Show all work to identify the asymptotes and zero of the function f of x equals 5 x over quantity x squared minus 25.
Answers
Answer:
asymptotes: x = -5, x = 5zero: x = 0Step-by-step explanation:
The function of interest is ...
[tex]f(x)=\dfrac{5x}{x^2-25}=\dfrac{5x}{(x-5)(x+5)}[/tex]
The asymptotes are found where the denominator is zero. It will be zero when either factor is zero, so at x = 5 and x = -5
__
The zeros are found where the numerator is zero. It will be zero for x = 0.
The asymptotes are x=-5, x=5; the zero is x=0.
Answer:
The asymptotes are x=-5, x=5; the zero is x=0.
Step-by-step explanation:
Related Questions
Santa's Wonderland is an extravagant holiday light display that is open from early November through January each year. The entry fee is $15 per vehicle for up to and including 5 people, with an additional $1.50 for each person over 5. Express this information as a piecewise function of x, where x represents the number of people in the vehicle.
Answers
Answer:
The expression
Y(x)= 15(v)+1.5(x)
Step-by-step explanation:
The entry fee is $15 per vehicle for up to and including 5 people, with an additional $1.50 for each person over 5.
Let the entrance fee be Y
Let the number of vehicle be V
Let X be the number of people more than 5
The expression
Y(x)= 15(v)+1.5(x)
the difference between the number in three fourths is one half
Answers
Answer:
3
Step-by-step explanation:
What is the solution for this inequality?
5x< 45
O A.
OB.
Oc.
XS-9
Answers
Answer:
x < 9
Step-by-step explanation:
Hello!
We solve inequalities the same we would solve equations. What we do to one side we have to do to the other.
5x < 45
Divide both sides by 5
x < 9
The answer is x < 9
Hope this helps!
Answer:
x<9 I hope help you Mark as Brainliest
if X^8 = (2^2)^4, what is X^2
Answers
Answer:
x^2 = 4
Step-by-step explanation:
X^8 = (2^2)^4
Rewriting
x^8 as (x^2) ^4 since we know that a^b^c = a^(b*c) and 2*4 = 8
(x^2) ^4 = (2^2)^4
Since the exponents are the same the bases must be the same
x^2 = 2^2
x^2 = 4
x^2 -9 divided by x+3
Answers
Step-by-step explanation:
Hey, there!!
Given that,
[tex] \frac{ {x}^{2} - 9 }{x + 3} [/tex]
{ we can write (a^2-4) as (a^2 - 2^2) also as (x^2- 9) can be written as (x^2 - 3^2)}.
[tex] \frac{ {x}^{2} - {3}^{2} }{x + 3} [/tex]
We have a^2-b^2= (a+b) (a-b), so keep same formula on it.
[tex] \frac{(x + 3)(x - 3)}{(x + 3)} [/tex]
(x+3) in numerator and denominator gets cancelled,
[tex](x - 3)[/tex]
Therefore, (x-3) is the final value.
Hope it helps...
Use the graph of f(x)=x^2 to find a number δ such that ∣x^2−1∣<0.1 whenever 0<|x−1|<δ.
Answers
Answer:
[tex]\delta=0.0333[/tex]
Step-by-step explanation:
[tex]|x^2-1}=|x-1||x+1|<0.1[/tex]
[tex]|x|-|1|<|x-1|<1[/tex]
[tex]|x|<2[/tex]
[tex]|x+1|<3[/tex]
Hence
[tex]|x-1|<\frac{0.1}{|x+1|}[/tex]
[tex]|x-1|<\frac{0.1}{3}=0.333 =\delta[/tex]
Hopefully you get what I meant!!
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 210 engines and the mean pressure was 5.0 pounds/square inch (psi). Assume the population standard deviation is 0.9. The engineer designed the valve such that it would produce a mean pressure of 4.9 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic.
Answers
Answer:
The test statistics is [tex]t = 1.610[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 210
The sample mean is [tex]\= x = 5.0 \ pounds /square \ inch[/tex]
The standard deviation is [tex]\sigma = 0.9 \[/tex]
The population mean is [tex]\mu = 4.9 \ psi[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu}{ \frac{\sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{5 - 4.9}{ \frac{ 0.9 }{ \sqrt{ 210 } } }[/tex]
=> [tex]t = 1.610[/tex]
Simplify the following expression. (3m/4-2)+8 A. 8m/4 B. 9m/4 C. 3m+24/4 D. 3m+28/4
Answers
Answer:
C
Step-by-step explanation:
Given
( [tex]\frac{3m}{4}[/tex] - 2 ) + 8 ( remove parenthesis )
= [tex]\frac{3m}{4}[/tex] - 2 + 8
= [tex]\frac{3m}{4}[/tex] + 6
= [tex]\frac{3m}{4}[/tex] + [tex]\frac{24}{4}[/tex] ← add the numerators leaving the denominator
= [tex]\frac{3m+24}{4}[/tex] → C
Explanation:
(3m/4 - 2) + 8
= (3m/4 - 8/4) + 8
= (3m - 8)/4 + 32/4
= (3m - 8 + 32)/4
= (3m + 24)/4
Therefore the answer is C
The bases of a trapezoid will measure 14.5 ft and 22.5 ft. What is the minimum height of the trapezoid of the patio is to have an area os no less than 259 sq ft?
Answers
Answer:
14 ft
Step-by-step explanation:
The area of a trapezoid is given by
A = (1/2)(b1 +b2)h
You want ...
A ≥ 259
(1/2)(14.5 +22.5)h ≥ 259
37/2·h ≥ 259
h ≥ 259(2/37)
h ≥ 14 . . . . . . . feet
The height must be no less than 14 feet.
A similar follow-up study is done on a sample of 25 meat-lovers who never eat vegetables, again randomly selected from the same general population (population mean life expectancy = 75, population standard deviation = 5). This new sample of meat-eaters live to an average age of 77. What is the lower limit and upper limit of the 95% confidence interval for the life expectancy of this sample of meat-lovers?
Answers
Answer:
The lower limit is 75.04
The upper limit is 78.96
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 25[/tex]
The sample mean is [tex]\= x = 77[/tex]
The standard deviation is [tex]\sigma = 5[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
The critical value for [tex]\frac{\alpha }{2}[/tex] obtained from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96* \frac{5 }{\sqrt{25} }[/tex]
=> [tex]E = 1.96[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
=> [tex]77 - 1.96 < \mu < 77 + 1.96[/tex]
=> [tex]75.04 < \mu < 78.96[/tex]
solve 7x-3y=14 for y
Answers
Answer:
y = - 14/3 +7x/3
Step-by-step explanation:
The reason for my answer is because let us move the -3y so it is before the equal sign. Let us also move 7x to the other side but make it so 14 would be to the right side of the equal sign. Now, that would mean 7x would be after 14. Our equation is now -3y=14-7x. We need to divide both sides of the equation by -3. There, we just divided -3y by 3 which equals to y. 14 divided by -3 equals to -14/3. -7x divided by -3 would equal to +7x/3. Finally, we get the answer of y = - 14/3 +7x/3.
Answer:
Step-by-step explanation:
● 7x-3y = 14
This a 1st degree equation with two variables.
● 7x-3y = 14
Substract 7x from both sides
● 7x-7x -3y = 14-7x
● -3y = 14-7x
Mulitply both sides by -1
● (-1)×(-3y) = (-1)×(14-7x)
● 3y = -14+7x
● 3y = 7x+14
Divide both sides by 3
● 3y/3 = (7x+14)/3
● y = (7/3)x + 14/3
There are infinite solutions for this equation. Keep replacing x with value and the output will change everytime.
HELP ASAP ROCKY!!! will get branliest.
Answers
Answer:
2nd Option.
Step-by-step explanation:
The 2 lines are intersecting each other. That means the point of intersection is the solution set to the systems of linear equations.
This translate into that point (4, 4) in the graph works for both line A and line B.
The two lines intersect at a point (4,4), which is the solution of the two linear equations.
An account earned interest of 5% per year. The beginning balance was $250. The equation t=log1.05E250 represents the situation, where t is the time in years and E is the ending balance.
Answers
Answer:
3 years
Step-by-step explanation:
The number of years that required for opening an account is shown below:
Given that
Opening balance = $250
ending balance = $289.41
t = [tex]log_{1.05} \frac{E}{250}[/tex]
Interest rate = 5%
Based on the above information, the number of years required is
[tex]t = log_{1.05} \frac{289.41}{250}[/tex]
= 3 years
Hence, the number of years required to open an account is 3 years and the same is to be considered by using the above formula
The cost and revenue are defined, in dollars, as C(x) = 30x + 100 and R(x) = -x2 + 90x.
Required:
a. Find and simplify the profit function, defined by P(x).
b. Use a. to find the marginal profit function.
Answers
Answer:
a) The profit function is [tex]P(x) = -x^{2}+60\cdot x -100[/tex], b) The marginal profit function is [tex]P'(x) = -2\cdot x + 60[/tex].
Step-by-step explanation:
a) Let be [tex]C(x) = 30\cdot x + 100[/tex] (cost function) and [tex]R(x) = -x^{2}+90\cdot x[/tex] (revenue function), the profit function is found by subtracting the cost function from the revenue function. That is:
[tex]P(x) = R(x)-C(x)[/tex]
[tex]P(x) = -x^{2}+90\cdot x -(30\cdot x + 100)[/tex]
[tex]P(x) = -x^{2}+90\cdot x -30\cdot x -100[/tex]
[tex]P(x) = -x^{2}+60\cdot x -100[/tex]
b) The marginal profit function is the first derivative of the profit function:
[tex]P'(x) = -2\cdot x + 60[/tex]
after spending 80% of gulnaza's money. she left with rupees 800. How much did she have in the beginning ?
Answers
Answer:
let her money in the beginning =X
20%of X=800.
4000
Solve the equation 6(x-5) =12
Answers
Answer:
x=7
Step-by-step explanation:
6(x-5)=12
We will use the distributive property to get the answer of 6(x-5)
6(x-5)=12
6x-30=12
6x=12+30
6x=42
6x/6=42/6
x=7
Proof:
6(x-5)=12
6(7-5)=12
42-30=12
12=12 or
6(7-5)=12
6(2)=12
12=12
Hope this helps ;) ❤❤❤
Convert -11°20'49" to decimal degree form. Round your answer to three decimal places.
I need the answer):
Answers
Answer:
Convertir- 11°20'49"
Step-by-step explanation:
I New the answer):
what is (3⁴×5⁴)-³ =?
Answers
Answer:
The solution to the given expression is 1/2562890625
Step-by-step explanation:
(3⁴ × 5⁴)⁻²
Simplify the terms inside the parentheses. 3⁴ × 5⁴ is the same as 15⁴ because even though the base numbers are different, the exponents are the same which makes it similar.
(15⁴)⁻²
Now, for this step, we are going to add the exponents because when multiplying, the exponential numbers add together. So 4 × -2 = -8.
15⁻⁸
Since we can not have a negative exponent, we are going to change this into a fraction. We do this by putting this term in a fraction where 1 is the numerator and the term is the denominator.
1 / 15⁻⁸
Now, we simplify the term on the bottom.
1 / 2562890625
So, this is the solution to the problem.
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n2+5/2n
Answers
Answer:
[tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex]
[tex](n + \frac{5}{4})^2[/tex]
Step-by-step explanation:
Given
[tex]n^2 + \frac{5}{2}n[/tex]
Required
(a) Make a perfect square trinomial
(b) Write as binomial square
Solving (a)
Let the missing part of the expression be k;
This gives
[tex]n^2 + \frac{5}{2}n + k[/tex]
To solve for k, we need to square half the coefficient of n;
i.e. Since the coefficient of n is [tex]\frac{5}{2}[/tex], then
[tex]k = (\frac{1}{2} * \frac{5}{2})^2[/tex]
[tex]k = (\frac{5}{4})^2[/tex]
[tex]k = \frac{25}{16}[/tex]
Hence;
[tex]n^2 + \frac{5}{2}n + k[/tex] = [tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex]
Solving (b)
[tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex]
Expand [tex]\frac{5}{2}n[/tex]
[tex]n^2 + \frac{5}{4}n+ \frac{5}{4}n + \frac{25}{16}[/tex]
Factorize
[tex]n(n + \frac{5}{4})+ \frac{5}{4}(n + \frac{5}{4})[/tex]
[tex](n + \frac{5}{4})(n + \frac{5}{4})[/tex]
[tex](n + \frac{5}{4})^2[/tex]
Hence:
[tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex] = [tex](n + \frac{5}{4})^2[/tex]
PLEASE HELP ME ASAP Tyler needs to score 100 points on his final math test of the year to improve his average score from 76 to 79. How many math tests are there in a year?
Answers
Answer:
8 tests
Step-by-step explanation:
Let's call the number of total math tests in a year as x. Therefore, excluding the final test, the total number of tests in a year is x - 1. Since his original average was 76, that means that the sum of his test scores without the final was 76(x - 1), and because getting a 100 on his final gets him a 79, the sum of all his scores is 76(x - 1) + 100, which will be equal to 79 * x, therefore:
76(x - 1) + 100 = 79x
76x - 76 + 100 = 79x
24 = 3x
x = 8 tests
The sales data from the past two months of a frozen yogurt shop are approximately normal. The mean daily sales for the first month was $200 with a standard deviation of $30. On the 15th of the first month, the shop sold $245 of yogurt. The mean daily sales for the second month was $220 with a standard deviation of $50. On the 15th of the second month, the shop sold $270 of yogurt. Which month had a higher z-score for sales on the 15th, and what is the value of that z-score? a.) The second month, with a z-score of 1. b.) The second month, with a score of 1.67. c.) The first month, with a score of 0.9. d.) The first month, with a z-score of 1.5.
Answers
Answer:
The correct option is D
Step-by-step explanation:
From the question we are told that
The mean for the first month is [tex]\mu _ 1 = \$ 200[/tex]
The standard deviation for first month is [tex]\sigma_1 = \$ 30[/tex]
The sale on 15th of first month is [tex]x_1 = \$245[/tex]
The mean for the second month is [tex]\mu _ 2 = \$220[/tex]
The standard deviation for second month is [tex]\sigma_2 = \$ 50[/tex]
The sale on 15th of second month is [tex]x_2 = \$ 270[/tex]
Generally the z-score is mathematically represented as
[tex]z = \frac{x - \mu }{ \sigma}[/tex]
For the first month
[tex]z_1 = \frac{x_1 - \mu_1 }{ \sigma_1 }[/tex]
[tex]z_1 = \frac{ 245 - 200 }{ 30 }[/tex]
[tex]z_1 = 1.5[/tex]
For the second month
[tex]z_1 = \frac{x_2 - \mu_2 }{ \sigma_2 }[/tex]
[tex]z_1 = \frac{ 270 - 220 }{ 50 }[/tex]
[tex]z_1 = 1[/tex]
Answer: 1.5
Step-by-step explanation:
Recall that .For the first month, .For the second month, .We can see the first month had the higher z-score of 1.5.
The maximum horizontal range of a projectile is given by the formula where u is the initial velocity and g is the acceleration due to gravity. Find the velocity with which a ball can be thrown to have a maximum range of 20 meters when the acceleration due to gravity is equal to 9.8 m/s.
Answers
Answer:
v=?
U=0
a=9.8m/s²
s=20m
V²=u+2as
v²=0+2*9.8*20
v²=392
v=✓392
v=19.789
v=19.80m/s
Question 1
A company makes a book bag and charges a one-time design fee of $100 and then $5 for each bag made. What equation shows how the cost of a book bag order depends on the number of bags, n?
Answers
Answer:
C = 5n + 100
Step-by-step explanation:
The cost (C) to make a book bag is an initial fee of $100 with an additional $5 for each bag (n) made. The equation will look like
C = 5n + 100
Xsquared =60 what is the value of x
Answers
Answer:
x = ±2√15
Step-by-step explanation:
x^2 = 60
x = ±√60
x = ±2√15
The inequality 5m-7 > 16 holds true for all numbers than in set {1,2,3,4,5,6,7,8,9,10}
Answers
Answer:
Greater than 4
This visual representation shows the sets of real numbers. Which statement is true regarding the number sets? a. All integers are also rational numbers. b. All rational numbers are also integers. c. Some integers are also rational numbers, but not all integers are rational numbers. d. Integers and rational numbers have no numbers in common. explain your answer and say the answer
Answers
Answer:
A.
Step-by-step explanation:
The visual representation is All integers are also rational numbers
what are rational number?A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0. The set of rational numbers is denoted by Q.
So, we have sets of real number.
As. we know
All natural numbers, whole numbers, and integers are rationals, but not all rational numbers are natural numbers, whole numbers, or integers.
Hence, integers are also rational numbers
Learn more about rational number here:
https://brainly.com/question/24398433
#SPJ2
solve for x 6 (8X minus 1) equals 9 (x + 2)
Answers
Answer:
x = [tex]\frac{8}{13}[/tex]
Step-by-step explanation:
Given
6(8x - 1) = 9(x + 2) ← distribute parenthesis on both sides
48x - 6 = 9x + 18 ( subtract 9x from both sides )
39x - 6 = 18 ( add 6 to both sides )
39x = 24 ( divide both sides by 39 )
x = [tex]\frac{24}{39}[/tex] = [tex]\frac{8}{13}[/tex]
An electrician disconnected 5 wires of different colors from their respective connections and forgot the order in which they were placed. Assuming you connect them by trying different sorts and that the last one is correct, how many tries must you do before getting it right?
Answers
Answer:
120 tries
Step-by-step explanation:
You can try 5 different wires in the first connection.
Then you have 4 wires left, so you try 4 wires in the second connection. Remember, you are now trying 4 wires for each of the first 5, so up to here you already made 4 * 5 tries = 20 tries.
Next you try 3, then 2, then you have 1 left.
Number of tries: 5 * 4 * 3 * 2 * 1 = 120
Answer: 120 tries
The figure below shows the correct construction of a segment bisector.
Answers
Answer:
it's false.... not sure
Any body know this? Zoom in to see
Answers
Answer:
Deon
Step-by-step explanation:
Gerain has 2 parts almonds in 5 parts total, i.e., 2/5 = 0.40
Deon has 3 parts almonds in 7 parts total, i.e., 3/7 ≈ 0.43
So Deon's concentration is higher
Answer:
Deon has a higher concentration
Step-by-step explanation: