The fourth term of the resulting four-term sequence is 206.
Let the four terms of the arithmetic sequence be a a+d, a+2d, and a+3d (where d is common difference)
Let the four terms of the geometric sequence be b, br, br^2, and br^3 (where r is the common ratio)
An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is always the same. The difference is called the common difference.
The resulting four-term sequence is a+b, a+d+br, a+2d+br^2, a+3d+br^3
Given that the first three terms of the resulting four-term sequence are 57, 60, and 91, we can set up the following equations:
a + b = 57
a + d + br = 60
a + 2d + br^2 = 91
By substituting the first equation into the second and third equations we get:
d + b(r-1) = 60 - 57 = 3
2d + b(r-1)^2 = 91 - 57 = 34
By substituting the first equation and the second equation into the third one we get:
2(3) + b(r-1)^2 = 34
6+b(r-1)^2 = 34
b(r-1)^2 = 28
Note that either b=28 or b=7. We proceed with casework:
If b=28, then r=2,a=29, and d=25.The arithmetic sequence is 29,4,-21,-46, arriving at a contradiction.
If b=7, then r=3,a=50, and d=-11.The arithmetic sequence is 50,39,28,17, and the geometric sequence is 7,21,63,189. This case is valid.
Therefore, The fourth term of the resulting four-term sequence is [tex]a+3d^{2}+br^{3}= 17 +189 =206[/tex].
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The hyperbolic orbit of a comet is represented on a coordinate plane with center at (0, 4). One branch has a vertex at (0, 10) and its respective focus at (0, 14). Which equation represents the comet's orbit
The equation of comet's orbit is [tex]\frac{(y-4)^2}{36} + \frac{x^2}{64}[/tex] =1
what is hyperbola?A hyperbola is a geometric shape made up of two branches that are symmetric about a center point and asymptotic to two lines called the asymptotes. It is defined by the equation (x^2/a^2) - (y^2/b^2) = 1. It is a type of conic section, similar to a parabola and an ellipse.
If the vertices and foci's of hyperbola have specified coordinates are of the form (0,10) and (0,14)
then
The y-axis serves as the transverse axis.
so
The formula for the equation is:
(y-k)^2/a^2-(x-h)^2/b^2=1
In this issue
The value of the center (h,k) is (0,4)
It follows that (0,a-k)) = (0,10)
a=10-4=6
(0,c-k) equals (0,14)
c=14-4=10
Identify b's value.
b^2=c^2-a^2
b^2=10^2-6^2
b^2=64
therefore
The formula reads as follows:
[tex]\frac{(y-4)^2}{36} + \frac{x^2}{64}[/tex] =1
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Lamonte has a bag that contains apple chews, strawberry chews, and lime chews. He performs an experiment. Lamonte randomly removes a chew from the bag, records the result, and returns the chew to the bag. Lamonte performs the experiment 34 times. The results are shown below:
An apple chew was selected 13 times.
A strawberry chew was selected 6 times.
A lime chew was selected 15 times.
Based on these results, express the probability that the next chew Lamonte removes from the bag will be apple chew as a percent to the nearest whole number.
The probability that the next chew Lamonte removes from the bag will be apple chew will be 38%
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur
In this case, Lamonte has a bag that contains apple chews, strawberry chews, and lime chews. He performs an experiment and then randomly removes a chew from the bag, records the result, and returns the chew to the bag.
Since Lamonte performs the experiment 34 times, the probability that the next chew Lamonte removes from the bag will be apple chew will be:
= 13 / 34
= 38%
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The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
1
1
a.
b.
c.
d.
y = f(x+3)
y = f(x-3)
y + 3 = f(x)
y-3 = f(x)
Answer:
the black graph is the graph of
y = f(x). Choose the equation for the
red graph.
1
1
a.
b.
c.
d.
y = f(x+3)
y = f(x-3)
y + 3 = f(x)
y-3=f(x)
Joseph has a bag filled with 2 red, 4 green, 10 yellow, and 9 purple marbles. Determine P(not yellow) when choosing one marble from the bag.
A. 8%
B. 24%
C. 40%
D. 60%
Answer:
D. 60
Step-by-step explanation:
Not yellow marbles are 15/25 = 60/100
Elijah currently owe a total of $2,127. 50 on hi revolving credit account. What i Elijah' debt-to-credit ratio if the total of hi revolving credit limit i $5,750. 00? Round the final anwer to the nearet whole percent. A
27%
b
37%
c
41%
d
50%
Elijah has a 41% debt-to-credit ratio. This means that for every $100 of available credit, he has used up $41. This ratio is calculated by dividing total debt by total credit limit.
Elijah's debt-to-credit ratio = Total Debt/Total Credit Limit
= $2,127.50/$5,750.00
= 0.37
= 37%
= 41% (rounded to the nearest whole percent)
Elijah's debt-to-credit ratio is a measure of how much of his available credit he has used. It is calculated by dividing his total debt by his total credit limit. In this case, Elijah currently owes a total of $2,127.50 on his revolving credit account, and his total credit limit is $5,750.00. When we divide his debit of $2,127.50 by his total credit limit of $5,750.00, we get a debt-to-credit ratio of 0.37. This is equivalent to 37%. When we round to the nearest whole percent, we get a debt-to-credit ratio of 41%. This means that for every $100 of available credit, Elijah has used up $41.
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pleae find perimeter and area!!!
Answer:
area: 576 cm ^2
perimeter: (48 + 24π) cm
Step-by-step explanation:
the semicircle taken out of the square (the white area) is equal to the semicircle added to the left of it. thus, we just have the area of a square. we know this because both have the same diameter and are semicircles. thus, our area is 24^2 = 576 cm ^2
for perimeter:
top: 24 cm
bottom: 24 cm
right: this is equal to half the circumference of a circle. this is because we know it's a semicircle taken out. circumference = πd = 24 * π. divide this by 2 to get 12π.
left: this is also equal to half the circumference of a circle = 12π
sum = 48cm + 24π
Consider the following statements. Select all that are always true.
The sum of a rational number and a rational number is rational.
The sum of a rational number and an irrational number is irrational.
The sum of an irrational number and an irrational number is irrational.
The product of a rational number and a rational number is rational.
The product of a rational number and an irrational number is irrational.
The product of an irrational number and an irrational number is irrational.
All of the statements are true.
hope this helps.
The following variances were calculated for two traits in a herd of hogs.Trait VP VG VABack fat 28.9 13.7 7.98Body length 49.1 27.2 12.4Part ACalculate broad-sense (H2 ) heritability for back fat in this herd.Enter your answer to three decimal places (example: 0.123).Part BCalculate broad-sense (H2 ) heritability for body length in this herd.Enter your answer to three decimal places (example: 0.123).Part CCalculate narrow-sense (h2 ) heritability for back fat in this herd.Enter your answer to three decimal places (example: 0.123).Part DCalculate narrow-sense (h2 ) heritability for body length in this herd.Enter your answer to three decimal places (example: 0.123).Part EWhich of the two traits will respond best to selection by a breeder?back fatbody length
Heritability is typically divided into two categories, namely broad sense and narrow sense heritability.
The following formulas are used to calculate heritability in the broad sense:
H² = Vg / Vp
Where,
H² = Heredity
Vg = Genotypic Variance
Vp = Phenotypic Variance
FOR BACK FAT:
Vg = 13.7
Vp = 28.9
H² = Vg / Vp
H² = 13.7 / 28.9
H² = 0.474
FOR BODY LENGTH:
Vg = 27.2
Vp = 49.1
H² = Vg / Vp
H² = 27.2 / 49.1
H² = 0.553
These formulas are used to calculate narrow sense heredity:
H² = Vg / Vp
Where,
H² = Heredity
Vg = Genotypic Variance
Va = Additive Genetic Difference
FOR BACK FAT:
Vp = 28.9
Va = 7.98
H² = Va / Vp
H² = 7.98 / 28.9
H² = 0.276
FOR BODY LENGTH:
Vp = 49.1
Va = 12.4
H² = Va / Vp
H² = 12.4 / 49.1
H² = 0.252
Because back fat has a high narrow sense of heredity and a low broad sense of heritability, it is the best pick. Additionally, heritability in the restricted sense has good breeding value.
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Find the length of side xx in simplest radical form with a rational denominator.x 1
10/√3 is the length of side x in simplest radical form with a rational denominator.
What is simplest radical form?The fundamentals of radical form are simple. When a number or algebraic expression is under a radical, the term refers to that form of the expression. To improve that, we can manipulate a number or an algebraic expression in radical form to convert it to simplest radical form.
Simply put, simplifying a radical eliminate any need to find more square roots, cube roots & fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.
The triangle is a right triangle, therefore we will apply trigonometry
To obtain the value of X which is the hypotenuse :
We know that
Cosθ = adjacent / hypotenuse
Cos 30 = 5 / X
√3/2 = 5 / X
√3 / 2 × X = 5
X = 5 ÷ √3 / 2
X = 5 × 2 / √3
X = 10/√3
Thus, 10/√3 is the length of side xx in simplest radical form with a rational denominator.
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the width is to be 14 feet less than 3 times the height. find the width and the height if the carpenter expects to use 28 feet of lumber to make it.
The width of the bookcase is 6 feet and height is 4 feet if the carpenter expects to use 28 feet of lumber to make it.
Let w = the width and h = the height of the bookcase. The width of the lumber you are using is not given.
Also, Let the height is x.
and, the width is 3x -14.
Since, we stated that this equals 28 feet and also that w = 3h - 14, we can insert this into the equation and use it to solve for h:
Now,
The total amount of lumber used to make the bookcase is:
L = 4w + 2h -------------------------- (1)
Now Putting Width and height in the Equation (1):
⇒ 28 = 4(3h - 14) + 2h
⇒ 28 = 12h - 56 + 2h
⇒ 28 = 14h - 56
⇒ 84 = 14h
⇒ h = 84/14
= 6 feet
Putting the value of height, h= 6 feet in
w = 3x -14
⇒ w = 3(6) - 14 = 4.
Therefore,
The width is 4 feet and the height is 6 feet.
Complete Question:
A bookcase is to have 4 shelves including the top as pictured below.
The width is to be 14 feet less than 3 times the height. Find the width and the height if the carpenter expects to use 28 feet of lumber to make it.
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PLS HEELP ME! I AM IN CLASS AND I DONT UNDERSTAND THIS
Answer:
it is not an option for the rest of your life with a new one of the year old girl who is the best friend and I have a great day to be a great day to be a great day to be a great 6
Step-by-step explanation:
or false hope I can I get to be a great day to be
In the diagram below, m∠A = 55° and m∠E = 35°. Which best explains the relationship between triangle ACB and triangle DCE?
The triangles are similar because all the pairs of corresponding angles are congruent. Therefore, the answer is D.
How to find similar triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
In a simpler term, similar triangle have the same shape but the sizes might varies.
Therefore, Let's check if ΔACB is similar to ΔDCE.
If two triangles have two of their angles equal, the triangles are similar.
Hence,
m∠A = 55 degrees
m∠E = 35 degrees
Therefore, using sum of angles of a triangle is 180 degrees,
∠ACE = ∠DCE = 90 degrees
m∠B = 35 degrees
Therefore,
m∠B = m∠E
∠ACE = ∠DCE = 90 degrees
Finally, the triangles are similar because al pairs of corresponding angles are congruent.
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Given that O is the center of the circle AB=40° CD=30° find <BCD
Answer:
Step-by-step explanation:
TO the center
What are the 4 types of slope from a graph?
Negative, positive, zero, and undefined are the 4 types of slopes from a graph.
Negative Slope: The line goes downward to the right as x increases, where m < 0.
Positive Slope: The line goes upward to the right as x increases, where m> 0
Zero Slope: A horizontal line has a slope of zero, m = 0
For any two points, the y values will be equal to the same real number. The equation will be y = some number. Ex:y=5
Undefined Slope: A vertical line has an undefined slope, m is undefined.
For any two points, the x values will be equal to the same real number. The equation will be x = some number. Ex=6
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The expression 62.4d-21062.4d−21062, point, 4, d, minus, 210 gives the number of Indian rupees you receive when you exchange \$d$ddollar sign, d at the local currency exchange.
How many Indian rupees do you receive when you exchange \$13$13dollar sign, 13?
The amount of Indian rupees that I would be able to receive when $13 is exchanged would be = 601.2
Indian rupees.
What is local currency exchange?Local currency exchange is defined as the exchange of a money currency from its local form to another form which depends of its current exchange rate.
From the expression given;
= 62.4d -210
Where d = $13, substitute into the given equation.
= (62.4 ×13) - 210
= 811.2 -210
= 601.2
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How do you find the number of ways of dealing a five-card hand from a regular 52 card deck, such that the hand contains at least one card in each suit?
The number of ways of dealing a five-card hand from a regular 52-card deck, such that the hand contains at least one card in each suit is 2,593,812
What is the combination?
In simple words, combination involves the selection of objects or things out of a larger group where order doesn't matter. The formula for combination helps to find the number of possible combinations that can be obtained by taking a subset of items from a larger set.
In order to find the number of ways of dealing with a five-card hand from a regular 52-card deck, such that the hand contains at least one card in each suit, we can use the combination formula.
The combination formula is used to find the number of ways to select a certain number of items from a larger group without regard to order.
First, we need to find the total number of ways to select 5 cards from a 52-card deck.
This is given by the combination formula: nCr = n! / (r!(n-r)!)
Where n is the total number of items (52) and r is the number of items to be selected (5).
So, nCr = 52! / (5!47!) = 2, 598, 960
Now we need to subtract the number of ways to select a hand that doesn't contain at least one card of each suit.
We can select 4 cards from one suit and only one card from another suit in 4C1 * 48C4 ways = 448454239/24 = 5148.
Now we can subtract this number from the total number of ways to select 5 cards from a 52-card deck to find the number of ways to select a five-card hand that contains at least one card in each suit:
2598960 - 5148 = 2,593,812
Hence, the number of ways of dealing a five-card hand from a regular 52-card deck, such that the hand contains at least one card in each suit is 2,593,812
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A telephone calling card allows for$0.25 per minute plus a one-time service charge of $0.75. Write and solve an equation to find the number of minutes you can use the card if the total amount on the card is $5
The linear function that models the problem of telephones call service is
y = $5 - $0.25x + $0.75How to model the required equationA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
The problem is represented using linear function as follows
c = $5
m = $0.25 per minute
x = minutes of calls
y = $5 - $0.25x + $0.75
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Okay so basically help and say what to label with and whoever says it I’ll give brainly or wtv
Answer:
The area is 254.34 [tex]yds^{2}[/tex]
The circumference is 56.52 yards.
Step-by-step explanation:
a = [tex]\pi r^{2}[/tex]
a = (3.14) ([tex]9^{2}[/tex])
a = 3.14(81)
a = 254.34
The area is 254.34 [tex]yds^{2}[/tex]
c = 2[tex]\pi[/tex]r
c = 2(3.14)(9)
c = 56.52
The circumference is 56.52 yards.
How many complex roots does a 5th degree polynomial have?
A 5th degree polynomial have five complex roots. This means that the polynomial can be written as the product of five linear or quadratic polynomials.
The general formula to calculate the roots of a 5th degree polynomial is:
[tex]x^5 + ax^4 + bx^3 + cx^2 + dx + e = 0[/tex]
The roots of the polynomial can be found by solving the following equation:
[tex]x^4 + (a - x)x^3 + (b - a x + x^2)x^2 + (c - bx + ax^2 - x^3)x + (d - cx + bx^2 - ax^3 + x^4) = 0[/tex]
To calculate the roots of the polynomial, we need to solve the quartic equation, which can be done by using the quadratic formula. Then, we can use the solutions of the quartic equation to find the roots of the 5th degree polynomial.
For example, if we have the polynomial x^5 + 2x^4 + 3x^3 + 4x^2 + 5x + 6 = 0, then the roots can be calculated as follows:
x1 = -1.7177
x2 = -0.3181
x3 = 0.5813
x4 = 1.2520
x5 = 2.1771
These are the five complex roots of the polynomial.
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Given rectangle MNOP below, NQ = 65. If MO = -6x+10, solve for x.
Answer:
x= -9.17
Step-by-step explanation:
To solve for x, we can use the information provided about the rectangle to set up an equation. Since opposite sides of a rectangle are congruent (have the same length), we know that MO = NP.
Therefore, we can set up the equation:
-6x + 10 = 65
To solve for x, we can subtract 10 from both sides:
-6x = 55
And then divide both sides by -6:
x = -9.17
the histogram above e shows the distribution of the number of abenses from school during one month in a class
The histogram shows that the majority of the students had between 0 and 5 absences. There were some students with 6 to 10 absences, and a few students with 11 to 15 absences. There were no students with more than 15 absences.
1. The histogram shows a distribution of the number of absences from school during one month in a class of 30 students.
2. The data is divided into frequency intervals of 1, meaning that each interval represents the number of students with a certain number of absences.
3. The highest frequency interval is between 0 and 5 absences, indicating that the majority of the students had between 0 and 5 absences.
4. The second highest frequency interval is between 6 and 10 absences, indicating that there were some students with 6 to 10 absences.
5. The third highest frequency interval is between 11 and 15 absences, indicating that there were a few students with 11 to 15 absences.
6. There were no students with more than 15 absences, as there is no frequency interval for numbers higher than 15.
the complete question is : the histogram above e shows the distribution of the number of abenses from school during one month in a class of 30 students. The data is divided into frequency intervals of 1.
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what is the mean absolute deviation of the following set of data 8 2 12 10 2 6 12 20?
sum all the following and divided it my 8
What principal you have to deposit in a 4.5% savings account compounded monthly in order to have a total of 100,000 after 8 years?
Answer: Please use this method
Periods N = 8 years x 12 = 96 periods
The interest rate I = 4.5 % per year, compounding, divided by 12 = 0.375 % for each period.
Present value PV = minus $ 6,981.46
Future value FV = $ 10,000.20
Step-by-step explanation:
One pipe can fill and drain the pool at a rate that is 1 more than 2 times faster than the other pipe. If both pipes are open and working properly, it will take 3.5 hours to fill the pool.
So the time taken to fill the pool by the slower pipe is 30 hours .
As mentioned about the time in the question stated below.
Let the slower pipe's time be x and the quicker pipe's time be x/2.
By slower pipe in an hour = 1/x, quicker pipe in an hour = 2/x, and by both = 1/10.
2/x+1/x = 1/10
we have to take reciprocal of the time taken by each pipes.
(1+2)/x = 1/10
=> 3/x = 10
=> x= 30
The slower pipe requires 30 hours of times to completely fill the pipe.
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Complete question:
A single pipe can fill a pool twice as quickly as a second one. The pool will be filled in ten hours once both pipes are opened. If only the slower pipe is utilized, how long would it take to fill the pool?
What is the equation of the line that passes through the point (−6,4) and has a slope of 0?
Answer:
Below
Step-by-step explanation:
A line with a slope of 0 is a HORIZONTAL line
to include the point (-6,4) the equation would just be
y = 4
What is a formula example?
Formula is an act or rule that uses mathematical symbols.
Equations, equalities, identities and inequalities are a few examples of formula.
An equation, also known as an equality, formula, or identity, is a mathematical phrase that states that two or more quantities are equal to one another.
A declaration of the mathematical equivalence of two quantities. The similarity A=B signifies that "A is equal to B."
A mathematical relationship that equalizes one quantity to another is known as an identity (which may initially appear to be different).
A proof in mathematics that one quantity is bigger or smaller than another A>b is used to indicate "A is bigger than B," whereas A<B is used to indicate "A is smaller than B." The symbols A<=B and A>=B stand for "A is less than or equal to" and "A is greater than or equal to B" respectively. The terms "A is much less than B" and "A is much more than B," respectively, are denoted by the symbols A<<B and A>>B.
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Jessica's hamster cage is shaped like a rectangular prism. The cage has a height of 24 inches and a volume of 6,480 cubic inches. Jessica puts a piece of paper on the bottom of the cage. The paper fits the bottom of the cage perfectly. What is the area of the paper on the bottom of the cage
As per the given measurement , the area of the paper on the bottom of the cage 2736 square inches.
The formula to calculate the volume of the prism is written as
V = l x w x h
Where l refers the length , w refers the width and h refers the height.
Here we have know that the height of 24 inches and a volume of 6,480 cubic inches.
Now we have to apply the values on the formula in order to get the width of the cage,
=> 6480 = w x 24 x 12
=> w = 6480/288
=> W = 22.5
Therefore, the area of the bottom of the cage is calculated as,
=> A = 2[(24 x 22.5) + (24 x 12) + (22.5 x 24)]
When we simplify this one then we get the value of the area as,
=> A = 2736 square inches.
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Determine the convergence set of the given power series. n = The convergence set is . (Type your answer in interval notation.) Find a power series expansion for f'(x) given the expansion for f(x). n=2 rw= n=3 Find the power series expansion X anx" for f(x) + g(x), given the expansions for f(x) and g(x). n=0 19 = E 2*. * = 571 n=0 n=1 The power series expansion for f(x) + g(x) is .
The convergence set of the given power series is the set of all values of x in the interval (-|x-7|, |x-7|).
In order to determine the convergence set of the given power series, we can use the ratio test.
The ratio test states that if the limit as n goes to infinity of the absolute value of aₙ₊₁ / aₙ is less than 1, then the series converges for all x in the interval (-R, R) where R is the reciprocal of the limit.
The given power series is:
sigma n = 1 to infinity (17/ (n² + 5n))×(x - 7)ⁿ
We can apply the ratio test as follows:
aₙ₊₁ / aₙ = |(17/(n+1)² + 5(n+1))×(x - 7)⁽ⁿ⁺¹⁾ | / |(17/ (n² + 5n))×(x - 7)ⁿ|
aₙ₊₁ / aₙ = |(17/(n+1)² + 5(n+1))/(n² + 5n) × |(x - 7)|⁽ⁿ⁺¹⁾ | / |(x - 7)|ⁿ
As we can see the limit as n goes to infinity of the absolute value of
aₙ₊₁ / aₙ = |(x - 7)|
Let R = |x - 7|, therefore, the series converges for all x in the interval (-R, R)
So the series converges for all values of x in the interval (-|x-7|, |x-7|).
--The given question is incomplete, answering to the question below--
"Determine the convergence set of the given power series.
sigma n = 1 to infinity ( 17/ (n² + 5n))×(x - 7)ⁿ"
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Someone please help me as fast as you can!!
I would really appreciate it!
Select all situations that could be represented by a graph with a Y -intercept of 10 .
The situations that could be represented by a graph with an y-intercept of 10 is given as follows:
A. Sign up fee of $10.
B. Lilly starts with $10 in her savings account.
E. Tank begins with 10 gallons of water.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the initial amount.Hence options A, B and E are the correct options as they have an initial amount of $10.
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