Considering the expression of a line, the equation of the line that passes through the pair of points (-66) and (3,-2) is 8/9x +y= 2/3.
Linear equation
A linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression y = mx + b, the value of the ordinate to the origin b can be obtained.
The standard form of the line is Ax +By= C
Equation in this case
In this case, being (x₁, y₁)= (-6, 6) and (x₂, y₂)= (3, -2), the slope can be calculated as:
m= (-2 - 6)÷ (3 - (-6))
m= (-2 - 6)÷ (3 + 6)
m= (-8)÷ 9
m= -8/9
Considering point 2 and the slope, you obtain:
-2= (-8/9)×3 + b
-2= -8/3 + b
-2 +8/3= b
2/3= b
The equation of the line is y= -8/9x +2/3.
Finally, the standard form of the line is 8/9x +y= 2/3
If leo is 6 years old and max is 12 years, how many years would it be until max is 3 times as old as leo
Answer:
Step-by-step explanation: max is already 3 times older than max. 6*3=18 and 6+12=18
Final answer:
Max cannot be 3 times as old as Leo based on the given information.
Explanation:
To find out how many years it will be until Max is 3 times as old as Leo, we can set up an equation.
Let's assume that it takes x years for Max to be 3 times as old as Leo.
So, Max's age in x years will be 12 + x, and Leo's age in x years will be 6 + x. According to the problem, Max will be 3 times as old as Leo, so we can write the equation as: 12 + x = 3(6 + x).
To solve for x, we can start by simplifying the equation: 12 + x = 18 + 3x. Now, let's isolate the variable x by moving all the x terms to one side and the constant terms to the other side. Subtracting x from both sides gives us: 12 = 18 + 2x. Subtracting 18 from both sides gives us: -6 = 2x. Finally, dividing both sides by 2 gives us: -3 = x.
This means that it will take -3 years for Max to be 3 times as old as Leo. However, since time cannot be negative, we can conclude that it is not possible for Max to be 3 times as old as Leo based on the given information.
Work out the area of the lawn.
Answer:
68 m^2
Step-by-step explanation:
Area of The entire enclosure ( rectangle)
Area rectangle = L * WL = 7 + 7 = 14W = 10 Area rectangle = 10*(7 + 7)Area of rectangle = 10 * 14Area of rectangle = 140 square meters.Area of the triangle
Area of the triangle = 1/2 b*hArea of the triangle = 1/2 * 8 * 3Area of the triangle= 12 square meters.Area of the Trapezoid
h = 10b1 = 5b2 = 7Formula
Area = (b1 + b2)*h /2Solution
Area = (5 + 7)*10/2Area = 12*10/2Area = 60Area of the Lawn
Area of the Lawn = rectangle area - triangle area - trapezoid areaArea of the lawn = 140 - 12 - 60Area of the lawn = 68 m^2The point located (3,-1) is reflected across the y-axis.What are the coordinates of the reflected point?
Answer:
(3,1)
Step-by-step explanation
All you have to do is change the y-coordinate to its opposite. Ex- (-2,3) coordinates of reflection. (-2,-3)
What is the solution set of the equation j+4/j+2=2−1/j ? Note: j≠0, −2
Answer:
values of j are: 2 , -1
Step-by-step explanation:
In the given case, The solutions are j = -4 and j = 1, and the solution set is {-4, 1}.
The given equation is:
j+4/j+2=2−1/j
We can solve for j by cross-multiplying:
(j+4)(j) = (j+2)(2-1/j)
Expanding the left side and right side, we get:
[tex]j^2 + 4j = 2j + 4 - 2/j[/tex]
Moving all the terms to the left side of the equation, we get:
[tex]j^2 + 2j - 4 = 0[/tex]
We can factor the left side of the equation as:
(j+4)(j-1) = 0
Therefore, the solutions are j = -4 and j = 1.
Note that the given equation is defined when j ≠ 0 and j ≠ -2. Therefore, the solutions are j = -4 and j = 1, and the solution set is {-4, 1}.
Here is a step-by-step solution:
n first move the constant term to the right side of the equation.
j² + 2j = 4
We can then factor the left side of the equation.
(j+4)(j-1) = 0
The solutions are j = -4 and j = 1.
We check that these solutions are valid by substituting them back into the original equation.
j+4/j+2=2−1/j
When j = -4, the left side of the equation is 0/-2 = 0, and the right side of the equation is 2 - 1/-4 = 2 + 0.5 = 2.5.
The equation is satisfied.
When j = 1, the left side of the equation is 5/3, and the right side of the equation is 2 - 1/1 = 2 - 1 = 1. The equation is satisfied.
Therefore, the solutions are j = -4 and j = 1, and the solution set is {-4, 1}.
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The movie theater sold 56 boxes of gummy bears during the week.At this rate how many boxes of gummy bears will the movie theater sell in a 6 week period
Answer:
Step-by-step explanation:
At a sales rate of 56 boxes of gummy bears per week, the movie theater will sell
= 56 × 6
= 336 boxes
This is on the assumption that the rate is sustained.
At that rate (of 56 boxes per week), the company (movie theater) would have sold 336 boxes.
The diameter at the center of the tower is_ meters. The center of the tower is _meters above the ground
Answer:
think 5 meters
Step-by-step explanation:
Answer:
The diameter at the center of the tower is 4 meters. The center of the tower is 8 meters above the ground.
Step-by-step explanation:
4x^2-y^2+16y-80=0
Completing squares in variable "y": Common factor -1:
4x^2-(y^2-16y)-80=0
4x^2-[(y-16/2)^2-(16/2)^2]-80=0
4x^2-[(y-8)^2-(8)^2]-80=0
4x^2-[(y-8)^2-64]-80=0
Eliminating the brackets:
4x^2-(y-8)^2+64-80=0
Adding like terms (constants):
4x^2-(y-8)^2-16=0
Adding 16 both sides of the equation:
4x^2-(y-8)^2-16+16=0+16
4x^2-(y-8)^2=16
Dividing all the terms by 16:
4x^2/16-(y-8)^2/16=16/16
Simplifying:
x^2/4-(y-8)^2/16=1
The hyperbola has the form:
(x-h)^2/a^2-(y-k)^2/b^2=1
Then:
h=0
k=8
a^2=4→sqrt(a^2)=sqrt(4)→a=2
The diameter (d) at the center of the tower is:
d=2a→d=2(2)→d=4 meters
The center of the tower is 8 (k) meters above the ground.
IN AN ATHLETIC EVENT 60 STUDENTS OF A SCHOOL PARTICIPATED LAST YEAR . THIS YEARTHE NUMBER OF STUDENTS OF THAT SCHOOLK TAKING PART IS DECREASED BY 5 % . FIND THE NUMBER OF STUDENTS TAKING PART IN THE ATHLETIC EVENT THIS YEAR
Answer: the number of students participating this year is 57.
Step-by-step explanation:
5% of 60 is 3.
60-3=57
I believe this is correct :)
Answer: Number of students participated this year = 57
Step-by-step explanation: Number of student participated last year = 60
Decreased by 5%
Decreased in number = 5% of 60 = 0.05x 60 =3
Number of Students this year = Number of student last year - decreased
= 60 - 3
= 57
You invest $1,000 in an account at 2.5% per year simple interest. How much will you have in the account after 4 years? Round your answer to the nearest whole dollar
Answer:
1000*(1,025)=1025 $ the 1st year
After 4 years, the account will be 4* 1025=4100
Answer:
Amount after 4 years = 1000+100=$1100
Step-by-step explanation:
To solve this, we will simply use the simple interest formula;
S.I = PRT/100
where p=principal
R=rate and T= time
S.I = simple interest
From the question
Principal=$1000
Rate = 2.5 and time=4
We can now proceed to inert the values into the equation
S.I = 1000×2.5×4 /100
Two zeros at the numerator will cancel-out the two zeros at the denominator, Hence;
S.I = 10×2.5×4
S.I =$100
Amount after 4 years = 1000+100=$1100
guys please answer me soon with an easy explanation
the diagonal of a rectangle is 20 metre and its parameter is 50 metre then what are its dimensions?
Answer:
Length 19.11 and width 5.89.
Step-by-step explanation:
Let the length be x and width be y metres.
Then, using the Pythagoras theorem:-
x^2 + y^2 = 20^2 = 400....................(1)
The perimeter = 50 so:-
2x + 2y = 50
Dividing through by 2:-
x + y = 25 .............................(2)
So y = 25 - x
Substitute for y in equation (1):-
x^2 + (25 - x)^2 = 400
x^2 + 625 - 50x + x^2 = 400
2x^2 - 50x + 225 = 0
x = 19.11 , 5.89, x = 19.11 as its the length
and y = 25 - 19.11 = 5.89 ( from equation (2).
"Parameter" = Perimeter.
Look at the picture.
We have the perimeter = 50 m.
The perimeter is 2l + 2w (l - length, w - width). Therefore
2l + 2w = 50 divide both sides by 2
l + w = 25 subtract w from both sides
l = 25 - w.
Use the Pythagorean theorem:
[tex]l^2+w^2=20^2\to(25-w)^2+w^2=20^2[/tex]
Use (a - b)² = a² - 2ab + b²
[tex]25^2-2(25)(w)+w^2+w^2=400\\\\625-50w+2w^2=400\qquad\text{subtract 400 from both sides}\\\\225-50w+2w^2=0\\\\2w^2-50w+225=0[/tex]
Use quadratic formula:
[tex]ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a};\ x_2=\dfrac{-b+\sqrt\Delta}{2a}[/tex]
We have:
[tex]a=2,\ b=-50,\ c=225[/tex]
Substitute:
[tex]\Delta=(-50)^2-4(2)(225)=2500-1000=1500\\\\\sqrt\Delta=\sqrt{1500}=\sqrt{100\cdot15}=\sqrt{100}\cdot\sqrt{15}=10\sqrt{15}\\\\w_1=\dfrac{-(-50)-10\sqrt{15}}{2(2)}=\dfrac{50-10\sqrt{15}}{4}=\dfrac{25-5\sqrt{15}}{2}\\\\w_2=\dfrac{-(-50)+10\sqrt{15}}{2(2)}=\dfrac{50+10\sqrt{15}}{4}=\dfrac{25+5\sqrt{15}}{2}[/tex]
[tex]l_1=25-w_1\\\\l_1=25-\dfrac{25-5\sqrt{15}}{2}=\dfrac{50}{2}-\dfrac{25-5\sqrt{15}}{2}=\dfrac{50-25+5\sqrt{15}}{2}=\dfrac{25+5\sqrt{15}}{2}\\\\l_2=25-w_2\\\\l_2=25-\dfrac{25+5\sqrt{15}}{2}=\dfrac{50}{2}-\dfrac{25+5\sqrt{15}}{2}=\dfrac{50-25-5\sqrt{15}}{2}=\dfrac{25-5\sqrt{15}}{2}[/tex]
[tex]Answer:\ \boxed{\dfrac{25+5\sqrt{15}}{2}\ m\times\dfrac{25-5\sqrt{15}}{2}\ m}[/tex]
Consider parallelogram ABCD. Choose all of the statements which MUST be true.
∠ADB ≅ ∠CBD
ADC + DCB = 180
∠CED ≅ ∠DEA
AE = EC AC = DB
Answer:
The first one is correct the rest are not
Step-by-step explanation:
I don't know if you need an explanation or not.
Answer:
it 1,2,and 4 just took it
Step-by-step explanation:
Identify the equation in point-slope form for the perpendicular bisector of the segment with endpoints B(−1,1) and C(−5,−7). PLEASE HELP!!!
Answer:
Equation in point-slope form= [tex]{y+3}=\frac{-1}{2}(x+3)[/tex]
Step-by-step explanation:
The given end points are B(−1,1) and C(−5,−7)
Mid point M of BC= [tex]\frac{-5-1}{2}[/tex] , [tex]\frac{-7+1}{2}[/tex]
Mid point M of BC = -3 , -3
Slope of BC = [tex]\frac{-7-1}{-5+1}[/tex] = 2
Slope of bisector= m= [tex]\frac{-1}{2}[/tex]
Equation of perpendicular bisector : [tex]\frac{y+3}{x+3}=\frac{-1}{2}[/tex]
⇒ [tex]{y+3}=\frac{-1}{2}(x+3)[/tex]
⇒ 2(y+3)= -(x+3)
⇒ [tex]2y+x=-9[/tex]
What is the solution to 4+5e^(x+2)=11?
(Answers Below)
Answer:
x = ln (7/5) - 2
Step-by-step explanation:
4+5e^(x+2)=11
Subtract 4 from each side
4-4+5e^(x+2)=11-4
5e^(x+2)=7
Divide by 5 on each side
5/5e^(x+2)=7/5
e^(x+2)=7/5
Take the natural log on each side
ln (e^(x+2))= ln (7/5)
x+2 = ln (7/5)
Subtract 2 from each side
x = ln (7/5) - 2
Answer:
option 1
Step-by-step explanation:
A geometric sequence is shown below.
2, – 6, 18, – 54, 162, ...
Part A:
Write a recursive relationship for this sequence. Explain how you determined your answer.
Part B:
Write an explicit formula for this sequence.
Which of the following best represents the relationship between angles A and B?
A = B
A = 180 degrees − B
B = 180 degrees − A
A = 2B
Answer:
A = B
Step-by-step explanation:
This is because they are alternate exterior angles and they equal the same thing.
Which input value produces the same output value for the two functions on the graph?
X= -3
X= -1
X= 1
X= 3
Answer:
D. [tex]x=3[/tex]
Step-by-step explanation:
We have been graph of two functions on coordinate plane. We are asked to find the input value that produces the same output value for the two functions.
To find the input value that produces the same output value for the two functions, we need to find x-value for which both functions has same y-value.
Upon looking at our given graph, we can see that at [tex]x=3[/tex], the value of both functions is [tex]-1[/tex].
Therefore, our required input value is [tex]x=3[/tex] and option D is the correct choice.
if 3y - 7= 23, then y =
Answer:
y=10 is the value of y
Step-by-step explanation:
The given equation is
3y - 7 =23 ..............................(i)
We have to find out the value of y from the equation (i)
Now the equation is
3y - 7 = 23
adding 7 on both sides of the equation
3y - 7 + 7 = 23 + 7
3y = 30
as we need the value of y so
Dividing both sides of the equation by 3
[tex]\frac{3y}{3}=\frac{30}{3}[/tex]
which will lead us to
y = 10
so this is the value of y
Answer:
y=10
Step-by-step explanation:
3y-7 =23
3y = 23+7 -move 7 over
3y=30 -add remaing
3y/3 =30/3 -divide 3
y=10 -answer
check work 3x10-7=23
Solve for x 15x+5x 14x-6
Look at the picture.
[tex\alpha+\beta=180^o[/tex] - supplementary angles
Therefore we hve the equation:
[tex](14x-6)+(15+5x)=180\\\\(14x+5x)+(-6+15)=180\\\\19x+9=180\qquad\text{subtract 9 from both sides}\\\\19x=171\qquad\text{divide both sides by 19}\\\\\boxed{x=9}[/tex]
Please help & explain 4th grade math
Answer:2/9
Step-by-step explanation:
If you count the lines form zero like 0/9 1/9 2/9 3/9 4/9 5/9 6/9 7/9 8/9 then 1 is the whole so that would be 9/9
Answer:
2/9 is the answer
what is the perimeter of triangle with side lengths of 29, 15, and 4xy?
The perimeter of any polygon is equal to the sum of the length of all sides of this polygon.
Therefore:
P = 29 + 15 + 4xy = 44 + 4xyAnswer:
The perimeter of a triangle is defined as the sum of all three sides.So, we know that sides are 29, 15 and 4xy long. The perimeter would be
[tex]P=29+15+4xy[/tex]
Now, we sum like terms
[tex]P=44+4xy[/tex]
Therefore, the perimeter of the triangle is[tex]P=44+4xy[/tex]
To arrive to his appointment on time, Mr. Jones had to drive all the way from his home with the average speed of 60 mph. Due to heavy traffic, he was driving 15 mph slower than he planned and arrived to the appointment 20 minutes later. How many miles from Mr. Jones' home was his appointment?
Answer:
60
Step-by-step explanation:
Mr Jone's home distance is 60 miles away from his appointment place .
Distance = Speed x Time
Distance planned & distance covered is same.
Time covered is 20 minutes more than time planned ; Actual Speed is 15mph lower than planned speed (60 mph) , ie = 45 mph.
Let the planned time be = t , Actual time = t + 20 mints = t + 20 / 60 = t + 1/3 = 4 t / 3
As distance is same : 60 t = 45 ( 4t / 3)
60t = 60t
t = 1 hour
Distance = Speed x Time :
60 x 1 = 45 ( 4/3) = 60 miles
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If the mass of a material is 45 grams and the volume of the material is 11 cm^3, what would the density of the material be?
I need the answer and than units
Answer:
Density of material would be 4.09 [tex]g/cm^3[/tex]
units is [tex]g/cm^3[/tex]
Step-by-step explanation:
Given: The mass of a material is 45 grams and the volume of the material is 11 cubic centimeter
Density is defined as mass per unit volume.
It is given by:
[tex]p= \frac{m}{V}[/tex] where p is the density , m is the mass and V is the volume of the material respectively.
Here, Density is expressed in grams per centimeter cubed (g/cubic cm)
Here, m = 45 g , V = 11 cubic cm
We get;
[tex]p= \frac{45}{11}[/tex] = 4.09 [tex]g/cm^3[/tex]
therefore, density of a material would be, [tex]4.09 g/cm^3[/tex]
and its units is [tex]g/cm^3[/tex]
for what values of k does kx^(2)-3x+2=0 have two equal real roots?
Tienes que usar la fórmula cuadrática:
(-b +/- √(b^2-4ac))/2a
Primero identificas los valores de a,b y c en kx^2-3x+2=0
K=a, b=-3, c=2
Luego sustituis en la fórmula y te queda:
(3+/-√(9-8k))/2k
Para que las raíces Sena reales se tienen que cumplir que 9-8k>=0
Answer:
Step-by-step explanation:
Therefore discriminant = b^2-4ac =0
b=-k, a=3,c=2
b^2-4ac= (-k)^2-4*3*2=0
k^2-24=0
k^2=24
k= +/- 2sqrt(6)
In an effort to control vegetation overgrowth, 139 139 rabbits are released in an isolated area free of predators. After 2 2 years, it is estimated that the rabbit population has increased to 556 556 . Assuming exponential population growth, what will the population be after another 6 6 months? Round to the nearest rabbit.
Answer:
197
Step-by-step explanation:
Initial population of rabbit is 139
after 2 years , rabbit population is 556
For exponential growth use y=ab^x
where a is the initial population
x is the time period
b is the growth rate, y is the final population
a= 139 is already given
when x=2, the value of y = 557
plug in all the values in the formula and find out 'b'
[tex]y=ab^x[/tex]
[tex]557=139(b)^2[/tex]
Divide both sides by 139
[tex]\frac{557}{139} =b^2[/tex]
take square root on both sides
b=2.00180 and b=-2.00180
growth factor cannot be negative
So b= 2.0018
The equation y=ab^x becomes
[tex]y=139(2.0018)^x[/tex]
To find population after 6 months
1 year = 12 months
so 6 months = 0.5 years
we plug in 0.5 for x
[tex]y=139(2.0018)^{0.5}[/tex]
y= 196.66
so population after 6 months = 197
NEED HELP!! 30 POINTS! HAS TO BE CORRECT AND NEED THE ANSWER NOOW!
Answer: options b and c
Step-by-step explanation:
∠ACD is supplementary to ∠ACE given
∠ACD is supplementary to ∠BCD given
⇒ ∠ACE is supplementary to ∠BCD transitive property
∠ACD ≅ ∠BCE given
⇒ ∠BCE is supplementary to ∠ACE substitution
and ∠BCE is supplementary to ∠BCD substitution
********************************************************************************
multiple choice options:
a) ∠ACE is supplementary to ∠BCD False
b) ∠BCE is supplementary to ∠ACE TRUE
c) ∠BCD is supplementary to ∠BCE TRUE
d) ∠ACE ≅ ∠BCE False
e) ∠BCD ≅ ∠ACE False
What is the solution to this system of equations?
Answer: No solutions
The two lines are parallel. They never intersect. You need a point of intersection to have a solution. Note how the lines have the same slope (2) but different y intercepts (3 and -4). This fact backs up the idea the lines are parallel.
The system has no solution, so we consider this system to be inconsistent. If we were to convert each equation into standard form, then we would have 2x-y = -3 and 2x-y = 4. If we made z = 2x-y, then z = -3 and z = 4 at the same time; but z is only one number at a time. This is one way to see the inconsistency.
Given that AD and BC bisect each other at E, which of the following justifies ΔABE ≅ ΔDCE? A. Definition of Segment Bisector B. SSS Postulate C. Definition of Congruent Triangles D. SAS Postulate
Answer:
A. Definition of Segment Bisector
Step-by-step explanation:
One have to understand that according to data given in the question, we only know that AD and BC are bisected at the intersection point E. Now two triangles are formed which are ΔABE and ΔCDE.
Now by definition of segment bisector, we know that
AE = DE
BE = CE
Now, what is to understand that this information is based on the clue which is given in the question that AD and BC bisects each other. All the remaining options like SAS postulate, SSS postulate and definition of congruent triangle are not useful here if we don't know that these two lines bisect each other. Because, the fact that
AE = DE
BE = CE
is only derived by the information that AD and BC bisect each other. Now we can derive SSS and SAS postulate both because we know by the theorems of trigonometry that if two sides of two different triangles are equal in length, then their third sides must be equal, or when two lines bisect or intersect each other, vertical angles are always equal. So the answer is A.
Evaluate the infinite sum
The sum converges to 1000.
The [tex]n[/tex]-th partial sum of the series is
[tex]S_n=\displaystyle\sum_{i=1}^n100\left(\dfrac9{10}\right)^{i-1}=100\left(1+\dfrac9{10}+\left(\dfrac9{10}\right)^2+\cdots+\left(\dfrac9{10}\right)^{n-1}\right)[/tex]
Then
[tex]\dfrac9{10}S_n=100\left(\dfrac9{10}+\left(\dfrac9{10}\right)^2+\left(\dfrac9{10}\right)^3+\cdots+\left(\dfrac9{10}\right)^n\right)[/tex]
so that
[tex]S_n-\dfrac9{10}S_n=\dfrac1{10}S_n=100\left(1-\left(\dfrac9{10}\right)^n\right)[/tex]
[tex]\implies S_n=1000\left(1-\left(\dfrac9{10}\right)^n\right)[/tex]
As [tex]n\to\infty[/tex], [tex]\left(\dfrac9{10}\right)^n\to0[/tex], so we're left with
[tex]\displaystyle\sum_{i=1}^\infty100\left(\dfrac9{10}\right)^{i-1}=\lim_{n\to\infty}S_n=1000[/tex]
The given infinite series is a converging geometric series with an initial term of 100 and a common ratio of 9/10. Using the formula for the sum of an infinite geometric series, we find that the sum is 1000.
Explanation:To evaluate an infinite sum, or a series, we need to recognize the series structure. The given series ∑^{∞}_{i=1} 100(9/10)^{i-1} is a geometric series where the initial term (a) is 100 and the common ratio (r) is 9/10.
A geometric series converges only when the absolute value of r is less than 1, which is true in this scenario. When it converges, the sum (S) of the infinite geometric series can be calculated using the formula S = a / (1 – r).
By plugging into this formula, we get: S = 100 / (1 - 9/10) = 100 / (1/10) = 1000.
Therefore, the sum of the infinite series ∑^{∞}_{i=1} 100(9/10)^{i-1} is 1000.
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Write the first five terms of the the sequence defined by the explicit formula an=72(1/3)^n-1
[tex]a_n=72\left(\dfrac{1}{3}\right)^{n-1}\\\\\text{Put}\ n=1,\ n=2,\ n=3,\ n=4,\ n=5\ \text{to the equation}:\\\\n=1\to a_1=72\left(\dfrac{1}{3}\right)^{1-1}=72\left(\dfrac{1}{3}\right)^0=72(1)=72\\\\n=2\to a_2=72\left(\dfrac{1}{3}\right)^{2-1}=72\left(\dfrac{1}{3}\right)^1=72\left(\dfrac{1}{3}\right)=\dfrac{72}{3}=24\\\\n=3\to a_3=72\left(\dfrac{1}{3}\right)^{3-1}=72\left(\dfrac{1}{3}\right)^2=72\left(\dfrac{1}{9}\right)=\dfrac{72}{9}=8\\\\n=4\to a_4=72\left(\dfrac{1}{3}\right)^{4-1}=72\left(\dfrac{1}{3}\right)^3=72\left(\dfrac{1}{27}\right)=\dfrac{72}{27}=\dfrac{8}{3}\\\\n=5\to a_5=72\left(\dfrac{1}{3}\right)^{5-1}=72\left(\dfrac{1}{3}\right)^4=72\left(\dfrac{1}{81}\right)=\dfrac{72}{81}=\dfrac{8}{9}\\\\Answer:\ \boxed{72,\ 24,\ 8,\ \dfrac{8}{3},\ \dfrac{8}{9}}[/tex]
Answer:
The first five terms are as follows:
72, 24, 8, 2.66, 0.88
Step-by-step explanation:
1) Explicit formula:
[tex]72 * 1/3^{n-1}[/tex]
2) Simply replace "n" with 2,3,4 and 5 in order to find the numbers associated with these terms.
a(1) = 72
a(2) = 24
a(3) = 8
a(4) = 2.66
a(5) = 0.88
Note:
In the explicit formula the first term is already provided, so you do not have to find the first term if it has already been given.
The length of a rectangle is three times its width. The perimeter of the rectangle is at most 112cm. Which inequality models the relationship between the width and the perimeter of the rectangle.
Answer: w ≤ 14 cm , L ≤ 42 cm
Step-by-step explanation:
width (w): w
Length(L): 3w
Perimeter (P) = 2w + 2L
P ≤ 112
2w + 2L ≤ 112
2(w) + 2(3w) ≤ 112
2w + 6w ≤ 112
8w ≤ 112
w ≤ 14
Mackenzie wrote the following paragraph proof for the Vertical Angles Theorem: Line segment NT intersects line segment MR forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles. The sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees by the definition of supplementary angles. The sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 _________________. Angle 1 is equal to angle 3 by the subtraction property of equality. Which phrase completes the proof? by construction using a straightedge by the definition of a perpendicular bisector by the transitive property of equality. by the vertical angles theorem
by the transitive property of equality
Answer:
the transitive property of equality
Step-by-step explanation: