Answers
This is one of those questions that is hard to explain, because I don't know what you know. I'll start with the most obvious reason I know. At x = -1 the top and bottom of the function is 0/0. zero/zero can give indeterminate results and you must look for other ways of explaining what is going on. Here's another thought which is less reliable.
The fraction factors.
(x + 1)*(x - 1)
============
(x + 1)
The two common factors cancel and you are left with f(x) = x - 1
If you have a graphing calculation you can put this in as y = x - 1 and you see that it is a straight line.
Question B is much nicer
when you put x = 1 into the fraction, you get 0 /2 which gives you 0. That's much easier to handle because the answer is 0.
you are still graphing y = x - 1, but this time the graph is much more well behaved.
This is still continuous I believe as the whole y equals 0, though I am not sure about this.
b. f(1) = (1-1)/(1+1)= 0
This is definitely continuous as the denominator did not equal 0.
Related Questions
At the beginning of this month, the balance of Nelson's checking account was $856.23. So far this month, he has received a paycheck via direct deposit of $876.25, been charged a monthly service fee from his bank of $10.00, used a debit card linked to his account to make a purchase of $23.96, written a check for $104.22 that has already been deposited, and deposited a check written to him for $25.00. What is the current balance of Nelson's checking account?
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Hope this helps<3
helppppppppppppppppppppppppppppppppp
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By doing the correct simplification we have:
((x ^ 60) / (x ^ -15))
(x ^ 75)
Therefore the error is:
answer:
He divided the exponents instead of subtracting them.
option 4
Please help me !! Thanks !
Answers
Hope this helps!
what is the approxmate area of the figure
plz look at picture and answer right will give brainlist and 20 extra points
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And the area of the rectangle would be 5 * 15 = 75
So.. the approximate area of the figure would be 75 + 20 = 95
Check the attachment.
Hope it helps you :)
Which box and whisker plot shows the scores of ten students on a mathematics exam? 89, 78, 93, 90, 75, 81, 91, 80, 89, 79.
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this is my educated guess not for sure so don`t get mad ..........
Find the simplified form of the expression. Give your answer in scientific notation. (4 x 10^10)(9 x 10^5) 3.6 x 10^4 3.6 x 10^49 36 x 10^5 3.6 x 10^6 and please explain
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60466176 x 10⁸³
(1.3t3 + 0.4t2 – 24t) – (0.6t2 + 8 – 18t)
What is the additive inverse of the polynomial being subtracted?
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1. You have that the the polynomial being subtracted is 0.6t²+8-18t, therefore, to find the additive inverse of the polynomial, you must multiply it by -1, as following:
(0.6t²+8-18t)
(-1)(0.6t²+8-18t)
2. Therefore, you obtain the following result:
-0.6t²-8+18t
Then, tas you can see, the answer is -0.6t²-8+18t.
Answer:
The first one is B then the second is B and the third question is D
Step-by-step explanation:
The length of a rectangle is 4 m longer than its width. if the perimeter of the rectangle is 36 m , find its area.
Answers
__________________________________________________________
Note: The formula for the area, "A" of a rectangle:
→ A = L * w ;
in which:
A = "area (of rectangle)" ; [in units of "m² " ; that is: "square meters" ] ;
L = length = "(4 + w)" {in units of "meters (m)" } ;
w = width {in units of "meters (m)" } ;
_______________________________________________________
So; " A = L * w " ;
Substitute the known expression for the "length, L" ; & rewrite the formula for the given area of OUR area for the rectangle in OUR GIVEN PROBLEM:
→ A = (4 + w) * w '' ;
______________________________________________________
Note the formula for the perimeter, "P" ;
→ P = 2L + 2w ;
↔ 2L + 2w = P
→ 2L + 2w = 36 m ;
_____________________________________________________
We want to find the "area" , "A" :
_____________________________________________________
Using the formula for the "perimeter, "P" (of the rectangle) ; & given that the perimeter is: "36" (meters) ;
→ 2L + 2w = 36 ;
→ Let us plug in the values for "Length (L)" & "width (w)" ;
→ 2(w + 4) + 2w = 36 ;
So; (2*w) + (2*4) + 2w = 36 ; Solve for "w" ;
→ 2w + 8 + 2w = 36 ;
→ Combine the "like terms" :
+ 2w + 2w = 4w ;
→ And rewrite:
4w + 8 = 36 ;
Now, subtract "8" from EACH SIDE of the equation:
4w + 8 − 8 = 36 − 8 ;
to get:
4w = 28 ;
Now, divide EACH SIDE of the equation by "4" ;
to isolate "w" on EACH SIDE of the equation ; & to solve for "w" ;
4w / 4 = 28 / 4 ;
→ w = 7 ; → The "width" of the rectangle is: " 7 m " .
Now, we can find the "length" of the rectangle:
The length, "L" , of the rectangle = 4 + w = 4 + 7 = 11 .
→ L = 11 . → The "length" of the rectangle is: " 11 m " .
___________________________________________________
Now, we can find the area, "A", of the rectangle.
A = L * w = 11 m * 7 m = " 77 m² " .
→ The area of the rectangle is: " 77 m² " .
__________________________________________________
To check our answer:
__________________________________________________
→ " P = 2L + 2w " ;
Given that "P = 36 m" ;
Plug in "36 m" (for "P") ; into the equation ;
and plug in our calculated values for
"length, L" (which is "11 m") ; & "width, w" (which is "7 m") ;
to see if the equation holds true ; that is, to see if both sides of the equation are equal ;
_______________________________________________________
→ 36 m = ? 2L + 2w ?? ;
→ 36 m = ? 2(11 m) + 2(7 m) ?? ;
→ 36 m = ? 22 m + 14 m ?? ;
→ 36 m = ? 36 m ? Yes!
__________________________________________________
The process involves setting up an equation using the given perimeter and the relation between length and width, solving for width, then calculating length and subsequently the rectangle's area, resulting in 77 square meters.
The question involves finding the area of a rectangle given the relationship between its length and width, and its perimeter. First, let's represent the width as w meters. Therefore, the length will be w + 4 meters, since the length is 4 meters longer than the width. The perimeter of a rectangle is calculated as 2(length + width). Given the perimeter is 36 meters, we can set up the equation: 2(w + w + 4) = 36.
Simplifying this equation gives 2(2w + 4) = 36, and further simplification results in 4w + 8 = 36. Solving for w, we subtract 8 from both sides getting 4w = 28, and divide by 4 to find w = 7 meters. The length, being 4 meters longer, is 11 meters.
Finally, to find the area of the rectangle, we multiply the length by the width: Area = length × width = 11m × 7m = 77 square meters. Therefore, the area of the rectangle is 77 square meters.
Use the formula A=bh , where A is the area, b is the base length, and h is the height of the parallelogram, to solve this problem. A sign on the side of a van is in the shape of a parallelogram. The area of the sign is 330 square inches. The base of the sign is 22 inches long. What is the height of the sign?
Enter your answer in the box.
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Adjacent angles whose exterior sides are opposite rays are
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Answer:
Adjacent angles whose exterior sides are opposite rays are "supplementary"
Step-by-step explanation: Theorem 3-2 states this fact
A telephone pole is perpendicular to the ground. What is the size of the angle between the ground and the telephone pole? How do you know?
Answers
perpendicular just means the angle between the two planes, in this case the ground and the pole, is 90 deg :)
simplify the expression (2-5i)-(4-4i)
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-2 - i is your answer. Hope it helps! :) If you could vote my answer as the brainiest, that would be awesome! :)
Can someone help and explain this to me please...?
Answers
Answer:
[j, k] →[9, 5]
[g, h] → [4, 2]
[x, y] → [−4, −4]
Step-by-step explanation:
{4j - 2k = 26
{5j - 2k = 35
−⅘[5j - 2k = 35]
{4j - 2k = 26
{−4j + 1⅗k = −28 >> NEW EQUATION
________________
−⅖k = −2
_____ ___
−⅖ −⅖
k = 5 [Plug this back into both equations above to get the j-value of 9]; 9 = j
__________________________________________________________
{6g + 8h = 40
{−6g + 2h = −20
________________
10h = 20
h = 2 [Plug this back into both equations above to get the g-value of 4]; 4 = g
__________________________________________________________
{4x - 9y = 20
{2x - 6y = 16
−½[4x - 9y = 20]
{−2x + 4½y = −10 >> NEW EQUATION
{2x - 6y = 16
_________________
−1½y = 6
______ __
−1½ −1½
y = −4 [Plug this back into both equations above to get the x-value of −4]; −4 = x
** Tip: Keep using the Elimination Method until you really have to use the Substitution Method. Use the Substitution Method only when one variable is given to you in one of or both equations, meaning that at least one of the equations has to be in Slope-Intercept Form [y = mx + b].
I am joyous to assist you anytime.
A toy rocket is launched from a platform 29 feet above the ground at a speed of 79 feet per second. The height of the rocket in feet is given by the polynomial −16t^2 + 79t + 29, where t is the time in seconds. How high will the rocket be after 3 seconds?
Answers
Height = -16t² + 79t + 29
3 sec means t = 3, we substitute t with 3
H = -16(3)² + 79(3) + 29
= -144 + 237 +29
= 122 feet
Answer:
[tex]h(3)=122ft[/tex]
Step-by-step explanation:
The problem gives you everything, basically you only have to replace the given value, which is t=3 into the equation:
[tex]h(t)=-16t^2+79t+29[/tex]
But, let's do a deeper analysis. This a projectile motion problem. For this kind of problems there are some fundamental equation. For example, we need to find the vertical displacement of the rocket. So the equation for the vertical displacement in projectile motion is given by:
[tex]h_f-h_o=v_ot-\frac{1}{2}gt^2[/tex] (1)
Where:
[tex]h_f=Final\hspace{3}height\\h_o=Initial\hspace{3}height\\t=Time\\v_o=Initial\hspace{3}velocity\\g=Gravitational\hspace{3}acceleration[/tex]
Isolating [tex]h_f[/tex] and rearranging the equation (1) we get:
[tex]h_f=-\frac{1}{2}gt^2+v_ot+h_o[/tex]
Looks familiar? It has exactly the same form of the equation given by the problem. As you can see, if you replace the values of the speed and the initial position given by the problem, we got the same equation. Besides gravitational acceleration is a constant and its value is approximately 32ft/s^2, dividing it by 2, we get 16. Having this in mind, let's resolve the problem:
[tex]h(3)=-16(3)^2+79(3)+29=-144+237+29=266-144=122ft[/tex]
The shorter leg of a right triangle is 12 yards. if the hypotenuse is 20 yards, how long is the other leg?
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If this answer helped you and was correct you can name me "Brainliest." ty :)
If y varies directly as x, and y is 18 when x is 5, which expression can be used to find the value of y when x is 11? mc018-1.jpg mc018-2.jpg mc018-3.jpg mc018-4.jpg
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If y varies directly as x, the expression that can used to determine the value of y when x is 11 is y = 18/5 × 11 .
What is the expression that can be used to determine the value of y?The equation that can be used to represent direct variation is:
y= kx
Where:
y = dependent variable k= constant of proportionality x = independent variablek = y/x
k = 18/5
y = 18/5 × 11
To learn more about direct variation, please check: https://brainly.com/question/4838941
what number produces an irrational number when multiplied by 1/5
Answers
Final answer:
To produce an irrational number by multiplying by 1/5, the other number must be irrational, such as √2.
Explanation:
The student is asking which number, when multiplied by 1/5, produces an irrational number. To produce an irrational number by multiplication, the other number must itself be irrational. Because rational numbers multiplied by rational numbers yield rational results. A classic example of an irrational number is √2, which, when multiplied by 1/5, gives 1/5√2 or √2/5, both of which are irrational.
Consider the table below.
x y
-3 0.5
-2 1
-1 2.5
0 5
1 8.5
y=ax2+bx
Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and c are constants.
Answers
y = ax2 + bx + c
For this case, what we need to do is to evaluate three points in the standard equation and solve the system of three equations with three unknowns.
We have then:
For (-3, 0.5):
0.5 = 9a - 3b + c
For (0, 5):
5 = c
For (1, 8.5):
8.5 = a + b + c
We solve the system:
0.5 = 9a - 3b + c
8.5 = a + b + c
5 = c
From here we get:
a = 1/2
b = 3
c = 5
The standard equation is:
y = (1/2) x ^ 2 + 3x + 5
Answer:
y = (1/2) x ^ 2 + 3x + 5
Answer:
y=x^2-6x+13
Step-by-step explanation:
Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and Golden Delicious apples are $1.25 each. Mary spent $21.00 on 22 apples. What should the second equation be?
d + g = 21
g – d = 21
0.75d + 1.25g = 21
0.75d – 1.25g = 21
Answers
The second equation, representing the total cost of both apples as 0.75d + 1.25g = 21.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and Golden Delicious apples are $1.25 each. Mary spent $21.00 on 22 apples.
Assume that the number of Delicious apples are (d) and Golden Delicious are (g) apples.
We can write the second equation as -
0.75d + 1.25g = 21
and the first equation as -
d + g = 22
Therefore, the second equation, representing the total cost of both apples as 0.75d + 1.25g = 21.
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Is it possible for a composite number to have more than one prime factorization? Yes. I'm I right @dirtydan667
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Yuma needs a singer. Singer A is offering her services for an initial $55 in addition to $20 per hour. Singer B is offering his services for an initial $85 in addition to $5 per hour. When will the two singers charge the same amount of money? The two singers will charge the same amount of money after :blank: hours.What is the answer to the blank.
Answers
Equation for Singer B: 85 + 5x
Make the two equations equal to each other and solve for x.
55 + 20x = 85 + 5x
20x - 5x = 85 - 55
15x = 30
x = 30/15 = 2 hours.
Answer:
At 2 hours both singers will charge the same amount of price.
Answer Check:
Singer A Cost: 55 + 20 (2 hours) = $ 95
Singer B Cost: 85 + 5 (2 hours) = $ 95
Given the pre-image ABCD and the image after a dilation, A'B'C'D', what is true about the polygons? Check all that apply.
Answers
literally everything is the same except for the side lengths
ex. angle measurements, orientation, some other stuff I can't think of right now.
Can you also explain how you solve it so i can do by myself:)
What is the sum of the first eight terms of the series?
(−500)+(−100)+(−20)+(−4)+(−0.8)+...
Round the answer to two decimal places if necessary.
−996.09
−625
−624.99
−623
Answers
The correct answer is option c) 624.99
To find the sum of the first eight terms of the series: (-500) + (-100) + (-20) + (-4) + (-0.8) +..., we first need to recognize that this is a geometric series where each term is a constant multiple of the previous term.
The first term (a) is -500, and the common ratio (r) can be found as follows: [tex]r = \frac{-100}{\ 500} = \frac{1}{5} \ or\ 0.2.[/tex]
Geometric Series Sum Formula
The sum ([tex]S_n[/tex]) of the first n terms of a geometric series is given by the formula:
[tex]S_n = a * \frac{1-r^n}{1-r}[/tex]
Here, a = -500, r = 0.2, and n = 8.
Calculate [tex]r^n: (0.2)^8 = 0.000256[/tex]Calculate [tex]1 - r^n[/tex]: 1 - 0.000256 = 0.999744Calculate the denominator 1 - r: 1 - 0.2 = 0.8Apply the values in the formula: [tex]S_8 = -500 * \frac{0.999744}{0.8}[/tex][tex]S_8 = -500 * 1.24968[/tex][tex]S_8 = -624.99[/tex]The sum of the first eight terms of the series, rounded to two decimal places, is -624.99.
The complete question is:
What is the sum of the first eight terms of the series?
(−500)+(−100)+(−20)+(−4)+(−0.8)+...
Round the answer to two decimal places if necessary.
a) −996.09
b) −625
c) −624.99
d) −623
BRAINLIESTTT ASAP!
The function f(x) = –x^2 + 60x – 116 models the monthly profit, in dollars, a shop makes for repairing windshields, where x is the number of windshields repaired, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
Answers
y+116=-x^2+60x
y+116=-1(x^2-60x)
y+116-900=-1(x^2-60x+900)
y-784=-1(x-30)^2
y=-1(x-30)^2+784
we know that
h=-b/2a
h=-60/(-2*1)
h=30
k=-30^2+60(30)-116
k=784
the vertex is at (30,784) this means that the point of symmetry of the parabola is at (30,784), in our context it means that the maximum number of windshields repaired is 30 and the minimum profit will be $784
Part B
x-intercept
to determine the x-intercept we let f(x)=0
thus
0=-2x^2+60x-116
solving for x we get:
x=2 and x=58
this means that when the shop repairs 2 windshields or 58 windshields, they will not make any profits
HELP SOMEONE SMART
What is the solution of the equation? Step by step.
Answers
Subtract 9, divide by 3, take the 5/3 power
.. 3*(a +4)^(3/5) +9 = 36 . . . . . original equation
.. 3*(a +4)^(3/5) = 27
.. (a +4)^(3/5) = 9
.. a +4 = 9^(5/3)
.. a = 9^(5/3) -4 ≈ 34.9407
Find sin q if q is an angle in standard position and the point with coordinates (4, 3) lies on the terminal side of the angle.
I don't understand what I'm suppose to be doing here.
Answers
Please help I have 2 questions. Thank you.
Answers
2 is
3x + 2 = 2
3x = 0
x = 0
Quadrilateral ABCD undergoes a series of transformations to become A’’B’’C’’D’’. If the first transformation is a reflection over the y-axis, what is the coordinate of C’? What transformation occurs after the reflection over the y-axis that results in the final image?
Answers
A 90 degree rotation counterclockwise around point A'
Quadrilateral ABCD undergoes a series of transformations to become A’’B’’C’’D’’.
The first transformation is a reflection over the y-axis.
The coordinate of C’ would be (-6,3) in this case.
If the image is rotated counter clock wise around the point A then it will result in the final image which is presented in the attached figure.
Hope this helps ..!!
Thank you :)
Heather is training for a long-distance run. Her data points listed below represent the days of practice, x, and the number of miles run, y.
(1, 2.5), (2, 4.2), (4, 5.6), (6, 7), (8, 8.1), (10, 11)
Use the equation to interpolate the value and estimate the distance that she could have run on day 3. Round to the nearest tenth of a mile.
Answers
Answer:
4.6
Step-by-step explanation:
What is the exact volume of the sphere? 36.868π m³ 94.46π m³ 147.456π m³ 463.01π m³ Sphere with dotted line extending from middle point of sphere to edge. Line is labeled four and eight-tenths meters.
Answers
The solution is Option C.
The volume of the sphere is given by the equation V = 147.456π m³
What is a Sphere?A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the volume of the sphere be represented as V
Now , the equation will be
Let the radius of the sphere be r
The value of r = ( 4 8/10 ) m
So , the radius of the sphere = 4.8 m
Now , Volume of a Sphere = ( 4/3 ) πr³
Substituting the values in the equation , we get
Volume of Sphere V = ( 4/3 ) π ( 4.8 )³
On simplifying the equation , we get
Volume of Sphere V = ( 4/3 ) π ( 110.592 )
On further simplification , we get
Volume of Sphere V = 147.456π m³
Hence , the volume of sphere is 147.456π m³
'
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