Where is the removable discontinuity of f (x) = startfraction x 5 over x squared 3 x minus 10 endfraction located? x = –5 x = –2 x = 2 x = 5
Answers
The removable discontinuity of the function f(x) = (x+5)/(x^2 +3x-10) is at x = -5 (given by Option A).
What are discontinuities?Holes in the graph of function, where its undefined, or non-continuous, is called discontinuity.
The points in the domain of the function over which its not continuous, is called point of discontinuity for that function.
What is removable discontinuity?A discontinuity is removable if the limit of the function at the point of discontinuity exists but this limiting value is not the value of the function at that point.
We can remove that discontinuity by making the value of the function equate to the limiting value of the function at that point.
The given function is:
[tex]f(x) = \dfrac{(x+5)}{(x^2 +3x-10)}[/tex]
Factoring the denominator, we get:
[tex]x^2 + 3x -10 = x^2 + 5x - 2x - 10 =x(x+5) - 2(x+5) = (x+5)(x-2)[/tex]
Therefore, we get:
[tex]f(x) = \dfrac{(x+5)}{(x+5)(x-2)}[/tex]
The function is not defined if x = -5, or x = 2 since at those places, the denominator would become 0. (we cannot cancel out (x+5) from numerator and denominator for all x, as it isn't defined for x = -5
Also, we have:
[tex]\lim_{x\rightarrow 2}f(x)= \infty\\\lim_{x\rightarrow -5}f(x) = \lim_{x\rightarrow -5}\dfrac{(x+5)}{(x+5)(x-2)} = \lim_{x\rightarrow -5}\dfrac{1}{(x-2)} = -\dfrac{1}{7}[/tex]
We cancelled out (x+5) from numerator and denominator because x is limiting to -5 but isn't equal to -5.
For discontinuity of x = -5, the limit of f(x) exist (left and right limit both will come as 1/3). But f(-5) is not defined. So we can remove this discontinuity by defining f(-5) = 1/3 and for rest of the values of x, it is same as before.
Thus, the removable discontinuity of the function f(x) = (x+5)/(x^2 +3x-10) is at x = -5 (given by Option A).
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Answer: Option A -5
Step-by-step explanation: Just took the test
Related Questions
A firm is considering projects s and l, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. The ceo wants to use the irr criterion, while the cfo favors the npv method. You were hired to advise the firm on the best procedure. If the wrong decision criterion is used, how much potential value would the firm lose?.
Answers
If the wrong discion criterion is used, the potential lose in value for the firm is $209.07.
What is the correct decision criterion?
The correct decision criterion is the net present value. Net present value is the present value of after-tax cash flows from an investment less the amount invested. The internal rate of return is the discount rate that equates the after-tax cash flows from an investment to the amount invested
What is the loss in value if the wrong decision criteria is used?The net present vaue and the internal rate of return can be calculated using the financial calcuator.
Project S:
Cash flow in year 0 = $-1025Cash flow each year from year 1 to 4 = $380I = 6%
NPV = 291.74
IRR = 17.86%
Project I:
Cash flow in year 0 = $-2150
Cash flow each year from year 1 to 4 = 765
I = 6%
NPV = 500.81
IRR = 15.78%
If the wrong criteria is used, Project S would be chosen.
Loss in value = 500.81 - 291.74 = $209.07.
Here are the cash flows used:
WACC: 6.00%
Year 0 1 2 3 4
CF S -$1,025 $380 $380 $380 $380
CF I -$2,150 $765 $765 $765 $765
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i need help with this
Answers
Answer: B) x=5, x=1
Step-by-step explanation:
To start multiply everything in the expression by 2
[tex]0.5x^{2} -3x+2.5\\x^{2} -6x+5[/tex]
Now factor the trinomials for when a=1
So you must find two numbers that add to -6 and multiply to 5
In this case, the numbers are -1 and -5
[tex]x^{2} -6x+5\\(x-1)(x-5)[/tex]
Now set each of the factors equal to 0 and solve for x
[tex]x-1=0\\x-1+1=0+1\\x=1[/tex]
[tex]x-5=0\\x-5+5=0+5\\x=5[/tex]
Simplify the expression 63 + 5(4-2)
Answers
Answer:
63 + 10
Step-by-step explanation:
when you do parenthesis and the number is next to another one with no symbol you multiply so 4-2 = 2 2 x 5 = 10 giving you 63 + 10
It took a car 3 hours to travel from town a to town b the wheel of a car completes a rotation in one second how many degrees has it turned
Answers
The number of degrees that have been turned by the car when it travels from town a to town b will be 1080°.
How to calculate the number of degrees?From the information given, it was stated that it took a car 3 hours to travel from town a to town b and the wheel of a car completes a rotation.
In this case, a rotation is 360°, since there are 3 rotations, the degrees will be:
= 360 × 3
= 1080°
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WILL GIVE BRAINLIESTTTT, FIVESTARS ANDTHANKS
PLEASEHELP
Answers
Answer:
3 is the answer
Step-by-step explanation:
answer up above
A large aircraft is flying on a bearing of 310° (50° west of north) with an airspeed of 700 mph. It is being affected by a 100 mph wind
blowing towards the west, as shown in the diagram below.
The distance, R, as indicated in the diagram, that the plane has travelled after 1 hour is, to the nearest mile,
Answers
Answer:
779
Step-by-step explanation:
Aiming to get the value of formula
Given that
50° + 80² = 140°.
:: Cos140² = 100 + 700²³ - R²
kaw of ousines axivox. T
·· R² = 607246
R≈ 780 miles
• The result is T80 miles
6. What is the area of the shared region to the nearest
tenth of square ft?
Answers
[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2-r^2)~~ \begin{cases} R=\stackrel{larger}{radius}\\ r=\stackrel{smaller}{radius}\\[-0.5em] \hrulefill\\ R=50\\ r=36 \end{cases}\implies \begin{array}{llll} A=\pi (50-36)\implies A=14\pi \\\\\\ A\approx 44.0 \end{array}[/tex]
Step right up for a brainliest
Answers
What is the circumference (rounded to the nearest meter) of a circular swimming pool that has a radius of 10 meters?
A. 120
B. 63
C. 60
D. 31
E. 30
Please help with the answer and explain it to me.
Answers
Answer:
63
Step-by-step explanation:
You get the answer by multiplying the radius by 2 to get the diameter and then multiplying the result by pi or 3.14, which gives you 62.83 and then round it up which is 63
An auditorium has 25 rows of seats and a total of 500 chairs.
How Many chairs in each row?
Answers
Explanation: 500 chairs/25 rows = 20 chairs per row
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Write in standard form
(4.6 x 10^6) x (5 x 10^-4)
Answers
The binomial (a 5) is a factor of a2 7a 10. what is the other factor? (a 2) (a 5) (a−2) (a−5)
Answers
An expression has numbers, variables, and mathematical operations. The other factor of the given binomial is a²+7a+10 except (a+5) is (a+2).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
To find the other factor of the binomial a²+7a+10, we can write it as,
[tex]a^2+7a+10\\\\=a^2+5a+2a+10\\\\=a(a+5)+2(a+5)\\\\=(a+5)(a+2)[/tex]
Thus, the other factor of the given binomial is a²+7a+10 except (a+5) is (a+2).
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Answer:
(a + 2)
Step-by-step explanation:
Find the surface area of a rectangular prism (like the rectangular prism below) that is 16 feet by 1.5 feet by 2 feet.
Solve and get 30pts!!
Answers
Answer:
Surface area of the rectangular prism=
Step-by-step explanation:
Given Dimensions of the rectangular prism are:
[tex]Length(L)=16yards[/tex]
[tex]Width(w)=2yards[/tex]
[tex]Height(H)=1.5yards[/tex]
Surface Area of a rectangular prism=
[tex]2(L*W+W*H+H*L)[/tex]
[tex]=2(16*2+2*6+6*16)[/tex]
[tex]=2(32+12+96)[/tex]
[tex]=2(140)[/tex]
[tex]=140yards^2[/tex]
The surface area of the rectangular prism is [tex]140yards^2[/tex]
5 Henry wants to add these numbers. 53 +81 +44 + 72 Explain how he can find the sum by breaking the numbers into tens and ones. What is the sum?
Answers
Answer:
50+3+80+1+40+4+70+2
Step-by-step explanation:
Pls thank if correct
Dont get mad if not correct.
Hope this helps <3
HELP ME PLEASE ILL MARK U THE BRAINLEST THING PLEASEE I BEG
Answers
Answer:
See below ~
Step-by-step explanation:
a)
The intersection of the points represents where they had travelled the same distance at that timeb)
Leslie passed Gale at approximately 2:00 PMc)
Leslie had travelled about 20 miles when they passed Galed)
Between 1:30 and 3:00, Gale had not moved any distance w.r.t time, meaning she had stopped, presumably to take a break, or to fix something that may have happened to her bikee
Rate of covering distance = 10 miles/1 hourTotal distance = 60 milesTotal time = 60/10 = 6 hoursNoon + 6 hours = 6:00 PMJoshua is trying to determine the equation of a quadratic function
whose vertex is (-3,5) and passes through the point (-1,2).
If he writes his final answer in the form (x)= a(x-1)2+k, what will be
the values(numbers) of a, h, and k?
And the last answer choice is
a=-3/4
h=-3
K=5
Please help
Answers
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{vertex}{(-3~~,~~5)}\qquad y=a[x-(-3)]^2+5\implies y=a(x+3)^2+5 \\\\\\ \textit{we also know that} \begin{cases} x=-1\\ y=2 \end{cases}\qquad 2=a(-1+3)^2+5\implies -3=a(2)^2 \\\\\\ -3=4a\implies -\cfrac{3}{4}=a~\hfill \boxed{y=-\cfrac{3}{4}(x+3)^2+5}[/tex]
molly is 4 years younger than Heidi. In 3 years, Heidi will be twice as old as Molly. How old are they now
Answers
Answer:
Molly would be 1 years old.
Step-by-step explanation:
"In three years..."
(m+3) will be Molly's age then.
(h+3) will be Heidi's age then.
(h+3) = 2(m+3) :: given.
.
Subsitute what we know about m, which is it equal h-4.
.
(h+3) = 2(m+3)
(h+3) = 2m + 6
substitute m=h-4
(h+3) = 2(h-4) +6
h +3 = 2(h -4) +6
h +3 = 2h -8 +6
h +3 = 2h -2
h = 2h -8 +3
-h = -5
h = 5
Heidi is 5 years old now.
.
m = h-4
m = 5-4
m = 1
Molly is 1 years old now.
A car speeds up from 0 to 15 m/s in 5 s. What is the car's acceleration?
A. 0.3 m/s/s
B. 3 m/s/s
C. 10 m/s/s
D. 20 m/s/s
Answers
Answer: B 3m/s²
Step-by-step explanation: Acceleration is difference in speed /time = 15-0/5
You’ll know actual physic’s of your going to take it
Gale the birthday clown is blowing up a fun spherical shaped balloon at a constant rate of 100 cubic inches per minute. How fast is the radius increasing when the sphere contains 50 cubic inches of clown breath
Answers
Answer:
Step-by-step explanatio the way the question is phrased Is confusing
Which expressions are perfect square trinomials? check all that apply. x2 16x 8 x2 14x 49 x2 – 5x 25 x2 – 24x 144 x2 9x – 81
Answers
The perfect square trinomial will be [tex]\rm x^2+14x+49[/tex] , [tex]x^2-24x+144[/tex]Expression 2 and 4 are correct.
What are trinomials?A mathematical expression with three terms or three monomials is called a trinomial. Polynomials having only three terms are known as trinomials.
The second and fourth expression seems to be the perfect square let's check it.
Expression 2;
[tex]x^2 + 14x+49 \\\\ x^2+7x+7x+49 \\\\ x(x+7)+7(x+7)\\\\ (x+7)(x+7) \\\\ (x+7)^2[/tex]
Expression 4;
[tex]x^2-24 x +144 \\\\ x^2-12x-12x+144 \\\\ x(x-12)-12(x-12) \\\\ (x-12)^2[/tex]
Hence the perfect square trinomial will be [tex]\rm x^2+14x+49[/tex] , [tex]x^2-24x+144[/tex] .Expressions 2 and 4 are correct.
To learn more about the trinomials refer to the link;
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Answer:
Options 2 and 4
Step-by-step explanation:
A ball was projected into the air with an initial upward velocity of 72 feet per second. The quadratic function graphed below shows the height, h, of the ball t seconds after it was projected into the air.
What is the domain of the function for this situation?
Question 20 options:
0≤t≤4.5
0
0
0≤h≤80
Answers
The domain is represented by the set of values of the time, that is, the horizontal axis, and the domain of the given function is represented by t ∈ [0, 4.5].
How to determine the domain of the function of the height of the ball in function
All functions are relations in which there is no value of the domain related to more than one value of the range, functions in explicit form related the variable of the range in terms of the variable of the domain.
Based on the information shown in the graph, the domain is represented by the set of values of the time, that is, the horizontal axis, and the range is represented by the set of values of the height, that is, the vertical axis.
Hence, the domain is represented by the set of values of the time, that is, the horizontal axis, and the domain of the given function is represented by t ∈ [0, 4.5].
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4.
1 in
14 in
2.5 in
Volume of each prisms
Answers
Answer:
ength l = 1 in
width w = 14 in
height h = 2.5 in
diagonal d = 14.3 in
total surface area Stot = 103 in2
lateral surface area Slat = 75 in2
top surface area Stop = 14 in2
bottom surface area Sbot = 14 in2
volume V = 35 in3
Tim bought 555 crayons that came in packs of of 15. There were 7 colors of crayons. How many crayons did Tim buy
Answers
Answer:
555
Step-by-step explanation:
The packs the colors came in and the colors do not matter. The initial value of crayons is 555.
The table shows us how many sit ups she has done over the past few days-
At this rate how many sit-ups will she do on day 12?
Answers
Answer:
177
Step-by-step explanation:
the number of sit-ups is going up in 4s , so if i take the 33 sit ups she does on the 5th day i add 4 to that 12 times , so you just do 33+12 and multiply that by 7 since thats how many days she has until 12.
A container in the shape of a rectangular prism has a height of 2 feet. Its length is four
times its width. The volume of the container is 200 cubic feet. Find the length and width of
the container.
Answers
Answer:
length = 20 feet and width = 5 feet
Step-by-step explanation:
Volume is equal to volume = height * width * length. The questions tells us the total volume is 200 cubic feet and that the lenght is equal to length = 4w. Set up the equation 4w * w * 2 = 200 cubic feet. Multiply to get 8w^2 = 200 and solve for w.
Find the outer perimeter of this figure. Round
your answer to the nearest hundredth. Use
3.14 to approximate pi.
P = [ ? ] ft.
Answers
Answer:
61.90 ft
Step-by-step explanation:
Perimeter: the boundary that surrounds a shape
1) Find the perimeter of the semicircle using this formula: [tex]\frac{1}{2} *2\pi r[/tex], where [tex]r[/tex] is the radius, and π is 3.14 (according to the question).
1.1) We need to find the radius first.
Radius = Diameter ÷ 2
So, 10 ÷ 2 = 5
1.2) Input the values into the semicircle formula.
[tex]\frac{1}{2} *2(3.14)(5)[/tex]
1.3) solve for the perimeter of the semicircle.
[tex]\frac{1}{2} *31.4[/tex]
= 15.7
2) Find the perimeter of the triangle and the rectangle.
= [tex]6 + 12.2 + 14 + 14[/tex]
= 46.2
3) Add them.
= [tex]46.2 + 15.7[/tex]
= 61.9 ft
3) Round the answer (61.9) to the nearest hundredth (according to the question).
= 61.90 ft
As per the total length of the arc of a semicircle, the outer perimeter of this figure is 61.9 feet.
What is the total length of the arc of a semicircle?A semicircle that has a radius of 'r' units, has the total length of it's arc is
= πr units
In the given figure, the semicircle has a diameter = 10 feet.
Therefore, the radius of the semicircle
= 10/2 feet
= 5 feet
Now, the total length of it's arc is
= πr units
= 3.14 × 5 feet
= 15.7 feet
Therefore, the outer perimeter of this figure is
= (12.2 + 6 + 14 + 15.7 + 14) feet
= 61.9 feet
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6 cm 4 cm 10 cm What is the surface area of the figure? square centimeters
Answers
Answer:
2 x 10 x 4 + (4 + 10) x 2 x 6 = 80 + 168 = 248
Simplify this equation is easiest form.
Answers
Answer:
no. 4
Step-by-step explanation:
=25x - 125/x^2 - 25
=25(x-5) / x^2 - 5^2
=25(x-5) / (x-5) (x+5) <use of formula a^2 - b^2=(a-b) (a+b)>
=25/x+5 <cut (x-5) on both side>
For 5 points and brainliest to the best correct answer, find the missing measures.
Thank you
Answers
Answer:
x = 7y = 97°z = 19Step-by-step explanation:
The markings on the figure show this to be a parallelogram. That means opposite sides are congruent. Because the sides are parallel, "alternate interior" angles are also congruent.
__
Angle y forms a linear pair with the one marked 83°, so is supplementary to it:
y = 180°-83° = 97°
__
The angle marked y is an exterior angle to the triangle containing the angle marked (7x -5)°. As such, it is equal to the sum of the remote interior angles, the one marked (7x -5)° and the unmarked one that is congruent to (3x +32)°.
(7x -5) +(3x +32) = 97 . . . . . angle relations in the left-side triangle
10x +27 = 97 . . . . . . . collect terms
10x = 70 . . . . . . . . subtract 27
x = 7 . . . . . . . . divide by 10
__
The side marked Z is congruent to the opposite parallel side, so ...
z = 19
__
The missing measures are ...
x = 7y = 97°z = 19_____
Additional comment
You can also find the value of y by adding up the interior angles of the right-side triangle. The one not shown there is "alternate interior" to the one marked (7x -5)°, hence has the same measure. This gives ...
(7x -5) +(3x +32) +83 = 180
Subtracting 83° from both sides gives the equation we used above.
Here is a pyramid with a base that is a pentagon with all sides the same length
Describe the cross section that will result if the pyramid is sliced:
horizontally (parallel to the base).
vertically through the top vertex (perpendicular to the base)
Answers
The shape of the cross section formed from slicing the pyramid is called; a triangle
What is the Pyramid's Cross Section?We are told that it is a pyramid with a base that is a pentagon with all sides the same length.
Now, the Pyramid's ap-ex is usually constructed by isosceles triangles. Thus, when they are sliced from its ap-ex to from the vertex, in the cross section a triangle will be formed, This triangle will be an isosceles triangle.
In conclusion, the shape of the cross section formed from slicing the pyramid is a triangle.
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