(36x^3-36x-1)/6x+6 or 6x^2-6x+(-1/6x+6)
For this case we must find the product of the following expression:
[tex]6 (x ^ 2-1) * \frac {6 (x-1)} {6 (x + 1)}[/tex]
We can rewrite [tex]x ^ 2-1[/tex] as:
[tex](x + 1) (x-1)[/tex], then:
[tex]6 (x + 1) (x-1) * \frac {6 (x-1)} {6 (x + 1)} =[/tex]
Canceling similar terms of the numerator and denominator:
[tex](x-1) * 6 (x-1) =\\6 (x-1) ^ 2[/tex]
ANswer:
[tex]6 (x-1) ^ 2[/tex]
A geometric sequence is defined by the recursive formula t1 = 64, tn =
tn - 1 / 2, where n ∈N and n > 1. The sequence is
A) -64, -16, -8, -4, -2, -1, ...
B) 64, 16, 8, 4, 2, 1, ...
C) 64, 32, 16, 8, 4, 2, ...
D) 64, 128, 256, 512, 1024, 2048, ...
Answer:
C) 64, 32, 16, 8, 4, 2, ...Step-by-step explanation:
[tex]t_1=64\\\\t_n=\dfrac{t_{n-1}}{2}\\\\\text{Therefore}\\\\t_2=\dfrac{t_1}{2}\to t_2=\dfrac{64}{2}=32\\\\t_3=\dfrac{t_2}{2}\to t_3=\dfrac{32}{2}=16\\\\t_4=\dfrac{t_3}{2}\to t_4=\dfrac{16}{2}=8\\\\t_5=\dfrac{t_4}{2}\to t_5=\dfrac{8}{2}=4\\\\t_6=\dfrac{t_5}{2}\to t_6=\dfrac{4}{2}=2\\\\t_7=\dfrac{t_6}{2}\to t_7=\dfrac{2}{2}=1\\\vdots[/tex]
The seniors on the student council bought a total of 36 plants to use in landscaping the front of the school. They bought some azaleas that cost $6 each and some lilies that cost $5 each. They spent a total of $196 on these plants. How many azaleas did the students buy?
a.) 18
b.) 16
c.) 20
d.) 5
Answer: B
Step-by-step explanation:
y = azaleas
x = lilies
6y + 5x =196 total cost
y + x = 36 total number of items
y = 36 – x
6(36 -x ) +5x =196
216 – 6x + 5x = 196
-x = 196 – 216
-x = -20
Divide by -1
X = 20 lilies
Plug into y equation
Y = 36 – 20
Y= 16 azaleas
To check
6(16) + 5(20) = 196
96 + 100 = 196
The answer is b 16 because you add the variables into the end of the numbers to identify you answer
Over the weekend, Brady and Jack drove to Key West to go scuba diving. Novw they're preparing to go home. Brady needs gas for his jeep, which gets 21 miles per gallon for gas mileage. When he stops at the gas station, he already has 5 gallons of gas in his tank. he buys more gas for $1.40 per gallon
Answer:
(I'm guessing the question is asking how much money Brady needs to pay.)
Step-by-step explanation:
21-5
(the original amount minus the 5 gallons he already has)
= 16.
so Brady needs 16 gallons.
and every gallon is 1.4
so 16 * 1.4
= 22.40
So brady needs 22.40 dollars.
The total cost of 16 gallons of gas is $22.4.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, 21 miles per gallon for gas mileage.
When he stops at the gas station, he already has 5 gallons of gas in his tank.
So, 21-5=16 miles
He buys gas for $1.40 per gallon
Now, total cost = 16×1.40
= $22.4
Therefore, the total cost of gas is $22.4.
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Identify the length of line BP
A) 9.75
B) 6.75
C) 15.75
D) 9
Answer:
I believe the answer is c because 4.5 can fit in BP almost 4 times so it is most accurate sorry if I'm wrong
A sphere has a volume of 500/3 π cubic centimeters. What is the total surface area , in square centimeters, of the sphere
Answer:
[tex]\large\boxed{S.A.=100\pi\ cm^3\approx314\pi\ cm^2}[/tex]
Step-by-step explanation:
The formula of a volume of a sphere:
[tex]V=\dfrac{4}{3}\pi R^3[/tex]
R - radius
We have
[tex]V=\dfrac{500}{3}\pi\ cm^3[/tex]
Substitute and solve for R:
[tex]\dfrac{500}{3}\pi=\dfrac{4}{3}\pi R^3[/tex] divide both sides by π
[tex]\dfrac{500}{3}=\dfrac{4}{3}R^3[/tex] multiply both sides by 3
[tex]500=4R^3[/tex] divide both sides by 4
[tex]125=R^3\to R=\sqrt[3]{125}\\\\R=5\ cm[/tex]
The formula of a Surface Area os a sphere:
[tex]S.A.=4\pi R^2[/tex]
Substitute:
[tex]S.A.=4\pi(5^2)=4\pi(25)=100\pi\ cm^2[/tex]
[tex]\pi\apprx3.14\to S.A.\approx(100)(3.14)=314\ cm^2[/tex]
Which number is an irrational number?
Answer
Square root 15
Step-by-step explanation:
When you square root the number 15 it will give you a decimal number with a lot of numbers that can't be rationalized. However the square root of 25 can be seen as 5, 1.15 is a rationalized number, 4th option can be seen 1.255555555... which is still rational.
find the equation of each line from the given information. write the equation in standard Form. show your work for. The line contains the points (3.0) and (4,6)
Answer:
y=6x-18
Step-by-step explanation:
To find the standard equation of a linear relationship given two points, you need to find the slope and y intercept.
slope is change in y divided by change in x.
(6-0)/(4-3)
(6)/(1)
The slope of the line is 6.
We can plug this in along with x and y values from a given coordinate into the standard equation format to solve for b, the y intercept.
y=mx+b
y=0
x=3
m=6
0=6(3)+b
0=18+b
b=-18
now we know that the y intercept is (0,-18). The standard equation would be y=6x-18
a circle has a circumference of 6. it has an arc of length 1/3
What is the central angle of the arc in degrees
Answer:
Ф = 10°
Step-by-step explanation:
Regarding arc length, s: s = r·Ф, where Ф is the central angle in radians and r is the radius.
We need to find the central angle, Ф, in this problem.
We know that C = circumference = 6, and that this leads to r = 6/π.
Substituting 6/π for r and 1/3 for s in Ф = s / r, we get:
Ф in radians = 1/3 / (6/π), or Ф = π/18 rad.
π 180°
Converting this into degrees, we multiply ------ by ----------
18 π rad
obtaining: Ф = 10°
Answer:
20
Step-by-step explanation:
A talk driver charges $3.50 per mile driver gives a 10mile ride a 5.5 mile ride and a 19 mile ride.he then spends $50 to fill up the gas tank before giving a final ride of 26 miles write a numeric expression to represent the dollar in amounts the driver had after each action in order.then find out how much money he had after the last ride if he started with $0
Answer:
3.50×10 +3.50×5.5 +3.50×19 -50 +3.50×26$161.75Step-by-step explanation:
You want an expression representing the cash flow of a taxi driver after giving three rides, filling the gas tank, then giving one more ride.
Income per rideAt $3.50 per mile, the driver will have income that is $3.50 multiplied by the number of miles for the ride. These income amounts are added.
OutflowA payment of $50 for gas is subtracted from the driver's income.
Net incomeThe desired expression is ...
3.50×10 +3.50×5.5 +3.50×19 -50 +3.50×26
The value of the expression is $161.75.
The driver had $161.75 after the last ride.
22n=418
what is the vaule of n.
Answer:
n = 19
Step-by-step explanation:
22n = 418
Divide both sides by 22.
n = 19
What is the probability that the student attended the jazz concert given that student is a junior
Answer: C. 0.60
Step-by-step explanation:
From the given table , the number of students are junior : 60
The total number of students = 137
The probability of selecting any junior is given by :-
[tex]\text{P(Junior)}=\dfrac{60}{137}[/tex]
The number of juniors which who attended Jazz = 36
Then , the probability of selecting a students is junior and attends jazz is given by :-
[tex]\text{P(Junior and Jazz)}=\dfrac{36}{137}[/tex]
Now, the conditional probability that the student attended the jazz concert given that student is a junior will be :-
[tex]\text{P(Jazz}|\text{Junior)}=\dfrac{\dfrac{36}{137}}{\dfrac{60}{137}}\\\\\\=\dfrac{6}{10}=0.60[/tex]
Answer: it’s 0.60
(I just took it)
At a local company, the ages of all new employees hired during the last 10 years are normally distributed. The mean age is 35 years old, with a standard deviation of 10 years.
If you were to take a sampling of 10 employees, what is the probability your mean age will be at least 37? Round to the nearest percent.
Answer:
The probability your mean age will be at least 37 is approximately 26%
Step-by-step explanation:
Let X denote the ages of all new employees hired during the last 10 years , then X is normally distributed with;
a mean of 35
a standard deviation of 10.
The sample size obtained is 10 employees. This implies that the sampling distribution of the sample mean will be normal with;
a mean of 35
a standard deviation of [tex]\sqrt{10}[/tex]
The sample mean is a statistic and thus has its own distribution. Its mean is equal to the population mean, 35 and its standard deviation is equal to [tex]\frac{sigma}{\sqrt{n} }[/tex]
where sigma is the population standard deviation, 10 and n the sample size which in this case is 10. [tex]\frac{10}{\sqrt{10} }=\sqrt{10}[/tex]
We are required to find the probability that this sample mean age will be at least 37;
P(sample mean ≥ 37)
Since we know the distribution of the sample mean we simply standardize it to obtain the z-score associated with it;
P(sample mean ≥ 37)
=[tex]P(Z\geq \frac{37-35}{\sqrt{10} })=P(Z\geq0.6325)=1-P(Z<0.6325)[/tex]
=1 - 0.7365 = 0.2635
=26%
Please help and thank you
Answer:
(3, 2)
Step-by-step explanation:
Given a graphical representation of a system of equation then the solution is at the point of intersection of the 2 lines, that is
solution is ( 3, 2)
The line plot shows amount of miles students ran in a week. What is the difference in the lowest miles and the highest miles run in a week? A) 1 1/2 B) 1 1/4 C) 1 3/4 D) 3/4
Answer:
C
Step-by-step explanation:
There are 4 lines in between 2 consecutive integers, so each division is:
1/4 = 0.25
As we see from the graph, the highest miles is at the division before 2, which is 1.75
Also, the lowest miles is at 0.
Hence, difference in highest and lowest is 1.75 - 0 = 1.75
In fraction, [tex]1.75=1\frac{3}{4}[/tex]
correct answer C
Which reason for step 4 completes the proof?
Prove: -(a + b) + a = -b
Answer:
Identity Property of Addition.
Answer:
Reason which completes the proof of step 4 is:
Identity property of addition
Step-by-step explanation:
-(a+b)+a= -b
= -a+ (-b)+a (distributive property)
= -a+a+(-b) (Commutative property of Addition)
= 0+ (-b) (Additive inverse property)
= -b (Identity property of addition)
(Identity property of addition says that if 0 is the identity element and a is any element
Then, a+0=0+a=a)
So, reason which completes the proof of step 4 is:
Identity property of addition
Iteration question 6 please help
Answer:
option A
1 , 1 , 1 , 1
Step-by-step explanation:
Given in the question a function
f(x) = x²
initial value[tex]x_{0}[/tex] = -1
First iteration
f(-1) = (-1)²= 1
[tex]x_{1} =1[/tex]
Second iteration
f(1) = (1)² = 1
[tex]x_{2} =1[/tex]
Third iteration
f(1) = (1)² = 1
[tex]x_{3} =1[/tex]
Fourth iteration
f(1) = (1)² = 1
[tex]x_{4} =1[/tex]
What is formula for following geometric sequence -5,-10,-20,-40
Answer:
x = -5 * (2)^(n-1)
Step-by-step explanation:
If we look a the supplied n elements of the sequence, and we divide each of them by -5.
1 = -5, -5/-5 = 1
2 = -10, -10/-5 = 2
3 = -20, -20/-5 = 4
4 = -40, -40/-5 = 8
We realize that we have all the powers of 2 there.
So the formula will start with -5 (the first element), then multiplied by a power of 2.
[tex]x = -5 (2)^{n-1}[/tex]
We can verify for the 4th element, where n = 4:
[tex]x = -5 (2)^{n-1} = -5 (2)^{4-1} = -5 (2)^{3} = -5 * 8 = -40[/tex]
Answer:
x = -5 * (2)^(n-1)
Step-by-step explanation:
ebony wants to buy a dvd player and dvds the equation relates the total cost for dvds and dvd player and N dvds is p=20n+200 what does the number 200 in the equation represent
____________________________________________________
Answer:
It represents the cost of the DVD player.
____________________________________________________
Step-by-step explanation:
The reason why it represents the cost of the DVD player is because in the question, it doesn't mention anything about buying multiple DVD players. Ebony would need to buy many DVD's, but doesn't need many DVD players because ebony could use one for all of the DVD's. If you noticed in the question, it says "a DVD player," what this means is that Ebony is only going to buy one DVD player, since it's singular (without and s at the end).
The equation is saying that she starts off with buying 1 DVD player for 200 dollars; and, she is buying n (number of DVDs) for 20 dollars each.
This shows that the 200 in the equation in the question represents the cost of the DVD player.
____________________________________________________
Write an equation for the line parallel to the given line that contains C.
Cleft parenthesis 3 comma 6 right parenthesis; y equals negative 4 x plus 5
ANSWER
[tex]y= - 4x + 18[/tex]
EXPLANATION
The given line has equation;
[tex]y = - 4x + 5[/tex]
The slope of this line is
-4
The given line is parallel to this line so it has the same slope:
[tex]m = - 4[/tex]
The equation of this line is in the form:
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the slope and the point:
(3,6)
[tex]y-6= - 4(x-3)[/tex]
[tex]y= - 4x + 12+ 6[/tex]
[tex]y= - 4x + 18[/tex]
If x = 5 cm, y = 12 cm, and z = 13 cm, what is the surface area of the geometric shape formed by this net?
A. 82 sq. cm
B. 270 sq. cm
C. 210 sq. cm
D. 320 sq. cm
Answer:
the answer is C. 210 sq. cm
Step-by-step explanation:
Find the area of the triangle
The area of one of the triangular faces can be found by using the formula below.
a = 1/2 bh
a = 1/2 (5 cm) (12 cm)
a = 30 sq. cm
Since there are two triangular faces, multiply the area of one triangular face by 2. The area of two triangular faces is 60 cm2.
Next, find the area of each of the three rectangular faces using the formula, area = lw.
1st rectangle
a = lw
a = (5 cm) (5 cm)
a = 25 sq. cm
2nd rectangle
a = lw
a = (5 cm) (12 cm)
a = 60 sq. cm
3rd rectangle
a = lw
a = (5 cm) (13 cm)
a - 65 sq. cm
Add the three rectangle areas to find a total of 150 sq. cm.
To find the surface area of the triangular prism, add the area of the two triangular faces to the area of the three rectangular faces.
60 sq. cm + 150 sq. cm = 210 sq. cm
Team one had 4 times less people than team two. After 6 people quit team two and 12 people were transferred from team two to team one, both teams became equal. How many people were there in team one?
please help me
Answer:
There were 10 people in team one.
Step-by-step explanation:
Let x= team one.
Let y= team two
Because there four times less people in team one than in two we know that x=(1/4)y
After 6 people quit and 12 people transfer from team two, the two teams become equal. Therefore, x + 12 = y - 6 - 12.
You can then insert the initial equation for x into the second equation and know that there were 10 people in team one and 40 people in team two.
The process to solve this problem involves setting up an equation based on the given information and solving for x, which represents the original number of people on team one. The numerical answer is 10 people.
Explanation:Let's denote the original number of people in team one as 'x'. Therefore, since team two had 4 times more people than team one, team two originally had '4x' people. The problem then tells us that 12 people were transferred from team two to team one and 6 people quit team two. This means that team two now has '4x - 12 - 6' people and team one has 'x + 12' people. Because both teams are equal in size after these changes, we can set these two expressions equal to each other. So, 'x + 12' is equal to '4x - 18'. Solving this equation for 'x' gives us x = 10.
So originally, team one had 10 people.
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Divide $414 into three parts such that first one is two-third of the second and the ratio between second and third is 5 : 7.
Answer:
$90, $135, $189
Step-by-step explanation:
Since the first part of the ratio is two- thirds of the second, then
first part = [tex]\frac{2}{3}[/tex] × 5 = [tex]\frac{10}{3}[/tex]
The ratio is then
[tex]\frac{10}{3}[/tex] : 5 : 7
Sum the 3 parts of the ratio
[tex]\frac{10}{3}[/tex] + 5 + 7 = [tex]\frac{46}{3}[/tex]
Divide the amount to be shared by the sum to find the value of one part of the ratio.
$414 × [tex]\frac{3}{46}[/tex] = $27 ← value of 1 part of the ratio, then
[tex]\frac{10}{3}[/tex] × $27 = $90
5 × $27 = $135
7 × $27 = $189
The 3 parts are $90, $135, $189
Write all the factors of 35
.
Use commas to separate them.
Factors of 35 :
1, 5, 7, 35
Answer:
1,5
Step-by-step explanation:
Need correct answer ASAP please
Answer:
C = 16pi
Step-by-step explanation:
Since we are evaluating for the circumference, we plug in the r. Since r=8, we get 2*pi*8 or 16pi.
answer should be C gl btw
express with positive exponents
Answer:
2b^2
--------------
5a^4
Step-by-step explanation:
2a^-4
-------------
5b^-2
Negative exponents go to the denominator when they are in the numerator
and to the numerator when they are in the denominator
a^-4 becomes 1/a^4
1/b^-2 becomes b^2
2/5 * 1/a^4 * b^2
2*b^2 * 1/5a^4
Rewriting
2b^2
--------------
5a^4
determine where f(x) = g(x) by graphing HELP PLEASE!!
Answer:
C: x=-4
Step-by-step explanation:
I would suggest using the website desmos.com to help you graph your equations.
As shown on the graph I posted, f(x)=g(x) at x=-4
Answer:
Step-by-step explanation:
Given are two functions f(x) and g(x)
[tex]f(x) = \frac{2}{x+3} +1\\[/tex]
and
[tex]g(x) = -|x+3|[/tex]
The two would be equal if
[tex]\frac{2}{x+3} +1=x+3 or -x-3\\\frac{2}{x+3} =x+2 /-x-4\\2=x^2+5x+6/-(x^2+7x+12)\\x^2+5x+6=0 / x^2+7x+14=0[/tex]
x=-4 or -1
Of these x=-4 is consistent as when x=-4, x<-3 hence
|x+3|= 1
So answer is -4
Help please with these problems
the box is considered a prism
any prism the formula for volume is V=area of the base times height so
the first two boxes have the base of 16 plus the height of 3
so 16*3=48
48*2=96
the other box has the height of 5 so
16*5=80
in total they want the volume of all boxes so
96+80=176
answers B:)
if you need to elaborate lmk
Answer:
(B) 176 ft³
Step-by-step explanation:
Volume of the first box with 3 feet:
= 16 x 3
= 48 ft³
Volume of the second box with 3 feet:
= 16 x 3
= 48 ft³
Volume of the third box with 5 feet:
= 16 x 5
= 80 ft³
Total volume
= 48 + 48 + 80
= 176 ft³
Choose the solution(s) of the following system of equations:
x2 + y2 = 6
x2 – y = 6
I think this is the answer X = 3 + 1/2y
The solutions for the system of equations are:
[tex]\[ (x, y) = (\sqrt{6}, 0), (-\sqrt{6}, 0), (\sqrt{5}, -1), (-\sqrt{5}, -1) \][/tex]
To solve the system of equations[tex]\(x^2 + y^2 = 6\)[/tex] and [tex]\(x^2 - y = 6\)[/tex], we can use substitution or elimination method. Let's solve it using the substitution method:
Given equations:
1.[tex]\(x^2 + y^2 = 6\)[/tex]
2.[tex]\(x^2 - y = 6\)[/tex]
From equation 2, we can express [tex]\(x^2\) as \(y + 6\):[/tex]
[tex]\[x^2 = y + 6\][/tex]
Now, substitute [tex]\(x^2 = y + 6\)[/tex] into equation 1:
[tex]\[y + 6 + y^2 = 6\][/tex]
Rearrange this equation:
[tex]\[y^2 + y + 6 = 6\][/tex]
Subtract 6 from both sides:
\[y^2 + y = 0\][tex]\[y^2 + y + 6 = 6\][/tex]
Factor out y:
[tex]\[y(y + 1) = 0\][/tex]
So, either [tex]\(y = 0\)[/tex] or [tex]\(y + 1 = 0\)[/tex] , which means[tex]\(y = 0\)[/tex] or [tex]\(y = -1\).[/tex]
Now, substitute these values of y back into equation 2 to find the corresponding values of x.
For [tex]\(y = 0\):[/tex]
[tex]\[x^2 - 0 = 6\][/tex]
[tex]\[x^2 = 6\][/tex]
[tex]\[x = \pm \sqrt{6}\][/tex]
For [tex]\(y = -1\):[/tex]
[tex]\[x^2 - (-1) = 6\][/tex]
[tex]\[x^2 + 1 = 6\][/tex]
[tex]\[x^2 = 5\][/tex]
[tex]\[x^2 = 5\][/tex]
So, the solutions for the system of equations are:
[tex]\[ (x, y) = (\sqrt{6}, 0), (-\sqrt{6}, 0), (\sqrt{5}, -1), (-\sqrt{5}, -1) \][/tex]
The system has four solutions: [tex]\((\sqrt{6}, 0)\), \((- \sqrt{6}, 0)\), \((\sqrt{5}, -1)\), and \((- \sqrt{5}, -1)\).[/tex]
Complete question:
Choose the solution(s) of the following system of equations:
x2 + y2 = 6
x2 – y = 6
Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation , where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is $2.85, what is the approximate price of a pint of veggies? (Round to the nearest cent.)
$1.75
$2.06
$2.39
$3.99
Answer: First Option
The approximate price of a pint of veggies is $1.75
Step-by-step explanation:
if v represents the cost of a pint of cut vegetables and f represents the cost of a pint of cut fruits then the equation that models the cost of "v" vegetables and "f" fruits is:
[tex]hv + 2.85f = z[/tex]
Where z represents the total cost of buying "v" vegetables and a "f" pints of fruits.
h represents the cost of a pint of cut vegetables .
We know that the cost "z" of 5 vegetables pints and 7 fruits pints is $ 28.70
So:
[tex]v = 5\\f = 7\\z = 28.70[/tex]
We substitute these values into the equation and solve for h.
[tex]h(5) + 2.85(7) = 28.70\\\\5h=28.70-2.85(7)\\\\5h=28.70-19.95\\\\5h=28.70-19.95\\\\h=\frac{8.75}{5}\\\\h=\$\ 1.75[/tex]
HELP ASAP PLEASEE!!!!
Answer:
In the TRUE column:
- 0.65 pound of almonds costs $2.20
- the price per pound of almonds equals $2.20/0.65
That's basically the same information, presented 2 different ways, and they match the info presented in the graph.
In the FALSE column:
- 2.2 pounds of almonds cost $0.65 (nope, wrong numbers)
- Almonds cost $0.65 per pound (nope, they cost $3.38 per pound)
In the CANNOT BE DETERMINED column:
- Each bag of almonds weighs 2.2 pounds. (Cannot be verified, but it's highly unlikely since the price point on the graph is at 0.65 pounds)