Answers
First, plug in the value -1 for x in f(x) first. [tex] \frac{1}{(-1)^2+1} [/tex] can then be simplified to [tex] \frac{1}{2} [/tex] because [tex](-1)^2=1[/tex]. Next, put the value -1 for x in the equation g(x). This will look like [tex]- \frac{1}{2} [/tex].
The final step is to evaluate f(x) divided by g(x). f(x) = 1/2 and g(x) = -1/2, so when divided, you get -1.
g(-1) = -1/2
1/2 / -1/2 =
1/2 * -2/1 = -1
Letter D
Related Questions
2[18-(5+9)÷7]
show how you did it
Answers
PEMDAS
do parntheases
then exponents
then mutiply or divide, whichever coms first
then addd or subtract, whichever comes first
so
when doing parenthases, simplify innermost parenthsees first
so
2(18-(5+9)/7)
innermost is (5+9)=14
now we gots
2(18-(14)/7)
we can distribute or multiply the invisible -1 in front of the 14
2(18-14/7)
now divide because division comes before adition
remember that it is -14/7, not just 14/7 because the negative is part of the 14
2(18-2)
now simplify parenthasees
18-2=16
so
2(16)
multiply
32
the result is 32
The tile pattern shown was used in Pompeii for paving. If the diagonals of each rhombus are 2 inches & 3 inches, what area makes up each cube in the pattern?
Answers
A ( rhombus ) = d1 * d2 / 2
d1 = 2 in, d2 = 3 in.
A ( rhombus ) = 2 * 3 / 2 = 3 in²
Finally: 3 * 3 = 9 in²
Answer: Area of each cube in the pattern is 9 in².
Using the Degree minute second method to describe an angle, one degree of angle measurement can be divided into how many minutes?
Answers
What is the number of degrees in the measure of each exterior angle of a regular polygon of 18 sides?
Answers
A game spinner is divided into 5 equal sections numbered 1 to 5. How many outcomes are in the sample space for 4 spins of this spinner? a. 625 b. 125 c. 20 d. 500
Answers
spin 2 ~ 5
spin 3 ~ 5
spin 4 ~ 5
5 * 5* 5 * 5 = 5^ 4 = 625
Letter A
The correct option is a. 625.
The total number of outcomes in 4 spins of the spinner can be found by multiplying the number of outcomes in one spin by itself 4 times, resulting in 625 outcomes.
The sample space for 4 spins of the spinner can be calculated by raising the number of outcomes in one spin to the power of the number of spins.
In this case, as there are 5 outcomes on the spinner, the total number of outcomes in 4 spins would be 5^4 = 625.
Therefore, the correct option is a. 625.
In ΔABC shown below, point A is at (0, 0), point B is at (x2, 0), point C is at (x1, y1), point D is at x sub 1 over 2, y sub 1 over 2, and point E is at the quantity of x sub 1 plus x sub 2 over 2, y sub 1 over 2: Triangle ABC is shown. Point D lies on segment AC and point E lies on segment BC. A segment is drawn between points D and E. Point A is at the origin. Prove that segment DE is parallel to segment AB.
Answers
Segment AB has slope 0. Segment DE, with midpoints of AC and BC, also has slope 0. Thus, DE is parallel to AB.
To prove that segment DE is parallel to segment AB, we need to show that the slopes of both segments are equal.
The slope of segment AB, denoted as [tex]\( m_{AB} \)[/tex], can be calculated using the coordinates of points A and B:
[tex]\[ m_{AB} = \frac{{y_B - y_A}}{{x_B - x_A}} \][/tex]
Given that point A is at (0, 0) and point B is at [tex]\((x_2, 0)\)[/tex], the slope [tex]\( m_{AB} \)[/tex] is:
[tex]\[ m_{AB} = \frac{{0 - 0}}{{x_2 - 0}} = 0 \][/tex]
Now, let's find the coordinates of points D and E.
Point D lies on segment AC, so it is at the midpoint of segment AC. Therefore, the coordinates of point D, denoted as [tex]\((x_{D}, y_{D})\)[/tex], are the average of the coordinates of points A and C:
[tex]\[ x_{D} = \frac{{x_1 + 0}}{2} = \frac{{x_1}}{2} \][/tex]
[tex]\[ y_{D} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]
Similarly, point E lies on segment BC, so it is at the midpoint of segment BC. Therefore, the coordinates of point E, denoted as [tex]\((x_{E}, y_{E})\)[/tex], are the average of the coordinates of points B and C:
[tex]\[ x_{E} = \frac{{x_1 + x_2}}{2} \][/tex]
[tex]\[ y_{E} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]
Now, let's calculate the slope of segment DE, denoted as [tex]\( m_{DE} \)[/tex]:
[tex]\[ m_{DE} = \frac{{y_{E} - y_{D}}}{{x_{E} - x_{D}}} \][/tex]
Substituting the coordinates of points D and E:
[tex]\[ m_{DE} = \frac{{\frac{{y_1}}{2} - \frac{{y_1}}{2}}}{{\frac{{x_1 + x_2}}{2} - \frac{{x_1}}{2}}} \][/tex]
[tex]\[ m_{DE} = \frac{0}{{\frac{{x_1 + x_2 - x_1}}{2}}} \][/tex]
[tex]\[ m_{DE} = 0 \][/tex]
Since the slopes of segments AB and DE are both equal to 0, we can conclude that segment DE is parallel to segment AB.
$5.50 markup 75% what is the selling prize
Answers
To calculate the selling price with a 75% markup on a $5.50 item, multiply the original cost by 0.75 to find the markup amount and then add it to the original cost. The final selling price is $9.63.
Calculating the Selling Price with a Markup
To determine the selling price of an item with a 75% markup, follow these steps:
Determine the original cost of the item, which is $5.50 in this case.Calculate the markup amount by multiplying the original cost by the markup percentage. Express the percentage as a decimal:Markup Amount = Original Cost × Markup Percentage
Markup Amount = $5.50 × 0.75 = $4.125Add the markup amount to the original cost to get the selling price:
Selling Price = Original Cost + Markup Amount
Selling Price = $5.50 + $4.125 = $9.625Optionally, round the selling price to two decimal places (if necessary):
Selling Price ≈ $9.63
Therefore, the selling price for the item with a 75% markup on an original cost of $5.50 is $9.63.
Grace is half her father joseph's age. in 10 years grace will be three-fifths joseph's age. ten years ago, grace was one third joseph's age. how old are grace and joseph now
Answers
After setting up a system of equations based on the given age relationships and solving for both Grace and Joseph, we deduce that Grace is 20 years old and Joseph is 40 years old currently.
Let's denote Grace's current age as G and Joseph's current age as J. According to the problem, Grace is half of Joseph's age, so we have the first equation:
G = 0.5 * J
In 10 years, Grace will be three-fifths of Joseph's age, giving us the second equation:
G + 10 = (3/5) * (J + 10)
Ten years ago, Grace was one-third of Joseph's age, which gives us the third equation:
G - 10 = (1/3) * (J - 10)
We now have a system of three equations with two variables. We can solve this system to find the current ages of Grace and Joseph. After solving for G and J, we find that Grace is 20 years old and Joseph is 40 years old.
What is 35 minus 3 times 8
Answers
Evaluate multiplication first (order of operations).
35-24
Then subtract
35-24=11
Final answer: 11
First you would multiply 8•3 which gives you 24.
Then you would subtract 24 from 35
35 - 24 = 11
Final answer: 11
:)
In which section of the number line is √32?
Answers
sqrt(32) = 5.66
so it is in section B
Answer:
section B.
YOUR WELCOME
How were the numbers 1 10 100 and 1000 written by romans?
Answers
10 -- X
100 -- C
1000 -- M
if z=2.5, x=102 and x=100, what is s?
Answers
I believe the problem ask for s which is the standard deviation. We must recall that the formula for z statistic is stated as:
z = (x – x over bar) / s
Where,
z = z statistic = 2.5
x = sample value or sample score = 102
x over bar = the sample mean or sample average = 100
s = standard deviation = unknown
Rewriting the equation in terms of s:
s = (x – x over bar) / z
Substituting the given values into the equation:
s = (102 – 100) / 2.5
s = 0.8
Therefore the standard deviation s is 0.8
What is the slope of a line that is parallel to the graph of y=3x-2
Answers
[tex]\bf y=\stackrel{slope}{3}x-2[/tex]
HELP PLEASE ASAP !!!! 80 POINTS !!!!!!!
There are 975 birds in an aviary. Each month, the number of birds decreases by 7%. There are 350 trees in the aviary. Each month, 7 trees are removed.
Part A: Write functions to represent the number of birds and the number of trees in the aviary throughout the months. (4 points)
Part B: How many birds are in the aviary after 12 months? How many trees are in the aviary after the same number of months? (2 points)
Part C: After approximately how many months is the number of birds and the number of trees the same? Justify your answer mathematically. (4 points)
Answers
Part A
months = m
since birds decrease by 7%, there will be 93% left. 93% = 0.93
birds: 975 x 0.93^m
trees: 350 - 7m
Part B
birds: 975 x 0.93^12 = 408
trees: 350-7(12) = 266
Part C
350 - 7m = 0.93^m(975)
We have intersection points at approximately 22.21 and 44.4781. round off to whole numbers, we have 22 and 44 months.
How do you simplify the square root of 27?
Answers
[tex] \sqrt{27} = \sqrt{9*3} [/tex]
Now break up the 9 into its perfect square:
[tex] \sqrt{(3*3)*3} [/tex]
Because there are 3 3's you can pull out the root of 9, which is one of those 3's. It will then simplify to
[tex]3 \sqrt{3} [/tex]
If you had the square root of 8, that would simplify to
[tex] \sqrt{8} = \sqrt{4*2} [/tex]
4 is a prfect square (2 times 2), so you can pull out a 2, leaving the other 2 under the radical
[tex] \sqrt{4*2} = \sqrt{(2*2)*2} =2 \sqrt{2} [/tex]
Hope that makes sense. If you'd like some more examples to help clarify, just ask!
A file that is 256 megabytes is being downloaded. If the download is 18.6% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Answers
The calculation would be: 256 megabytes x 0,186= 47.616 megabytes.
If you round up the answer to nearest tenth it will be 47.6 megabytes
Name the binomial you can multiply by (x + 9) to get the product x 2 + 5x – 36. A. 4 – x B. x + 6 C. x – 4 D. x – 6
Answers
To factor the quadratic equation, find two numbers that add to 5 and multiply to -36.
I got 9 and -4.
So, the factors are (x + 9) and (x - 4).
So, C x - 4 is the answer.
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 20 and 2500, respectively.
Answers
The formula for geometric sequence is given by:
nth=ar^(n-1)
where:
a=1st term
r=common ratio
n=nth term
thus the 2nd term is:
20=ar^(2-1)
20=ar......i
the 5th term is:
2500=ar^(5-1)
2500=ar^4.......ii
from i
a=20/r
from ii
a=2500/r^4
therefore:
20/r=2500/r^4
multiplying through by r^4 we get:
20r^3=2500
dividing both sides by 20 we get:
r^3=125
hence;
r=5
substituting the value of r in i we get:
20=ar
20=5a
thus;
a=4
the formula for the sequence will therefore be:
nth=ar^(n-1)
nth=4*5^(n-1)
Answer:
The explicit formula of the geometric sequence is:
[tex]a_n=4\times 5^{n-1}[/tex]
Step-by-step explanation:
The explicit formula is the expression where the nth term is given in terms of the first term of the sequence.
We know that the explicit formula for a geometric sequence is given by:
[tex]a_n=(a_1)^{r-1}[/tex]
Here we are given:
The second and fifth terms as: 20 and 2500 respectively.
i.e.
[tex]a_2=20[/tex] and [tex]a_5=2500[/tex]
i.e.
[tex]ar=20\ and\ ar^4=2500[/tex]
Hence,
[tex]\dfrac{ar}{ar^4}=\dfrac{20}{2500}\\\\\\\dfrac{1}{r^3}=\dfrac{1}{125}\\\\\\(\dfrac{1}{r})^3=(\dfrac{1}{5})^3\\\\\\\dfrac{1}{r}=\dfrac{1}{5}\\\\\\r=5[/tex]
Also,
we have:
[tex]ar=20\\\\i.e.\\\\a\times 5=20\\\\i.e.\ a=4[/tex]
Hence, the explicit formula is given by:
[tex]a_n=4\times 5^{n-1}[/tex]
If the area of a rectangle is 16 then the length is 4 and the width is 4 what is the counterexample
Answers
Indicate a general rule for the nth term of this sequence. 12m, 15m, 18m, 21m, 24m,...
a. = 3mn + 9m
b. = -3mn - 9m
c. = -3mn + 9m
d. = 3mn - 9m
Answers
12m, 15m, 18m, 21m, 24m, ...,
The 1st term is a₁ = 12m
The 2nd term is a₂ = 15m = a₁ + 3m = a₁ + (2-1)*3m
The 3rd term is a₃ = 18m = a₂ + 3m = a₁ + (3-1)*3m
Because each successive term is 3m more than the previous term, we have an arithmetic sequence with a common difference of 3.
Answer:
The n-th term is
[tex]a_{n} = a_{1} + (n-1)*(3m),\\for\, n=1,2,3,\,...,[/tex]
In recursive form,
[tex]a_{n+1}=a_{n}+3m[/tex]
A city's current population is 1,000,000 people. It is growing at a rate of 3.5% per year. The equation P=1,000,000(1.035)^x models the city's population growth where x is the number of years from the current year. In approximately how many years will the pooulation be 1,400,000? Round to nearest tenth
Answers
P=1,000,000(1.035)^x
We substitute the population desired to be reached to the equation and evaluate the value of x.
P=1,000,000(1.035)^x
1400000=1,000,000(1.035)^x
7/5 = 1.035^x
ln 7/5 = ln 1.035^x
x = ln 7/5 / ln 1.035
x = 9.78
Therefore, the number of years needed to reach a population of 1400000 with a starting population of 1000000 would be approximately 10 years.
Help thank you :((((((((((((((((((
Answers
The line is not dashed, so it is more than or equal to since the shading is above the line.
The slope of the line going up is 1 (rise over run). The line is dashed and it is shaded below the line so the sign must be <.
Final answer: D
If 4 less than a number is less than 4 and greater than -3, find the number.
Answers
many (if integers: 2, 3, 4, 5, 6, and 7) Are you sure it is greater than -3?
What is the tangent ratio for angle f
Answers
hope it helps
tan(f)=8/6=4/3
Evaluate the expression m + o for m = 9 and o = 7.
Answers
o = 7
m + 0 = 9 + 7 = 16
Hence, the answer is 16.
LAW ENFORCEMENT: A police accident investigator can use the formula S=25L‾‾‾√S=25L to estimate the speed s of a car in miles per hour based on the length l in feet of the skid marks it left. How fast was a car traveling that left skid marks 109 feet long?
Answers
sqrtS=25L
where:
L is the length in feet of skid marks it left.
Thus the speed of a car with skid marks L=107 ft =107/5280=0.02 miles, will be:
sqrtS=25*0.02=0.5
thus the speed will be given by:
S=(0.5)^2=0.25 miles per hour
I just need the answers for this.im really confused
Answers
We have weekly saving of $2.50, the target amount of $85.98 and the amount carried forward from birthday present of $35, We want to work out the number of weeks we need to save to buy season pass
By working backwards, the steps are
[tex]85.98-35=50.98[/tex] ⇒ We subtract the birthday money from the season-pass fee
[tex]50.98/2.50 = 20.392[/tex] ≈ 21 Weeks ⇒ We divide by the amount we save every week
The answer is rounded up to 21 weeks
Question b)
Let the number of weeks be '[tex]x[/tex]' and the season-pass fee be '[tex]y[/tex]'
The equation that represents the context is
[tex]y=35+25x[/tex]
In words: To achieve the value [tex]y[/tex] we need to multiply [tex]x[/tex] by $2.50 (saving) and add $35 (birthday money)
We know that [tex]y=85.98[/tex] as this is the amount we aim to achieve by saving $2.50 per week. Substituting this into the equation we formed earlier we have
[tex]85.98=35+2.5x[/tex] ⇒ Subtract 35 from both sides
[tex]85.98-35=35-35+2.5x[/tex]
[tex]50.98=2.5x[/tex] ⇒ Divide both sides by 2.5
[tex] \frac{50.98}{2.5}= \frac{2.5x}{2.5} [/tex]
[tex]x=20.392[/tex] ≈ 21
We round the answer to 21 weeks. We achieve the same answer with part a)
Question c)
This time, we aim to save $85.98 by the end of 11th week. We might need to adjust the amount we save per week. We will use the same equation we form in part b) but this time we will use the variable [tex]'s'[/tex] to represent the amount of weekly saving.
[tex]y=35+11s[/tex] ⇒ where [tex]y[/tex] is the season pass fee, '35' is the birthday money, '11' is the number of weeks, and [tex]'s'[/tex] is the amount of saving
We have [tex]y=85.98[/tex]
[tex]85.98=35+11s[/tex]
[tex]85.98-35=11s[/tex]
[tex]50.98=11s[/tex]
[tex]s= \frac{50.98}{11}=4.6345 [/tex] ≈ 5
The answer is $5 to be saved for 11 weeks to achieve $85.98
----------------------------------------------------------------------------------------------------------------
Use the same equation to work out the number of weeks we need to save $2.50 per week if we have to pay the higher price of season pass fee of $120.98
[tex]y=35+2.50x[/tex]
[tex]120.98=35+2.5x[/tex]
[tex]120.98-35=2.5x[/tex]
[tex]85.98=2.5x[/tex]
[tex]x= \frac{85.98}{2.5}=34.392 [/tex]≈ 35 weeks
-----------------------------------------------------------------------------------------------------------
If we can start saving as early as possible, then 21 weeks of $2.50/week would work for the cheaper price of season-fee and we don't need to adjust the budget. However, if we still want to aim for $85.98 season pass fee, but only have fewer weeks to save, then adjusting budget is necessary. We can perhaps decide not to go bowling every week so we can use the budget for saving instead, or we can alternate between bowling and movie every week.
Question d)
Using the original budget, we work out a third of $2.50 which is 2.5÷3 = 0.83
It means we have 2.5-0.83 = 1.6 left to save weekly.
Using the same equation with part b)
[tex]y=35+1.6x[/tex] ⇒ Notice that we adjust the constant 2.5 to 1.6
[tex]85.98 = 35+1.6x[/tex] ⇒ We still aim to save for the cheapest season-pass
[tex]85.98-35=1.6x[/tex]
[tex]50.98=1.6x[/tex]
[tex]x= \frac{50.98}{1.6}=31.8625 [/tex] ≈ 32 weeks
We will have 32 weeks × $0.83 = $26.56 to buy gift for Mother.
Question e)
From information from part a) to part d), there are many different ways to adjust the budget.
Someone pls help me!! and thank you if you do !
Answers
Based on the chart, which would be considered the dependant variable?
Answers
Answer:
u didn't provide a chart but the dependent variable is the y axis, or the vertical line
Step-by-step explanation:
It's always the y axis (the vertical line)
How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed?
Answers
Final answer:
There can be 900,000 unique 6-digit numbers formed using the digits 0-9 with repetitions allowed, considering the first digit cannot be 0.
Explanation:
Calculating 6-Digit Numbers with Repetitions
The question pertains to the number of unique 6-digit combinations that can be made from the digits 0-9 when repetitions are allowed. Since the first digit of a 6-digit number cannot be 0 (as it would make the number a 5-digit number), there are 9 possibilities for the first digit (1-9). For each of the five remaining positions, all 10 digits (0-9) are possibilities because we are allowing repetitions. Therefore, the total number of combinations is calculated by multiplying the possibilities for each digit place.
The solution is as follows: 9 possibilities for the first digit times 10 possibilities for each of the second, third, fourth, fifth, and sixth digits.
9 (first digit) * 10 (second digit) * 10 (third digit) * 10 (fourth digit) * 10 (fifth digit) * 10 (sixth digit) = 900,000 unique 6-digit numbers that can be formed.