An equation or inequality to model the situation: The distance d to school is 1 1/2 miles more than the distance p to the park is d = p + 3/2
What is an equation ?a statement that the values of two mathematical expressions are equal indicated by the sign =, is known as equation.
What is inequality ?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions is known as inequality.
For this situation, we would assume that both the distances i.e 'd' and 'p' are in miles.
It is mentioned that the distance d is more than the distance p by 3/2 miles.
It means that if we add 3/2 miles to the distance 'p' the output will be distance 'd'
The equation for this is as follows :- d = p + 3/2
It also means that if we substract 3/2 miles from distance 'd', the output will be distance 'p'
The equation for this is as follows :- p = d - 3/2
But we are asked in the situation that distance d is more than than the distance 'p'.
Therefore , an equation or inequality to model the situation: The distance d to school is 1 1/2 miles more than the distance p to the park is d = p + 3/2.
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For
f(x) = (x − 1)3
and
g(x) = 1 − 6x,
find the following.
(a)
(f ∘ g)(x)
(b)
(g ∘ f)(x)
(c)
f(f(x))
(d)
f 2(x) = (f · f)(x)
For function f(x) = (x − 1)³ and g(x) = 1-6x ,value of following function is:
a. (f ∘ g)(x)=-216x³
b. (g ∘ f)(x)=-6x³+18x²-18x+7
c. f(f(x))=(x³ -3x² +3x -2)³
d. f²(x)=(x-1)⁶
As given,
Given function :
f(x)=(x − 1)³
g(x)=1-6x
The value of following functions are:
a.(f ∘ g)(x)
=f(g(x))
=f(1-6x)
=(1-6x -1)³
=(-6x)³
=-216x³
b. (g ∘ f)(x)
= g(f(x))
=g(x − 1)³
=1 -6(x − 1)³
=1 -6(x³ -3x² +3x -1)
=-6x³+18x² -18x+7
c. f(f(x))
=f(x-1)³
=((x-1)³ -1)³
=(x³ -3x² +3x -1-1)³
=(x³ -3x² +3x -2)³
d. f²(x)= (f · f)(x)
=f(x) × f(x)
=(x-1)³ × (x -1)³
=(x -1)⁶
Therefore, for function f(x) = (x − 1)³ and g(x) = 1-6x ,the value of following function is:
a. (f ∘ g)(x)=-216x³
b. (g ∘ f)(x)=-6x³+18x²-18x+7
c. f(f(x))=(x³ -3x² +3x -2)³
d. f²(x)=(x-1)⁶
The complete question is:
For function f(x) = (x − 1)³ and g(x) = 1-6x find the value of the following.
a. (f ∘ g)(x)
b. (g ∘ f)(x)
c. f(f(x))
d. f²(x)= (f · f)(x)
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The functions f and g are defined as follows.
f (x) = -2x^3 - 3 g (x) = 2x + 4
Find f (-2) and g (-6).
Simplify your answers as much as possible.
If the function are f(x) = [tex]-2x^{3}-3[/tex] and g(x)= 2x+4, then the values of
f(-2) = 13
g(-6) = -8
The functions are
f(x) = [tex]-2x^{3}-3[/tex]
g(x) = 2x+4
The function is an expression that represents the relationship between one variable and another variable. if one variable is independent variable another variable will be dependent variable.
First we have to find the value of f(-2)
Substitute the value of x= -2 in the given function
f(-2) = [tex]-2(-2)^3-3[/tex]
= -2×-8-3
= 16-3
= 13
Next we have to find the value of g(-6)
Substitute the value of x= -6 in the given function
g(-6) = 2×-6+4
= -12+4
= -8
Hence, if the function are f(x) = [tex]-2x^{3}-3[/tex] and g(x)= 2x+4 then the values of
f(-2) = 13
g(-6) = -8
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Plot the points (-8, 7) and (5, 7) on the coordinate plane below.
What is the distance between these two points?
The distance between two points is 15.
What is distance between two points?The length of the line segment bridging two points on a plane is known as the distance between the points. Counting each number in between them is a quick and easy approach to determine how far apart two numbers are on a number line. Finding the distance by taking the absolute value of the values' difference is a quicker method. For instance, |4| and |-4| have the same absolute value of 4, which is 4.
Given Data
Points (-8,7) and (5,7)
Formula of distance between two points
d = [tex]\sqrt{(x_{2} - x_{1})^{2}+(y_{2} - y_{1})^{2} }[/tex]
x₂= 7 x₁= -8
y₂ = 7 y₁ = 7
d = [tex]\sqrt{(7-(-8))^{2}+(7-7)^{2} }[/tex]
d = [tex]\sqrt{(7+8)^{2}(0) }[/tex]
d = [tex]\sqrt{15^{2} }[/tex]
d = 15
The distance between two points is 15.
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b. Evaluate 2w-60 when w=140.
Answer: 220
Step-by-step explanation: quick maths ;)
3.A car starts from A and is driven 50km to B on a bearing of 072 0 . It is then driven 30km to C on a bearing of 326 0 .
Answer:
aaaaaaaaaa
Step-by-step explanation:
aaaaaaaa
1. What is the value of 10/0?2. Which of the following fractions is equivalent to 3/4?
Answer:
1. Undefined
2. A
Explanation:
Part 1
[tex]\frac{10}{0}=\text{Undefined}[/tex]The value of 10/0 is undefined because you cannot divide by 0.
Part 2
From the given options:
[tex]\begin{gathered} \frac{-3}{-4}=\frac{3}{4}\text{ (Cancel the minus on both the top and bottom)} \\ -(\frac{3}{4})=-\frac{3}{4} \\ -(\frac{-3}{-4})=-\frac{3}{4} \\ \frac{-3}{4}=-\frac{3}{4} \end{gathered}[/tex]Therefore, A is the correct choice.
Solve the following linear equation using equivalent equations to isolate the variable. Express youranswer as an integer, as a simplified fraction, or as a decimal number rounded to two places.3y - y = -5AnswerHow to enter your answer (opens in new window)KeypadKeyboard Shortcutsy =
3y - y= -5
2y= -5
y= -5/2
y= -2.5
rounded of answer is 3
Find the distance between the two points in simplest radical form (-6,8) and (-1,-4)
Answer:
13
Step-by-step explanation:
d) = √(-1 - -6)2 + (-4 - 8)2
= √(5)2 + (-12)2
= √169
= 13
Answer:
13
Step-by-step explanation:
We use the distance formula to find the distance between two points
d = sqrt ( (x2-x1)^2 + y2-y1) ^2)
Where ( x1,y1) and ( x2,y2) are the two points
d = sqrt( ( -1 - -6) ^2 + ( -4 - 8) ^2)
= sqrt ( ( -1+6) ^2 + ( -12) ^2)
= sqrt( 5^2 + 144)
= sqrt ( 25+ 144)
= sqrt ( 169)
= 13
F(x)=|x|-7 describe the transformation of each function compared to its parent function
Compared to the parent function f(x)=|x|, the graph of F(x) is a translation 7 units down.
Which equation shows a slope of -5 and a y-intercept of (0,1)?
Answer: second option
y= -5x +1
Find the average rate of change of f(x)=x^2-4x+1 from x=2 to x=6
Answer:
The answer is 4
How can the rational zero theorem be used to find the zeros of polynomials
P is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P if P(x) is a polynomial with integer coefficients and if is a zero of P(x) (P() = 0). (x).
The Reasonable Zeros Theorem can be used to locate every rational zero in a polynomial.
What does the theorem of rational zeros state?According to the Rational Zeros Theorem, if P(x) is an integer-coefficient polynomial and is its zero (P() = 0), then p is a factor of P(xconstant )'s term and q is a factor of P's leading coefficient (x).
What does rational number theorem determines?Finding the rational solutions to a polynomial equation is done using the rational root theorem, as its name suggests (or zeros or roots of a polynomial function). The answers obtained from any polynomial equation are referred to as the roots or zeros of polynomials. It's not necessary for a polynomial to have rational zeros.
So, to find rational zero theorem states:
If P(x) is a polynomial with integers coefficients and if is a zero of P(x)(P()=0), then
P is a factor of the constant term of P(x) and q is a factor of of the leading coefficient
Of P(x).
To find all the rational zero of a polynomial we can use the rational zeros theorem
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Your original grades on your exams were: 75, 85, 90, 90, 100, 75, 80, 100, 90. You retake the exams and now your scores are: 85, 85, 100, 90, 100, 85, 80, 100, 90. By how many percentage points did you improve your average score? Hint: Find the mean of both sets of data. Then find the difference between the two. Round to the nearest %.
Based on your original grades in your exams and the scores after you retake your exams, the percentage points you improved your average score by is 3.83%
How to find the percentage improvement?To find the percentage that you improved by, the first thing to do is to find your average score in the first exam:
= (75 + 85 + 90 + 90 + 100 + 75 + 80 + 100 + 90) / 9
= 785 / 9
= 87.22
The average score after the exam was retaken was:
= (85 + 85 + 100 + 90 + 100 + 85 + 80 + 100 + 90) / 9
= 815 / 9
= 90.56
The percentage increase is:
= (90.56 - 87.22) / 87.22 x 100%
= 0.0382939692731024994267369869296 x 100%
= 3.83%
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Fill in the table using this function rule.
y = 5x-4
a movie theater is offering a special summer pass.passholders pay $8 per movie for the first 5 movies and watch additional movies for free up to maximum of 15 movies. the function c gives the total cost in dollars for a pass holder to watch n movies. describe as completely as possible the range of c
The function that completely describes the condition is a piecewise function;
[tex]\begin{cases}c=8n\text{ }\mleft\lbrace1\leq n\leq5\mright? \\ c=0\text{ }\mleft\lbrace n>5\mright?\end{cases}[/tex]Select the correct answer from each drop-down menu.
Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?
co N
The graph represents the system of inequalities
The test point
v satisfies both of the inequalities in the system represented by the graph.
Reset
Next
Only D satisfies both of the inequalities in the system represented by the graph. (Please check the graph attached)
What is inequalities ?Equations are not necessarily about having a "equal to" sign balanced evenly on both sides. It can occasionally refer to a "not equal to" connection, where one object is more than the other or less than. A connection that compares two numbers or other mathematical expressions in an unequal way is referred to as an inequality in mathematics. These mathematical statements are classified as inequalities in the algebraic language.
To test point in that system satisfies both of the inequalities
The system of inequalities is shown by the graph.
While x + 2y is more than or equal to 3, 2x + 3y is less than or equal to 4.
Both of the system's inequalities represented by the graph are satisfied at the test point (4, -1).
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Mr. Vigrass was driving at a constant speed he drove 168 miles in 3 1/2 hours at that speed how many miles will he drive in one hour
Using speed, distance and time relation, Mr. Vigrass will travel 48 miles in an hours.
What is the relation between speed, distance and time?If we know how far something travels and how long it takes, we can determine how fast something is moving in a straight line. This equation illustrates the link between journey time, distance, and speed:
Distance divided by travel time equals speed.
Distance equals Time * Speed
Time = Speed / Distance
Distance x Time equals Speed
Given,
distance = 168 miles
time = 3 1/2 hours
speed = distance / time
speed = 168 × 2/7
speed = 48 miles/hour
At same speed,
distance travelled in 1 hour will be
distance = speed × time
distance = 48 × 1
distance = 48 miles.
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Explain why when multiplying powers you add rather than multiply the exponents.
use real numbers for the proof
3^3 times 3^2 =
27 times 9 =
243 which is
3^5
If 4 bags of chips cost $3.00, how
much would 5 bags cost?
Answer: 6.67
Step-by-step explanation: first you divide 4 and 3 to then get 1.3 and times that by 5
Assume that A TUVE AWXY. Which of the following congruence statements
are correct? Check all that apply.
A. VU a YX
B. TV WY
C. ZY ZV
D. LT LX
E. ZWLV
F. ZX=ZU
For the congruent triangles TUV ≅ WXY, the correct statement are-
option B; TV ≅ WYoption c: ∠Y = ∠Voption f: ∠x = ∠UWhat is defined as the congruent triangles?The dimensions of the sides and angles of two or even more triangles determine their congruence. A triangle's size is determined by its three sides, and its shape is determined by its three angles. Two triangles have been shown to be congruent if the pairs of their corresponding sides and angles are equal.For the congruent triangles TUV ≅ WXY
By the property of congruency, the respective side and angles of each triangles are equal.
Thus, the correct option described the property of congruency are-
option B; TV ≅ WYoption c: ∠Y = ∠Voption f: ∠x = ∠UThus, the correct statement for congruent triangles are obtained.
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If N = 15 and P = .50, what is the probability of getting exactly 12 P events? Please go to 4 decimal places.
The probability of getting 12 p events is 0.0139
The expected value, or mean, of a binomial distribution is calculated by multiplying the number of trials (n) by the probability of successes (p), or n x p.
The binomial distribution formula is calculated as:
[tex]P(x:n,p) = ^nC_x * p^x*(1-p)^ {n-x}[/tex]
where:
n is the number of trials (occurrences)
X is the number of successful trials
p is probability of success in a single trial
is the combination of n and x. A combination is the number of ways to choose a sample of x elements from a set of n distinct objects where order does not matter and replacements are not allowed.
So, we have given that N = 15, P = 0.50 , and x = 12
So,
[tex]^{15}C_1_2 * (0.50)^{12}*(1-0.50)^ {15-12}\\^{15}C_1_2 * 0.50^{12}*(0.50)^ {3}\\[/tex]
=0.0139
Therefore, the probability of getting exactly 12 P events is 0.0139
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10. Supose you bought a digital album from your favorite artist and set iTunes to play
the album in random order without repeats. The album has 10 songs and it turns
out you really like 5 of them. Find the following probabilities for the first 2 songs
played at random.
a) You like both of them 2
b) B) you like neither of the songs ,
c) C) you like at least one of the songs
Probability to like both of them is 0.02.
Probability to like neither of the songs is 0.62.
Probability to like at least one of the songs is 0.44
What is probability?
Probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Given Data
The album has 10 songs and
it turns out you really like 5 of them.
a) You like both of them
P(like both of them )
= [tex]\frac{2}{10}[/tex] ×[tex]\frac{1}{9}[/tex]
= 0.02
Probability to like both of them is 0.02.
b )you like neither of the songs
P(like neither of the songs)
= [tex]\frac{8}{10}[/tex] ×[tex]\frac{7}{9}[/tex]
= 0.62
Probability to like neither of the songs is 0.62.
c) you like at least one of the songs
P( like at least one of the songs)
2 ×[tex]\frac{2}{10}[/tex] ×[tex]\frac{1}{9}[/tex]
= 0.44
Probability to like at least one of the songs is 0.44
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An artist has been commissioned to make a stained glass window in the shape of a regular octagon. The octagon must fit inside a 10 in square space. Determine the length of each side of the octagon. Round to the nearest hundredth of an inch.
The length of each side of the octagon would be 8.23 inches.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
We are aware that one side of the square is 20 inches long and that one side is made up of the length of the octagon added. We also know that two sides of a right triangle have smaller angles inside that are 45 degrees, making those two sides equal to one another. Therefore, we add the two sides of the right angle triangle to the side of the octagon, which equals 20 inches, to determine the value of x, which is designated as the side of the octagon.
Since a side of the square is 20 inches
Here, y is the two equal sides of the right-angle triangle
So y + x + y = 20
Using Pythagoras's theorem for the right angle triangle
y² + y² = x²
2y² = x²
y² = (x²)/2
y = x /√2
So substitute the value of y = x /√2 in the equation
x /√2 + x + x /√2 = 20
2x /√2 + x = 20
2x /√2 + x√2 /√2 = 20
x[2/√2 + √2 /√2] = 20
x[(2 + √2) /√2] = 20
x(2 + √2) = 20√2
x = 20√2/(2 + √2)
x = 28.2843/3.4142 = 8.2343
Round to the nearest hundredth of an inch
x = 8.23
Therefore, the length of each side of the octagon would be 8.23 inches.
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8x^2+9=313 match to correct answer round to nearest 10th if Necessary
Based on the equation, the value of x in 8x^2 + 9 = 313 is 6.2
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to evaluate the quadratic equation?The quadratic equation is given as
8x^2 + 9 = 313
Subtract 9 from both sides of the quadratic equation
So, we have
8x^2 + 9 - 9 = 313 - 9
Evaluate the difference in the above equation
So, we have
8x^2 = 304
Divide both sides of the quadratic equation by 8
So, we have
8x^2/8 = 304/8
Evaluate the quotient in the above equation
So, we have
x^2 = 38
Take the square root of both sides
x = 6.2
Hence, the value of x in the quadratic equation given as 8x^2 + 9 = 313 is 6.2
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$6500 earning 25% compounded
weekly for 1 year. What number goes in
the circle?
$8,125 is the compound interest.
What is compound interest?
When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest.As an illustration, if you put $1,000 in an account that offers 1% yearly interest, you will receive $10 in interest after a year. Compound interest allowed you to earn 1 percent on $1,010 in Year Two, which amounted to $10.10 in interest payments for the year.P = $6500
R = 25%
T = 1
compound Interest A = P( 1 + r/100)ⁿ
= 6500( 1 + 25/100)¹
= 6500( 5/4)
= 6500 * 5/4
= $8,125
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The points at which a graph changes direction (from increasing to decreasing or decreasing to increasing) are called _______.
The points at which a graph changes direction (from increasing to decreasing or decreasing to increasing) are called turning point.
What is a turning point?A turning point is when the derivative's sign changes. A relative maximum or relative minimum might mark a turning point (also known as local minimum and maximum). A turning point is a stationary point if the function is differentiable, however not all stationary points are turning points.
A turning point is a location on a graph where the trend shifts from rising to dropping or from decreasing to increasing (falling to rising). To determine the point, identify the leading term of the polynomial function if the function were enlarged. A polynomial of degree n will have at most n1 turning points. Next, determine the polynomial function's degree.
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Q/ evaluate.
(27) 2 over 3
1 If you are paid $232.95 for 22 hours of work, what amount should you be paid for 33 hours of work at this same rate of pay? 2 You should be paid $ (Round to the nearest cent as needed.) Question 3 of 12 for 33 hours of work.
Answer:
349.42499999998
Step-by-step explanation:
$232.95 divided by 22 hours of work = amount per hour = 10.588636363636
If you get paid 10.588636363636 per hour then multiply this by 33 hours to get the answer of : $349 and 42499999998 cents
The graph of an absolute value function has a vertexat(-2.3) and passes through the point (-1,0).Using transformations of the parent function, has thegraph been dilated by a scale factor other than 1?Explain.
Step 1 of the solution:
Let the parent function of the absolute value function is f(x) = |x|
Step 2 of the solution:
This function passes through (0, 0) and slope = 1 or -1.
Step 3 of the solution:
After transformation vertex (0, 0) becomes (-2, 3) and a point through which this function passes through is (-1, 0)
Step 4, let's find the slope of the absolute value funtion, this way:
[tex]S\text{lope = (3 - 0)/(-2 + 1) = 3/}-1\text{ = -3}[/tex]Step 5: Interpretation
Since slope of the absolute value function is less than the parent function: -3 < -1
Therefore, the parent function will be dilated by a scale factor other than 1.
if f(x)= 2x(1-x) ^2 then f(1)=
The value of f(1) is the value of function f(x) at x = 1 which is 0.
What is function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
So,
We have given that the function
f(x)=[tex]2x(1-x)^2[/tex]
So, when x = 1
f(x)= [tex]2(1)(1-1)^2[/tex]
f(x)= 2(1)(0)
f(x)= 0
Therefore, The value of function f(x ) at x = 1 is f(1) 0.
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