The ratio of Revani's nickels to dimes to quarters is 40nickels:40dimes:40quarters.
What is ratioA ratio is a comparison of two or more numbers that indicates their sizes in relation to each other numbers.
The total coin = 120
2/6 of 120coins that are nickels = (2 × 120)/6
2/6 of 120coins that are nickels = 40 nickels
2/6 of 120coins that are dimes = (2 × 120)/6
2/6 of 120coins that are dimes = 40 dimes
since the rest coins are quarters;
the numbers of quarters = 120 - (40nickels +40dimes)
numbers of quarters = (120 - 80)coins
numbers of quarters = 40coins
Therefore, the ratio of nickels to dimes to quarters is 40:40:40 respectively.
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Find the perimeter of a quadrilateral with the following vertices.
(−6, −2), (0, −10), (5, 2), (−1, 10)
a.40
b.52
c.23
d.46
The perimeter of the quadrilateral is 46 units, so the correct option is d.
How to find the perimeter of the quadrilateral?The perimeter is equal to the sum of the lengths of all the sides of the quadrilateral.
Remember that the length of a segment whose endpoints are (x₁, y₁) and (x₂, y₂) is:
L = √( (x₁ - x₂)^2 + (y₁ - y₂)^2)
The length between the first two vertices: (−6, −2), (0, −10)
L₁ = √( (-6 - 0)^2 + (-2 + 10)^2) = 10
The length between the second two vertices: (0, −10), (5, 2)
L₂ = √( (0 - 5)^2 + (-10 - 2)^2) = 13
The length between the third two vertices: (5, 2), (−1, 10)
L₃ = √( (5 + 1)^2 + (2 - 10)^2) = 10
The length between the fourth two vertices: (−1, 10), (−6, −2)
L₄ = √( (-1 + 6)^2 + (10 + 2)^2) = 13
Then the perimeter is:
P = 10 + 13 + 10 + 13 = 46
The correct option is D.
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The soccer field is 105 meters long. The football field is 120 yards long. Which is longer?
The football field is longer than soccer field.
What is a expression? What is a mathematical equation? What is unit conversion?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
We have a soccer field that is 105 meters long and a football field is 120 yards long.
In one yard, we have -
1 yard = 0.9144 meters
Then, in 120 yards, we will have -
120 x 0.9144 = 109.728 meters
Now, 109.728 meters > 105 meters.
Therefore, the football field is longer than soccer field.
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Vivi needs to solve the system of equations below using elimination.
4× + 6y =-14
-× +3y=-10
Which correctly describes a possible first step Vivi could take?
D. Multiply each term in the 2nd equation by 2.
b. Multiply each term in the 2nd equation by -4.
C. Multiply each term in the 2nd equation by 4.
d. Both a and c could work.
A possible first step Vivi could take is multiply each term in the second equation by 2 and she can also multiply each term in the second equation by 4. The correct option is d. Both a and c could work.
Elimination method: Determining a possible first stepFrom the question, we are to determine the statement that correctly describes a possible first step Vivi could take
From the given information,
The given system of equations is
4x + 6y = -14
-x + 3y = -10
To eliminate y, we can multiply each term in the second equation by 2 and then subtract
2 × [-x + 3y = -10
-2x + 6y = -20
Then, subtract
4x + 6y = -14
-{ -2x + 6y = -20
------------------------
6x = 6
To eliminate x, we can multiply each term in the second equation by 4 and add the equations,
4 × [-x + 3y = -10
-4x + 12y = -40
Then, add
4x + 6y = -14
+{ -4x + 12y = -40
--------------------
18y = -54
Hence, we can multiply each term in the second equation by 2 and we can also multiply each term in the second equation by 4.
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observations 1 2 3 4 5 6 num. of defects 10 18 13 15 9 12the number of runs up and down for the preceding data is:
The number of runs up and runs down for the preceding data is 5.
What is runs up ?Runs up refers to the number of observations that are higher than the number of observations before them.
What is runs down ?Runs down refers to the number of observations that are lower than the number of observations before them.
As 2nd observation is higher than 1st observation, 4th observation is higher than 3rd observation and 6th observation is also higher than 5th observation so 2nd, 4th,6th observation should be included in runs up.
Therefore,
Runs up = 2nd + 4th + 6th observations
= 3
As 3rd observation is lower than 2nd observation,5th observation is also lower than 4th observation so 3rd,5th observation should be included in the runs down
Therefore,
Runs down= 3rd +5th observations
=2
Therefore,
Runs up + Runs down =3+2
=5
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Question
Solve for p.
2(p+1)=18
Responses
p = 8
p, = 8
p = 8.5
p, = 8.5
p = 9.5
p, = 9.5
p = 10
Answer:
p=8
Step-by-step explanation:
[tex]2(p+1)=18\\\frac{2(p+1)}{2}=\frac{18}{2}\\p+1=9\\p+1-1=9-1\\p=8[/tex]
Answer:P=8
Step-by-step explanation:
I TOOK THE TEST
If X is the midpoint of TV, TV bisects RS, and TR is parallel to VS, state five pairs of objects (segments or angles) that must be congruent and give a reason why for each pair.
According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
Alternate Interior Angle Theorem?According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.Is it true or false that different interior angles are always congruent? Although untrue, this assertion is a typical misunderstanding. Keep in mind that when the lines are parallel, alternate inner angles are congruent.Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposing sides of the transversal when two lines are crossed by another line (referred to as the Transversal). These two pairs of alternate interior angles in this illustration are c and f.To learn more about Congruent refer to:
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HELP LIKE ASAP
WXY is the image of RST after a translation 3 units up. Select all of the statements that are always true.
options:
_ The length of side TR equals the length of side WX
_ The length of side RS equals the length of side WX
_ The measure of angle R equals the measure of angle W
_ The measure of angle R equals the measure of angle X.
The correct options are: The length of side RS equals the length of side WX and The measure of angle R equals the measure of angle W.
What is translation transformation?A geometry translation is an isometric transformation, meaning that the original figure and the image are congruent.
Given that, WXY is the image of RST after a translation 3 units up.
As we know in translation, both figures are congruent so, we have,
WX = RS
XY = ST
WY = RT
And
∠ R = ∠ W
∠ S = ∠ X
∠ T = ∠ Y
Hence, The correct options are: The length of side RS equals the length of side WX and The measure of angle R equals the measure of angle W.
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A shopping mall has 226 stores on 4 levels. Each level of the mall has about the same number of stores. Which of the following are reasonable estimates for the number of stores on each level
The number of stores in each level of the shopping mall are 56 stores.
How to solve an equation?An equation is an expression that can be used to show the relationship between variables and numbers. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
Let x represent the number of stores on each level.
A shopping mall has 226 stores on 4 levels. If there are same number of stores in each level:
(4 × x) = 226
4x = 226
Divide
x = 226 / 4
x = 56.5
There are about 56 stores per level.
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One morning after sunrise, Kimberly was standing facing a pole. The shadow of the pole fell exactly to her right. Which direction was she facing? a. North b. South c. West d. East
South direction was she facing.
What does the word "direction" mean?
Direction can refer to the way something moves, the way you must go to get somewhere, the way something is beginning to take shape, or the direction you are facing.
When you turn right rather than left, that is an illustration of direction.
Which forms of direction are there?
There are only four genuine directions north, south, east, and west. Northeast, Southeast, Southwest, and Northwest are the directions on the compass that are located midway between these cardinal points.
These transitional locations are referred to as intermediate directions. Maps and globes only display east-west and north-south lines.
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SET AT 50 POINTS AND BRAINLIEST
Which expression is equivalent to −6 + 8 − 3x − 9x?
−12x + 14
−12x + 2
12x + 14
−12x − 2
Answer:
-12x + 2
Step-by-step explanation:
-6+8 = 2
-3x - 9x = -12x
-12x + 2
Answer:
Step-by-step explanation:
-12x+14 i believe
It cost Juan $7.30 to send 73 text messages. How many text messages did he send if he spent $10.20?
Answer:
102
Step-by-step explanation:
First, divide 7.30 by 73 to find how much 1 text message costs. We get 0.1. Next, divide 10.20 by 0.1, which gives us the final answer of 102.
Answer:
99 text messages
Step-by-step explanation:
$7.50 = 73
÷73 ÷73
---------------------
amount to = $0.102739726
send one text
0.102739726x = $10.20
÷0.102739726 ÷0.102739726
-------------------------------------------------
x ≈ 99.28
I hope this helps!
An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 0.31. You want to estimate the probability that exactly one of the next four calls result in a reservation being made. Describe the design of a simulation to estimate this probability. Explain clearly how you will use the partial table of random digits below to carry out your simulation.
The probability that exactly one of the next four calls results in a reservation being made is 40.75%
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here, we have
A random call to their reservation phone line results in a reservation being made is 0.31
Now, we find
Exactly one call gets resevervation = 4 * (1-0.31)3(0.31)
= 0.4075 = 40.75%
Now we can simulate an experiment by using random numbers from 0 to 100,000 as probability values between 0 and 31,000 are p to reservation otherwise they don't.
Hence, the probability that exactly one of the next four calls results in a reservation being made is 40.75%
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18 Which expression uses the greatest common factor and distributive property to write 18 + 24 as a product? Circle the letter of the correct answer.
The expression that uses the greatest common factor and distributive property to write the given expression, 18 + 24, is 6(3 + 4)
Writing an expression using the Greatest common factor and distributive propertyFrom the question, we are to determine the expression that uses the greatest common factor and the distributive property to write the given expression.
The given expression is
18 + 24
First, we will determine the greatest common factor of 18 and 24
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
Thus,
The greatest common factor is 2 × 3 = 6
Now, we will write the expression using the greatest common factor and the distributive property
18 + 24
6(3 + 4)
Hence, the expression is 6(3 + 4)
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use strong induction to show that every positive integer can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers 20
MAIN ANSWER: using strong induction that every positive integer can be written as sum of distinct powers of two is 20=2²+2⁴
supporting answer The statement is true for all positive integers by mathematical induction. Strong induction can be used to demonstrate that every positive integer n can be written as a sum of distinct powers of two, that is, as a sum of a subset of the
2²=4
2⁴=16
4+16=20
final answer is 20=2²+2⁴
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Using strong induction that every positive integer can be written as sum of distinct powers of two is 20=2²+2⁴
What is positive integer?
Natural numbers are those in mathematics that are utilised for counting and ordering. Cardinal numbers are those used for counting, and ordinal numbers are those used for ordering.
The statement is true for all positive integers by mathematical induction. Strong induction can be used to demonstrate that every positive integer can be written as a sum of distinct powers of two, that is, as a sum of a subset of the
2²=4
2⁴=16
4+16=20
Final answer is 20=2²+2⁴
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A boat travels about 6 kilometers per hour in still water. If the boat is on a river that flows at a constant speed of
kilometers per hour, it can travel at a speed of (6+r) kilometers per hour downstream. On one particular river, a
boat travels 12 kilometers down stream. The amount of time it takes the boat travel depends on the speed of river
and is expressed by the equation t(r) =
12
(6+r)
The graph is shown below.
What does t(3) mean in this situation?
At what value of r does the graph have a vertical asymptote? Explain
how you know and what this asymptote means in this situation.
The function in the context of this problem is modeled as follows:
t(r) = 12/(6 + r)
In which the input and output of the function are given, respectively, by:
r is the velocity of the river.t(r) is the time it takes to cross the river considering the given velocity.Then the numeric value at t = 3 represents the time in hours it takes for the boat to cross the river when the velocity of the river is of 3 kilometers per hour.
What is the vertical asymptote of the function?The vertical asymptote of a function are the values of the input for which the function is not defined.
A fraction is not defined at the zeros of the denominator, hence:
t + 6 = 0
t = -6 is the vertical asymptote of the function.
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The length of a
rectangular garden is
three feet less than twice
its width. If the perimeter
of the garden is 42 feet,
what is its length?
Systems word problems
Answer:
The length will be 13 feet.
Step-by-step explanation:
Let the width be represented by w.
Based on the information given, the length will be:
= (2 × w) - 3
= 2w - 3
Therefore, the perimeter will be:
2(w) + 2(2w - 3) = 42
2w + 4w - 6 = 42
6w = 42 + 6
6w = 48
w = 48/6
w = 8
Therefore, the length will be:
L = 2w - 3
L = 2(8) - 3
L = 16 - 3
L = 13 feet
The length is 13 feet.
Answer:
The length will be 13 feet.
Step-by-step explanation:
Let the width be represented by w.
Based on the information given, the length will be:
= (2 × w) - 3
= 2w - 3
Therefore, the perimeter will be:
2(w) + 2(2w - 3) = 42
2w + 4w - 6 = 42
6w = 42 + 6
6w = 48
w = 48/6
w = 8
Therefore, the length will be:
L = 2w - 3
L = 2(8) - 3
L = 16 - 3
L = 13 feet
The length is 13 feet.
1. Write two equivalent expressions to represent the area of this rectangle.
2. Write two equivalent expressions to represent the perimeter of this rectangle.
(pls add an explanation)
The perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.
Given that, the breadth of a rectangle =5 units and the length of a rectangle =(x-2) units.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Here, perimeter =2(x-2+5)
= 2(x+3)
= 2x+6 units
Area of a rectangle =length × width
= (x-2) × 5
= 5x-10 square units
Therefore, the perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.
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Help help please help
Answer:
AB=45
Step-by-step explanation:
This is an isosceles triangle meaning AB and AC are congruent.
4x+1=2x+23
2x+1=23
2x=22
x=11
4(11)+1
44+1
45
A garden in the shape of a right triangle has a perimeter of 72 feet. If the
lengths of the sides of this garden are each lengthened by a factor of 8,
what would be the perimeter of the new enlarged garden?
OA) 352 ft.
OB) 488 ft
OC) 576 ft
OD 692 ft.
The perimeter of the new enlarged garden whose side length lengthened by factor of 8 is equal to 576ft.
As given in the question,
Shape of the garden is right triangle
Let 'x' , 'y' , and 'z' represents the three sides of the triangle shape garden.
Perimeter of the garden = 72 ft
⇒ x + y + z = 72 ft __(1)
Now, length of the each sides of the new garden is lengthened by factor of 8.
Sides of the new garden are '8x' , '8y' , and '8z'
Perimeter of the new garden = 8x + 8y + 8z
⇒ Perimeter of the new garden = 8 ( x + y + z )
⇒ Perimeter of the new garden = 8 (72)
⇒ Perimeter of the new garden = 576 ft
Therefore, perimeter of the new garden is equal to 576ft.
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Graph the solution to the inequality on the number line.
Solution to the inequality on the number line is y < 4 and y > −4.
What is inequality?
In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
When resolving an inequality, you can do one of the following:
• Add the same amount to each side;
• Subtract the same amount from each side;
• Multiply or divide each side by the same positive amount.
You must flip the inequality symbol if you multiply or divide each side by a negative number.
Let's solve your inequality step-by-step.
|y| < 4
Solve Absolute Value.
|y| < 4
We know y < 4 and y > −4
y < 4 (Condition 1)
y > −4 (Condition 2)
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5. What is the value of 6(x-2)(x-3) + 4(x-2)(x - 5) when x = -3?
Answer:
340Step-by-step explanation:
[tex]\tt 6(x-2)(x-3) + 4(x-2)(x - 5)[/tex]
When, x = -3
----------------------------------------------
To find the value of 6(x-2)(x-3) + 4(x-2)(x - 5), we need to substitute x with -3.
[tex]\tt 6\left(-3-2\right)\left(-3-3\right)+4\left(-3-2\right)\left(-3-5\right)[/tex]
[tex]\tt (6)(-5)(-3-3)+4(-3-2)(-3-5)[/tex]
[tex]\tt -30\left(-6\right)+4\left(-3-2\right)\left(-3-5\right)[/tex]
[tex]\tt -30\left(-6\right)+4\left(-5\right)\left(-3-5\right)[/tex]
[tex]\sf -30\left(-6\right)+4\left(-5\right)\left(-8\right)[/tex]
[tex]\tt 180+4\left(-5\right)\left(-8\right)[/tex]
[tex]\tt 180-\left(-160\right)[/tex]
[tex]\tt 180-\left(-160\right)[/tex]
[tex]\tt =340[/tex]
Therefore, the value of 6(x-2)(x-3) + 4(x-2)(x - 5) is 340!
____________________
Hope this helps!
Have a great day!
PLEASE HELP 50 POINTS
The trigonometric expression cos 3x / (sin x · cos x) is equivalent by trigonometric formulas to the trigonometric expression csc x · cos 2x - sec x · sin 2x. (Correct choice: A)
How to find an expression equivalent to another trigonometric expressionIn this problem we find the definition of a trigonometric expression, whose equivalent expression must be found by using algebra properties and trigonometric formulas. First, write the trigonometric function:
cos 3x / (sin x · cos x)
Second, use trigonometric formulas:
cos (x + 2x) / (sin x · cos x)
(cos x · cos 2x - sin x · sin 2x) / (sin x · cos x)
cos 2x / sin x - sin 2x / cos x
csc x · cos 2x - sec x · sin 2x
The equivalent trigonometric expression is csc x · cos 2x - sec x · sin 2x.
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If you roll a standard six-sided die a thousand times and add up the total number of pips, which approximate sum could you reasonably expect to end with?
1) 16.7% probability of rolling 10+.
2) 50% probability an odd number is rolled.
3) 7 is the most likely total result.
These are all the possible outcomes:
(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)
(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)
(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)
(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)
(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)
(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)
There are 36 possible outcomes
1) what is the probability of rolling 10+?
There are 6 possible outcomes in which 10+ is rolled:
(4,6), (5,5),(5,6), (6,4), (6,5),(6,6).
So there is a 6/36 = 0.167 = 16.7% probability of rolling 10+.
2) what is the probability of rolling an odd number?
There are 18 possible outcomes in which an odd number is rolled.
So there is a 18/36 = 0.5 = 50% probability an odd number is rolled.
3) what is the total that is most likely to result?
There are 6 outcomes in which 7 is rolled.
So 7 is the most likely total result.
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Make your angle measures correct to the nearest degree and side measures to 1 decimal place.
The value of angle Z= 39°, line XY= 21.9 and line XZ= 34.7
What is a right-angled triangle?A right-angled triangle is a type of triangle which as one of it's sides equal to 90°. Since angle Y is 90°, then ∆ABC is a right-angled triangle
angle Z = 180-(90+51)
angle Z= 180- 141= 39°
using trigonometry ratio
tan51 = 27/XY
XY= 27/tan51
XY= 27/1.2
XY= 21.9
using Pythagoras theorem
XZ²= 21.9²+27²
XZ²= 1208.6
XZ= √1208.6
XZ= 34.7
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help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!
Answer:
272 bison
Step-by-step explanation:
y(5)=240[tex](1+0.025)^{5}[/tex]
y(5) = 271. 5 bison ≈272 bison
Factor the expression completely over the complex numbers. Y^4+14y^2+49
the answer is ((y+i√7)(y-i√7))^2
Am I right
Factors over the complex numbers for the given expression y⁴ + 14y² + 49 is equal to [ ( y + i√7) (y - i√7 ) ]² .
As given in the question,
Given expression is :
y⁴ + 14y² + 49
Simplify the given expression to get the factors of it , we get ,
y⁴ + 14y² + 49
= y⁴ + 2 ( 7 )y² + ( 7 )²
= ( y² + 7 )²
Now convert the factors into complex numbers ,
= [ y² - (-1)(√7)²]²
We know that ( -1 ) = i²
= [ y² - ( i√7)² ]²
= [ ( y - i√7 )( y + i√7) ]²
Therefore, the complex numbers factors of the given expression is equal to [ ( y - i√7 )( y + i√7) ]².
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. The function f ( x ) = x 2 . The graph of g ( x ) is f ( x ) translated to the right 3 units and down 3 units. What is the function rule for g ( x ) ?
The function rule for g(x) is g(x) = (x - 3)² - 3
How to determine the transformation of g(x) from the parent function?From the question, we have the following function
f(x) = x²
Also, we have the following transformation statements:
f(x) is translated to the right 3 unitsf(x) is translated down 3 unitsFirst, we have: f(x) is translated to the right 3 units
This means that
g(x) = f(x - 3)
So, we have
g(x) = (x - 3)²
Next, we have: f(x) is translated down 3 units
This means that
g(x) = f(x - 3) - 3
So, we have
g(x) = (x - 3)² - 3
Hence, the transformation is g(x) = (x - 3)² - 3
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Simplify. Rewrite the expression in the form y^n. y^5/y^3=
Answer:
y^2
Step-by-step explanation:
a^m/a^n = a^(m - n)
y^5/y^3 = y^2
Givenf(x)=4x^2 - 1, and g(x) = 2x - 1, find g(f(2)).
Given f(x) = x^2 and g(x)=x - 1, write each composite function.State the domain of each:2.f(g(x)) 3.g(f(x))
The value of the function g(f(2)) is 29 and 2.f(g(x)) is (x - 1)(2x - 2).
What is a composite function?When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
Given, f(x) = 4x² - 1. and g(x) = 2x - 1.
Now, g(f(2)) is the output of f(2) is the input of g(x).
∴ f(2) = 4(2)² - 1.
f(2) = 15.
Now, g(f(2)) = 2(15) - 1.
g(f(2)) = 29.
Also given,
f(x) = x² and g(x) = x - 1.
Now, 2.f(g(x)).
2.f(g(x)) = 2.f(x- 1).
2.f(g(x)) = 2(x - 1)².
2.f(g(x)) = 2(x² - 2x + 1).
2.f(g(x)) = 2x² - 4x + 2.
2.f(g(x)) = 2x² - 2x - 2x + 2.
2.f(g(x)) = 2x(x - 1) - 2(x - 1).
2.f(g(x)) = (x - 1)(2x - 2).
There is no restriction to the domain of this quadratic function.
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The Johnson twins were born eight years after their older sister.
This year, the product of the three siblings' ages is exactly
1422 more than the sum of their ages. How old are the twins?
The age of the twins is 9 if the Johnson twins were born eight years after their older sister.
What are ages?When a ratio, such as p:q, is used to express age, qx and px are taken into account. The current age will be (xn) years if you assume the current age to be x. If you're assuming that x is the age you are now, then 1/n of your age will be equivalent to (x/n) years.
What are known as age problems are one use for linear equations. The ages of two separate persons (or objects), both present and future (or past), are typically compared for solving age-related problems. These issues typically seek to determine the current age of each subject.
Let the age of twins be x
The age of older sister be x+8
x(x)(x+8) = x + x + (x+8)+1422
x²(x+8) = 3x+1430
x³+8x² = 3x+1430
x³+8x²- 3x-1430=0
x=9.2045≈9
Therefore, the age of the twins is 9
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