At which values of x does the graph of the function F(x) have a vertical asymptote? Check all that apply
Answers
Solution
Step 1:
Write the rational expression:
[tex]\begin{gathered} f(x)\text{ = }\frac{x+4}{x^2+5x-24} \\ \end{gathered}[/tex]Step 2:
Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value).
Step 3
[tex]\begin{gathered} x^2+5x-24=0 \\ \\ x^2+8x\text{ - 3x - 24 = 0} \\ \\ x(x\text{ + 8\rparen-3\lparen x + 8\rparen = 0} \\ \\ (x\text{ - 3\rparen\lparen x + 8\rparen = 0} \\ \\ x\text{ - 3 = 0, x + 8 = 0} \\ x\text{ = 3, x = -8} \end{gathered}[/tex]Step 4:
\ertical} Asymptote is =-8,\ =3,
Related Questions
Find the probability of the following card hands from a 52-card deck. In poker,
aces are either high or low. A bridge hand is made up of 13 cards.
In poker, four of a kind (4 cards of the same value)
O 2.40 x 104
O 2.00 × 10-5
O 1.85 x 10-5
O4.34 x 10-4
Answers
Answer: 2.40 * 10^(-4)
This value is approximate.
=====================================================
Explanation:
A four of a kind is where we have 4 cards of the same value, as mentioned in the instructions. For example, we could have 4 queens and some other card, such as a 10 of clubs.
There are 13 cards to pick from for any given suit. Once that card is chosen, the other 3 slots are fixed to whatever that first card is. The fifth slot will have 52-4 = 48 choices.
In short we have 13 choices for the first four cards and 48 choices for the fifth card.
Overall we have 13*48 = 624 different four of kind poker hands.
Let's now calculate how many possible poker hands there can be.
A poker hand consists of 5 cards. I don't know why your teacher mentioned a bridge hand of 13 cards since that's for a different game.
We'll use n = 52 and r = 5 in the nCr combination formula below.
[tex]n C r = \frac{n!}{r!(n-r)!}\\\\52 C 5 = \frac{52!}{5!*(52-5)!}\\\\52 C 5 = \frac{52!}{5!*47!}\\\\52 C 5 = \frac{52*51*50*49*48*47!}{5!*47!}\\\\ 52 C 5 = \frac{52*51*50*49*48}{5!}\\\\ 52 C 5 = \frac{52*51*50*49*48}{5*4*3*2*1}\\\\ 52 C 5 = \frac{311875200}{120}\\\\ 52 C 5 = 2598960\\\\[/tex]
There are 2,598,960 possible five-card poker hands.
624 of those hands are four of a kind, so the probability we want is
624/(2,598,960) = 0.000240 = 2.40 * 10^(-4)
The approximate decimal value 0.000240 converts to 0.0240%
Solve for .
5x - 4 ≥ 12 OR 12x + 5 < -4
Answers
Second one is x < -3/4
Answer:[tex]x\geq 3.2[/tex] and [tex]x < -0.75[/tex]
Step-by-step explanation
[tex]5x-4\geq 12[/tex]
First you would add 4 to each side.
[tex]5x\geq 16[/tex]
Then divide each side by 5.
[tex]x\geq 3.2[/tex]
Next one,
[tex]12x+5 < -4[/tex]
First you would subtract 5 from both sides.
[tex]12x < -9[/tex]
Then divide both sides by 12.
[tex]x < -0.75[/tex]
if m(x)=x-7 and n(x)= 1/x+7 find the function value if possible of (mxn)(7)
Answers
The function value if possible of (mxn)(7) is mathematically given as
(m.n)(7) =0
This is further explained below.
What is the function value if possible of (mxn)(7)?Generally, the equation for the is mathematically given as
m(x) &=x-7
Therefore
[tex]n(x) = \frac{1}{x}+7[/tex]
(m * n)(x) = m(x) * n(x)
[tex]=(x-7) \cdot\left(\frac{1}{x}+7\right)[/tex]
(m * n)(7) = (7-7) * n(1/7 + 1)
(m.n)(7) =0
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A dairy farm has a real estate tax rate of $57.26 per thousand dollars of assessed value. If the farm is assessed at $665,500.00 what is the real estate tax?
Answers
Answer:
the real estate 5726per thousand dollars
Step-by-step explanation:
A car uses 3 1/8 gallons of gasoline per hour when driving on the highway. How many gallons will it use after 4 2/3 hours? It will use _____________ gallons.
Answers
If the car uses 3 1/8 gallons per hour and the number of hours is 4 2/3, we can multiply both values to find the total amount of gallons used in this time.
First, we need to convert 3 1/8 and 4 2/3 into improper fractions:
[tex]\begin{gathered} 4\text{ }\frac{2}{3}=4+\frac{2}{3}=\frac{12}{3}+\frac{2}{3}=\frac{14}{3}\\ \\ 3\text{ }\frac{1}{8}=3+\frac{1}{8}=\frac{24}{8}+\frac{1}{8}=\frac{25}{8} \end{gathered}[/tex]Now, multiplying the values, we have:
[tex]\frac{25}{8}\cdot\frac{14}{3}=\frac{350}{24}=14.58[/tex]So the car will use 14.58 gallons.
10. Find the value of a²-b if a = 3 and b = -5.
Answers
Rodney opens a savings account with $75 and also deposits $40 each month. Morgan opens an account with $50 and also deposits $40 each month. Will they have the same amount in their account at any point? If so, after how many months? Explain.
Show an equation
Answers
No, they will not have the same amount in their account at any point of time.
Given that:-
Money deposited by Rodney at the opening of savings account = $ 75
Money deposited by Rodney each month in the account = $ 40
Money deposited by Morgan at the opening of savings account = $ 50
Money deposited by Morgan each month in the account = $ 40
Let us imagine that they will have equal amount of money in their accounts at a particular point of time.
Let us consider x to be the number of months when they will have same amount of money in their account.
Hence, we can write,
75 + 40x = 50 + 40x
We can see that,
75 - 50 = 40x - 40x
25 = 0
But this is not possible.
Hence, they will never have the same amount of money in their accounts at a particular point of time.
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FIND THE DOMAIN AND RANGE(Algebra 1)
Answers
The domain and range of the function are {-4, -2, 0, 4} and {-3, -1, 0, 1} respectively.
Domain and range of an equationThe domain of the function is defined as the value of the independent function for which the function exist.
The range of the function is defined as the value of the dependent function for which the function exist.
From the given table, the domain are the values in the x-column which the range in the y-column are the values in the y-axis.
From the table, the domain are D = {-4, -2, 0, 4} while the range is R = {-3, -1, 0, 1}.
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In her notebook, Pia wrote these steps to construct a square inscribed in a circle:Use a compass and a straightedge to find chord LM, which is the perpendicular bisector of JK. Then, use a straightedge to draw the four chordsthat make up the square: JL, LK, KM, and MJ.Which instruction is Pia missing?
Answers
We want to draw chord LM such that it is a perpendicular bisector of line JK. The square would be drawn by joining lines JL, KL, KM and MJ
To achieve this, the daigram should look like the one shown below
This diagram is only possible if JK passes through the center of the circle. This means that JK is the diameter of the circle. Thus, the correct option is
B
Answer:
B
Step-by-step explanation:
the sum of two consecutive natural numbers is 313
Answers
explanation:
Let the numbers be x and x+1.
x2 + (x+1)2 = 313
2x2 + 2x + 1 = 313
2x2 + 2x - 312 = 0
x2 + x - 156 = 0
x2 + 13x - 12x - 156 = 0
x(x + 13) - 12(x + 13) = 0
(x - 12) (x + 13) = 0
x = 12 or -13. Since x cannot be negative, x = 12. Hence, numbers are 12 and 13.
Answer:
156 and 157
Step-by-step explanation:
PLEASE HELP ME PLS !!!!!!!!Connor has three number cards, as shown
below.
The minimum of the three cards is 6.
The range of the three cards is 7.
What is the mean of Connor's three cards?
Answers
Answer:
Mean of Connors 3 card is 9
Step-by-step explanation:
Solution
Minimum of 3cards is 6
range is 7
max -min=7
max=min+7
max=7+6
max=13
Mean=6+13+8/3=27/3=9
Answer:
Mean of Connors 3 card is 9
Step-by-step explanation:
Solution
Minimum of 3cards is 6
range is 7
max -min=7
max=min+7
max=7+6
max=13
Mean=6+13+8/3=27/3=9
is (-2, -6) a solution of y less than 7x + 8
Answers
Answer:
Not a solution.
Step-by-step explanation:
[tex]y < 7x+8\\-6 < 7(-2)+8\\-6 < -14 + 8\\-6 < -6; False[/tex]
This is not true because -6 is not less than -6.
Answer: No.
Step-by-step explanation: First of all you need to know that (x,y) x goes in front of y because of alphabetical order. Second, plug in your points (-2,-6) into your equation y < 7(-2) + 8. After you solve, you will get y < -14+8. Then, you get y < -6. On your point it said that -6 is your y point. Plug in -6 into y and you get -6 < -6. So no, y is not less than 7x +8. Hope this helps!
The measure of DF the center of the given circle
Answers
Solution:
Given the circle;
[tex]|OF|\cong|OE|=r[/tex]Thus;
[tex]\triangle FOE\text{ is isosceles triangle}[/tex]Then;
[tex]\begin{gathered} \angle OFE=38^o \\ \\ \angle Arc\text{ }DF=38^o+38^o..............(\text{ An exterior angle of a triangle is equal to the sum of the two interior opposite angles\rparen} \\ \\ \angle Arc\text{ }DF=76^o \end{gathered}[/tex]CORRECT OPTION: B
Jennifer bought a bracelet at original cost $25 to sell in her handicraft store. She marked the price up 45%.
a) Find the amount of the mark-up price.
S
b) Find the list price.
S
(Round to two decimal places if necessary.)
(Round to two decimal places if necessary.)
Answers
Answer:
Mark up $11.25
Selling price $36.25
Step-by-step explanation:
25(.45) = 11.25 This is the mark up, The selling price is then 25 + 11.25, which is $36.25
please help with this
Answers
Answer:
supplementary, not congruent.
The following numbers represents the number of phone calls a class made in a given week:
125, 86, 142, 98, 126, 128, 90, 88, 98, 121
Use this data to find the following information. SHOW ALL WORK FOR CREDIT!
Mean: 110
e
Range:
Mode:
Answers
The mode and range of the given data is 98 and 42 respectively.
What is data?
Data, which can describe quantity, quality, fact, statistics, other fundamental units of meaning, or simply sequences of symbols that can be further interpreted, is a collection of discrete values that convey information in the pursuit of knowledge. A datum is a distinct state within a collection of data. Typically, data is arranged into structures like tables that give it additional context and meaning and can also be used as their own form of data in larger structures. It's possible to use data as variables in a computation. Data can represent both concrete measurements and abstract concepts. Data is used frequently in virtually every aspect of human organisational activity, including finance and science. Stock prices, crime rates, unemployment rates, literacy rates, and census data are a few examples of data sets.
Mode = 98 ( 98 occurs two times)
Range = 128-86=42
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The size of the graduating class of Kyle’s school has been growing at a constantrate. Kyle’s older brother’s class had 257 students when he graduated in 2015. Kyleis going to graduate in 2018, and his class has 329 students. Write a linear function that models the school’s graduating class size (y) in terms of the year (x).
Answers
The linear equation that models the school’s graduating class size (y) in terms of the year (x) after 2015 is given as y = 24x + 257
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
Let y represent the graduating class size in terms of the year (x) after 2015.
Kyle’s older brother’s class had 257 students when he graduated in 2015. That is (0, 257)
In 2018, and his class has 329 students, That is (3, 329)
The linear equation is calculated using (0, 257) and (3, 329):
y - 257 = [(329 - 257)/(3 - 0)](x - 0)
y - 257 = 24x
y = 24x + 257
The linear equation is given as y = 24x + 257
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The hypotenuse of a triangle is 13 long. The leg is 7 inches longer than the shorter leg. Find the side lengths of the triangle.
Answers
Twice a number minus another numberis 8. Their sum is -2. Find thenumbers.
Answers
Set x and y to be the two numbers we need to find; then, according to the question,
[tex]\begin{gathered} 2x-y=8 \\ and \\ x+y=-2 \end{gathered}[/tex]Solve the system of equations as shown below
[tex]\begin{gathered} \Rightarrow y=2x-8 \\ \Rightarrow x+(2x-8)=-2 \\ \Rightarrow3x=6 \\ \Rightarrow x=2 \end{gathered}[/tex]Finding y,
[tex]\begin{gathered} x=2 \\ \Rightarrow y=2*2-8=-4 \\ \Rightarrow y=-4 \end{gathered}[/tex]Thus, the answer is 2 and -4, option E.Which has a greater value?
√8 + 3 or 8 + √3
Answers
Answer:
8 + √3 is greater.
Step-by-step explanation:
8 + √3 equals 9.73
whereas
√8 + 3 equals 5.83
ill give brainly HURRY PLEASE
Answers
Convert 5yd^2 to square centimeters
Answers
Since 1 yard = 0.914 meters
Since 1 m = 100 cm
Then 1 yard = 91.4 cm
Square them to find the square yard
[tex]\begin{gathered} (1)^2=1 \\ (91.4)^2=8353.96 \end{gathered}[/tex]1 square yard = 8353.96 square cm
Then to find 5 square yards in square cm, multiply 5 by 8353.96
[tex]5\times8353.96=41769.8[/tex]5 square yards = 41769.8 square cm
equations that are parallel to y=2x+11
Answers
y = 2x is the equation that is parallel to the given line in the question .
WHAT IS PARALLEL LINE ?If two non-vertical lines in the same plane have the same slope, they are said to be parallel. Never will two parallel lines cross. If two non-vertical lines in the same plane cross at a right angle, they are said to be perpendicular.
CALCULATIONy = 2x + 11
choose a point which the line will pass through
(0,0)
using y = mx + b
m = 2
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
[tex]y_{2} - y_{1} = m(x_{2} - x_{1} )[/tex]
y - 0 = 2x -0
y = 2x
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Please answer question 8, I’d really appreciate it!!
Answers
Answer:
t = 8
Step-by-step explanation:
1. 2.5(t-2)-6 = 9 = 2.5t-5-6=9
2. add common terms = 2.5t - 11 = 9
3. add 11 on both sides to eliminate the 11
4. 2.5t= 20
5. 20/2.5 = 8
6. t = 8
The rear windshield wiper blade on a car has a length of
10
inches. The blade is mounted on a
18
inch arm,
8
inches from the pivot point. If the wiper turns through an angle of
145
degrees, how much area is swept clean?
Answers
The area that is swept clean by the wiper is 329.13 inches².
What is the Area of the Sector?The area of a circle encompassed between its two radii and the arc next to them is known as the sector of a circle. A circle's sector area is the total area contained inside the sector's perimeter.The following formulas can be used to determine a sector's area: Area of a Sector of a Circle = (θ/360°)πr², where r is the circle's diameter and θ is the sector angle, in degrees, that the arc at the center subtends.Given:
Radius of arm(r₁) = 18 inch
Length of wiper blade = 10 inches
Radius of the point at which the blade is mounted(r₂) = 8 inches
Angle of the sector,θ = 145°
Required Area is calculated as,
Area = (θ/360°)πr₁² - (θ/360°)πr₂²
= (θ/360°) (πr₁² - πr₂²)
= (145°/ 360°) π(18² - 8²)
= (145°/ 360°) π(324 - 64)
= 329.13 inches²
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A triangle is congruent to triangle b what sequence would transform triangle a to triangle b
Answers
To transform congruent triangle a to triangle b: vertical reflection, then horizontal reflection and then 90° counter clockwise direction.
What are congruent triangles?Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them.
Triangles a and b are congruent to each other. So when we flip them the sequence which would transform triangle a to triangle b is vertical reflection, then horizontal reflection and then 90° counter clockwise direction.
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АBсDIf AC = 22x - 19, find x. Round your answer to the nearest tenth ifnecessary.AB = 4x + 31BC = 29
Answers
Answer:
The value of x is equal to 4.4.
[tex]x=4.4[/tex]Explanation:
Given;
[tex]\begin{gathered} AC=22x-19 \\ AB=4x+31 \\ BC=29 \end{gathered}[/tex]The length AC is the sum of length AB and BC;
[tex]AC=AB+BC[/tex]substiuting the given values;
[tex]\begin{gathered} AC=AB+BC \\ 22x-19=4x+31+29 \\ 22x-19=4x+60 \end{gathered}[/tex]let's add 19 to both sides, and then subtract 4x from both sides;
[tex]\begin{gathered} 22x-19=4x+60 \\ 22x-19+19=4x+60+19 \\ 22x=4x+79 \\ 22x-4x=4x-4x+79 \\ 18x=79 \end{gathered}[/tex]divide both sides by 18;
[tex]\begin{gathered} \frac{18x}{18}=\frac{79}{18} \\ x=4.388888 \\ x=4.4 \end{gathered}[/tex]The value of x is equal to 4.4.
[tex]x=4.4[/tex]Park a cover 4,926 square kilometers. It is 1,845 square kilometers larger than park b. Park c is 4,006 square kilometers larger than park a. What is the are of all three parks
Answers
Park a cover 4,926 square kilometers, It is 1,845 square kilometers larger than than park b. Park c is 4,006 square kilometers larger than park a, the area of all three parks is 16939 [tex]km^{2}[/tex]
What is an area?Area is amount of space occupied by a two-dimensional figure. In other words, it is quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of the area is square units which is generally represented as square inches, square feet, etc.
Word 'area' means a vacant surface. The area of shape is calculated with the help of its length and width. Length is the unidimensional and measured in units such as feet (ft), yards (yd), inches (in), etc. However, area of a shape is a two-dimensional quantity. Hence, it is measured in the square units like square inches or ([tex]in^{2}[/tex]), square feet or ([tex]ft^{2}[/tex]), square yard or ([tex]yd^{2}[/tex]), etc. Most of the objects or the shapes have edges and corners. The length and width of these edges are considered while calculating area of a specific shape.
Since,
Park a= 4926 [tex]km^{2}[/tex]
Park b= (4926-1845) = 3081 [tex]km^{2}[/tex]
Park c= (4006+4926) = 8932 [tex]km^{2}[/tex]
The area of all the three parks = (4926+3081+ 8932) [tex]km^{2}[/tex] = 16939 [tex]km^{2}[/tex]
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Circles on a coordinate plane
Answers
Given: The center and radius of a circle
[tex]\begin{gathered} center=(h,k) \\ radius=r \end{gathered}[/tex]To Determine: The equation of the circle
1) Circle A centered at the origin with radius 6
The equation of a circle is given by the formula
[tex]\begin{gathered} (x-k)^2+(y-h)^2=r^2 \\ \text{center(origin)}=(0,0),r=6 \\ Equation=(x-0)^2+(y-0)^2=6^2_{} \\ =x^2+y^2=36 \end{gathered}[/tex]ence, the equation of circle A centered at the origin with radius 6 is
x²+y²=36
2)Circle D with center (3, 3) and radius 2
The equation would be
[tex]\begin{gathered} (x-3)^2+(y-3)^2=2^2 \\ =(x-3)^2+(y-3)^2=4 \end{gathered}[/tex]ence, the equation of a circle D with center (,3, 3) and radius 2 is
(x-3)² + (y-3)² = 4
Adult male heights have a normal probability distribution with a mean of 70 inches and a standard deviation of 4 inches.
What is the probability that a randomly selected male is more than 70 inches tall?
Answers
There is a 0.5 percent probability that a randomly chosen male will be taller than 70 inches.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.So,
Mean height of the adults: μ = 70 inchesThe standard deviation: σ = 4 inchesThen, the formula will be:
Z = x-μ/σInsert the values in the formula as follows:
Z = x-μ/σZ = 70-70/4Z = 0Then,
0.5 is the p-value at z=0.P(x>70)=1-P(x<70)=1-0.5 = 0.5Therefore, there is a 0.5 percent probability that a randomly chosen male will be taller than 70 inches.
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