Rewrite the numerator as
x ² + 3x + 5 = (x - 1/2)² + 4 (x - 1/2) + 27/4
Then
(x ² + 3x + 5) / (2x - 1) = 1/2 × (x ² + 3x + 5) / (x - 1/2)
… = 1/2 × ((x - 1/2)² + 4 (x - 1/2) + 27/4) / (x - 1/2)
… = 1/2 × ((x - 1/2) + 4 + 27 / (4 (x - 1/2)))
… = 1/2 x + 7/4 + 27 / (8 (x - 1/2))
which clearly has a non-removable singularity at x = 1/2, which is to say this function has a domain including including all real numbers except 1/2.
For every number other than x = 1/2, the function takes on every possible real numbers, since 1/2 x + 7/4 alone takes on all real numbers.
So:
domain = {x ∈ ℝ | x ≠ 1/2}
range = {x ∈ ℝ}
The manager of a school store orders 250 pencils at the beginning of the
school year to sell to students. The function f(x) = 250 – 7x represents the
number of pencils remaining after I days of school.
How many pencils are remaining after 14 days of school?
Answer:
152 pencils remain after 14 days of school.
Step-by-step explanation:
Replace x in this formula with 14 (14 days):
f(14) = 250 - 7(14) = 250 - 98 = 152
152 pencils remain after 14 days of school.
Answer:...
Step-by-step explanation:
What are the solutions to the equation (2x – 5)(3x – 1) = 0?
x = 5/2 or x = 1/3
C is the answer.
Answer:
x = 5/2 or x = 1/3
Step-by-step explanation:
Simplify
( 2 x − 5 )( 3 x − 1 ) .
6 x 2 − 17 x + 5 = 0
Use the quadratic formula to find the solutions.
[tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] or [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
Substitute the values a = 6 , b = − 17 , and c = 5 into the quadratic formula and solve for x .
17 ±sqrt(-17)^2-4*(6*5)
_________________
2*6
Simplify.
x = 17 ± 13 /12
The final answer is the combination of both solutions.
x = 5 /2 , 1 /3
A standardized test is designed so that scores have a mean of 50 and a standard deviation of 4.
What percent of scores are between 46 and 54?
Answer:
68.3%
Step-by-step explanation:
Using the relation :
Zscore = (x - Mean) / standard deviation
For, x between 46 and 54
Zscore = ((54 - 50) / 4) - ((46 - 50) / 4)
P(Z < 4/4) - P(Z < -4/4)
P(Z < 1) - P(Z <-1)
0.84134 - 0.15866
= 0.68268
= 0.68268 * 100%
= 68.3%
Answer:
A standardized test is designed so that scores have a mean of 50 and a standard deviation of 4. What percent of scores are between 42 and 58?
Step-by-step explanation:
about 95.4%
Explicit formula for an, the nth term of the sequence 48,12,3,...
Answer:
a(n) = 48*(1/4)^(n - 1)
Step-by-step explanation:
Here the first term, a(1), is 48 and the common ratio is r = 1/4.
Thus, the specific formula for the information given is
a(n) = 48*(1/4)^(n - 1)
What is the length of X to Y
answers r
Answer:
8.6
Step-by-step explanation:
GIVING BRAINLIEST!!!!!!!
Two numerical patterns are shown below:
Pattern A: 6, 12, 18, 24, 30
Pattern B: 12, 24, 36, 48, 60
Select the statement that describes the numerical patterns.
The rule for Pattern B is "multiply by 2."
The rule for Pattern A is "multiply by 2."
Each term in Pattern B is one half the corresponding term in Pattern A.
Each term in Pattern A is one half the corresponding term in Pattern B.
Answer:
ITS A
i took the quiz :)
Step-by-step explanation:
The two true statements are:
The rule for Pattern B is "multiply by 2."
Each term in Pattern A is one-half the corresponding term in Pattern B.
Wich statements are the correct ones?
Here we have two patterns:
Pattern A: 6, 12, 18, 24, 30Pattern B: 12, 24, 36, 48, 60First, let's analyze the patterns. For pattern A we can see that we just add 6 to each consecutive term, so this is an arithmetic sequence.
6 + 6 = 12
12 + 6 = 18
18 + 6 = 24
And so on.
For pattern B we multiply each term by 2 to get the next one, so this is a geometric sequence.
2*12 = 24
2*24 = 48
and so on.
Then we already can see that. "The rule for Pattern B is "multiply by 2." Is true
And:
The rule for Pattern A is "multiply by 2." is false.
Finally, let's compare the terms. The first term of B is 12, and the first ter of A is 6, so we can see that the first term of B is two times the first one of A. The second term of B is 24, while the second of A is 12, so again, we can see that the second term of B is two times the second of A.
So we can see a pattern, meaning that the statement: "Each term in Pattern A is one-half the corresponding term in Pattern B."
Is true.If you want to learn more about sequences, you can read:
https://brainly.com/question/7882626
I don’t understand how to solve this question
Answer:
142
Step-by-step explanation:
if m angle A = 109, then arc DCB = 2(109)= 218
360 - 218 = 142
PLEASE QUICK
The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
v (c) = 20,000(0.88)
Find the initial value of the car and the value after 11 years.
Round your answers to the nearest dollar as necessary.
Initial value:
Value after 11 years:
9514 1404 393
Answer:
initial value: $20,000after 11 years: $4,902Step-by-step explanation:
Assuming your equation is ...
v(t) = 20,000(0.88^t)
The value for t=0 is 20,000.
The value for t=11 is 20,000(0.88^11) ≈ 4,902.
The initial value is $20,000; the value after 11 years is $4,902.
The ordinate of every point on the x-axis is zero. True or false?
Answer:
true
Step-by-step explanation:
the first number is mostly known as 1 but actually is 0 because it is a separation between the negative and positive numbers
● The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of distance travelled by their tips in 2 days.
Class - 10th
No spam ❌
Juniors stay away ~
Step by step explanation please
Step-by-step explanation:
short hand radius = 4
distance travellled in 1 day revolution = 2πr= 2 x 22/7 x 4= 25.1cm (approx)
distance travellled in 2 day revolution= 25.1+ 25.1 = 50.2
long hand radius= 6
each hour 1 revolution by long hand so in 24 hr 24 revolutions and 48 he 48 revolution
distance travelled in 1 hr = 2πr= 2 x 22/7 x 6= 37.7
distance in 48hr = 37.7 x 48= 1809.6 (approx)
so sum of both= 1809.6 + 50.2 = 1859.8
Answer:
1910.12 cm
Step-by-step explanation:
2 days = 48 hrs = 2880 mins
One cycle of the short hand (4 cm) would be 12 hrs.
48/12 = 4 cycles
Circumference of a circle = [tex]2\pi r[/tex]
r = 4 cm
2*pi*4 ≈ 25.13 cm (I only rounded to the hundredth, adjust as u need)
25.13 * 4 = 100.52 cm
One cycle of the long hand (6 cm) would be 60 mins (which is 1hr and two days would be 48hrs or 48 cycles. But let's keep this consistent).
2880/60 = 48 cycles
Circumference of a circle = [tex]2\pi r[/tex]
r = 6 cm
2*pi*6 ≈ 37.70 cm (I only rounded to the hundredth, adjust as u need)
37.70 * 48 = 1809.6
100.52 + 1809.6 = 1910.12 cm
^^ I'm not a junior I'm a senior so lol
Use r = 2
When r + 4(2 + r) – 12 =
Answer:
6
Step-by-step explanation:
2+r=4
4x4=16
16+r=18
18-12=6
Answer:
6
Step-by-step explanation:
r + 4(2 + r) - 12 =
2 + 4(2 + 2) - 12 =
2 + 4(4) - 12 =
2 + 16 - 12 =
18 - 12 =
= 6
Look at screen shot below
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Answer:
1st option is the correct answer
Write both an explicit equation and a recursive equation for the sequence 4, 2, 1.0.5.0.25
help pleasee
Answer:
Step-by-step explanation:
This is a geometric sequence with first term a1 = 2 and common ratio r = 0.5.
an = a1 r^^n-1)
an = 2(0.5)^(n-1).
Recursive equation:
an = 0.5a(n-1) where n > 2
Find the surface area of a sphere with a diameter of 14
Answer:
SA = 615.44
Step-by-step explanation:
d = 14
r = d/2
r = 7
SA of a Sphere:
SA = 4πr²
SA = 4(3.14)(7²)
SA = 4(3.14)(49)
SA = 12.56(49)
SA = 615.44
please help!!!No links
Answer:
is 53
heart if it helped brain if im cooll
A pair of shoes costs $60, and is on sale for 35% off. What is the sales price of the shoe
Answer:
$39
Step-by-step explanation:
does anyone know what lazor wulf is? if so send me a picture
Answer:
I think its like a cartoon or something like that
https://hbomax-images.warnermediacdn.com/images/GXyniGAhmEcJZOgEAAABz/tileburnedin?size=1280x720&format=jpeg&partner=hbomaxcom&productCode=hbomax&host=artist.api.cdn.hbo.com&w=1200
there image I think
Rashon left his house to go
to his office. He walked 30 m east and 40 m north.
How far is Rashon's office
from his house?
Answer:
70
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
Solve for x using the diagram of circle C.
B В.
(3x+49)
(5x-7)
Answer:
googl it
Step-by-step explanation:
its on googl and it has the anwser
A school principal wants to find out what the students think about the teaching
quality in the school. Which of these samples is unbiased?
Hello! please help ! Find the exact perimeter of hexagon A B C D E F plotted below.
Answer:
23 + [tex]\sqrt{29}[/tex] + [tex]\sqrt{58}[/tex]
Step-by-step explanation:
|x+5|=x
Solve these equations
Answer:
do yourself a favor and download photomath. It'll save your life
Step-by-step explanation:
Solve the equation 2x + 9 = -15
Please and thank you!!
What percent of 315 is 63?
Answer:
20%
Step-by-step explanation:
Write the problem as a mathematical expression.
63/315
Convert to decimal
0.2
Times by 100
0.2 times 100
20%
According to the line of best fit, if a batter practices 0 hours, about how many strikeouts did they have?
pls help fast
Alyssa wants to buy a computer for $600. If she
pays $75 now and $25 each month, she can pay
for it in 21 months. If she were to pay $75 now
and $35 each month, how would the number of
payments change?
A She would make 15 fewer monthly payments.
B She would make 3 fewer monthly payments.
C She would make 5 fewer monthly payments.
D She would make 6 fewer monthly payments.
Answer:
D
she would make 6 fewer monthly payments
Step-by-step explanation:
:)
Can someone solve for me please? Simply each expression. I myst show work
Answer:
37/20y
you find LCM first
find the value of x an y
Answer:
x=46
Step-by-step explanation:
Help this is due in 2 minutes
Answer:
a) 3000(1 + 0.02)^16
Step-by-step explanation:
Each row contains the degree measures of two supplementary angles. Complete the table.
the measure of an angle measure of its supplement
80°
°
25°
°
119°
°
x
°
(From Unit 7, Lesson 2)
Answer:
Step-by-step explanation:the answer will be 100