Answer:
p(x) = (x + 1) (x - 3) (x + 2)
Step-by-step explanation:
x³ - 7x - 6
(x+1) (x² - x - 6) found by doing long division
(x+1) ( x - 3) (x + 2) are the factors
The polynomial p(x) as a product of linear factors is; p(x) = (x + 1) (x - 3) (x + 2)
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
We are given the polynomial as;
x³ - 7x - 6
Then we found by doing long division;
(x+1) (x² - x - 6)
(x+1) ( x - 3) (x + 2)
These are the factors.
Hence, The polynomial p(x) as a product of linear factors is; p(x) = (x + 1) (x - 3) (x + 2)
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At a central train station, there are 4 different train routes with trains that leave every 6 minutes, 10 minutes, 12 minutes, and 15 minutes. If each train can hold up to 200 passengers, what is the maximum number of passengers who can leave the station on a train in one hour?
Answer:
5,000 passengers
Step-by-step explanation:
1. Find out how many trains leave each hour.
6 min – 60/6 = 10 x 200 passengers = 2000
10 min – 60/10 = 6 x 200 passengers = 1200
12 min – 60/12 = 5 x 200 passengers = 1000
15 min – 60/15 = 4 x 200 passengers = 800
2. Add it all up.
2000 + 1200 + 1000 + 800 = 5000 passengers
Answer:
5000
Step-by-step explanation:
6 minute train leaves 10 times
10 x 200 = 2000 passengers
10 minute train leaves 6 times
6x200 = 1200
12 minute train leaves 5 times
5x200 =1000
15 minute train leaves 4 times
4x200 =800
2000+1200+1000+800=5000
assuming more than 1 train can be at the station at once
A total of $10,000 is invested in two mutual funds. The first account yields 5% and the second account yields 6%. How much was invested in each account if the total interest earned in a year is $575?
Answer:
$2,500 was invested in the first account while $7,500 was invested in the second account
Step-by-step explanation:
Here in this question, we want to find the amount which was invested in each of the accounts, given their individual interest rates and the total amount that was accorded as interest from the two investments
Now, since we do not know the amount invested , we shall be representing them with variables.
Let the amount invested in the first account be $x and the amount invested in the second account be $y
Since the total amount invested is $10,000, this means that the summation of both gives $10,000
Mathematically;
x + y = 10,000 ••••••(i)
now for the $x, we have an interest rate of 5%
This mathematically translates to an interest value of 5/100 * x = 5x/100
For the $y, we have an interest rate of 6% and this mathematically translates to a value of 6/100 * y= 6y/100
The addition of both interests, gives 575
Thus mathematically;
5x/100 + 6y/100 = 575
Multiplying through by 100, we have
5x + 6y = 57500 •••••••••(ii)
From 1, we can have x = 10,000-y
let’s substitute this into equation ii
5(10,000-y) + 6y = 57500
50,000-5y + 6y = 57500
50,000 + y = 57500
y = 57500-50,000
y = 7,500
Recall;
x = 10,000-y
so we have;
x = 10,000-7500 = 2,500
The mean one-way commute to work in Chowchilla is 7 minutes. The standard deviation is 2.4 minutes, and the population is normally distributed. What is the probability of randomly selecting one commute time and finding that: a). P (x < 2 mins) _____________________________ b). P (2 < x < 11 mins) _____________________________ c). P (x < 11 mins) ________________________________ d). P (2 < x < 5 mins) _______________________________ e). P (x > 5 mins)
Answer:
The answer is below
Step-by-step explanation:
Given that:
The mean (μ) one-way commute to work in Chowchilla is 7 minutes. The standard deviation (σ) is 2.4 minutes.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
a) For x < 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
From normal distribution table, P(x < 2) = P(z < -2.08) = 0.0188 = 1.88%
b) For x = 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
For x = 11:
[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]
From normal distribution table, P(2 < x < 11) = P(-2.08 < z < 1.67 ) = P(z < 1.67) - P(z < -2.08) = 0.9525 - 0.0188 = 0.9337
c) For x = 11:
[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]
From normal distribution table, P(x < 11) = P(z < 1.67) = 0.9525
d) For x = 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
For x = 5:
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]
From normal distribution table, P(2 < x < 5) = P(-2.08 < z < -0.83 ) = P(z < -0.83) - P(z < -2.08) = 0.2033- 0.0188 = 0.1845
e) For x = 5:
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]
From normal distribution table, P(x < 5) = P(z < -0.83) = 0.2033
Carrie can inspect a case of watches in 5 hours.James can inspect the same case of watches in 3 hours.After working alone for 1 hour,Carrie stops for lunch.After taking a 40 minute lunch break,Carrie and James work together to inspect the remaining watches.How long do Carrie and James work together to complete the job?
Will mark brainlist if it correct and well explained
Answer:
It takes Carrie and James an hour and a half to finish the job.
Step-by-step explanation:
assuming they have to inspect ONE case of watches.
Carrie can inspect 1/5 case in one hour.
James can inspect 1/3 case in one hour.
Carrie worked alone for 1 hour, so she finished 1/5 of a case.
She leaves 4/5 case to finish.
She had lunch.
After that, Carrie and James worked together for x hours to finish the job.
When they work together, the finish 1/5+1/3 = 8/15 case per hour.
So time to finisher the remaining case
Time = 4/5 / (8/15)
= 4/5 * 15/8
= 3/2 hours
= an hour and a half.
Solve the equation and show the solution set on a number line: |x+5|=x+5
Answer: x ≥ -5
Step-by-step explanation:
First, let's see how the function f(x) = IxI works:
if x ≥ 0, IxI = x
if x ≤ 0, IxI = -x
Notice that for 0, I0I = 0.
Ok, we want that:
|x+5| = x+5
Notice that this is equivalent to:
IxI = x
This means that |x+5| = x+5 is only true when:
(x + 5) ≥ 0
from this we can find the possible values of x:
we can subtract 5 to both sides and get:
(x + 5) -5 ≥ 0 - 5
x ≥ -5
So the graph in the number line will be a black dot in x = -5, and all the right region shaded.
something like:
-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4__ ...
How does the period of f(x)= cos(2x) relate to the period of the parent function cos x?
Answer:
Both have the same period which is 2π
Step-by-step explanation:
find the value of x and y if the distance of the point (x,y) from (-2,0) and (2,0) are both 14 units.
Answer:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex] are both 14 units from points (-2, 0) and (2, 0).
Step-by-step explanation:
distance formula
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
We want the distance, d, from points (-2, 0) and (2, 0) to be 14.
Point (-2, 0):
[tex] 14 = \sqrt{(x - (-2))^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
Point (2, 0):
[tex] 14 = \sqrt{(x - 2)^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
We have a system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
Since the right sides of both equations are equal, we set the left sides equal.
[tex] \sqrt{(x + 2)^2 + y^2} = \sqrt{(x - 2)^2 + y^2} [/tex]
Square both sides:
[tex] (x + 2)^2 + y^2 = (x - 2)^2 + y^2 [/tex]
Square the binomials and combine like terms.
[tex] x^2 + 4x + 4 + y^2 = x^2 - 4x + 4 + y^2 [/tex]
[tex] 4x = -4x [/tex]
[tex] 8x = 0 [/tex]
[tex] x = 0 [/tex]
Now we substitute x = 0 in the first equation of the system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(0 + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{4 + y^2} = 14 [/tex]
Square both sides.
[tex] y^2 + 4 = 196 [/tex]
[tex] y^2 = 192 [/tex]
[tex] y = \pm \sqrt{192} [/tex]
[tex] y = \pm \sqrt{64 \times 3} [/tex]
[tex] y = \pm 8\sqrt{3} [/tex]
The points are:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex]
In a different plan for area codes the first digit could be any number from 3 through 6 the second digit was either 5,6,7 or 8 and the third digit could be any number except 5. With this plan how many different area codes are possible?
Answer:
144 codes are possible
Step-by-step explanation:
Okay for the first digit, we shall be selecting one out of 3,4,5,6.
Meaning we are selecting one out of four choices
The number of ways this can be done is 4C1 ways = 4 ways
For the second digit, we have 5,6,7 or 8, we are still selecting 1 out of 4 selections and the number of ways we can do this is also 4 ways
And lastly , we can choose any digit for the last number expect 5 , so from 0 to 9, we are removing 1 which means we are left with 9 choices
So the number of different area codes possible are ; 9 * 4 * 4 = 144 codes
If a cone is 5 meters tall and has a radius of 3 meters, What is its volume? 15π m3 60π m3 45π m3 30π m3
Answer:
V = 15 pi m^3
Step-by-step explanation:
The volume of a cone is
V = 1/3 pi r^2 h
The radius is 3 and the height is 5
V = 1/3 pi ( 3)^2 *5
V = 15 pi m^3
Answer:
15 pi m3
Step-by-step explanation:
Find the area of the shape shown below.
Answer:
28
Step-by-step explanation:
We divide the shape covenientely, like this, and area 1 is 4*4=16
area 2=4*4/2=8
area 3= 2*4/2=4
Area total = Area 1 + Area 2 + Area 3=16+8+4=28
Colin leaves school to go home. He walks 3 blocks south and then 9 blocks west. If Colin could walk in a straight line to the school, what is the exact distance between Colin and the school?
Answer:
9.48*
Step-by-step explanation:
This is a right triangle. The formula for solving the Hypotenuse, or the longest side of the right triangle is A^2 + B^2 = C^2. If we put the numbers from the problem into the formula this is what we get :
3^2 + 9^2 = C^2
9 + 81 = C^2
90 = C^2
9.48 = C
* This is rounded, the exact number is closer to 9.486832980505138. Your class should tell you what to round to.
Answer:
The answer would be A. 3√10 blocks
Step-by-step explanation:
I have had this question and its 3√10 blocks.
Hope this helps you other people :))
Please help me with this question!! TRIGONOMETRY
Work Shown:
sin(angle) = opposite/hypotenuse
sin(35) = 10/x
x*sin(35) = 10
x = 10/sin(35)
x = 17.434467956211 make sure your calculator is in degree mode
x = 17.4
Answer:
[tex]\boxed{17.4}[/tex]
Step-by-step explanation:
sin [tex]\theta[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
sin (35) = [tex]\frac{10}{x}[/tex]
x = [tex]\frac{10}{sin(35)}[/tex]
x = 17.4344679562...
x ≈ 17.4
List some typical benefits an employee might receive on top of their wage?
Answer:
paid vacation
paid medical
401k
Eiko is wearing a magic ring that increases the power of her healing spell by 30\%30%30, percent. Without the ring, her healing spell restores HHH health points. Which of the following expressions could represent how many health points the spell restores when Eiko is wearing the magic ring?
Answer:
Options B: and C:
Step-by-step explanation:
Remember that 30% in fraction form is
The amount of health points (H) restored would depend on the amount of the current H so it means it would add 30% of the current which we can write as:
And since it would add that to the current total we can right the current total as:
So our equation would be:
For option B:
We can factor out the H and you will be left with:
Combine or add the fractions inside the parenthesis and you will have:
For option C:
We can simplify the fractions which will result in:
Then factor out the H and you will have:
Options B: and C:
Step-by-step explanation:
Remember that 30% in fraction form is
The amount of health points (H) restored would depend on the amount of the current H so it means it would add 30% of the current which we can write as:
And since it would add that to the current total we can right the current total as:
So our equation would be:
For option B:
We can factor out the H and you will be left with:
Combine or add the fractions inside the parenthesis and you will have:
For option C:
We can simplify the fractions which will result in:
Then factor out the H and you will have:
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
anyone plss heeelp me...i only need answer 6c..
Answer:
6c1; [tex]Area = 81.12m^2[/tex]
6cii: See Explanation
Step-by-step explanation:
Given
[tex]A = 3p^2[/tex]
[tex]0 \leq p \leq 6[/tex]
Where A represents Area and P represents Width
Required
Solve 6c
Please note that because you only need 6c, I'll solve using calculations;
Solving 6ci:
Area of the cage, when width is 5.2m
Substitute 5.2m for p in[tex]A = 3p^2[/tex]
[tex]A = 3 * 5.2m^2[/tex]
[tex]A = 3 * 27.04m^2[/tex]
[tex]A = 81.12m^2[/tex]
Hence, the area of the cage is 81.12m²
Solving 6cii:
Area of the cage, when width is 40m
From the range of value of p: [tex]0 \leq p \leq 6[/tex], 40m is out of range of the values of p
However, if the range is extended; the value of Area is as follows;
Substitute 40m for p
[tex]A = 3 * 40m^2[/tex]
[tex]A = 3 * 1600m^2[/tex]
[tex]A = 4,800m^2[/tex]
An item is selling for $7,000. This item gets a discount and it is now $4,900. What percentage was the discount?
Answer:
30%Step-by-step explanation:
Discount =$7000-$4900
Discount% =
[tex] \frac{2100}{7000} \times 100 \\ = \frac{210000}{7000 } \\ = \frac{210}{7} = 30[/tex]
Which best describes the relationship between the lines with equations 5x +y = 4 and 20.0 + 4y = 16?
Answer:
There is no relationship, except they do intersect at the point (1, -1). Hope this helps :)
Brainliest?
Both given lines are going to intersect at ( 1,-1 ) that's it.
What is a line segment?A line section that can connect two places is referred to as a segment.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
Given that
Line 1 ; 5x +y = 4
Line 2 ; 20 + 4y = 16 ⇒ y = -1
At y = -1 the first line is
5x - 1 = 4 ⇒ x = 1
So,
It is clear that line 1 has a point ( 1 .-1 ) and line 2 also passes
through it hence there will an intersection.
For more about line segment
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Select all that apply. If x^2+b/ax+c/a=0 ; then: The sum of its roots = -b/a? The difference of its roots =-b/a? The product of its roots = c/a?The division of its roots = c/a? I can select multiple.
Answer:
The first and the thirdStep-by-step explanation:
[tex]x^2+\frac bax+\frac ca=0\\\\ ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\qquad\quad x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\\x_1+x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}+\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-2b}{2a}=\dfrac{-b}a\\\\\\x_1\cdot x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\cdot\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\\\\{}\ \ =\dfrac{b^2-b\sqrt{b^2-4ac}+b\sqrt{b^2-4ac}-(\sqrt{b^2-4ac})^2}{2a}=\dfrac{b^2-(b^2-4ac)}{4a^2}=\\\\{}\ \ =\dfrac{b^2-b^2+4ac}{4a^2}=\dfrac{4ac}{4a^2}=\dfrac{c}{a}[/tex]
[tex]x_1-x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}-\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-2\sqrt{b^2-4ac}}{2a}=\frac{-\sqrt{b^2-4ac}}{a}\\\\\\x_1\div x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}\div\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-b-\sqrt{b^2-4ac}}{2a}\,\cdot\,\frac{2a}{-b+\sqrt{b^2-4ac}}=\\\\=\frac{-b-\sqrt{b^2-4ac}}{-b+\sqrt{b^2-4ac}}=\frac{b+\sqrt{b^2-4ac}}{b-\sqrt{b^2-4ac}}=\frac{b^2+2\sqrt{b^2-4ac}+b^2-4ac}{b^2-b^2+4ac}=\frac{2b^2+2\sqrt{b^2-4ac}-4ac}{4ac}=[/tex]
[tex]=\frac{b^2+\sqrt{b^2-4ac}-2ac}{2ac}[/tex]
My age if I am half as old as two more than twice Mack's age if Mack is m years old.
Answer:
You are m + 1 years old.
Step-by-step explanation:
Let's say that you are x years old, and Mack is m years old.
x = 1/2( two plus twice m)
x = 1/2(2 + 2m)
x = 1 + m
x = m + 1
Hope this helps!
What does the denominator of the fraction \dfrac23 3 2 start fraction, 2, divided by, 3, end fraction mean?
Answer: It represents that 2 will be divided into 3 equal parts.
Step-by-step explanation:
Numerator is the top number in a fraction. It represents the total item it has to divide.Denominator is the bottom number in a fraction. it represents the number of equal parts the item is divided into.The given fraction : [tex]\dfrac{2}{3}[/tex]
here, Numerator = 2
Denominator = 3
It represents that 2 will be divided into 3 equal parts.
im stuck on this question helm me out I will mark you as brainliest
Answer: it is =4176000000000000
Step-by-step explanation:
(2.9)(100000)(7.2)(10^2)
5(10^−8)
=
(290000)(7.2)(10^2)
5(10^−8)
=
2088000(10^2)
5(10^−8)
=
(2088000)(100)
5(10^−8)
=
208800000
5(10^−8)
=
208800000
5(1/100000000)=
208800000/1
20000000
=4176000000000000
hope i helped
-lvr
Answer the problem below
Answer:
D. 4z^3
Step-by-step explanation:
First, you see what cubed is 64, which is 4, so you know it is either A or D, but it can not be A because it is not z to the power 5 but x to the power of 3
Hope this helps, if you want me to explain more, feel free to ask questions.
Have a good day! :)
Answer:
4 z^3
Step-by-step explanation:
( 64 z^9) ^ 1/3
Rewriting 64 as 4^3
( 4^3 z^9) ^ 1/3
We know that ( ab) ^c = a^c * b^c
4^3 ^ 1/3 z^9 ^ 1/3
We know that a^ b^c = a^ ( b*c)
4^(3 * 1/3) z^ (9 * 1/3)
4 ^ ( 1) z^ ( 3)
4 z^3
which geometric solid is formed by rotating the rectangle about line m?
Answer:
rectangular prism
Step-by-step explanation:
check by rotating the shape in images
F(x) = 3x+2 what is f(5)
Answer:
f(5) = 17Step-by-step explanation:
f(x) = 3x + 2
To find f(5) substitute 5 into f(x)
That's
f(5) = 3(5) + 2
= 15 + 2
= 17
Hope this helps you
Answer:
17
Step-by-step explanation:
You just plug 5 into the equation
f(5)= 3(5)+2
=15+2
=17
Hope this helped! :)
[tex] \sqrt[3]{y} = a(c + \frac{1}{x})[/tex]
Greetings from Brasil...
Here we don't have much to go
∛Y = A.(C + 1/X)
∛Y = (AC + A/X)
raising both members to the cube.....
(∛Y)³ = (AC + A/X)³
from Notable Products: (a + b)³ = a³ + 3a²b + 3ab² + b³
Y = (AC)³ + 3(AC)².(A/X) + 3AC(A/X)² + (A/X)³
Y = A³[C³ + (3C²/X) + (3C/X²) + (1/X³)]
Use De Morgan's laws to write negations for the statement. Sam is an orange belt and Kate is a red belt.
A. Sam is an orange belt or Kate a red belt.
B. Sam is not a red belt and Kate is not an orange belt.
C. Sam is not an orange belt and Kate is not a red belt.
D. Sam is not a red belt or Kate is not an orange belt.
E. Sam is not an orange belt or Kate is not a red belt.
Answer:
C. Same is not an orange belt and Kate is not a red belt.
Step-by-step explanation:
The negation for the statement is Sam is not an orange belt or Kate is not a red belt.
What is Negation of De- Morgan's Law?The negation of a conjunction is equivalent to the disjunction of the negation of the statements making up the conjunction. To negate an “and” statement, negate each part and change the “and” to “or”.
Given statement:
Sam is an orange belt and Kate is a red belt.
Now, to make the negation we have to consider the rule "To negate an “and” statement, negate each part and change the “and” to “or”."
So, the negation statement would be
Sam is not an orange belt or Kate is not a red belt.
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The cosine function reaches a value of 0 when x is equal to
Answer:
Step-by-step explanation:
The values of the cosine function are represented by the axis OX of the goniometric circumference (circumference centered at the origin and of radius 1). Therefore the cosine is zero for the 90º and 270º angles.
Find the perimeter of a square with a diagonal of 15√2.
Answer:
15
Step-by-step explanation:
Answer:
21.213
Step-by-step explanation:
Consider the functions. F(x)=(x+1)2-4 and g(x)=-4|x+1| which statement compares the range of the functions?
Answer:
The fourthStep-by-step explanation:
Vertex of f is (-1, -4) so its range is limited to y≥-4
|x+1| is always ≥0 therefore -|x+1| is always ≤0 {4 is insignificant to this - slope doesn't mean in range} so its range is limited to y≤0
Answer:
D
Step-by-step explanation:
i just took the test
Six friends went to a restaurant and agreed to share the bill equally. However, two people forgot their wallets so the other four friends' portions of the bill went up by $7 each. How many dollars was the total bill?
Answer:
The total bill was $84
Step-by-step explanation:
Ok so we know a few things, we know that the total cost of the bill is divisible by both 6 and 4, and we know that if we call the total cost of the bill x and the amount each person would pay if it was divided for 6 people y we can write these equations:
[tex]\frac{x}{6}=y[/tex]
[tex]\frac{x}{4}=y+7[/tex]
Now we can substitute the first equation into the second and solve for x
[tex]\frac{x}{4}=\frac{x}{6}+7\\\frac{x}{4}-\frac{x}{6}=7\\\frac{x}{12}=7\\x=7*12=84[/tex]
Therefore, the total bill was $84