Since the year 2000 I've collected statues of frogs, and now that my family knows this, I get the same number of frogs every year. In 2010 I owned 104 frog statues, and in 2014 I owned 136 frog statues. Let x be the years since 2000, and y be the number of frog statues I own. Find an equation for the number of frog statues Town in a given year, and then use your equation to find the number of statues I had in 2000 when I started my collection, and the number of frog statues I expect to own in 2025.
Answers
Our equation model will be of the form.
y= ax +b, let us use known values to get a and b
In 2010, you owned 104 frog statues, here, x = 2010 - 2000 = 10, y=104
so 104 = 10a + b
In 2014, you owned 136 frog statues, here, x = 2014 - 2000 = 14, y = 136
so, 136 = 14a + b.
Lets solve this system of equation simultaneously,
136 = 14a + b ---1
104 = 10a + b ---2
Subtract equation 2 from 1, we have
32 = 4a, a = 32/4 = 8
Plug 8 into equation 1
136 = 14(8) +b , b = 136 - 112 = 24
So, our equation is ,
y = 8x + 24
1. in 2000, x = 0, we have y = 8(0) + 24 = 24 frog statues, meaning that you started your collection with 24 frog statues.
2. in 2025, x = 25, thus y = 8(25) +24 = 224 frog statues you expect to own.
Related Questions
rename 3.5 as a mixed number
Answers
Answer:
3 1/2
Step-by-step explanation:
.5 equals one half or 1/2
3.5 equals 3 1/2
Answer:
3 ½
Step-by-step explanation:
when you convert your decimal to a mixed number it is the easiest to find a common value of it. if you take ½ and turn it into a decimal it would be .5 or 50/100. its all about finding the lowest common denominator
A grid that represents 1 whole , what would you shade for 0.4 and 0.04? 100 squares in rows of 10.
Answers
The diagram shows a prism. Draw the front and side elevation of the prism on the grid. Use the scale 2 squares to 1m.
I know that the side elevation is correct but I can't get the front. Please help!
Answers
The sketch of the front elevation and the side elevation of the prism are added as an attachment
How to draw the front elevation and the side elevation of the prismFrom the question, we have the following parameters that can be used in our computation:
The prism
Using the figure as a guide, we understand that:
The front elevation is a rectangle of 2m by 0.5m
While the side elevation is a rectangle merged with a trapezoid
Next, we draw the elevations (see attachment)
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Hi there please help :)
Answers
Answer:
∠ a = 30° , ∠ b = 90°
Step-by-step explanation:
∠ a and 150° are a linear pair and sum to 180° , that is
∠ a + 150° = 180° ( subtract 150° from both sides )
∠ a = 30°
------------------
the sum of the 3 angles in a triangle = 180° , that is
∠ b + ∠ a + 60° = 180°
∠ b + 30° + 60° = 180°
∠ b + 90° = 180° ( subtract 90° from both sides )
∠ b = 90°
There are 30 red marbles, 16 blue marbles, and 14 green marbles in a jar.
What is the probability of picking out a red marble without looking?
30%
50%
23%
0 27%
Answers
Answer:
B or 50%
Step-by-step explanation:
First, you add all of them together
30 + 16 + 14 = 60
Then you do the part/whole
30/60 = 1/2
1/2 = 50%
Find BD if AC = 47 yards
Answers
9514 1404 393
Answer:
21 yards
Step-by-step explanation:
The area of a quadrilateral with diagonals that are right angles to each other is given by ...
A = (d1)(d2)/2 . . . . where d1 and d2 are the lengths of the diagonals
493.5 yd² = (47 yd)(BD)/2 . . . . . . . . . . fill in the given information
Dividing by the coefficient of BD, we have ...
(2)(493.5 yd²)/(47 yd) = BD = 21 yd
Please help me !!!
Question 1 of 15
Which algebraic rule describes the translation of quadrilateral HIJK to
quadrilateral HTJK?
79
199
K
23456
H
OA. (x,y)
(x+6, y+4)
OB. (x, y)
(x+1, y-2)
OC. (x,y) - (x+1, y-8)
OD. (x, y) - (x-8, y+1)
Answers
The algebraic rule describes the translation of quadrilateral HIJK to quadrilateral H'I'J'K' is (x, y) => (x+1, y-8)
What in mathematics is a quadrilateral?
A quadrilateral, a two-dimensional shape, is made up of four sides, four vertices, and four angles. The most prevalent shapes are concave and convex. Also included in the list of convex quadrilateral subgroups are trapezoids, parallelograms, rectangles, rhombuses, and squares.
Given: quadrilateral HIJK to that translated H'I'J'K'
To determine the algebraic rule, we need to get the coordinates of HIJK and H'I'J'K' and then subtract them to get the translation:
H => (x, y) = (4, 6) | H' => (x, y) = (5, -2)
I => (x, y) = (6, 4) | I' => (x, y) = (7, -4)
J => (x, y) = (4, 2) | J' => (x, y) = (5, -6)
K => (x, y) = (4, 2) | K' => (x, y) = (3, -6)
Using points H and H' (you can use any point):
The difference in x is 5-4 = +1 => x+1
The difference in y is -2-6 = -8 => y-8
Therefore, the algebraic rule describes the translation is (x, y) => (x+1, y-8). Option C is the answer
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A rail road crew can lay 5 miles of track each day. They need to lay 135 miles of track. The length L (in miles) that is left to lay after d days is given by the following function.L (d) =135-5d
Answers
In this case, we are given a function L(d) = 135 - 5d that models the miles of track that are left after d days, by replacing 19 for d into the given function, we can determine how many miles of track does the crew have left to lay after 19 days, like this:
L(19) = 135 - 5(19) = 135 - 95 = 40
(a) Then, the team have left to lay 40 miles of track
Now we need to determine how many days will it take the crew to lay all the track, if the team finished laying all the track the team will not have left any miles, and then L(d) = 0, then we can calculate the day this happens like this:
L(d) = 0
135 - 5(d) = 0
Adding 5d on both sides:
135 - 5d + 5d = 5d
135 = 5d
Dividing both sides by 5:
135/5 = 5d/5
27 = d
d = 27
(b) Then, it will take 27 days for the team to lay all the track
ayuda porfavor
necesito resolver esto es simplificarlo no resolverlo ayuda pls
Answers
The Simplification of the algebraic expression gives:
a. -2/3x² - (4/15)xy + (11/4)y²
b. -(12/7)x³ + (20/9)y
How to simplify algebraic expressions?Simplification of an algebraic expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression
a. (1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²
To simplify this, add or subtract like terms. That is:
(1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²
= (1/3)x² - 3x² - (2/5)xy + (2/15)xy + 2y² + (3/4)y²
= -2/3x² - (4/15)xy + (11/4)y²
b. (2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y
To simplify this, add or subtract like terms. That is:
(2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y = (2/7)x³- 2x³ - (1/3)y + 2y + (5/9)y
= -(12/7)x³ + (20/9)y
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The counting number just before C5F sixteen is
Answers
the counting number just before C5F16 is 3,072.
what is six hundred eighty and fourteen thousandths written in standard form?
Answers
Answer:618.014
Step-by-step explanation: It may look like hundredths which is where must people mess up but it is instead thousandths.
2. Which is correct when using the Box Method ?
No work needed
(A) Factor (Divide)
(C)Solve (equals)
(B) Evalúate (Substitute)
(D) Distribute (Product)
I need help :(
Answers
Answer:
D
Step-by-step explanation:
distribute (product)
10 times as many as 2 hundred is 20 hundreds or 2 thousand
Answers
Answer:
2 thousand 10s
Step-by-step explanation:
Please help
The price of a pair of shoes increases from $65 to $69. What is the percent increase to the nearest percent?
Answers
Answer:
Step-by-step explanation:
65÷4
Answer:
The answer is 6.15
Step-by-step explanation:
Solve by graphing
x + 3y = 1
-3 - 3y = -15
Answers
The solution of the given equation is (-11, 4). the graph is attached below.
What are Systems of equations?Simultaneous equations, a system of equations are Two or more equations in algebra that must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.
Given a system of equation x + 3y = 1 and -3 - 3y = -15
Before solving it with a graph we need to simplify the equation:
From equation 1
=> -3 - 3y = -15
=> -3y = -12
=> y = 4
From substitution in equation 1
x = -11
therefore, The solution of the given equation is (-11, 4).
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DQ2 Do all linear transformations have a matrix representation? If so, what theorem establishes this? If not, provide a counter-example
Answers
Yes, This is established by the Rank-Nullity Theorem, A counter-example would be a transformation that is not linear.
Yes, all linear transformations have a matrix representation. The theorem that establishes this is the Matrix Representation Theorem. This theorem states that given a linear transformation T : V → W where V and W are vector spaces over a field F, then there is a unique matrix A such that T(v) = Av for any v in V. This theorem proves that any linear transformation can be represented by a matrix.
A counter-example of a linear transformation that does not have a matrix representation is a transformation that maps a vector in one vector space to a vector in a different vector space. For example, if V is a vector space over the field F, and W is a vector space over another field K, then the linear transformation T : V → W does not have a matrix representation since the size of the matrix would need to be different for each vector in the different vector spaces.
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which function is best represented by this graph
Answers
Answer:
Step-by-step explanation:
e
H(x)=-(x-2)^2+16
How many seconds after being thrown will the ball hit the ground?
Answers
Answer:
three seconds
It takes three seconds for the ball to hit the ground.
Note: On Earth, it would take a little over nine seconds for the ball to fall back to the ground.
Step-by-step explanation:
elected at
pants?
D. 음
is divided
oun once,
will land
5.
To order a burrito from Teresa's Burrito Shop, Jim
always chooses 1 item from each column in the
table below.
Burrito Choices
Topping
beans sour cream
guacamole
Wrap Filling
plain
wheat beef
chicken
What is the total number of ways that Jim can
order a burrito at Teresa's Burrito Shop by
choosing 1 wrap, 1 filling, and 1 topping?
A. 6 B. 7 C. 10 D. 12
Answers
Answer: d.12
Step-by-step explanation:
Consider the line 3x+2y=-1.
Find the equation of the line that is perpendicular to this line and passes through the point (5, 3).
Find the equation of the line that is parallel to this line and passes through the point (5, 3).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of perpendicular line:
Equation of parallel line:
0
Answers
The given line is in the form Ax + By = C, where A = 3, B = 2, and C = -1. To find the slope of this line, we can rearrange the equation in slope-intercept form (y = mx + b), where m is the slope:
3x + 2y = -1
2y = -3x - 1
y = (-3/2)x - 1/2
The slope of the given line is -3/2. Since a line perpendicular to this line will have a negative reciprocal slope, we can find the perpendicular slope by taking the negative reciprocal of -3/2:
Perpendicular slope = -1 / (-3/2) = 2/3
Now we have the slope of the perpendicular line, and we can use the point-slope form of a line (y - y₁ = m(x - x₁)) to find its equation. Plugging in the values (5, 3) for (x₁, y₁) and 2/3 for m:
y - 3 = (2/3)(x - 5)
Expanding and simplifying:
3y - 9 = 2x - 10
2x - 3y = 1
Therefore, the equation of the line that is perpendicular to 3x + 2y = -1 and passes through the point (5, 3) is 2x - 3y = 1.
To find the equation of a line parallel to the given line and passing through the point (5, 3), we can use the same method. Since parallel lines have the same slope, the slope of the parallel line will also be -3/2.
Using the point-slope form with (5, 3) and -3/2:
y - 3 = (-3/2)(x - 5)
Expanding and simplifying:
2y - 6 = -3x + 15
3x + 2y = 21
Therefore, the equation of the line that is parallel to 3x + 2y = -1 and passes through the point (5, 3) is 3x + 2y = 21.
Question 5(Multiple Choice Worth 2 points)
(Sample Spaces MC)
Julia had a bag filled with gumballs. There were 2 watermelon, 3 lemon-lime, and 5 grape gumballs. What is the correct sample space for the gumballs in her bag?
A) Sample space = watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape, grape, grape, grape, grape
B) Sample space = watermelon, lemon-lime, grape
C) Sample space = 2, 3, 5
D) Sample space = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Answers
The sample space is (a) watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape gumballs, grape gumballs, grape gumballs, grape gumballs, grape gumballs
How to determine the sample spaceFrom the question, we have the following parameters that can be used in our computation:
2 watermelon, 3 lemon-lime, and 5 grape gumballs
Rewrite the items according to their frequencies
So, we have the following representation
watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape gumballs, grape gumballs, grape gumballs, grape gumballs, grape gumballs
The above represents the sample space
Hence, the sample space is (a)
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Thando would like to beat the record for the 1600m race ,the previous record was a time of 7 minutes 23 seconds .if her race starts at 11:05:17 what time does she need to end the race to beat the record ?
Answers
Answer: 11:12:40
Step-by-step explanation: If im right pls give brainliest
If 30% of x =60. then c=
Answers
Answer:
I think answer is c 1800.
When entering a power, you can use a caret (SHIFT-6).
Enter
as w^5:
Use the fraction tool (fraction tool) to enter the numerator and denominator.
Enter
:
Answers
The power expression "w^5" can be entered as "w^5".
To represent a power using the caret symbol, follow these steps:
Start with the base variable or term, in this case, "w".
Type the caret symbol (^), which can be accessed by pressing SHIFT-6 on your keyboard.
Immediately after the caret symbol, enter the exponent or power value, in this case, "5".
The resulting power expression "w^5" represents the variable "w" raised to the power of 5.
Regarding the use of the fraction tool, it is not required to represent the power "w^5" as it does not involve any fraction. The fraction tool is typically used to enter fractions or rational expressions in the form of numerator/denominator.
Therefore, to represent the power "w^5", simply write it as "w^5" without using the fraction tool.
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solve the equation -16=a- 19
Answers
Answer:
a = 3
Step-by-step explanation:
Collect like-terms:
\( - 16 = a - 19\)
\(a = - 16 + 19\)
\(a = 3\)
Answer: 3
Step-by-step explanation: you take 19 from 3 giving you -16
how would I find the equation of this graph
Answers
Answer:
y = sec(x-2) - 1
Step-by-step explanation:
We can determine the graph is of a secant by the repeating parabolas. From there, graph sec(x) and add the transformations necessary to replicate the graph.
PLZ HELP!!! 25 POINTS I NEED AN ANSWER IN THE NEXT 15 MINUTES!!! I WILL MARK BRAINLIEST!
Answers
9514 1404 393
Answer:
6.75 square units
Step-by-step explanation:
The formula for the area of a rectangle of base 'b' and height 'h' is ...
A = bh
The formula for the area of a triangle of base 'b' and height 'h' is ...
A = (1/2)bh
That is, the area of a triangle is half the area of a rectangle with the same base and height. Here, the area of the triangle is ...
(1/2)(13.5 square units) = 6.75 square units
6. Emily receives an inheritance of $20,000 and decides to invest the money. She puts some money in her savings
account that earns 1.5% simple interest per year. The remaining money is invested in a bond fund that returns 4.5% and a
stock fund that returns 6.2%. She makes a total of $942 at the end of 1 yr. If she invested twice as much in the bond fund
as the stock fund, determine the amount that she invested in each fund.
Answers
Emily funded $6000 in stocks and $12,000 in bond funds. She also funded the remaining $2,000 in her savings account.
Future value = $20,000
Simple interests rate = 1.5%
The return rate on bonds= 4.5%
The return rate on stocks = 6.2%
Total amount made on invests = $942
Time period = 1 year
Let us assume that the amount of money Emily invested = x
Amount invested in stock = y
If the amount is twice = 2y
The interest earned = x * 0.015
Interest on bond = 2y * 0.045
Interest on stocks = y * 0.062
The equation will be:
(x * 0.015) + (2y * 0.045) + (y * 0.062) = 942
0.015x + 0.152y = 942 ------ Equation 1
Total future value is given as $20,000
x + 2y + y = 20000
x + 3y = 20000
x = 20000 - 3y
Substituting the x value in the first equation:
0.015(20000 - 3y) + 0.152y = 942
300 - 0.045y + 0.152y = 942
0.107y = 642
y = 6000
Therefore, we can conclude that Emily funded $6000 in stocks and $12,000 in bond funds.
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If A=(4,-5) and B=(7,-9), what is the length of AB
Answers
The length of line segment AB is 5 units.To find the length of line segment AB, we can use the distance formula, which is based on the Pythagorean theorem.
The distance formula calculates the distance between two points (x1, y1) and (x2, y2) in a coordinate plane.
Let's calculate the length of AB using the given coordinates for points A and B:
Coordinates of point A: A = (4, -5)
Coordinates of point B: B = (7, -9)
The distance formula is given by:
\(d = [(x2 - x1)^2 + (y2 - y1)^2]\)
Substituting the coordinates of A and B into the formula:
\(d = [(7 - 4)^2 + (-9 - (-5))^2]\\d =[(3)^2 + (-4)^2]\)
d = √[9 + 16]
d = √25
d = 5
Therefore, the length of line segment AB is 5 units.
The distance formula calculates the straight-line distance between two points in a two-dimensional space. In this case, it determines the distance between points A and B in the coordinate plane. By applying the formula and substituting the given coordinates, we find that the length of AB is 5 units.
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9 Continuously compounded interest: word problems 82J
Learn with an example
Gigi opened a savings account and deposited $600.00 as principal. The account earns 3%
interest, compounded continuously. What is the balance after 2 years?
Use the formula A = Pe", where A is the balance (final amount), P is the principal (starting
amount), e is the base of natural logarithms (~2.718 28), r is the interest rate expressed as
a decimal, and t is the time in years.
Round your answer to the nearest cent.
$
Submit
Answers
The final amount in Gigi's amount after two years is $637.102.
Compound interest is also known as interest on principal and interest is the practice of adding interest to the principal amount of a loan or deposit.
Gigi opened a savings account.
The principal amount she deposited, P = $600
The interest rate, r = 3% = ( 3 / 100 ) = 0.03
The formula for the compound interest is given as:
\(A=Pe^{rt}\)
Where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years.
Then the amount in the account after t = 2 years will be:
\(A=Pe^{rt}\\A = 600 \times e^{(0.03 \times 2)}\)
A = 600 × e⁰·⁰⁶
A = 600 × 1.06183654655
A = 637.101927927
A = $637.102
Therefore, the final amount in the account is $637.102.
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