The equation which represents the population, P after t months is:
y = 1600(1+ 0.25)^t.
Given,
A population of beetles grows by 25% every month.
the beetle population starts with 1,600 beetles,
we are asked to determine the equation which represents the population, P after t months.
The equation for the population is:
Pf = Pi(1-r)^t
where pf = final value
pi = initial value
r = growth factor
t = time in years.
substitute the values in the equations.
let y represent the final population after t years.
r = 25%
convert percentage to decimal.
r = 0.25
y = 1600(1+ 0.25)^t
Hence we get the required answer.
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I need to write an equation the Aline’s with the stars so that the purple ball will fall on to the line and hit all the stars
Answer:
y = - [tex]\frac{3}{4}[/tex] x - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 12, 4 ) and (x₂, y₂ ) = (0, - 5 ) ← coordinates of 2 end stars
m = [tex]\frac{-5-4}{0-(-12)}[/tex] = [tex]\frac{-9}{0+12}[/tex] = [tex]\frac{-9}{12}[/tex] = - [tex]\frac{3}{4}[/tex]
the lowest star is on the y- axis at (0, - 5 ) ⇒ c = - 5
y = - [tex]\frac{3}{4}[/tex] x - 5
Convert 7/10 into a decimal
What is the value of q in the solution to this system of equations?
2m - 5q = 8
4m + 2q = 64
Answer:
q = 4
Step-by-step explanation:
Step 1: Set up the equation
The system of equations can be solved algebraically by substitution or elimination.For substitution, solve one of the equations for m and plug it into the other equation in order to solve for q.For elimination, cancel the m terms in order to solve for q.Step 2: Solve for q
Substitution:2m - 5q = 84m + 2q = 644m = 64 - 2qm = [tex]\frac{64-2q}{2}[/tex]m = 16 - [tex]\frac{1}{2}[/tex]q2(16 - [tex]\frac{1}{2}[/tex]q) - 5q = 832 - q - 5q = 8-6q = -24q = 4Elimination:2m - 5q = 8 (multiply whole equation by -2 in order cancel m terms)4m + 2q = 64-2(2m - 5q = 8)-4m + 10q = -164m + 2q = 6412q = 48q = 4Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60\%60%60, percent of their plants are flowers and 40\%40%40, percent are vegetables. They have 505050 plants growing in the garden.
How many vegetable plants do they have?
If Emily's family loves to work together in the garden . The number of vegetable plants they have is :20.
How to determine the number of vegetable plants?Using this formula to determine the number of vegetable plants
Number of vegetable plants = Percentage of vegetable plants × Number of plants
Let plug in the formula
Number of vegetable plants = 40% × 50
Number of vegetable plants = 20
Therefore we can conclude that the number of vegetable plants is 20.
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The correct question is :
Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60 percent of their plants are flowers and 40 percent are vegetables. They have 50 plants growing in the garden.
How many vegetable plants do they have?
Answer please with proofs and statements
Proved that ΔABC ≅ ΔDEC
SAS rule of congruent states that if two sides and one angle of the triangle is equal to the two sides and one angle of the another triangle, then the both triangles are congruent
The line BE and AD intersect at point C
The measure of the angle BCA = The measure of the angle ECD
The length of the side BC = The length of the side EC
The length of the side AC = The length of the side DC
Consider the triangle ABC and triangle DEC
Two sides and one angle of the triangle ABC is equal to the two sides and one angle of the triangle DEC, according to SAS rule of congruent the triangle ABC and triangle DEC are congruent
Hence, proved that ΔABC ≅ ΔDEC
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Find the measures of the numbered angles.
Answer: <1=104 degrees, <2=76 degrees, <4=104 degrees, <5=104 degrees, <6= 76 degrees, <7= 76 degrees, <8= 104 degrees
Step-by-step explanation:
<76 & < 2 are vertical angles, which means they are congruent. <1 & <2 are supplements, meaning when you add them up they equal 180 degrees (180-76=104 degrees). <1 & <4 are vertical angles. Using the Alternating Exterior Angles Theorem (AIA), <2 & <7 are congurent. Using the same theorem, <1 & < 8 are congruent. <7 & <5 are supplements, and so is <8 & <6.
Find x and y please
10 points
The value of x is 15 and the value of y is 4 for the given triangle.
According to the question,
We have the following information:
We have a figure of triangle and a line parallel to the base is drawn. Some measurements of the sides are given.
Now, to find the values of x and y, we will use Basic Proportionality theorem which states that the ratio of the corresponding sides are equal.
For the larger triangle, we have:
12/y = 18/6
Using the cross multiplication method:
y = 12*6/18
y = 4
Now, using the same theorem for the smaller triangle:
12/y = x/5
12/4 = x/5
Using the cross multiplication method:
x = 15
Hence, the value of x is 15 and the value of y is 4 for the given triangle.
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The selling price of an item is $600. It is marked down by 10% , but this sale price is still marked up from the cost of $450. Find the markup from
cost to sale price.
$135 is markup price when cost is $450.
What is the cost price and an example?
Cost price, for instance, equals selling price plus profit ( when selling price and profit is given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ) Cost price = 100 Selling Price + 100 + Profit (where the Selling Price and Profit Percentage are supplied)selling price of item = $600
cost = $450
10%×$650=$585
$585-$450=$135
$135 is markup price .
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1. The floor of a building is 120 feet long
and 80 feet wide. A scale model of the
building has a length of 24 inches. What
is the width of the model?
Step-by-step explanation:
120 ft relate to 24 inches.
120/80 must be the same ratio as 24/model width.
120/80 = 3/2
so,
24/width = 3/2
48/width = 3
48 = 3width
width = 48/3 = 16 inches
Simplify the expression.
the linear expression quantity negative 1 over 4 times r minus 8 minus 5 over 7 times r end quantity minus the linear expression quantity negative 3 over 4 times r plus 9 end quantity
negative 48 over 28 times r minus 1
negative 3 over 14 times r plus negative 17
negative 3 over 14 times r minus 1
9 over 28 times r plus negative 17
The value of the linear expression quantity negative 1 over 4 times r minus 8 minus 5 over 7 times r end quantity minus the linear expression quantity negative 3 over 4 times r plus 9 end quantity is B. negative 3 over 14 times r plus negative 17
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Based on the information given, the expression will be:
= (-1/4r - 8 - 5/7r) - (-3/4r + 9)
Collect like terms
-1/4r - 5/7r + 3/4r - 8 - 9.
= - 3/14r - 17
In conclusion, the correct option is B.
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Answer:
Step-by-step explanation:
b
The sum of 2 numbers is 27. One half of the first number plus one third of the
second number is 11. Find the numbers.
Answer:
x = 12, y = 15
Step-by-step explanation:
x + y = 27
1 / 2 x + 1 / 3 y = 11
y = 27 - x
1 / 2 x + (27 - x) / 3 = 11
1 / 2 x + 9 - 1 / 3 x = 11
1 / 6 x = 2
x = 12
12 + y = 27
y = 15
8: fatuma's frower Garden is a Squase. If the enlarge it by increasing the Width by 1 m the length by 3m the area will be 19 square meters morethan the Present area.
A,find the length of the side of original garden B,What is the width of the new garden?
C,what is the length of the new garden?
D,find the area of the new garden?
A. The length of the side of original garden is 4 m
B. The width of the new garden is 5m
C. The length of the new garden is 7m
D. The area of the new garden is 35 m²
Let the side of the garden = x m.
area = x² m²
From the question, we have
The new length is (x+3) m and the new width is (x+1) m.
Then the new area = (x+3)(x+1) m².
(x+3)(x+1)=x²+19
⇒ x²+3x+x+3=x²+19
⇒ 4x+3=19
⇒ 4x=19-3
⇒ 4x=16
⇒ x = 4 m
The length of the side of original garden is 4 m
new length = (x+3) m = (4+3)m = 7 m
new width = (x+1) = (4+1) = 5 m
new area = (x+3)(x+1) m² = 7*5 = 35 m²
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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Find the slope of the line shown of the graph to the right
The slope will be 1, for the right.
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
We know that formula two find the slope of the line joining two points which is
m = (4-3)/(4-3)
m = 1
Hence the slope of the line is shown in the graph is 1.
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Conider the polynomial function []
p
given by p(x)=5x38x2−3x1
A(x). Evaluate the function at x=−2
x
The polynomial function p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 value at x = -2 is -1
given that
polynomial function p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 at x=-2
To find the value of a function at x = -2, put in all the places of in the function.
Polynomial is made up of two words, poly, and nomial. "Poly" means many, and "nomial" means the term, and hence when they are combined, we can say that polynomials are "algebraic expressions with many terms".
Polynomial functions are expressions that may contain variables of varying degrees, coefficients, positive exponents, and constants.
Here,
p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 put x =-2
p(-2) = 5[tex](-2)^{3}[/tex]+8[tex](-2)^{2}[/tex] - 3(-2)+1
p(-2) = 5(-8) + 8(4) + 6+1
p(-2) = -40+32+6+1
p(-2) = -40+39
p(-2) =-1
At So, the value of the function at x= -2 is -1
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Can u help me please
The slope of the line as shown in the diagram is 4/3.
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount.
To calculate the slope from the diagram, we use the formula below.
Formula:
S = Δy/Δx........... Equation 1Where:
S = Slope.From the graph,
At x = 30, y = 20
And at x = 60, y = 60
Therefore,
Δy = 60-20 = 40Δx = 60-30 = 30Substitute these values into equation 1
S = 40/30S = 4/3Hence, the slope of the is 4/3.
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9/g +2h +5 when g=3 and h=6
Answer:answer is 20
Step-by-step explanation:9/3=3 then add that to 2 times 6 which is 12+3=15 then 15+5+20
answer the question in the screenshot please?
The value of x and y in the vector matrix are 2 and 5
What is a vector Matrix?If a matrix has only one row or only one column it is called a vector.
A matrix having only one row is called a row vector.
A matrix having only one column is called a column vector.
The matrix for two equations
3 - x/4 = 5/2 ---------------------1
8 - 12/4 = y ----------------------2
From equation 1,
collect like terms
x/4 = 3-5/2
x/4 = 1/2
cross multiply
2x = 4
x = 4/2
x = 2
From equation 2,
8 - 3 = y
y = 5
In conclusion, the value of x = 2 and the value of y = 5
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You work a basic week of 40 hours and your basic rate is $19.50 per hour. A rival company offers you an annual salary is $36.000. Except for the pay, everything is identical between the conpanies. Do you accept or reject the rival company's offer, and why ?
I will have to reject the offer of the rival company since it's lesser than $40560.
How to calculate the amountFrom the information, the person works a basic week of 40 hours and the basic rate is $19.50 per hour. It should be noted that there are 52 weeks in a year. The total amount will be:
= 40 × 19.50 × 52
= $40560
The rival company offers you an annual salary is $36000.
I'll reject the rival company's offer since it's lower.
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PLEASE HELP ME!!
A soccer team receives a discount on each jersey purchased. The original price of each jersey is x dollars. The team buys 18
jerseys for a total of (18x-36) dollars. What can you conclude about the discount?
If the team buys 18 jerseys for a total of (18x-36) dollars then we can conclude that the discount the team has received is $36.
According to the question,
We have the following information:
A soccer team receives a discount on each jersey purchased. The original price of each jersey is x dollars. The team buys 18 jerseys for a total of (18x-36) dollars.
Now, the original price of 18 jerseys will be 18x.
Now, when 36 is subtracted from 18x to find the total cost then it means that this is the discount from the original price.
Hence, if the team buys 18 jerseys for a total of (18x-36) dollars then we can conclude that the discount the team has received is $36.
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(a) 11³ x 11=11
11³
||³ + x = || 2
Step-by-step explanation:
I suspect you mean
11³ × 11 = ?
11³ ÷ 11 = ?
11³ × 11 = 11⁴
11³ ÷ 11 = 11²
why ?
11³ = 11×11×11
11³ × 11 = 11×11×11 × 11 = 11×11×11×11 = 11⁴
11³ ÷ 11 = 11×11×11 / 11 = 11×11 × 1 = 11×11 = 11²
Please help me please
Answer:
x = 2
Step-by-step explanation:
The image shows a large rectangle with a similar, smaller triangle inside of it. The small leg on the small rectangle is 4, and the small leg on the large rectangle is 12. This tells me that the scale factor is 3.
If the scale factor is 3, then
[tex]6*3=6+6x[/tex]
Simplify
[tex]18=6+6x\\12=6x\\x=2\\[/tex]
[tex]\frac{2\sqrt{3 }-1 }{3\sqrt{3}+4 }[/tex]
A television can be purchased cash for $1800 or on hire purchase for a deposit of 20% and 18 monthly payments of $90. If taken on hire purchase calculate:
A) the deposit
B) the hire purchase price
C) Hence, the amount saved if the television is bought for cash.
- 12 = 10n - 40n + 3
Answer:
[tex]\sf n=\cfrac{1}{2}[/tex]
Step-by-step explanation:
[tex]\sf -12=10n-40n+3[/tex]
[tex]\sf 10n-40n+3=-12[/tex]
Combine like terms:-
[tex]\sf \:(10n-40n)=-30n[/tex]
[tex]\sf -30n+3=-12[/tex]
Subtract 3 from both sides:-
[tex]\sf -30n+3-3=-12-3[/tex]
Simplify:-
[tex]\sf -30n=-15[/tex]
Divide both sides by -30:-
[tex]\sf \cfrac{-30n}{-30}=\cfrac{-15}{-30}[/tex]
Simplify:-
[tex]\sf n=\cfrac{1}{2}[/tex]
_________________
Hope this helps!
Have a great day! :)
Given: AB || CE
Find: ED
Answer:
49
Step-by-step explanation:
18/42=21/ED
18 ED=882
ED=49
The (i,j) minor of a matrix A is the matrix Aij obtained by deleting row i and column j from A.
The (i,j) minor of a matrix A is the matrix Aij obtained by deleting row i and column j from A it is true.
The (i,j) minor of a matrix A is the matrix Aij obtained by deleting row i and column j from A. A determinant of an n×n matrix can be defined as a sum of multiples of determinants of (n−1)×(n−1) sub matrices.
This is done by deleting the row and column which the elements belong and then finding the determinant by considering the remaining elements. Then find the co factor of the elements. It is done by multiplying the minor of the element with -1i+j. If Mij is the minor, then co factor, [tex]c_{ij}[/tex] [tex]= -1^{i+j}[/tex] + [tex]m_{ij}[/tex].
Each element in a square matrix has its own minor. The minor is the value of the determinant of the matrix that results from crossing out the row and column of the element .
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You go out to dinner and tip the waiter 21%. If your bill was $86.20, then what was your bill after
tipping 21%? Round to the nearest hundredth.
Answer:
The bill after tipping 21 percent would be $104.30.
Step-by-step explanation:
$86.20 x 0.21 = $18.102
$86.20 + $18.102 = $104.302
$104.302 ≈ 104.30
Hope my answer helped! Have a great afternoon.
Factor: 4x + 18 =
I don't understand Pre-algebra
Answer:
2(2x+9)
Step-by-step explanation:
Just break each number up
2 X 2 = 4
2 X 9 = 18
2(2x+9)
Answer:
-4.5
......
......
A biologist uses a box-shaped fish trap that measures 1/4 meter by 2/3 meter by 3/5 meter. What is the volume of the trap in cubic meters?
Answer:
1/10 or 0.1 m^3
Step-by-step explanation:
V = 1/4 * 2/3 * 3/5 = 6/60 = 1/10 m^3 = 0.1 m^3
you receive a $60 gift card to a move theater. a ticket to an afternoon show costs $6 and a ticket to an evening show costs $10. the rules of the gift card state that you can only buy a maximum of 8 total tickets with the card. let x
The constraints for this situation in the form of a system of inequalities is 6x + 10 y = 60.
Given:
you receive a $60 gift card to a move theater. a ticket to an afternoon show costs $6 and a ticket to an evening show costs $10. the rules of the gift card state that you can only buy a maximum of 8 total tickets with the card.
x = the number of afternoon tickets and y = the number of evening tickets.
6x ≤ 60
10y ≤ 60.
so
6x + 10 y = 60.
Therefore the constraints for this situation in the form of a system of inequalities is 6x + 10 y = 60.
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