[tex]f(x) = 0 \\\\\implies x^3-13x^2+59x -87 =0\\\\\implies x^3 -3x^2 -10x^2 +30x +29x - 87=0\\\\\implies x^2(x-3) - 10x(x-3) + 29(x-3) =0\\\\\implies (x-3)(x^2 -10x +29) =0\\\\\implies x - 3 = 0 ~~ \text{or}~~x^2 -10x +29 = 0\\\\\implies x =3~~ \text{ or} ~~ x = \dfrac{-(-10) \pm \sqrt{(-10)^2 -4 \cdot 1 \cdot 29}}{2(1)}\\\\\implies x =3~~ \text{ or} ~~ x = \dfrac{10\pm \sqrt{-16}}{2}\\\\\implies x =3~~ \text{ or} ~~ x = \dfrac{10\pm 4i }{2}\\[/tex]
[tex]\\\implies x =3~~ \text{ or} ~~ x =5 \pm 2i\\\\\text{Hence the complex roots are,}~ 5- 2i ~~ \text{and} ~~5 + 2i[/tex]
Kevin will be taking six classes next semester (Algebra, World History, Psychology, Political Science, Chemistry, and Art Theory) and would like to know how many different ways he can order his class schedule given that his university offers six time slots for classes each day. Assuming there are no constraints and each class can be taken in any time slot, how many different ways can Kevin order his classes?
=========================================================
Explanation:
We have 6 slots to fill A,B,C,D,E,F
There are 6 choices for choice A, then 5 choices for slot B, 4 for C, and so on until we reach one choice for slot F. Count down by 1 each time a slot is filled.
Multiply out those values to get: 6*5*4*3*2*1 = 720
For more information, check out the concept of factorials.
---------
Another approach is to use the nPr permutation formula which is
[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]
where in this case n = 6 and r = 6.
What's The Interest Rate?
I = $200
P = $800
T = 24 months
Talia’s Australian Shepherd weighed 11 pounds when they first brought him home. By the time he was 6 months old, he weighed 33 pounds. What is the percent increase? *
Answer:
11+ 200% = 33 pounds
The percent increase is 200%
Step-by-step explanation:
QUESTION 1
A conical cup is 4 cm across and 6 cm deep. Water leaks out of the bottom at the rate of 2 cm/sec. How fast (in cm/sec) is the water level dropping
when the height of the water is 3 cm?(Round your answer two (2) decimal places)
The water level will be dropping at the rate of [tex]0.64 cm/sec[/tex] when the height of the water reaches [tex]3cm[/tex]
We are give a cone with dimensions as seen in the diagram in the attached image.
The volume changes at the rate
[tex]\frac{dV}{dt}=-2cm^2/sec[/tex]
the negative sign is used because the volume of water is reducing.
what we need to know is the rate the height is changing when [tex]h=3cm[/tex]. That is, we need to evaluate
[tex]\frac{dh}{dt}|_{h=3cm}[/tex]
The relationship between the volume and the height is given by
[tex]V=\frac{1}{3}\pi r^2h[/tex]
but both [tex]h[/tex] and [tex]r[/tex] are changing when [tex]V[/tex] changes. So we need to eliminate [tex]r[/tex] somehow. From the diagram, we can use the similar triangle property to accomplish this
[tex]\frac{r}{2}=\frac{h}{6}\\\\\implies r=\frac{h}{3}[/tex]
substitute into the volume formula to eliminate [tex]r[/tex]
[tex]V=\frac{\pi h^3}{27}[/tex]
differentiate both sides with respect to time, [tex]t[/tex], since both the volume and height are functions of time. They will both be differentiated implicitly
[tex]\frac{dV}{dt}=\frac{\pi h^2}{9}\frac{dh}{dt}[/tex]
to find [tex]\frac{dh}{dt}|_{h=3cm}[/tex], substitute the values for [tex]\frac{dV}{dt}[/tex] and [tex]h[/tex]
[tex]-2=\frac{\pi 3^2}{9}\frac{dh}{dt}\\\\\frac{dh}{dt}=-\frac{2}{\pi}\\\\\approx -0.64 cm/sec[/tex]
So the rate at which the height is reducing when it reaches [tex]3cm[/tex] is [tex]0.64cm/sec[/tex]
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A group of students organized a car wash to raise money for a local charity. The students charged $9.99 for each car they watched.In 3.5 hours they washed 14 cars.at that rate how much money could they earn in 8 hours?
Answer:
First you would divide 12 cars by 3 hours to see how many cars get washed per hour
Then you know that 4 cars get washed in one hour so you multiply it by $5.00 because you want to see how much money they earn in one hour
After you know they earn $20.00 per hour you multiply that by 8 because you want to see how much money they earn in eight hours
So your final answer is $160 for washing cars in 8 hours
I need some help please
The answer is A.
A negative x a negative equals a positive so the square root of a negative value cannot be a negative value.
Can someone help me please
Graph the equation of the line parallel to 2x−y=6 and passing
through (-3, 1). Show work.
Answer:
It's a graph, see the image.
Step-by-step explanation:
Use the equation to find the slope. Use the slope and the point to graph the line.
This question on your unit test is a fill in the blank. Be prepared to type your answer. The graph show how many minutes it takes Ziah to run a certain distance in the city. What is the meaning of the point (4, 6)?
The point (4,6) means it took Ziah 4 minutes to run 6 blocks.
This is because any point is of the form (x,y) where in this case
x = number of minutes
y = number of blocks
Mark’s birthday is 32 weeks away. How many days until his birthday?
It takes 6 hours to clean and detail a luxury car. During the morning of
cleaning, the workers were able to clean for 4 hours. If the variable t stands
for the amount of time the workers have left to clean the windows after lunch,
which of the following units could apply to this variable?
2. If Jordan's section contains 35 rows, how many seats are in her section?
seat(s)
Answer:
5
Step-by-step explanation:
3 movie tickets cost 36$. at this rate, the cost per ticket is $..
Answer: The cost per ticket is $12.
Step-by-step explanation:
Can someone help please?
NEED NOW PLEASE.....
Answer:
2+(-6)
Step-by-step explanation:
hope this helps
The diagonal of a side of rhombus are of equal length. Find the measures of angles of the rhombus.
Explanation:
Consider ABCD is a rhombus
We know that
All sides are equal in rhombus i.e,
⇛AB=BC=CD=DA
and AC and BD are digonals
Given that
Diagonal and the side of the rhombus are equal.
⇛AB = BC = CD = DA = AC
Diagonal AC divides the rhombus into two triangles .
They are ∆ BAC and ∆ DAC
In triangle BAC
BA=BC=AC,(Given)
⇛∠ BAC=∠ABC= ∠ACB =60°→→→Eqn(i)
Similarly in ∆DAC ,
DA=DC=AC
⇛∠DAC=∠ACD=∠ADC=60°→→→Eqn(ii)
From eqn(i) and eqn(ii)
∠A=∠BAC+∠DAC=60°+60°=120°
and
∠B= ∠ABC = 60°.
and
∠C=∠ACB+∠ACD=60°+60°=120°
and
∠D =∠ADC=60°
∴ ∠A = 120° , ∠B = 60° ,∠C = 120° & ∠D = 60°
Answer:-The measures of the all angles in the rhombus are 120° , 60° ,120° and 60°.
Note: [Figure refers in the attached file.
Write the equation of the line perpendicular to y = 8 - 5z that contains the point (0, 0) . Fill in the slope and y-intercept
The equation of the line perpendicular to y = 8 - 5z is 5x+8y=16.
8y=-5x+16
y=-5/8x+2.
To be perpendicular, the slope has to be 8/5.
What is the slope-intercept form of the line?
The slope-intercept form is y=mx+c
Where m is the slope and c is the y-intercept.
So y=8/5x+b.
We can plug in the given coordinates to get
7=8/5*-5+b
7=-8+b
b=15.
So eqn is y=8/5x+15 or in point-slope form, y=8/5x+15
5y=8x+75
5y-8x=75
The equation of the line perpendicular to y = 8 - 5z is 5x+8y=16.
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Pre college need help this
A room has a rectangular floor 5.5 m long and 4.5 m wide. The room is 2.5 m in height.
A. What is the area of wall space in the room?
B. How much paint is required to paint the
walls with two coats if one litre of paint
can cover 11.25 m??
Answer:
Length=8 m,Breadth=6 m,Height=3 m
We know,
LSA=2(l+b)×h
LSA=2×14×3=84 m
2
Therefore, cost of painting = 84×60=Rs.5040.
Which triangle has vertices (–3, –5), (7, 4), (0, 4)?
Answer:
see attached
Step-by-step explanation:
The one that matches the triangle shown in the attachment has the given vertices.
Suppose a quadratic equation has the form x^2 + x + c = 0. Show that the constant c must be less than 1/4 in order for the equation to have two real solutions.
Answer:
see explanation
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
Then for the equation to have 2 real roots , the discriminant must be greater than zero , that is
b² - 4ac > 0
x² + x + c = 0 ← is in standard form
with a = 1, b = 1, c = c , then
b² - 4ac > 0
1² - (4 × 1 × c) > 0
1 - 4c > 0 ( subtract 1 from both sides )
- 4c > - 1
Divide both sides by - 4, reversing the inequality as a result of dividing by a negative quantity.
c < [tex]\frac{1}{4}[/tex]
Dr. M wanted to estimate the mean cholesterol level for men living in Hartford. He took a sampled of 20 men from Hartford and found that mean cholesterol level is 86 with a standard deviation of 12. He wants to construct a 99 % confidence interval for mean cholesterol level of men.
In this case, the level of significance a and the critical value?
Answer:
answer is in an image here
imageshare.best/image.php?id=JS9NDO
Explanation:
copy n paste in browser
not a bot btw
Pls need help
Also making this 10 points so i have 169 points left B)
Answer:
Second and fourth
Step-by-step explanation:
A line is in point-slope form when you write down as [tex]y-y_0=m(x-x_0)[/tex] - do not be distracted by the signs, +1 and +5 can both be written as -(-1) or -(-5) rispectively.
11. Select the proper order from least to greatest for 2/3, 7/6, 1/8, 9/10.
O A.1/8, 2/3, 9/10, 7/6
O B.2/3, 9/10, 7/6, 1/8
O C.7/6,9/10, 2/3, 1/8
O D. 1/8, 9/10, 7/6, 2/3
Step-by-step explanation:
Option A is the correct answer
Answer:
A is correct
Step-by-step explanation:
[tex]\frac{1}{8}[/tex] is 0.125
[tex]\frac{2}{3}[/tex] is 0.667
[tex]\frac{9}{10}[/tex] is 0.9
[tex]\frac{7}{6}[/tex] is 1.167
which from this you can see that A represents the order from smallest to largest
When divide f(x)=ax³+bx²+cx+d by (x+3), the remainder is 4, then what is the remainder when divide 2f(x)-6 by (x+3)?
Answer:
2Step-by-step explanation:
When divide f(x)=ax³+bx²+cx+d by (x+3), the remainder is 4:
f(x) = m*(x + 3) + 4, where m is the quotientThen 2f(x) - 6 is:
2[m(x + 3) + 4] - 6 = 2m(x + 3) + 8 - 6 = 2m(x + 3) + 2As we see the remainder is 2
what is the value of x in m(x+n)=n
The equation m(x + n) = n si solved for x will be given as x = n / m (1 - m).
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The equation is given below.
m(x + n) = n
By simplifying for x, then we have
x + n = n / m
x = n / m - n
x = (n - mn) / m
x = n / m (1 - m)
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Figure F is a scaled copy of E.
What is length of each missing measurement.
Answer:
answer
Step-by-step explanation:
what are do u mean what is f and e explain properly and then people will tell u
Which is a composite number? A.97 B.89 C.95 D.13
PLEASE I REALLY NEED THE CORRECT ANSWER RIGHT NOW!!!!
Answer: C. 95 is a composite number.
Step-by-step explanation:
You can look at the ones place of each number to see if any end in 0, 2, 5, or any other digit that indicates that the number is not prime. Since 95 ends in a 5, it can be divided by 5, making it have more factors than 1 and itself. Therefore, 95 is the composite number of the list of numbers.
Answer:95
Step-by-step explanation:composite numbers are numbers that have more factors than 1 and itself, factors are numbers you can multiply to get a number. 95 is a composite number since 1,95, AND 5 are all factors of 95 making it a composite number
A deposit of $1000 is made in an account that earns 8% interest compounded quarterly. The balance in the account after n quarters is given by the following sequence. Find the balance in the account after ten years.
a
=100.000)
n=1,2,3
The balance after ten years.
The balance after ten years is $2,208.04.
When an amount of money is compounded quarterly, it means that the amount deposited and the interest earns interest every quarter. The formula that can be used to determine the balance in 10 years is:
FV = P (1 + r)^nm
FV = Future value P = Present value = $1000 R = interest rate = 8%/4 = 2% m = number of compounding = 4 N = number of years = 10$1000 x (1.02)^40 = $2,208.04
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Melanie was training for a race. The line plot below shows the number of miles Melanie ran last week.
2. How many times did Melanie run ½ a mile?
Answer:
5 miles
Step-by-step explanation:
add the points together.
it seems like each point is how many miles they ran each day.
1/4 + 2(1/2) + 3/4 + 3(1) = 5