Answer:
The function [tex]f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}[/tex] has a zero: [tex]x = 2[/tex], and two poles: [tex]x = 0[/tex] and [tex]x = 5[/tex].
Step-by-step explanation:
Let be [tex]f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}[/tex] a rational function armed with polynomial function. We proceed to factor the expression to the find the zeros and poles of the rational function:
1) [tex]f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}[/tex] Given
2) [tex]f(x) = \frac{(x + 2)\cdot (x-2)}{x\cdot (x^{2}-3\cdot x -10)}[/tex] [tex]a^{2} - b^{2} = (a + b)\cdot (a - b)[/tex]/Associative, commutative and distributive properties.
3) [tex]f(x) = \frac{(x+2)\cdot (x-2)}{x\cdot (x-5)\cdot (x+2)}[/tex] [tex]x^{2} -(a+b)\cdot x + a\cdot b = (x-a)\cdot (x-b)[/tex]
4) [tex]f(x) = \frac{x-2}{x\cdot (x-5)}[/tex] Commutative property/Existence of multiplicative inverse/Modulative property/Result
The function [tex]f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}[/tex] has a zero: [tex]x = 2[/tex], and two poles: [tex]x = 0[/tex] and [tex]x = 5[/tex].
The rectangle below has an area of x2 - 16 square meters and a width of x + 4 meters.
What expression represents the length of the rectangle?
x +4
Length
x2 - 16
Length
meters
Answer:
Length = x - 4 meters
Step-by-step explanation:
Area of a rectangle = length × width
Area of a rectangle = x² - 16
width of the rectangle = x + 4 meters.
Length of the rectangle = ?
Recall:
Difference of two perfect square x² - 16 = (x + 4)(x - 4)
Area of a rectangle = length × width
(x + 4)(x - 4) = length * x + 4
Length = (x + 4)(x - 4) ÷ x + 4
Length = x - 4 meters
Pls help I’ll give crown
Answer:
B
Step-by-step explanation:
because area of prism = L×W×H
so
[tex] \frac{3}{4} \times \frac{5}{2} \times \frac{5}{4} [/tex]
answer is 75/32
hope this make sense:)
Answer:
Hi there uwu The answer is 75/32, also explained by the other answerer!
Step-by-step explanation:
Can U pls help with this number in the sequence
Answer:
First one:
1², 2², 3² and so on (Square of 1,2,3,4,5,6,7.....)
Second one:
2, 13, 26, 41...
add 11, add 13, add 15 (add increasing odd numbers, beginning from 11)
Third one:
4, 14, 29, 49
+10, +15, +20 and so on (add the multiple of 5,beginning from 10)
Fourth one:
1, 8, 27, 64
1³, 2³, 3³, 4³ and so on(cube of 1,2,3,4,5,6,7.....)
Brainliest please
What’s is the answer for
5x + 15=
What is x equivalent to?
if the angles (4x+4) and 6x-4 are supplement Ary angles find value of x plzz helppp
Angles (4x + 4°) and (6x - 4°) are supplementary.
That is :
[tex](4x + 4°) + (6x - 4°) = 180°[/tex]Solution :[tex]\hookrightarrow \: 4x + 4 \degree + 6x -4 \degree = 180 \degree[/tex]
[tex]\hookrightarrow10x = 180 \degree[/tex]
[tex]\hookrightarrow x = 18 \degree[/tex]
__________________________
[tex] \mathrm{✌TeeNForeveR✌}[/tex]
The value of a boat is depreciating at a rate of 9% per year. In 2006,
the boat was worth $17,800. Find the worth of the boat in 2013.
Write an exponential decay function for this situation. Graph the
function and state its domain and range. What does the y-intercept
represent in the context of the problem?
Answer:
Hello yes indeed I am here now vote me brainliest.
Step-by-step explanation:
Why you ask? well first I want it even though I did not do anything to help him/her even though, it is funny. :)
A baker uses 20 cups of flour to make 4 loves of bread. Use this to solve the question in the picture!
Answer:
60 cups of flour
Step-by-step explanation:
Since it takes 20 cups of flour for 4 loves of bread this means we're going to need to multiply 20x3=60
need help again still struggling
Answer:
0.111111...
Step-by-step explanation:
Hi,
this function is stating that for any x the f is 9(3)^x.
SO if x was -4 it would be 9(3)^-4
Following order of operations we calculate the exponent first.
the answer is 0.1111111...
Can anybody help me with this one ??
Which is an equation of a direct proportion? CLEAR CHECK y=8x y=12x+4 y=12x y=4x−4
Answer:
[tex]y=8x, \\y=12x[/tex]
Step-by-step explanation:
Proportional functions can be written as [tex]y=kx[/tex], where [tex]k[/tex] is some constant of proportional. Since directly proportional functions always pass through the origin, the y-intercept must be 0 (no additional number before or after [tex]x[/tex] term). The only answers that fit this format are:
[tex]\rightarrow \boxed{y=8x}\\\rightarrow \boxed{y=12x}[/tex]
Answer: Y=8x
Step-by-step explanation:
Which graph represents an exponential function?
On a coordinate plane, a curve decreases rapidly and then levels out.
On a coordinate plane, a curve decreases, changes directions, and then decreases again.
Answer:
A
Step-by-step explanation:
A
Choose the function whose graph is given by:
+1
2
x
+-1
- -2
-4
O
A. y= 4sin(x+1) - 2
B.y= 6sin(x+1) - 2
c. y= 4cos(x- 1) +2
D. y= 4sin(x-1) - 2
Your answer would be y=4sin(x+1)-2. That would be A.
The required function is y = 3 sin (x -2) + 1.
What is Function?A relation between a collection of inputs and outputs is known as a function.
A mathematical phrase, rule, or legislation that establishes the link between an independent variable and a dependant variable (the dependent variable).
From the graph that is provided to us we observe that,
when x=2
then f(x)=1
Here, from the function y = 3 sin (x -2) + 1
So, when x=2
we get: y=1
Also, all the other points are satisfied.
Learn more about Function here:
https://brainly.com/question/12801690
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a) Write down the exact value of tan 60' b) Find the value of h in this triangle, h= c) Write down the exact area of this triangle, h 60° 43
Step-by-step explanation:
maybe this can help you with your problem
a) The exact value of tan 60 degree is [tex]\sqrt{3}[/tex].
b) The value of h in the given triangle is √3.
c) The area of the given triangle is 24[tex]\sqrt{3}[/tex].
What is tangent of an angle?The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
What is the value of tan 60 degrees?The value of tan 60 degree is [tex]\sqrt{3}[/tex].
What is the formula for area of a triangle?[tex]Area = \frac{1}{2}bh[/tex]
Where,
b is the base of the triangle.
h is the height of the triangle.
a) Since, the value of tan60 degree is [tex]\sqrt{3}[/tex].
Hence, the exact value of tan 60 degree is [tex]\sqrt{3}[/tex].
b). According to the given question, we have a right angled triangle in which
The length of the adjacent side w.r.t angle 60 degrees is [tex]4\sqrt{3}[/tex].
And, the length of the opposite side w.r.t angle 60 degrees is h.
Therefore, the value of h in the given triangle is given by
[tex]tan60 = \frac{h}{4\sqrt{3} }[/tex]
⇒[tex]\sqrt{3} =\frac{h}{4\sqrt{3} }[/tex] (because tan60=√3)
⇒[tex]h=4\sqrt{3} \sqrt{3}[/tex]
⇒[tex]h = 12[/tex]
Hence, the value of h in the given triangle is √3.
c) For the given triangle
Length of base = 4[tex]\sqrt{3}[/tex] unit.
And, the height of the given triangle is 12 unit.
The area of the given triangle is given by
[tex]Area = \frac{1}{2} (4\sqrt{3} )(12)[/tex]
⇒[tex]Area =24\sqrt{3}[/tex]
Hence, the area of the given triangle is 24[tex]\sqrt{3}[/tex].
Learn more about tangent of an angle and area of a triangle here:
https://brainly.com/question/15110994
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For tran appreciate it
The trip odometer reading will be between 378.3 km and 378.4 km. Nominally, it will read 378.3 km.
the dishes have been cleaned by us into active voice
Answer:
the dishes sparkled after we washed them.
Step-by-step explanation:
can someone help please??
Answer:
The scores in order from least likely to most likely is 8, 3, 4, and 5.
Step-by-step explanation:
1. Calculate the probability of the spinner adding up to 1, 2, 3, 4, .... 8
You will get:
2 (1/16)
3 (2/16)
4 (3/16)
5 (4/16)
6 (3/16)
7 (2/16)
8 (1/16)
2. Given the scores from the problem, the probability of each number is 3 (2/16), 4 (3/16), 5 (4/16), and 8 (1/16).
3. With this, we can determine the scores in order from least likely to most likely is 8, 3, 4, and 5.
The question and multiple choice answers are in the image. Hope you can help!
Answer:
answer b, SAS rule
Step-by-step explanation:
The ASA rule states that: If two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent.
Simon makes 30 cakes.
He gives 1/5 of the cakes to sali.
He gives 10% of the cakes to Jane.
What fraction of the 30 cakes does he have left?
Answer:
1/5 of 30 = 6 hes left with 24
10% of 24 = 2.4 hes left with 21.6
he has 21.6/30 left
Multiply number of cakes by 1/5 and 10%
Sali = 30 x 1/5 = 20/5 = 6 cakes
Jane = 30 x 10% = 30 x 0.10 = 3 cakes
Total he kept = 30-6-3 = 21 cakes left
What are the coordinates of the point on the directed line segment from (- 3, - 9) to (4, 5) that partitions the segment into a ratio of 5 to 2?
Answer:
(2,1)
Step-by-step explanation:
the best way to figure it out is with a graph
(-3,-9) to (4,5)
for the x
-3 to 4 is exactly 7 points away so you should count 5 over and stop.
for the y
-9 to 5 is exactly 14 points away so you should count in twos and stop at 5 sets of 2
hope this helps <3
evaluate the function for x = -8.
f(x) = -2x - 12
Answer:
4
Step-by-step explanation:
f(-8)=-2(-8)-12
f(-8)=16-12
=4
Helpppp i need this quick im taking a timed test!!!
Answer: c
Step-by-step explanation:
Answer:c
Step-by-step explanation: it makes the most sense
Which of the following best describes the graph of the polynomial function
below?
Answer:
Step-by-step explanation:
The given curve crosses the x-axis in two places, (-2, 0) and (0, 0), which are the zeros. This parabolic curve opens up and has its vertex (minimum) at (-1, -1).
Answer: The graph has two zeros.
Step-by-step explanation:
The given graph is the graph of parabola open upward. In the graph of parabola, we will have two solutions since the highest degree of the function is 2.
y = ax^2 + bx + c, where a, b, c are real number and a ≠ 0.
You can see the height degree of the function is 2.
Therefore, there should be two zeros of the function.
According to the given graph of parabola has two zeros at x = -2 and x = 0.
The graph cross the x-axis at x = -2 and x = 0.
Hence, the graph has two zeros.
Answer is A. The graph has two zeros
What’s the answer for this
155/18 x 2
Step-by-step explanation:
[tex] \tt{} \frac{155}{18} \times 2[/tex]
[tex]\tt{} \frac{155}{9} [/tex]
[tex]\tt{}17 \frac{2}{9} \\ \\ \\ [/tex]
Solve for x. Enter the solutions from least to greatest. Round to two decimal places. (x+7)^2 - 11 = 0
Answer:
lesser x = -10.32
greater x = -3.68
Step-by-step explanation:
Jacob wants to enlarge a 4 in. By 6 in. Photo so that the longer side will be 14 in. How long will the shorter side be? (MUST SHOW WORK) HINT: Refer to your notes on Scale Drawings.
Answer: 9.3 in.
Step-by-step explanation:
Jacob wants to enlarge the larger side of the photo which is the 6 in. part, to becomes 14 in.
This means that Jacob wants to increase the larger side by a scale factor of:
= Length of enlarged picture / Length of original
= 14 / 6
= 2.33
2.33 is therefore the scale factor.
The shorter side will also increase by this same scale factor:
= 4 * 2.33
= 9.3 in.
Pls help I’ll give crown
Answer:
C) (0,5)and(-4,5)
Step-by-step explanation:
Math help please help thanks
Answer:
62
Step-by-step explanation:
Draw a line from the bottom of the 4 foot line straight across (horizontally) until it hits the vertical line on your left.
The two lines (the one you drew and the left vertical line) meet at right angles.
The upper figure is a rectangle.
Area = L * W
L = 5
W = 4
Area = 5 * 4
Area = 20
Now the bottom rectangle can be found the same way.
Area = L * W
L = 14
W = 3
Area = 14 * 3
Area = 42
The total area = 42 + 20
Total area = 62.
The comment was correct.
Evaluate b^2 c^-1 for b = 8 and c = -4.
A. -16
B. 1/16
C. 16
D. 256
Answer:
-16
Step-by-step explanation:
b^2 c^-1
We know that c^-1 can also we written as 1/ c
b^2 / c
Let b =8 and c = -4
8^2 / (-4)
64 / -4
-16
did I choose the right graph?
Answer:
Step-by-step explanation:
The - tells you that it is upside down. So that much of your choice is correct for certain.
The 1/8 squishes the graph something fierce. So of those graphs given, the one you chose is most likely correct. But you are right to be a little miffed at the question. You should never have to choose an answer with only a picture to guide you. If you have a graphing calculator, try y = -1/8 x^2 which is a good candidate for all the graphs.
Please help
Honestly cant understand