The denominator, (x+5)(x-2) + 1, ensures that the function is never zero and avoids any potential holes in the graph. The numerator, (x+5)(x-2), is zero precisely when x=-5 or x=2, which leads to the vertical asymptote
What is equation?A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.
One possible function whose graph has two vertical asymptotes located at x = -5 and x = 2 is:
f(x) = (x+5)(x-2) / ((x+5)(x-2) + 1)
The denominator, (x+5)(x-2) + 1, ensures that the function is never zero and avoids any potential holes in the graph. The numerator, (x+5)(x-2), is zero precisely when x=-5 or x=2, which leads to the vertical asymptotes.
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How many minutes are in two days
2880 minutes in 2 days.
One day has 24 hours in it.
One hour = 60 minutes
One day in minutes = 24*60 = 1440 minutes
Two days in minutes = 1440 * 2 = 2880 minutes.
Answer:
2880
Step-by-step explanation:
4320÷3=1440
1440+1440=2880
Hope this helps!
y+x^2=16x-100 complete the square
Answer:
First, we need to move the constant term to the other side of the equation:
y + x^2 - 16x = -100
Next, we need to "complete the square" by adding and subtracting a constant term that will allow us to write the left-hand side of the equation as a perfect square. To do this, we need to take half of the coefficient of the x-term (-16), square it, and add that to both sides of the equation:
y + x^2 - 16x + 64 = -36 + 64
Now, we can simplify the left-hand side by factoring it as a perfect square:
(y + (x - 8)^2) = 28
So the equation, in completed square form, is:
y + (x - 8)^2 = 28
Step-by-step explanation:
gg
Write 122° 43’ 12” in decimal degree form to the nearest thousandth
122° 43’ 12” is written in decimal degree form, to the nearest thousandth, as approximately: 122.720.
How to Write in Decimal Degree Form?In order to convert 122° 43’ 12” to decimal degree form, we can use the formula which is expressed as:
decimal degrees = degrees + (minutes / 60) + (seconds / 3600)
Substituting the given values into the stated formula above, we have the following:
decimal degrees = 122 + (43 / 60) + (12 / 3600)
decimal degrees = 122.720
Rounding to the nearest thousandth, we get:
122.720 ≈ 122.720
Therefore, 122° 43’ 12” is approximately equal to 122.720 degrees to the nearest thousandth.
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Last year at a certain high school, there were 100 boys on the honor roll and 50 girls on the honor roll. This year, the number of boys on the honor roll increased by 19% and the number of girls on the honor roll increased by 20%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Pls help im d.u.m.b
The total number of students on the honor roll increased by approximately 19.3%.
What is percenatge?
Percentage is a way of expressing a fraction or a portion of a whole number as a portion of 100. It is often denoted by the symbol %. For example, 50% represents 50 parts out of 100, or 50/100, which simplifies to 1/2.
Let's first find the total number of students on the honor roll last year:
Total number of students on the honor roll last year = 100 (boys) + 50 (girls) = 150
This year, the number of boys on the honor roll increased by 19%, which means the new number of boys on the honor roll is:
New number of boys on the honor roll = 100 + 0.19(100) = 119
Similarly, the new number of girls on the honor roll is:
New number of girls on the honor roll = 50 + 0.20(50) = 60
Therefore, the total number of students on the honor roll this year is:
Total number of students on the honor roll this year = 119 (boys) + 60 (girls) = 179
The percentage increase in the total number of students on the honor roll is:
Percentage increase = [(Total number of students on the honor roll this year - Total number of students on the honor roll last year) / Total number of students on the honor roll last year] x 100%
Percentage increase = [(179 - 150) / 150] x 100% = 19.3%
Therefore, the total number of students on the honor roll increased by approximately 19.3%.
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What are the solutions to the equation 2(x2 + x − 11)32 = 54? Check for extraneous solutions. Enter the values in increasing order.
Answer:
To solve the equation, we can begin by isolating the expression in the parentheses:
2(x^2 + x - 11)^3/2 = 54
Divide both sides by 2:
(x^2 + x - 11)^3/2 = 27
Take the cube root of both sides:
x^2 + x - 11 = 3∛27
Simplify the cube root:
x^2 + x - 11 = 3∛(27) = 3*3 = 9
Rearrange the equation:
x^2 + x - 20 = 0
Factor the quadratic:
(x + 5)(x - 4) = 0
Therefore, the solutions are x = -5 and x = 4.
To check for extraneous solutions, we need to make sure that these values do not make the original equation undefined. Since there are no square roots or denominators, there are no restrictions on x, and both solutions are valid.
So, the solutions to the equation are -5 and 4, in increasing order.
Slope and y-Intercept
Find the slope and y-intercept of a line that passes through these points.
5. (2, 2) and (3, 0)
6. (1,5) and (4, 10)
7. (8, 2) and (-8, 6)
The slope and y-intercepts of each line, respectively, are:
5. m = -2; b = 6 6. m = 5/3; b = 10/3 7. m = -1/4; b = 4
What is the Slope of a Line?Slope of a line is calculated as, m = change in y / change in x.
5. Given (2, 2) and (3, 0):
Slope of the line (m) = change in y / change in x = 2 - 0 / 2 - 3
m = 2/-1
m = -2
To find the y-intercept (b), substitute m = -2 and (x, y) = (2, 2) into y = mx + b:
2 = -2(2) + b
2 = -4 + b
2 + 4 = b
b = 6
6. Given (1,5) and (4, 10):
Slope of the line (m) = change in y / change in x = 10 - 5 / 4 - 1
m = 5/3
To find the y-intercept (b), substitute m = 5/3 and (x, y) = (1, 5) into y = mx + b:
5 = 5/3(1) + b
5 - 5/3 = b
b = (15 - 5)/3
b = 10/3
7. Given (8, 2) and (-8, 6):
Slope of the line (m) = change in y / change in x = 6 - 2 / -8 - 8
m = 4/-16
m = -1/4
To find the y-intercept (b), substitute m = -1/4 and (x, y) = (8, 2) into y = mx + b:
2 = -1/4(8) + b
2 = -2 + b
2 + 2 = b
b = 4
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Mieko bought
2
gallons of paint. She used
14
of the paint on her bedroom,
3
quarts on the hallway, and the rest of the paint in the living room. How many quarts of paint did Mieko use in the living room?
The quarts of paint used by Mieko to paint his living room is equal to 3 quarts.
Total paint bought by Mieko = 2 gallons
Amount of paint used to paint bedroom = 1/4 of the paint.
Amount of paint used on the hallway = 3 quarts
Since 1 gallon is equal to 4 quarts.
Convert gallons to quarts.
Mieko bought 2 gallons of paint, which is equivalent to 8 quarts
She used 1/4 of the paint on her bedroom,
which is 1/4 x 8 quarts = 2 quarts.
She also used 3 quarts of paint on the hallway.
This implies,
The total amount of paint used on the bedroom and hallway is equal to,
2 quarts + 3 quarts = 5 quarts
The amount of paint used in the living room is the remaining amount of paint is equal to,
8 quarts - 5 quarts = 3 quarts
Therefore, Mieko used 3 quarts of paint in the living room.
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The above question is incomplete, the complete question is:
Mieko bought 2 gallons of paint. She used 1/4 of the paint on her bedroom, 3 quarts on the hallway, and the rest of the paint in the living room. How many quarts of paint did Mieko use in the living room?
please help me figure this out for 100 points
Answer:
Step-by-step explanation:
If 9 units = 36 inches,
then 9 ÷ 9 = 36 ÷ 9 inches
∴ 1 unit = 36/9 inches
Answer:
The answer is 4/1(in)
Step-by-step explanation:
1/9 yard to in
1yd=36in
1/9yards=4in
and
9unit=36in
1 unit=36/9
1unit=4in
therefore 1unit=1/9yards
What does 12 tons equal to?
Answer:24,000 pounds
Step-by-step explanation: a ton is 2,000 pounds so 12 times 2,000 is 24,000
Write the equation of a circle where the endpoints of a diameter are (4,9) and (4,-3).
The equation of a circle having endpoints of diameter as (4,9) and (4,-3) is (x - 4)² + (y - 3)² = 36.
The "center" of circle is called as midpoint of diameter.
The "x-coordinate" of "mid-point" is = (4+4)/2 = 4, and
The "y-coordinate" of "mid-point" is = (9+(-3))/2 = 3.
So, center of circle is (4,3),
The radius of circle is half the length of the diameter, which is distance between two endpoints of diameter. We find distance using distance formula:
⇒ distance = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁,y₁) and (x₂,y₂) are "end-points" of diameter.
⇒ distance = √((4 - 4)² + (9 - (-3))²)
⇒ √(144) = 12.
So, radius is 6.
The equation of circle with center (h,k) and radius "r" is : ⇒ (x - h)² + (y - k)² = r²,
Substituting the values
We get,
⇒ (x - 4)² + (y - 3)² = 6²,
⇒ (x - 4)² + (y - 3)² = 36,
Therefore, the equation of the circle is (x - 4)² + (y - 3)² = 36.
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brainliest and 100 points! i really appreciate the help, and please let me know if you need help on anything, thanks!!
Given that the triangles are congruent, we can conclude that
ΔBRN is the image of one or more rigid transformations on ΔQGLThe area of ΔQGL equals the area of ΔBRNLG ≅ NR∠LQG = ∠NBRCongruent trianglesFrom the question, we are to determine what can be concluded from the fact that triangle QGL and triangle BRN are congruent
If ΔQGL and ΔBRN are congruent, we can infer that
QG = BR
LG = NR
QL = BN
Also, in terms of angles
∠LGQ = ∠NRB
∠QLG = ∠BNR
∠LQG = ∠NBR
In addition,
If two triangles are congruent, the areas of the triangles will be equal to each other
Thus,
We can conclude that
ΔBRN is the image of one or more rigid transformations on ΔQGLThe area of ΔQGL equals the area of ΔBRNLG ≅ NR∠LQG = ∠NBRLearn more on Congruent triangles here: https://brainly.com/question/10713965
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The regular polygon has the following measures.
a = 7√3 cm
s = 14 cm
Segment a is drawn from the center of the polygon perpendicular to one of its sides.
What is the vocabulary term for segment a?
What is the area of the polygon?
Round to the nearest tenth and include correct units.
Show all your work.
The apothem is the vocabulary for a. The regular polygon's area is 319.8 cm².
We may use the following formula to calculate the area of the polygon:
Area = (1/2) × Perimeter × Apothem
The perimeter of a polygon is calculated by multiplying the number of sides by the length of each side, as shown below:
Perimeter = the number of sides multiplied by the length of each side
Perimeter = 6 × 14 cm (because to the regular hexagon shape)
Perimeter = 84 cm
Use the fact that it forms a right triangle with half of one side length and the apothem as the legs and the apothem as the hypotenuse to find the apothem. Thus,
a² = s² - (s/2)²
a² = 196 - 49
a² = 147
a = √(147) = 7.65 cm
Now we can enter our values into the area formula:
Area = (1/2) × Perimeter × Apothem
Area = (1/2) × 84 cm × 7.65 cm
Area = 319.8 cm²
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Which triangle congruence postulate or theorem proves that these triangles are
congruent?
1
K
Figure (i)
28
M
X
Figure (ii)
2
pls help!!
Answer: figure ii
Step-by-step explanation:
ANGEL CHARGES A FLAT RATE OF $25 AND 10$ per hour to babysit. Which expression gives angela the total amount of money she will make per hour? A y=25 x + 10 B y=10x+25 X y=35x y=25(x+10)
The expression that gives Angela the total amount of money she will make per hour is y = 10x + 25.
In equation y = 10x + 25, x represents the number of hours she babysits, and y represents the total amount of money she will make, which is equal to the flat rate of $25 plus $10 per hour.
So, for example, if she babysits for 3 hours, the total amount of money she will make is:
y = 10(3) + 25 = 30 + 25 = $55
Therefore, the correct answer is A, y = 10x + 25.
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The diameter of a hat is 5.3 inches. What is the distance around the hat using π = 3.14? Round to the hundredths place.
22.05 inches
16.64 inches
8.32 inches
1.69 inches
A special deck of cards has 6 red cards, and 5 black cards. The red cards are numbered 1, 2, 3, 4, 5, and 6. The black cards are numbered 1, 2, 3, 4 and 5. The cards are well shuffled and you randomly draw one card.
a) Number of elements in sample size is 11.
b) Probability P(E) is 0.45.
a) The sample space is the set of all possible outcomes when drawing a single card from the deck. Since there are 11 cards in total, the sample space has 11 elements.
b) We want to find the probability of drawing an even-numbered card, which includes the red cards numbered 2, 4, and 6, and the black cards numbered 2 and 4. There are five such cards in total, so the probability of drawing an even-numbered card is:
P(E) = number of even-numbered cards / total number of cards
P(E) = 5 / 11
P(E) = 0.4545 or approximately 0.45
Therefore, the probability of drawing an even-numbered card from the deck is about 0.45.
Correct Question:
A special deck of cards has 6 red cards, and 5 black cards. The red cards are numbered 1, 2, 3, 4, 5, and 6. The black cards are numbered 1, 2, 3, 4 and 5. The cards are well shuffled and you randomly draw one card.
R = card drawn is Red
E = card drawn is even-numbered
a) How many elements are there in the sample space.
b) What is the probability P(E).
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What is 4x-2y=6 in slope-intercept form?
Step-by-step explanation:
Slope intercept form is y = mx + b
Re-arrange given equation to
2y = 4x-6 divide by 2
y = 2x -3 done.
After obtaining two heads from two tosses of a coin, the probability of obtaining a head on the next toss is __________.
The probability of obtaining a head on the next toss of a coin after obtaining two heads from two tosses is still 1/2 or 50%.
This is because each coin toss is an independent event, and the outcome of one toss does not affect the outcome of another toss. Therefore, the fact that two heads have been obtained in the previous two tosses does not change the probability of obtaining a head on the next toss, which is always 1/2 or 0.5 for a fair coin.
What is probability?Probability is the likelihood of an event occurring. The values are between 0 and 1. The closer it is to 1, the greater the probability.
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Tell whether the p = 6 is a solution of p + 5 ≤ 12.
Peter has three sticks measuring 19 inches, 23 inches, and 27 inches. He lays them down to form a triangle. Find the measure of the angle enclosed by the 19 inch and 23 inch sides to the nearest degree.
The measure of the angle enclosed by the 19 inch and 23 inch sides is 81 degrees in the triangle.
In a triangle, the sum of the measures of the three angles is always 180 degrees.
Let the angle enclosed by the 19 inch and 23 inch sides x.
The Law of Cosines states that for a triangle with sides a, b, and c, and angle C opposite side c:
c² = a² + b² - 2ab cos(C)
Let's choose the 27 inch side as side c.
Then we have:
27² = 19² + 23²- 2(19)(23)cos(x)
729 = 850 - 874cos(x)
-121 = -874cos(x)
cos(x) = 0.1386
x=81 degrees
Hence, the measure of the angle enclosed by the 19 inch and 23 inch sides is 81 degrees.
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Please help me i really need it
Answer:
MO/KO = NO/LO
5/10 = 3/LO
5/10 = 3/x
Step-by-step explanation:
Since KLO and MNO are similar, that means the corresponding sides share a common proportion:
Note how corresponding sides MO and KO are given measurements, that means we can find the common proportion by dividing MO/KO (which is 5/10). Knowing the proportion between the corresponding sides between MO and KO, we can find LO by finding its corresponding side and setting up a proportion. LO's corresponding side is NO (with a measurement of 3):
5/10 = 3/LO
Other options also work:
MO/KO = NO/LO since MO = 5 units, KO = 10 units, & NO = 3 units
5/10 = 3/x since any value can be set to a variable, LO = x
[tex]x^{2} +6x+8\\[/tex]
For the equation x²+6x+8 the roots are -4 and -2.
The given equation is x²+6x+8
We have to find the roots of the equation
x²+6x+8
Let us factorize the equation to find the roots
x²+4x+2x+8
x(x+4)+2(x+4)
(x+2)(x+4)
x=-2 and x=-4 are the roots
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It cost Ximena $3.40 to send 68 text messages. How
many text messages did she send if she spent $2.45?
Answer:
49 text messages
Step-by-step explanation:
3.49/68 = 0.05 oer text
we can use this unit rate for text sent $2.45
$2.45/.05 per text message = 49 text messages
£30 in the ratio 3:1
Answer:
A ratio of 3:1 means that there are 4 parts altogether. The fractions from the ratio can therefore be deduced as. 43 and 41. These represent the percentages: 75%:25%
Answer:
Step-by-step explanation:
The ratio can be converted into a fraction
therefore we can divide by the denominator in order to convert 30 Euros to a 3:1 ratio.
The fraction =3/4 and 1/4
so we have to divide 30 by 4
= 7.5 Euros
so;
3:1
(22.5):(7.5)
(45/2):(15/2)
45:15
divide by 15
3:1
f(x) = 6 - x and g(x) = x/3 + 8 .Simplify f(2x) + g(3x + 9)
Answer:
18 - x
Step-by-step explanation:
f(x) = 6 - x
g(x) = x/3 + 8
f(2x) = 6 - (2x) => 6 - 2x
g(3x + 9) = (3x+9)/3 + 9 = x + 3 + 9 => x + 12
(6 - 2x) + (x + 12)
Simplified:
18 - x
A county library manager wants to find out what types of activities residents in the
county want at the library. Which sample is the most representative of the population of
interest?
A-every 30 person on a list of county residents
B-every 30th person who enters a local restaurant
C-every child who enters the county library
D-every student who enters the local high school
Every 30th person on a list of county residents, is the most representative sample of the population of interest. Option A
What is a representative sample?A representative sample is a small group of individuals who, as closely as possible, reflect a larger group.
The best representative sample will be obtained by taking every 30th person on a list of county residents.
This is due to the fact that it requires choosing people from the entire county's resident population as opposed to only those who frequent a certain region (options B and C) or a particular group (option D, high school students).
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Find the selling price. original price: $20.00 percent of markup: 15%
The selling price of the item after a percentage of markup by 15 % is given by S = $ 23
Given data ,
Let the initial price of the item be A = $20
Now , let the selling price of the item after percentage mark up be S
where percentage markup = 15 %
So , the amount of markup is M = ( 15 )% x 20
M = 20 x 0.15
M = $ 3
And , the selling price S = A + M
S = $ 20 + $ 3
S = $ 23
Hence , the selling price is S = $ 23
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what has a slope of 15?
A slope of 15 simply means that the rate of change of the value on the y-axis with respect to the x-axis is equal to 15.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting an assumed data points into the slope formula, we have the following;
Slope (m) = (80 - 20)/(6 - 2)
Slope (m) = 60/4
Slope (m) = 15.
In this context, we can reasonably infer and logically deduce that a slope of 15 denotes the rate of change of a straight line on a graph.
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a grocery store is sponsoring a sales promotion where the cashiers give away one of the letters a, e, l, s, u, and v for each purchase. if a customer collects all six (spelling values) the customer gets $25 worth of free groceries. what is the expected number of trips to the store customer needs to make in order to get a complete set? (assume the different letters are given away randomly.)
The expected number of trips a customer needs to make to get a complete set of letters is 6 trips.
This problem can be modeled using the concept of a geometric distribution, where the number of trials required to achieve the first success (getting a complete set of letters) follows a geometric distribution.
The probability of getting a specific letter on any given purchase is 1/6, since there are six letters and they are equally likely to be given away. Therefore, the probability of not getting a specific letter on any given purchase is 5/6.
Let X be the random variable representing the number of purchases needed to obtain a complete set of letters. Since each purchase is independent of the others, X follows a geometric distribution with a probability of success p = 1/6.
The expected value of a geometric distribution with probability of success p is given by E(X) = 1/p. Therefore, the expected number of trips to the store that a customer needs to make to get a complete set is:
E(X) = 1/p = 1/(1/6) = 6
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Please help
Cindy is buying a new car and wants to learn how the value of
her car will change over time. Insurance actuaries predict the
future value of cars using depreciation functions. One such
function is applied to the car whose declining value is shown at
the right.
A. Describe how the value of the car decreases from year to year.
B.model with mathematics what kind of function would explain this type of pattern
C. Giver your answer to part B, what is needed to find the function the actuary is using? Explain
The value of the car decreases from year to year by 15%.
A kind of function that would explain this type of pattern is an exponential decay function [tex]f(x) = 10000(0.15)^x[/tex].
You need the decay rate to find the function the actuary is using.
How to determine the value of the car after x years?In Mathematics and Statistics, a population or physical asset (car) that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or physical asset that decreases by r percent per unit of time is an exponential equation of this form:
P(t) = I(1 - r)^t
Where:
P(t ) represents the future amount or value.t represents the time or number of months.I represents the initial amount of physical asset.r represents the exponential decay rate or constant ratio.Next, we would determine the constant ratio in each representation as follows;
Constant ratio, r = a₂/a₁ = a₃/a₂ = a₄/a₃ = a₅/₄
Constant ratio, r = 8520/10,000 = 7213/8250 = 6,100/7213 = 768/192
Constant ratio, r = 85.
By substituting the given parameters, we have the following:
P(t) = I(1 - r)^t
f(x) = 10,000(1 - 85/100)^x
f(x) = 9,600(1 - 0.85)^x
f(x) = 9,600(0.15)^x
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