Answer: 8
Step-by-step explanation:
EQ1: a + b + c = 2 --> b + c = 2 - a
EQ2: ab + bc + ac = -1 --> b + c = (-1 - bc)/a
EQ3: abc = -2 --> bc = -2/a
Set EQ1 = EQ2 and substitute bc using EQ3 to solve for "a":
[tex]2-a=\dfrac{-1-bc}{a}\\\\\\\text{Clear the denominator:}\\a(2-a)=-1-bc\\\\\text{Substitute bc:}\\a(2-a)=-1-\dfrac{-2}{a}\\\\\\\text{Clear the denominator:}\\a^2(2-a)=-a+2\\\\\\\text{Simplify and set equal to 0:}\\2a^2-a^3=-a+2\\0=a^3-2a^2-a+2\\\\\text{Factor:}\\0=a^2(a-2)-1(a-2)\\0=(a^2-1)(a-2)\\\\\text{Solve for a:}\\a^2-1=0\qquad a-2=0\\a=\pm1}\qquad \qquad a=2[/tex]
Consider the solution a = 2 and plug it into EQ1 to solve for "b"
b + c = 2 - 2
b + c = 0
b = -c
Plug in a = 2, b = -c, and c = c into a³ + b³ + c³
2³ + (-c)³ + c³
= 8 - c³ + c³
= 8
Df = 9x -39 find EF.
DE =47
Greetings from Brasil....
Looking at the figure we can say that:
DF = DE + EFDF = 9X - 39
DE = 47
EF = 3X + 10
inserting these data in the 1st expression....
DF = DE + EF
9X - 39 = 47 + (3X + 10)
9X - 39 = 47 + 3X + 10
9X - 3X = 57 + 39
6X = 96
X = 96/6
X = 16
EF = 3X + 10 anb X = 16, so
EF = 3·16 + 10
EF = 48 + 10
EF = 58A cyclist rides her bike at a rate of 21 kilometers per hour. What is this rte in kilometers per minute? How many kilometers will the cyclist travel in 5 minutes? Do not round your answers.
Answer: 0.35km per minute
Step-by-step explanation:
Divide by 60 because it was in "km per HOUR".
Which of the following circumstances would likely make completing the square th
best method for solving a quadratic equation?
The leading coefficient is 1 and the linear term coefficient is an even number
The leading coefficient is not 1 and the constant is large
The difference of 2 perfect squares
The difference of 2 perfect cubes
Answer:
The leading coefficient is 1 and the linear term coefficient is an even number
Step-by-step explanation:
Leading coefficient must be one for the application of completing square method. If the completing square is not one than we must apply other methods like Ac method, quadratic formula to solve the equation. To solve the equation with completing square the numerical value must be on other side of the equation. In this method we multiply linear term’s coefficient with one-half and square it therefore, completing square is suitable method for the equation having leading coefficient is 1 and linear coefficient is even.
Between 10pm and 7:45am, the water level in a swimming pool decreased by 3/8 in. Assuming that the water decreased at a constant rate, how much did the water level drop each hour?
Answer:
[tex]\frac{1}{26}[/tex] inches
Step-by-step explanation:
In order to solve this problem, we need to create a ratio.
Since we're looking for the rate per hour, we need to find how long it is from 10pm to 7:45am.
10pm + 2 hours = 12 AM
12 AM + 7.75 hours = 7:45 AM
So in total, it's 9.75 hours.
[tex]\frac{3}{8}[/tex] is the same as 0.375.
Our fraction will become [tex]\frac{0.375}{9.75}[/tex], which can simplify down to [tex]\frac{1}{26}[/tex].
Now we can create the proportion:
[tex]\frac{1}{26}=\frac{x}{1}[/tex]
Now we solve for x by cross multiplying.
[tex]1\cdot1=1\\\\1\div26=\frac{1}{26}[/tex]
Hope this helped!
A round wading pool has a diameter of 115\text{ cm}115 cm115, start text, space, c, m, end text and is 25\text{ cm}25 cm25, start text, space, c, m, end text deep. A hose is filling the pool at a rate of 34{,}000\text{ cm}^334,000 cm 3 34, comma, 000, start text, space, c, m, end text, cubed per minute. How long will it take to fill the pool to a depth of 20\text{ cm}20 cm20, start text, space, c, m, end text?
Answer: 6
Step-by-step explanation:
Answer:
6 minutes
Step-by-step explanation:
got answer from Khan and ml78786maggie
adam bought a box of fruit that weighed 6 1/4 pounds. if he bought a second box that weighed 8 1/8 pounds , what is the combined weight of the boxes?
Answer:
14 3/8 pounds
Step-by-step explanation:
6 pounds plus 8 pounds= 14 pounds. 1/4 + 1/8= 3/8. 1/4 can be turned into 2/8, and 2/8 plus 1/8 equals 3/8. Hope this helps :)
Select the correct answer
Answer:
D. 5 weeks
Step-by-step explanation:
A population of pea aphids double every week beginning with 300 aphids.
Week 1: 300 × 2 = 600
Week 2: 600 × 2 = 1200
Week 3: 1200 × 2 = 2400
Week 4: 2400 × 2 = 4800
Week 5: 4800 × 2 = 9600
It will take 5 weeks
Minato drove 390 miles. Part of the drive was along local roads, where his average speed was 20 mph, and the rest was along a highway, where his average speed was 60 mph. The drive took 8 hours. What distance, in miles did Minato drive along local roads?
Answer:
45 miles.
Step-by-step explanation:
Given that the:
Total distance covered = 390 miles
Total time = 8 hours
Let the distance covered along the local way = L
And the distance covered along the highway = H
Along with local way,
Speed = distance/ time
20 = L / T
T = L /20 .... (1)
Along the highway,
Distance covered H = 390 - L
Let the time = t
Speed = distance/time
60 = (390 - L)/t
t = ( 390 - L)/60
But total time = T + t
That is
8 = L/20 + (390 - L)/60
The LCM at right hand side will be 60
8 = ( 3L + 390 - L )/60
Cross multiply
480 = 2L + 390
Collect the like terms
2L = 480 - 390
2L = 90
L = 90/2
L = 45 miles.
Therefore, the distance Minato drive along local roads is 45 miles
evaluate 3+jk+k^3 when j=2 and k=6
Answer:
[tex]231[/tex]
Step-by-step explanation:
[tex]3 + jk + k {}^{3} = 3 + 2(6) + 6 {}^{3} = 3 + 12 + 216 = 231 [/tex]
Answer:
231Step-by-step explanation:
[tex]3+jk+k^3\\\\j = 2\\k=6\\\\3+ 2(6) + 6^3\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:exponents}\:6^3\::\quad 216\\=3+2\left(6\right)+216\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:2\left(6\right)\::\quad 12\\=3+12+216\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:3+12+216\:\\:\quad 231[/tex]
Simplify each expression by combining like
terms.
21a + (-18b) - 6a + 1lb
Answer:
My answer is
21a-18b-6a+11b.
which is 21a-6a-18b+11b.
=15a-7b.
Find the area of the shaded region. All measurements are in centimeters. Show your reasoning. Place your answer in the box to the right.
The price of a share of stock started the day at $37. During the day it went down $3, up $1, down $7 and up $4. What was the price of a share at the end of the day
Answer:
32
Step-by-step explanation:
Find the value of n and YZ if Y is between X and Z.
XY = 5n, YZ = 2n, XZ = 91
The value of n and YZ are 13 and 26 respectively
If Y is between X and Z, then:
XY + YZ = XZ
Given the following
XY = 5n
YZ = 2n
XZ = 91
Substitute the given expressions into the formula as shown:
5n + 2n = 91
7n = 91
Divide both sides by 7
7n/7 = 91/7
n = 13
Get the measure of segment YZ
YZ = 2n
YZ = 2(13)
YZ = 26
Hence the value of n and YZ are 13 and 26 respectively
Learn more here: https://brainly.com/question/23423083
What is the degree for 6p-8
Charle has 10 guests over at his house. If he gives each guest bacon, he will have given
out a total of 30 pieces of bacon. How much bacon did each guest get?
This needs to be converted into and algebraic expression plz help its due soon
Answer:
Each guest got 3. (if he doesn't have any for himself).
Step-by-step explanation:
if each guest is x
30=10x
divide by 10
x=3
hope this helps and if you want please consider giving me brainliest! :)
please helpp
me with this question and thank you
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \frac{4x}{(x + 2)(x - 2)}}}}}} [/tex]
Step-by-step explanation:
[tex] \sf{ \frac{1}{x + 2} + \frac{1}{x - 2} + \frac{2x}{ {x}^{2} + 4} }[/tex]
Use the formula of a² - b² = ( a + b ) ( a - b )
[tex] \longrightarrow{ \sf{ \frac{1}{x + 2} + \frac{1}{x - 2} + \frac{2x}{ {x}^{2} + {2}^{2} } }}[/tex]
[tex] \longrightarrow{ \sf{ \frac{1}{x + 2} + \frac{1}{x - 2} + \frac{2x}{(x + 2)(x - 2)}}} [/tex]
[tex] \longrightarrow{ \sf{ \frac{x - \cancel{2} + x + \cancel{ 2} + 2x}{(x + 2)(x -2 )} }}[/tex]
[tex] \longrightarrow{ \sf{ \frac{4x}{(x + 2)(x - 2)}} } [/tex]
Hope I helped!
Best regards! :D
20 POINTS: If tan= 3/4, find the CSC I don't know the relationship between tan and csc, please explain your answer
Answer:
[tex]\csc(x)=5/3[/tex]
Step-by-step explanation:
So we know that:
[tex]\tan(x)=3/4[/tex]
Recall that tangent represents the side opposite over the side adjacent.
This means that the opposite side is 3 while the adjacent side is 4.
Therefore, by using the Pythagorean Theorem, we can solve for the third side, which is the hypotenuse:
[tex]a^2+b^2=c^2[/tex]
Substitute a for 3 and b for 4. Thus:
[tex]3^2+4^2=c^2[/tex]
Square and add:
[tex]9+16=c^2\\25=c^2[/tex]
Square root:
[tex]c=5[/tex]
Now, recall that cosecant is the reciprocal of sine. So, find sine first.
Sine is opposite over hypotenuse. From tangent, the opposite is 3 and the hypotenuse as we now know is 5. Thus:
[tex]\sin(x)=3/5[/tex]
And cosecant is the reciprocal of that. Thus:
[tex]\csc(x)=5/3[/tex]
And that's our answer :)
A savings account rounds the amount of money deposited to the nearest hundredths place. After tax returns on April 15th, Mulan earned
exactly $239.1639 in retums.
How much money was deposited into the savings account?
A. $200
B. $239.16
C. 236.17
D. 239.164
E. I don’t know yet
Answer:
Step-by-step explanation:
how many fewer alligators were in bite swamp than in chomp lake and reptile creek combined
Answer:
4
Step-by-step explanation:
ik it
Answer:
The answer is 4
Step-by-step explanation:
The answer is 4 because i did it on khan and it was right.
Using the digits 0-9, at most one time each, create five ordered pair that represent a linear
function that has a greater rate of change than the following (explain how u got that answer)
Answer:
(-9, 0), (-8, 1), (-7, 2), (-6, 3) and (-5, 4)
Step-by-step explanation:
From the graph attached,
Ordered pairs which lie on the given line (-9, 0), (0, 3), (3, 4), (6, 5) and (9, 6).
Since all the points lie on the same line, rate of change of the linear function will be defined by the slope of the given line.
Slope of the line passing through (0, 3) and (3, 4) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{4-3}{3-0}[/tex]
[tex]m_1[/tex] = [tex]\frac{1}{3}[/tex]
Now we have to find the ordered pairs which represent a linear function having slope greater than [tex]\frac{1}{3}[/tex].
So the points will be (-9, 0), (-8, 1), (-7, 2), (-6, 3) and (-5, 4).
Slope of the linear function passing through (-9, 0) and (-8, 1)
[tex]m_2[/tex] = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{1-0}{-8+9}[/tex]
= 1
Here [tex]m_2>m_1[/tex]
I’m being timed help!!!!!!!!!!!!!!
Answer: light blue
Step-by-step explanation: Ax + By = C
Answer:
3x - y = -2
Step-by-step explanation:
is √13 greater or less than 3.5
Answer:yes it is greater
Step-by-step explanation:
Step-by-step explanation:
Hey, there!!
[tex] \sqrt{13 \: } \: is \: not \: greator \: than \: 3.5[/tex]
Because, root 13 means 3.60 also,
So, when you see 3.5 and 3.6 then it's obvious that 3.6 is greator.
Or if you see it in fractional form.
it will be,
18/5 and 7/2.
when we take a like term,
18×2/10 and 7×5/10
They will be ,
36/10 and 35/10.
Which implies 36/10>35/10.
So, the answer is root 13 is not greator than 3.5.
Hope it helps....
Assuming these rates continue, how many likes does Dagogo get, on average, for each minute of video he uploads?
Answer:
2000
Step-by-step explanation:
Khan Academy :)
Answer:
2000
Step-by-step explanation:
bc
Let f(x) = 4x + 8 and g(x) = 2x - 12. Perform the function operation, (f+g)
(x), and then find the domain of the result.??
you just add these functions:
(f+g)(x)=4x+8+2x-12=6x-4
domain of this function is still all reals (R)
how many fewer alligators were in bite swamp than in chomp lake and reptile creek combined
Answer:
4
Step-by-step explanation:
Find X. Need help ASAP
Answer:
A
Step-by-step explanation:
Given a tangent and a secant from an external point to the circle, then
the product of the external part and the whole of the secant is equal to the square of the tangent, that is
48(48 + x) = 60² = 3600 ( divide both sides by 48 )
48 + x = 75 ( subtract 48 from both sides )
x = 27 → A
dear friends answer is
x= 27
Find the lowest number divisible by 15, 20 & 25.
Answer:
300.
Step-by-step explanation:
This is the LCM.
15 = 3 * 5
20 = 2 * 2 * 5
25 = 5 * 5
One 5 appears in all 3 factors so we only use this once in the calculation:
LCM = 2 * 2 * 3 * 5* 5 = 300
Express in simplest radical form.
Sqrt (27)
3√3
Step-by-step explanation:√27 =
= √3×9
= √3×3²
= 3√3
Mia climbs 2/5 of the height of the rock wall. Lee climbs 3/8 of Mia's distance. What fraction of the wall did Lee climb?
Answer:
you got this
Step-by-step explanation: be a smart person like you are
the data set represents the shoe sizes of 19 students in a fifth grade physical education class 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7.5, 7.5, 8, 8, 8.5, 8.5, 9 a. create a box plot to represent the distribution of the data
Answer:
The minimum value = 4
The maximum value = 9
The first quartile, Q₁ = 6
The second quartile, (median) Q₂ = 7
The third quartile, Q₃ = 8
The box plot showing the above data is attached
Step-by-step explanation:
The given data set is 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7.5, 7.5, 8, 8, 8.5, 8.5, 9
From the data, we have;
The minimum value = 4
The maximum value = 9
The first quartile, Q₁ = (n + 1)/4th term = (19 + 1)/4 = the 5th term = 6
The second quartile, (median) Q₂ = (n + 1)/2 term = (19 + 1)/2 = the 10th term = 7
The third quartile, Q₃ = 3×(n + 1)/4th term = 3×(19 + 1)/4 = the 15th term = 8
Please find the attached box plot as plotted on Excel.