Answer:
Revenue , Cost and Profit Function
Step-by-step explanation:
Here we are given the Price/Demand Function as
P(x) = 253-2x
which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.
Now let us revenue generated from this demand i.e. x units
Revenue = Demand * Price per unit
R(x) = x * (253-2x)
= [tex]253x-2x^2[/tex]
Now let us Evaluate the Cost Function
Cost = Variable cost + Fixed Cost
Variable cost = cost per unit * number of units
= 3*x
= 3x
Fixed Cost = 6972 as given in the problem.
Hence
Cost Function C(x) = 3x+6972
Let us now find the Profit Function
Profit = Revenue - Cost
P(x) = R(x) - C(x)
= [tex]253x-2x^2 - (3x + 6972)[/tex]
= [tex]253x-3x-2x^2-6972\\= 250x-2x^2-6972\\=-2x^2+250x-6972\\[/tex]
Now we have to find the quantity at which we attain break even point.
We know that at break even point
Profit = 0
Hence P(x) = 0
[tex]-2x^2+250x-6972=0\\[/tex]
now we have to solve the above equation for x
Dividing both sides by -2 we get
[tex]x^2-125x+3486=0[/tex]
Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83
Hence we now solve the above quadratic equation using splitting the middle term method .
Hence
[tex]x^2-42x-83x+3486=0\\x(x-42)-83(x-42)=0\\(x-42)(x-83)=0\\[/tex]
Either (x-42) = 0 or (x-83) = 0 therefore
if x-42= 0 ; x=42
if x-83=0 ; x=83
Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.
The cost function is C(x) = 3x + 6972, the revenue function is R(x) = 253x - 2x², and the profit function is P(x) = 250x - 2x²- 6972. The smallest break-even point occurs at 16 bins.
To solve the given problem, let's break it down step-by-step:
Cost FunctionThe cost function includes both the fixed cost and the variable cost. The fixed cost is $6972, and the unit cost to produce one bin of cat food is $3. Therefore, the cost function C(x) where x is the number of bins is:
C(x) = 3x + 6972
Revenue FunctionThe price-demand function is given by p(x) = 253 - 2x. Revenue R(x) is the product of the price per bin and the number of bins sold, so:
R(x) = x * (253 - 2x) = 253x - 2x²
Profit FunctionThe profit function is the revenue function minus the cost function. So, the profit function P(x) is:
P(x) = R(x) - C(x) = (253x - 2x²) - (3x + 6972) = 250x - 2x² - 6972
Break-Even PointTo find the smallest break-even point, we need to solve the equation where profit equals zero:
0 = 250x - 2x² - 6972
Rewriting the equation, we get:
2x² - 250x + 6972 = 0
Solving this quadratic equation using the quadratic formula x = [-b ± sqrt(b² - 4ac)] / 2a, where a = 2, b = -250, and c = 6972:
x = [250 ± sqrt(62500 - 4*2*6972)] / 4
x = [250 ± sqrt(62500 - 27888)] / 4
x = [250 ± sqrt(34612)] / 4
x = [250 ± 186.01] / 4
So, the two solutions for x are approximately:
x = (250 + 186.01) / 4 = 109
x = (250 - 186.01) / 4 = 15.997 ≈ 16
The smallest break-even point is at a quantity of 16 bins.
The cost function is C(x) = 3x + 6972, the revenue function is R(x) = 253x - 2x², and the profit function is P(x) = 250x - 2x² - 6972. The smallest break-even point occurs at 16 bins.
please help asap reward
Hello There!
-The Numbers Ordered From Least To Greatest-
-59 -41 -23 -11
The closer the number is to zero, it is going to be a bigger number than a number far away from zero.
Find an equation for the nth term of the arithmetic sequence.
a14 = -33, a15 = 9
HELP ASAP!! THANK YOU!
Answer:
The equation of the nth term is an = -621 + 42n
Step-by-step explanation:
* Lets revise the arithmetic sequence
- There is a constant difference between each two consecutive numbers
- Ex:
# 2 , 5 , 8 , 11 , ……………………….
# 5 , 10 , 15 , 20 , …………………………
# 12 , 10 , 8 , 6 , ……………………………
* General term (nth term) of an Arithmetic sequence:
- U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d
- Un = a + (n – 1)d, where a is the first term , d is the difference
between each two consecutive terms
, n is the position of the term
* Lets solve the problem
∵ an = a + (n - 1)d
∴ a14 = a + (14 - 1)d
∴ a14 = a + 13d
∵ a14 = -33
∴ a + 13d = -33 ⇒ (1)
- Similar we can find another equation from a15
∵ a15 = a + (15 - 1)d
∴ a15 = a + 14d
∵ a15 = 9
∴ a + 14d = 9 ⇒ (2)
- We will solve equations (1) and (2) to find a and d
* Lets subtract equation (2) from equation (1)
∴ (a - a) + (13 - 14)d = (-33 - 9)
∴ -d = -42 ⇒ × both sides by -1
∴ d = 42
- Substitute this value of d in equation (1) or (2)
∵ a + 13d = -33
∵ d = 42
∴ a + 13(42) = -33
∴ a + 546 = -33 ⇒ subtract 546 from both sides
∴ a = -579
* Now lets write the equation of the nth term
∵ an = a + (n - 1)d
∵ a = -579 and d = 42
∴ an = -579 + (n - 1) 42 ⇒ open the bracket
∴ an = -579 + 42n - 42
∴ an = -621 + 42n
* The equation of the nth term is an = -621 + 42n
What is the vertex of the parabola defined by the equation
(x − 2)2 = -12(y − 2)?
A.
(-12, 2)
B.
(2, 2)
C.
(6, 2)
D.
(2, -2)
Answer:
The vertex of the parabola is (2 , 2) ⇒ answer B
Step-by-step explanation:
* Lets revise the equation of a parabola
- The equation is in the form (x − h)² = 4p (y − k), where h and k are the
vertex of the parabola
- If p > 0, the parabola opens up
- If p < 0, the parabola opens down
* Lets solve the problem
∵ The equation of the parabola is (x - h)² = 4p (y - k)
∵ The equation of the parabola is (x - 2)² = -12 (y - 2)
- By comparing the two equations
∴ 4p = -12 ⇒ divide both sides by 4
∴ p = -3 ⇒ -3 < 0
∵ p < 0
∴ The parabola opens down
- From the two equations
∴ h = 2 ⇒ the x-coordinate of the vertex
∴ k = 2 ⇒ the y-coordinate of the vertex
∴ The vertex of the parabola is (2 , 2)
The vertex of the given parabola (x - 2)^2 = -12(y - 2) is at the point (2, 2), which corresponds to Option B.
The vertex of the parabola defined by the equation (x - 2)^2 = -12(y - 2) can be found by identifying the point (h, k), where the equation fits the general form (x \\- h)^2 = 4p(y \\- k). Here, h and k represent the coordinates of the vertex, and p indicates the distance from the vertex to the focus or directrix. The given equation can be rearranged to match the general form with h = 2 and k = 2, making the vertex (2, 2). Hence, the correct answer is Option B.
(01.03)
Solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.
square root of the quantity x minus 3 end quantity plus 5 equals x
Answer:
x=7 satisfy the equation, so it is the solution.
x=4 doesn't satisfy the equation so it is extraneous solution.
Step-by-step explanation:
The equation given is:
[tex]\sqrt{x-3}+5=x[/tex]
Adding -5 on both sides
[tex]\sqrt{x-3}=x-5[/tex]
Taking square on both sides
[tex](\sqrt{x-3})^2=(x-5)^2[/tex]
Now solving
[tex]x-3 = x^2 -10x+25\\Arranging\\x^2-10x-x+3+25=0\\x^2-11x+28=0\\Factorizingx^2-7x-4x+28=0\\\\x(x-7)-4(x-7)=0\\(x-4)(x-7)=0\\x-4=0 \,\,and\,\, x-7=0\\x=4 \,\,and\,\, x=7[/tex]
Verifying solutions:
Putting x=4 in the equation
[tex]\sqrt{x-3}+5=x[/tex]
[tex]\sqrt{4-3}+5=4[/tex]
[tex]\sqrt{1}+5=4[/tex]
[tex]1+5=4[/tex]
[tex]6\neq 4[/tex]
So, x=4 doesn't satisfy the equation so it is extraneous solution.
Now Putting x=7 and verifying
[tex]\sqrt{x-3}+5=x[/tex]
[tex]\sqrt{7-3}+5=7[/tex]
[tex]\sqrt{4}+5=7[/tex]
[tex]2+5=7[/tex]
[tex]7=7[/tex]
x=7 satisfy the equation, so it is the solution.
Answer:
= 7
Step-by-step explanation:
Will vote brainliest.
Answer:
The last choice availablle
Step-by-step explanation:
The way you can tell the points the function has in common with the x-axis (also known as the solutions, roots, or zeros of the functiion) you have to factor it to solve for x. When you throw this into the quadratic formula you get that there is a negative under the square root sign, which is indicative of imaginary solutions. Imaginary solutions do NOT cross the x-axis. So the answer to your problem is the last choice.
Answer:
21 jk
Step-by-step explanation:
Nathan is flipping a coin three times.
What is the probability that it will land on tails twice and heads once?
Answer:
There is a 1 and 6 chance (16.666...%)
How many solutions does the nonlinear system of equations graphed below have?
Answer:
its one
Step-by-step explanation:
ape x legends
What is the inverse of the function f(x) = x + 2?
h(x) = 18x – 2
h(x) = 9x – 18
h(x) = 9x + 18
h(x) = 18x + 2
The inverse of the function f(x) = x + 2 is found by swapping the variables and solving for y, resulting in f^-1(x) = x - 2.
Explanation:The function f(x) = x + 2 is a simple linear function in Mathematics. The inverse of any function can be found by swapping the x and the y, and then solving for y. In this case, step-by-step, it would work like this:
Swap x and y to get x = y + 2.Solve for y by subtracting 2 from both sides to get y = x - 2.So the inverse of the function f(x) = x + 2 is f^-1(x) = x - 2.
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The inverse of the function f(x) = x + 2 is found by switching the roles of x and y and solving for y, resulting in the inverse function h(x) = x - 2. None of the provided options is correct.
Explanation:To determine the inverse of the function f(x) = x + 2, you need to first replace f(x) with y, resulting in the equation y = x + 2. Next, swap x and y to get x = y + 2. Solve for y to find the inverse function: y = x - 2. Therefore, none of the options provided is the correct inverse of the function f(x) = x + 2. The correct inverse is h(x) = x - 2.
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A triangle has vertices of (1, 5), (2, 2), and (6, 3). What are the vertices of the image created by applying the translation (x,y) --> (x+6,y-4)?
Answer:
Step-by-step explanation:
the translation (x,y) --> (x+6,y-4):
(1, 5)--> (1+6,5-4)=(7,1)
(2, 2)--> (2+6,2-4)=(8,- 2)
(6, 3)--> (6+6,3-4)=(12,- 1)
the image of A triangle has vertices of (1, 5), (2, 2), and (6, 3) is :
the triangle has vertices of (7, 1), (8,- 2), and (12, -1)
Which one of the following is an example of deductive reasoning?
A) The first term of a sequence of numbers is 1, the second term is 3, and the third term is 5. Thus, the nth term is 2n-1.
B) The sum of the angles in Which one of the following is an example of deduct and in Which one of the following is an example of deduct is 180 degrees. Therefore, the sum of the angles in any trianlge is 180 degrees.
C) All rectangles have four right angles. Since ABCD is a rectangle, it must have four right angles.
D) Line l1 has a slope of 5 and line l2 has a slope of 4. Line l1 is closer to the appearance of a vertical line than l2. Thus, the larger the slope of a line, the more vertical the line will appear.
Answer:
I want to say that the answer is C.
Hope this helps!
Ordered 145 packs of printer paper based on average daily use she knows that the paper will last about 65 days how many packs of printer paper should the manager expect to have after 5 days
Answer:
11.15 packs of paper are used in 5 days; therefore, 133.85 are left
Step-by-step explanation:
Set this up as ratio with days on top and packs of paper on the bottom. Filling in the ratio with the info we have, keeping in mind we are looking for packs of paper left after 5 days:
[tex]\frac{days}{packs}:\frac{65}{145}=\frac{5}{x}[/tex]
Cross multiply to get 65x = 725 and x = 11.15. This represents the number of packs used. To get the number of packs remaining, subtract 11.15 from 145 to get 133.85 remaining after 5 days.
In a basketball drill, two players start at the same spot on the court. One player runs 6 feet
down the court and the other player runs 4.5 feet across the court (in a direction perpendicular
to the first player). What is the distance that one player must pass the ball for it to reach the
other?
Answer:
7.5 ft
Step-by-step explanation:
The distance can be found using the Pythagorean theorem. The given distances form the legs of a right triangle, and the ending distance (d) between the players is its hypotenuse. The Pythagorean theorem tells you ...
d² = (6 ft)² +(4.5 ft)² = 36 ft² +20.25 ft²
d² = 56.25 ft² = (7.5 ft)² . . simplifying and rewriting as a square
d = 7.5 ft . . . . . . . . . . . . . . . taking the positive square root
The ball must be passed a distance of 7.5 ft for it to reach between players.
_____
If you recognize the given numbers as having the ratio 3:4, then you may realize they are the legs of a 3-4-5 right triangle with a scale factor of 1.5. The distance between players will be 1.5×5 = 7.5 feet.
Answer:
[tex]\boxed{\text{7.5 ft}}[/tex]
Step-by-step explanation:
If the players are running perpendicular to each other, we have a right triangle, as in the diagram below.
We can apply Pythagoras' Theorem.
[tex]\begin{array}{rcl}a^{2} & = & b^{2} + c^{2}\\& = & 4.5^{2} + 6^{2}\\& = & 20.25 +36\\& = & 56.25\\a & = & \sqrt{56.25}\\& = & \mathbf{7.5}\\\end{array}\\\text{The distance between the two players will be } \boxed{\textbf{7.5 ft}}[/tex]
Please help 10points
Answer:
x = 9
Step-by-step explanation:
Those are chords of a circle, and the theorem to find x is, in this context:
6(3) = 2(x) so
18 = 2x and
x = 9
Jack plays cards with friend each afternoon here are his scores from the last 5 games 8,-6,-3,4,7 which is the least of his scores
Answer:
-6
Step-by-step explanation:
8,-6,-3,4,7 rearranged in ascending order produces -6, -3, 4, 7, 8.
-6 is the least of these scores (i. e., -6 is the lowest score).
Final answer:
Jack's least score from his last 5 card games is -6, as it is the smallest number in the set of his scores.
Explanation:
The question involves identifying the least score from a set of given numbers. To find the least score, Jack's scores from the last 5 card games are considered: 8, -6, -3, 4, 7.
Upon reviewing these numbers, it can be determined that -6 is the least because it is the smallest number and also it has a negative value, which makes it less than all the positive scores or any potential zero scores. Thus, the least of Jack’s scores is -6.
Please help me with this question, I'm actually sick of people who keep answering dumb things just to get the points. I really need help with this.
Answer:
see below
Step-by-step explanation:
Events are independent when the probability of one of them does not depend on the other one. That is, P(A|B) = P(A) and P(B|A) = P(B).
They are not independent if the above condition is not met.
A quick assessment of the given table shows ratios of one row to the next are different between columns, and vice versa. Hence the events are not indpendent.
A pizza shop offers the toppings shown below how many different three topping pizzas can you make ?
Pepperoni
Mushrooms
Sausage
Onion
Ham
A. 6
B. 10
C. 4
D. 5
Answer:
B. 10.
Step-by-step explanation:
This is the number of combinations of 3 from 5.
5C3 = 5! / 3! (5-3)!
= 5*4*3*2*1 / 3*2*1 * 2*1
= 5*4/2*1
= 10.
Answer: 10 i think
Step-by-step explanation:
Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled 3/4 for the flowers to last yhe longest. Her cylinder vase has a radius of 2 in and a height of 9 in how much water should mary pour into the vase?
Answer:
84.8 in³
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h
The volume Mary will be filling will be 3/4 of the 9-inch height of the vase, so is ...
V = π(2 in)²(3/4·9 in) = 27π in³ ≈ 84.8 in³
_____
Comment on the answer
In more conventional units of measure, that is very nearly 3 pints of water.
If the graphs of the lines in the system of equations above the intersect at (-3,1), what is the value of K/H?
A) 3/2
B) 2
C) 3
D) 6
Answer:
h = 2 and k = 6
Step-by-step explanation:
Since the lines intersect at (- 3, 1) then this is the solution to the system of equations.
That is x = - 3 and y = 1
Substitute these values into the equations and solve for h and k
hx - 4y = - 10
- 3h - 4 = - 10 ( add 4 to both sides )
- 3h = - 6 ( divide both sides by - 3 )
h = 2
Similarly
kx + 3y = - 15
- 3k + 3 = - 15 ( subtract 3 from both sides )
- 3k = - 18 ( divide both sides by - 3 )
k = 6
In a week, a light bulb factory produces 12,500 light bulbs. The ratio of light emitting diodes (LED bulbs) to compact fluorescent lamps (CFL bulbs) is 2:3. Of the LED bulbs produced, 3% were defective. How many LED bulbs were not defective?
A) 150
B) 2,425
C) 4,850
D) 7,275
Answer:
C) 4,850
Step-by-step explanation:
No. of
LED bulbs : CFL bulbs : Total
2 : 3 : 5
5000 : 7500 : 12 500
Percentage of non-defective LED bulbs = 100% - 3% = 97%
No. of non-defective LED bulbs = 97% x 5000 = 4850
A party store has 54 packs of plates in stock. The packs are either sets of 8 or sets of 12. If the store has 496 total plates in stock, how many plates would the customer buy if he or she buys all of the 12 that the store has in stock?
A) 16
B) 38
C) 192
D) 304
Answer:
a 16
Step-by-step explanation:
16 x 12 = 192 plates
496 total plates - 192 = 304
304 packages of 8 plates
304 / 8 = 38 sets of 8 plates
38 + 16 = 54 packs of plates
please help asap will mark brainliest
Answer:
10x
Step-by-step explanation:
Note the place values of the value 3 in both of the decimals.
The value of the 3 in 46.132 is in the hundredths place.
The value of the 3 in 8.553 is in the thousandths place.
Divide thousands with hundreds: 1000/100 = 10
The value of the 3 in 46.132 is 10x larger than the value of 3 in 8.553
~
What do you know to be true about values of p and q?
Answer:
p = q
Step-by-step explanation:
There are 180 degrees in a triangle. If you subtract 50 and 60 from 180, you get 70. If you subtract 30 an 80 from 180, you get 70. therefore p = q.
The length of a rectangular garden ABCD is 9 feet more than its width. It is surrounded by a brick walkway 4 feet wide as shown below. Suppose the total area of the walkway is 400 square feet. 25. What are the dimensions of the garden?
Answer:
16.5 ft by 25.5 ft
Step-by-step explanation:
Let w represent the width of the garden in feet. Then w+9 is the garden's length, and w(w+9) represents its area.
The surrounding walkway adds 8 feet to each dimension, so the total area of the garden with the walkway is ...
(w+8)(w+9+8) = w^2 +25w +136
If we subtract the area of the garden itself, then the remaining area is that of the walkway:
(w^2 +25w +136) - (w(w+9)) = 400
16w + 136 = 400 . . .simplify
16w = 264 . . . . . . . . subtract 136
264/16 = w = 16.5 . . . . . width of the garden in feet
w+9 = 25.5 . . . . . . . . . . .length of the garden in feet
PLS HELP SHOW ALL YOUR WORKING OUT
THANK YOU IN ADVANCE :D
Answer:
[tex]AB =3 \sqrt{5} = 6.708203932...[/tex]
Step-by-step explanation:
[tex]A( - 1,6) \:,\: B(5,3)\\ AB = \sqrt{{(x1 - x2)}^{2} + {(y1 - y2)}^{2} } \\ AB = \sqrt{ {( - 1 - 5)}^{2} + {(6 - 3)}^{2} } \\ AB = \sqrt{ {( - 6)}^{2} + {(3)}^{2} } \\ AB = \sqrt{36 + 9} \\ AB = \sqrt{45} = 3 \sqrt{5} = 6.708203932...[/tex]
The distance between A and B to 3 significant figure is 6.71
The formula for calculating the distance between two points is expressed as:
[tex]D =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Given the coordinate points (-1, 6) and (5, 3)
Substitute the given coordinates into the formula;
[tex]D =\sqrt{5+1)^2+(3-6)^2}\\D =\sqrt{(6^2+(-3)^2}\\D=\sqrt{36+9}\\D=\sqrt{45}\\D= 6.71\\[/tex]
Hence the distance between A and B to 3 significant figure is 6.71
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Find the mean of the data summarized in the given frequency distribution. compare the computed mean to the actual mean of 51.8 degrees. low temperature (circlef) 40minus44 45minus49 50minus54 55minus59 60minus64 frequency 3 4 10 6 2
Answer:
Mean = 47.52 degrees
Step-by-step explanation:
We will use the following method to find the mean
Class interval Frequency(f) Class Mark(X) fx
40-44 3 42 126
45-49 4 47 188
50-54 10 52 520
55-59 6 57 342
60-64 2 62 124
.........................................................................................................
25 1188
.........................................
The formula for mean is:
Mean = ∑fx / ∑f
= 1188/25
= 47.52 degrees
The computed mean is less than the actual mean of 51.8 degrees ..
Use the graph of each polynomial function to find the factored form of the related polynomial. Assume the polynomial has no constant factor.
What are the zeros of this function? (2 points) _______, _______
What is the factorization of the polynomial? (2 points)
Answer:
zeros: x = -2; x = +4factorization: y = (x +2)(x -4)Step-by-step explanation:
The zeros are where the graph crosses the x-axis (y=0). They are x=-2 and x=4.
The factors are the binomials that are zero when x has the value of a zero:
y = (x +2)(x -4)
What is the surface area of this rectangular prism
Answer:
C. [tex]490 \textrm{ units}^{2}[/tex]
Step-by-step explanation:
The formula for surface area is
LA + 2B
LA indicated Lateral Area and can be found multiplying perimeter of base by the height.
7 + 7 + 14 + 14 = 42 * 7 = 294
Multiply the LA from above with the area of base times 2.
98 * 2 = 196
294 + 196 = 490, so the surface area of the rectangular prism is 490 units.
To find the surface area of a rectangular prism, add up the areas of all six faces by multiplying length by width.
Explanation:To find the surface area of a rectangular prism, you need to add up the areas of all six faces. Each face is a rectangle, so to find the area, you multiply the length by the width. Then, you add up the areas of all the faces to get the total surface area.
For example, if the length of one side is 4 units, the width is 2 units, and the height is 3 units, the surface area would be:
Face 1: 4 units x 2 units = 8 square units
Face 2: 4 units x 2 units = 8 square units
Face 3: 4 units x 3 units = 12 square units
Face 4: 4 units x 3 units = 12 square units
Face 5: 2 units x 3 units = 6 square units
Face 6: 2 units x 3 units = 6 square units
Total surface area: 8 + 8 + 12 + 12 + 6 + 6 = 52 square units.
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Suppose $r$ and $s$ are the values of $x$ that satisfy the equation
\[x^2 - 2mx + (m^2+2m+3) = 0\]for some real number $m$. Find the minimum real value of $r^2+s^2$.
Answer:
-8
Step-by-step explanation:
For roots r and s, the quadratic can be factored ...
f(x) = (x -r)(x -s) = x^2 -(r+s)x +rs
Then the value of r^2+s^2 can be determined from the coefficient of x (-(r+s)) and the constant (rs) by ...
r^2 +s^2 = (-(r+s))^2 -2(rs) = (r^2 +2rs +s^2) -2rs = r^2 +s^2
Comparing this to your given equation, we have the coefficient of x as (-2m) and the constant term as (m^2+2m+3). Forming the expression ...
(x-coefficient)^2 -2(constant term)
we get ...
r^2 +s^2 = (-2m)^2 -2(m^2 +2m +3) = 2m^2 -4m -6
r^2 +s^2 = 2(m -1)^2 -8
The minimum value of this quadratic expression is where m=1 and the squared term is zero. That minimum value is -8.
A deposit of $10,000.00 was made to an account the year you were born. After 12 years, the account had earned $6,600.00 in interest. What simple interest rate did the account earn?
Answer:
5.5% per year
Step-by-step explanation:
Using Formula A = P (1 + rt)
Where
A = Final amount = $10,000 + $6,600 = $16,600
P = Principal = Beginning Amount = $10,000
t = time = 12 years
r = rate in $/year (which we need to find)
Assembling the formula
A = P (1 + rt)
16,600 = 10,000 (1 + 12r)
[tex]\frac{16,600}{10,000}[/tex] = 1 + 12r
1.66 = 1 + 12r
1.66 - 1 = 12r
0.66 = 12 r
r = 0.055 = 5.5%
Given the exponential function f(x) = 54(0.45)x, classify the function as exponential growth or decay and determine the percent rate of growth or decay.
A.Exponential decay, 55% decrease
B.Exponential growth, 45% increase
C.Exponential decay, 45% decrease
D.Exponential growth, 55% increase
Answer:
Option A.Exponential decay, 55% decrease
Step-by-step explanation:
we have
[tex]f(x)=54(0.45)^{x}[/tex]
This is a exponential function of the form
[tex]f(x)=a(b)^{x}[/tex]
where
a is the initial value
b is the base
b=(1+r)
r is the rate of change
In this problem
a=54
b=0.45
so
0.45=1+r
r=0.45-1
r=-0.55
Convert to percentage
r=-55% ------> is negative because is a exponential decay
Answer:
Exponential decay, 55% decrease
Step-by-step explanation:
[tex]f(x) = 54(0.45)^x[/tex]
General exponential growth function is [tex]y=a(1+r)^x[/tex]
exponential growth function is [tex]y=a(1-r)^x[/tex]
The value of 1-r is less than 1 then it is exponential decay
In the given f(x) , the 1-r is 0.45 that is less than 1
So it is exponential decay.
[tex]1-r= 0.45[/tex]
Subtract 1 on both sides
[tex]r=0.55[/tex]
Multiply by 100 to get %
r= 55%
Exponential decay, 55% decrease