The function g(x) = f(-x) represents a reflection of the graph of f(x) across the y-axis. This transformation swaps the values of the function for positive and negative x values, creating a mirror image. So since the max of f was when x = 2, the max of g will be when x = -2.
Understanding the Transformation of Function g(x) = f(-x)
function g(x) = f(-x).
This indicates a transformation where the function f(x) is reflected across the y-axis.
To put it simply, the graph of y = f(-x) is the mirror image of the graph of y = f(x) across the y-axis.
f g(x) = f(-x), the graph of g looks like a mirror image of f, where the y-axis is the mirror.
For example, g(1) will be what f's value at -1 was (-1). g(2) = f(-2) = -3. g(3) = f(-3) = -1. etc.
So since the max of f was when x = 2, the max of g will be when x = -2.
Here’s an example to illustrate:
Suppose f(x) = x².
The graph of y = f(x) is a parabola facing upwards.
For y = f(-x), or y = (-x)²,
the graph will still be a parabola facing upwards.
Since g(x) = f(-x), the absolute values are not changed but the sign change in x reflects each point across the y-axis.
This reflection happens because negating the independent variable x means we swap the values of the function at positive and negative x values.
Question:
If the function g is defined so that g(x)=f(-x), then for what value of x does g attain its maximum value?
30 POINTS + BRAINLIEST FOR THE CORRECT ANSWER!
Question:
In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)
My work:
x = 155 - 62 which leaves you with x being 53 (Credits to those who helped me in my previous asked question)
That's all I could come up with which completes part A, if you know the answer to part B feel free to just answer part B! Part A is not needed but I added it there for those who need to see it.
The angles of 115 degrees and (52+x) are the same, because they are alternate interior angles.
Answer:
62º + x = 115º
because AB and CD are parallel, which means 115º and 62+x are "alternate angles"
ALTERNATE ANGLES
Step-by-step explanation:
What is the standard form of (7 - 5i)(2 + 3i)?
A. 29 + 11i
B. -11 + 29i
C. 11 - 29i
D. -29 + 11i
Answer:
A
Step-by-step explanation:
Note that i² = - 1
Given
(7 - 5i)(2 + 3i) ← expand factors using FOIL
= 14 + 21i - 10i - 15i² ← collect like terms
= 14 + 11i + 15
= 29 + 11i → A
Answer:
A
Step-by-step explanation:
A book has 500 pages numbered 1,2,3 and so on. How many times does the digit 1 appear in the page numbers?
Answer:
[tex]200[/tex]
Step-by-step explanation:
This book has 500 pages in total.
We should split up the place values.
1 - 9
One only appears once.
1
10 - 19
One appears 11 times.
1 + 11
20 - 99
One only appears 8 times.
1 + 11 + 8
Add:
1 + 11 + 8
=> 20
Since the same is for 200-299, and so on. Let us add twenty four times.
20 * 4
=> 80
Looking back to 100-199, there are 120 ones.
Add:
120 + 80
=> 200
The total number of times that the digit 1 appears in the page numbers is: 200
How to find the number of pages of the book?In the first 99 pages there are:
1 one in the first 9 pages,
11 ones in pages 10-19 (one each for 10 and 12-19, and two for 11)
8 ones in pages 20-99 (21, 31, 41, 51, 61, 71, 81, and 91)
So we have 20 ones in the first 99 pages.
Likewise we have 20 ones in pages 200-299, 20 ones in pages 300-399, and 20 ones in pages 400-499. There are 0 ones on page 500.
For pages 100-199, there are 100 ones for the hundreds digits in addition to the 20 ones found in the tens and ones digits.
So we have a total of 20 + 120 + 20 + 20 + 20 = 200 ones on the page numbers.
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PLEASE HELP The function f(x) = x2 − 2x + 8 is transformed such that g(x) = f(x − 2). Find the vertex of g(x).
(1, 5)
(3, 7)
(1, 9)
(−1, 7)
Answer: Second option.
Step-by-step explanation:
Given the function f(x):
[tex]f(x) = x^2 - 2x + 8[/tex]
Find [tex]f(x -2)[/tex]:
[tex]f(x -2)=(x-2)^2 - 2(x-2) + 8[/tex]
Remember that:
[tex](a\±b)^2=a^2\±2ab+b^2[/tex]
Then, simplifying:
[tex]f(x -2)=x^2-2(x)(2)+2^2 - 2x+4+ 8\\\\f(x-2)=x^2-6x+16[/tex]
So the function g(x) is:
[tex]g(x)=x^2-6x+16[/tex]
Use the following formula to find the x-coordinate of the vertex of g(x):
[tex]x=\frac{-b}{2a}[/tex]
In this case:
[tex]a=1\\b=-6[/tex]
Then:
[tex]x=-\frac{-(-6)}{2(1)}=3[/tex]
Substitute this value into the function g(x) in order to find the y-coordinate of the vertex. Since [tex]g(x)=y[/tex], you get:
[tex]y=3^2-6(3)+16=7[/tex]
Therefore, the vertex of g(x) is:
[tex](3,7)[/tex]
Answer:
Second one
Step-by-step explanation:
3x - 6 = -4 idk how to do this
Hey!
--------------------------------
Solution:
3x - 6 = -4
3x + (-6) = -4
3x + (-6) + 6 = -4 + 6 (Add 6 to both sides)
3x = 2 (Simplify)
3x/3 = 2/3 (Divide both sides by 3)
x = 2/3 (Simplify)
--------------------------------
Answer:
x = 2/3
--------------------------------
Hope This Helped! Good Luck!
four 3 megawatt wind turbines can supply enough electricity to power 3000 homes. How many turbines would be required to power 55,000 homes?
Answer:
The number of turbines is 74
Step-by-step explanation:
* Lets explain how to solve the problem
- Four 3 megawatt wind turbines can supply enough electricity
to power 3000 homes
∴ The number of turbines is 4
∵ Each turbine give 3 megawatt
∴ The four turbines give ⇒ 4 × 3 = 12 megawatt
- This quantity give enough electricity to power 3000 homes
∴ The number of homes for the 12 megawatt is 3000
- We need to find how many turbines can cover enough electricity
to power 55,000 homes, so we must to know the quantity of
electricity that be enough to power 55,000 homes
* Lets use the cross multiplication to solve the problem
∵ megawatt : number of homes
12 : 3,000
? : 55,000
- By using cross multiplication
∴ [tex]?=\frac{(55,000)(12)}{3,000}=\frac{660,000}{3000}=220[/tex]
∴ The enough electricity to power 3000 homes = 220 megawatt
∵ Each turbine gives 3 megawatt
- Find the number of turbines divides the total megawatt by the the
megawatt of one turbine
∴ The number of turbines = 220 ÷ 3 = 73.3
- If we take 73 only the electricity will not be enough to cover all
homes, so we must to take 74 turbines
∴ The number of turbines is 74
To power 55,000 homes, approximately 74 wind turbines are required. Each turbine can power 750 homes, derived from the initial data where 4 turbines power 3,000 homes.
To determine how many 3 megawatt wind turbines are required to power 55,000 homes, we can use a simple proportion based on the given data.
We know that:
4 turbines can power 3,000 homes.Therefore, 1 turbine can power 750 homes (since 3000 / 4 = 750).Now, we need to find out how many turbines are needed to power 55,000 homes:
Number of turbines needed = 55,000 homes / 750 homes per turbine.This calculation gives us approximately 73.33 turbines.Since we can't have a fraction of a turbine in practical terms, we would need 74 turbines to ensure all 55,000 homes are powered.
Area of a parallelogram with a base length of 2.9 ft and a height of 5.5 ft
Step-by-step explanation:
Area of parallelogram = ( base ) ( height )
area of parallelogram = ( 2.9 ft ) ( 5.5 ft )
( as given )
area of parallelogram =15.95 ft²
The cost in dollars of making x items is given by the function C(x) = 10x + 500. a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item. b. What is the cost of making 25 items? c. Suppose the maximum cost allowed is $1500. What are the domain and range of the cost function, C(x)?
Answer:
a. $500
b. $250
Step-by-step explanation:
a. For zero items produced, cost will be-
[tex]C(0) = 10(0) + 500 = 0 + 500 = 500[/tex]
b. For zero items produced, cost will be-
[tex]C(25) = 10(25) + 500 = 250 + 500 = 750[/tex]
c. If [tex]C(x)_{max} = 1500[/tex]
[tex]10x + 500 = 1500\\10x = 1000\\x = 100[/tex]
∴ domain for cost function will be [tex][0,100][/tex] and range will be 100
Answer: A) fixed cost is $500
B) Cost of making 25 items is $750
C) Domain: [0,100]
Range :[500,1500]
I got 100% on test with these answers
15- [(3^2+ 6) ÷5=12
my teacher told me it was 12 but idk how to do it idk the strategy
4×[50-3(1+3)^2]= 8
idk the strategy pls help ?? plzzzz
Answer:
The strategy to evaluate these expressions is called PEMDAS.
Step-by-step explanation:
Problem #1[tex]15-[(3^2+6)\div5][/tex]
We're going to be following the rule of PEMDAS:
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionKeep in mind that multiplication/division and addition/subtraction are done from left to right.
In the first expression (written above), we'll first evaluate everything inside the brackets first (brackets are used when there are parentheses inside of it - but they serve the same function). There are parentheses in these brackets, so that will be the absolute first step in evaluating.
Solve for [tex]3^2+6[/tex] then rewrite the expression.
[tex]15-[(15)\div5][/tex]Now finish evaluating inside the parentheses by dividing 15 by 5.
[tex]15-[3][/tex]The last step to evaluate the expression is to subtract 3 from 15.
12Problem #2[tex]4\times[50-3(1+3)^2][/tex]
Evaluate everything inside the the brackets. Start with the parentheses since that is first according to PEMDAS. Add 1 and 3 together then rewrite the expression.
[tex]4\times[50-3(4)^2][/tex]Exponents are solved next after parentheses in PEMDAS, so evaluate the exponent.
[tex]4\times[50-3(16)][/tex]Multiplication is done before subtraction, so multiply 3 and 16 together.
[tex]4\times[50-(48)][/tex]Finish evaluating inside the brackets by subtracting 48 from 50.
[tex]4\times[2][/tex]The last step in evaluating the second expression is to multiply 4 and 2 together, which gives us 8.
8The average mass of a grain of sand on a beach is about 0.000015. What is 0.000015 in scientific notation ?
Answer:
15*10∧-5
Multiple 15 x 0,000001 = 0,000015.
50 Point Question...
A dog owner observes that from birth to age 14 weeks, the puppy’s weight can be modelled by the equation w = 365×(1.23)t (0 ≤ t ≤ 14),
(1) Write down the scale factor, and use this to find the percentage increase in the weight each week.
(2) Use the law of logs to find the age at which the puppy will weigh 4000 grams
Answer:
See explanation
Step-by-step explanation:
A dog owner observes that from birth to age 14 weeks, the puppy’s weight can be modelled by the equation
[tex]w = 365\cdot (1.23)^t \ (0\le t \le 14)[/tex]
In this equation,
number 365 represents the initial weight of puppy;number 1.23 can be rewritten as 1+0.23, where 0.23 (or 23%) is the rate of weight increase.When w=4,000, then
[tex]4,000=365\cdot (1.23)^t\\ \\(1.23)^t =\dfrac{4,000}{365}=\dfrac{800}{73}\\ \\t=\log_{1.23}\dfrac{800}{73}\approx 11.5651[/tex]
This means that puppy will weight 4,000 grams nearly at the middle between 11th week and 12th week.
Find two consecutive integers whose sum is 373.
Final answer:
The two consecutive integers whose sum is 373 are 186 and 187. We derived the equations n + (n + 1) = 373 and solved for n to find the first integer.
Explanation:
To find two consecutive integers whose sum is 373, let's denote the first integer as n. The next consecutive integer will be n + 1. When we add these two integers together, their sum should equal 373, which gives us the equation:
n + (n + 1) = 373
Simplifying this equation, we get:
2n + 1 = 373
To solve for n, we subtract 1 from both sides of the equation:
2n = 372
Divide both sides by 2:
n = 186
So the first integer is 186. The next consecutive integer is:
n + 1 = 186 + 1 = 187
Therefore, the two consecutive integers that sum to 373 are 186 and 187.
PLEASE HELP! ILL MARK BRAINLIEST
Describe how the graph of y= x^2 can be transformed to the graph of the given equation. y = (x - 2)2 - 10
Shift the graph of y = x^2 down 2 units and then left 10 units.
Shift the graph of y = x^2 left 2 units and then down 10 units.
Shift the graph of y = x^2 right 2 units and then down 10 units.
Shift the graph of y = x^2 right 2 units and then up 10 units.
Subtracting a number from x shifts the graph that may places tot he right
Subtracting a number at the end of the equation, shifts the graph that many units down.
The answer would be: Shift the graph of y = x^2 right 2 units and then down 10 units.
Answer:
Shift the graph of y = x^2 right 2 units and then down 10 units.
Step-by-step explanation:
The graph of y= x^2 can be transformed to the graph of the given equation: y = (x - 2)2 - 10. This can be done by shifting the graph of y = x^2 right 2 units and then down 10 units.
Divide 381 by 29 what do you think it is
Answer:
Im pretty sure its 13.137
I hope this helps!
Answer:
[tex]13.13[/tex]
Step-by-step explanation:
We first we need to look at the equation:
381 ÷ 29
So we first have to look at how many times 29 goes into 38, since 29 is already in the tens place.
It only goes in once. Meaning that right now you have one as your tens place.
1
Now you need to subtract 29 by 38
==> 9
So drop down the one from 381 to get 91, then find out how many times 29 goes into 91
==> 3 times
So now 3 is your tens place
13
Now do 91 - 29
==> 62
62 left?!
That means we need to [tex]annex^{1}[/tex] :
drop down 0 into 62 to get 620:
Find out how many times 29 goes into 620:
==> 13
13.13
FOOTNOTE:
annex = drop down 0 after a decimal
What is the solution to the following system of equations?
[x+y=5
(x-y= 1
0 (-2,7)
(2,3)
(3, 2)
(7-2)
Answer:
(3,2)
Step-by-step explanation:
The system is
x + y = 5
x -y = 1
Add the equations to eliminate y
2x = 6----->x=3
Substitute this value in any equation
3+y = 5----->y=2
The solution is (3,2)
The horizontal line through (3,7) in point-slope form
In mathematics, a horizontal line has a slope of 0, and its equation is always 'y = b', where 'b' is the y-coordinate of any point on the line. In this situation, since our line passes through the point (3,7), the equation of the horizontal line is 'y = 7'.
Explanation:In the context of mathematics, a horizontal line is a line whose equation is in the form y = b where 'b' represents the y-intercept, or the y-coordinate of a certain point on the line. In this question, you are asked to find the point-slope form of a horizontal line passing through the point (3,7).
However, for a horizontal line, the point-slope form y = mx + b becomes y = b because m, the slope of a horizontal line, is 0. And the y-coordinate of any point on a horizontal line is the same.
So, since the line is passing through the point (3,7), the y-coordinate 7 is constant throughout the horizontal line. Therefore, the equation of the horizontal line through (3,7) would be y = 7.
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-2.5 + (-3.5)
Which number line shows the sum?
Final answer:
The sum of -2.5 and (-3.5) is -6.0, which is found by adding the absolute values of the numbers and giving the result a negative sign. The correct number line representation for this sum would show a leftward movement from -2.5 by 3.5 units to end at -6.0.
Explanation:
When calculating the sum of -2.5 and (-3.5), we follow the rule that when two negative numbers are added, the answer has a negative sign. Both numbers in the sum are negative, therefore, we add their absolute values and then give the result a negative sign. The calculation is as follows:
-2.5 + (-3.5) = -(2.5 + 3.5) = -6.0
The number line that shows this sum would start at -2.5 and move left (which indicates adding a negative number) 3.5 units, landing on -6.0.
2- + (2+7) Use number properties to simplify the following expression
Answer:
-7.
Step-by-step explanation:
2- + (2+7)
First work out the parentheses ( by order of operations PEMDAS)
= 2 - + 9
= 2 - 9 (as - + = -)
= -7.
One positive number is three more than twice another. Their product is 119
Answer: The numbers are 7 and 17
Step-by-step explanation: twice of 7 is 14 and 3 + 14 = 17
1. f(x) = 5x +4
for Range = {5, 6, 7, 8}
Determine the domain
Answer:
see explanation
Step-by-step explanation:
Given the range of f(x), find the domain by equating f(x) to each of the values in the range, that is
5x + 4 = 5 ( subtract 4 from both sides )
5x = 1 ( divide both sides by 5 )
x = [tex]\frac{1}{5}[/tex]
5x + 4 = 6 ( subtract 4 from both sides )
5x = 2 ( divide both sides by 5 )
x = [tex]\frac{2}{5}[/tex]
5x + 4 = 7 ( subtract 4 from both sides )
5x = 3 ( divide both sides by 5 )
x = [tex]\frac{3}{5}[/tex]
5x + 4 = 8 ( subtract 4 from both sides )
5x = 4 ( divide both sides by 5 )
x = [tex]\frac{4}{5}[/tex]
Thus
domain = { [tex]\frac{1}{5}[/tex], [tex]\frac{2}{5}[/tex], [tex]\frac{3}{5}[/tex], [tex]\frac{4}{5}[/tex] }
which fraction is equivalent to 3?
Mistake in the Question:
The number 3 is not a fraction.
Answer:
Suppose if it is 3/8 then do the following:
Multiply
3
__ by an equivalent fraction that equals 1.
8
An equivalent fraction is equal to 1 such as 2 or 3
__ __
2 3
An equivalent fraction is the same as multiplying by 1 so the ratio does not change.
This fraction would be equal to a where a is an integer.
__ = 1
a
Hence an example would be that
2 3 6
__ . __ = __
2 8 16
Request: Please mark me as the brainliest.
How many 1/16 inches are in one inch?
PLZ HELP 25 POINTS THIS IS AN EMERGENCY THANKS!!
Bobby wants to invest $100. His brother invested $2,000 for one year and earned $60 in simple interest.
If Bobby invests his money for one year at the same interest rate as his brother, how much interest will he earn?
O A. $3
OB. $6
OC. $12
OD. $30
OE. $33
Answer:
$3
Step-by-step explanation:
By investing $2,000 Bobby will earn $60 interest
∴By investing $1 Bobby will earn =$(60/2000) interest
so,
By investing $100,
He will earn =$ {(60/2000 ) .100}
=$3
If Bobby invests his money for one year at the same interest rate as his brother, then he will earn $3 amount.
Thus, option A $3 is correct.
Given that:Amount Bobby wants to invest = $100Time for which Bobby wants to invest = 1 year.Amount his brother invested = $2000Time interval for which his brother invested money = 1 year.Simple interest earn by his brother = $60To find:Interest that Bobby will earn at same interest rate as his brother after 1 year of investment of $100.
Calculations:If someone invests P amount for T years with simple interest rate R% per year, then the simple interest that that person will earn is given by:
[tex]SI = \dfrac{P \times R \times T}{100}[/tex]
Putting values of P, R and T of Bobby's brother's investment, we have:
[tex]60 = \dfrac{2000 \times 1 \times R}{100}\\\\6000 = 2000R\\\\R = \dfrac{6000}{2000} = 3\%[/tex]
At that rate, the SI for Bobby's $100 investment for 1 year is:
[tex]SI = \dfrac{100 \times 3 \times 1}{100} = \$3[/tex]
Thus, Bobby will get $3 as interest.
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There are two boxes, one has a dimension of 6x2x3 and the other has dimension of 2x3x6. Which is bigger?
15-3(-x+5)=-21+6x Can someone help me find the value of X
Step-by-step explanation:
first 3(-x+5) you distribut
then you would get 15-3x+15=21+6x and u combine like terms which is 3x and 6x which is 9 and u get 15-9x+15=21tthen u sabtract 15x on both side and get 15-9=21 then u subtract 15 ok both side and get x = 0.7
could you guys pls be so kind and help me out❤️
—-
i promise i will mark brainliest!
Answer:
10 years
Step-by-step explanation:
spends 2 hours and 20 minutes trading stickers and 125 minutes doing homework. What activity does he spend more time on? How much more time?
Evaluate 6j+23+kl−3, when j=3, k=7, and l=33.
Enter your answer in the box.
Answer:
269
Step-by-step explanation:
1) Substitute in the given values for each variable:
6(3)+23+(7)(33)-3
2) Simplify:
18+23+231-3
3) Simplify again:
269
Max scored 6 marks more than what he did in the previous
examination in which he scored 30. Maria scored 30 marks more
than she did in the previous examination in which she scored 60.
Who showed less improvement?
♡
Answer:
max showed less improvement!
Step-by-step explanation:
Max percentage improvement in the first exam = (6/30 × 100) %
= (600/30) %
= 20 %
Maria percentage improvement in the first exam = (30/60 × 100) %
= (3000/60) %
= 50 %
Hence, 20 % < 50 %
Final answer:
Max improved by 6 marks from his previous score, while Maria improved by 30 marks. Therefore, Max showed less improvement than Maria.
Explanation:
Max scored 6 marks higher than his previous score of 30, making his new score 36. Maria scored 30 marks more than her previous score of 60, taking her new score to 90. To determine who showed less improvement, we compare the amount of increase in their scores.
Max's improvement: 30 + 6 = 36
Maria's improvement: 60 + 30 = 90
Max improved by 6 marks, and Maria improved by 30 marks. Therefore, Max showed less improvement.
When comparing improvement, it's useful to look at the actual increase in marks gained, not necessarily the percentage improvement unless specifically asked. Here, the simple comparison of the additional marks scored determines who improved less. Though both students improved their scores, the difference in their points increased is a clear indicator of whose improvement was less significant.