Considering the given function and the asymptote concept, we have that:
The vertical asymptote is of x = 25.The horizontal asymptote is of y = 5.The end behavior is that as [tex]x \rightarrow \infty, f(x) \rightarrow 5[/tex].What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity. Hence it also gives the end behavior of the function.In this problem, the function is:
[tex]f(x) = \frac{5x}{x - 25}[/tex].
The vertical asymptote is found as follows:
x - 25 = 0 -> x = 25.
The horizontal asymptote is found as follows:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = \lim_{x \rightarrow \infty} 5 = 5[/tex].
Hence the end behavior is that as [tex]x \rightarrow \infty, f(x) \rightarrow 5[/tex].
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please help me I'm in a rush
Answer:
78 m²
Step-by-step explanation:
V = bh
V = 13 m × 6 m
V = 78 m²
Plug x back in. What is the measurement of (8x - 20) degrees
The complement of y is 110 - 8x degrees.
What are complementary angles?Complementary angles are angles that add up to 90 degrees.
Therefore,
y = 8x - 20
The complement of y can be found as follows;
complement of y = 90 - (8x - 20)
complement of y = 90 - 8x + 20
complement of y = 110 - 8x
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Whats the easiest way to solve a modulu problem. For example we can use 2^100/3. Whats the easiest way to find the remainder? Without using shortcuts that only work with specific numbers.
The easiest way to solve a modulu problem is by
Start by taking the initial number (before carrying our the modulo operation). Then select the divisor. Then one have to divide one number by the other and then round down.Then Multiply the divisor using the quotient. Then subtract the above number from one's initial number (dividend).The number gotten is the outcome of the modulo operation.2^100/3
=3√2^100
=3√2^99×2
=2^33×3√2
The [tex]\sqrt{2}[/tex] is the reminder.
What is the easiest way to find remainders?The easiest way to find the remainder that only work with specific numbers is that this can be done when one solve the division by the use of a calculator by:
First if you answer is in decimal form, you have to subtract the whole number and later multiply the decimal value that is said to be left by the divisor of the original problem. The outcome is your remainder.
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2. Simplify the expression. (x3)(x7)²
1
x18
x14
x126
Step-by-step explanation:
[tex] = ( {x}^{3} ) { ({x}^{7} )}^{2} [/tex]
[tex] = {x}^{3} \times {x}^{7 \times 2} [/tex]
[tex] = {x}^{3} \times {x}^{14} [/tex]
[tex] = {x}^{3 + 14} [/tex]
[tex] = {x}^{17} [/tex]
______Is obtained by dividing the population into groups and selecting all individuals from within a random sample of the groups.
20% of the cross-country runners in
a school team weigh between 60 kg
and 70 kg. If 4% of the school of 1125 students are in the cross-country team, how many students in the team weigh between 60kg and 70kg ?
Answer:
9 students
Step-by-step explanation:
First find the amount of cross-country team students, 4% * 1125 = 45
Then 20% * 45 = 9, so 9 students in the team weigh between 60 and 70 kilos.
Find the missing side lengths.
AB=
BC=
Answer:
Step-by-step explanation:
What are the solutions of this quadratic equation?
x^2 = 16x - 65
substitute the values of a and b to complete the solutions.
x = a + bi
x = a - bi
answers:
x = 8 + i
x = 8 - i
i hope this helps.
The solutions for the given quadratic equation are:
[tex]x = 8 \pm i[/tex]
How to find the solutions of the quadratic equation?
Here we have the quadratic equation:
[tex]x^2 = 16x - 65[/tex]
We can rewrite it as:
[tex]x^2 - 16x + 65 = 0[/tex]
Using Bhaskara's formulas, we get:
[tex]x = \frac{-(-16) \pm \sqrt{(-16)^2 - 4*65} }{2} \\\\x = \frac{16 \pm \sqrt{(-4)} }{2}[/tex]
Now, remember that:
[tex]\sqrt{-1} = i[/tex]
Then we can rewrite:
[tex]x = \frac{16 \pm \sqrt{-1} *\sqrt{4} }{2}\\\\x = 8 \pm i[/tex]
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7. Which transformation of (x, y) is a dilation? (TEKS G.3.A)
F (3x, y)
G (-y, x)
H (3x, 3y)
J (x + 3, y + 3)
Answer:
H (3x,3y)
Step-by-step explanation:
Dilation is a transformation when figure is enlarged or reduced by scale factor. During dilation, every point of preimage is dilated by scale factor, so it means each coordinate of that point must be multiplied by scale factor.
Hence, H(3x,3y) can be the result of dilation with scale factor of 3.
70 more points ez ez ez
[tex]y = 3x + 6 \\ switch \: y \: and \: x[/tex]
[tex]x = 3y + 6 \\ solve \: for \: y \\ x - 6 = 3y \\ y = \frac{x - 6}{3} [/tex]
A is the answerAnswer:
free tokens or something
Step-by-step explanaon
um i do not know so um bye?
Add the following polynomials, then place the answer in the proper location on the grid.
- 4.1x^2 + 0.9x - 9.8
1.7x^2 - 2.4x - 1.6
Answer: - 2.4x^2 - 1.5x - 11.4
Step-by-step explanation:
- 4.1x^2 + 0.9x - 9.81.7x^2 - 2.4x - 1.6 = - 2.4x^2 - 1.5x - 11.4
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 6^2+10^2<10^2
Step-by-step explanation:
The given triangle whoe sides are 6cm, 10cm, and 12cm is an obtuse triangle and it can be determine by using pythagorian theorem, i.e. 6^2 + 10^2 < 12^2.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a^2 + b^2 = c^2.
here, we have,
Given :
The side lengths of a triangle are: 6cm, 10cm, and 12cm.
Pythagorian theorem can be used to find out that the triangles are acute or obtuse. According to pythagorian theorem, the sum of square of shorter side is equal to the square of the third side of the right angle triangle.
According to pythagorian theorem:.
That is, H^2 = P^2 + B^2.
There are some rules to find the triangle is obtuse or acute:
If H^2 > P^2 + B^2, than the triangle is obtuse.
If H^2 < P^2 + B^2, than the triangle is acute.
Now, applying pythagorian theorem:
we get,
6^2 + 10^2 = 12^2
136 = 144
Here, it is clearly observe that 136 < 144, i.e. 6^2 + 10^2 < 12^2 therefore, the triangle is obtuse.
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At the amusement park, Jack bought child and adult tickets costing $1.50
and $2.50, respectively. He bought a total of 9 tickets and paid $16.50.
How many of each kind of ticket did he buy?
La ecuación h(x) =23 es lineal?
Domanin and range...
GEOMETRY)
In the accompanying diagram of circle O, the m angle AOB=36^o. What is the m angle ACB ?
Answers…
A. 9^o
B. 36^o
C. 72^o
D. 18^o
(Picture is below) Thank you!
Answer:
SOLUTION :-
There is theorem/proof that tells that in these types of figure the other angle is double of the previous one
Means , the required angle will be ( 36 x 2 ) i.e. 72°.
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How does the image triangle compare to the pre-image triangle?
A triangle undergoes a sequence of transformations.
First, the triangle is dilated by a scale factor of 1/3 about the origin. Then the triangle is reflected over the x-axis. Finally, the triangle is translated left 3 units and up 2 units.
r
A model car racetrack is formed by two semicircles as shown below.
9 cm
Find the perimeter of the entire figure.
Use T = = 3.14
2 cm
17
The diameter of the inner semicircles is 9 cm.
The width between the outer and inner semicircles is 2 cm.
>
The perimeter of the entire figure is 62.8 cm.
Given, that the diameter of the inner semicircles is 9 cm and the width between the outer and inner semicircles is 2 cm.
The radius of the inner semicircle =4.5 cm and the radius of outer semicircle =5.5 cm (∵Diameter=9+2=11 cm)
We need to find the perimeter of the entire figure.
What is the perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.
We know that, the circumference of a semicircle=πr and the circumference of two semicircles=2πr
Thus, the circumference of inner semicircles=2×3.14×4.5=28.26 cm
The circumference of outer semicircles=2×3.14×5.5=34.54 cm
The perimeter of the entire figure=28.26+34.54=62.8 cm
Therefore, the perimeter of the entire figure is 62.8 cm.
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The perimeter of whole path is 12.56 cm
What is Perimeter?Perimeter is the distance around the edge of a shape.
r1= 4.5cm, r2= 6.5cm
Perimeter of semicircle 1,
=πr1
= 3. 14 * 4.5
= 14.13 cm
Perimeter of semicircle 2
=πr2
= 3. 14 * 6.5
= 20.41 cm
Perimeter of path = 20.41 - 14.13 =6.28 cm
Perimeter of whole path = 2 * 6.28 =12.56
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The layout of a playground uses the scale 1:50. If the dimensions of the playground in the layout are given by 180 cm x 240 cm, what is the actual area of the playground in square meters?
The area of the playground of dimensions 18 and 240is 432 [tex]m^{2}[/tex].
Given If the dimensions of the playground in the layout are given by 180 cm x 240 cm.
The area of rectangle is length *breadth.
The given playground is in the shape of rectangle because there are two sides given and both the sides are different. In a rectangle length of opposite side found to be equal and each side form an angle of 90 degree.
Area=length*breadth
=180*240
=43200 [tex]cm^{2}[/tex]
We have to convert in meters so we have to divide by 100.
Area=43200 [tex]cm^{2}[/tex]
=43200/100
=432 [tex]m^{2}[/tex]
Hence the area of playground having dimensions 180 cm and 240 cm is 432[tex]m^{2}[/tex].
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The oven temperature was at 325325325 degrees because my mom just finished baking a pie. i increased the temperature 757575 degrees so i could bake a pizza. after the pizza was cooked, i turned off the oven. the oven cooled to the room temperature of 686868 degrees.
The amount of the temperature decrease will be 332 °C.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The oven temperature was at 325 degrees because my mom just finished baking a pie.
I increased the temperature, 75 degrees, so I could bake a pizza.
Then the temperature will be
⇒ 325 °C + 75 °C
⇒ 400 °C
After the pizza was cooked, I turned off the oven.
The oven cooled to the room temperature of 68 degrees.
Then the amount of the temperature decrease will be
⇒ 400 °C – 68 °C
⇒ 332 °C
The remaining question is given below.
How much did the temperature decrease?
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Isosceles triangle ABC contains angle bisectors segment BF, segment AD, and segment CE that intersect at X.
triangle ABC with diagonals BF, AD, and EC that intersect at point X
If segment BA is congruent to segment BC and m∠BCA = 46°, what is m∠CXA?
46°
67°
115°
134°
Answer:
115
Step-by-step explanation:
this app wont be with you forever
Part 4: model a real world problem using an ellipse
An artist wants to make an elliptical sign out of a rectangular piece of wood. The wood piece has a length
of 60 inches and a width of 40 inches. The artist wants to make the largest elliptical piece possible from
the wood.
a) Write the equation of the ellipse by placing the center at the origin of the coordinate plane and making
the x-axis the major axis. (3 points)
PLEASE ANSWER ALL AND GRAPH
a. The equation of the ellipse is x²/900 + y²/400 = 1
b. the foci of the ellipse are at (±10√5,0)
c. Find the graph in the attachment
How to find the equation of the ellipse?Since the ellipse is made from a block of wood and centered at the origin, and x- axis major axis.
So, the equation of an ellipse with center at origin and x - axis major axis is
x²/a² + y²/b² = 1 where
2a = length of major axis 2b = length of minor axis anda > bSince the rectangular piece of wood has a length of 60 inches and a width of 40 inches.
The length of the rectangle equals the length of the major axis
So, 2a = 60
a = 60/2
= 30
Also, the width of the rectangle equals the length of the minor axis
So, 2b = 40
b = 40/2
= 20
a. The equation of the ellipseSo, substituting a and b into the equation of the ellipse, we have
x²/a² + y²/b² = 1
x²/30² + y²/20² = 1
x²/900 + y²/400 = 1
So, the equation of the ellipse is x²/900 + y²/400 = 1
b. The foci of the ellipse
The foci of the ellipse are at (±c,0) where c² = a² - b²
= 30² - 20²
= 900 - 400
= 500
c = ±√500
c = ±10√5
So, the foci of the ellipse are at (±10√5,0)
c. Find the graph in the attachment
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Stephen has made a 91, 96, and 95 on the first three quizzes this six weeks. If he makes the same score on the last two quizzes, what grade does he need to make on each quiz to have a quiz average of EXACTLY 94 this grading period?
Answer:
A 94
Step-by-step explanation:
If we take the mean of 91, 96, and 95, we find that it is equal to 94. Thus, if he scores a 94 on his last two quizzes, his average will remain a 94.
Please help. I am so confused.
The fourth proportional is found by applying the formula
The product of extremes = The product of means.
The fourth proportional is equal to bc/a and st/r
Let the fourth proportional be x then this can be written as
a:b::c:x
Applying the formula of product of extremes
ax= bc
or
x= bc/a
The fourth proportional can be obtained by multiplying the variables bc and dividing by a
Similarly
Let the fourth proportional be y then this can be written as
r:s::t:y
Applying the formula of product of extremes
ry= st
or
y= st/r
The fourth proportional can be obtained by multiplying the variables st and dividing by r
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Using desmos
A. Locate, plot, and label on your graph where the pH value is 0.1
B. Locate, plot, and label on your graph where the pH value is 1.
The attached graph represents the location of the pH values 0 and 1
How to plot the points?The given parameters are:
pH value 0 = (1, 0)
pH value 1 = (0.1, 1)
This means that we plot a point at the coordinate (1, 0) and another point at the coordinate (0.1, 1).
See attachment for the graph
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Complete question
The pH value is 0 at (1, 0) and 1 at (0.1, 1).
Using desmos
A. Locate, plot, and label on your graph where the pH value is 0.1
B. Locate, plot, and label on your graph where the pH value is 1.
the sum of a number and 10
Answer:
x+10
Step-by-step explanation:
x is any number and sum means addition, so x(number) +(sum) 10(10)
Dr. Benton just got his PhD, and he wants to print copies of his thesis in hardcover book format. He could use Middletown Printing, paying a setup fee of $39 and $3 for every book printed. Alternately, he could go through Oxford University, paying an up-front fee of $35 and $5 per book. It turns out that, given the number of books Dr. Benton wants to print, the two options cost the same amount. How many books is that? What is the amount?
A rectangular yard measures 8m x 6m. What happens to the area if each dimension is doubled?
Answer: 192
Step-by-step explanation:
2×8=16
2×6=12
17×12=192
So, the answer is 192.
On babylonian tablet ybc 4652, a problem is given that translates to this equation: x x plus startfraction x over 7 endfraction plus startfraction 1 over 11 endfraction left-parenthesis x plus startfraction x over 7 endfraction right-parenthesis equals 60.(x ) = 60 what is the solution to the equation? x = 48.125 x = 52.5 x = 60.125 x = 77
The correct option is (A). The solution of the equation is x=48.125.
Given an equation [tex]x+\frac{x}{7}+\frac{1}{11}\left(x+\frac{x}{7}\right)=60[/tex].
A statement that uses the equal sign to show that two expressions have the same value is called an equation. The equation is represented as ax+by=c.
Firstly, we will apply the distributive property to the given equation a×(b+c)=ab+ac, we get
[tex]x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60[/tex]
Now, we will simplify the right-hand side equation by taking LCM, we get
[tex]\begin{aligned}\frac{77x+11x+7x+x}{77}&=60\\ \frac{96x}{77}&=60\end[/tex]
Further, we will multiply both sides with 77, we get
77×(96x/77)=77×60
96x=4620
Then, we will divide both sides with 96, we get
96x/96=4620/96
x=48.125
Hence, the solution of the given equation [tex]x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60[/tex] is x=48.125.
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Answer:
The correct option is (A). The solution of the equation is x=48.125.
Given an equation .
A statement that uses the equal sign to show that two expressions have the same value is called an equation. The equation is represented as ax+by=c.
Firstly, we will apply the distributive property to the given equation a×(b+c)=ab+ac, we get
Now, we will simplify the right-hand side equation by taking LCM, we get
Further, we will multiply both sides with 77, we get
77×(96x/77)=77×60
96x=4620
Then, we will divide both sides with 96, we get
96x/96=4620/96
x=48.125
Hence, the solution of the given equation is x=48.125.
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Step-by-step explanation:
What are the domain and range of the function (x)=3/4x+5?
O domain: (-00,00)
range: (-00,00)
3
O domain:
range: (-∞0,5)
domain:
range: (5,00)
O domain:
range: (5,00)
Answer: Option (1)
Step-by-step explanation:
The domain and range of all linear functions is the set of real numbers.
The domain and range of the function is
Domain = (-∞, ∞) and Range = (-∞, ∞)
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = ( 3/4 )x + 5
The domain of the function is the set of all possible input values for x, which in this case is all real numbers, since there are no restrictions on the value of x that can be plugged into the function. Therefore, the domain of the function is:
Domain = (-∞, ∞)
The range of the function is the set of all possible output values that the function can produce. Since the function is a linear function of the form y = mx + b, where m is the slope and b is the y-intercept, we know that the range of the function is all real numbers, since a line can take on any y-value.
Range = (-∞, ∞)
Hence , the domain and range are set of all real numbers
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