Answer:
a) growth b) decay
Step-by-step explanation:
In the function f (x) = b^x when b > 1, the function represents exponential growth.
In the function f (x) = b^x when 0 < b < 1, the function represents exponential decay.
a)b=2 > 1 this function growth
b)b=0.5 < 1 this function decay
A new car is purchased for $ 33 , 000 $33,000 and over time its value depreciates by one half every 7 years. What is the value of the car 4 years after it was purchased, to the nearest hundred dollars?
The equation of the value of the car over a year is 2357.14x + y = 33,000. Then the value of the car 4 years after it was purchased is $23571.43.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
A new car is purchased for $33,000 and overtime its value depreciates by one half every 7 years.
Then the value of the car is given by the linear equation. Then the line is passing through (0, $33,000) and (7, $16,500). Then we have
Let y be the value of the car and x be the number of years. Then we have
[tex]\rm y \ - \ 33000 \ \ = -\dfrac{16,500}{7} (x-0)\\\\y+2357.14x = 33000[/tex]
Then the value of the car 4 years after it was purchased, to the nearest hundred dollars will be
[tex]\begin{aligned} \rm y +2,357.14 \times 4 &= 33,000\\\\\rm y + 9,428.57 &= 33,000\\\\\rm y &= 23,571.43 \end{aligned}[/tex]
More about the linear system link is given below.
https://brainly.com/question/20379472
#SPJ1
Please help me pretty please
Answer: D.
Step-by-step explanation:
The equation [tex]f(x) = (x-1)^{2} - 2[/tex] works only for option D. If x is 2, for example, the equation would look like this: [tex]f(2) = (2-1)^{2} - 2[/tex]. This equals [tex](1)^{2} - 2[/tex] which equals negative one. Therefore, when x is 2, y is -1. All of the graphs have the point (2, -1). We can still tell though that it is not A or B because there are spaces in between the points. If x = 2.2, the equation would not work for A or B because there is not a point with an x value of 2.2. This is different for both C and D. Δ
Answer C ends off early. There are endpoints to the figure. If x = 4, the equation would not work. This is because there is no point in answer C that has an x value of 4. On the other hand, question D does have a point with an x value of 4.
If x = 4, the equation looks like [tex]f(4) = (4-1)^{2} - 2[/tex].
We can simplify this to [tex]f(4) = (3)^{2} - 2[/tex]
and then [tex]f(4) = 7[/tex]
This means that when x is 4, y is 7. This is true for no graph but option D. Therefore the answer to this problem is D.
What is the equation of the directrix to the right of the center of = 1? express the answer in decimal format. x =
The equation of the directrix to the right of the center is equal to 2.8.
Given the following data:
(x - 1)²/9 - (y - 2)²/16 = 1.
How to determine the equation of the directrix?Mathematically, the standard equation of the directrix lines for a hyperbola of the form (x - h)²/a² - (y - k)²/b² = 1 is given by:
x = h ± a²/√(a² + b²)
Where:
a² = 9.b² = 16.h = 1.Substituting the given parameters into the standard equation, we have;
x = 1 ± a²/√(a² + b²)
x = 1 ± 9/√(9 + 16)
x = 1 ± 9/√25
x = 1 ± 9/5
x = 1 + 9/5
x = 1 + 1.8
x = 2.8.
Read more on directrix here: https://brainly.com/question/2346582
Answer: The answer is 2.8
Step-by-step explanation:
The conditional relative frequency table was generated using data that compares the favorite subjects of male and female students at a high school. the survey was given to 120 male students and 180 female students. a 4-column table with 3 rows. the first column has no label with entries male, female, total. the second column is labeled math favorite subject with entries 0.35, 0.45, 0.41. the third column is labeled other favorite subject with entries 0.65, 0.55, 0.59. the fourth column is labeled total with entries 1.0, 1.0, 1.0. how many students in the survey said that math was their favorite subject? 42 81 120 123
The number of students in the survey said that math was their favorite subject is given by: Option D: 123
What is conditional relative frequency?Conditional relative frequency is relative frequency conditional to some special characteristic.
For this case, we're specified the following table:
[tex]\begin{array}{cccc}&\text{Math}&\text{Other favorite subject}&\rm Total\\\text{Male}&0.35&0.65&1.0\\\text{Female}&0.45&0.55&1.0\\\rm Total &0.41&0.59&1.0 \end{array}[/tex]
It is given that:
the survey was given to 120 male students andthe survey was given to 180 female studentsWe have to find how many students in the survey said that math was their favorite subject.
From males, 0.35 out of 1 male said math was their favorite subject. (since total in male is 1, showing that the row of males got conditional relative frequency conditional to the gender male, and relative to the total count of males).
Thus, as out of 1, there was 0.35 supporter of math (from males), so from 120 male students, there were [tex]120\times 0.35 = 42[/tex] male students who had chosen math as their favorite subject.
Similarly, 0.45 per 1 female student chose their favorite subject as math.
Since there are 180 female students, therefore, total [tex]180\times 0.45 = 81[/tex] female students had chosen math as their favorite subject.
So, total 42+81=123 students had chosen math as their favorite subject.
Thus, the number of students in the survey said that math was their favorite subject is given by: Option D: 123
Learn more about conditional relative frequency here:
https://brainly.com/question/12165221
Answer: D-123
Step-by-step explanation:
150% of a number is x. What is 100% of the number? Assume x>0
Answer:
0.667x
Step-by-step explanation:
150% = x
100% = ?
=> 100% * x / 150% = 0.667x
which graph shows the solution set for -5/2x-3<_2?
solving the equation given to us first:
-5x/2 = 5/1 ( ignore the ≤ symbol for now and replace with =) and cross multiply
you will get
-5x = 10
x = -10/5 ( minus doesn't stay in denominator so so we take up to numerator )
x = -2
so x ≤ -2
NOTE: if we have ≤ we shade the dot but if we have just < or we don't shade the dot.
soooo
x ≤ -2 will be going backwards
so the answer is option (C).
Hope this helps.
Good luck.
The selling price of a sweater is the cost plus the markup minus the discount. Write an expression to show the selling price s of a sweater. Use c for cost, m for markup, and d for discount.
Answer:
Step-by-step explanation:
Selling price = Cost price + Marked price - discount
s = c + m - d
PLS HELP ASAP! (show work)
Solve the compound inequality.
3 < 2x − 1 < 9
Answer: x = 2
Step-by-step explanation:
find the largest prime factor of 2820
Answer:
47
Step-by-step explanation:
2820 = 2 * 2 * 3 * 5 * 47
Prime factors:
2, 3, 5, 47
Largest prime factor:
47
Step-by-step explanation:
The largest prime factors of 2820 is 2*2*3*5*47 is the answer
Write an equation and solve it. Anything goes as long as you address the following points:
a. The equation must start with an 'x' variable in an exponent. B. The equation must require logarithms to solve. C. In the solution you must use the power rule, the product rule and the quotient rule at least once each. D. Explain each step as you solve; which rules are you using and why?
e. What challenges did you face as you were writing your problem? Did you run into any dead ends?
Im having trouble thinking up an equation that uses all three rules. The power rule, the product rule, and the quotient rule. I can create one that uses 2 but i cant quiet imagin 3. Im probably just not thinking about it in the right way but any help would be appreciated.
The equation is 4^{3x} is equal to 8^{1/x} 2^{x+3} and the values of x are x is equal to (3+√69)/(10) or x is equal to (3-√69)/(10)
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]
where 'a' is a constant and a>1
After following the rules to model the equation.
The equation becomes:
[tex]\rm 4^3^x= 8^{1/x}\times 2^{x+3}[/tex]
After solving, we get:
[tex]2^{6x}= 2^{3/x \ +x+3}[/tex] (power rule)
Taking log on both sides with base 2
[tex]\rm log_2(2^{6x})= log_2(2^{3/x \ +x+3})[/tex]
After solving, we will get a quadratic equation:
[tex]\rm 5x^2-3x-3 = 0[/tex]
After using quadratic formula, we will get,
[tex]\rm x=\dfrac{3+\sqrt{69}}{10}[/tex] or
[tex]\rm x=\dfrac{3-\sqrt{69}}{10}[/tex]
Thus, the equation is 4^{3x} is equal to 8^{1/x} 2^{x+3} and the values of x are x is equal to (3+√69)/(10) or x is equal to (3-√69)/(10)
Learn more about the exponential function here:
brainly.com/question/11487261
#SPJ1
PLS HELPPP WHAT IS THE ANSWER????
Answer:
212
Step-by-step explanation:
starting with (xy)
you first plug in x=2 and y=3
(2×3) = 6
then we add in the exponent of 3
6^3 = 216
this is because an exponent shows you how many times the number is multiple by itself (6×6×6)
next we work on x^4 by plugging in x=2
2^4=16
2×2×2×2
we do the same for x^2
2^2=4
2×2
next we do the division
16/4=4
finally we take the 216 and 4 and do the subtraction
216-4=212
What value of k is the expression x^4+kx^2+36 a perfect square?
[tex]\text{ The discriminant is 0 if the quadratic expression is a perfect square.}\\\\~~~~~b^2 -4ac =0\\\\\implies k^2-4\cdot 1 \cdot 36 = 0\\ \\\implies k^2 - 144 = 0\\\\\implies k^2 = 144\\\\\implies k = \pm\sqrt{144}\\\\\implies k= \pm12\\\\\text{Hence}~ k=12 ~\text{and}~ k=-12.[/tex]
Find the approximate value of g(6) for the function below.
g(x) = e^x - 139
A. 403.43
B. -8.61
C. 4.98
D. 264.43
Answer:
The answer is letter B-8.61Step-by-step explanation:
Have a great day✧◝(⁰▿⁰)◜✧
A. 403.43
I hope it's help
Lauren has 12 boxes of rocks. There are 60 rocks total. How many rocks are in each box?
Answer:5
Step-by-step explanation: Divide 60 By 12
Answer:
the answer is 5 rocks.
Step-by-step explanation:
Sinice there are 12 boxes and has 60 rocks. So that means we will divide the two to get 5bwhich is in each box.
Luke and Quinten are discussing what shapes the composite figure can be broken into. Luke wants to break it into four right triangles and one rectangle. Quinten wants to break it into two right triangles and two rectangles. Who identified a correct way to break up the shape?
A. Luke
B. Quinten
C. Both Luke and Quinten
D. Neither Luke nor Quinten
Answer:
it's C
Step-by-step explanation:
i took the test and got it right
Answer:
it's [C] I got it right on my test
Step-by-step explanation:
A bottle of vitamins has 90 capsules in it. Each capsule has 450 milligrams of the supplement. What is the total number of grams of the supplement in one capsule?
The total number of grams of the supplement in one capsule will be 0.45 grams.
What is unit conversion?The measurement of any quanity is expressed by its unit. Now the units for the same matter can be expressed in different ways for higher quanity or lower quanity so we need to convert the units for the calculations.
Here in the question
Each capsule has 450 miligrams of supplement.
Total grams in one capsule will be calculated by unit conversion
[tex]\rm 1 \ gram=1000\ miligram\\\\\\1 \ Mg=\dfrac{1}{1000}\ gram\\\\\\450\ Mg=\dfrac{450}{1000}\ gram\\\\\\450 Mg=0.45\ gram[/tex]
Hence the total number of grams of the supplement in one capsule will be 0.45 grams.
To know more about Unit conversion follow
https://brainly.com/question/21196956
#SPJ1
I need help with problem 22
Answer:
6 art course and 7 writing coures
82, 62, 95, 81, 89, 51, 72, 56, 97, 98, 79, 85 order from least to greatest find the The median of the lower half of the data and The median of the upper half of the data is
Answer:
The median of the lower half of the data was determined to be 67 while the median of the upper half of the data was determined to be 92.
Step-by-step explanation:
Step 1: Order from least to greatest
51, 56, 62, 72, 79, 81, 82, 85, 89, 95, 97, 98
Step 2: Determine the median of the lower half of the data
There are 12 numbers which means that there is going to be 6 numbers on both sides of the data. So using the first 6 numbers we will be able to determine the median of the lower half of the data.
51, 56, 62, 72, 79, 81
Since there is an even amount of numbers, that means that we will need to find the middle between the 3rd and 4th number. We can do that by adding them up together and dividing by 2.
(62 + 72) / 2 = 67
Step 3: Determine the median of the upper half of the data
So using the first 6 numbers we will be able to determine the median of the upper half of the data.
82, 85, 89, 95, 97, 98
Since there is an even amount of numbers, that means that we will need to find the middle between the 3rd and 4th number. We can do that by adding them up together and dividing by 2.
(89 + 95) / 2 = 92
Answer: The median of the lower half of the data was determined to be 67 while the median of the upper half of the data was determined to be 92.
4. Find the area of the circle. Round to the nearest tenth. Us 34 in. can anyone help/answer?
Answer:
907.9 in²
Step-by-step explanation:
D = 2r
r = D/2
r = 34/2
r = 17 in
A = πr²
A = π(17)²
A = 289π
A ≈ 907.9 in²
please help! it’s select all that apply :)
Answer:
•The function models exponential decay
•The rate of decay is 75%
•350 represents the amount of money Alicia had in the budget at the beginning of the summer
•Alicia spent $262.50 during the first week of summer
Tell me the answer please 6*5=
Answer:
6*5=30
Step-by-step explanation:
Answer: 30
Step-by-step explanation: it means multiply 6 by 5
simplify: (2x-3)(5x+1)
Answer:
[tex]\huge\boxed{\sf 10x^2-13x-3}[/tex]
Step-by-step explanation:
[tex]=(2x-3)(5x+1)\\\\=2x(5x+1)-3(5x+1)\\\\Distribute\\\\= 10x^2+2x-15x-3\\\\= 10x^2-13x-3\\\\\rule[225]{225}{2}[/tex]
which shows a right triangle
Answer:
2nd one - blue triangle
Step-by-step explanation:
A right angle triangle is a triangle that has a angle of 90°
Therefore our answer is second one - blue triangle.
Hope this helps and branliest please
Answer:
2nd triangle.
Step-by-step explanation:
For a triangle to be considered as a eight triangle it should have one angle which is equal to 90° in measure.
Here, the second triangle has 90° & hence is a right triangle.
________
Hope it helps ⚜
12. If Aryial can read 3 pages of his book in 6 minutes. How many pages can he read in
Se an hour at the current rate?
Answer:
30 Pages
Step-by-step explanation:
Make a ratio:
[tex]\frac{3}{6} =\frac{x}{60}[/tex]
Cross multiply:
180=6x
Divide both sides by 6:
x=30
Answer:
30
Step-by-step explanation:
divide 60 by 6 and you get 10. Then take 10 and times it by 3
Flaming bbq restaurant makes a dipping sauce
Jamel is asked to create triangles using three of four given sticks. The sticks measure 3 in., 6 in., 7 in., and 8 in. He creates these 4 triangles.
Triangle 1: 3 in., 6 in., 7 in.
Triangle 2: 3 in., 6 in., 8 in.
Triangle 3: 3 in., 7 in., 8 in.
Triangle 4: 6 in., 7 in., 8 in.
How many of his triangles are obtuse?
1
2
3
4
Based on the calculations, the number of Jamal's triangle that are obtuse are: C. 3.
How to determine an obtuse triangle?In order to determine an obtuse triangle, we would apply Pythagorean theorem:
c² = a² + b²
Where:
c is the hypotenuse.a is the adjacent side.b is the opposite side.For an obtuse triangle, the square of the hypotenuse is greater than the sum of the square of both the adjacent and opposite side:
c² > a² + b²
For Triangle 1, we have:
7² > 6² + 3²
49 > 36 + 9
49 > 45 (obtuse triangle).
For Triangle 2, we have:
8² > 6² + 3²
64 > 36 + 9
64 > 45 (obtuse triangle).
For Triangle 3, we have:
8² > 7² + 3²
64 > 49 + 9
64 > 58 (obtuse triangle).
For Triangle 4, we have:
8² > 6² + 7²
64 > 36 + 49
64 < 85 (not obtuse triangle).
Read more on Pythagorean theorem here: https://brainly.com/question/16176867
#SPJ1
Answer: the answer is C 3.
Step-by-step explanation: it show below.
Graphs of Function,
Write in interval notation the areas of increase and decrease.
I don't need all of them answered maybe 1 or 2? I want to do some myself.
Thank you for any help on this.
Answer:
A function is increasing when the gradient is positive
A function is decreasing when the gradient is negative
Question 7
If you draw a tangent to the curve in the interval x < -2 then the tangent will have a positive gradient, and so the function is increasing in this interval.
If you draw a tangent to the curve in the interval x > -2 then the tangent will have a negative gradient, and so the function is decreasing in this interval.
If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -2 will be zero.
The function is increasing when x < -2
[tex](- \infty,-2)[/tex]
The function is decreasing when x > -2
[tex](-2, \infty)[/tex]
Additional information
We can actually determine the intervals where the function is increasing and decreasing by differentiating the function.
The equation of this graph is:
[tex]f(x)=-2x^2-8x-8[/tex]
[tex]\implies f'(x)=-4x-8[/tex]
The function is increasing when [tex]f'(x) > 0[/tex]
[tex]\implies -4x-8 > 0[/tex]
[tex]\implies -4x > 8[/tex]
[tex]\implies x < -2[/tex]
The function is decreasing when [tex]f'(x) < 0[/tex]
[tex]\implies -4x-8 < 0[/tex]
[tex]\implies -4x < 8[/tex]
[tex]\implies x > -2[/tex]
This concurs with the observations made from the graph.
Question 8
This is a straight line graph. The gradient is negative, so:
The function is decreasing for all real values of x
[tex](- \infty,+ \infty)[/tex]
But if they want the interval for the grid only, it would be -4 ≤ x ≤ 1
[tex][-4,1][/tex]
Question 9
If you draw a tangent to the curve in the interval x < -1 then the tangent will have a negative gradient, and so the function is decreasing in this interval.
If you draw a tangent to the curve in the interval x > -1 then the tangent will have a positive gradient, and so the function is increasing in this interval.
If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -1 will be zero.
The function is decreasing when x < -1
[tex](- \infty,-1)[/tex]
The function is increasing when x > -1
[tex](-1, \infty)[/tex]
i’ll give brainlist
Answer:
option B
option C
4:40pm
2:45pm
option d
3:30
Step-by-step explanation:
please consider as brainlest que.
In △ABC, ∠B is a right angle, AB=30, and sec A=5/3. Find the value csc C in fraction and in decimal form.
Answer:
csc C = 5/3 = 1. (6)
Step-by-step explanation:
Given:
∠B = 90° is a right angle
AB = 30
We know that:
sec A = 5/3 = 1/ cos A = 1/ ( adjacent side/hypothenuse) =
hypothenuse/ adjacent side to angle A
csc C = 1/ sin C = 1/ sinC = 1/ (opposite side /hypothenuse) =
hypothenuse/ opposite side to angle C
Note that :
adjacent side to angle A is the same as opposite side to angle C
Therefore sec A = csc C = 5/3 ( fraction form) = 1.(6) (decimal form)
solve the system:
2x+6y=36
x+4y=20
Let's solve this problem step-by-step
Let's set:
2x + 6y = 36 -- equation 1
x + 4y = 20 -- equation 2
(equation 2) * 2
2x + 8y = 40 -- equation 3
(equation 3) - (equation 1)
2y = 4
y = 2 -- equation 4
Plug (equation 4)'s value of y into (equation 2)
x + 4(2) = 20
x = 20 - 8
x = 12
Thus x = 12 and y = 2
Let's check, by substituting these values
[tex]2x + 6y = 36\\2(12)+6(2) = 36\\24+12=36\\36=36\\\\x+4y=20\\12+4(2)=20\\12+8=20\\20=20[/tex]
Answer: x = 12 and y = 2
Hope that helps!