Answer:
[tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex]
Step-by-step explanation:
We have been given an expression [tex]q^2+11q[/tex]. We are asked to complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.
We know that a perfect square trinomial is in form [tex]a^2+2ab+b^2[/tex].
To convert our given expression into perfect square trinomial, we need to add and subtract [tex](\frac{b}{2})^2[/tex] from our given expression.
We can see that value of b is 11, so we need to add and subtract [tex](\frac{11}{2})^2[/tex] to our expression as:
[tex]q^2+11q+(\frac{11}{2})^2-(\frac{11}{2})^2[/tex]
Upon comparing our expression with [tex](a+b)^2=a^2+2ab+b^2[/tex], we can see that [tex]a=q[/tex], [tex]2ab=11q[/tex] and [tex]b=\frac{11}{2}[/tex].
Upon simplifying our expression, we will get:
[tex](q+\frac{11}{2})^2-\frac{11^2}{2^2}[/tex]
[tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex]
Therefore, our perfect square would be [tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex].
Adding 121/4 to the equation will make it a perfect square to have [tex]q^2+11q + \frac{121}{4}[/tex]
The standard form of a quadratic equation is expressed as [tex]ax^2+bx+c=0[/tex]
Given the equation [tex]q^2+11q[/tex], we need to add a constant value that will make the expression a perfect square.
To complete the square, we will add the square of the half of the coefficient of q to the equation
Coefficient of q = 11
Half of the coefficient = 11/2
Square of the result = (11/2)² = 121/4
Adding 121/4 to the equation will make it a perfect square to have [tex]q^2+11q + \frac{121}{4}[/tex]
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a computer costs 400 dollars. Its 20 percent off with an additional 5 percent off, there's no sales tax. How much does the computer cost now?
The computer costs $304 now.
Step-by-step explanation:
Given,
Cost of computer = $400
First discount = 20%
Amount of discount = 20% of $400
Amount of discount = [tex]\frac{20}{100}*400=\frac{8000}{100}[/tex]
Amount of discount = $80
Price after first discount = 400-80 = $320
Additional discount = 5%
Amount of additional discount = 5% of price after first discount
Amount of additional discount = [tex]\frac{5}{100}*320=\frac{1600}{100}[/tex]
Amount of additional discount = $16
Final cost = 320-16 = $304
The computer costs $304 now.
Keywords: discount, subtraction
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Teresa stated that the heights of the students in her class were not a function of their ages. Which reasoning could justify Teresa’s statement?
Answer: Two students are the same age but have different heights.
Write a fraction greater than 1 for the parts that are shaded. + a mixed #. Please I need an answer for all of them
Answer:
2. 7/4 and 1 3/4
3. 5/3 and 1 2/3
4. 14/5 and 2 4/5
5. 21/6 and 3 3/6 (Lowest terms=3 1/2)
6. 20/8 and 2 4/8 (lowest terms= 2 1/2)
Hope it helped!!
The circumference of the Astrodome in Houston, Texas is 2,230 ft. Find the area of the astrodome and explain how you did this using the words area, circumference and radius. (π = 3.14)
Answer:
The radius of Astrodome is 355.09 foot,
The Area of Astrodome is 395919.146 square foot .
Step-by-step explanation:
Given as :
The circumference of Astrodome = 2230 foot
∵ The circumference of circular shape = 2 × [tex]\pi[/tex] × radius
where [tex]\pi[/tex] = 3.14
So, The circumference of Astrodome = 2 × [tex]\pi[/tex] × radius
Or, 2230 foot = 2 × 3.14 × radius
Or, 2230 foot = 6.28 × radius
∴ radius = [tex]\dfrac{2230}{6.28}[/tex]
I.e radius = 355.09 foot
Now,
∵The area of circular shape = [tex]\pi[/tex] × radius²
So, The area of Astrodome = [tex]\pi[/tex] × radius²
Or, The area of Astrodome = 3.14 × radius²
Put the value of radius = 355.09 foot
So , The area of Astrodome = 3.14 × (355.09)²
or, The area of Astrodome = 3.14 × 126088.9
∴ The area of Astrodome = 395919.146 square foot
Hence , The radius of Astrodome is 355.09 foot, and The Area of Astrodome is 395919.146 square foot . Answer
Please help me!! I have been stuck for hours
Answer:
The optimum price to sell the app is $2.55
Step-by-step explanation:
Modeling With Functions
The equation of the demand for the app store is given by
U=10000-2000P
Where U is the number of units sold and P is the price for each unit.
a.
The money from sales (Revenue) is U times the price of each unit, so
[tex]S=U.P[/tex]
Using the equation above
[tex]S=(10000-2000P).P=10000P-2000P^2[/tex]
b. The upfront costs function is given by
[tex]C=2000+0.1U[/tex]
Again, we use the equation for U
[tex]C=2000+0.1(10000-2000P)[/tex]
[tex]C=2000+1000-200P[/tex]
[tex]C=3000-200P[/tex]
c.
The profit is the sales minus the cost
[tex]Profic=S-C=10000P-2000P^2-(3000-200P)[/tex]
[tex]Profit=10000P-2000P^2-3000+200P[/tex]
[tex]Profit=-2000P^2+10200P-3000[/tex]
d.
The vertex of a quadratic function shown as
[tex]f(x)=ax^2+bx+c[/tex]
has an x-coordinate equal to
[tex]\displaystyle x=-\frac{b}{2a}[/tex]
The optimum price for selling the app can be found in the vertex of the above equation.
The P-coordinate of the vertex is given by
[tex]\displaystyle x=-\frac{10200}{-4000}=2.55[/tex]
The optimum price to sell the app is $2.55
At a local food store a child stole $500 from the shopkeeper's cash register to purchase goods in the store. The items the child purchased total $350 which he paid using the money he stole and received change of $150. How much money in total did the shopkeeper lose
Answer:
$650
Step-by-step explanation:
the child stole $500 then the shopkeeper gave him change of $150 that equals to the amount of money the shopkeeper lost.
working....
$500+$150=$600
Final answer:
The shopkeeper lost a total of $500 due to the child stealing $500, buying items worth $350, and receiving $150 in change.
Explanation:
The question involves determining the total amount of money the shopkeeper lost due to a theft. When the child stole $500 from the cash register and then used some of this money to buy items worth $350, the shopkeeper effectively lost that amount due to the child not legitimately paying for the goods. Furthermore, the child received $150 in change when they used the stolen money to pay for the items. Therefore, the total money lost by the shopkeeper is the sum of the cost of the goods taken and the change given out, which amounts to $350 + $150, equating to a total loss of $500.
A trapezoid has a set of parallel bases with lengths 3 inches and 5 inches and a height of 8 inches. What is the area of the trapezoid? Type a numerical answer in the space provided. Do not include units or spaces in your answers.
Answer:
The area \(A\) of a trapezoid can be calculated using the formula:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
where \(b_1\) and \(b_2\) are the lengths of the parallel bases, and \(h\) is the height.
For this trapezoid:
- \(b_1 = 3\) inches
- \(b_2 = 5\) inches
- \(h = 8\) inches
Plugging in the values:
\[ A = \frac{1}{2} \times (3 + 5) \times 8 \]
\[ A = \frac{1}{2} \times 8 \times 8 \]
\[ A = \frac{1}{2} \times 64 \]
\[ A = 32 \]
The area of the trapezoid is 32.
If 4 bushels of oats weigh 112 kg, how much do 8.5 bushels of oats weigh?
1. Find the missing side length.
Can someone please help??? I'll give extra points!!
And mark as brainliest. PLEASEEEE!!!
Answer:
Therefore the missing length is AC = 24.46 units
Step-by-step explanation:
Consider a Δ ABC with
∠ B = 43°
AB = c = 18
BC = a = 8
To Find:
AC = c = ?
Solution:
We know in a Triangle Cosine Rule Says that,
[tex]b^{2} =c^{2}+ a^{2}-2\times a\times c\times \cos B[/tex]
Substituting the given values in above formula we get
[tex]b^{2} =18^{2}+ 8^{2}-2\times 8\times 18\times \cos 43\\\\b^{2} =324+64+288\times 0.7313\\\\b^{2} =598.6144\\\\Squaare\ Rooting\\\therefore b = 24.46\ units[/tex]
Therefore the missing length is AC = 24.46 units
Answer:
13.32
Step-by-step explanation:
if the missing side length is b,
1.) b^2 = 18^2 + 8^2 - 2(8)(18)(cos43)
2.) b^2 = 177.3701
then take square root of 177.3701
3.) √(b^2) = √(177.3701)
4.) b = 13.32
see ya have a good day
P is the centroid of triangle ABC. AE = 21, CD = 14, and BF = 11. What is the length of AP?
Answer
[tex]AP=14[/tex]
Step by Step Explanation
1) Due to the Centroids Theorem we can say that:
AP=2/3AE
AP=2/3*21
∴AP=14
2) Finally, AE =AP+AE
21=14+7 ⇒21=21 True
AP =2PE verifies the Theorem too.
So, the size is 14 .
[tex]AP=14\:u[/tex]
which equation could represent the area of a square as a function of a side A: A(s)=2s B: A(s)=4s C: A(s)= s2
Answer:
[tex]A(s)=s^2[/tex]
Step-by-step explanation:
we know that
The square is a regular polygon that has four right angles and four parallel and congruent sides.
The area of a square is equal to the length side squared
Let
s ----> the length side of the square
we have that
[tex]A(s)=s^2[/tex]
A recipe for cookies calls for 2⁄3 of a cup of chocolate chips and 4 cups of flour. If you want to make a bigger batch, using 6 cups of flour, how many cups of chocolate chips will you need?
The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 101010 denarius per day to support 333 legionaries and 333 archers. It only costs 333 denarius per day to support one legionary and one archer. Use a system of linear equations in two variables.
Can we solve for a unique cost for each soldier?
Answer:
The system cannot be solved by a unique cost for each soldier
Step-by-step explanation:
The correct question is
The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 10 denarius per day to support 3 legionaries and 3 archers. It only costs 3 denarius per day to support one legionary and one archer. Use a system of linear equations in two variables.
Can we solve for a unique cost for each soldier?
Let
x-------> the cost of a legionary per day
y-------> the cost of an archer per day
we know that
[tex]3x+3y=10[/tex]
isolate the variable y
subtract 3x both sides
[tex]3y=10-3x[/tex]
Divide by 3 both sides
[tex]y=-x+\frac{10}{3}[/tex] ------> equation A
[tex]x+y=3[/tex]
isolate the variable y
subtract x both sides
[tex]y=-x+3[/tex] ------> equation B
Remember , If two lines are parallel, then their slopes are equal
In this problem Line A and Line B are parallel lines, because their slopes are equal.
we know that that the solution of the system of equations is the intersection point both graphs
If the lines are parallel, then the lines don't intersect
see the attached figure to better understand the problem
therefore
The system has no solutions (Is a inconsistent system)
What is the equation of a line that contains the points (5.0) and (5,-2)?
x = 5
x = 0
y=0
y = 5
Answer:
C) y=0
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-2-0)/(5-5)
m=-2/0
m=0
y-y1=m(x-x1)
y-0=0(x-5)
y-0=0
y=0+0
y=0
Answer:
x=5
Step-by-step explanation:
a
Plz I need help with geometry homework FIND THE ANGLES
Answer:
a = 36°b = 36°c = 72°d = 72°e = 108°f = 16°g = 74°h = 70°Step-by-step explanation:
You are expected to know and make use of the following relations:
vertical angles are congruentangles of a linear pair are supplementaryangles of a triangle sum to 180°alternate interior angles are congruent (at parallel lines)corresponding angles are congruent (at parallel lines)acute angles of a right triangle are complementarybase angles of an isosceles triangle are congruent__
For this problem, it isn't always easiest to work the questions in order. It is best to start with the angles easiest to find from those given.
b and 144° are a linear pair, so b = 180° -144° = 36°
a and b are alternate interior angles, so a = b = 36°
2d and 144° are corresponding angles, so d = 144°/2 = 72°
e is the apex angle of an isosceles triangle with base angles 36°, so is 180° -2(36°) = 108° = e
f and 164° are a linear pair, so f = 180° -164° = 16°
g and f are complementary, so g = 90° -16° = 74°
g+h is a vertical angle with 144°, so is congruent to that. h = 144° -74° = 70°
c is the base angle of an isosceles triangle with b as the vertex angle. That means c = (180° -36°)/2 = 72°
Each cube in this rectangular prism is 1 cm3.What is the volume of the rectangular prism?
A.40 cm3
B.20 cm3
C.48 cm3
D.9 cm3
The volume of the rectangular prism is b. 20 cubic cm
What is the volume of the rectangular prism?
From the question, we have the following parameters that can be used in our computation:
the rectangular prism
Where, we have
Length = 2
Height = 2
Width = 5
The volume of the rectangular prism is the product of the dimensions
So, we have
Volume = 2 * 2 * 5
Volume = 20 cubic cm
Hence, the volume of the rectangular prism is b. 20 cubic cm
Find the area of the trapezoid by decomposing it into other shapes. A) 56 cm2 B) 60 cm2 C) 64 cm2 D) 72 cm2 Eli
Answer:
Option C. [tex]64\ cm^2[/tex]
Step-by-step explanation:
see the attached figure N 1 to better understand the problem
we know that
The trapezoid can be decomposed into two right triangles and a rectangle
see the attached figure N 2
so
The area of the trapezoid is equal to the area of two right triangles and one rectangle
The area of trapezoid is equal to
[tex]A=\frac{1}{2}(5)(4)+(12)(4)+\frac{1}{2}(3)(4)[/tex]
[tex]A=10+48+6[/tex]
[tex]A=64\ cm^2[/tex]
The price of a certain stock fell $2 each day for 4 consecutive days. Write an expression that you could use to find the change in the stock’s price after 4 days. Suppose the original price of the stock was $41. What was the price of the stock after 4 days?
Answer:
35
Step-by-step explanation:
[tex]d=-2\\n=4\\a_4=a_1+3d\\if\; a_1=41\; then\; a_4=41+3\times(-2)=41-6=35[/tex]
Solve: 2(4x - 6) = 6x - 4 A) 4 Eliminate B) 8 C) -4 D) no solution
Answer:
x = 4
A
Step-by-step explanation:
2(4x - 6) = 6x - 4
8x -12 = 6x - 4
8x - 8 = 6x
8x = 6x + 8
2x = 8
x = 4
Hope this helps :)
I don’t understand question 49 someone pls explain.
Answer:
Below in bold.
Step-by-step explanation:
a, That would be
m = 7 + 8(d - 1) where m = the no. of minutes and d = the day number.
b. On day 9 the number of minutes m = 7 + 8(9 - 1)
= 7 + 64
= 71.
Maya has $2740 of play money
Emily has $3560 of play money. Maya gives some money to Emily. If Emily ends up with 4 times Maya amount. How much money does each girl has in the end
Answer:
Maya = $1260
Emily = $5040
Step-by-step explanation:
2740+3560 =6300
M + (4M) = 6300
5M=6300
M=6300/5
M=1260
E=5040
Maya has $1260, and Emily has $5040 in the end. Maya gives $1480 to Emily.
How the amount of money was calculatedMaya has $2740, and Emily has $3560.
We're looking for the amount Maya gives to Emily so that Emily ends up with 4 times as much as Maya.
Let M be the amount Maya gives to Emily.
Emily ends up with 4 times Maya's amount:
Emily's amount = 4 * Maya's amount
$3560 + M = 4 * ($2740 - 4M
Simplify:
$3560 + M = $10960 - 4M
$3560 + M + 4M = $10960
5M = $10960 - $3560
5M = $7400
Divide by 5 to solve for M:
M = $7400 / 5
M = $1480
So, Maya gives $1480 to Emily.
To find how much each girl has in the end:
Maya: $2740 - $1480 = $1260
Emily: $3560 + $1480 = $5040
Maya has $1260, and Emily has $5040 in the end.
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What is the equation of the line in slope-intercept form?
Answer:
Step-by-step explanation:
Answer:
[tex]y=\dfrac{3}{5}x+3[/tex]
Step-by-step explanation:
From the given graph it is clear that the graph passes through the points (0,3) and (-5,0).
It a line passes through wo points then the equation of line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The equation of given line is
[tex]y-3=\dfrac{0-3}{-5-0}(x-0)[/tex]
Add 3 on both sides.
[tex]y=\dfrac{-3}{-5}x+3[/tex]
[tex]y=\dfrac{3}{5}x+3[/tex]
Therefore, the required equation is [tex]y=\dfrac{3}{5}x+3[/tex].
find the unit cost of each of the following to determine which is the better value: 8 CDs for $56.99 or 3 CDs for $22.99
Answer:
8 CD's for $56.99 is better value than 3 CD's for $22.99.
Step-by-step explanation:
We are given that,
Cost of 8 CD's is $56.99 and cost of 3 CD's is $22.99.
Now, to determine which is the better value, we will find the cost of 1 CD in both the cases. The case which will give cost per CD less will represent the better value.
CASE 1 :
Cost of 8 CD's = $ 56.99
So, cost of 1 CD = $ 56.99 ÷ 8 = $ 7.12 (approx.)
CASE 2 :
Cost of 3 CD's = $ 22.99
∴ Cost of 1 CD = $ 22.99 ÷ 3 = $ 7.66 (Approx.)
So, the CD's are available in cheaper rates in the first case in comparison to second case.
So, 8 CD's for $56.99 is better value than 3 CD's for $22.99.
Answer:
The unit cost of 8 CDs for $56.99 is $7.12 and the unit cost of 3 CDs for $22.99 is $7.66.
And the better value is of 8 CDs for $56.99.
Step-by-step explanation:
Given:
8 CDs for $56.99 or 3 CDs for $22.99.
Now, to find the unit cost to determine which is better value.
By using unitary method we find it:
So, to get the unit cost of 8 CDs for $56.99:
If 8 CDs cost $56.99.
Then, 1 CD cost = [tex]56.99\div 8=\$7.12.[/tex]
Thus, the unit cost = $7.12.
Now, to get the unit cost of 3 CDs for $22.99:
If 3 CDs cost $22.99.
Then, 1 CD cost = [tex]22.99\div 3=\$7.66.[/tex]
Thus, the unit cost = $7.66.
Now, on comparing we determine the better value is of 8 CDs for $56.99.
Therefore, the unit cost of 8 CDs for $56.99 is $7.12 and the unit cost of 3 CDs for $22.99 is $7.66.
And the better value is of 8 CDs for $56.99.
Isaac purchased a house for $179,300,00. Every year, Isaac makes improvements so that the value of the house goes up by 4%.
Which of the following equations can be used to determine the number of years after purchase, that the value of Isaac's house will
be equal to 5197.230.002
Answer:
The number of years in which house value goes up is 145 years .
Step-by-step explanation:
Given as :
The initial purchased value of the house = p = $179,300,00
The value of house goes up every years at the rate = r = 4%
Let The number of years in which house value goes up = t years
The value of the house after t years = $A = $5197,230,002
Now, According to question
The value of the house after t years = The initial purchased value of the house × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
I.e A = $p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or,$5197,230,002 = $17930000 × [tex](1+\dfrac{\textrm 4}{100})^{\textrm t}[/tex]
Or, [tex]\dfrac{5197,230,002}{179,300,00}[/tex] = [tex](1+\dfrac{\textrm 4}{100})^{\textrm t}[/tex]
Or, 289.86 = [tex](1.04)^{t}[/tex]
Now, taking Log both side
So, [tex]Log_{10}[/tex]289.86 = [tex]Log_{10}[/tex] [tex](1.04)^{t}[/tex]
or, 2.462 = t × [tex]Log_{10}1.04
or, 2.462 = t × 0.01703
∴ t = [tex]\dfrac{2.462}{0.01703}[/tex]
I.e t = 144.56 ≈ 145
So, Number of years = t = 145 years
Hence The number of years in which house value goes up is 145 years . Answer
To determine the number of years it will take for the value of Isaac's house to reach $5,197,230.002 with an annual appreciation rate of 4%, use the compound interest formula. Solving for the number of years, the approximate result is 84 years.
Isaac purchased a house for $179,300. Every year, the value of the house increases by 4%. To determine the number of years after purchase that the value of Isaac's house will reach $5,197,230.002, we can use the formula for compound interest:
FV = PV × (1 + r)ⁿ
FV is the future value of the house, $5,197,230.002.PV is the present value or the initial value of the house, $179,300.r is the annual increase rate, 4% or 0.04.n is the number of years.We need to solve for n in the equation:
$5,197,230.002 = $179,300 × (1 + 0.04)ⁿFirst, isolate the exponential expression:
(1 + 0.04)ⁿ = $5,197,230.002 / $179,300(1.04)ⁿ ≈ 29Next, apply the natural logarithm to both sides to solve for n:
ln[(1.04)n] = ln(29)n × ln(1.04) = ln(29)n = ln(29) / ln(1.04)n ≈ 83.95 yearsSo, the value of Isaac's house will reach $5,197,230.002 approximately 84 years after purchase.
Simplify the expression 6y to the 4th power+3y to the 4th power.
Answer:
6y^4 + 3y^4
1296y + 81y
1377y
Step-by-step explanation:
If a single point satisfies the equations of two lines, the point is on both lines?
Answer:
yes
Step-by-step explanation:
Answer:
Yes. This is called a solution of the equations and is the intersection point.
Which system is equivalent to
{y=-2x2
y=x-2}
Answer:
OPTION C: y = -2y² - 8y - 8
x = y + 2
Step-by-step explanation:
The given equations are:
[tex]$ y = -2x^2 \hspace{20mm} \hdots (1) $[/tex]
[tex]$ y = x - 2 \hspace{20mm} \hdots (2) $[/tex]
From Equation (2), we get:
x = y + 2
Substituting this value of x in Equation (1), we get:
y = -2(y + 2)²
Expanding it in [tex]$ (a + b)^2 = a^2 + 2ab + b^2 $[/tex], we get:
y = -2{y² + 4y + 4}
⇒ y = - 2y² - 8y - 8
Therefore, OPTION C is the answer.
Answer: C on edge 2022
Step-by-step explanation:
if wrong i’m gay and Bidens a good president *they almost all suck anyways*
25. Paulo's family arrived at the reunion at
8:30 A.M. How long do they have before
the trip to Scenic Lake Park?
DATA
Trip to Scenic
Lake Park
10:15 A.M. to 2:30 P.M.
Slide show
4:15 P.m. to 5:10 P.M.campfire 7;55p.m.to 9;30p.m
26. How much longer is dinner than the
25 states, Paulo's family arrived at the reunion at
8:30 A.M. How long do they have before
the trip to Scenic Lake Park?
So the question asks how long it takes.
8:30AM to 10:15AM would be a 1:15 hour difference. This would be the answer to #25.
Let me know if you have any extra questions.
25 states, Paulo's family arrived at the reunion at
8:30 A.M. How long do they have before
th
Step-by-step explanation:
Car Survey in a survey of 3,200 people who owned a certain type of car, 2,240 said they would buy
that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
30%
Step-by-step explanation:
1.) subtract 3200 and 2240. Since you need to find the amount of people who were satisfied with the car.
2.) divide 960 and 3200. this is because you need to find the percent of people who were satisfied with the car.
Answer: 30%
The percentage satisfied with the purchase is 30%
The percentage who were satisfied can be calculated thus :
(Difference/ Number surveyed ) × 100%Difference = 3200 - 2240 = 960
Now we have :
(960 / 3200) × 100%
= 0.3 × 100%
= 30%
Hence, percentage who were satisfied is 30%
Which decimals are rational numbers? Select all that apply
A. 72/100
B. π
C. 1 1/3
D. 8/526
E. 0.212212221...
F. 5/9
Answer:
Your answers are A, C, D, FStep-by-step explanation:
Fractions are always rational.
A --> this is rational because it can be represented by a fraction.
B --> this is irrational because it cannot be represented by a fraction
C --> 1 1/3 is rational because it can be represented as a fraction
D --> 8/526 is rational because it can be represented as a fraction
E --> this is irrational because it cannot be represented by a fraction
F --> this is rational because it can be represented as a fraction
I hope this helps!
Rational numbers can be expressed as the ratio of two integers. From the list provided, the rational numbers are 72/100 (A), 1 1/3 (C), 8/526 (D), and 5/9 (F). The number π (B) is irrational, and it is unclear if 0.212212221... (E) is a repeating decimal, so it cannot be confirmed as rational without additional information.
Explanation:Rational numbers are numbers that can be written as a fraction, where both the numerator and the denominator are integers and the denominator is not zero.
This includes both terminating and repeating decimals.
A. 72/100 is a rational number because it can be simplified to the fraction 18/25, which is a ratio of two integers.B. π (pi) is not a rational number because it is an irrational number; it cannot be expressed as a fraction of two integers.C. 1 1/3 is a rational number as it is equivalent to the fraction 4/3, a ratio of two integers.D. 8/526 is a rational number as it is already in fraction form with two integers.E. 0.212212221..., if this is a non-terminating, non-repeating decimal, it would be irrational; however, if the pattern repeats at some point, it would be rational. Since the pattern is not explicitly stated as repeating, we cannot assume it is rational.F. 5/9 is a rational number because it is a fraction that represents a ratio of two integers.Thus, the rational numbers from the list provided are A, C, D, and F.