Using translation concepts, the functions are given as follows:
1. F(x) = x² - 9x + 8.
2. [tex]G(x) = x^{19} + 8x^6 - x^5 - 7x^2 + x - 9[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In item 1, the function is:
f(x) = x² + 9x + 8.
When the function is reflected over the y-axis, we have that:
F(x) = f(-x),
Hence:
F(x) = (-x)² + 9(-x) + 8.
F(x) = x² - 9x + 8.
For item 2, the function is:
[tex]g(x) = x^{19} - 8x^6 - x^5 + 7x^2 + x + 9[/tex]
When the function is reflected over the x-axis, we have that:
G(x) = -g(x).
Hence:
[tex]G(x) = -x^{19} + 8x^6 + x^5 - 7x^2 - x - 9[/tex]
When the function is reflected over the y-axis, we have that:
Hence:
G(x) = G(-x).
[tex]G(x) = -(-x)^{19} + 8(-x)^6 + (-x)^5 - 7(-x)^2 - (-x) - 9[/tex]
[tex]G(x) = x^{19} + 8x^6 - x^5 - 7x^2 + x - 9[/tex]
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Evaluate the following expression. 7 1/4 x 2^2 +(8 1/2 -2) ÷ 3
Answer:
31.1666666667
Step-by-step explanation:
Caculator
Which equation represents a proportional relationship?
Answer:
y = 3x
Step-by-step explanation:
A proportional relationship should be represented by an equation in this format:
y = kx
Which area on the map is home to the most petroleum fields in Europe?
A) A
B) B
C) C
D) D
Answer: I think the answer is D
Step-by-step explanation:
Find the distance between (3,8) and (7,-11) round to the nearest hundredth
Answer:
[tex]d \approx 19.42[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra II
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (3, 8)
Point (7, -11)
Step 2: Find distance d
Substitute: [tex]d = \sqrt{(7-3)^2+(-11-8)^2}[/tex]Subtract: [tex]d = \sqrt{(4)^2+(-19)^2}[/tex]Exponents: [tex]d = \sqrt{16+361}[/tex]Add: [tex]d = \sqrt{377}[/tex]Evaluate: [tex]d = 19.4165[/tex]Round: [tex]d \approx 19.42[/tex]The graph represents the fees in thousands of dollars,
y, depending on the amount invested in millions, x,
with one financial investment firm.
Over what interval is the change constant?
[0,5)
(1,5)
[0, 20)
[1, 20)
Dejah is proving that perpendicular lines have slopes that are opposite reciprocals. She draws line s and labels two points on the line as (−a, 0) and (0, b).
Enter the answers, in simplest form, in the boxes to complete the proof.
Answer:
math is hard :(
Step-by-step explanation:
The volume of a pyramid is 650. Calculate the dimensions of the base of the square if the pyramid has a height of 15.
Answer:130
Step-by-step explanation:
1. By definition, sea level has an elevation of zero. Denver, Colorado is called "The Mile High
City" because its elevation is 5280 feet above sea level. Use a text box to type or the drawing
tool to write. Goal 3 (6.NS.5)
a. Calipatria, California has an elevation of 180 feet below sea level. What integer would
represent this elevation?
b. How many feet higher is Denver than Calipatria?
Answer:
pp
Step-by-step explanation:
pp
slope intercept equation of a line with a slope of -2/5 that passes through the point (15,-9/2
Answer:
im not sure if this is right but -0.358
Step-by-step explanation:
do y2-y1 over x2-x1 then subtract your y values then subtract your x values then you get your numbers then divide those numbers from top divided by bottom.
Sarah goes to her local pizza parlor and orders a two-topping pizza. She can choose either a large or a medium pizza, has a choice of seven different toppings, and can have three different choices of crust. How many different pizzas could Sarah order?
84
252
42
126
None of the above.
The total number of different pizzas that Sarah can order is 42. The correct option is C.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given the following choices for selecting a pizza. Therefore, we can write,
Number of choices for size = 2
Number of choices for toppings = 7
Number of choices for crust = 3
Total number of choices available with Sarah = Number of choices for size × Number of choices for toppings × Number of choices for crust
Total number of choices available with Sarah = 2 × 7 × 3 = 42
Hence, the total number of different pizzas that Sarah can order is 42.
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Convert from 1257, a BASE-10 NUMBER
to a BASE-7 NUMBER
Answer:
1267-7
Step-by-step explanation:
1257-10-7
1247-7
1240
5 over nine converted into decimal
Answer: See attached
Step-by-step explanation:
5/9 will give a repeating decimal 0.55555. You would write it as 0.5 with a "bar" line over the 5. See attached file of how it looks
12x + 14 + 3x - 5
I need help
Answer:
15x + 9
General Formulas and Concepts:
Algebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define
12x + 14 + 3x - 5
Step 2: Simplify
Combine like terms (x): 15x + 14 - 5Combine like terms (Z): 15x + 9For a certain company, the cost for producing x items is 55x+300 and the revenue for selling x items is 95x−0.5x2 .
Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces.
Part b: Find two values of x that will create a profit of $300 .
Part c: Is it possible for the company to make a profit of $15,000
a.) The equation for profit is - 0.5x² + 40x - 300
b.) The two values of x for profit = $300 are 20 and 60
c.) Profit of $15000 is not possible.
What is a profit?
Profit is defined as the total extent of benefit gained from selling some things. Mathematically, it is illustrated as the difference between the selling price and the cost price of an object.
Calculating the expression for profit
Given: the cost of producing x items = 55x + 300 and the revenue for selling x items is 95x - 0.5x²
a.) Profit = selling price/revenue - cost price
According to the question, we get,
Profit = 95x - 0.5x² - 55x - 300
= 40x - 0.5x² - 300
= - 0.5x² + 40x - 300 —–— 1
b.) Finding two values of x, when profit is $300
Using equation 1, we get,
300 = - 0.5x² + 40x - 300
0.5x² - 40x + 600 = 0
0.5x² - 10x - 30x + 600 = 0
0.5x(x - 20) - 30(x - 20) = 0
(x - 20)(0.5x - 30) = 0
i.e. x = 20 or x = 60
Two values of x for profit = $300
c.) Let us consider the profit to be $15000
15000 = - 0.5x² + 40x - 300
0.5x² - 40x + 15300 = 0
Using the quadratic formula, x = (- b ± √b² - 4ac) / 2a, we get,
x = (40 ± √40² - 4(0.5)(15300)) / 2(0.5)
The roots of this equation will be imaginary. Thus, it can be said that profit can not be $15000.
Hence, a.) The equation for profit is - 0.5x² + 40x - 300
b.) The two values of x for profit = $300 are 20 and 60
c.) Profit of $15000 is not possible.
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Be ready to discuss your answer.
Makayla got 12 out of 15 questions correct on her test. Jaden got 27 out of 35 questions correct on his test. Convert each score to a percent and determine who had the highest percentage. To run to the nearest whole number. (show all work)
Answer:
Makayla got the highest
Step-by-step explanation:
if you do 100÷15=answer×12=80%
if you do 100÷35=answer×27=77%
what fraction is equivalent to 1.5/9
Answer:
1.5/9 = 1 1/2 / 9 = 3/2 /9 = 3/18 = 1/6
Step-by-step explanation:
The fraction that is equivalent to 1.5 / 9 is expressed as:
3/18.
How to Find the Equivalent Fraction?Equivalent fractions are different fractions that represent the same value or proportion, although they may have different numerators and denominators.
To find an equivalent fraction for 1.5/9, divide both the numerator and denominator by their greatest common divisor (GCD), which in this case is 0.5.
Dividing 1.5 by 0.5 and 9 by 0.5, we will have the following:
(1.5 ÷ 0.5) / (9 ÷ 0.5) = 3/18
Hence, the equivalent fraction for 1.5/9 is 3/18.
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2 groups of 3 tenths pls answer today I need this answer
Answer:
6/10
Step-by-step explanation:
2 groups of 3/10 =
2 × 3/10 =
6/10
Which of the following would be a good name for the function that takes the length of a race and returns the time needed to complete it?
A. Time(race)
B. Time(length)
C. Length(time)
D. Cost(time)
Answer:
B. Time(length)
Step-by-step explanation:
The function that would be represented as a good name for a function for the length of the race and the return the time required to finished it
here the independent variable or the INPUT is the length while the output would be the time that required to finish it
Hence, the correct option is B,
Therefore all the other options would be incorrect
(\tan ^(2)\theta \cos ^(2)\theta -1)/(1+\cos (2\theta ))=
(tan²(θ) cos²(θ) - 1) / (1 + cos(2θ))
Recall that
tan(θ) = sin(θ) / cos(θ)
so cos²(θ) cancels with the cos²(θ) in the tan²(θ) term:
(sin²(θ) - 1) / (1 + cos(2θ))
Recall the double angle identity for cosine,
cos(2θ) = 2 cos²(θ) - 1
so the 1 in the denominator also vanishes:
(sin²(θ) - 1) / (2 cos²(θ))
Recall the Pythagorean identity,
cos²(θ) + sin²(θ) = 1
which means
sin²(θ) - 1 = -cos²(θ):
-cos²(θ) / (2 cos²(θ))
Cancel the cos²(θ) terms to end up with
(tan²(θ) cos²(θ) - 1) / (1 + cos(2θ)) = -1/2
A polynomial function of the root of -6 wth multipcily 1, a root of -2 with multiplicity 3, a root of 0 wth multiplicity 2, and a root of 4 wth multiplicity 3. If the function has a positive coefficient and is of odd degree, Which statement about the graph is true?
What is the quotient of 480 divided by -60
The quotient when 480 is divided by -60 is 8.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
The numbers given are 480 and -60.
Both are in opposite signs, that is one negative and other positive.
So the quotient will be negative.
Now divide 480 by 60.
Since both of the numbers contain 0 at the end, cancel it.
Then it becomes 48 divided by 6.
48 / 6 = 8
Hence the quotient is 8.
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Which of the following statements is true?
a.
sin 30° = cos 30°
b.
sin 35° = cos 55°
c.
sin 60° = cos 60°
d.
sin 55° = cos 25°
Option ' B ' [ sin 35° = cos 55° ] is true!
- Used a calculator ! The value is shown in the calculator in the attached picture!
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A random sample of 144 observations has a mean of 20. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is
Answer:
The population mean is 19.2 to 20.8.
Step-by-step explanation:
The formula of Confidence interval is
CI = mean ± z*[tex]\frac{s}{\sqrt{n} }[/tex]
where
n = sample size
s = Population standard deviation.
mean = Sample mean
z(α/2) = Two tailed z-value for significance level of .
Given : Confidence level = 95.44% = 0.9544
Significance level = α = 1-0.9544 = 0.0456
Now we Use standard z-value table
z-value for Significance level of 0.0456 :
z(α/2) = z(0.0228) = 1.99 = 2(approximately)
And we are given
n=144
s = 4.8
mean = 20
so the required Confidence interval is
CI = 20± 2*[tex]\frac{4.8}{\sqrt{144} }[/tex]
= 20 ± 2*[tex]\frac{4.8}{12}[/tex]
= 20 ± (0.8)
= (20-0.8, 20+0.8 )
= (19.2 , 20.8)
Therefore the 95.44% CI value for the population mean of 20 is 19.2 to 20.8.
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Martin has a $250 gift card to a bookstore. He used the card to spend $56.73 on books. How much is left on the gift card?
$194.27
$306.73
$193.27
$194.73
Answer:
193.27
Step-by-step explanation:
Answer:
$193.27 left on his gift card
In simplest radical form, what are the solutions to the quadratic equation 0 =3x4x + 5?
Quadratic formula: x= btyb- 4ac
Given:
The quadratic equation is
[tex]0=-3x^2-4x+5[/tex]
To find:
The simplest radical form of the solution.
Solution:
Quadratic formula:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]0=-3x^2-4x+5[/tex]
Here, a=-3, b=-4 and c=5. Putting these values in the quadratic formula, we get
[tex]x=\dfrac{-(-4)\pm \sqrt{(-4)^2-4(-3)(5)}}{2(-3)}[/tex]
[tex]x=\dfrac{4\pm \sqrt{16+60}}{-6}[/tex]
[tex]x=\dfrac{4\pm \sqrt{76}}{-6}[/tex]
[tex]x=\dfrac{4\pm 2\sqrt{19}}{-6}[/tex]
Taking 2 common, we get
[tex]x=\dfrac{2(2\pm \sqrt{19})}{-6}[/tex]
[tex]x=\dfrac{(2\pm \sqrt{19})}{-3}[/tex]
[tex]x=-\dfrac{(2\pm \sqrt{19})}{3}[/tex]
Therefore, the correct option is A.
help asap >3
Multiplicative inverses (reciprocals) are two number whose product is 1. Which pair of numbers are multiplicative inverses?
Answer choices-
0 and 1
0.25 and 4
1/2 and 1/2
3 and -3
Answer:
HERE FOR POINTS SORRY
Step-by-step explanation:
Ray was in charge of filling the soccer team’s water jug for practice. At the beginning of practice he filled the jug. Halfway through practice the team took a water break. After the break Ray refilled the jug so the players could have water after practice. At the end of practice Ray drained the jug. Which graph could represent the level of the water in the jug during and after practice?
Answer:
D
Step-by-step explanation:
I took the exam
Based on the times that Ray filled the water jug and the times it was drained, the best graph to show the water level is Graph 4.
What does Graph 4 show?In the 4th graph, the water level increases at the beginning to a stable level. It doesn't change till halfway through the graph which is most likely when the team took a water break.
The water level then rises to a similar level which shows Ray refilling the water jug. At the end of the practice, Ray empties the jug which is why the water level then goes the zero.
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question one pls
algebra 2
logarithms
Condense the logarithm on the right side:
[tex]3\log_b(p)-\left(2\log_b(t)+\dfrac12\log_b(r)\right)[/tex]
[tex]n\log_b(m)=\log_b(m^n) \implies \log_b(p^3)-\left(\log_b(t^2)+\log_b\left(r^{\frac12}\right)\right)[/tex]
[tex]\log_b(m)+\log(n)=\log_b(mn) \implies \log_b(p^3)-\log_b\left(t^2r^{\frac12}\right)[/tex]
[tex]\log_b(m)-\log(n)=\log_b\left(\dfrac mn\right) \implies \log_b\left(\dfrac{p^3}{t^2r^{\frac12}}\right)[/tex]
So,
[tex]x=\dfrac{p^3}{t^2r^{\frac12}}[/tex]
and [tex]r^{\frac12}=\sqrt{r}[/tex], which makes (4) the correct choice.
Write a number sentence that illustrates the following. A number with two decimal places multiplied by a number with one decimal place. The product has only two nonzero digits. Choose the correct answer below.
A. 0.08 x 0.6 = 0.48
B. 0.08 x 0.6 = 0.0048
C. 0.8 x 0.6 = 0.48
D. 0.08 x 0.6 = 0.048
Answer:
D
Step-by-step explanation:
the number of digits in the square root of 436149 is
Answer:The square root of 436149 is 660.41577812769