The recursive function that gives the number of books Ashley has at any time is f(t) = f(t-1) - n where f(0) =100
How to determine the recursive function?The given parameters are:
Initial = 100
Rate per week, r = n
The initial number of books means that:
f(0) = 100
The rate of n means that Ashley has n less books each week.
So, we have:
f(t) = f(t-1) - n
Where t represents the number of weeks
Hence, the recursive function that gives the number of books Ashley has at any time is f(t) = f(t-1) - n where f(0) =100
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Substratum is an open-source network that allows anyone to allocate spare computing resources to support the foundation of the decentralized web. SUB is the cryptocurrency that supports this network. On the 10th of January 2018, the price of SUB was $2.88 and on the 5th of April 2019 the price was $0.02. When rounded to one decimal place, which of the below gives the percentage decrease of the price of SUB from the 10th of Jan 2018 to the 5th of April 2019?
The percentage decrease will be equal to 99.30 %.
What are percentages?The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
SUB is the cryptocurrency that supports this network. On the 10th of January 2018, the price of SUB was $2.88 and on the 5th of April 2019 the price was $0.02The percentage decrease will be calculated as:-
Percentage decrease = [tex]\dfrac{2.88 - 0.02}{2.88}[/tex]
Percentage decrease = 0.9930 = 99.30%
Therefore the percentage decrease will be equal to 99.30 %.
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4. (#18) A vine is 1.3 inches long now and it will grow 0.2 inches a day. Identify a rule for the linear function that describes the length of the vine. Use the rule to find the number of days it will take the vine to grow to be 10.3 inches long.
5. (#24) Multiply (q-1)^2
2. (#6) The French club is sponsoring a bake sale to raise at least $305. How many pastries must they sell at $2.05 each in order to reach their goal?
The rule for the linear function that describes the length of the vine is L = 1.3 + 0.2d
The number of days it would take the vine to grow to be 10.3 inches long is 45 days
Linear functions
From the question, we are to determine a linear function that describes the situation
From the given information,
Then vine is 1.3 inches long now
and it grows 0.2 inches a day
∴ After the days, the vine will increase by 0.2d in length
Then,
If L represents the length of the vine, d represent the number of days
The length of the vine after d number of days will be
L = 1.3 + 0.2d
Hence, the rule for the linear function that describes the length of the vine is L = 1.3 + 0.2d
Now, we are to determining the number of days it will take the vine to grow to be 10.3 inches long
Using the above linear function
L = 1.3 + 0.2d
10.3 = 1.3 + 0.2d
0.2d = 10.3 - 1.3
0.2d = 9
d = 9 / 0.2
d = 45
Hence, the number of days it would take the vine to grow to be 10.3 inches long is 45 days
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A recipe for 8 servings lists: 6 cups spaghetti sauce 4 cups ricotta cheese and 4 cups mozzarella cheese. Determine the amount of ingredients necessary to serve 5 people.
The amount of ingredients necessary to serve 5 people is 3.75 cups spaghetti sauce, 2.5 cups ricotta cheese, and 2.5 cups mozzarella cheese.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
A recipe for 8 servings lists: 6 cups spaghetti sauce 4 cups ricotta cheese and 4 cups mozzarella cheese.
First we take the ratio of ingredients for 8 servings:
spaghetti sauce : ricotta cheese : mozzarella cheese = 6:4:4
The ratio of ingredients for 1 servings:
spaghetti sauce : ricotta cheese : mozzarella cheese = 6/8 : 4/8 : 4/8
The ratio of ingredients for 5 servings:
spaghetti sauce : ricotta cheese : mozzarella cheese
= 5×0.75 : 5×0.5 : 5×0.5
= 3.75 : 2.5 : 2.5
The amount of ingredients necessary to serve 5 people:
3.75 cups spaghetti sauce 2.5 cups ricotta cheese2.5 cups mozzarella cheese.Thus, the amount of ingredients necessary to serve 5 people is 3.75 cups spaghetti sauce, 2.5 cups ricotta cheese, and 2.5 cups mozzarella cheese.
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If-5x + 4y = -3 is a true equation, what would be the value of
-6(-5x+4y)?
Answer:
Step-by-step explanation:
-5x+4y=-3
-6(-5x+4y)=-6×(-3)=18
help me solve this I will gave u brilliant answer please help
Answer:
4 and 7/12
Step-by-step explanation:
This is addition with fractions.
We must convert to the same denominator.
1/3 and 1/4 becomes 4/12 and 3/12
This makes 7/12
1 add 3 add 7/12 is 4 and 7/12
The number of compact discs N purchased each year, in millions, can be
approximated by the function
N(t) = 384(1.13)
where t is the number of years since 1991.
After what amount of time will two billion compact discs be sold?
What is the doubling time for the number of compact discs sold in one year?
Answer:
126.5 years
Step-by-step explanation:
N(t) = 384(1.13)^t
2,000,000,000 = 384(1.13)^t
(1.13)^t = 2,000,000,000/384
log [(1.13)^t) = log (2,000,000,000/384)
t × log 1.13 = log (2,000,000,000/384)
t = [log (2,000,000,000/384)]/(log 1.13)
t = 126.5
Which expresstion is equivalent to 22 - 3
Which function is a translation of the parent absolute value function?
f(x) = 2|x|
f(x) = |x+61
f(x) = |x|
F(x) = -4|x|
f(x) = | x + 61 | function is a translation of the parent absolute value function.Option B is correct.
What exactly is a function?A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.
A single vertical parenthesis separating the equation on either side identifies an absolute value function. Option B is the only one with this indication.
B. f(x) = | x + 61 |
There are two ways to answer this equation;
1.f(x) = - (x + 61)
2.f(x) = x + 61
Hence,f(x) = | x + 61 | function is a translation of the parent absolute value function.
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A car purchased for $15,000 depreciates under a straight-line method in the
amount of $950 each year. Which equation below best models this
depreciation?
A. y = 15000x-950
OB. y = 15000 +950x
OC. y = 15000-950x
OD. y = 15000x+950
Answer:
i can't send full page of it sorry
The equation y = 15000 - 950x best models the depreciation.
Option C is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The equation y = 15000 - 950x.
Here, y represents the value of the car after x years.
The initial value of the car is $15,000, which means the value of the car at x = 0 is $15,000.
The car depreciates by $950 each year, so after one year, the value of the car will be $15,000 - $950 = $14,050.
After two years, the value of the car will be $14,050 - $950 = $13,100, and so on.
This linear relationship between the value of the car and the number of years can be modeled by the equation y = 15000 - 950x,
where 15000 is the initial value and -950x represents the amount of depreciation each year.
Thus,
The equation y = 15000 - 950x best models the depreciation.
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what is the least common multiple of 6 and 2
1cm(6,2) =
Can you help me please!!
The ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.
What is parallelogram?In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
We have ABCD is a parallelogram.
BE is perpendicular to FC
FA is perpendicular to FC
As we know in the parallelogram ABCD:
AB ≅ DC
AD ≅ CB
As the DC is extended to F
So, AB ≅ FE
And BE is perpendicular to FC
FA is perpendicular to FC (given)
∴ FA ≅ BE
∴ ABEF is a parallelogram.
Thus, the ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.
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does anyone know what is 20% of 120?
Answer:
24
Step-by-step explanation:
Hello there!
To determine the amount (percentage) as from our question above, we have to divide the given percentage by 100% (original percentage) and then multiply by 120.
This is as shown below;
[tex] \frac{20\%}{100\%} \times 120 \\ \\ = 0.2 \times 12 \\ = 24[/tex]
. ° . = 24 <<<<<< Ans
I hope this helps.
Have a nice studies.
HELP PLEAAASEEE Ireland opened a bag or skittles and recorded the colors and their frequencies.
What is the RELATIVE FREQUENCY, rounded to the NEAREST HUNDREDTH, for
the number of PURPLE candies?
=================================================
Explanation:
We want the relative frequency of the purple candies.
There are 16 purple out of 18+20+10+16 = 64 total
Divide the values to get 16/64 = 0.25
Exactly 25% of the candies are purple. This converts to the fraction 1/4.
The correct answer is 25%
What is Relative Frequency?The number of times an event occurs divided by the total number of events occurring in a given data. How to solve the problem?This problem can be solved by following steps.The data of color and frequency is given in table.We need find the relative frequency for PurpleFirst calculate the the total number of frequency
18+20+10+16
= 64
The total number of frequency is 64
Hence the relative frequency of purple is 16/64
Therefore , relative frequency of purple is 1/4 = 0.25
Therefore 25% of purple candies are there
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Find the values of a and b that make the quadrilateral a parallelogram.
Step-by-step explanation:
both halves of a diagonal must be equal.
so,
8b - 30 = 6b + 6
2b = 36
b = 18
and
9a - 13 = 5a + 5
4a = 18
a = 18/4 = 4.5
Después de leer un libro sobre el antiguo
Egipto, Cassie decidió construir con cartón un
modelo de una pirámide.
30 cm
25 cm
Cassie need to make the model is 2250 cm²
What is square pyramid?A square pyramid has a square base and four lateral faces in geometry. A pyramid is a polyhedron with a base and three or more triangular faces that meet above it .
The complete question is attached below:
We know,
A= a(a+ √(a²+4h²))
and, a =25cm, h=30 cm
So,
A= 25(25+ √(25²+4*30²))
=25(25+65)
= 2250 cm²
Hence, Cassie need to make the model is 2250 cm²
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The listed price of the phone was $43, but the price with tax came to $46.87. Find the percent sales tax.
Answer:
9%
Step-by-step explanation:
(final - initial )/ initial * 100
3.87 / 43 * 100
= 9%
Determine if the function is an even function, an odd function or neither. > = −6x² – 5x² −2 even neither odd
Answer: even
Step-by-step explanation:
A function is even if f(x)=f(-x), and odd if f(x)=-f(-x). If a function satisfies neither of these, it is neither even nor odd.
[tex]f(x)_=-6x^{2}-5x^{2}-2=-11x^{2}-2\\\\f(-x)=-11(-x)^{2}-2=-11x^{2}-2\\\\\therefore f(x)=f(-x)[/tex]
Therefore, the function is even.
find the slope of the lined graph
Answer:
1
Step-by-step explanation:
The points go rise:1 up:1 so the slope is 1.
Answer:
hey!! we can taIk here
Step-by-step explanation:
Can you help me with a question? What is the equation of the blue line?
Answer:
y = -x - 1
Step-by-step explanation:
y = mx + b
slope (m): Since the line is going downhill, the slope will be negative
slope = rise / run
slope = 1 / 1
slope = 1
m = -1
y - intercept (b): this when x = 0, the line is crossing the vertical line (y-axis)
b = -1
so y = mx + b is
b = -1, m = -1
y = (-1)x + (-1)
Answer:
y = - x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line
m = [tex]\frac{-1-0}{0-(-1)}[/tex] = [tex]\frac{-1}{0+1}[/tex] = [tex]\frac{-1}{1}[/tex] = - 1
the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1
y = - x - 1 ← equation of blue line
someone please help ASAP will give brainliest
The scale factor have been categorized into Expansion and Contraction.
What is a Scale Factor ?It is the measure by which two figures are same in appearance but different in size.
It can be positive or negative as the figure is getting bigger or smaller.
Different scale factors are given and it has been asked they describe which type of dilation.
1. -2/3 This will contract the figure
2. 3.25 This shows expansion
3. 2/3 This will contract the figure
4. -3 This will expand but the image will be form on the other side of Center of Enlargement.
Therefore the scale factor have been categorized into Expansion and Contraction.
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please help! what is the angle of depression from point C to point A
Answer:
The angle shows 90° so that means
90° - 42° = 48°
Therefore the angle of the depression is 48°
The angle of depression from C to point A 48°. The correct option is c. 48°
Angles of depressionFrom the question, we are to determine the angle of depression from C to point A
The angle of depression is the angle formed between the horizontal line and the line of sight when an observer looks downwards at an object
Thus, in the given diagram
The angle of depression is 90° - 42°
Angle of depression = 48°
Hence, the angle of depression from C to point A 48°. The correct option is c. 48°
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writing equations from graphs pixel art graph
Answer:
y= -2/3x - 4
Step-by-step explanation:
the 2/3 comes from going up 2 spaces and over left 3 spaces. the b is negative 4 because of where it falls. the line is negative because of the direction it is in.
The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer leg. Find the side lengths of the triangle.
Answer:
longer leg: 20 in
shorter leg: 15 in
hypotenuse: 25 in
Formulas:
Pythagorean Theorem
[tex]c^2 = a^2 + b^2[/tex]
c ... hypotenuse
a ... one leg
b ... another leg
Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).
Step-by-step explanation:
longer leg: x
shorter leg: x - 5
hypotenuse: x + 5
To find x (longer leg), let's use Pythagorean theorem.
[tex]c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x[/tex]
Now let's factorize to get solutions for x.
[tex]0 = x(x-20)[/tex]
First solution:
[tex]x = 0[/tex]
Second solution:
[tex]x - 20 = 0\\x = 20[/tex]
Since a side of a triangle has to be a positive number, x is equal to 20.
Now let's just substitute x back to get side lengths. From the question the lengths are in inches.
longer leg: x = 20 in
shorter leg: x - 5 = 20 - 5 = 15 in
hypotenuse: x + 5 = 20 + 5 = 25 in
Find the measure of x
Answer:
6
Step-by-step explanation:
By the alternate exterior angles theorem,
120=15(x+2)
8=x+2
x=6
Solve the following equation by factoring
8x²-9x-14=0
Answer:
[tex]x = 2\\ \\x= -\dfrac 78[/tex]
Step-by-step explanation:
[tex]~~~~~~~8x^2 -9x -14=0\\\\\implies 8x^2+7x-16x-14=0\\\\\implies x(8x+7)-2(8x+7)=0\\\\\implies (x-2)(8x+7) = 0\\\\\implies x = 2,~ x= -\dfrac 78[/tex]
please help! acellus
find the missing side of this right triangle.
30
3
x
x= [?]
Answer:
The number that belongs in the green box is equal to 909.
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTrigonometry
[Right Triangles Only] Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2[/tex]
Step-by-step explanation:
Step 1: Define
Identify given variables.
a = 30
b = 3
c = x
Step 2: Find x
Let's solve for the general equation that allows us to find the hypotenuse:
[Pythagorean Theorem] Square root both sides [Equality Property]:Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:
[Equation] Substitute in variables:∴ the hypotenuse length x is equal to √909 and the number under the square root, our answer, is equal to 909.
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___
Topic: Trigonometry
How do i solve this one
Answer:
900π
Step-by-step explanation:
Hello!
RadiusThe radius is represented by the function [tex]r(t) = 15\sqrt{t +2}[/tex].
The radius of the ripple can be found when [tex]t=2[/tex]
Solve:
[tex]r(t) = 15\sqrt{t + 2[/tex][tex]r(2) = 15\sqrt{2 +2}[/tex][tex]r(2) = 15\sqrt4[/tex][tex]r(2) = 15*2[/tex][tex]r(2) = 30[/tex]The radius of the ripple is 30 inches
AreaThe area of a circle is calculated by the formula [tex]A = \pi r ^2[/tex]
Given the radius is 30, we can find the area of the circle.
Solve:
[tex]A = \pi r^2[/tex][tex]A = \pi (30^2)[/tex][tex]A = 900\pi\\[/tex]A lighthouse sits at the edge of a cliff, as shown. A ship at sea level is 980 meters from the base of the cliff. The angle of elevation from sea level to the base of the lighthouse is 47.3. The angle of elevation from sea level to the top of the lighthouse is 51.3. Find the height of the lighthouse from the top of the cliff.
Using the tangent ratio, the height of the lighthouse from the top of the cliff ≈ 161.2 meters.
What is the Tangent Ratio?For solving a right triangle, the tangent ratio that can be applied is: tan ∅ = opposite length / adjacent length.
Find the height of the light house and the cliff using the tangent ratio:
tan 51.3 = height/980
Height of lighthouse + cliff = (tan 51.3)(980)
Find the height of the cliff only using the tangent ratio:
tan 47.3 = height/980
Height of cliff = (tan 47.3)(980)
Height of the lighthouse from the top of the cliff = (tan 51.3)(980) - (tan 47.3)(980)
Height of the lighthouse from the top of the cliff ≈ 161.2 meters.
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Kyle is going grocery shopping today. He has $35 to spend. He must buy a gift card for $10. If burgers cost $5.75 per pound, how many pounds of burgers can he buy?
Answer:
4
Step-by-step explanation:
35-10=25
25÷5.75= 4.3
Pls help me with my math
Answer:
The definition for the given piecewise-defined function is: [tex]\boxed{\displaystyle\sf\ Option\:D:\:\: f(x) = \begin{cases}\displaystyle\sf\ x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ 2x + 4 & \sf\:{if\:\:x > -1}\end{cases}}[/tex].
Step-by-step explanation:
General Concepts:Piecewise-defined functions.Interval notations.What is a piecewise-defined function?
A piecewise-defined function represents specific rules over different intervals of the domain.
Symbols used in expressing interval notations:Open interval: This means that the endpoint is not included in the interval.
We can use the following symbols to indicate the exclusion of endpoints in the interval:
Left or right parenthesis, "( )" (or both). Greater than (>) or less than (<) symbols. Open dot "[tex]\circ[/tex]" is another way of expressing the exclusion of an endpoint in the graph of a piecewise-defined function.Closed interval: This implies the inclusion of endpoints in the interval.
We can use the following symbols to indicate the inclusion of endpoints in the interval:
Open- or closed brackets (or both), "[ ]." Greater than or equal to (≥) or less than or equal to (≤) symbols. Closed circle or dot, "•" is another way of expressing the inclusion of the endpoint in the graph of a piecewise-defined function. Determine the appropriate function rule that defines different parts of the domain.The best way to determine which piecewise-defined function represents the graph is by observing the endpoints and orientation of both partial lines.
Open circle on (-1, 2): The graph shows that one of the partial lines has an excluded endpoint of (-1, 2) extending towards the right. This implies that its domain values are defined when x > -1. Closed circle on (-1, 1): The graph shows that one of the partial lines has an included endpoint of (-1, 1) extended towards the left. Hence, its domain values are defined when x ≤ -1.Based on our observations from the previous step, we can infer that x > -1 or x ≤ -1 apply to piecewise-defined functions A or D. However, only one of those two options represent the graph.
Solution:a) Test option A:[tex]\boxed{\displaystyle\sf Option\:A)\:\:\:f(x) = \begin{cases}\displaystyle\sf\ 2x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ x + 4 & \sf\:{if\:\:x > -1}\end{cases}}[/tex]
Piece 1: If x ≤ -1, then it is defined by f(x) = 2x + 2.We must choose a domain value that falls within the interval of x ≤ -1 whose output is included is included in the graph of the partial line with a closed dot.
Substitute x = -2 into f(x) = 2x + 2:
f(x) = 2x + 2f(-2) = 2(-2) + 2f(-2) = -4 + 2f(-2) = -2 ⇒ False statement.⇒ The output value of f(-2) = -2 is not included in the graph of the partial line whose endpoint is at (-1, 1).
Piece 2: If x > -1, then it is defined by f(x) = x + 4.
We must choose a domain value that falls within the interval of x > -1 whose output is included in the graph of the partial line with an open dot.
Substitute x = 0 into f(x) = x + 4:
f(x) = x + 4f(0) = (0) + 4f(0) = 4 ⇒ True statement.⇒ The output value of f(0) = 4 is included in the graph of the partial line whose endpoint is at (-1, 2).
Conclusion for Option A:
Option A is not the correct piecewise-defined function because one of the pieces, f(x) = 2x + 2, does not specify the interval (-∞, -1].
b) Test option D:[tex]\boxed{\displaystyle\sf Option\:D)\:\:\:f(x) = \begin{cases}\displaystyle\sf\ x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ 2x + 4 & \sf\:{if\:\:x > -1}\end{cases}}[/tex]
Piece 1: If x ≤ -1, then it is defined by f(x) = x + 2.We must choose a domain value that falls within the interval of x ≤ -1 whose output is included is included in the graph of the partial line with a closed dot.
Substitute x = -2 into f(x) = x + 2:
f(x) = x + 2f(-2) = (-2) + 2f(-2) = 0 ⇒ True statement.⇒ The output value of f(-2) = 0 is included the graph of the partial line whose endpoint is at (-1, 1).
Piece 2: If x > -1, then it is defined by f(x) = 2x + 4.
We must choose a domain value that falls within the interval of x > -1 whose output is included is included in the graph of the partial line with an open dot.
Substitute x = 0 into f(x) = 2x + 4:
f(x) = 2x + 4f(0) = 2(0) + 4f(0) = 0 + 4 = 0 ⇒ True statement.⇒ The output value of f(0) = 4 is included in the graph of the partial line whose endpoint is at (-1, 2).
Final Answer:
We can infer that the piecewise-defined function that represents the graph is:
[tex]\boxed{\displaystyle\sf\ Option\:D:\:\: f(x) = \begin{cases}\displaystyle\sf\ x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ 2x + 4 & \sf\:{if\:\:x > -1}\end{cases}}[/tex].
________________________________________
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