If the allocation doubles every week, that represents exponential growth.
Given there are many types of growth models, and models that grow at a constant rate are linear and models that grow exponentially at an increasing rate.
Linear growth is characterized by growth by the same amount per unit time.
Exponential growth is a process of increasing numbers over time. This happens when the instantaneous rate of change of a quantity over time is proportional to the quantity itself.
Exponential growth because the first week you may only get a dollar, but the next week you get 2, then 4, and so on. Your allowance doesn't grow by the same amount every week, so the number it doubles is exponential.
Therefore, if the allowance doubles every week, it represents a exponential growth multiplier because samples growing at a constant rate are linear.
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Simplify the expression to a polynomial in standard form
(x+6)(3x² + 4x − 3)
Answer:
3x^3 -8*x^2 + 8*x + 3
Step-by-step explanation:
The standard form for a plolynomial is:
a*x^n + b*x^(n-1) + c*x^(n - 2) ........
We have:
(x-1)(3x^2-5x-3)
this is equal to:
3*x^3 - 5*x^2 + 3*x - 3*x^2 +5*x + 3
where the thing that i did is distribute the multiplication
this is equal to:
3x^3 -8*x^2 + 8*x + 3
You are given that f(x)=x²+4 and g(x)=3 x-1 .
a. What are the domain and range of f(x) and g(x) ?
The domain of f ( x ) = R , its range = y ≥ 4 and the domain of g ( x ) = R and its range = R as well .
Domain : The set of all the possible values of x is called domain of the function .
Range : The set of all the possible values of y is called the range of the function .
Given : f ( x ) = [tex]x^{2}[/tex] + 4 , g ( x ) = 3 x - 1 .
To find : Domain and Range of functions .
f ( x ) = [tex]x^{2}[/tex] + 4
Domain = R ( real nos. )
Range = y ≥ 4 .
g ( x ) = 3 x - 1
Domain = R ( real nos. )
Range = R ( real nos. )
Therefore , the domain of f ( x ) = R , its range = y ≥ 4 and the domain of g ( x ) = R and its range = R as well .
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Find the two consecutive asymptotes, the period (in radians), the phase shift (in radians) and the vertical shift of the function: y = 4csc(5θ - 3π/4)
Answer:
Phase shift = [tex]\frac{3\pi }{5}[/tex]
Vertical shift = [tex]0[/tex]
Step-by-step explanation:
Shift Definition
[tex]\text{For\:}f\left(x\right)=A\cdot g\left(Bx-C\right)+D\text{,\:where\:}g\left(x\right)\text{\:is\:one\:of\:the\:basic\:trig\:functions,\:}[/tex] [tex]\frac{C}{B}\text{\:is\:phase\:shift}[/tex], [tex]D\text{\:is\:vertical\:shift}[/tex]
Here we have
[tex]\left(x\right)=4\csc \left(\frac{5\theta-3\pi }{4}\right)[/tex]
which can be written in the form [tex]g\left(Bx-C\right)=\csc \left(\frac{5\theta-3\pi }{4}\right)[/tex]
So comparing the two we get [tex]B=\frac{5}{4}, C=\frac{3\pi }{4},\:D=0[/tex]
Phase shift = [tex]\frac{C}{B} = \frac{\frac{3\pi }{4}}{\frac{5}{4}}[/tex] [tex]= \frac{3\pi }{5}[/tex]
Vertical shift [tex]D = 0[/tex]
what is the value of this equation?:
[tex]( \sqrt[3]{9} )^{2} \times ( \sqrt{30} ^{2}[/tex]
Answer:
Step-by-step explanation:
When we apply the exponent rule: [tex](\sqrt[n]{x})^n = x[/tex]
[tex](\sqrt[3]{9})^2 * (\sqrt{20})^2 = 30(\sqrt[3]{9})^2[/tex]
[tex]= \mathrm{Decimal:\quad }\:129.80246\dots[/tex]
Laura can make six flower arrangements in 25 minutes if she makes a 18 flower arrangements how many minutes will it take her
Answer:
75 flowers
Step-by-step explanation:
she needs to make 18 arrangements, so we divide 18 by 6 and get 3. 3 * 25 is 75 so the answer is 75.
Laura will arrange 18 flowers within 75 minutes of the time.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Laura can make six flower arrangements in 25 minutes if she makes 18 flower arrangements. The time will be calculated as,
Time = ( 25 x 18 ) / 6
Time = 25 x 3
Time = 75 minutes
Hence, it will take 75 minutes to arrange 18 flowers.
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is –10 an irrational number?
in 2012 the total value of exports from the United States was $2,210,585,000,000 that year sports were $837,965,000,000 more than half of the US imports. find the value of imports of the United States In 2012
The required value of sports imports of the United States in 2012 is $2,745,240,000,000.
.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it is given that,
the total value of exports from the United States in 2012 = $2,210,585,000,000
Now it is also given that,
the total value of exports from the United States in 2012 = $837,965,000,000 more than half of the US imports
Therefore, we can write
the total value of exports from the United States in 2012 = $837,965,000,000 + imports/2
Putting the value of exports we get,
2,210,585,000,000 = 837,965,000,000 + imports/2
Taking alike terms together we get,
Imports/ 2 = 2,210,585,000,000 - 837,965,000,000
Solving we get,
Imports/ 2 = 1,372,620,000,000
Multiplying by 2 both the side by 2 we get,
Imports = 2,745,240,000,000
Thus, the value of imports of the United States in 2012 = $2,745,240,000,000
Thus, the required value of imports of the United States in 2012 is $2,745,240,000,000.
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The correct question is :
in 2012 the total value of exports from the United States was $2,210,585,000,000 that year exports were $837,965,000,000 more than half of the US imports. find the value of imports of the United States In 2012
18
Kylie recorded the number of pears on a pear tree at the end of every week. The following function represents the number of pears on
the pear tree, where x represents the number of weeks.
Which statement is true?
A. The number of pears on the tree doubles each week.
B.
P(x) = 2(2+x)
O D.
The number of pears on the tree increases by 2 each week.
OC. The number of pears on the tree quadruples each week.
The number of pears on the tree increases by 4 each week.
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Based on the given function on the number of pears on the pear tree, the true statement is that The number of pears on the tree increases by 2 each week.
How to find the meaning of function?A linear regression line takes the form:
y = mx + b
y = number of pears
m = change in the number of pears per week
x = number of weeks
b = number of pears at first week
When the function is converted to a linear regression form, it takes the form:
P(x) = 2(2+x)
P(x) = 4 + 2x
This shows that the change in the number of pears per week is 2. This means that the number of pears on the tree increases by 2 each week
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Can anybody answer and simply this. (-8) × (-6)-(-5)²
Step-by-step explanation:
[tex] = - 8( - 6) - (25) \\ = 48 - 25 \\ = 23[/tex]
HOPE THIS HELPS!!
Morgan spent $42 for a jacket. This was $14 less than twice what she spent for a a pair of jeans. How much were the jeans?
Responses
$28
$28
$21
$21
$22
$22
$31
Determine whether the vectors in each pair are normal to each other. (6,-3) and (2,4).
Since their dot product is zero, then (6,-3) and (2,4) are normal to each other.
Step-by-step explanation:
Two vectors are said to be normal or perpendicular to each other if the result of their dot product is equal to zero.
These two vectors are also called orthogonal to each other.
Let u = (u₁, u₂) and v = (v₁, v₂), then the dot product u . v is defined as:
u . v = u₁v₁ + u₂v₂
To check whether the vectors are normal to each other, let us check their dot product.
The given vectors are: (6,-3) and (2,4).
Let u = (6, -3) and v = (2, 4), then,
u . v = 6 . 2 + (-3) . 4
= 12 + (-12) = 0
Since u.v = 0, then (6,-3) and (2,4) are normal to each other.
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When a number is decreased by 10% of itself, the result is 81, what is the number?
The number is 90.
What is the number?
Percentage can be described as the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentage is %. Percentages are a measure of frequency.
When the number is decreased, the number becomes smaller. This means that the original number is larger than 81.
The equation that can be used to represent the information in the question is:
(1 - percentage decrease) initial number = 81
(1 - 0.1)x = 81
0.9x = 81
x = 81 / 0.9
x = 90
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Please help me please help me
Solve each equation.
2y+1=25
Solution of this polynomial equation is y = 12
What is a polynomial ?In mathematics, simply polynomial or polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Types of polynomial equations :
Monomial equationBinomial equationCubic EquationsLinear Polynomial Quadratic PolynomialSome examples of polynomial equation are :
2y+52 x + 1 =253x² + 5x+19(x-3)³According to question,
2y+1=25
=> 2y +1 -1 = 25-1
=> 2y = 24
=> y = 12
Thus solution for given equation is y=12.
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Point G is the center of the small circle. Point X is the center of the large circle. Points G, H, and X are all on line segment GX.
what should be the area of a new circle that has a line segment GX as the diameter
The area of a new circle that has line segment GX as its diameter is 121 pi cm² .
Suppose that,
The radius of the small circle (GH) = 10 cm.
The radius of the big circle (HX) = 12 cm.
We will add the line GH and HX to get the total length of line segment GX.
So, GX = GH + HX
= 10 + 12
GX = 22 cm.
So, the diameter of new circle will be equal to line segment GX as it is given in the question.
Then, the area of new circle = π r² ( r = radius)
Radius = D/2 = 22/2 (D = Diameter)
r = 11
Now, Area = π × 11²
= 121π cm²
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Solve the following radical equations.
√(x+3) = 4√x-2
The solution for the radical equation √(x+3) = 4√x-2 is 7 / 3.
The phrase "algebraic expression" refers to any arrangement of terms that have undergone operations like addition, subtraction, multiplication, division, etc. (or variable expression).. Let's use the equation 5x + 7 as an example. Thus, 5x + 7 is an illustration of an algebraic expression.
Eliminate the radical on the both sides by squaring on both sides-
Both sides must be raised to the second power.
√(x+3) ²=(4√x-2 )²
After squaring we get
x+3=16(x-2)
Solving the equation-
We get rearranged equation as :
x+3=16x-32
15x=35 x=35/15 which further reduces to 7/3 .
Check if the solution is correct by putting it in original equation-
putting x=7/3 in the equation √(x+3) = 4√x-2
we get √16/3=√16/3
Therefore, the solution for the radical equation √(x+3) = 4√x-2 is 7 / 3.
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What is the measure of line AD
Simplify each expression.
ln e
ln (e) = 1, by the properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
As seen by the definition of logarithms, [tex]log_b(a)=x[/tex]
In case of natural logarithm, b = e, i.e., [tex]log_e(a)=x[/tex] = ln (a) = x
In the given expression, a = e
Hence, ln (e) = x
By properties of logarithms, we get that: ln (e) = 1.
Hence, ln (e) = 1, by the properties of logarithm.
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can someone help me pls !!!!!!!
a. An undefined term is a term that has been given no formal definition. In geometry, there are three undefined terms that form the basis for the subject. What are those three undefined terms? Do your best to define those terms.
The three undefined terms that form the basis for geometry are:
- Point
- Line
- Plane
What is undefined?The term undefined is often used to refer to an expression that is not assigned an interpretation or a value.
The main three undefined terms of geometry are:
- Point
In geometry, a point has no dimension.
A point is represented by a dot.
The point has no length, width, or thickness.
A dot can be very tiny or very large.
- Line
A line is a straight one-dimensional figure that has a length but does not have a thickness, and it extends endlessly in both directions.
A line is made of a set of points that is extended in opposite directions infinitely.
- Plane
A plane, in geometry, prolongs infinitely in two dimensions.
It has zero thickness, zero curvature, infinite width, and infinite length.
It is also known as a two-dimensional surface.
Thus,
The three undefined terms that form the basis for geometry are:
- Point
- Line
- Plane
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does anyone know how to do this question?
The diameter of the given sphere is; 39.5 cm
What is the Volume of the Sphere?
The formula for Volume of Sphere is;
V = 4/3 πr³
where;
V is volume
r is radius
We are given; V = 32250 cm³
Thus;
4/3 πr³ = 32250
Make r the subject of the formula to get;
r = ∛((32250 * 3/4)/π)
r = ∛7699.12
r = 19.75 cm
Now, radius * 2 = diameter
Thus; diameter = 2 * 19.75 = 39.5 cm
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Which angles are complementary to each other?
Answer:
C. <3 and<4
Step-by-step explanation:
Complementary angles are angles whose two angles make the sum 90°.
Guess bestie slay you'll do great!
What is the common difference in this recursive equation?
GIVING BRAINLIEST
look at the picture i attached :)
The common difference for the recursive equation [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 5 is 5.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
The recursive equation:
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 5
and [tex]a_{1}[/tex] = -3
We can find the consecutive term using the recursive equation.
[tex]a_{2}[/tex] = [tex]a_{1}[/tex] + 5 = -3 + 5 = 2
[tex]a_{3} =a_{2}[/tex] + 5 = 2 + 5 = 7
The sequence we get is:
-3, 2, 7, 12,....
The common difference means the differences in between two consecutive terms.
2 - (-3) = 5
7 - 2 = 5
12 - 7 = 5
Thus the common difference is 5.
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numbers like 2%, 3%, 4% and 6% are often used to represent the grade of a road. such a number tells how steep a road is. 3% grade means that for every horizontal distance of 100 ft, the road rises or descends 3 feet. in each of the following cases, find the road grade to two decimal places.
(a) Grade = 2.86%
(b) Grade = 5.85%
What is the horizontal distance?The projectile's horizontal range is the distance it travels while in flight. Since there is no acceleration in the horizontal direction, the greatest distance traveled in the horizontal direction is what this definition means.Vertical distance is the distance following the direction of gravity, and horizontal distance is the distance along the ground surface. The distance between a building and the observer is an example of a horizontal distance, and the building's height is an example of a vertical distance.Anything that forms a 90-degree angle (right angle) with the horizontal or the horizon is referred to as vertical because it is the opposite of the horizontal. The line that spans from left to right is therefore considered horizontal.By the angle's tangent, multiply the object's height. Let's assume, for the purposes of this illustration, that the item is 150 feet tall. The product of 150 and 1.732 is 86.603. 86.603 feet separate you from the thing horizontally.Find the road grade to two decimal places:
Grade in terms of percentage = (rise/run) * 100%
(a) Grade = (40/1400) * 100% = 2.86%
(b) Grade = 5.85%
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help me please!!! will mark brainliest!!
Answer:
2
Step-by-step explanation:
(0,2) is the y-intercept
PLEASE HELP!THIS IS DUE TODAY!I REALLY NEED ANSWERS!
The solutions to the equations are:
A. b = ac² (dark green); b = 2
B. v = m - k (light blue); v = 5
C. p/q = r/s; q = 8
D. m = 3n/4 (red); m = 6
E. x = y(w + z) (light green); x = 10
F. d1 = 2m - d2 (dark blue); d1 = 7
G. s = 8r/9 (purple); s = 4
H. w = [tex]\sqrt{\frac{x - y}{v} }[/tex] (orange); w = 3
I. x = [tex]\frac{y - y_1 }{m} + x_1[/tex] (pink); x = 1
J. c = 5a - 7 (brown); c = 9
How to Solve and Evaluate Equations?To solve for a variable in an equation, we need to isolate the variable to one side of the equation.
A. a = b/c²
a(c²) = b/c²(c²) [multiplication property of equality]
ac² = b
b = ac² (dark green)
Substitute a = 1/8 and c = 4 into the equation
b = (1/8)(4²)
b = (1/8)(16)
b = 2
B. m - v = k
m - v - m = k - m [subtraction property]
-v = k - m
v = -k + m
v = m - k (light blue)
Substitute k = -7 and m = -2 into the equation
v = -2 - (-7)
v = -2 + 7
v = 5
C. p/q = r/s
Cross multiply
qr = ps
qr/r = ps/r [division property]
q = ps/r (yellow)
Substitute k = -7 and m = -2 into the equation
q = (14)(-4)/-7
q = 8
D. 4m + 2n = 5n
4m + 2n -2n = 5n - 2n [subtraction property]
4m = 3n
4m/4 = 3n/4 [division property]
m = 3n/4 (red)
Substitute n = 8 into the equation
m = 3(8)/4
m = 6
E. w = x/y - z
w + z = x/y - z + z [addition property]
w + z = x/y
y(w + z) = x/y(y) [multiplication property]
y(w + z) = x
x = y(w + z) (light green)
Substitute w = -8, y = -5, and z = 6 into the equation
x = -5(-8 + 6)
x = -5(-2)
x = 10
F. m = 1/2(d1 + d2)
2m = d1 + d2 [multiplication property]
2m - d2 = d1 [subtraction property]
d1 = 2m - d2 (dark blue)
Substitute m = 10 and d2 = 13 into the equation
d1 = 2(10) - 13
d1 = 20 - 13
d1 = 7
G. 2r = 5s/2 - s/4
2r = (10s - s)/4
2r = 9s/4
2r(4) = 9s/4(4) [multiplication property]
8r = 9s
8r/9 = 9s/9 [division property]
8r/9 = s
s = 8r/9 (purple)
Substitute r = 9/2 into the equation
s = 8/9(9/2)
s = 4
H. vw² + y = x
vw² + y - y = x - y
vw² = x - y
vw²/v = (x - y)/v
w² = (x - y)/v
w = [tex]\sqrt{\frac{x - y}{v} }[/tex] (orange)
Substitute v = 5, x = 38, y = -7 into the equation
w = [tex]\sqrt{\frac{38 - (-7)}{5} }[/tex]
w = √9
w = 3
I. [tex]y - y_1 = m(x - x_1)[/tex]
[tex]\frac{y - y_1 }{m} = x - x_1\\\\\frac{y - y_1 }{m} + x_1 = x[/tex]
x = [tex]\frac{y - y_1 }{m} + x_1[/tex] (pink)
Substitute x1 = 9, y = 19, y1 = -5, and m = -3 into the equation
x = (19 - (-5))/-3 + 9
x = -8 + 9
x = 1
J. 2a + 3c = 17a - 21
2a - 17a = -3c - 21
-15a = -3c - 21
-15a + 21 = -3c
-15a/-3 + 21/-3 = -3c/-3
5a - 7 = c
c = 5a - 7 (brown)
Substitute a = 16/5 into the equation
c = 5(16/5) - 7
c = 16 - 7
c = 9
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If x^2 + x = 1
what is (x^5 + 8)/ x+1
The value given expression of (x⁵ + 8)/(x + 1) is (x⁶ + 8x).
What is termed as indices/index?In mathematics, an index (indices) is the power but rather exponent raised to the a number or variable. In number 2⁴, for example, 4 is the index of 2. Indexes is the plural form of index. We encounter constants and variables in algebra. A constant is just a value that cannot be altered. A variable quantity, on the other hand, can be assigned such a number or have its value changed.The given expression is-
(x⁵ + 8)/(x + 1) .......equation 1
It is stated that;
x² + x = 1
Taking x common;
x(x + 1) = 1
Bring x on the other side.
(x + 1) = 1/x
Put the value of (x + 1) in equation 1.
= (x⁵ + 8)/(x + 1)
= (x⁵ + 8)/[1/x]
Simplifying;
= (x⁵ + 8)x
Multiplying x on both values;
= x⁵x + 8x
= x⁶ + 8x
Thus, the value of the given expression is (x⁶ + 8x).
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please help If f(x)=sinx, then f′(π/3) =
Answer:
[tex]f' \left(\dfrac{\pi}{3}\right) =\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=\sin x[/tex]
The differentiation of sin(x) is cos(x).
[tex]\implies f'(x)=\cos x[/tex]
Therefore:
[tex]\implies f' \left(\dfrac{\pi}{3}\right) = \cos \left(\dfrac{\pi}{3}\right)[/tex]
[tex]\implies f' \left(\dfrac{\pi}{3}\right) =\dfrac{1}{2}[/tex]
SOMEONE PRETTY PLEASE HELP MEE
The value of x in the angles is 14.
How to find angles when parallel lines are cut by transversal?When parallel lines are cut by a transversal, angle relationships are formed.
The angle relationships that are formed includes corresponding angles, alternate angles, vertical angle etc.
Therefore, the value of x can be found as follows;
m∠1 = m∠7 (vertical angles)
Therefore,
m∠7 = m∠15(corresponding angles)
Hence,
m∠1 = m∠15
m∠1 = 8x - 4
m∠15 = 6x + 24
Therefore,
8x - 4 = 6x + 24
8x - 6x = 24 + 4
2x = 28
divide both sides by 2
x = 28 / 2
x = 14
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SR = 18cm, Given that SR:CD = 3:4 Find The Value of the Ratio
The value of the ratio is CD = 24 cm
How to Find The Value of the Ratio?The given parameters are
SR : CD = 3 : 4
SR = 18 cm
Substitute SR = 18 cm in the ratio SR : CD = 3 : 4
So, we have
18 cm : CD = 3 : 4
Express the ratio as a fraction
So, we have
18 cm/CD = 3/4
This gives
CD = 18 cm * 4/3
Evaluate
CD = 24 cm
Hence, the value of the ratio is CD = 24 cm
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