Answer:
y=4x+13
y=3x2-x-1
Step-by-step explanation:
the two are only functions given in the option
A bacterial culture starts with 400 bacteria and grows at a rate proportional to its size. After 2 hours there will be 800 bacteria.
1) Express the population, P(t) after t hours as a function of t
2) Using your equation from above, what will the population be after 8 hours?
3) Using your equation from above, after how many hours will the population reach 2270 bacteria?
Answer:
P(t) = 400×2^(t/2)64005.0Step-by-step explanation:
The wording "a rate proportional to its size" is an indication that growth (or decay) is exponential.
1) For many problems involving exponential growth, I like to use the numbers given in the problem statement as follows.
population = (initial population) × (growth factor)^(t/(growth period))
where the "growth period" is the period of time in which the population is multiplied by the "growth factor".
Here, we're given ...
(initial population) = 400
(growth factor) = 800/400 = 2
(growth period) = 2 . . . . hours
So, our population function can be written as ...
P(t) = 400×2^(t/2)
__
2) Putting t=8 into the formula, we get ...
P(8) = 400×2^(8/2) = 400×16 = 6400
After 8 hours, the population will be 6400.
__
3) Fill in the given number and solve for t.
2270 = 400×2^(t/2)
2270/400 = 2^(t/2)
Taking logs, we have ...
log(227/40) = (t/2)log(2)
t = 2×log(227/40)/log(2) ≈ 5.009
After 5.0 hours, the population will reach 2270.
QR is tangent to circle P at point Q.
Circle P is shown. Line segment P Q is a radius. Line segment Q R is a tangent that intersects the circle at point Q. A line is drawn from point R to point P and goes through a point on the circle. Angle Q P R is 53 degrees.
What is the measure of angle R?
37°
53°
90°
97°
Answer:
A. 37 degrees
Step-by-step explanation:
Since QR is tangent to the circle, it means that is in a right angle. Meaning that angle Q is equal to 90 degrees.
Since you know what two angles are equal to, you can use the triangle angle sum theorem by setting them all up to 180.
53+90+x=180
Simplify the answer
143+x=180
Subtract 143 from both sides
X=37
:
The measure of angle ∠QRP = 37°.
What is a tangent to a circle ?Tangent to a circle is a straight line which touches the circle at only one point and the point of contact is perpendicular to the radius drawn from the center of the circle.
In the given question
Line segment PQ is radius, Line segment QR is is a tangent to the circle(P) at point Q.
Here QR is perpendicular to PQ because tangent to a circle is perpendicular to the point of contact and a line (PQ) drawn from the center of the circle (P).
∴ ∠PQR = 90° given ∠QPR = 53° We have to find ∠QRP .
We know the sum of all the interior angles in a triangle is = 180°
∠PQR + ∠QPR + ∠QRP = 180°
90° + 53° + ∠QRP = 180°
∠QRP = 180° - (90° + 53°)
∠QRP = 180° - 143°
∠QRP = 37°
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The point A(4, –1) is reflected over the x-axis. Use a mapping to find the coordinates of A’. A’(4, –1) A’(–4, –1) A’(4, 1) A’(–4, 1)
Answer:
(C) A'(4, 1)
Step-by-step explanation:
When a point is reflected across the x-axis, the following happens
The x-coordinate remains the sameThe y-coordinate is transformed into its opposite (its sign is changed).Given the Point A(4, –1)
When it is reflected, following the rules above
The x-coordinate remains 4The y-coordinate changes from -1 to 1.The coordinates of A' will therefore be: A'(4,1)
Answer:
c
Step-by-step explanation:
just did it on ed 2020
Which graph models the function f(x) = -4(2)x? (2 points)
Answer:
pls mark me brainliest
Step-by-step explanation:
Answer:
Step-by-step explanation:
How many places do you need to move the decimal to the left to write the
number below in scientific notation?
6000000000000
Answer: 6 x 10^12
Step-by-step explanation:
Move the decimal to the left so there is one non-zero digit number left of the decimal point. This will be the exponent placed on 10
PLEASE HELP! Is my answer correct?
We know angle P is 90 degrees because of Thales Theorem, and angle N is 60 degrees. Because the angles in a triangle have to add up to 180 degrees, angle PMN has to be 30 degrees.
Angle QMO is half of angle PMN, so it's 15 degrees. Angle MQO is equal to angle QMO because the radii make Triangle OQM isosceles, so angle MQO is 15 degrees.
Answer:
yes this is right
Step-by-step explanation:
the triangle MOQ is icosceles and angle O is 150 degrees so that leaves 30/2... 15.
Lou started his savings account with 50$ he now only has 31$. What percent of change did his savings account have?
Answer:
Step-by-step explanation:
50 - 31 = 19
38%
Are you winning or losing?
Answer:
You are winning
Step-by-step explanation: If you drop in $2 a day for 10 weeks you have spent $20. You have won $75 from the slots which leaves you with a gain of $55.
Milton has his money invested in a stock portfolio. The value, v(.r), of his
portfolio can be modeled with the function y(x) = 30,000(0.78)", where x is the
number of years since he made his investment. Which statement describes the rate
of change of the value of his portfolio?
A) It decreases 78% per year. B) It decreases 22% per year.
C) It increases 78% per year. D) It increases 22% per year.
Answer:
B) It decreases 22% per year.
Step-by-step explanation:
We are given that The value, v(.r), of his portfolio can be modeled with the function : [tex]y(x) = 30,000(0.78)^x[/tex]
Where x is the number of years since he made his investment.
Formula :[tex]P(1-r)^t=A[/tex]
Where P = Principal
r = rate of decrease
t = time
A = Amount after t years
So, On comparing
P = 30000
t=x
A=y(x)
[tex]1-r=0.78[/tex]
[tex]\Rightarrow 1-0.78=r[/tex]
[tex]\Rightarrow 0.22=r[/tex]
So, r = 0.22
r=22%
So, Rate of decrease is 22%
So, Option B is true,
It decreases 22% per year.
Please help me how do you recognize and complete a geometric sequence
Answer:
Step-by-step explanation:
If the sequence is being multiplied, for instance:
1, 2, 4 ,8 ,16
It is being multiplied by 2 every term.
Consider Brainliest.
Which of the following is not equal to 63.7 mm?
6.37 x 10 4 µm
6.37 x 10 -5 km
637 cm
0.637 dm
The correct option is c. 637 cm is not equal to 63.7 mm.
To solve this problem, we need to convert each of the given units to millimeters (mm) and then compare them to 63.7 mm.
a. [tex]\(6.37 \times 10^4 \, \mu m\)[/tex] to mm:
Since 1 mm = \(1 \times 10^3 \, \mu m\), we have
\[6.37 \times 10^4 \, \mu m \times \frac{1 \, mm}{1 \times 10^3 \, \mu m} = 63.7 \, mm\]
This is equal to 63.7 mm.
b. [tex]\(6.37 \times 10^{-5} \, km\)[/tex] to mm:
Since 1 km = [tex]\(1 \times 10^6 \, mm\)[/tex], we have
[tex]\[6.37 \times 10^{-5} \, km \times \frac{1 \times 10^6 \, mm}{1 \, km} = 63.7 \, mm\][/tex]
This is also equal to 63.7 mm.
c. 637 cm to mm:
Since 1 cm = 10 mm, we have
[tex]\[637 \, cm \times \frac{10 \, mm}{1 \, cm} = 6370 \, mm\][/tex]
This is not equal to 63.7 mm.
d. 0.637 dm to mm:
Since 1 dm = 100 mm, we have
[tex]\[0.637 \, dm \times \frac{100 \, mm}{1 \, dm} = 63.7 \, mm\][/tex]
This is equal to 63.7 mm.
Therefore, the only option that is not equal to 63.7 mm is 637 cm.
please help i’ll mark brainlest
Answer:i really dont know but i think it 27.5
Step-by-step explanation:
i think i've answered this before dont trust mee
Answer:
∠ A = 68°
Step-by-step explanation:
The sum of the interior angles of a kite = 360°
The opposite angles A and C are congruent
360° - (123 + 101)° = 360° - 224° = 136°
Thus since ∠ A = ∠ C, then
∠ A = [tex]\frac{136}{2}[/tex] = 68°
I know why but I can’t explain it and it won’t except my explanation someone help!
Abdul is creating a cushion that is 1 foot by 2 feet by 3 feet. He wants to find the least amount of fabric he will need to cover the cushion. He starts by drawing the net shown here.
A net is formed by 2 rectangles. 1 rectangle has a base of 4 feet and height of 3 feet. The other rectangle has a base of 5 feet and height of 2 feet.
What is the least amount of fabric he will need to cover the cushion?
Answer:
22 ft²
Step-by-step explanation:
Surface area:
2×(1+3+1) + 3×(1+2+1)
2×5 + 3×4
10 + 12
22 ft²
Answer:
22
Step-by-step explanation:
im with you . i suck at math too
simplify 3 square root of 4/ 3 square root of 5
The final simplified expression is 2 over the square root of 5, represented as [tex]\( \frac{2}{\sqrt{5}} \).[/tex]
Let's break it down step by step:
1. Simplify the square roots:
[tex]- \(\sqrt{4}\) equals 2 because \(2 \times 2 = 4\). So, \(\sqrt{4} = 2\).[/tex]
- We have [tex]\(\sqrt{5}\)[/tex] in the denominator, which cannot be simplified further because 5 is a prime number and doesn't have any perfect square factors.
2. Substitute the simplified square roots:
- After simplifying [tex]\(\sqrt{4}\)[/tex] to 2, the expression becomes [tex]\(\frac{3 \times 2}{3\sqrt{5}}\).[/tex]
3. Cancel out the common factor:
- Both the numerator and the denominator have a factor of 3. So, we can cancel out 3 from both sides:
[tex]\[\frac{3 \times 2}{3\sqrt{5}} = \frac{2}{\sqrt{5}}\][/tex]
4. Final simplification:
- The expression [tex]\(\frac{2}{\sqrt{5}}\)[/tex] is simplified as far as it can go because the square root of 5 cannot be simplified further.
So, the simplified expression is [tex]\(\frac{2}{\sqrt{5}}\).[/tex]
Mark, Chase, and Beatrice are running a 100-meter race. Which list represents the sample space of all the possible ways in which the three runners can win first, second, and third places? If there were four runners and three positions to be won, what would the sample size be?
A.
The sample space is {MBC, BCM, CMB}. If there were four runners, the sample size would be 4.
B.
The sample space is {MBC, MCB, BCM, BMC, CBM, CMB}. If there were four runners, the sample size would be 24.
C.
The sample space is {MBC, BCM, CMB}. If there were four runners, the sample size would be 4.
D.
The sample space is {MBC, MCB, BCM, BMC, CBM, CMB}. If there were four runners, the sample size would be 16.
the answer is B: 24
i know it
at the grocery store, you bought 4 boxes of cereal and a carton of strawberries. The carton of strawberries costs $2.89. The bill came to a total of $12.25. How much was one box of cereal?
Answer:
$2.34
Step-by-step explanation:
Cost of 4 boxes
The cost of 4 boxes must be the difference between the total and the strawberries
total-strawberries
12.25-2.89=9.36
4 boxes costs $9.36
Cost of 1 box
You bought 4 boxes for $9.36, and each box costs the same, so we can divide the cost by the number of boxes
cost/boxes
9.36/4=2.34
Each box of cereal costs $2.34
Answer:
$2.34
Step-by-step explanation:
So first you have to subtract 2.89 from 12.25. then you should get 9.36. After you get that you have to divide 9.36 by 4 because there are 4 boxes of cereal and we need to know how much is the cost of one box of cereal. ONce you get that the answer would be $2.34.
Solve the system of equations below by graphing both equations with a
pencil and paper. What is the solution?
y = 2x - 3
y = -2x + 5
A.) (-2,5)
B.) (-2,-7)
C.) (2,1)
D.) (2,-3)
Answer:
4
Step-by-step explanation:
Answer:
The answer is C. (2,1)
Step-by-step explanation:
Sophia invests $12,500 in an account that earns 4% annual simple interest. Assuming she makes no additional deposits or withdrawals, how much interest will Sophia earn after 3 years?
[tex]\text{Simple interest formula:}\\\\A=P(1+rt)\\\\\text{Plug in your given values:}\\\\A=12,500(1+0.04(3))\\\\\text{Solve:}\\\\A=12,500(1+0.04(3))\\\\A=12,500(1+0.12)\\\\A=12,500(1.12)\\\\A=14,000\\\\\boxed{\$14,000}[/tex]
Sophia will earn $14, 000 in interests after 3 years.
What is Interest?The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.
We have,
Sophia invests $12,500 in an account.
R= 4%
Time= 3 years
So, Amount = P(1+ rt)
A = 12500 (1 + 0.04(3))
A = 12500 ( 1 + 0.12)
A = 12500 + 1.12
A = $14, 000
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8 times the sum of 2 and 15
Answer:
136
Step-by-step explanation:
15 plus 2 is 17,then multiplied by 8
What is side Bc round to nearest hundredth
Answer:
BC = 15.01
Step-by-step explanation:
Solve this question using a trigonometry ratio, which you can remember them all with SohCahToa, which says:
sinθ = opp / hyp
cosθ = adj / hyp
tanθ = opp / adj
θ means the "angle of reference" (angle we are talking about).
In this problem, θ is A = 65°,
To decide which trig. ratio to use, find out which sides we want to use. We will use AC = 7 because we know it.
We also use BC because we need to find it.
In relation to ∠A or θ, AC is adjacent and BC is opposite.
The ratio with adjacent and opposite is tangent.
tanθ = opp / adj Substitute the variables for this question
tanA = BC / AC Substitute the values you know
tan65° = BC / 7 Rearrange this and isolate C
BC = 7tan65° Multiply 7 and tan65 to find the missing side
BC = 15.011548...... Exact answer on your calculator
BC ≈ 15.01 Round to nearest hundredth
What ordered pair corresponds to point G?
Answer:
(-5,-2)
Step-by-step explanation:
g is on those coordinates.
Answer:
(-5,-2)
Step-by-step explanation:
Refer to the image, please.
Answer:
7
Step-by-step explanation:
140*.60, 140*.55
=84 - 77 = 7
Heather has a bag with 16 red blocks, 11 bile blocks, 9 purple blocks, 15 green blocks, 8 yellow blocks, and 20 orange blocks. If she
was to draw a block out of the bag, record the color and replace the block back in the bag, repeating 500 times, what would most
likely be the probability of drawing a green block (round to the nearest hundredth)?
Answer:0.19
Answer:
it would be 0.25
Step-by-step explanation:
I think the answer would be 0.19
(Hope this helps!)
PLEASE HELP!!!!!!
Look at the figure. Find the value of x.
A.) 90
B.) 30
C.) 15
D.) 45
Answer:
15
Step-by-step explanation:
An isosceles triangle has equal base angles.
Hence,
[tex] 3x=5x-30\\
\implies 30=2x\\
\implies x=15[/tex]
Answer:
C
Step-by-step explanation:
Well all triangles need to be equal to 180°. When you substitute a, b, and d in for x, the result are bigger than 180 not including the 3rd angle. With C the angles equal 45° and 45° angle which leave the appropriate sized angle for the 3rd angle at 90°. So x is equal to 15.
In triangle ABC a=8. b=6, and angleC= 60°. Find the measure of angleA
16 degrees
46 degrees
74 degrees
106 degrees
Answer: The correct answer is 74˚
Please answer ASAP. What is the negative angle of rotation for the angle with positive angle
of rotation 270º?
Answer:
-90
Step-by-step explanation:
The full circle is 360 degrees, so is you turn one way say 10 degrees, then you would need to move 350 degrees in opposite direction.
So, in this case moving 270 one way would be equivalent to moving 360-270=90 degrees in the opposite direction
You sell tires for $65 each at your automotive service shop. At this price, what does it cost to purchase a set of 4 tires, not including tax?
$69
$105
$260
$280
$325
Answer:
$260
Step-by-step explanation:
you multiply $65 by 4 for the set of four and the product is $260.
Answer:
A set of 4 tires cost $260.
Step-by-step explanation:
It is given that each tire is sold for $65. In order to find a set of 4 tires, you have to multiply it by 4 :
1 tire = $65
4 tires = $65×4
= $260
Find the value of X.
Answer:
x = 109
Step-by-step explanation:
In pentagons, the total degrees for the interior angles is always 540 degrees.
540 = 91 + 160 + 100 + 80 + x
540 = 431 + x
109 = x
I hope this helped!
3/4 + 1/2=
7/8-3/8 =
5/6 1/4 =
4/6/1/4 =
178.96 - 25.78 =
10.25 - 110.25 + 1110.25 =
2.789 * 1.458 =
56.64/S =
Answer:
Okay so,
Step-by-step explanation:
the first one is
1.25 or 1 [tex]\frac{1}{4}[/tex]
second one is
0.5 or [tex]\frac{1}{2}[/tex]
the third one is
i'm not sure what the question is
the fourth one is
i'm not sure what the question is. Are you dividing?
the fifth one is
153.18
the sixth one is
1010.25
the seventh one is
4.066362
the eight one is
i'm not sure what the question is
Can you make me brainliest please