The graph which represents the rational function is; On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.
Which graph represents the rational function?It follows from the task content that the rational function given is; f(x) = 3x-2/x-2.
Hence, since the numerator and denominator polynomials are of the same order, it follows that the horizontal asymptote is the quotient; 3/1 = 3.
Additionally, the vertical asymptote of the function is the value of x which renders the denominator equal to 0 and consequently, the function undefined.
Hence, x -2 = 0 and x= 2.
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Answer: THE PERSON ABOVE IS CORRECT!!
The answer is D.) On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.
On a coordinate plane, a curved line with a minimum value of (negative 1.25, negative 3.25) and a maximum value of (0.25, negative 1.75), crosses the x-axis at (negative 2.25, 0), and crosses the y-axis at (0, negative 2). The line exits the plane at (negative 2.75, 6) and (1.5, 6).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero.
As the x-values go to positive infinity, the function's values go to positive infinity.
The correct option is:
As the x-values go to positive infinity, the function's values go to positive infinity.
What is the end behavior of the function?
By the description, We know that the function has the points:
(-1.25, -3.25), (0.25, -1.75) (-2.25, 0), (0, -2), (-2.75, 6), (1.5, 6)
Notice that from x = 0.25 to x = 1.5 the function goes upwards, then in the right side, the function goes up, so as x goes to positive infinity, also does f(x).
On the left side, we can see that from x = -2.75 to x = -2.25 the function goes downwards.
So, as x goes to the left (negative infinity) f(x) goes upwards.
Then as x tends to negative infinity, f(x) tends to infinity.
The correct option is:
As the x-values go to positive infinity, the function's values go to positive infinity.
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Answer:
D
Step-by-step explanation:
edge 23
Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?
acute, because 62 + 102 < 122
acute, because 6 + 10 > 12
obtuse, because 62 + 102 < 122
obtuse, because 6 + 10 > 12
Answer:
obtuse because 62 + 102 < 122
S
its c, obtuse, becuase 6^2+10^2<12^2
Write an expression equivalent to the following problems using the fewest number of terms. 2x + 10) + (−3x + 15)
Combining the like terms, the equivalent expression is given as follows:
-x + 25.
How to add polynomials?
To add polynomials, we combine the like terms, that is, those with the same variable and exponent.
In this problem, the expression is:
(2x + 10) + (-3x + 15).
2x + 10 - 3x + 15
Combining the like terms:
2x - 3x + 10 + 15 = -x + 25.
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Twelve of the 20 students in Mr. Skinner’s class brought lunch from home. Fourteen of the 21 students in Ms. Cho’s class brought lunch from home. Siloni is using two 15-section spinners to simulate randomly selecting students from each class and predicting whether they brought lunch from home or will buy lunch in the cafeteria.
If each spinner is divided into 15 congruent sectors, how does the spinner representing Mr. Skinner’s class differ from the spinner representing Ms. Cho’s class?
For Ms. Cho's class, the formula is =randBetween(1,21). The result of interest is 14 or less.
12/20 reduces to 4/5 --> 4/5 of 15 is 12.
So using the spinner to model Mr. Skinner's class, an outcome of the select 12 sections of interest represent, symbolize, and model a student bringing lunch from home.
LIkewise, 14/21 reduces to 2/3 --> 2/3 of 15 is 10.
So using the spinner to model Ms. CHo's class, an outcome of only 10 of the 15 sections of interest represent, model, and symbolize a student who brings lunch from home.
The same can be done in Excel: The function is =randBEtween( minVal, maxVal)
For example =randBetween(1,20) will model Mr. Skinner's class. A result of 12 or less represents, model, simulates, and symbolizes a student who packed their lunch.
For Ms. Cho's class, the formula is =randBetween(1,21). The result of interest is 14 or less.
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Find the area and the perimeter of the shaded regions below. Give
your answer as a completely simplified exact value in terms of T (no
approximations). The figures below are based on semicircles or
quarter circles and problems b), c), and d) are involving portions of
a square.
Pls explain as best as you can i cant understand this stuff
Based on the definition of composite figure, the area of the composite figure ABC formed by a semicircle and right triangle is approximately 32.137 square centimeters.
How to find the area of the composite figure
The area of the composite figure is the sum of two areas, the area of a semicircle and the area of a right triangle. The formula for the area of the composite figure is described below:
A = (1/2) · AB · BC + (π/8) · BC² (1)
If we know that AB = 6 cm and BC = 6 cm, then the area of the composite figure is:
A = (1/2) · (6 cm)² + (π/8) · (6 cm)²
A ≈ 32.137 cm²
Based on the definition of composite figure, the area of the composite figure ABC formed by a semicircle and right triangle is approximately 32.137 square centimeters.
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44. Each child born to a particular set of parents has a probability of 0.25 of having blood type O. If these parents have 5 children.
What is the probability that
a. Exactly two of them have blood type O
b. At most 2 have blood type O
c. At least 4 have blood type O
Using the binomial distribution, the probabilities are given as follows:
a. 0.2637 = 26.37%.
b. 0.8965 = 89.65%.
c. 0.0148 = 1.48%.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters for this problem are:
n = 5, p = 0.25.
Item a:
The probability is P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637[/tex]
Item b:
The probability is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373[/tex]
[tex]P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955[/tex]
[tex]P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637[/tex]
Then:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2373 + 0.3955 + 0.2637 = 0.8965[/tex]
Item c:
The probability is:
[tex]P(X \geq 4) = P(X = 4) + P(X = 5)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{5,4}.(0.25)^{4}.(0.75)^{1} = 0.0147[/tex]
[tex]P(X = 5) = C_{5,1}.(0.25)^{5}.(0.75)^{0} = 0.0001[/tex]
Then:
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0147 + 0.0001 = 0.0148[/tex]
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Drag each expression to show whether the expression is equivalent to 12x - 6,
24x+12, or neither.
Answer:
Drag and drop 6(2x-1) to 12x-6.
Drag and drop 6(4x-2) to Neither.
Drag and drop 3(8x+4) to 24x+12.
Drag and drop 6(4x+2) to 24x+12.
Drag and drop 2(6x-3) to 12x-6.
Step-by-step explanation:
To check these, use distributive property to solve each one.
6(2x-1) = 12x-6
6(4x-2) = 24x-12
3(8x+4) = 24x+12
6(4x+2) = 24x+12
2(6x-3) = 12x-6
Hope this helps!
Please mark brainliest! Thanks!
HELPPPPPP please !!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
Determine the domain and range of (g ○ f)(x) if f of x is equal to 2 over the quantity x squared minus 1 end quantity and g(x) = x + 1.
The domain of the function is (-∞, 1) U(1, ∞) while the domains are values greater than or equal to 1 that is y ≥1
Domain and range of a functionThe domain are independent variable for which the equation exist while the range are dependent variable for which the equation exist
Given the following functions
f(x) =2/x-1
g(x) = x+1
Determine (g ○ f)(x)
(g ○ f)(x) = g(f(x))
(g ○ f)(x) = g(2/x-1)
(g ○ f)(x) = (2/x-1) + 1
(g ○ f)(x) = 2+(x-1)/x-1
(g ○ f)(x) = x+1/x-1
Hence the domain of the function is (-∞, 1) U(1, ∞) while the domains are values greater than or equal to 1 that is y ≥1
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TG and TH are tangent to circle Z. If TG measures 4.2 cm, what is the measure of TH?
Based on the two-tangent theorem, the measure of TH is also: 4.2 cm.
What is the Two-Tangent Theorem?According to the two-tangent theorem, the length of two tangents (TG and TH) that are drawn from a circle to intersect at an external point are equal. That is, they are congruent to each other.
Thus, we are given that, TG = 4.2 cm. Therefore, based on the two-tangent theorem, the measure of TH is also: 4.2 cm.
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Michelangelo was starving for a slice of pizza. he started at -50 feet in the sewers, climbed the ladder to the street, and ran 20 feet to the pizza restaurant. how many feet did michelangelo go for pizza?
Michelangelo went 30 feet for a pizza to a pizza restaurant.
How to calculate the distance traveled for pizza?It is given that,
Michelangelo was starving for a slice of pizza. He started -50 feet in the sewer, climbed the ladder to the street, and ran 20 feet to the pizza restaurant.
So, the total feet he traveled is,
= -50 feet + 20 feet = 30 feet.
Therefore, Michelangelo went 30 feet for pizza.
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Identify the range of the function shown in the graph.
The range of a function is all possible y values that a function can take on.
In the case of the given function, the y values fluctuate between -1 and 1. Therefore, the range of the function is -1 <= y <= 1 (Option A).
Hope this helps!
Pierre found a new store where he hopes to save
money on his supplies. He bought 4 brushes and 7
tubes of paint for $32. He has another order for 6
brushes and 8 tubes of paint that will cost $43.
What is the cost of one brush? What is the cost of
one tube of paint?
Answer:
A brush: $4.50
A tube of paint: $2
Step-by-step explanation:
Let b = brushes
Let p = paint
1) Set up equations.
4b + 7p = 32
6b + 8p = 43
2) Solve the system of equations using elimination.
(4b + 7p = 32)3
(6b + 8p = 43)2
-----------------------
12b + 21p = 96
12b + 16p = 86
----------------------
5p = 10
p = 10/5
p = 2
Substitute 2 into p of any of the two equations.
4b + 7(2) = 32
4b + 14 = 32
4b = 32 - 14
4b = 18
b = 18/4
b = 4.50
Therefore, a brush costs $4.50, while a tube of paint costs $2.
Using f(x) = 2x + 7 and g(x) = x-3, find f(g(-2)).
Answer:
f(g(-2)) = -3
Step-by-step explanation:
g(-2) = -2 - 3 = -5
f(-5) = 2(-5) + 7 = -10 + 7 = -3
A cylindrical can, open at the top, is to hold 230 cm3 of liquid. find the height and radius that minimize the amount of material needed to manufacture the can. enter answer with rational exponents.
The height and the radius that minimize the material needed to manufacture the can is 4.18336 cm and 4.18337 cm respectively.
Computed using differentiation.
We assume the radius of the can be r cm, and its height to be h cm.
We are given that the can is to hold 230 cm³ of liquid, thus the volume of the can is:
V = 230,
or, πr²h = 230 {Since, the volume of a cylinder is πr²h, where r is the radius, and h is the height},
or, h = 230/(πr²) ... (i) .
We are asked to find the height and radius that minimize the amount of the material.
To calculate the amount of the material, we calculate the surface area of the can (A).
The surface area of the can = area of the base + area of the side,
or, A = πr² + 2πrh = πr(r + 2h).
Substituting h = 230/(πr²), we get:
A = πr(r + 2{230/(πr²)}),
or, A = {πr(πr³ + 460)}/πr² = πr² + 460/r.
Differentiating both sides with respect to the radius r, we get:
dA/dr = 2πr - 460/r² ...(ii)
To find the point of inflection, we equate this to zero, to get:
2πr - 460/r² = 0,
or, 2πr = 460/r²,
or, r³ = 460/2π = 73.2113,
or, r = 4.18337 cm.
To check whether the point of inflection shows the point of maximum or minimum, we differentiate (ii) with respect to the radius r, to get:
d²A/dr² = 2π + 920/r³, which is always positive when the radius r is positive.
Thus, the area is minimum when the radius r = 4.18337 cm.
Height, h = 230/(πr²) = 4.18336 cm.
Thus, the height and the radius that minimize the material needed to manufacture the can is 4.18336 cm and 4.18337 cm respectively.
Computed using differentiation.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each graph to the inequality it represents.
The graphs and their inequalities are
Graph 1 ⇒ 3x + 4y > 6Graph 2 ⇒ 2x - 7y ≥ 14Graph 3 ⇒ 3x + 4y < 6Graph 4 ⇒ 7x + 2y ≥ 14How to match the inequalities?The inequalities are given as:
2x - 7y ≤ 14
7x + 2y ≥ 14
2x - 7y ≥ 14
3x + 4y < 6
4x - 3y > 6
3x + 4y > 6
To represent the inequalities on a graph, we use the following guides:
> uses a dotted line, and the upper parts are shaded< uses a dotted line, and the lower parts are shaded≥ uses a thick line, and the upper parts are shaded≤ uses a thick line, and the lower parts are shadedUsing the above as a guide, we have:
Graph 1 ⇒ 3x + 4y > 6
Graph 2 ⇒ 2x - 7y ≥ 14
Graph 3 ⇒ 3x + 4y < 6
Graph 4 ⇒ 7x + 2y ≥ 14
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The reflexive property makes triangle XYW congruent or equal to ZWY by
a SAS
b ASA
c AAS
d SSS
Answer: D: SSS Congruency
Step-by-step explanation:
- SSS congruency stands for side-side-side congruency
- if the 3 side lengths are equal for both triangles they are equivalent
- the reflexive property states that an angle, line segment, or shape is always congruent to itself
- so the reflexive property is just saying that WY = YW, therefore creating 3 equal sides for both triangles
- so the triangles are congruent by SSS
hope this helps :)
Angle B is a complement of angle A and the measurement of angle A = 65.2°. Find the measurement of angle B
Answer:
24.8°
Step-by-step explanation:
Complementary angles sum 90°
65.2° + B° = 90°
B° = 90° - 65.2°
B° = 24.8
Angle B from the information given is 24. 8°
How to determine the angleNote that complementary angles sum up to 90°
From the information given, we have that
Angle A + Angle B = 90°
If angle A = 65. 2°
Angle B = 90 - 65. 2
Angle B = 24.8°
Thus, angle B from the information given is 24. 8°
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Ellen is currently twice as old as Maria, but in 6 years, Maria will be 2/3 as old as Ellen. How old is Ellen now?
Find the gradient of the line segment between the points (4,3) and (5,6).
[tex]\Large\maltese\underline{\textsf{A. \space What is Asked}}[/tex]
Find the gradient of the line segment between the points [tex]\bf{(4,3)\:and\:(5,6)}[/tex]
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
The formula used, here is
[tex]\bf{m=\dfrac{y2-y1}{x2-x1}[/tex]
[tex]\cline{1-2}[/tex]
Now let's put in the co-ordinates from these two points.
[tex]\bf{m=\dfrac{6-3}{5-4}}[/tex] | subtract on top & bottom
[tex]\bf{m=\dfrac{3}{1}}[/tex] | divide
[tex]\bf{m=3}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=m=3}[/tex]
[tex]\boxed{\bf{ aesthetic\not101}}[/tex]
Answer:
g=3
Step-by-step explanation:
gradient=change ofY/change of X
3-6/4-5
-3/-1 simply
gradient =3
Kenyan formula easy
Triangle RST is circumscribed about the circle below. What is the
perimeter of the triangle?
Answer:
I think the answer is B.36
Step-by-step explanation:
hope this helps if not let me know have a blessed day
SOMEONE PLEASE HELP!
a = 4, b = 7, c = 10. What is the measure of angle A to the
nearest tenth?
Answer:
17.2°
Explanations
To find angle A, use the cosine rule.
a^2 = b^2 + c^2 - 2 × a × c cos A
4^2 = 7^2 + 10^2 - 2 × 7 × 10 cos A
16 = 49+ 100 - 140 × cosA
16 = 149 - 140cosA
16- 149 = - 140cosA
-133 = - 140cosA
cosA = 133/140
cosA = 0.95
A = 17.2°
Questions in the picture
i need help with this page
The figure below is not drawn to scale. ABCD is a parallelogram, Find
LAEB and L CDE.
A
B
[tex]\angle BAD=100^{\circ}[/tex] (opposite angles in a parallelogram)
[tex]\angle EAD=80^{\circ}[/tex] (subtraction)
[tex]\angle ADE=65^{\circ}[/tex] (angles in a triangle add to 180 degrees)
[tex]\angle CDA=80^{\circ}[/tex] (adjacent angles in a parallelogram are supplementary)
[tex]\boxed{\angle CDE=15^{\circ}}[/tex] (subtraction)
[tex]\angle CED=65^{\circ}[/tex] (angles in a triangle add to 180 degrees)
[tex]\boxed{\angle AEB=80^{\circ}}[/tex] (angles on a straight line add to 180 degrees)
A young sumo wrestler decided to go on a special diet to gain weight rapidly. He gained weight at a constant rate.
The table compares the wrestler's weight (in kilograms) and the time since he started his diet (in months).
The wrestler's weight before he went on his diet is 78 kg
How to find the y-intercept?
The formula for slope is;
m = (y2 - y1)/(x2 - x1)
Thus, using two points we have;
m = (93.6 - 85.8)/(3 - 1.5)
m = 5.2
At the start of his diet, time in months = 0 months and so x = 0. Thus;
5.2 = (85.8 - y0)/(1.5 - 0)
5.2 * 1.5 = 85.8 - y0
y0 = 85.8 - (5.2 * 1.5)
y0 = 85.8 - 7.8
y0 = 78 kg
Thus, the wrestler's weight before he went on his diet is 78 kg
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Please help ill give whoever answers the best the brainliest answer :)
Answer: Quadratic
Step-by-step explanation:
I'm too lazy to explain. Trust me
(1/2 + 3/2)² + (2/3 x 1/2)³
The result of the mathematical expression given as follows: (1/2 + 3/2)² + (2/3 x 1/2)³ is 5.59 or 5⅔.
How to calculate mathematical expressions?According to this question, the following expression is given to solve: (1/2 + 3/2)² + (2/3 x 1/2)³
First, we solve the both parts as follows:
½ + 3/2 = 2⅔ + ½ = 1..16Next, we solve the exponential function as follows:
= (2)² + (1.16)³
= 4 + 1.59
= 5.59 or 5⅔
Therefore, the result of the mathematical expression given as follows: (1/2 + 3/2)² + (2/3 x 1/2)³ is 5.59 or 5⅔.
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PLEASE HELP I HAVE 45 min to SUBMIT WILL GIVE BRAINLESSLY
Answer:
Step-by-step explanation:
Using f(x) = log x, what is the x-intercept of g(x) = log (x + 4)?
X5
Answer:
a
Step-by-step explanation: