Four transformations of the function ()
f
(
x
)
are given below.
For each transformation, drag the graph that shows the result of that transformation into the box under it.
On a coordinate plane, a line f goes through (0, 1) and (1, negative 1).
CLEAR CHECK
On a coordinate plane, a line f begins at the top of the second quadrant, extends downward toward the fourth. The line is shifted 4 units to the right.
On a coordinate plane, a line f begins at the top of the second quadrant, passes through (0, 1), and extends toward the bottom of the fourth. The line is shifted 4 units up.
On a coordinate plane, a line f begins at the top of the second quadrant, goes through (0, 1), and extends toward the bottom of the fourth. The line is shifted 4 units down.
On a coordinate plane, a line f begins at the top of the second quadrant and extends toward the bottom of the fourth. The line is shifted 4 units to the left.
On a coordinate plane, a line f begins at the top of the second quadrant, passes through (0, 1), and extends toward the bottom of the fourth. The line is shifted 3 units up.
()=(−4)
m
(
x
)
=
f
(
x
-
4
)
()=()−4
n
(
x
)
=
f
(
x
)
-
4
()=(4+)
p
(
x
)
=
f
(
4
+
x
)
()=4+()
q
(
x
)
=
4
+
f
(
x
)
On a coordinate plane, a line f begins at the top of the second quadrant, passes through (0, 1), and extends toward the bottom of the fourth. The line is shifted 5 units down.
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Answer:
Step-by-step explanation:
300000000000000000000000000
Related Questions
please help me with these problems
Answers
The values of the missing sides are;
1. q = 4. 1, p = 11. 3
2. y = 56. 6, x = 35. 6
3. b = 16. 7, a = 9.1
How to determine the valuesUsing the sine and cosine identities, we have;
sin θ = opposite/ hypotenuse
cos θ = adjacent/hypotenuse
We have that;
sin 20 = q/12
find the values
q = 4. 1
Also
cos 20 = p/12
p = 11. 3
For the second triangle
cos 39 = 44/y
cross multiply
y = 44/0. 7777
y = 56. 6
Also,
sin 39 = x/56.6
x = 35. 6
For the third triangle
sin 57 = 14/b
cross multiply
b = 16. 7
Also,
cos 57 = a/16. 7
cross multiply
a = 9. 1
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Review the table of values for function g(x). x g(x) 32.9 –7 32.99 –6.1 32.999 –6.01 33.001 –15.01 33.01 –15.1 33.1 –16 What are the values of Limit of g (x) as x approaches 33 minus and Limit of g (x) as x approaches 33 plus? Limit of g (x) = negative 16 as x approaches 33 minus and limit of g (x) = negative 7 as x approaches 33 plus Limit of g (x) = negative 15 as x approaches 33 minus and limit of g (x) = negative 6 as x approaches 33 plus Limit of g (x) = negative 7 as x approaches 33 minus and limit of g (x) = negative 16 as x approaches 33 plus Limit of g (x) = negative 6 as x approaches 33 minus and limit of g (x) = negative 15 as x approaches 33 plus
Answers
The values of the limits of g(x) as x approaches 33 minus and 33 plus can be determined by examining the table of values and looking for the values of g(x) as x gets closer and closer to 33 from the left and the right sides.
As x approaches 33 from the left (i.e., values of x slightly less than 33), we can see from the table that the values of g(x) decrease from -7 to -16. Therefore, the limit of g(x) as x approaches 33 from the left is -16.
As x approaches 33 from the right (i.e., values of x slightly greater than 33), we can see from the table that the values of g(x) increase from -6.1 to -7. Therefore, the limit of g(x) as x approaches 33 from the right is -7.
Therefore, the correct answer is:
Limit of g(x) = negative 16 as x approaches 33 minus and limit of g(x) = negative 7 as x approaches 33 plus.
 Using the graph of the function f, find the following
Here is the other questions that get cut off by the picture
On which intervals is the graph decreasing? A) The graph is decreasing on _ (type ur anseer in interval notation using pi as needed B) There is no interval on which the graph is decreasing
On which intervals is the graph constant? A) the graph is constant on _ (type your answer in interval notation, type an exact answer using pi as needed)
B) There is no interval on which the graph is constant
The function is: A)odd B) even
C) neither even nor odd
Answers
The intercepts are (0, 0), (-π, 0) and (π, 0)
The domain is (-∝, ∝)The range is [-2, 2]The graph is increasing on (-π/2, π/2)The graph is decreasing on (-π, -π/2] u [π/2, π)The function is oddHow to determine the key features of the graphThe intercepts
The intercepts of a graph are the points where the graph intersects the x-axis (horizontal axis) and the y-axis (vertical axis).
From the given graph, we have the intercepts to be
(0, 0), (-π, 0) and (π, 0)
The domain and the range
The domain of a graph refers to the set of all possible input values, while the range refers to the set of all possible output values.
Using the above definition as a guide, we have
Domain = (-∝, ∝)
Range = [-2, 2]
The increasing and the decreasing interval
From the graph, we can see that the y values decrease from x = -π till x = -π/2 and also decrease from x = π/2 till x = π
Also, it increase from -π/2 till π/2
These are the increasing and the decreasing intervals
The function type
Based on the appearance of the graph, the function is an odd function
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Tina is getting broadband for her new flat.
She finds this deal.
Broadband deal
router normal price £39.99
15% discount on the normal router price
18 months contract at £56.99 each month
Tina buys the router and the 18 months contract.
Work out the total cost of this deal for Tina.
Answers
The total cost of the deal for the router for Tina is given by A = $ 1059.81
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the total cost of the deal be represented as A
Let the initial price of the router be = $ 39.99
Now , the percentage of discount for the router = 15 %
So , the final cost of the router = ( 85/100 ) x 39.99
On simplifying , we get
The final cost of the router = $ 33.9915
Now , the number of months = 18 months
The contract rate = $ 56.99 per month
So , the total contract rate for 18 months = 18 x 56.99
The total contract rate for 18 months = $ 1,025.82
Now , total cost of the deal A = final cost of the router + total contract rate for 18 months
On simplifying the equation , we get
The total cost of the deal A = $ 1,025.82 + $ 33.9915
The total cost of the deal A = $ 1059.8115
The total cost of the deal A = $ 1059.81
Hence , the total cost of the deal is $ 1059.81
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2
MP Use Tools Cal orders 1 ton of gravel to use in 2 cactus beds.
If he uses the same amount in each bed, how much gravel does
he use in one bed? Write an equation to model the situation.
Then represent the problem on the number line.
Answers
According to the information, the equation that expresses this situation is x = 1/4 / 2
How to identify the equation that corresponds to this expression?To identify the equation that corresponds to this expression, we must take into account that the amount of gravel that he used in a single cactus is equal to x.
Additionally, we must take into account that x is equal to half of 1/4. Therefore, we must write the equation as follows:
x = 1/4 / 2If we want to know the result we can develop the operation as shown below:
x = 1/4 / 2x = 0.25 / 2x = 0.125Learn more about mathematical expressions in: https://brainly.com/question/30350742
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If ∑X = 4,390 and n= 4, what is M?
a. 1,097.5
b. 17,560
c. need more information
d. .0100
Answers
Answer:
c. need more information
Step-by-step explanation:
You want M, given that ∑X = 4390 and n=4.
RelationshipTwo expressions for different variables are given, but there is no given relationship between them or to the variable of interest: M.
You need more information.
What is the sum of the first 4 terms of an arithmetic sequence in which the 7th term
is 19 and the 11th term is 29?
Hint: create a system of equations to find d.
A 09
B 31
C 48
D 11.5
E 45
Answers
Answer:
it's 48 I think that's the answer for the question.
a. Use the appropriate formula to find the value of the annuity.
b. Find the interest.
Periodic Deposit
$2000 at the end of each year
Rate
3.5% compounded annually
Time
10 years
Answers
The annuity is $2800 and interest is $800.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, P= $2000 at the end of each year, R= 3.5% compounded annually and time = 10 years
Amount = 2000(1+3.5/100)¹⁰
= 2000(1+0.035)¹⁰
= 2000(1.035)¹⁰
= 2000×1.4
= $2800
Interest = 2800-2000
= $800
Therefore, the annuity is $2800 and interest is $800.
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The expression −−18−−−−√−−18 can be rewritten as −1⋅−1−−−√⋅9–√⋅2–√−1⋅−1⋅9⋅2. Which expression is equivalent to −1⋅−1−−−√⋅9–√⋅2–√−1⋅−1⋅9⋅2?
Answers
The answer of imaginary expression is option a. The value is -3i[tex]\sqrt2[/tex] .
What is Imaginary expression?Imaginary expression is a specific type of algebraic expression which involves the square root of a negative number. For example 2+3i is an Imaginary expression.
Given that,
-1[tex]\sqrt{-1[/tex] [tex]\sqrt9[/tex] [tex]\sqrt{2[/tex]
=-1×i×3×√2 [since [tex]\sqrt-1[/tex]= i and [tex]\sqrt{9[/tex] =3]
[Here [tex]\sqrt-1[/tex] is an imaginary number]
= -3i√2
Hence the answer is -3i√2 .
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the spaghetti has ? g of fibers per serving
Answers
The correct answer is 4g. Spaghetti is a great source of fiber, with 4g per serving.
What is fiber?Fiber is a type of carbohydrate found in plant-based foods. It is not digested or absorbed by the body, but instead passes through the digestive system and out of the body. Fiber helps promote healthy digestion by adding bulk to the stool, helping it to pass through the intestines more quickly.
Fiber is an essential part of a healthy diet. It helps to keep your digestive system functioning properly, reduce cholesterol levels, and aid in weight management. It can be found in many plant-based foods, as well as some animal-based products. Spaghetti is a great source of fiber, with 4g per serving. This is a good amount for a meal, and it can help you meet your daily fiber needs. Eating a variety of foods that are high in fiber can help you stay healthy and reach your dietary goals. Getting enough fiber in your diet can also help reduce your risk of diabetes, heart disease, and stroke. So, the correct answer is 4g of fiber per serving of spaghetti.
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Super Scary Circles
This figure is NOT drawn to scale.
a = 90°
b=12°
C=
d=
e=
F=
g=
h=
I=
J=
Need to find the angle for each letter . Will be great if I can get the answer tonight
Answers
The measure of the angle for each letter found by finding the variables representing the angles simultaneously using circle theorems are;
a = 90°, b = 12°, c = 64°, d = 52°, e = 52°, f = 48°, g = 66°, h = 32°, i = 36°, j = 20°
What is a simultaneous equation?A simultaneous equation consists of two or more equations that consists of the same variables.
The evaluation of the angles in the circle are presented as follows;
a + a = 180° (linear pair angles)
2·a = 180°
a = 180°/2 = 90°
a = 90°
The 32° angle indicates that the base angle of the large isosceles triangle is 2 × 32° = 64°
Angle c is a base angle of the isosceles triangle, therefore, we get;
c = 64°
Angle b + 90° + 78° = 180° (Angle sum property of a triangle)
b = 180° - (90° + 78°) = 12°
b = 12°
In the isosceles triangle with angle 2·b, and the isosceles triangle formed by the radii to the vertices, we get;
2·b + 2·b = f, therefore;
f = 2·b + 2·b = 4·b
f = 4·b
f = 4 × 12° = 48°
f = 48°
The measure of angle g is equivalent to the measure of a base angle of the isosceles triangle with the angle 2·b, with angle f = 48° being a vertex of the triangle, therefore;
g = (180° - 48°)/2 = 66°
g = 66°
Vertex angle of the cyclic quadrilateral with 5·b can be found as follows;
2·f + The vertex angle = 180°
Vertex angle = 180° - 2 × 48° = 84°
Vertex angle = 84°
5·b + 2·h + i + j = 180°
5 × 12 + 2·h + i + j = 180°
60° + 2·h + i + j = 180°
2·h + i + j = 180° - 60° = 120°
2·h + i + j = 120°...(1)
2 × 2·h + 2 × j = 2 × 84°
2·h + j = 84°...(2)
2·f + 5·b + i + 168° = 360°
i = 360° - 2·f + 5·b + 168°
i = 360 - (96 + 60 + 168) = 36
2·h + i + j - (2·h + j) = 120° - 84° = 36°
i = 36°
5·b + 2·h + 2·f + i + j + 84° = 360°
60° + 2·h + 96° + 36° + j + 84° = 360°
2·h + j = 360° - 84° - 36° - 60° - 96° = 84°
2·h + j = 84°
The two tangent theorem indicates that we get;
90° - 64° = 26°
180° - 2 × 26° = 128°
h = (180° - 128°/2)/2 - 26° = 32°
h = 32°
2·h + j = 84°
j = 84° - 2·h
j = 84° - 2 × 32° = 20°
j = 20°
d = e (Angles subtended by the same chord)
2·c + d = 180°
2 × 64° + d = 180°
d = 180° - 2 × 64° = 52°
d = 52° = e
e = 52°
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Help what’s the value of x ?
Answers
The value of x, given the triangle and the sides, would be 21. 67 units .
How to find x ?We are given the hypotenuse of the triangle and the length of the side that is adjacent to the angle given.
This means that the value of x would be found by the operation of Cos. The value of x can be found to be :
Cos ( 37 degrees ) = 17. 3 / x
x × Cos ( 37 degrees ) = 17. 3
x = 17. 3 / Cos ( 37 degrees )
x = 17. 3 / 0. 7986355
x = 21. 67 units
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ΔABC and ΔDEF are similar
triangles. Find BC.
Answers
The length of BC in the triangle is 24 units.
How to find the similar triangle?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Therefore, using proportion,
BC / x = 12 / x - 4 = x + 7 / 5
12 / x - 4 = x + 7 / 5
cross multiply
12 × 5 = (x - 4)(x + 7)
60 = x² + 7x - 4x - 28
x² + 3x - 28 - 60 = 0
x² + 3x - 88 = 0
x² - 8x + 11x - 88 = 0
x(x - 8) + 11(x - 8) = 0
(x + 11)(x - 8) = 0
Therefore,
x = - 11 and x = 8
Hence,
BC / x = 12 / x - 4
BC / 8 = 12 / 8 - 4
BC / 8 = 12 / 4
4BC = 96
BC = 96 / 4
BC = 24 units
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A line passes through the point (2, - 3) and has a slope of - 4.
Write an equation in slope-intercept form for this line.
Answers
Answer:
y = -4x + 5.
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Given that the line passes through the point (2, -3) and has a slope of -4, we can use the point-slope form of a linear equation to find the y-intercept:
y - y1 = m(x - x1)
where x1 and y1 are the coordinates of the given point, and m is the slope.
Substituting the given values, we get:
y - (-3) = -4(x - 2)
Simplifying and rearranging, we get:
y + 3 = -4x + 8
Subtracting 3 from both sides, we get:
y = -4x + 5
Therefore, the equation in slope-intercept form for the given line is y = -4x + 5.
Calculate the simple interest and find the new balance on a principal of $575 deposited at 6.5% for a period of 10 years round the the nearest cent
Answers
Answer:
Step-by-step explanation:
The simple interest can be calculated using the formula:
I = P * r * t
where:
P = principal amount = $575
r = annual interest rate = 6.5% = 0.065
t = time period = 10 years
I = 575 * 0.065 * 10
I = $373.75
The new balance can be found by adding the interest to the principal:
New balance = Principal + Interest
New balance = $575 + $373.75
New balance = $948.75
Rounded to the nearest cent, the new balance is $948.75.
Express the absolute value function f(x)=7|x| as a piecewise-defined function.
Answers
And f(x) =7(-x) =-7(x) for x<=0.
It’s usually written as f(x) ={ with both outputs and conditions inside the bracket if that makes sense!
Which statement sentence is true?
A) 0.35 > 0.36
B) 0.3 < 0.04
C) 0.3 > 0.20
D) 0.75 < 0.7
Answers
Answer: C
Step-by-step explanation: 0.3 is greater than 0.20
0.3 could be 0.30 or 0.35 or even 0.31, depends.
if you looked through a spectroscope and saw light with a wavelength of 450nm, what color would you see? How would its energy and frequency compare to red light?
I know I put it under the wrong subject but math is the most looked at and I know I'll get an answer faster
Answers
Answer:
The visible spectrum can be broken up into particular ranges of wavelengths; each corresponding to what we call colors: violet and indigo: 380 - 450 nm. blue and aqua: 450 - 500 nm. green: 500 - 570 nm.
Which expression represents the prime factorization of 192?
A. 2 x 2 x 2 x 2 x 12
B. 2 x 2 x 2 x 2 x 2 x 3
C. 3 x 2 x 2 x 2 x 2 x 2 x 2
D. 2 x 2 x 2 x 2 x 2 x 3 x 3
Answers
Answer:
c
Step-by-step explanation:
2 x 2=4
2 x 2 =4
2 x 2 = 4
4 ^3 = 64
48 x 3 =192
Or:
192/2 = 96
96/2=48
48/2 = 24
24/2= 12
12/3=4
4/2=2
2 x 2 x 2 x 2 x 2 x 2 x 3
Find the slope
y = -5x - 2
Answers
Answer: -5
Step-by-step explanation:
from slope-intercept form, y=mx + b, where b is (-2), and the slope/m is (-5).
hope this helps, and please respond if I'm wrong
M = -5
That’s the answer
Can someone answer this just read the picture? Right answers only please!
Answers
Answer:
6 + 40 *3 = 126
Step-by-step explanation:
first is 6 and you add 3 in every step
Answer:
126 smileys
Step-by-step explanation:
[tex]a_{1} =[/tex] First term
= 6
[tex]d =[/tex] Common difference
= 3
[tex]n =[/tex] [tex]n^{th} term[/tex]
= Step number
Arithmetic sequence will be applied:
[tex]a_{n} = a_{1} + (n - 1)d[/tex]
For n = 2:
[tex]a_{2} = 6 + (2 - 1)(3)[/tex]
[tex]= 6 + (1)(3)[/tex]
[tex]= 9[/tex]
For n = 3:
[tex]a_{3} = 6 + (3-1)(3)[/tex]
[tex]= 6 + (2)(3)[/tex]
[tex]= 6 + 6[/tex]
[tex]= 12[/tex]
∴For n = 41:
[tex]a_{41} = 6 + (41 - 1)(3)[/tex]
[tex]= 6 + (40)(3)[/tex]
[tex]= 6 + 120[/tex]
[tex]= 126[/tex]
∴There will be 126 smiley faces in Step 41
Men have XY (or YX) chromosomes and women have XX chromosomes. X-linked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. Represent a defective X chromosome with lowercase x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child. Complete parts a through d below.
Question content area bottom
Part 1
a. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a son will inherit the disease?
enter your response here
(Type an integer or a decimal. Do not round.)
Answers
The probability that a son will inherit the disease would be
P{E} = 1/4.
What is probability?The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%Given is that men have XY (or YX) chromosomes and women have XX chromosomes. X-linked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. Represent a defective X chromosome with lowercase x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child.
The probability that a son will inherit the disease if a father has the
defective {x} chromosome and the mother has good {XX} chromosomes
as -
P{E} = 4/16
P{E} = 1/4
Therefore, the probability that a son will inherit the disease would be
P{E} = 1/4.
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Bella owns a small business selling ice-cream. She knows that in the last week 50 customers paid cash, 2 customers used a debit card, and 4 customers used a credit card. Based on these results, express the probability that the next customer will pay with cash or a credit card as a decimal to the nearest hundredth.
Answers
Answer:
0.96
Step-by-step explanation:
Bella owns a small business selling ice-cream. She knows that in the last week 50 customers paid cash, 2 customers used a debit card, and 4 customers used a credit card.
Based on these results, express the probability that the next customer will pay with cash or a credit card as a decimal to the nearest hundredth.
50 cash, 2 debit card, and 4 credit card.
50+2+4= 56
There were a total of 56 customers. 50+4=54 customers paid with cash or a credit card.
Probability the next customer will pay with cash or a credit card:
54
56
= 0.964285...
≈ 0.96
Round to the nearest hundredth
The probability as a decimal to the nearest hundredth is
0.96
Write a real-world problem that could be solved using the system of equations below. HELP RIGHT AWAY!!
Answers
Answer:
Step-by-step explanation:
y=4x + 10
y=3x + 15
How much do we need to invest at 12% simple interest in order to have a total of $12,400 in 2 years?
Answers
Answer:
$10,000
Step-by-step explanation:
Let
Principal= x
Rate = 12%
Time = 2 years
Interest = (Final amount with interest placed on it) - Principal
Therefore,
Interest = 12,400 - x
Using
I = (P·r·t) / 100
Making P, subject of formula,
P = (100·I) / (R·T)
x = [100·(12,400 - x)] / (12.2)
x = (1,240,000 - 100x) / 24
Cross multiply,
24x = 1,240,000 -100x
24x + 100x = 1,240,000
124x = 1,240,000
x = 1,240,000 / 124
x = 10,000
Therefore, the principal, amount we need to invest is
$10,000
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Thanks.
Which system of inequalities is graphed to the right?
Answers
The system of inequalities graphed is given as follows:
y > -1.y ≤ -x + 1.How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.The lower bound of the graph is a horizontal line at y = -1, hence:
y > -1.
For the upper bound of the graph, we have a linear function with these following parameters:
b = 1, as when x = 0, y = 1.m = -1, as when x increases by 1, y decays by 1.The upper bound is also a closed interval, as the line is solid, hence:
y ≤ -x + 1.
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A young executive is going to purchase a vacation property for investment purposes. She needs to borrow $127,000.00 for 28 years at 4.3% compounded monthly, and will make monthly payments of $650.71. (Round all answers to 2 decimal places.)
What is the unpaid balance after 15 months? $
During this time period, how much interest did she pay? $
Answers
Jeremy is saving money for new tires for his car. What he saves
goes into his savings account. After one month, he has saved
$230. After four months, he has $329 saved.
Answers
According to the given information, Jeremy is saving approximately $20.56 per week for his new tires.
What is basic arithmetic?
Basic arithmetic refers to the fundamental operations of arithmetic, which include addition, subtraction, multiplication, and division. These operations are used to perform calculations with numbers, such as counting, computing sums, finding differences, calculating products, and determining quotients.
We can use this information to find Jeremy's weekly savings rate.
To find the weekly savings rate, we need to first find out how much Jeremy saves in a week.
For the first month, which is four weeks, Jeremy saves $230.
For the next three months, which is 12 weeks, he saves an additional $329 - $230 = $99.
Therefore, in total, Jeremy saves $230 + $99 = $329 in 16 weeks.
His weekly savings rate is then:
$329 / 16 weeks = $20.56 per week (rounded to the nearest cent)
So, Jeremy is saving approximately $20.56 per week for his new tires.
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[tex]P(x) = x^4 - x^3 - 11x^2 + 9x + 18[/tex]. Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviours of the graph and where the company will break even (where P(x) = 0)
Answers
The graph of the function P(x) = x^4 - x^3 - 11x^2 + 9x + 18 rises on both ends and intersects the x-axis at x = -2, x = -1, and x = 3. The graph intersects the y-axis at the point (0, 18). The company will break even at the points where P(x) = 0, which are x = -2, x = -1, and x = 3.
How did we arrive at this assertion?The function P(x) = x^4 - x^3 - 11x^2 + 9x + 18 is a polynomial function of degree 4.
To sketch the graph of this function without using technology, we can start by analyzing the end behaviors of the function. As x approaches negative infinity, the leading term of the function, x^4, dominates and the function approaches positive infinity. As x approaches positive infinity, the leading term also dominates and the function again approaches positive infinity. This means that the graph will have a shape that rises on both ends.
Next, we can find the x-intercepts of the function, which are the values of x where P(x) = 0. We can use synthetic division or factorization to find that the function has three real roots: x = -2, x = -1, and x = 3. These values represent the points where the graph intersects the x-axis.
Finally, we can find the y-intercept of the function, which is the value of P(0). We can plug in x = 0 into the function to find that P(0) = 18. This means that the graph intersects the y-axis at the point (0, 18).
Putting all of this information together, we can sketch a rough graph of the function. The graph rises on both ends and intersects the x-axis at x = -2, x = -1, and x = 3. The graph intersects the y-axis at the point (0, 18). The function is positive between x = -2 and x = -1, and between x = 3 and positive infinity. The function is negative between x = -1 and x = 3.
To summarize, the graph of the function P(x) = x^4 - x^3 - 11x^2 + 9x + 18 rises on both ends and intersects the x-axis at x = -2, x = -1, and x = 3. The graph intersects the y-axis at the point (0, 18). The company will break even at the points where P(x) = 0, which are x = -2, x = -1, and x = 3.
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PLEASE HELPP!!!
The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Marco is studying the change in the amount of money in two accounts, A and B, over time.
The amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 9,628(0.92)x
Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the amount g(r), in dollars, of money in account B after r years:
r (number of years) 1 2 3 4
g(r) (amount in dollars) 8,972 8,074.80 7,267.32 6,540.59
Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer. (5 points)
Answers
The amount of money in account A is decreasing by 8% per year. Account B recorded a greater percentage change in amount of money over the previous year.
What is amount?Amount is an indefinite quantity of something, usually money or a measurement of quantity. It is often used to describe the total amount of money received or spent in a particular instance or over a period of time.
The amount of money in account A is decreasing by 8% per year. This can be seen by looking at the 0.92 in the equation. This is the rate of decay, and represents a 8% decrease every year.
Part B: Account B recorded a greater percentage change in the amount of money over the previous year. Looking at the table, the amount of money decreased by 10.51%, 10.22%, and 11.94% in the first, second, and third years respectively. This is greater than the 8% decrease in account A.
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