what are the discontinuities of the function f(x) = x^2+5x+6/2x+16
Answers
If you mean ...
[tex]f(x)=\dfrac{x^{2}+5x+6}{2x+16}[/tex]
it will have a discontinuity where the denominator is zero, at x=-8.
Answer:
The discontinuity of the function is at x=-8.
Step-by-step explanation:
Given : Function [tex]f(x)=\frac{x^2+5x+6}{2x+16}[/tex]
To find : What are the discontinuities of the function?
Solution :
Discontinuity of the function is happen when denominator is zero.
First we factor the function,
[tex]f(x)=\frac{x^2+5x+6}{2x+16}[/tex]
[tex]f(x)=\frac{(x+2)(x+3)}{2(x+8)}[/tex]
Denominator = 0
[tex]2(x+8)=0[/tex]
[tex]x+8=0[/tex]
[tex]x=-8[/tex]
The discontinuity of the function is at x=-8.
Related Questions
You randomly select one card from a 52-card deck. find the probability of selecting a black seven or a red three.
Answers
Number of back sevens = 2
Number of red three = 2
P(Black seven or red three) 4/52 = 1/13
Answer: 1/13
The probability of selecting a black seven or a red three will be 1/13.
What is Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
You randomly select one card from a 52-card deck.
Now,
Number of black sevens = 2
Number of red three = 2
So, The probability of selecting a black seven or a red three is;
= (2 + 2) / 52
= 4 / 52
= 1 / 13
Thus, The probability of selecting a black seven or a red three will be 1/13.
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Please help me understand this.
Answers
Number of tiles in yellow ring = 12
Number of tiles in blue ring = 18
Observe the terms, they are forming an Arithmetic series as each term is 6 more than the previous term. We are to find the number of tiles in 30th ring, which will be the 30th term of the A.P.
So,
30th term of AP = 1st term +(30 - 1) x Common Difference
30th term of AP = 6 + 29 x 6 = 180
Thus, there will be 180 tiles in the 30th ring of white tiles
How to find the of each figure #5,6,7,8
Answers
6. The base area = (8 yd)(10 yd) = 80 yd^2. The height = 11 yd, so the volume = (1/3)bh = 293.3 yd^3.
7. The lateral area is (11)(10) for the slanted surface, (11)(6) for the vertical rectangular surface, and (1/2)(8)(6) for each of the triangular surfaces. This is a lateral area of 110 + 66 + 2(24) = 224 in^2.The bottom surface is (11)(8) = 88, so the total surface area is 312 in^2.
8. The lateral area is (5 triangles)(1/2)(7.3 yd height)(6 yd base) = 109.5 sq. yd.The base is (1/2)(4.1 yd apothem)(5*6 yd perimeter) = 61.5 sq. yd. This is a total surface area of 109.5+61.5 = 171 sq yd.
Please, see the attached files.
Thanks.
1. demand for product
2. example of fixed cost buyer's
3. sales receipts
4. credit discount
5. example of variable cost
6. moves slow-moving goods
7. business upturn
8. used for business expansion
9. depends on prime rate
10. assures profit on item sold
2/10, net 30
credit
interest rate
workers' wages
revenue
recovery
rent
markdown
markup
buyer's willingness to pay
Answers
2. example of fixed cost buyer's ----rent
3. sales receipts
4. credit discount
5. example of variable cost
6. moves slow-moving goods ---markdown
7. business upturn
8. used for business expansion
9. depends on prime rate
10. assures profit on item sold markup
2/10, net 30
credit
interest rate
workers' wages
revenue
recovery
Answer:
Interest rate - 9
Revenue - 3
Recovery - 7
Markdown - 6
Buyer's willingness to pay - 1
Markup - 10
Worker's wages - 5
2/10 net 30 - 4
Credit - 8
Rent - 2
Step-by-step explanation:
Just did this on odyssey
find the value of q in the following system so that the solution to the system is(4,2) 3x-2y=8
2x+3y=Q
Answers
3x-2y=8 -----> equation 1
2x+3y=Q----> equation 2
the solution is the point (4,2)
in the equation 2 substitute the value of
x=4
y=2
so
2x+3y=Q------> 2*4+3*2=Q-------> Q=8+6------> Q=14
the answer is
Q=14
the lengths of three line segments are 4 centimeters,5 centimeters,and 9 centimeters?is it 1,
Answers
No triangles can be constructed from line segments of 4 cm, 5 cm, and 9 cm in length, because the Triangle Inequality Theorem requires the sum of any two sides to be greater than the third side, which is not the case here.
The lengths of three line segments are 4 centimeters, 5 centimeters, and 9 centimeters. To determine how many triangles can be constructed with these segments as sides, we need to apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the sum of the two shortest sides, 4 cm and 5 cm, is 9 cm, which is equal to the length of the longest side. Because one condition for the Triangle Inequality Theorem is not strictly being met (the sum must be greater, not equal), we can conclude that no triangles can be constructed using these three segments as sides.
When constructing triangles from three measures of angles or sides, it's important to realize that these conditions determine whether you can create a unique triangle, more than one triangle, or no triangle at all.
What is the explicit formula for the sequence? 6, 5, 4, 3, 2, . .
Answers
an = a1 +(n-1)d
For your sequence, this is
an = 6 +(n-1)*(-1)
an = 7 - n
Answer: [tex]a_n=5+n[/tex]
Step-by-step explanation:
The explicit formula for an arithmetic sequence is given by:-
[tex]a_n=a+d(n-1)[/tex], where a is the first term , di sthe common difference and n is the number of terms.
The given sequence : 6, 5, 4, 3, 2, . .
Common difference d = 1
First term = 1
Now, the explicit formula for given arithmetic sequence will be:
[tex]a_n=6+1(n-1)\\\\\Rightarrow\ a_n=6+n-1\\\\\Rightarrow\ a_n=5+n[/tex]
Hence, the explicit formula for given arithmetic sequence : [tex]a_n=5+n[/tex]
What is the LCD of the following rational expressions?
x/x+1 , 7x/x-1
please help I'm so confused!?
Answers
[tex] \dfrac{x (x -1)}{(x+1)(x -1)} \ , \ \dfrac{7x(x+1)}{(x-1)(x+ 1)} [/tex]
We know that (a + b)(a - b) = a² - b²:
[tex]\dfrac{x (x -1)}{x^2 - 1}} \ , \ \dfrac{7x(x+1)} {x^2 - 1}[/tex]
Answer: LCD = ( x + 1) (x - 1)
To find the least common denominator, multiply [tex] \frac{x}{x + 1} [/tex] by (x - 1) and multiply [tex] \frac{7x}{x - 1} [/tex] by (x + 1).
(x + 1)(x - 1) = x² - x + x - 1 ⇒ x² - 1
x² - 1 is the LCD.
In Ms. Dole's class, students received grades of 87, 72, 99, 93, and 84 on yesterday's quiz. What was the mean of the quiz grades?
Answers
The mean is the average of the numbers
To find the average you add them all up and divide the sum by the amount of numbers added
87 + 72 + 99 + 93 + 84 = 435
Divide the sum by the amount of numbers added
435 / 5 = 87
The answer is 87
Hope this helps!
To find the average, or the mean, the numbers must be added together and then the sum is divided by the total amount of numbers in the set.
87 + 72 + 99 + 93 + 84 = 435
435 / 5 = 87
The mean of the quiz grades is 87
Quadrilateral ABCD is an isosceles trapezoid. If AB || CD, AB = m + 6, CD = 3m + 2, BC = 3m, and AD = 7m - 16, solve for m.
A.) 2
B.) 3
C.) 4
D.) 5
Answers
Answer:
C.) 4
Step-by-step explanation:
we are given ABCD is an isosceles trapezoid
AB || CD
AB = m + 6
CD = 3m + 2
BC = 3m
AD = 7m - 16
Since, ABCD is an isosceles trapezoid
so, two sides must be equal
[tex]BC=AD[/tex]
now, we can plug values
[tex]3m=7m-16[/tex]
now, we can solve for m
[tex]3m-7m=7m-16-7m[/tex]
[tex]-4m=-16[/tex]
Divide both sides by -4
and we get
[tex]m=4[/tex]
Answer:
M= 4
Step-by-step explanation:
Look at the table. Make a conjecture about the sum of the first 15 positive even numbers.
Answers
The conjecture about the sum of the first 15 positive even numbers is 15 * 16
Making a conjecture about the sum of the first 15 positive even numbers.
From the question, we have the following parameters that can be used in our computation:
The table of values
Where, we have
2 = 1 * 2
2 + 4 = 2 * 3
2 + 4 + 6 = 3 * 4
And so on
This means that
Sum of first n positive even numbers = n * (n + 1)
So, for the first positive even numbers, we have
n = 15
This gives
Sum of first 15 positive even numbers = 15 * (15 + 1)
Evaluate
Sum = 15 * 16
Sum = 240
Hence, the sum is 15 * 16
A restaurant uses 290 pounds of onions every 2 and a half weeks. If they continue to use onions at the same rate, how many pounds of onions will they use in 6 weeks?
Answers
116 * 6 = 696 pounds
290/2.5 = 116
Now that we have a single rate, we find the amount for 6 weeks:
116*6 = 696
696 pounds are used in 6 weeks
The histogram shows the number of vacation days taken by employees in the past year. Based on the histogram, which statement is true?
A.)Four employees took 20 vacation days in the past year.
B.) Four employees took 25 vacation days in the past year.
C.) Four employees took between 20 and 25 vacation days in the past year.
D.) Between 20 and 25 employees took four vacation days in the past year.
Answers
so answer is
C.) Four employees took between 20 and 25 vacation days in the past year.
Answer:
Option(C)
Step-by-step explanation:
As per histogram, given below
3 students took holidays between 5-10 days.
5 students took holidays between 10-15 days.
5 students took holidays between 15-20 days.
4 students took holidays between 20-25 days.
3 students took holidays between 25-30 days.
therefore, option (C) is correct.
Question 11 please solve
Answers
We can conclude that you will need 6 segments to connect each point to every other point.
4+2= 8
the answer is 8 4 plus 2 equals 8 even if the circle has four dots you draw four more which equals 8 either one
Write the standard form of the equation of the circle with the given center and radius.
(-3, 6); 10
Answers
Here we have (x+3)^2 + (y-6)^2 = 10^2 (answer)
Answer:
A circle with center at (-3, 6) and a radius of 10 has the following standard form equation
[tex](x+3)^2+(y-6)^2=100[/tex]
Step-by-step explanation:
This is the general standard equation for the circle centered at (h, k) with radius r
[tex](x-h)^2+(y-k)^2=r^2[/tex]
It shows all the important information at a glance: the center (h, k) and the radius r.
A circle with center at (-3, 6) and a radius of 10 has the following standard form equation
Start with:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Put in (h, k) and r
[tex](x-(-3))^2+(y-6)^2=10^2\\(x+3)^2+(y-6)^2=100[/tex]
The graph of the function f(x)=4sqrt x is shifted down by three units. What is the domain of the resulting function
Answers
x ≥ 0.
Estimate the probability that if the company books 225 persons. not enough seats will be available. 1-.81^225
Answers
1-.81^225 = 1
What is the perimeter of the rectangle? Write your answer in scientific notation. The area is 2.76 x 10 pw12
the width is 4.6 x 10 pw5
pw is the power
Answers
To calculate the perimeter of a rectangle given the area and the width, divide the area by the width to find the length, then use the formula Perimeter = 2(Length + Width), adjusting for scientific notation as necessary. This will provide the perimeter in scientific notation.
Explanation:To find the perimeter of the rectangle when we have the area and the width, we need to first calculate the length of the rectangle using the formula Area = Length × Width. The width is given as 4.6 x 105 and the area is 2.76 x 1012. To find the length, we divide the area by the width:
Length = Area ÷ Width = (2.76 x 1012) ÷ (4.6 x 105)
After performing the division, we obtain the length in scientific notation. The next step is to use the formula Perimeter = 2(Length + Width). After calculating the sum of the length and width, we multiply by 2 to obtain the perimeter of the rectangle in scientific notation.
Let's assume after performing the calculation that the length is found to be L x 10n where L and n are specific numbers. The perimeter now would be calculated as:
Perimeter = 2((L x 10n) + (4.6 x 105))
Be sure to adjust the exponents so they match before adding the length and width together. This might involve converting one or the other so that you can add them directly. Once that is done, you can multiply by 2 to find the total perimeter of the rectangle and express it in scientific notation.
25 pt question amd will mark brainliest
Answers
The angles are supplementary meaning they add to 180°
a + 2a + 3 = 180
Combine like terms
3a + 3 = 180
Subtract 3 from both sides
3a = 177
Divide both sides by 3
a = 59
the answer is 59°
Hope this helps!
These angle are supplementary.
use the following equation to solve for a.
2a + 3 + a = 180
Solve for a now.
3a + 3 = 180
3a = 177
a = 59
Hope this helps :)
if 3 m equals 12 what is the value of 6(m-1)
Answers
3m = 12
divide both sides by 3:
m = 12/3
m = 4
now yo know m so replace m with 4 in the second equation:
6(m-1) = 6(4-1)
do the subtraction inside the parenthesis first
6(4-1) = 6(3)
now multiply 6 and 3: 6 x 3 = 18
A bakery has total receipts for the month of $24,150 including sales taxes. if the sales tax rate is 5%, what are the bakery's sales for the month?
a.$24,000
b.$23,000
c.$23,100
d.$22,943
Answers
Option B= $23000 is the answer.
Explanation:
Let the bakery's sales for the month be represented by = x
As given, the bakery has total receipts for the month = $24150
Rate of sales tax = 5%
This implies that total monthly sales(x) + sales tax on 'x' = 24150
[tex]x+\frac{5x}{100}=24150[/tex]
[tex]x+0.05x=24150[/tex]
[tex]1.05x=24150[/tex]
x=23000
Hence, the bakery's sale for the month is $23,000
Cable hangs between two poles of equal height and 37 feet apart. at a point on the ground directly under the cable and x feet from the point on the ground halfway between the poles the height of the cable in feet is
Answers
The digits 1,2,3,4,5,6,7 and 8 are arranged randomly to form a three-digit number find the probability that the number is even and greater than 800
Answers
Let's start counting desired outcome.
Hundred position need to be at least 8. There is only one possible digits. So we will go with 8 and then there are 7 remaining digits.
One position can only be 2,4,6. because we need number to be even. So that's 3 possible digits. We will take one. 6 digits remaining.
Ten position can be anything so that would be 6 possible digits.
So the number of desired outcomes is 3·6 = 18.
Now count all outcomes.
Hundred, ten, and one position can get any digits
So that's 8·7·6 = 336
So the probability would be 18 / 336 = 3 / 56 ≈ 0.0536
Hope this helps.
[tex] |\Omega|=8\cdot7\cdot6=336\\
|A|=\underbrace{1\cdot6\cdot3}_{\text{8,any,even}}=18\\\\
P(A)=\dfrac{18}{336}=\dfrac{3}{56}=5\% [/tex]
To test upper h 0: muequals50 versus upper h 1: muless than50, a random sample of size nequals22 is obtained from a population that is known to be normally distributed. complete parts (a) through (d) below.
Answers
The question relates to a statistical hypothesis test, specifically comparing a sample mean to a known population mean. This involves recognizing null and alternative hypotheses, identifying and calculating a test statistic, deciding a significance level, determining a critical value, and finally comparing the test statistic to this critical value to decide whether to reject or not reject the null hypothesis.
Explanation:The subject matter posed in the question concerns a statistical hypothesis test.
In these cases, we have two contradictory hypotheses about a population: the null hypothesis, denoted as 'H₀', which generally represents the status quo or a statement of no effect (e.g. a population mean is equal to 50), and the alternative hypothesis, denoted 'H₁', the contrary of the null hypothesis (population mean is not equal to 50). In your specific case, the null hypothesis 'H₀' is that the mean is equal to 50 (μ = 50) and the alternative hypothesis 'H₁' is that the mean is less than 50 (μ < 50).
To test these hypotheses, you could follow these steps:
Identify a test statistic: Since we know the population is normally distributed and we are comparing the sample mean to the population mean, we can use a z-test statistic.
Compare the test statistic to the critical value to decide whether to reject or fail to reject the null hypothesis.
After these steps, interpret the results in terms of the problem.
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What is the surface area of a rectangular prism that has a length of 9 feet, a width of 5 feet, and a height of 7.5 feet?
Answers
A = 2(LW +H*(L +W))
Filling in the given information, we have
A = 2((9 ft)*(5 ft) +(7.5 ft)*(9 ft +5 ft))
A = 2(45 ft² +(7.5 ft)*(14 ft)) = 2(150 ft²)
The surface area of the rectangular prism is 300 ft².
Answer: 300 ft²
Step-by-step explanation:
If Henry's home has a market value of $145000 and the assessment rate is 35% what is its assessed valuation
Answers
Answer:
Assessment value of Henry's home is $50750
Step-by-step explanation:
Henry's home has a market value of $145000 and the assessment rate is 35%.
This means value of home is 35% of the total cost $145000
Now we will solve it by calculating percentage
Assessment = 35% of 145000 = [tex](145000)(\frac{35}{100})=(1450).(35)=50750[/tex]
So the answer is assessment of Henry's home = $50750.
A 25-foot-long footbridge has two diagonal supports that meet in the center of the bridge. Each support makes a 65∘ angle with a short vertical support.
What is the length x of a diagonal support, to the nearest tenth of a foot?
x≈_____ feet
Answers
sin(65°) = (12.5 ft)/x
x = (12.5 ft)/sin(65°)
x ≈ 13.8 ft
Answer:
13.
Step-by-step explanation:
Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. Using the formula A(t) =P*e^rt , how much will you have in the account after 4 years
Answers
A = $1600*e^(0.046*4) = $1923.23 (rounded up to the nearest cent)
Yahtzee is played with 5 dice player attempt to score point buy rolling various combinations. when all 5 dice show the same nubmer
Answers
Linda needs 20 gallons of juice that has 75%fruit juice. she has a mixture that has 80% fruit juice and another mixtures that has 60% fruit juice. how much of each mixture should she use to get what she need?
Answers
15 gallons of 80% juice
5 gallons of 60% juice
_____
Let g represent the number of gallons of 80% juice needed. Then (20-g) is the number of gallons of 60% juice Linda will use. The amount of juice in the mixture can be written as
0.80g +0.60(20 -g) = 0.75×20
0.20g = 20(0.75 -0.60) = 20×0.15
g = 20×0.15/0.20 = 15
The amount of 80% juice needed is 15 gallons, so 5 gallons of 60% juice are needed.