Answer:
(x+2y)(x+2y)
x²+2xy+2xy+2y²
x²+4xy+2y²
(2x+3y)(2x+3y)
4x²+6xy+6xy+9y²
4x²+12xy+9y²
A population of bacteria is treated with an antibiotic. It is estimated that 5,000 live bacteria existed in the sample before treatment. After each day of treatment, 40% of the sample remains alive. Which best describes the graph of the function that represents the number of live bacteria after x days of treatment?
f(x) = 5000(0.4)x, with a horizontal asymptote of y = 0
f(x) = 5000(0.6)x, with a vertical asymptote of x = 0
f(x) = 5000(1.4)x, with a horizontal asymptote of y = 0
f(x) = 5000(1.6)x, with a vertical asymptote of x = 0
Answer:
Step-by-step explanation:
The function is modeled after
[tex]y=a(b)^x[/tex] where a is the initial amount and b is the growth/decay factor. If we start with 5000 bacteria, then a = 5000. The decay factor is determined by the rate at which the bacteria decrease. We know that rate at which the bacteria decrease is 60% because 40% are left alive; therefore, b = .4:
[tex]f(x)=5000(.4)^x[/tex] with a horizontal asymptote of y = 0, the first choice.
The function that represents the number of live bacteria after x days of treatment can be written as f(x) = 5000(0.4)ˣ
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that 40% of the sample remains alive, which means that the number of live bacteria is decreasing exponentially over time.
The base of the exponential function is 0.4, as 40% can be written as 0.4. The initial population of bacteria is 5000, so we multiply the base by 5000 to get the total number of live bacteria after x days.
The graph of this function will have a horizontal asymptote of y = 0, since the number of live bacteria will approach zero as time goes on.
f(x) = 5000(0.4)ˣ is the function represents the number of live bacteria after x days of treatment
Hence, option A is correct, f(x) = 5000(0.4)ˣ with a horizontal asymptote of y = 0.
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Help I don’t understand this
find the sum (12p+9) + (4p-3) please help me
1.Round off 378811 to the nearest hundreds,thousands and ten thousand
2.Round off 267988 to the nearest hundreds,thousands and ten thousand
3.Round off 250260 to the nearest hundreds,thousands and ten thousand
4.Round 196596 to the nearest hundreds,thousands and ten thousand
5.Round off 193171 to the nearest hundreds,thousands and ten thousand
Given:
The numbers are 378811, 267988, 250260, 196596, 193171.
To find:
The approximate value of the given numbers to the nearest hundreds, thousands and ten thousand.
Solution:
The required values shown in the below table:
Numbers Nearest hundreds Nearest thousands Nearest ten thousand
378811 378800 379000 380000
267988 268000 268000 270000
250260 250300 250000 250000
196596 196600 197000 200000
193171 193200 193000 190000
Add-ons Helplast edit was seconds ago
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2
E A monthly service fee to download ebooks is $4.96 plus $3.99 per book downloaded White an
equation that represents the total cost, c, in a month when books are downloaded Explain how
yos gation represents the greem
Graph
Create a graph for
CAN SOMEONE HELP ME PLEASE
Answer:
.54 (54%)
Step-by-step explanation:
the polygons in each pair are similar. Find the missing side length
Answer:
Since they are similar, 45/27=30/18=x/24. x=40
Bart is going to paint his bedroom. His uncle told him that a gallon of paint would cover a surface of approximately 40 square feet. He knew that the ceiling in his room was 9 feet high and the paint was $22 a gallon. He also had to buy brushes, a drop cloth, and a ladder. How many gallons of paint should he buy to paint the walls in his bedroom
Answer:
The measurement for the length of the walls.
Step-by-step explanation:
Given
[tex]Cost = \$22[/tex] per gallon
[tex]Height = 9ft[/tex]
[tex]1\ gallon = 40ft^2[/tex]
See comment for complete question
Required
The additional information needed to solve the question
First, we need to calculate the area of the walls of the bedroom.
The height of the ceilings represents the length/width of the walls; so, we need the width of each side of the bedroom.
Since the width is not given, then we can conclude that the additional information needed is the length/width of the walls.
Please help!!
Martha works at a small jewelry store. She designs 2 rings in the first hour. Every additional hour, she designs 3 new rings.
Select all the functions that can be used to find the number of rings, r(n), she designs in n hours.
Answer:
2nd option and 4th option, other functions don't apply, remember r(1) can't be 3 since the she designs 2 rings in the first hour.
Answered by GAUTHMATH
Enda has job offers at two companies. One company offers a starting salary of $75,000 with a raise of $2,500 each year. The other company offers a starting salary of $55,000 with a raise of $5,000 each year. In how many years would Brenda's salary be the same with both companies? What will the salary be?
Answer:
8 years
Salary: $95000
Step-by-step explanation:
Write an equation to model the salary and its raise per year. Add the base salary to the raise per year salary times (x). Where the parameter (x) represents the number of years spent in the company.
Company (1):
75000 + 2500x
Company (2):
55000 + 5000(x)
One is asked at which year will the salaries be the same. Equate the two expressions and solve for the variable (x):
75000 + 2500x = 55000 + 5000(x)
Inverse operations:
75000 + 2500x = 55000 + 5000x
20000 + 2500x = 5000x
20000 = 2500x
8 = x
Substitute (x) into any one of the experssions and simplify to solve the epxression,
55000 + 5000(x)
x = 8
= 55000 + 5000(8)
= 55000 + 40000
= 95000
please help me with this on the picture
Answer:
-3, 7, 17, 27, 37
Step-by-step explanation:
Essentially, you just put -3 for the first box, and add 10. Then you take that new number and put it in the next box.
Given an aritmetic progression 2,6,10,14.. find the smallest value of n such that the sum of the first n terms is greater than 200.
Answer:
Without thinking too hard, by adding the progression of number until we reach >200 and counting what n value we have we can solve this question.
The rule of this progression is to + 4 every time.
2 + 6 + 10 + 14 + 18 + 22 + 26 + 30 + 34 + 38 + 42
This will give us 242, which is greater than 200. There are 11 numbers here, so the n value is 11.
Answer:
Hello,
Step-by-step explanation:
Using n terms, the arithmetic sequence will be:
2,6,10,14,...,?
=0*4+2,1*4+2,2*4+2,3*4+2,...,(n-1)*4+2
s=(0*4+2)+(1*4+2)+(2*4+2)+(3*4+2)+...+(n-1)*4+2 >200
(2+2+2+...+2)+4(0+1+2+...+(n-1)) > 200
2*n+4*(0+(n-1))*n/2 >200
2n+2(n²-n) > 200
2n² >200
n² > 100
n >10
the smallest value of n is 11.
11 th term is (11-1)*4+2=42
sequence={2,6,10,14,...,42} which sum is 2*11²=242
please help me solve this answer, it is really crucial
Answer:
Parabolas have an axis of symmetry. If we assume that x=2 is that axis of symmetry, them that must mean the x values -2 and 6 should have the same y values, which they don't, thus an equation is not possible.
what is the correct answer for this question ?
Answer:
[tex]b)\ 61m[/tex]
Step-by-step explanation:
The given triangle is a right triangle. This means that one can use right-angle trigonometry to solve the triangle. The right angle trigonometric ratios are a set of ratios that relate the sides and angles of a triangle. These ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Bear in mind, the names (opposite) and (adjacent) change depending on the angle of reference. However, the side (hypotenuse) refers to the side opposite the right angle, this side doesn't change depending on the reference angle.
In this problem, one is given the measure of an angle, and the measure of the hypotenuse, the problem asks one to solve for the side opposite the given angle measure. It would make the most logical sense to use the ratio of sine (sin) to do this.
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
Substitute,
[tex]sin(56)=\frac{h}{73}[/tex]
Inverse operations,
[tex]sin(56)=\frac{h}{73}[/tex]
[tex]73(sin(56))=h[/tex]
[tex]60.519\approx h[/tex]
Find the area of this circle please and thank you..
Answer:
452.39
Step-by-step explanation:
Hope this is right
select the right one
Answer:
W
Step-by-step explanation:
9^(-1/2)*9^(3/2)=(1/3)*(3^3)=3^2=9
Write the equation of the line that goes through points (0, 4) and (6, 16).
Answer:
y = 2x + 4
Step-by-step explanation:
(x₁ , y₁) --> (0 ,4) & (x₂ , y₂) = (6 , 16)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
[tex]= \frac{16-4}{6-0}\\\\=\frac{12}{6}\\\\m = 2[/tex]
(x₁ , y₁) --> (0 ,4)
y - y₁ = m(x - x₁)
y - 4 = 2(x - 0)
y - 4 = 2x
y = 2x + 4
In a quiz, team A secured -5,6,2 and team B secured 6, 5,-2 in three successive rounds. Which team secured more?
a)Team A
b)Team B
c)Both secured same
d)Not possible to say
Answer:
i think b
because -5 and -2
!!!!!!URGENT!!!!!
Two similar rectangles have a proportional coefficient of 1:2, and the perimeter of the smallest one is 80 m, find the
perimeter of the small rectangle
Answer:
160m
Step-by-step explanation:
Since the rectangles are similar and we have their proportion of coefficient, the larger rectangle is twice the smaller rectangle.
Furthermore, the ratio of two longer sides should equal the ratio of the two shorter sides.
Therefore, for our case, we multiply the smaller rectangle by 2.
Hence;
(80 × 2)m
= 160 m
NB:
The ratio of the areas of two similar shapes or figures is equivalent to the square of the corresponding sides.
What is the slope of a line with points (5, 1) and (8,3)?
A. m= 3/2
B. m=2/3
C. m=-3/2
D.m=-2/3
Answer:
2/3
Step-by-step explanation:
If we know two points we can find the slope using
m = ( y2-y1)/(x2-x1)
= ( 3 -1)/(8 - 5)
= 2/3
Which points have an x value less than zero? (last answer choice says (D,J,E)
Answer:
CDJ
Step-by-step explanation:
Answer:
Choice C. C,D,J
Step-by-step explanation:
When it asks for x-values less than zero (x<0), a point that lies on the y-axis is not included.Every other option has a point lying on the y-axis or greater than zero.In order for the parallelogram to
be a square, x = [?].
4x + 17
12x - 23
Answer:
x = 5
Step-by-step explanation:
4x + 17 = 12x - 23
23 + 17 = 12x - 4x
40 = 8x
8 8
5 = x
The value of x should be 5.
What is parallelogram?A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal).
As, to from the square using the dimension of parallelogram the value of x should be 5
as the side of square is equal.
4x + 17 = 12x - 23
23 + 17 = 12x - 4x
40 = 8x
5 = x
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find the area of this circle
Radius: 7ft
Area of circle =153.86ft²
Answer:
Solution given;
Radius[r]: 7ft
To find;
Area of circle;
Step-by-step explanation:
use formula:
Area of circle =πr²
Calculation:
Area of circle =πr²
substitute value
.Area of circle =3.14*7²=153.86ft²
An ice cream shop uses the following ingredients to make 1 sundae.
Ingredient Amount
Ice cream 2 scoops
Sprinkles 4 spoonful's
Whipped cream 2 tablespoons
How many sundaes did the shop make if they used 32 spoonfuls of sprinkles?
Pleaseee help :( Its about ratios :( :0
Answer:
8 sundaes
4:32
.......
.......
...
Step-by-step explanation:
To make 1 sundae, the total number of spoons use of sprinkles=4. Let the number of sundaes made in 32 spoonfuls of sprinkles be x. Also the number of sprinkles and the number of sundaes are directly proportional. Therefore, Hence, if 32 spoonfuls of sprinkles is used, then the ice-cream shop can make 8 sundaes.
[tex]\sqrt{2} \frac{7}{8}[/tex]
Answer:
[tex]\sqrt{2\frac{7}{8} } =\\\sqrt{\frac{25}{8} } =\\\sqrt{\frac{25*2}{16} } =[/tex]
±5√2/4
.
A football is punted from a height of 2.75 ft above the ground, with an initial velocity of 48 feet per
second. The motion of the football can be modeled by the equation h = -16t2 + 48t +2.75, where
h represents the height of the football, in feet, and t represents the timelin seconds.
If the football is caught 5.25 ft above the ground, approximately how long did it remain in the air?
Roundyour answer to the nearest hundredth of a second.
Answer:
Step-by-step explanation:
The position function for this is given as
[tex]h(t)=-16t^2+48t+2.75[/tex] where h(t) is the height of the football at any time t. If the ball is caught at 5.25 feet, that h(t) value is 5.25 since we are looking for the time the ball was in the air from its initial 2.75 feet to 5.25 feet, when it was caught.
[tex]5.25=-16t^2+48t+2.75[/tex] and set this equal to 0:
[tex]-16t^2+48t-2.5=0[/tex] and factor.
When we factor we get
t = .05 and t = 2.95 in seconds.
That first time tell us how long it takes to go from the initial height of 2.75 to a point 2.5 feet higher, 5.25. To get get back down to the 5.25 foot height on the other side of the vertex, is 2.95 seconds. So the total time the ball was in the air was 3 seconds exactly.
Which of the following statements must be true based on the diagram below?
(Diagram is not to scale.)
Answer:
i dont know
Step-by-step explanation:
i dont kow
Jessica purchased a DVD that was on sale for 12% off. The sales tax in her county is 3%. Let y represent the original price of the DVD. Write an expression
that can be used to determine the final cost of the DVD. HELP URGENTLY PLEASE
Answer:
If u add the number it will show u te answer which is 7
Step-by-step explanation:
Multiply: -14(y+11)
Answer:
-14y -154
Step-by-step explanation:
Multiply -14 and y = -14y
Multiply -14 and 11 = -154
Answer:
[tex]-14\left(y+11\right)[/tex]
[tex]=-14y+\left(-14\right)\cdot \:11[/tex]
[tex]=-14y-14\cdot \:1[/tex]
[tex]=-14y-154[/tex]
OAmalOHopeO
What is 25 over 1363
Answer:
25/1363
0.0183
Step-by-step explanation:
This question includes division. When a number is "over" that number should be the numerator of the fraction and the other number should be the denominator. So, 25 over 1363 would look like [tex]\frac{25}{1363}[/tex] in fraction form. They have no common factors so it cannot be simplified further. However, if wanted, then you could divide the two numbers to get a decimal, 0.0183. But, this is rounded because the exact answer is not rational.
