By applying definition of limits, the end behavior of the rational function f(x) = 10/(x² - 7 · x - 30) is represented for the horizontal asymptote x = 0.
What is the end behavior of a rational function
The end behavior of a rational functions is the horizontal asymptote of the rational function when x tends to ± ∞. Then, we find the end behavior by applying limits:
[tex]\lim_{x \to \pm \infty} \frac{10}{x^{2}-7\cdot x - 30}[/tex]
[tex]\lim_{n \to \infty} \frac{10}{x^{2}-7\cdot x - 30}\cdot \frac{x^{2}}{x^{2}}[/tex]
[tex]\lim_{x \to \pm \infty} \frac{\frac{10}{x^{2}} }{1 - \frac{7}{x}-\frac{30}{x^{2}}}[/tex]
[tex]\lim_{x \to \pm \infty} 0[/tex]
0
By applying definition of limits, the end behavior of the rational function f(x) = 10/(x² - 7 · x - 30) is represented for the horizontal asymptote x = 0.
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Which expression is equivalent to 14 times 14?
2 squared
2 Superscript 14
14 squared
14 Superscript 14
Answer:
[tex]14^{2}[/tex]
Step-by-step explanation:
14*14
14 is the base. We are multiplying 14 two times. Two would be the exponent
14 ^2
D
A fabric mill produces 4953 metres of fabric in a day. How much fabric will it
365 days]
produce in a year? [1 year =365 days
The fabric mill produce 1,807,845 meters of fabric in 365 days.
A fabric mill produces 4953 meters of fabric in a day.
What is simplification?operations and interpretations to function to make function simple or more understandable called simplify and the process is called simplification.
We have 4953 meter of fabric in a day.
So for 365 days
fabric = 4953 x 365
= 1,807,845
Thus, the fabric mill produce 1,807,845 meters of fabric in 365 days.
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Which exponential function has a faster rate f(x)=5^x or g(x)=(1/3)^x. How do you know?
Answer:
f(x)
Step-by-step explanation:
This question isn't to difficult, since all you need to know is: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. If the you're not quite sure why this is true, I'll try to express this in another way. [tex](\frac{a}{b})^x=\frac{a}{b}*\frac{a}{b}*\frac{a}{b}...\text{ x amount of times}[/tex], and as you may know when multiplying fractions, you simply multiply the numerators by the numerators and the denominators by the denominators, this means that you can simplify it to: [tex]\frac{a*a*a...\text{ x amount of times}}{b*b*b...\text{ x amount of times}}[/tex] this is literally what an exponent is which is why you can distribute the exponent as such: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. The next thing you need to know is that: [tex]1^x=1[/tex] for any real number. This is you can express this as: [tex]1*1*1...\text{ x amount of times} = 1[/tex], since 1 times 1 times 1, will always remain 1. You may think this will not apply for rational exponents, but it still does since: [tex]1^{\frac{a}{b}}=\sqrt[b]{1}^a[/tex], and no matter what b is, it's going to be 1. The square root of 1, is 1..., the cube root of 1 is 1.... This is because the very definition of a radical is what number times times it self index amount of times is equal to the number under the radical, and no matter how many times you multiply 1, you're going to get 1. If that's a bit confusing what I'm saying is: [tex]\sqrt[n]{b}\implies\text{?}^n=b[/tex].
Anyways hopefully you understand that, if not I'm sorry if I went a bit overboard trying to explain it. Anyways all you need to really know is that: [tex](\frac{1}{3})^x=\frac{1^x}{3^x}=\frac{1}{3^x}[/tex]. So this means as x increases, all you're really doing is increasing the denominator which is decreasing the number. The f function has an integer as a base, so the function will overall be increasing. This is not true for g(x) since as x increases the y-value decreases. So this means that f(x) has a faster rate. This is because the g(x) has a horizontal asymptote, since as x approaches infinity, g(x) approaches 0, since the denominator is increasing towards infinity. So the rate of change will be slowing down as x increases, since there is only so much the g(x) can change, since it has a horizontal asymptote. This is not true for f(x) as it has no horizontal asymptote and just goes towards infinity. So the f(x) has a faster rate.
30 points and mark brainlest
A rectangular picture has dimensions 3 inches by 2 inches. Find the dimensions of the pictures if it has to be enlarged with a scale factor of 5. Question 18 options: 15 inches × 10 inches 3 5 inches × 2 5 inches 8 inches × 7 inches 12 inches × 8 inches
The dimensions of the enlarged rectangular picture is 15 x 10 inches.
What are the dimensions of the enlarged rectangular picture ?When the dimensions of the enlarged rectangular picture is enlarged by a scale factor of 5, it means that the dimensions would be five times larger what they were initially.
New dimensions : (3 x 5) x (2 x 5)
15 x 10 inches
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Answer:
I’m just adding so you can mark brainliest
Step-by-step explanation:
Using the markings in the following image, answer the questions below:
a. Determine whether group A or group B (or both) show a pair of similar triangles or not. Tell how you know this.
b. For the group(s) with similar triangles, calculate all unknown side lengths. If possible, calculate the unknown angles. Explain your answers.
c. For the group(s) with similar triangles, calculate the scale factor. What is the relationship of the area of the original figure to the area of the translated figure? Explain.
d. For the group(s) with similar triangles, tell (roughly) what transformations would be needed to make one of the triangles carry onto the other triangle in its group.
The two triangles in group A are similar because two angles of one are congruent to two angles of the other.
How to explain the triangle?The two triangles in group A are similar because two angles of one are congruent to two angles of the other.
The two triangles in group B are not similar. The ratio of the short sides of the two triangles is 10:4 or 2.5:1, and that is the same ratio as the two sides 24 and 9.6.
However, using the fact that an angle bisector in a triangle divides the opposite side into two segments in the same ratio as the lengths of the two sides that include the angle, the length of the third side of the left triangle can be found to be about 25.12; and 9.25 times 2.5 is not close to 25.12.
b. In group A, the third side of the first triangle, by the Pythagorean Theorem, is sqrt(306).
The scale factor between the two triangles is 3:5, so the length of the third side of the second triangle is 15*(5/3) = 25.
In both triangles, the third angle measure is 31 degrees, since the sum of the three angles is 180.
c. The scale factor, again, is 3:5 which means the ratio of the areas of the two triangles is 3²:5² or 9:25.
d. The first triangle can be carried onto the second with the following transformations:
(1) dilate by a factor of 5/3 to make it the same size;
(2) rotate 90 degrees counterclockwise;
(3) translate so the hypotenuses of the two triangles are the same line segment; and
(4) reflect on the hypotenuse.
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A car travels 24 km between 9:30 am and 10:15 am. What is its average speed in km/h?
Answer:
32 km / hr
Step-by-step explanation:
930 to 1015 is 45 min = .75 hr
24 km / .75 hr = 32 km /hr
The triathletes were offered water as they rode by the volunteer station. The volunteers handed them cones with the dimensions shown. If each triathlete sloshed 1/3 of the water out before they drank it, how many cubic cm of water did they slosh out? Round to the nearest tenth.
Height 7cm
radius 3.5cm
The slosh-out water is 29.9 cubic cm.
What is volume?Volume is defined as the space covered by any solid body in the three-dimensional plane. For the cylinder, the parameters are height and radius.
The volume of the cone is calculated as:-
V = ⅓r^2h
V = ⅓r^2h
V = ⅓(3.5)^2(7)
V = ⅓(12.25)(7)
V = 1/3(85.75)
V = 85.75/3
1/3 cup of water is sloshed out:
Sloshed water = (85.75/3 )/3
Sloshed water = 29.9 cubic cm
Therefore, the sloshed-out water is 29.9 cubic cm.
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19. What is the coordinate for the vertex of the function f(x)=-16x² + 64x?
Answer:
vertex = (2, 64 )
Step-by-step explanation:
given a parabola in standard form
f(x) = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
f(x) = - 16x² + 64x ← is in standard form
with a = - 16, b = 64, c = 0 , then
x = - [tex]\frac{64}{-32}[/tex] = 2
substitute x = 2 into f(x) for corresponding y- coordinate
f(2) = - 16(2)² + 64(2) = - 16(4) + 128 = - 64 + 128 = 64
vertex = (2, 64 )
In circle O, R_T and S_U are diameters
Applying the vertical angles theorem, the measure of VU is determined as: 64°.
What is the Vertical Angles Theorem?If two angles lie directly opposite each other, they are vertical nagles and are therefore equal.
13x = 15x - 8 [vertical angles theorem]
13x - 15x = - 8
-2x = -8
x = 4
Let y represent m(VU). Since m(RV) = m(VU), therefore:
13x + 2y = 180 [angles on a straight line]
Plug in the value of x
13(4) + 2y = 180
52 + 2y = 180
2y = 180 - 52
2y = 128
y = 64°
m(VU) = 64°.
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Suppose that x and y vary inversely, and x = 12 when y = 8 . Write the function that models the inverse variation.
Answer:
[tex]y=\frac{96}{x}[/tex]
Step-by-step explanation:
So when x and y, vary inversely, it means that the product of x and y will remain constant such that: [tex]xy=c[/tex]. This means that the function can be defined as [tex]y=\frac{c}{x}[/tex] by dividing both sides by x. In this case x=12, and y=8, this means the constant is equal to 12 * 8 which is 96. So we have the equation: [tex]xy = 96[/tex], which can be defined as [tex]y=\frac{96}{x}[/tex]
Select the equivalent expression. 2^-4=
Choose 1 answer
a)1/2^4
b)-2^4
c)(-2)^4
Answer: A 1/2 ^4
Step-by-step explanation:
Answer:
a)1/2^4
Step-by-step explanation:
First solve 2^-4.
Use negative power rule: x^-a = 1/xa
⇒ 1/2^4
Simplify 2^4 to 16
⇒ 1/16
Just evaluate the other options.
The first one is correct.
Here's why:
⇒ Simplify 2^4 to 16.
⇒ 1/16
They have the same steps, therefore making Option A correct.
Note: This is the longer way, there is a easier way of dealing with these types of problems. Example: Without using a calculator problem.
What is the inverse of function ??
f(x) = 64x³ - 1
Answer:
The inverse of the function f(x) = 64x³ - 1 is [tex]\frac{\sqrt[3]{x+1}}{4}[/tex]
Step-by-step explanation:
First replace x with y.
[tex]x=64y^3-1[/tex]
Then solve for y.
[tex]y^3=\frac{x+1}{64}[/tex]
Cube root both sides.
[tex]y=\frac{\sqrt[3]{x+1}}{4}[/tex]
Hence, the inverse is [tex]\frac{\sqrt[3]{x+1}}{4}[/tex]
You buy 12 packages of discounted socks for a total cost of $85.50, which includes a 5% discount.
Before the discount, how much did a single package of socks cost?
a.)
$7.50
b.)
$4.75
c.)
$6.78
d.)
$10.68
Answer:
a) $7.50
Step-by-step explanation:
The total cost of $85.50 includes a 5% discount, so 95% of what price is $85.50?
[tex].95x = 85.50[/tex]
[tex]x = 90[/tex]
So the original price is $90. Divide this by 12, obtaining $7.50.
Answer:
a)$7.5
Step-by-step explanation:
Solution:
Let X represents socks
Given,
Selling price (SP) of 12x=$85.50
Discount precent (d%)=5%
So,
SP=(100-d)% of MP. [this formula really exist believe it or not]
85.50= (100-5)/100 ×MP
or, 85.50×100 =95×MP
or, 8550/95=MP
So,MP=$90
Now At last ,
cost of 1 shocks before discount is 90/12
which is $7.50 ans√
What effect does it have when there are exceptions to the overall trend in a relationship between two variables?
Option 3. The effect that it has when there are exceptions to the overall trend between two variable is that It is irrelevant to the relationship.
What is a trend between two variables?This is used in statistics to show that there is the existence of two variables that are positively correlated.
These two variables would then have a positive slope trend line. Hence the answer to the question is option 3.
Complete questionWhat effect does it have when there are exceptions to the overall trend in a relationship between two variables?
O It increases the relationship
O It decreases the relationship
O It is irrelevant to the relationship.
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In your opinion, which is the best and simplest way to factor polynomials (including quadratics)? Explain why you chose this method compared to other methods. Are there some exceptions to this, maybe a polynomial that might factor better with another method?
The simplest way to factor polynomials is to use the greatest common factor.
How to illustrate the polynomial?It should be noted that the polynomial simply means the expression of more than two algebraic terms.
In this case, the simplest way to factor polynomials is to use the greatest common factor. This simply had to do with the largest factor that the numbers share.
Other methods that can be utilized include the grouping method, the sum of the difference in cubes and in two squares.
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ABC is a triangle. ACD is an isosceles triangle. Find ACB and ABC.
Answer:
∠ ACB = 128° and ∠ABC = 32°
Step-by-step explanation:
∠ ADC = ∠ CAD (base angles theorem)
∠ ACD = 82° (angles in a triangle add to 180°)
∠ ACB = 128° (angles around a point add to 360°)
∠ ABC = 32° (angles in a triangle add to 180°)
Michael is renting a bicycle for $12 per hour.
Which of the following is equivalent to this rate?
a.)
20 cents per minute
b.)
14 cents per minute
c.)
5 cents per minute
d.)
7 cents per minute
Answer:
20 cents/minute
Step-by-step explanation:
We need to convert both units
1 dollar is 100 cents
12 dollars * 100 cents/1 dollar = 1200 cents
1 hour = 60 minutes
1 hours * 60 minutes / 1 hour = 60 minutes
12 dollars/ hour = 1200 cents / 60 minutes
Simplify
20 cents/minute
Answer: A. 20 cents per minute
Unit rate given: $12 per hour
Conversion:
$1 = 100 cents
$12 = 1200 cents
1 hour = 60 minutes
Solving steps:
amount in cents/time in minutes = 1200/60 = 20 cents per minute
here is the histogram of a data distribution. all class widths are 1. which of the following is the closest to the mean of this ditribution
A circus is composed of acrobats, ballerinas, clowns, and dogs. The number of acrobats and ballerinas, minus the number of clowns, is one fewer than the number of dogs. Twice the combined number of acrobats and ballerinas is five more than three times the number of clowns. If the number of dogs is one more than the number of clowns, how many people and animals belong to the circus
If we make appropriate equation then we can find that there are 21 people and animals belong to the circus.
Given The number of acrobats and ballerinas, minus the number of clowns, is one fewer than the number of dogs. Double the combined number of acrobats and ballerinas is five more than three times the number of clowns.
We have to find total people and animals belong to the circus.
An equation is relationship between variables that are expressed in equal to form. It is solved to find the variables in equal to form Equations of two variables look like ax+ by=c.
let the number of acrobats be x, ballerinas be y, clowns be z, clowns be u.
According to given information in question the equations are:
x+ y-z=u-1-----------------------1
2(x+ y)=3z+5-------------------2
u=z+1----------------------------3
Put the value of u from 3 in 1
x+y- z=z+1-1
x+y-2z=0
from 2
z=2x+2y-5/3
put the value of z in x+y-2z=0
x+y-2(2x+2y-5/3)=0
-x-y+10=0
x+ y=10-------------------------4
put put the value of x+y=10 in 1
10-z=u-1
u+z=11-----------------------------5
solving 3
u-z=1------------------------6
Now add 5&6
u+z+u-z=11+12
2u=12
u=6
Put the value of u in 6
6-z=1
z=5
From above we get x+y=10, u=6, z=5
Add all three we get the total number of people and animals belong to circus.
x+y+u+z=10+6+5
=21
Hence there are total 21 people and animals belong to the circus.
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One can convert temperature from fahrenheit into newton using the formula . what is the temperature in fahrenheit corresponding to n degrees newton?
If r= 1 and 0=3.14/4, what is the approximate arc length?
=
A. 1.047 units
B. 0.524 units
C. 0.785 units
D. 1.571 units
The approximate arc length from the task content is; Choice C; 0.785 units.
What is the approximate arc length?Since the arc length is given mathematically by the formular;
Arc length = (A/360) × 2πr
Hence, since A = π/4 = 18/4 = 45.
Hence; Arc Length = (45/360) × 2 × 3.14 ×1
Arc length = 6.28/8 = 0.785 units.
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A
Ф
Ф
center of triangle ABC.
30° R
15
в
What is m/QOB?
0000
30°
60°
75°
90°
Answer:
75757575757575757575757575757575757575757575ext → Post Test: Systems of Linear Equations and Inequalities
1
Use the drawing tool(s) to form the correct answers on the provided graph.
1
Graph the system of equations given below on the provided graph.
2x - 3y = -18
3x + y = -5
Then, use the Mark Feature tool to plot the solution to the system.
The way to construct the equation in a graph is illustrated.
How to illustrate the information?Converting the equation in slope-intercept form
2x-3y= -18
-3y= -2x-18
-3y= -(2x+18)
3y=2x+18
y=(2x+18)/3
And for equation 2
y= -5-3x
The points can be calculated by putting negative and positive values of x in both equations.
The graph is attached as a picture.
As we can see from the graph that two lines intersect at (-3,4) so it is the solution of the given system of linear equations.
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Multiply:
-9w(w + 10)
asap answer plsss
Answer:
-9w^2-90w
Step-by-step explanation:
You just use the distributive property and watch the negatives and positives.
[tex]\huge\boxed{-9w^2-90w}[/tex]
Distribute [tex]-9w[/tex] to both [tex]w[/tex] and [tex]10[/tex] as shown in the attached image. Then, just simplify the terms with multiplication.
[tex](-9w)\cdot w+(-9w)\cdot10\\\boxed{-9w^2-90w}[/tex]
Alexandra needs to reshingle her roof. She leans a ladder against the the wall of the house so that the top of the ladder is 8 feet above the ground. The bottom of the ladder is 5 feet from the base of the wall. Find the angle formed between the ladder and the house. Round the answer to the nearest whole degree. A. B. C. D. Please select the best answer from the choices provided A B C D
If the top is 8 feet above the ground and ladder is 5 feet away from bottom of wall then the angle between ladder and house is 58°.
Given top is 8 feet above the ground, ladder is 5 feet away from bottom of the wall.
Trigonometric ratios are the ratios of the sides of a right angled triangle. sin is the ratio of perpendicular and hypotenuse , cos is the ratio of base and hypotenuse, tan is the ratio of perpendicular and base, cosec is the ratio of hypotenuse and perpendicular, sec is the ratio of hypotenuse and base, cot is the ratio of base and perpendicular.
Here we use tan d where d is the angle between ladder and wall of the house.
tan d= P/B
tan d=8/5
tan d=1.6
[tex]d=tan^{-1} 1.6[/tex]
d=57.99
After rounding off it will be 58°.
Hence the angle between ladder and house is 58°.
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Complete the input-output table for linear function y=3x
The input and output table for the linear function y = 3x is (-2, -6), (-1, -3), (0, 0), (1, 3) and (2, 6).
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the linear function y = 3x:
When x = -2; y = 3(-2) = -6
When x = -1; y = 3(-1) = -3
When x = 0; y = 3(0) = 0
When x = 1; y = 3(1) = 3
When x = 2; y = 3(2) = 6
The input and output table for the linear function y = 3x is (-2, -6), (-1, -3), (0, 0), (1, 3) and (2, 6).
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Answer: ( -6/ 6/ 9
Step-by-step explanation:
Circle Q is centered at the origin. Is point (-5, 0) on the circle? Justify your answer
Answer: D
Step-by-step explanation: I just took the quiz
Which of the following could represent the interval −4 ≤ x ≤ 6?
Answer:
Step-by-step explanation:
-4 [tex]\leq[/tex] x [tex]\leq[/tex] 6
x = {-4,-3,-2,-1,0,1,2,3,4,5,6}
Hope I helped...
If a ⊥ y and x ∥ y, then _____
Answer:
x⊥a
Step-by-step explanation:
If we draw this out, we see that x is perpendicular to a as well.
For 7,440 blank shares could have been bought ?
Answer:
$2,000
Step-by-step explanation:
7,440/3.72