For this case we have the following expression:
[tex] \frac{c-5}{c^2-5} [/tex]
To simplify the expression, the first thing to do is factor the denominator.
We have then:
[tex]\frac{c-5}{(c-5)(c+5)}[/tex]
Then, canceling similar terms we have:
[tex]\frac{1}{(c+5)}[/tex]
From here, we must find any value that should be excluded from the expression.
We must exclude values of c that make the denominator equal to zero.
We have then:
[tex] c+5=0
c=-5 [/tex]
Answer:
The simplified expression is:
[tex]\frac{1}{(c+5)}[/tex]
The value to be excluded from the expression is:
[tex] c=-5 [/tex]
solve for z (attachment)
For the function f(x) = x2, what effect will multiplying f(x) by 1/2 have on the graph?
Write the equation of a horizontal line that passes through the point (3, -3).
Use the grouping method to factor the polynomial below completely.
x3 – 4x2 + 3x – 12
A. (x2 + 4)(x – 3)
B. (x2 – 4)(x + 3)
C. (x2 – 3)(x + 4)
D. (x2 + 3)(x – 4)
How would I find the diameter?
Which of the following gives all of the coefficients of the algebraic expression -2x^2 +17-15x+7xy
The coefficients of the algebraic expression -2x² + 17 -15x + 7xy are -2, 17, -15 and 7
How to determine the coefficient of the expression
From the question, we have the following parameters that can be used in our computation:
-2x² + 17 -15x + 7xy
Consider an expression represented as
Ax
Where A is a constant and x is the variable
The coefficient of the expression is A
Using the above as a guide, we have the following:
The coefficients of the algebraic expression are -2, 17, -15 and 7
Question
Which of the following gives all of the coefficients of the algebraic expression -2x^2 +17-15x+7xy
a. 2, 17, 15 and 7
b. -2, 17, -15 and 7
c. -2, -17, -15 and 7
d. -2, -17, 15 and 7
how do you convert cos(x) into sin(x) and tan(x) ?
PLEASE ANSWER + BRAINLIEST!!!
What is the value of 3x^2 - 5xy + 5y^2 for x = -6 and y = 2?
A. -68
B. -4
C. 188
D. 208
Anyone know this geometry question? Will give brainiest
Help Please
A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.
Enter your answers in the boxes to complete the two-way table based on the given data.
First picture is how they want you to put the answers in & the second one is the grid with the numbers
A. (-3,-5)
B.( -2,-2)
C. (4,9)
D.(13,5)
The square root of 53 lies between which two numbers?
A rectangular plot of land that contains 1500 square meters will be fenced and divided into two equal portions by an additional fence parallel to two sides. find the dimensions of the land that require the least amount of fencing.
What is the radius of convergence of the maclaurin series (2x)/(1+x^2)?
The radius of convergence of the maclaurin series is 1 unit.
It is given that maclaurin series [tex]\rm \frac{2x}{(1+x^2)}[/tex]
It is required to find the radius of the convergence of the maclaurin series.
What is maclaurin series?It is defined as the expansion of a function that provide the approximation of the given function at any point of function.
We have:
[tex]\rm \frac{2x}{(1+x^2)}[/tex]
To find the radius of convergence of the maclaurin series, we must find the roots of denominator hence:
[tex]\rm 1+x^2= 0\\\\\rm x^2 = -1\\\\[/tex]
From the complex number: the roots are imaginary:
[tex]\rm x_1 = i\\x_2 = -i[/tex]
i is the iota
and the distance from the origin (0,0) is 1.
Thus, the radius of convergence of the maclaurin series is 1 unit.
Learn more about the maclaurin series:
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After creating a new email address, Gareth initially receives n emails per year. The number of emails received increases by 7% each year after that. The following expression represents the number of emails received after x years.
x(1 + 0.07)^x
Which of the following best represents the expression?
the product of the number of emails received initially and one plus the factor of increase raised to the number of years that the amount of emails Gareth received has increased
the product of the number of emails received initially and the factor of decrease raised to a period of x years
the product of the number of emails received initially and one plus the factor of decrease raised to the number of years that the amount of emails Gareth received has increased
the product of the number of emails received initially and the factor of increase raised to a period of x years
Answer:
The correct answer is Option A.
Step-by-step explanation:
After a 40% discount an item costs $360. what is the original cost
Answer:
It is $600
Step-by-step explanation:
hope it helps, murdle
The solution to 15 a2 − 1 = 5 2a − 2 is a = . The extraneous solution is a = .
Answer:
5 and 1
1 is extraneous
Step-by-step explanation:
Write the function associated with the graph below
Since the value of the function is decreasing exponentially as x decreases ,
The function is of the form [tex] y=ae^{bx}+c,b>0 [/tex].
Since the curve passes through (0,6),
[tex] 6=ae^{0}+c,6=a+c [/tex],
Since the curve passes through (-1,0),
[tex] 0=ae^{-b}+c [/tex].
Since [tex] y=-3 [/tex] is a horizontal asymptote,
[tex] -3=ae^{-\infty}+c,c=-3 [/tex]
From the above 3 equations,
[tex] c=-3,a=9,9e^{-b}=3,e^b=3,b=\ln 3 [/tex].
Therefore, the required function is
[tex] y=9e^{\ln 3 x}-3\\
y=9*3^{ x}-3 [/tex].
It can be verified that the curve [tex] y=9*3^{ x}-3 [/tex] passes through [tex] (-2,-2) [/tex].
A typist charges $0.90 a page and averages 45 pages per work day. If she works 3 days a week, how much does she earn in a week?
Final answer:
The typist earns $121.50 per week by multiplying the charge per page ($0.90) with the daily page average (45 pages) and the number of days worked per week (3 days).
Explanation:
The question asks us to calculate the weekly earnings of a typist who charges $0.90 per page and averages 45 pages per day, working 3 days a week. To find the total weekly earnings, we can multiply the number of pages typed per day by the charge per page, and then multiply that result by the number of days worked in a week.
Multiply the number of pages (45) by the charge per page ($0.90): 45 pages × $0.90 = $40.50 per day.
Multiply the daily earnings by the number of days worked in a week (3): $40.50 × 3 days = $121.50 per week.
Therefore, the typist earns $121.50 per week.
Find the approximate surface-area-to-volume ratio of the Moon. The radius of the Moon is 1,080 miles. A. 0.0009 B. 0.0028 C. 360 D. 3,240
Express answer in exact form.
Find the area of one segment formed by a square with sides of 6" inscribed in a circle.
(Hint: use the ratio of 1:1:√2 to find the radius of the circle.)
Answer:
A = { 9/2 π - 9 } in^2
Step-by-step explanation:
I just did this
Hope this helps !
To find the area of the segment, subtract the area of the triangle from the area of the sector.
Explanation:To find the area of one segment formed by a square with sides of 6 inches inscribed in a circle, we need to find the area of the sector formed by the circle and subtract the area of the triangle formed by the diagonal of the square.
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22 POINTS, NEED URGENT HELP
Write the equation of each circle:
1. R with center R(-1, 8) and radius 5
2. K with center K(4,0) and that passes through (2,0)
20 points!
Looking at circle O, ∠BOC is a(n)
Please contact your teacher immediately if you do not see the image.
Question options:
minor angle
central angle
inscribed angle
major angle
What is the equation of the line that passes through the points (0, -4) and (2, 8)?
A. y = 6x - 4
B. y = 6x + 4
C. y = 4x + 6
D. y = -4x + 6
If and represent rational expressions and b0 and y0, what is true of their product? Check all that apply.
Correct options are Options B, D, E. The product of two rational expressions (a/b) and (x/y) is a rational expression, specifically the ratio of ax and by, or equivalently ax/by. Incorrect options include ay/bx and a/y(x/b).
To determine the product of two rational expressions (a/b) and (x/y), where b ≠ 0 and y ≠ 0, let's explore the given options. Here are the truths about the product:
The product is a rational expression: When you multiply two rational expressions, the result is also a rational expression. This follows from the definition of rational expressions, which are ratios of polynomials.
The product is the ratio of ax and by: Mathematically, multiplying the numerators and denominators of the two rational expressions gives us (ax)/(by).
The product is equivalent to ax/by: This restates the above ratio in a simplified expression form, confirming that the multiplication results in (ax)/(by).
As we can see, the other expressions mentioned (ay/bx, a/y(x/b), a/(y(x/b))) are not correct representations of the product. Correct options are Options B, D, E.
Complete question:
If a/b and x/y represent rational expressions and b0 and y0, what is true of their product? Select three options.
A. The product is equivalent to ay/bx
B. The product is a rational expression.
C. The product is equivalent to a/y(x/b)
D. The product is the ratio of ax and by.
E. The product is equivalent to ax/b(y)
A quilt is in the shape of a regular pentagon. It is made from 5 pieces of fabric that are congruent triangles. Each triangle has an area of 16 inches.What is the area of the quilt?
Final answer:
The area of the quilt, which is a regular pentagon made from five congruent triangles, is 80 square inches, determined by multiplying the area of one triangle (16 inches) by five.
Explanation:
The area of the quilt which is in the shape of a regular pentagon can be determined by calculating the area of the five congruent triangles that make up the pentagon. Since each triangle has an area of 16 inches, we can find the total area by simply multiplying the area of one triangle by the number of triangles.
To calculate the total area of the quilt:
First, determine the area of one triangle, which is given as 16 inches.Next, since there are five congruent triangles in the pentagon, multiply the area of one triangle by 5.The total area of the quilt would be 16 inches (per triangle) × 5 triangles = 80 inches.Therefore, the total area of the quilt is 80 square inches.
Complete the equation of the line through (-8,8) and (1,-10). Use exact numbers.
The equation of the line through (-8,8) and (1,-10) is y = -2x - 8
Using the slope intercept form equation.
y = mx + b
where
m = slope
b = y-intercept
Therefore,
(-8,8) (1,-10)
m = -10 - 8 / 1 + 8 = - 18 / 9 = -2
Therefore,
let's find b as follows:
(1, -10)
y = -2x + b
-10 = -2(1) + b
b = -10 + 2
b= -8
Therefore,
y = -2x - 8
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Daniela is a stain glass artist; she created the window below for her living room. What is
the area of the window she created?
If you add the lengths of the focal radii of an ellipse, what other value will you produce?
2a
2b
2c
The eccentricity
Equation of an ellipse
→having center (0,0) , vertex ([tex](\pm a ,0)[/tex] and covertex [tex](\pm b ,0)[/tex] and focus [tex](\pm c ,0)[/tex] is given by:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2}=1[/tex]
As definition of an ellipse is that locus of all the points in a plane such that it's distance from two fixed points called focii remains constant.
Consider two points (a,0) and (-a,0) on Horizontal axis of an ellipse:
Distance from (a,0) to (c,0) is = a-c = [tex]F_{1}[/tex]
Distance from (-a,0) to (c,0) is = a + c = [tex]F_{2}[/tex]
[tex]F_{1} + F_{2} =[/tex] a -c + a +c
= a + a
= 2 a →(Option A )
What is the surface area of a conical grain storage tank that has a height of 43 meters and a diameter of 14 meters? Round the answer to the nearest square meter.
A. 1,100 square meters
B. 1,112 square meters
C. 2,507 square meters
D. 2,605 square meters