Answer:
Jared and Nicole are correct.
Step-by-step explanation:
You can solve for either variable and use the equivalent expression to create a one-variable equation. They manipulated the equation right. They can either write the equation as y as a function of x then substitute it to the y in the other equation and solve for x. For both solutions, they'll still get the same answers.
A scientist began a study with a sample of 1,500 bacteria. He noticed that
the number of bacteria in the sample after t days can be modeled by the
equation P=1,500.5. In this equation, what does 5t represent?
A. The number of bacteria increases by a factor of t each day for 5 days.
B. The number of bacteria increases by t bacteria after 5 days.
C. The number of bacteria increases by 5 bacteria each day.
D. The number of bacteria increases by a factor of 5 each day.
Answer:
C
Step-by-step explanation:
Latoya buys a board that is 8 feet long. She cuts 3 1/2 feet off to make a shelf , and 2 feet off to make a sign. She divides the rest equally to make 2 trays. What is the length of one tray, in inches?
Answer:
1 1/4 feet
Step-by-step explanation:
3 1/2 feet + 2 feet = 5 1/2 - 8 = 2 1/2 ÷ 2 = 1 1/4
jill uses some of her honey to make lotion. if each bottle of lotion requires 1/4 gallon and she uses a total 3 gallons how many bottles of lotion does she make
Answer:
am gonna need more imformation
Step-by-step explanation:
Can someone solve for x and y
Answer
Calculator.net
i hope you use this it will help a lot
i need help learning how to find the nth term in sequences like 8,6,4,2?
i haven’t a clue how to solve things like this and i have a test tomorrow
Answer:
-8
Step-by-step explanation:
Its actually simple once you get the basics
Find out the difference between the first two digits given e.g 8,6: the difference is 2 so you check if it's the same difference e.g 6,4: the difference is also 2 so you keep subtracting or adding 2 as the case may be.
In a right-angled triangle ,right angled at B,if AB=5cm andAC=13cm ,then BC=
Answer:
BC = 12cmStep-by-step explanation:
by phythagoras theorm
AB² + BC² = AC²
5² + BC² = 13²
25 + BC² = 169
BC² = 169 - 25
BC² = 144
BC = √144
BC = 12cm
is this positive or negative explain why
Answer:
a-1 would still be positive if not exactly on 0
Step-by-step explanation:
Answer:
A is positive
Step-by-step explanation:
Because a is after 0, and anything after 0 is postive. If it was negative, it would be before 0.
Write a function that represents the total cost of your family's outing to the soccer game after x hours.
Answer:
Please attach an image.
f(x) = (cost)x
Answer:
c=s*x
Step-by-step explanation:
C will be the total cost of our family's outing to the soccer game
While x will be the hours
and S will be the soccer game
So s*x will equal the cost
Making c=.
Hope this helps!
:D
(2.6 x 106) + (4.2 x 106)
a
6.8 x 106
b
6.8 x 1012
c
8.4 x 106
d
3.2 x 1012
Answer:
720.8
Step-by-step explanation:
(2.6 × 106) + (4.2 × 106)
275.6 + 445.2
720.8
Giving more a lot of points!
What is 3 /1 ÷3
Answer:
3
Step-by-step explanation:
Janet paid 5% interest on a $628 loan for 4 months. How much interest did she pay on her loan
Answer:
Total interest paid:$6.56
Step-by-step explanation:
I used multiple loan calculators.
A store pays $433.78 for a robot. The store marks up the price by 50%. What is the new price?
Can you help me I will mark you brainiest if you awnser all of them please put work into this
It is trigonometry. Please find the dimensions of the box. Thanks.
Answer:
Step-by-step explanation:
Will give brainliest if you can help me better understand this! Determine whether sine, cosine, or tangent is the best choice for finding x.
Answer: Cos, Cosine
Step-by-step explanation:
You can use SOH CAH TOA to help you find out whether you are using Sine, Cosine or Tangent.
SOH- The 'S' is for Sine, then the 'O' and the 'H' is for Opposite over Hypotenuse.
CAH- The 'C' is for Cosine, the 'A' and the 'H' is for Adjacent over Hypotenuse.
TOA- The 'T' is for Tangent, then the 'O' and the 'A' is for Opposite over Adjacent.
As you have the Adjacent (the side next to the angle you are looking for) and Hypotenuse (the side opposite the right angle), you would be using Cosine.
I haven't answered it because I read this as though you wanted the explanation. If you do want an answer just let me know then I can edit my answer.
Hope this helps :)
There are _______ kilometers in 5,000 centimeters.
The park service that administers a state park estimates that there are 495 deer in the park. They decide to remove deer according to the differential equation dP/dt = −0.1P.
a. Show that the solution to the differential equation dP/dt = −0.1P is P = 495e^−0.1t , where t is measured in years and P is the population of deer. Use it to find the deer population in 5 years to the nearest deer.
b. After this 5-year period, no human intervention is taken and the deer population grows again. From that time, the deer population increases directly proportional to 650−P, where the constant of proportionality is k. Find an equation for the deer population P(t) in terms of t and k for this 5-year period.
c. Using the growth model from part b), 1 year later the deer population is 350. Find k.
d. Using the growth model from part b) and the value of k from part c), find lim t→∞ P(t)
The deer population in 5 years is approximately 294 deer.
What are exponential growth and decay?A rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay. Over time, exponential functions monitor constant growth. Examples from the actual world include radioactive decay, compound interest, and bacterial proliferation.
a. To solve the differential equation dP/dt = −0.1P, we can separate the variables and integrate:
dP/P = −0.1 dt
Integrating both sides gives:
ln|P| = −0.1t + C
where C is the constant of integration. To solve for C, we can use the initial condition that P = 495 when t = 0:
ln|495| = −0.1(0) + C
C = ln|495|
Substituting this value of C back into the equation gives:
ln|P| = −0.1t + ln|495|
Simplifying using logarithm properties, we get:
ln|P/495| = −0.1t
Exponentiating both sides gives:
|P/495| = e^−0.1t
Taking the absolute value off and multiplying both sides by 495, we get:
P = 495e^−0.1t
To find the deer population in 5 years, we can substitute t = 5 into the equation:
[tex]P = 495e^{-0.1(5)} = 294[/tex] deer (rounded to the nearest deer).
Therefore, the deer population in 5 years is approximately 294 deer.
b. To find an equation for the deer population P(t) in terms of t and k for the period after 5 years, we can use the differential equation:
dP/dt = k(650−P)
Separating the variables and integrating, we get:
∫dP/(650−P) = ∫k dt
Using partial fraction decomposition and integrating, we get:
ln|650−P| = −kt + C
where C is the constant of integration. To solve for C, we can use the initial condition that P = 294 when t = 5:
ln|650−294| = −k(5) + C
C = ln|356| + 5k
Substituting this value of C back into the equation gives:
ln|650−P| = −kt + ln|356| + 5k
Simplifying using logarithm properties, we get:
ln|(650−P)/356| = −kt
Exponentiating both sides gives:
[tex]|(650-P)/356| = e^{-kt[/tex]
Taking the absolute value off and multiplying both sides by 356, we get:
[tex]650-P = 356e^{-kt[/tex]
Solving for P gives:
[tex]P = 650-356e^{-kt[/tex]
Therefore, the equation for the deer population P(t) in terms of t and k for the period after 5 years is P = 650−356e^−kt.
c. Using the growth model from part b), if the deer population is 350 one year later, we can substitute t = 1 and P = 350 into the equation and solve for k:
350 = 650−356e^−k
Solving for [tex]e^{-k[/tex] gives:
[tex]e^{-k = (650-350)/356 = 3/2[/tex]
Taking the natural logarithm of both sides gives:
−k = ln(3/2)
Solving for k gives:
k = −ln(3/2) ≈ 0.4055
Therefore, k ≈ 0.4055.
d. Using the growth model from part b) and the value of k from part c), the long-term behavior of the deer population as t → ∞ is determined by the limit:
lim P(t) as t → ∞
We can use the fact that [tex]e^{-kt[/tex]approaches 0 as t →
Learn more about exponential growth and decay here:
https://brainly.com/question/17161065
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3√x^2
I need to write this as a fractional exponent.
[tex]3\sqrt{x^2}[/tex][tex]=3x[/tex]
[tex]\sqrt[3]{x^2}[/tex][tex]=x^\frac{2}3}[/tex]
I do not know which one you mean but still one of them is still your answer. :)
Find the value of x in the isosceles triangle shown below.
Answer:
12
Step-by-step explanation:
x is the height, and we notice that this isosceles triangle is two 5-12-13 triangles put together. Therefore, x = 12
Another method. Use pythagorean theorem. x^2 + (10/2)^2 = 13^2
x^2 + 25 = 169
x^2 = 144
x = 12
if the cost 6 books is Rs.720. find the cost of 9 books.
Answer:
Rs.1080
Step-by-step explanation:
1 book=720/6=120
9 books=120*9=1080
PLISS ANSWER :C DONT ANSWER IF YDK THAnKSSS
*also pls look at both images :)*
Answer:
First image: (6, -1)
2nd image: y = 63
Explanation:
1)
2x + y = 11
1/2x - 5y = 8
y = -2x + 11
1/2x - 5(-2x + 11) = 8
1/2x + 10x - 55 = 8
10.5x - 55 = 8
10.5x = 63
x = 6
2x + y = 11
2(6) + y = 11
12 + y = 11
y = -1
(x , y) = (6, -1)
2)
1/4(8y - 4.8) = 2 (0.9y + 5.4) + 3/5
2y - 1.2 = 1.8y + 10.8 + 0.6
0.2y - 1.2 = 11.4
0.2y = 12.6
y = 63
pls help me!
(7th grade math)
help is very much appreciated :)
Answer:
If we are working with numbers 26m, 24m, 20m, 26m, 39m
Than the surface area of the shape would be 0.24
Work:
3.46 × 106 = 366.76
366.76 + 20 =386.76
386.76 in square meters is 0.24
Which of the following is another way of expressing 4 out of 5
Answer:
4/5
Step-by-step explanation:
I believe this is looking for a fraction? 4 over 5 or 4/5 means 4 out of 5.
I need help please please I appreciate it! ):
Answer:
!. Scale factor = 5
2. Scale factor = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
scale = [tex]\frac{length in drawing}{actual length}[/tex]
1. To increase the numbers, let the scale factor be [tex]\frac{5}{1}[/tex] = 5. So that;
0.05 x 5 = 0.25
[tex]\frac{1}{2}[/tex] x 5 = 0.5 x 5 = 2.50
7 x 5 = 35.00
13 x 5 = 65.00
25 x 5 = 125.00
102 x 5 = 510.00
2. To decrease the numbers, let the scale factor be [tex]\frac{1}{5}[/tex]. So that;
0.05 x [tex]\frac{1}{5}[/tex] = 0.01
[tex]\frac{1}{2}[/tex] x [tex]\frac{1}{5}[/tex] = 0.5 x [tex]\frac{1}{5}[/tex] = 0.10
7 x [tex]\frac{1}{5}[/tex] = 1.40
13 x [tex]\frac{1}{5}[/tex] = 2.60
25 x [tex]\frac{1}{5}[/tex] = 5.00
102 x [tex]\frac{1}{5}[/tex] = 20.40
Write the equation of a circle with center (0,−6) and radius 4 in general form.
Answer:
x^2 + (y + 6)^2 = 4^2
Step-by-step explanation:
The general form we need here is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
If the center is at (0, -6) and the radius is 4, then the desired equation is
(x - 0)^2 + (y + 6)^2 = 4^2, or just
x^2 + (y + 6)^2 = 4^2
can somebody please solve for x and y, if you get the answers correct I'll give you extra points
Answer:
1) x = 18 2) x = 7
Step-by-step explanation:
Edit: Decided to solve the second too! :)
1)
12/16 = x/(x+6)
12x + 72 = 16x
72 = 4x
x = 18
2)
(-4 + 4x)/64 = 27/72
-288 + 288x = 1,728
288x = 2,016
x = 7
What is the area of this figure?
Answer:
c
Step-by-step explanation:
rectangle: 6×7=42
triangle: (4×6)÷2= 12
the whole area: 42+12=54
Meadow purchased a pair of jeans for $49.99 and a shirt for $19.99. How much money did Meadow spend?
Answer:
69.89-exact
70-rounding up
Answer:
She spent $69.98
Step-by-step explanation:
49.99 + 19.99 = 69.98 because people place .99 at the end of the cost in order to try to confuse customers that they are getting a better price then they really are, this is true because since many people read left to right, they will see the smaller number first, and they see the bigger number last, makin them believe its a better price. when at the end of a number lies a .99 it only counts as .99 not 1.00, thus this information is what helped me find my answer.
The formula shows that c, the total cost of buying pizzas at Al's restaurant depends on p, the number of pizzas ordered.
c=9p
What is the independent variable in the equation?
Answer:
p, the number of pizzas ordered
Step-by-step explanation:
The independent variable in the equation will be the variable that controls the cost.
Since the total cost will depend on the number of pizzas ordered, the number of pizzas ordered will be the independent variable.
The total cost is the dependent variable, since it depends on the number of pizzas.
So, the independent variable in the equation is p, the number of pizzas ordered.
I have a test tmrw pls help
So first you would have to find the slope using the two points and the equation: y2-y1/x2-x1, which in this case means you take 6+4/3+1, which would be a slope of 10/4 or 5/2, or 2.5. Using this, we can take a point, use point slope form, and rearrange it. So:
y-6=2.5(x-3)
y-6=2.5x-7.5
-2.5x+y=1.5