The function g(x) = –7x² + x³ is the reflection of the function f(x) = 7x² – x³ about the x-axis. This is observed by the change in signs of each term in the function's equation after performing the reflection.
Explanation:By observing the given equation, f(x) = 7x² – x³ and g(x) = –7x² + x³, it is clear that the function f(x) reflects about the x-axis to create function g(x). This is indicated by the change of signs of each term in the equation of the function.
To elaborate, a reflection about the x-axis sees a function's equation change y(x) to -y(x). In our example, f(x) becomes -f(x) or –(7x² – x³), which after simplifying gives us –7x² + x³ = g(x). Therefore, g(x) is the reflection of f(x) about the x-axis.
Furthermore, to identify a reflection about the y-axis, observe if the equation changes from f(x) to f(-x). An even function or a function symmetric about the y-axis would not change with this transformation. Conversely, an odd function would change signs, just like our function did when reflecting over the x-axis.
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Marianna buys a snack combo for 2.50 if the sales tax rate is 8% what is the total price of the combo including tax
Solve the equation. (find only the real solutions. enter your answers as a comma-separated list.) x4 − 7x2 6
A theater manager is planning an upcoming concert. Regular tickets will cost $12 and student tickets will cost $8. The theater can seat at most 200 people. The manager wants to collect at least $1000 from ticket sales.
Let x represent the number of regular tickets sold. Let y represent the number of student tickets sold.
Which inequalities are among the constraints for this situation?
Select each correct answer.
12x+8y≤1000
12x+8y≥1000
x+y≥1000
x+y≤200
x+y≥200
12x+8y≤200
Answer:
Option B and Option D is correct.
The inequalities are among the constraints for the given situation is,
[tex]12x+8y\geq 1000[/tex] and [tex]x+y\leq 200[/tex]
Explanation:
Let x represents the number of regular ticket sold.
and y represents the number of student ticket sold.
then, 12x represents the regular tickets at $12 each,
and 8y represents the student tickets at $8 each.
As the manager wants to collect at least $ 1000 from the ticket sale or we can say that the manager wants $ 1000 or more from the ticket sale.
then, we have the inequalities for this;
[tex]12x+8y\geq 1000[/tex]
As, the theater can seat at most 200 people or we can also say that the theater can seat 200 or less people .
therefore, the inequalities for this we have;
[tex]x+y\leq 200[/tex]
Therefore, the inequalities are among the constraints for the given situation is,
[tex]12x+8y\geq 1000[/tex] and [tex]x+y\leq 200[/tex]
Kyle works at a nature observatory where they are tracking a bird's speed. He enters the distance the bird flies into cell A1 and the time it took into cell A2. Which formula should Kyle use? =A1*A2 =A1/A2 =A1*(A2+ A1) =A1+A2
Answer:
[tex]\frac{A1}{A2}[/tex]
Step-by-step explanation:
We are give that the distance travelled by the bird is A1.
And the time taken to fly this distance is A2.
Now we will find the speed with the formula mentioned below:
[tex]Speed=\frac{Distance}{time}[/tex]
Replacing Distance as A1 and Time as A2. We get speed of the bird as
[tex]\frac{A1}{A2}[/tex]
Which of the following inequalities is not true?
-22 < 3
|-1| ≥ 0
|-9| ≠ |9|
-7 ≤ -5
Answer:
ccccccccccccccccccccc
Step-by-step explanation:
The false statement is |-9| ≠ |9|.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
For example, In the 12U Softball division, Olivia gets chosen. What is Olivia's age? Olivia's age is unknown to you because the word "equals" is missing. However, since you are aware that she should be under or equal to 12, you can write Olivia's Age ≤ 12. This is a real-world example of an inequality.
Given:
-22 < 3 is true.
|-1| ≥ 0
It is true because |-1| is +1. which is greater than 0.
|-9| ≠ |9|
It is false because |-9| = +9 and |9|= 9 which are equal.
-7 ≤ -5
It is true because the smaller the small the negative number the greater its value.
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Help Please?
In which diagram do angles 1 and 2 form a linear pair?
Answer:
Step-by-step explanation:
it is the 4th one
What is m∠PTS? ??????????
How many times longer is the diameter of a grain of sand than the diameter of the average cell in the human body? Show your work.
You put $150 in a bank account that offers a 1% interest rate, compounded annually. How much will you have after 10 years?
Put 1/2 1.1 5/3 20 0.4 -2 and 5/8 in order
A watermelon seed is 0.4cm long. How far would a line of 124 watermelon seeds stretch? Write your answer in meters.
Write this scientific notation in standard form.
3x10^-3
To write 3 × [tex]10^{-3}[/tex] power in standard notation, we first will start with
3. Next, we look at the exponent which in this case is negative so we will
have to move the decimal point 3 places to the left.
3. ⇒ 0.003
Therefore, 3 × [tex]10^{-3}[/tex] turned into standard notation is 0.003.
Gabriela works at a nearby electronics store. She makes a commission of 14\%14%14, percent on everything she sells. If she sells a camera for \$589.00$589.00dollar sign, 589, point, 00, how much money does Gabriela make in commission?
The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?
x=−5; y=−(−5)2−10(−5)+16
y= −25+50+16 = −25+66 = 41
Vertex (−5,4)
Find the mean of the data set. if necessary, round to the nearest tenth 18.1, 17.9, 16.8, 18.7, 15.1
2% of the students at Hamilton Middle School have red hair. There are 700 students at Hamilton Middle School. How many students at Hamilton Middle School have red hair?
2% = 0.02
700 * 0.02 = 14
14 students have red hair
Answer:
There are 14 students at Hamilton Middle School having red hair.
Step-by-step explanation:
The total number students at Hamilton Middle School is 700. And it has been given that 2% of the total number of students have red hair.
Hence, in order to find the number of students having red hair, we can find 2% of 700.
[tex]\text{Number of student having red hair}=0.02\times 700\\=14[/tex]
Therefore, 14 students at Hamilton Middle School have red hair.
There is 1 in. of water in a pool. The water level is increasing at 0.75 in./min . Which linear equation represents the total depth of the water, in inches, after x minutes?
y=0.75x
1+y=0.75x
y=0.75x+1
x=0.75y
Let
x-------> the time in minutes
y------> the water level in inches
we know that
the slope of the linear equation is equal to
[tex]m=0.75\frac{in}{min}[/tex]
The y-intercept is the value of y when the value of x is equal to zero
In this problem the y-intercept is equal to
[tex]b=1\ in[/tex]
the equation of the line in the slope-intercept form is equal to
[tex]y=mx+b[/tex]
substitute the values
[tex]y=0.75x+1[/tex]
therefore
the answer is
[tex]y=0.75x+1[/tex]
One cubic foot is equal to 144 cubic inches.
true
false
False
A cubic foot would be 12 x 12 x 12 = 1728 cubic inches
Evaluate 6j+23+k when j=3, k=7, and l=33.
______
l−3,
SOLVED IT IT"S 19!
Its 19 bro.
Hope this helps
~Onyx~
Point (w, z) is transformed by the rule (w+5, z). What type of transformation occurred?
a) a translation of 5 units to the left
b) a translation of 5 units down
c) a translation of 5 units to the right
d) a translation of 5 units up
How do you write in numbers a hundred and one thousand dollars?
To write 'a hundred and one thousand dollars' in numbers, combine the place values to get $101,000. The number 101 represents 'one thousand' plus 'one hundred,' followed by 'thousand,' which is represented by three zeros after 101.
Writing 'a hundred and one thousand dollars' in numbers involves understanding the place value of numbers and how to represent large numbers. In the decimal number system, the place values increase as powers of 10 from right to left, starting with the 1's place, 10's place, 100's place and so on. When dealing with large numbers, we use the powers of 1000, such as thousand (103), million (106), and billion (109).
To write 'a hundred and one thousand dollars' in numbers, you would write $101,000. Here, 'hundred' refers to the 100's place, and 'one thousand' refers to the 1,000's place. Therefore, you have one thousand plus one hundred, which is '101' followed by the 'thousand' represented by three zeros to make 101,000. When writing amounts in dollars, you use the dollar sign '$' in front of the number.
It's essential to remember that when expressing large numbers in written form, no apostrophes are used for the plurals. Also, in general, we use numerals to express numbers 10 and above, which helps in clarity and readability, especially when dealing with money or scientific notation.
What is the value of the dependent variable if the value of the independent variable is –1?
f(x) = 8x^5+2x
A. –10
B. 6
C. –6
D. 10
Which of these is the distance from the head of the piston not including any dishes or domes to the deck surface of the engine block?
A white-tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animanl is faster and by how many miles per hour? There are 5,280 feet in one mile
the bison runs 3520 feet per minute
convert that to miles per hour
3520/5280 = 2/3 of a mile per minute
2/3 x 60 = 40 miles per hour
the bison runs 10 miles per hour faster
A class has 12 boys and 18 girls. the class as a whole has a gpa (grade point average) of 2.88, and the boys have a gpa of 2.52. what is the gpa of the girls?
EASY QUESTION PLEASE HELP ME!!!!!!!!
A home run hit in a professional baseball game was measured to have traveled a distance of 8.5×10^−2 miles.
Which unit of measurement is most appropriate to measure this distance?
kilometers
centimeters
inches
feet
Answer:- D is the right answer. 'Feet' is most appropriate unit to measure this distance.
Explanation:-
Given distance =.
[tex]=8.5\times10^{-2}\text{ miles}=\frac{8.5}{100}\text{ miles}=0.085\text{ miles}[/tex]
We know that the units of length near to the mile is kilometers and feetsuch that 1 mile = 1.6093 km
1 mile = 5280 feet
Thus 'feet' is most appropriate unit to measure this distance.
Then the given distance[tex]=0.085\text{miles}=0.085\times5280\text{ feet}=448.8\text{ feet}[/tex]
ABCD is a square. What is the measure of angle BAC? °
Answer:
∠BAC = 45° is the measure.
Step-by-step explanation:
In a square all sides are equal and all the angles are 90°.
We have to measure the angle BAC.
since both the sides AB and BC of the triangle BAC are equal. Therefore angles opposite to these sides ∠BAC and ∠ACB will be equal.
Since ∠BAC + ∠ACB + 90° = 180° ( Sum of all angles of ΔABC = 180°)
∠BAC + ∠BAC + 90° = 180°(∠BAC = ∠ACB)
2∠BAC = 180 -90 = 90°
∠BAC = 90/2 = 45°
∠BAC = 45° is the answer.
A rectangle is no more than six inches wide, and its perimeter measures 28 inches. At least how long is the rectangle?
Subtract.
(5x^2−3x−2)−(−2x^2−x+10)
Express the answer in standard form.
Final answer:
To subtract two polynomials, change the sign of the second polynomial and combine like terms. The result of subtracting (5x^2-3x-2) and (-2x^2-x+10) is 7x^2 - 2x - 12.
Explanation:
To subtract the given polynomials, (5x^2−3x−2) and (−2x^2−x+10), we need to change the sign of each term in the second polynomial and then combine like terms with the first polynomial. This is similar to subtracting negative numbers, where subtraction turns into addition when the number being subtracted is negative.
The subtraction process step-by-step is as follows:
Change the signs of the second polynomial: +2x^2 + x - 10
Add the results to the corresponding terms in the first polynomial:
5x^2 + 2x^2 = 7x^2
−3x + 1x = −2x
−2 − 10 = −12
So the answer to the subtraction in standard form is 7x^2 − 2x − 12.
A diver needs to descend to a depth of 100 feet. She wants to do it in 5 equal descendants. How far should she travel in each descent?
divide total distance by the number od descents they want to do it in
100 / 5 = 20
so each one should be 20 feet