Answers
Answer:
V = 10 in^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
We have the diameter
r = d/2 = 2.7/2 =1.35
V = 4/3 ( 3.14) (1.35)^3
V =10.30077
Rounding to the nearest whole number
V = 10 in^3
Answer:
10 in^3
Step-by-step explanation:
A chemist is adding pure (100%) acid to a 12 liter solution that is 15% acid in order to increase it to 49% acid. How much pure acid must she add?
How many ounces of 35% ethanol must be added to a 23 ounce mixture that contains 26% ethanol in order to obtain a mixture of 30.86% ethanol?
How many liters of 30% acid must be added to 10 liters of 53.66% acid in order to obtain a mixture that is 43% acid?
Answers
Answer:
1) 8 liters of pure acid
2) 27 liters of 35% ethanol
3) 8.2 liters of 30% acid
Step-by-step explanation:
The inicial amount of acid is 15% of 12 L, and the inicial volume is 12L.
Adding 'x' L of 100% acid, we have the amount of acid equal to 12 * 0.15 + x * 1, and the volume of 12 + x. The concentration is the amount of acid over the volume, so we have that:
(12*0.15 + x) / (12 + x) = 49/100
(1.8 + x)*100 = (12 + x) * 49
180 + 100x = 588 + 49x
51x = 408
x = 8 liters of pure acid
Similar to the solution above, for the second question we have:
(23*0.26 + 0.35*x) / (23 + x) = 30.86/100
(5.98 + 0.35*x)*100 = (23 + x) * 30.86
598 + 35x = 709.78 + 30.86x
4.14x = 111.78
x = 27 liters of 35% ethanol
For the third question, we have:
(10*0.5366 + 0.3*x) / (10 + x) = 43/100
(5.366 + 0.3x)*100 = (10 + x)*43
536.6 + 30x = 430 + 43x
13x = 106.6
x = 8.2 liters of 30% acid
value of a in simplest form?
Answers
Answer:
Step-by-step explanation:
When base is same, add the powers
[tex]x^{\frac{2}{3}}*x^{\frac{1}{2}}=x^{a}\\\\x^{\frac{2}{3}+\frac{1}{2}}=x^{a}\\\\x^{\frac{4}{6}+\frac{3}{6}}=x^{a}\\\\x^{\frac{7}{6}}=x^{a}[/tex]
Compare the powers,
a = 7/6
