The number that belongs to both sequences is 26.
The formula known as the nth term allows us to locate any term in a series. The letter "n" stands for "number."
By changing the term number's value, we can create a series that uses the nth term (n).
To find the 10th term we would follow the formula for the sequence but substitute 10 instead of ‘n‘; to find the 50th term we would substitute 50 instead of n.
We have two sequences, let's call one as A and the other as B.
The n-th term of sequence A is written as:
aₙ = 3*n^2 - 1
the nth term of sequence B is written as:
bₙ = 30 - n^2
We want to find a term that belongs to both sequences, (it can be for different integers, we can use n for sequence A and x for sequence B)
Then we want to find:
aₙ = bₓ
where n and x are integer numbers.
Then we will heave:
3*n^2 - 1 = 30 - x^2
To find the pair, we could isolate one of the variables, then input different integers in the other variable and see if the outcome is also an integer.
Let's isolate n.
3*n^2 = 30 - x^2 + 1
3*n^2 = 31 - x^2
n^2 = (31 - x^2)/3
n = √( (31 - x^2)/3)
Now let's input different values for x, and see if the outcome is also an integer, notice that x is in a negative term inside a square root, then we have only a few values of x such that the equation can be true.
Then let's start with x = 1.
n(1) = √( (31 - 1^2)/3) = √(30/3) = √10
We know that √10 is not an integer.
now with x = 2,
n(2) = √( (31 - 2^2)/3) = √( (31 - 4)/3) = √(27/3) = √9 = 3
then if x = 2, we have n = 3.
Both of them are integers, then we get:
a₂ = 3*(3)^2 - 1 = 27 - 1 = 26
b₃ = 30 - 2^2 = 30 - 4 = 26
Therefore, The number that belongs to both sequences is 26.
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8. Given DF bisects LEDF, find n and then find FG. The diagram is not drawn to scale.
2 points
Show your work to find FG
Show your work to find n
GIVING 20 POINTS!!
The measure of length of FG is 105 units.
What is bisection?
To determine the roots of a polynomial problem, utilise the bisection method. It splits and separates the interval in which the equation's root is located. The continuous functions intermediate theorem serves as the method's guiding premise.
From the given diagram, since Line DF bisects angle EDG, then -
EF = FG
Given the following parameters -
EF = 9n - 3
FG = 8n + 9
Equating both expressions -
9n - 3 = 8n + 9
9n - 8n = 9 + 3
n = 12
Get the measure of FG -
FG = 8n + 9
FG = 8(12) + 9
FG = 96 + 9
FG = 105
Hence, the line FG measures as 105 units.
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Please help me!
Will give you brainlist!!!!
y-int coordinates of y=x^2-5x+6, please explain
The y intercepts of the quadratic equation y = x² - 5x + 6 is given by (0 , 6)
and the x intercepts are ( 3 , 0 ) and ( 2, 0 )
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
y = x² - 5x + 6 be equation (1)
On simplifying the equation , we get
y = x² - 2x - 3x + 6
Taking the common factors of the equation , we get
y = x ( x - 2 ) - 3 ( x - 2 )
On factorizing the equation , we get
y = ( x - 3 ) ( x - 2 )
To find the y intercepts , substitute the value of x = 0 , we get
y = ( 0 - 3 ) ( 0 - 2 )
y = ( -3 ) ( -2 )
So , y = 6
Hence , the y intercepts of the equation is ( 0 , 6 )
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How do you solve a 3 variable 2 equation?
The process of solving the 3 variable with 2 equation is explained below.
The term equation is defined as a relationship between two terms on either side of an equal sign.
Here we have the following steps to solve the 3 variable for two equation is solved accordingly.
First of all we have to take any two equations and solve it for one variable.
And then again we have to take another two pair of equations and solve for the same variable.
Now, we have a system of two equations with two unknown variables.
Then we have to solve the equation by using the appropriate arithmetic operations.
and then substitute it accordingly until all the value of the variable are solved.
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The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system.
[1 7 3 -5]
[0 0 0 3]
[0 0 1 2]
[0 1 -1 4]
Select the correct choice below and; if necessary; fill in the answer boxes to complete your choice A: The solution set has exactly one element; (Type integers or simplified fractions B. The solution set has infintely many elements C. The solution set is empty:
For the given Augmented Matrix ,the correct option is :
A) The solution set has exactly one element.
The exact solution is x = -25 , y = 2 and z = 2.
Augmented Matrix:
An augmented matrix is a means of solving simple linear equations. Coefficients and constant values of linear equations are represented as matrices called augmented matrices. Simply put, an augmented matrix is a combination of two simple matrices along columns. If the first matrix has m columns and the second matrix has n columns, then the augmented matrix has m + n columns.
Now, as given the Augmented matrix:
[1 7 3 -5]
[0 0 0 3]
[0 0 1 2]
[0 1 -1 4]
From this system we get:
y - z = 4 --------------------------- (1)
z = 2
and, z = 3
and, x + 7y + 3z =-5 ---------------- (2)
Now, Solving the equation with z = 2,
y - 2 = 4
⇒ y = 6
and, putting y = 6 and z = 2
x + 7× 6 + 3×2 = -5
⇒ x + 42 + 6 = -5
⇒ x +48 = -5
⇒ x = -53
Therefore, x = -53, y=6 and z =2
Now, for z = 3 in equation (1)
y - 3= 4
⇒ y = 7
Putting y =7 and z =3, we get:
x + 7 × 7 + 3×3 = -5
⇒ x + 49 + 9 =-5
⇒ x + 58 = -5
⇒ x = -63
Therefore, x = -63, y =7 and z =3
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HIJK is a square and KI = 6√2. Find HI
The length of HI will be;
⇒ 6 units.
What is Pythagoras theorem?The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given that;
HIJK is a square.
The length of KI = 6√2
Now,
Since, HIJK is a square.
Hence, There are all sides are equal.
Let the side of square = x
So, By Pythagoras theorem, we get;
⇒ KI² = HI² + HK²
Substitute the given values, we get;
⇒ (6√2)² = x² + x²
⇒ 72 = 2x²
⇒ x² = 36
⇒ x = √ 36
⇒ x = 6
Thus, The length of HI = 6 units
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Pula need to make an 80% on her test to pass the class. she has 25 questions on the test. How many does she need to get correct
Answer:
Step-by-step explanation:
25×80%=20
so she need to get 20 questions right
Answer:
20
Step-by-step explanation:
total question: 25
marks need to pass: 80%
25-20% = 20
What is the discriminant of 3x^2 2x 1 0?
The discriminant of quadratic equation 3x^2 + 2x + 1 =0 is -8
We know that the standard form of quadratic equation is ax^2 + bx + c = 0, with a ≠ 0
The discriminant of quadratic equation ax^2 + bx + c = 0 is:
D = b^2 - 4ac
Comparing given quadratic equation 3x^2 + 2x + 1 =0 with ax^2 +bx + c = 0 we get,
a = 3, b = 2 and c = 1
So, the discriminant of given equation would be,
D = b^2 - 4ac
D = 2^2 - 4(3)(1)
D = 4 - 12
D = -8
Therefore, the discriminant is D = -8
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1. From the information given in the triangles, are these triangles always, sometimes, or never congruent?
A. always
B. sometimes
C. never
D. cannot be determined
On solving the provided question, we can say that - the both triangle similar triangle ABC and triangle DEF
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
here,
AB = DE
BC = EF
AC = DF
so, by SSS both triangles are similar
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using multiple properties of exponents simplify the expression
2a^3b^-4/3a^5b^-2
2a³b⁻⁴/3a⁵b⁻² = 2/3(ab)²
What are exponents?The exponent of a number shows how many times the number is multiplied by itself.
Example: 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power."
In general, xⁿ means that x is multiplied by itself for n times.
Properties of exponents:
Law of Product: a ^m × a ^n = a ^(m + n)
Law of Quotient: a ^m/a ^n = a ^(m - n)
Law of Negative Exponent: a^-m = 1/a ^m
Law of Power of a Product: (ab)^m = a ^m . b ^m
Law of Power of a Quotient: (a/b) ^m = a ^m/b ^m
Given expression
2a³b⁻⁴/3a⁵b⁻²
= 2/3 . a³/a⁵ . b⁻⁴/b⁻²
Law of Negative Exponent: [tex]a^{-m} = 1/a^{m}[/tex]
= 2/3 . a³/a⁵ . b²/b⁴
Law of Quotient: [tex]a^{m} /a^{n} = a^{m-n}[/tex]
= 2/3 . a³⁻⁵ . b²⁻⁴
= 2/3 . a⁻² .b⁻²
Law of Power of a Product: [tex]a^{m} .b^{m}= (ab)^{m}[/tex]
= 2/3 . (ab)⁻²
Law of Negative Exponent: [tex]a^{-m} = 1/a^{m}[/tex]
= 2/3 . 1/(ab)²
= 2/3(ab)²
Hence the simplified expression of 2a³b⁻⁴/3a⁵b⁻² is 2/3(ab)².
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Molly and Liza are exercising. Molly does
10 push-ups at the same time
as Liza
does 15 push-ups. When Molly does
40 push-ups, how many push-ups does
Liza do?
Answer:
25
Step-by-step explanation:
so molly and liza are exercising right?.so 10 push-ups at the same time wich means they do 10 push-ups together and liza push-ups 15 and molly does 40 pushups so. its addition so 10+15=25 so thats the answer.
Suppose that $a$ is a multiple of $3$ and $b$ is a multiple of $6$. Which of the following statements must be true? A. $b$ is a multiple of $3$. B. $a-b$ is a multiple of $3$. C. $a-b$ is a multiple of $6$. D. $a-b$ is a multiple of $2$. List the choices in your answer separated by commas. For example, if you think they are all true, then answer "A,B,C,D".
The statements that are true, based on the multiples of 3 and 6 are:
A. $b$ is a multiple of $3$. B. $a-b$ is a multiple of $3$. How do multiples relate ?When a number is a multiple of a smaller number, then all the multiples of that larger number, will be the multiples of the smaller number.
This means that all the multiples of 6 ( including b ) will be multiples of 3 as well because 6 is a multiple of 3.
It is also interesting to note that the difference between the multiples of 3 are also multiples of 3. This means that a - b will result in a number that is a multiple of 3.
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1. What is the measure of angle ABE?
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2. Select all true statements about the figura
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A
B
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40°
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The solution is 40°
The measure of the angle ∠ABE = 40°
What are Parallel Lines Cut by Transversal?Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
Let the angle be represented as ∠ABE
Now , let the line be EBC and the total angle of a straight line = 180°
And , the measure of ∠CBD = 40°
Since , ∠ABE and ∠CBD are vertically opposite angles ,
The measure of ∠ABE = measure of ∠CBD
Therefore , the value of ∠ABE = 40°
Hence , the measure of vertically opposite angle ∠ABE = 40°
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Boxes A and B contain some counters.
6y + 2
counters
Box A
Clip A19b
4y + 6
counters
Box B
The number of counters in each box is the same.
Work out the value of y
Find a Clip
106
Please give me the answer it’s really hard no one will help
By simple algebra, The number of counters in each box is 2.
What is Algebra?Algebra is the study of mathematical symbols and the methods for incorporating them into formulas.
Why is algebra so difficult?Since algebra is the first math subject most students take where they must deal with variables, complex concepts, and problem-solving abilities, many find it scary.
Given,
counter in Box A = 6y+2
counter in Box b=4y+6
Since there are the same amount of counters in both boxes.
hence
6y+2=4y+6
6y-4y=6-2
2y=4
y=2
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A bag contains:
1 red beads
2 yellow beads
2 green beads
1 blue bead
A bead is chosen at random.
What is the probability that it is green?
What is the probability that it is green or yellow?
Pls pls help!
I'll give you brainliest answer!
Thx!
The probability to draw a green bead is 1/3 and the probability to draw a green or yellow bead is 2/3
It is given that the bag contains 1 red bead, 2 yellow beads, 2 green beads, and 1 blue bead.
Hence the total no. of beads in the bag = no. of red + yellow + green + blue beads
= 1 + 2 + 2 + 1 beads
= 6 beads.
Let the event to draw a green bead be A
Let the event to draw a yellow bead be B
Probability of any event = no. of outcomes favorable to that event/ total number of outcomes
Hence P(A) = no. of green beads/ total no. of beads
= 2/6
= 1/3
Hence the probability that a green bead is drawn is 1/3
P(B) = no. of yellow beads/ total no. of beads
2/6 = 1/3
We need to find P(A or B)
= P(A U B) = P(A) + P(B) - P(A ∩ B)
P(A ∩ B) = P(A and B)
Since no bead is of 2 colors, P(A ∩ B) = 0
Hence we get
P(A U B) = 1/3 + 1/3
= 2/3
Hence the probability to draw a green or yellow bead is 2/3
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The three steps which Patel could use to solve the quadratic equation include the following:
A. 8(x² + 2x + (2/2)²) = -3 + 8.
B. x = -1 ±√5/8
E. 8(x² + 2x) = -3.
How to solve the quadratic equation?In order to solve the given quadratic equation, we would use the completing the square method as follows;
Separating the variables in the quadratic equation from constant, we have the following;
8x² + 16x + 3 = 0
8x² + 16x = -3
By factorizing the common variables in the quadratic equation from constant, we have the following;
8(x² + 2x) = -3 (step 1).
By completing the squares in the brackets and then balancing the expression on the right-hand side, we have the following;
8(x² + 2x + (2/2)²) = -3 + 8 (step 2).
8(x² + 2x + 1) = -3 + 8
8(x + 1)² = 5
Dividing both sides of the quadratic equation by 8, we have the following;
(x + 1)² = 5
Taking the square root of both sides of the quadratic equation, we have the following;
(x + 1) = ±√5/8
x = -1 ±√5/8 (step 3).
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Does anyone know the question to this ?? :(
Answer:
The ratio of the new area to the old area will be 16:1
Step-by-step explanation:
I remember learning this in class. The radius is quadrupled, which means the radius is 4 times bigger. This will make the new area 16 times bigger than the old area.
Let's check
Area of circle: 3.14 x r^2
Area of the circle when radius 6:
3.14 (6)^2 = 113.04 ft^2
Area of the new circle when the radius is quadrupled:
3.14 (24)^2 = 1808.64 ft^2
1808.64 divided by 113.04 = 16
So, the ratio of the new area to the old area will be 16:1
How to do log2 in Excel?
The syntax for using BASE in Excel is "=LN(number,base)" where "number" is the number for which you want to calculate the logarithm and "base" is the base to which the logarithm should be calculated.
For example, if you want to calculate the logarithm of 10 to the base 2, you would use the formula "=LN(10,2)".
The idea is to express the given integer (20) in terms of either the base or the values given (3 and 5).
Next, since we have the multiplication sign, we use the addition law:
The power of the number becomes the product of the log, so we have:
When you have the same base and number, the result is always 1.
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Write the standard equation of the circle.
PLEASE HELP DUE TN 01/06
GEOMETRY B
Answer:
Center: = (-1,-3)
Radius: = 1
Step-by-step explanation:
A school wants to buy a chalkboard that measures 1 meter by 2 meters. The chalkboard costs $31.00 per square meter. How much will the chalkboard cost?
Answer:
62$
Step-by-step explanation:
Board in square meters = 2×1 = 2 m²
Cost per square meter = $31.00
Total cost = 31×2 = $62.00
Answer:
The cost of the chalkboard is $27.74
Step-by-step explanation:
right!!
Solve for w
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions
53w+13<56w+16
Can someone help me solve this?
The value of x is 15 units and the value of y is 12 units from the given figure.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
From the figure, AB is parallel to CD.
∠AOB=∠COD (Vertically opposite angles)
∠OAB=∠ODC (Alternate angles)
By AA similarity ΔAOB similar to ΔCOD
Now, 9/x =y/20 =3/5
9/x=3/5
x=15 units
y/20=3/5
y/4=3/1
y=12 units
Therefore, the value of x is 15 units and the value of y is 12 units from the given figure.
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-2y - 10 = x -10x
- y = −14
Answer:
Step-by-step explanation:
-2y-10=x-10x
-2(-14) - 10= x - 10x
28 - 10 = x - 10x
18= x-10x
18= -9x
/-9 /-9
-2=x
Each side when you plug in (-2) for x and (-14) for y you get 18.
If, when you plug in the number, you get different numbers for each side, then that means there's a mistake and the answer is wrong.
Hope this helps!
tomatoes cost 1.19 per pound which equation best represents y the total cost of x pounds of tomatoes
Answer:y=1.19x
Step-by-step explanation: Since each pound of tomato costs 1.19, you multiple the price by the amount of pounds to get the total cost.
BRAINLIEST FOR THIS QUESTION
A shop sells orange juice in the following ways: 500 ml bottle for £1.40 2 litre carton for £2.50 each or 2 cartons for £4.50 3 litre carton for £3.50 What's the cheapest way of buying exactly 7 litres with no extra? Find the amount of each type of bottle or carton you need and the total cost of buying 7 litres.
The cheapest way of buying exactly 7 litres with no extra is buying 500 ml bottle for £1.40
The amount of buying 7 litres of orange juice at the cheapest buy is £2.52
What is the cheapest buy?500 ml bottle for £1.40
Convert ml to liters:
500 ml = 0.5 liters
Unit rate = 0.5/1.40
= £0.36 per liter
2 litre carton for £2.50
Unit rate = 2/2.50
= £0.8 per liter
2 cartons for £4.50
Unit rate = 2/4.50
= $0.44 per carton
3 litre carton for £3.50
Unit rate = 3 / 3.50
= £0.86 per liter
The cheapest buy per liter of the orange juice is buying 500 ml bottle for £1.40.
Therefore, the cost of 7 liters at the cheapest buy
= £0.36 per liter × 7
= £2.52
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What is 2 point midpoint?
The 2-point midpoint formula is a method for finding the equation of a line that passes through the midpoint of two given points.
The formula for the 2-point midpoint is:
y - y1 = m(x - x1)Where (x1, y1) and (x2, y2) are the two given points, and m is the slope of the line.
The slope of line is calculated by (y2-y1)/(x2-x1)
By using the midpoint of two given points, the 2-point midpoint formula eliminates the need for calculating the y-intercept of the line, which can save time and effort. It is particularly useful when working with geometric figures or real-world applications that involve moving objects or changing data. It also helps in predicting the values of future point when we know the past point.
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Vivian and her dad drive 4 hours to the rock and roll hall of fame in Cleveland, Ohio. if they drive at the same rate how far do they travel.
Vivian and her dad travelled for a total distance of 12 miles
How to determine how far they travelFrom the question, we have the following parameters that can be used in our computation:
Time taken = 4 hours
Rate of travel = 3 miles per hour
The distance travelled can be calculated using the following equation
Distance = Rate of travel * Time taken
Substitute the known values in the above equation, so, we have the following representation
Distance = 3 miles per hour * 4 hours
Evaluate the product
So, we have the following representation
Distance = 12 miles
Hence, the distance is 12 miles
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Complete question
Vivian and her dad drive 4 hours to the rock and roll hall of fame in Cleveland, Ohio. if they drive at the same rate how far do they travel if the rate is 3 miles per hour
Selena has 9 homemade bracelets for $12 each then 14 bracelets for $8 each. How much did she make in sales?
(Use the correct operation or combination of operations to solve the problem)
She will make a total profit of $220. Profits are amounts of money paid to a person with the right of immediate occupation for using the land when no permission has been granted for that use.
What are the different types of profit?Profit is the term used to describe the monetary gain experienced when the revenue from a commercial activity outpaces the costs, costs, and taxes incurred to support the activity in question. There are three primary ways to measure profit. These include operating profit, net profit, and gross profit. Gross profit and operating profit are indicators of how efficiently your company uses its resources to produce its goods and run day-to-day operations.
number of bracelets sold for $12 each=9
number of bracelets sold for $8 each=14
Total profit=9x12+8*14=$220
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I really need help on this one too
The solution is Option C and Option D.
The exponential function is given by f ( x ) = 2 ( 3 )ˣ
The exponential function is given by f ( x ) = 800 / 4ˣ
What are the laws of exponents?
When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 7 , 19 , 31 , 43 }
The equation of line is y = 12x + 7
This is a linear equation
b)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 5 , 10 , 15 , 30 }
The equation is a quadratic equation
c)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 2 , 6 , 18 , 54 }
The equation is y = 2 ( 3 )ˣ
This is an exponential function
d)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 800 , 200 , 50 , 12.5 }
The equation is f ( x ) = ( 800 / 4ˣ )
This is an exponential function
Hence , the exponential equations are solved
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Kate has $400. She wants to have $430 to buy a couch. How much interest would she have to earn in order to get the additional $30?
Select the best answer from the choices provided.
A. 3%
B. 4.5%
C. 6%
D. 7.5%
Answer:
D) 7.5%
Step-by-step explanation:
We can solve this through guessing and checking, or we can do this mathematically. We will try both approaches.
Mathematically:
We know that to get the extra $30 if we have $100, is a 30% interest. Now, since we have 4x 100, and these numbers are inversely proportional, we will need to divide 30 by 4. Doing this gives us 30/4 = 7.5, so the answer is 7.5%.
Guess and Check:
This way is a bit slower, but we will go through each answer and find how much money we would get from them. So, we would take our percent, change it to a number of that percent, considering we are taking it from 100, and multiply it by 4 since we have $400. We will get each of these respectively:
A) 3% = 3 * 4 = $12
B) 4.5% = 4.5 * 4 = $18
C) 6% = 6 * 4 = $24
D) 7.5% = 7.5 * 4 = $30
As you can see, D) gives us that extra $30, so the answer is D) 7.5%.
Hope this helped!