Answer:
Exponential function.
Step-by-step explanation:
We are given that a function of the form
[tex]y=ab^x[/tex]
Where [tex]b\neq 0[/tex] and b>0
Exponential function: The function is of the form
[tex]y=b^x[/tex]
Where b is a positive constant and greater than 0 and x is any real number.
The given function satisfied the define of exponential function.
Hence, the function of the form [tex]y=ab^x[/tex]
Where b>0 and [tex]b\neq 0[/tex] are called exponential function.
Functions of the form y = ab^x, where b > 0 and b ≠ 0, are called Exponential Functions. They are widely used in mathematical and scientific contexts.
Explanation:
Functions of the form y = abx, where b > 0 and b ≠ 0, are called Exponential Functions. These functions represent a wide range of phenomenons in mathematics and natural science. An exponential function represents a quantity which is increasing or decreasing at a rate proportional to the magnitude of the quantity itself. For example, a savings account with an interest rate of 2% would exhibit exponential growth since the magnitude of the account balance would increase at a rate proportional to the balance itself.
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Write an equation for an ellipse centered at the origin, which has foci at (\pm8,0)(±8,0)left parenthesis, plus minus, 8, comma, 0, right parenthesis and vertices at (\pm17,0)(±17,0)left parenthesis, plus minus, 17, comma, 0, right parenthesis
Answer:
The equation of the ellipse is [tex]\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1[/tex]
Step-by-step explanation:
The standard form of the equation of an ellipse with center (0 , 0) is
[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex] , where
The coordinates of the vertices are (± a , 0) The coordinates of the foci are (± c , 0) , where c ² = a² - b²∵ The ellipse is centered at the origin
∴ The center of it is (0 , 0)
∵ It has foci at (± 8 , 0)
- The coordinates of the foci are (± c , 0)
∴ c = ±8
∵ It has Vertices at (± 17 , 0)
- The coordinates of the vertices are (± a , 0)
∴ a = ±17
∵ c² = a² - b²
- Substitute the values of c and a to find b
∴ (8)² = (17)² - b²
∴ 64 = 289 - b²
- Add b² to both sides
∴ b² + 64 = 289
- Subtract 64 from both sides
∴ b² = 225
- Take √ for both sides
∴ b = ± 15
∵ The equation of the ellipse is [tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex]
- Substitute the values of a and b in it
∴ [tex]\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1[/tex] ⇒ [tex]\frac{x^{2}}{289}+\frac{y^{2}}{225}=1[/tex]
∴ The equation of the ellipse is [tex]\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1[/tex]
The standard form equation for this ellipse is (x²/17²) + (y²/15²) = 1.
To find the equation of an ellipse centered at the origin with foci at (±8,0) and vertices at (±17,0), we need to follow these steps:
Determine the values of 'a' and 'c': The vertices give us the value of 'a', which is the distance from the center to a vertex. Here, a = 17.
The foci give us the value of 'c', which is the distance from the center to a focus. Here, c = 8.
Using the relationship c² = a² - b², we can calculate 'b'.
c² = a² - b²
8² = 17² - b²
64 = 289 - b²
b² = 225
b = 15
So, the standard form of the equation of the ellipse is: (x²/17²) + (y²/15²) = 1
A TV has a listing price of $596.95 before tax if the sale rate is 9.25% what’s the total cost
Answer:
$651.46
Step-by-step explanation:
$596.95 * 9.25% = 55.21
$596.25 + 55.21 =651.46
PLEASE HELP!!!! Write the equation of the circle in general form.
Show all of your work please.
Answer:
x^2 +y^2 -8x +4y +11 = 0
Step-by-step explanation:
The center of the given circle is located at (x, y) = (4, -2). Its radius is 3.
You know this because the center is halfway between the vertical and horizontal extremes, and the radius is half the difference of those extremes. You can determine this by counting squares, or "by eye," or by working with the coordinates of the extreme points.
For example, the horizontal extremes are (1, -2) and (7, -2). The diameter is the difference of the x-values: 7 -1 = 6, so the radius is 6/2 = 3. The x-coordinate of the center is (1+7)/2 = 4.
__
The standard form of the equation of a circle is ...
(x -h)^2 + (y -k)^2 = r^2
where (h, k) is the center, and r is the radius.
For this circle with center (4, -2) and radius 3, the standard form equation is ...
(x -4)^2 + (y +2)^2 = 9
General form has the parentheses removed and the polynomial written in descending powers of the variables:
x^2 -8x +16 +y^2 +4y +4 = 9
x^2 +y^2 -8x +4y +11 = 0
Simplify the expression.
7x2 + 3 - 5(x2 - 4)
Final answer:
To simplify the expression, distribute the 5 to both terms inside the parentheses, combine like terms, and obtain the simplified expression 2x^2 + 23.
Explanation:
To simplify the expression 7x2 + 3 - 5(x2 - 4), we can distribute the 5 to both terms inside the parentheses:
7x2 + 3 - 5x2 + 20
Combining like terms:
2x2 + 23
So, the simplified expression is 2x2 + 23.
Pipe b can fill a pool in 9 hours. The amount of time it takes pipe c to fill the same pool is unknown. When pipes b & c are both open, the pool can be filled in 4 hours. If pipe c is filling the pool by itself how many hours will it take
Answer: it will take pipe c 7.2 hours to fill the pool.
Step-by-step explanation:
Let t represent the number of hours it will take pipe c to fill the pool alone. It means that the rate at which pipe c fills the pool per hour is 1/t
Pipe b can fill a pool in 9 hours. It means that the number of hours it takes pipe b to fill the pool alone per hour is 1/9
By working together, they would work simultaneously and their individual rates are additive. When pipes b & c are both open, the pool can be filled in 4 hours. It means that the rate at which both pipes fill the pool per hour is 1/4. Therefore,
1/t + 1/9 = 1/4
(9 + t)/9t = 1/4
Cross multiplying, it becomes
4(9 + t) = 9t
36 + 4t = 9t
9t - 4t = 36
5t = 36
t = 36/5
t = 7.2 hours
In the right triangle shown, AC = BCAC=BCA, C, equals, B, C and AB = 12\sqrt{2}AB=12 2 A, B, equals, 12, square root of, 2, end square root. How long are each of the legs?
Given:
ABC is a right triangle and AC = BC
The length of AB is [tex]AB=12\sqrt{2}[/tex]
We need to determine the length of each of the legs.
Length of AC and BC:
Let the length of AC and BC be x.
The length of AC and BC can be determined using the Pythagorean theorem.
Thus, we have;
[tex]AB^2=AC^2+CB^2[/tex]
Substituting the values, we have;
[tex](12\sqrt{2})^2=x^2+x^2[/tex]
Simplifying, we get;
[tex]288=2x^2[/tex]
Dividing both sides by 2, we get;
[tex]144=x^2[/tex]
Taking square root on both sides, we get;
[tex]12=x[/tex]
Thus, the length of each legs is 12 units.
Hence, the length of AC and BC are 12 units each.
Answer:
AC= 18 units for khan academy
Step-by-step explanation:
In circle Z, what is m∠2?
Answer:
In a circle, interior angles that are not inscribed or central can be found using the formula < = larger arc + smaller arc / 2. So, in order to find <2, the formula would be <2 = 147 + 133 / 2, so 140.
Answer:
m < 2 is 140
Step-by-step explanation:
Kenji packed an exercise ball into a cylindrical package. The inflatable exercise ball is made out of vinyl. How much vinyl was used to make the exercise ball? Express your answer in terms of pi.
Considering it's surface area, it is found that [tex]48\pi \text{ft}^2[/tex] of vinyl was used to make the exercise ball.
What is the surface area of a cylinder?The surface area of a cylinder of radius r and height h is given by:
[tex]S = 2\pi r(r + h)[/tex]
In this problem, we have that r = 3 ft and h = 5 ft, hence the surface area in ft² is given by:
[tex]S = 2\pi r(r + h) = 2\pi \times 3(3 + 5) = 48\pi[/tex]
Hence, [tex]48\pi \text{ft}^2[/tex] of vinyl was used to make the exercise ball.
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Construct a consistent and independent system of equations that has ( − 1 , − 4 ) as its solution. Use x and y as your variables, and put your equations in the form A x + B y = C with A ≠ 0 and B ≠ 0 using the four answer boxes below. Note that there are many possible correct answers.
To create a consistent and independent system of equations with the solution (-1, -4), we generate two linear equations: 2x - 3y = 10 and 5x + 4y = -21, both of which are satisfied by the given solution.
Explanation:To construct an independent and consistent system of equations that has the solution (-1, -4), we can create two distinct linear equations where the point (-1, -4) satisfies both.
As an example, we choose two arbitrary linear equations, ensuring that they are not multiples of each other, and that they are satisfied by x = -1 and y = -4.
The general form of a linear equation is Ax + By = C.
For our first equation, we could have 2x - 3y = 2(-1) - 3(-4) = 10. To ensure the second equation is not a multiple of the first, we could choose 5x + 4y = 5(-1) + 4(-4) = -21.
The system of equations would then be:
2x - 3y = 105x + 4y = -21is the decimal 2.030330333 terminating or not?
Answer:
it repeating not terminating
Step-by-step explanation:
this is because after 3 numbers behind the decimal
and if the number keeps going it's repeating
Two armadillos and three aardvarks sat in a five-seat row at the Animal Auditorium. What is the probability that the two animals on the ends of the row were both armadillos or both aardvarks?
Answer:
[tex]\dfrac{1}{15}[/tex]
Explanation:
The number of different ways in which the two armadillos would be at the ends of the row is 2:
[tex]P(2,2)=\dfrac{2!}{(2-2)!}=\dfrac{2}{0!}=2[/tex]
The number of different combinations in which two of the three aardvarks can sit at the ends of the row is P(3,2):
[tex]P(3,2)=\dfrac{3!}{(3-2)!}=\dfrac{3\times 2\times 1}{1}=6[/tex]
Therefore, there are 2 + 6 = 8 different ways in which the two animlas on the ends of the row were both armadillos or both aardvarks.
Now calculate the total number of different ways in which the animals can sit. It is P(5,5):
[tex]P(5,5)=\dfrac{5!}{(5-5)!}=5!=5\times 4\times 3\times 2\times 1=120[/tex]
Thus, the probability that the two animals on the ends of the row were both armadillos or both aardvarks is equal to the number of favorable outputs divided by the total number of possible outputs:
[tex]Probability=\dfrac{8}{120}=\dfrac{1}{15}[/tex]
Answer:
2/5
Step-by-step explanation:
2/5 1 1 1 1/4
A R R R A
2/20 or 1/10 is the odds that there will be an armadillo both ends
3/5 1 1 1 1/2
R A A R R
3/10 are the odds that there will be an aardvark on both ends and so you then have to add the two to get 4/10 or 2/5 which is the answer
The diameter of a basketball is approximately 9.5 inches and the diameter of a tennis ball is approximately 2.5 inches .The volume of a basketball is about how many times greater than the volume of the tennis ball ?
Answer:
The correct answer is the basket ball is 54.87 times bigger in volume than the tennis ball.
Step-by-step explanation:
The diameter of a basketball is approximately given to be 9.5 inches.
The radius of the basket ball is given by [tex]\frac{9.5}{2}[/tex] = 4.75 inches.
The volume of the basket ball is given by = [tex]\frac{4}{3}[/tex] × π × [tex]radius^{3}[/tex] = 449.1012 cubic inches.
The diameter of a tennis ball is approximately given to be 2.5 inches.
The radius of the tennis ball is [tex]\frac{2.5}{2}[/tex] = 1.25 inches.
The volume of the tennis ball is given by = [tex]\frac{4}{3}[/tex] × π × [tex]radius^{3}[/tex] = 8.1845 cubic inches.
Ratio between the volume of the basketball and tennis is given by [tex]\frac{449.1011}{8.1845}[/tex] = 54.87.
Thus the volume of the basket ball is 54.87 times greater than the volume of the tennis ball.
Final answer:
To find how many times greater the volume of a basketball is than a tennis ball, calculate the volumes using the sphere volume formula and divide the basketball's volume by the tennis ball's volume, which yields approximately 54.86 times greater.
Explanation:
To determine how many times greater the volume of a basketball is compared to a tennis ball, we start by calculating the volume of each using the formula for the volume of a sphere, V = 4/3 π r3, where r is the radius of the sphere. The radius is half the diameter, so for the basketball, r = 9.5 inches / 2 = 4.75 inches, and for the tennis ball, r = 2.5 inches / 2 = 1.25 inches.
The volume of the basketball is approximately
Vbb = 4/3 π (4.75)3 = 448.74 cubic inches. The volume of the tennis ball is approximately
Vtb = 4/3 π (1.25)3 = 8.18 cubic inches.
To find out how many times greater the volume of the basketball is, we divide the volume of the basketball by the volume of the tennis ball:
448.74 cubic inches / 8.18 cubic inches ≈ 54.86. Therefore, the volume of a basketball is approximately 54.86 times greater than that of a tennis ball.
Find the hypotenuse,c, of the triangle!
Answer:
B
Step-by-step explanation
a squared plus b squared equals c squared.
16 plus 144 equal 160.
now square 160
Last year, Jasleen was 150 cm tall. This year, her doctor measures her height and tells her that she has grown 20%. How many centimetres has she grown?
Answer:
30cm
Step-by-step explanation:
150*0.2=30cm, 20% of 150 is 30cm.
Translate the following statement into a mathematical equation:
Six, plus four times a number, is eighteen.
(6 + 4) n = 18
4 n + 18 = 6
6 + 4 n = 18
6 + 4 + n = 18
Correct answer will get brainliest!!!
Answer:
I think it is the third:
6 + 4 n = 18
All points from which of the following patterns would be contained on the given graph?
The first four terms of a linear pattern are given below.
x y
1 10
2 12
3 14
4 16
5 ?
Jenna earned 557 her first week working at a coffee stand.The next week she weared 773. How much did jenna earn her fist two weeks working at the coffee stand
Answer:
Jenna earned 1330 in first two weeks working at the coffee stand.
Step-by-step explanation:
Given:
Amount earned in 1 week = 557
Amount earned in next week =773
We need to find the amount earned in 2 weeks.
Solution:
Now we know that;
Amount earned in 2 weeks is equal to sum of Amount earned in 1st week and Amount earned in next week.
framing in equation form we get;
Amount earned in 2 weeks = [tex]557+773 = 1330[/tex]
Hence Jenna earned 1330 in first two weeks working at the coffee stand.
Toenails grow about 13 millimeters per year. Using that data, how many milimeters will grow in one week
Answer:
.25mm a week
Step-by-step explanation:
There are 52 weeks in a year.
13/52=.25
If Toenails grow about 13 millimeters per year as a result .25 millimeters will grow in one week.
What is an arithmetic operation?
It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.
It is given that Toenails grow about 13 millimeters per year.
As we know there are 52 weeks in a year.
Toenails growth in one week is obtained by dividing the growth per year by the total number of weeks,
= 13/52
=.25
Thus, if Toenails grow about 13 millimeters per year as a result .25 millimeters will grow in one week.
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Multiply 6+2i and it’s conjugate. Simplify.
Help me please ASAP
Answer:
40
Step-by-step explanation:
(6 + 2i)(6 – 2i) = 36 – 4i²
= 36 + 4 = 40
(C) 40.
Conjugate:In mathematics, a pair of binomials with identical phrases that part opposite arithmetic operators in the midst of these similar terms are referred to as conjugates. For instance, the conjugate of [tex]p+q[/tex] is [tex]p-q[/tex].By switching the sign in the middle of the two terms—from plus to minus or vice versa—you may find the conjugate of a binomial.Given that 1 is regarded as the real component of a complex number or as a single term, the conjugate of 1 is 1. Change of sign is therefore not relevant in this case.Solution -[tex]6+2i\\(6+2i)(6+2i)=36-4i^{2} \\36+4+40\\=40[/tex]
`Therefore, the correct option is (C) 40.
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which of the following answers is the simplified form of 3^2 x 3^-6?
Answer:
where are the answer choices?
Step-by-step explanation:
Answer:
It is 3^-4
Step-by-step explanation:
-6+2=-4
A baseball team plays in a stadium that holds 52,000 spectators. With ticket prices at $10, the average attendance had been 5,000. When ticket prices were lowered to $8, the average attendance rose to 15,000. (a) Find the demand function (price p as a function of attendance x), assuming it to be linear.
Answer:
p = (-1/5000)x +11
Step-by-step explanation:
We are given two points (x, p) as (5000, 10) and (15000, 8). Using the two-point form of the equation of a line, we can find the equation to be ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1 . . . . . 2-point form
p = (8 -10)/(15000 -5000)(x -5000) +10
p = -2/10000(x -5000) +10
p = -x/5000 +11 . . . . . linear demand function
Final answer:
A student asked how to find the demand function for a baseball team's ticket prices based on attendance. By finding the slope between two given points and using the point-slope form, the demand function is determined to be p = $11 - 0.0002x.
Explanation:
To find the demand function that relates the price p of baseball tickets to the average attendance x, we can use the two given points (x, p) = (5,000, $10) and (15,000, $8) and assume the relationship is linear. We can express the demand function as p = mx + b, where m is the slope and b is the y-intercept.
First, find the slope m:
m = (p2 - p1) / (x2 - x1)
m = ($8 - $10) / (15,000 - 5,000)
m = -$2 / 10,000 = -0.0002
Next, we'll use the slope and one of the points to find b, the y-intercept. Plugging into the point-slope form:
p - p1 = m(x - x1)
$10 - p = -0.0002(5,000 - x)
$10 - p = -1 + 0.0002x
p = $11 - 0.0002x
The demand function is p = $11 - 0.0002x.
PLEASE MATH HELP ( EASY )
Answer:
[tex]\frac{169\pi }{180}[/tex]
Step-by-step explanation:
To convert from degree measure to radian measure
radian = degree × [tex]\frac{\pi }{180}[/tex], thus
radian measure = 169 × [tex]\frac{\pi }{180}[/tex] = [tex]\frac{169\pi }{180}[/tex]
Recognizing Components of Cylinders
What solid will be produced if rectangle ABCD is
rotated around line m? Assume that the line bisects
both sides it intersects. What will the dimensions of the
three-dimensional solid be?
A
6 in.
6 in.
B
O
rectangular prism; length = 12 in.; width = 6 in.;
height = 5 in
triangular prism; length = 12 in.; width = 6 in.;
height = 5 in.
5 in.
O
O cylinder, radius = 12 in.; height = 5 in.
O cylinder; radius = 6 in.; height = 5 in.
es
Answer:
Cylinder: Radius: 6 in, height: 6 in
Step-by-step explanation:
See the attached image for a visual explanation!
Someone needs to borrow $14,000 to buy a car and the person has determined that monthly payments of $250 are affordable. The bank offers a 4-year loan at 6% APR, a 5-year loan at 6.5%, or a 6-year loan at 7% APR. Which loan best meets the person's needs? Explain.
7% at 6 years would best fit their payment option as they would then be paying $238.69 monthly and that is under the $250
The volume of this cube is 64 cubed cm. What is the cube's height? *hint l x w x h = 64 ----The shape is a cube PLZ HURRY WILL GIVE BRAINLIEST!
Answer:
4 cm
Step-by-step explanation:
It's just what cubed is 64. The answer is 4 by the way since
4*4*4=16*4=64
The height (or length of one side) of the cube is 4 cm.
To find the cube's height, we need to use the formula for the volume of a cube.
The volume of a cube is given by the formula:
V = s³, where V is the volume and s is the length of one side of the cube.
In this case, we are given that the volume of the cube is 64 cubic cm. So, we can set up the equation:
64 = s³
To find the height (or length of one side), we need to take the cube root of both sides of the equation:
∛64 = ∛(s³)
Taking the cube root of 64, we get:
∛64 = 4
Therefore, the height (or length of one side) of the cube is 4 cm.
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Juanita has saved $65 for vacation. She plans to save an additional $5 per week. How many weeks will it take for Juanita to save a total of $125?
Answer: 12 weeks
Step-by-step explanation:
125-65=60
60/5=12
Teresa is maintaining a camp fire. She has kept the fire steadily burning for 4 hours with 6 logs. She wants to know how many logs she needs to keep the fire burning for 18 hours.
Select the equations Teresa can use, and determine the number of logs she needs to maintain the fire for 18 hours. Select all that apply.
x/6=4/18
x/18=6/4
x/4=18/6
4/6=18
Answer:
X/18=6/4
Step-by-step explanation:
4hrs=6 logs
18hrs=x
4x=18×6
Which can also be written as
[tex] \frac{x}{18 } = \frac{6}{4} [/tex]
For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
Answer:
x=4.36
this is rounded
Step-by-step explanation:
a^2 + b^2 = c^2
A^2 + 9^2 = 10^2
a^2 + 81 = 100
Then subtract 81 from each side
a^2 = 19
then you have to square root 19 and you get
x=4.3588989
Brainliest?
Find the missing length of the triangle.
1.1 yd
6.1 yd
Answer:
6 yards.
Step-by-step explanation:
You can find this answer by using the Pythagorean theorem. Because c in the equation will always stand for the hypotenuse, the longest side, it's easier to fill in the blanks with the stuff given to you.
In this case, 1.1^2 + a^2 = 6.1^2
If you simplify, the answer should be 6 yards.
If x = 2y + 3 and 3x = 7 – 4y, what does x equal?
Answer:
x = 17/5
Step-by-step explanation:
Plug in 2y + 3 as x in the second equation and solve for y to get 1/5
Then plug in y into the first equation and solve for x to get 17/5
Answer:
Step-by-step explanation:
x=2y+3
3x=7-4y
Rearrange the numbers so they compare,
x=2y+3
3x=-4y+7
Multiply the first equation by 2 (this is so the variable with y matches in both equations)
2x=4y+6
3x=-4y+7
Add the two equations together
2x=4y+6
+
3x=-4y+7
5x=13
Divide both sides by 5 to isolate x
x=13/5
Simply the equation
x=2 3/5