Answer
Area of the square = 36 square cm
Step-by-step explanation:
Given:
The perimeter of an equilateral triangle = the perimeter of a square
In an equilateral triangle, all sides are equal
Each side of the equilateral triangle = 8cm
Perimeter of the equilateral triangle = 3 * 8cm
Perimeter of the equilateral triangle = 24cm
Since, perimeter of square = perimeter of an equilateral triangle
Perimeter of a square = 24cm
We need to find each side of the square
Perimeter of a square = 4s
24 = 4s
Divide both side by 4
24/4 = 4s/4
s = 6cm
Since the length of each side of the square is 6cm
Therefore, area = l^2
Area = 6 * 6
Area of a square = 36 square cm
4 gallons of water weigh 33.4 pounds how much do 7.5 gallons of water weigh
4 gallons of water weigh 33.4 pounds how much do 7.5 gallons of water weigh
Applying proportion
33.4/4=x/7.5
solve for x
x=(33.4/4)*7.5
x=62.625 poundscan you give me a step by step problem to this
Answer:
y = m x * b equation for a straight line
When x = 0 you have b = y = 4
y = m x + 4 revised equation
When y = 0, m = -4 / x = -4 / 2 = -2
y = -2 x + 4 or -2 x - y = -4
(a) is the correct answer
Rewrite the set G by listing its elements. Make sure to use the appropriate set notation.G = ( z l z is an integer and -3 < z <_ 0)
Given the set G = ( z l z is an integer and -3 < z <_ 0) , we are to write out all the elements in the set.
First you must take note of the inequality signs.
First aspect of the inequality-3 < z means that z is a value greater than -3 exclusive -3. The values are -2, and -1
The second part of the inequality z <_ 0 means that z is less than or equal to 0, this means that 0 is inclusive because of the equal to sign.
Hence the set of element G will be -2, -1 and 0. In set notataion, it is represented as:
G = {-2, -1, 0}
Note that -3 is not part of the element G
The arc length of the semicircle shown in green is 34. What is the radius of the circle? R=
Given:
[tex]\begin{gathered} \text{length of arc = 32}\pi \\ \theta=180^0(angle\text{ on a straight line or angle in semi circle)} \\ r=\text{?} \end{gathered}[/tex]To calculate the length of an arc, the formula is;
[tex]\begin{gathered} l=\frac{\theta}{360}\times2\pi r \\ \text{Substituting all the parameters into the formula;} \\ 32\pi=\frac{180}{360}\times2\pi r \\ 32\pi=\frac{360\pi\text{ r}}{360} \\ 32\pi=\pi r \\ r=\frac{32\pi}{\pi} \\ r=32 \end{gathered}[/tex]Therefore, the radius of the circle 32 units.
Flying Home A bird flies from the bottom of a canyon that is 70 5 feet below sea level to a nest 7. that is 652 feet above sea level. What is the difference in elevation between the bottom of the 10 canyon and the bird's nest?
If we refer the level 0 to the sea level.
Then, 10 feet belox the sea level is -10 and 10 above is 10 feet (positive).
Then, the bottom of the canyon is at level y=-70 4/5 (referred to the sea level) and the nest is y=652 feet.
Then, the distance is D=y2-y1=652-(-70)=652+70=772 feet.
The distance between canyon bottom and nest is 772 feet.
et
Drag the tiles to the boxes to form correct pairs.
Match each addition operation to the correct sum.
Please look at the image below
Answer:
• -23.24 = 28.98 +(-52.22)
• 131.87 = 56.75 + 75.12
• 84 5/8 = 45 2/9 + 39 3/9
• 6 2/9 = -24 5/9 + 30 7/9
Two containers designed to hold water are side by side both in the shape of a cycle see. Container A has a radius of 4 feet and a height of 9 feet. Container B has a radius of 3 feet and height of 11 feet. Container A is full of water and the water is pumped into container B until container B is completely full. After the pumping is complete what is the volume of water remaining in container A to the nearest tenth of a cubic foot
We have to calculate the water remaining in A after B is complete.
This will be equal to the volume of A minus the volume of B.
The volume of each cylinder is equal to the area of the base times the height, so we can calculate this difference as:
[tex]\begin{gathered} V=V_A-V_B \\ V=\pi(r_A)^2h_A-\pi(r_B)^2h_B \\ V=\pi(4)^2(9)-\pi(3)^2(11) \\ V=\pi(16)(9)-\pi(9)(11) \\ V=144\pi-99\pi \\ V=45\pi \\ V\approx141.4 \end{gathered}[/tex]Answer: the remaining volume is approximately 141.4 cubic feet.
To measure how much gasoline she uses on her road trip , Hortense makes a graph that shows the amount remaining in the tank as a function of the miles she has driven ( see figure ) .
It is important to know that the domain set is formed by all the x-values shown by the graph.
Having said that, the domain of the given graph is from 0 to 400, positive real numbers.
Hence, the answer is B.Please help on my question I have the graph part done, I need help on the other parts
the Here the equation of amount of salt in the barrel at time t is given by
[tex]Q(t)=21(1-e^{-0.06t})[/tex]a
At time t=7 minute the amount of salt will be
[tex]Q(7)=21(1-e^{-0.06\times7})\Rightarrow Q(7)=21\times0.342953\Rightarrow Q(7)=7.20[/tex]The amount of salt after 7 min will be 7.20lb.
b
At time t=14minute the amount of salt will be
[tex]Q(14)=21(1-e^{-0.06\times14})\Rightarrow Q(14)=11.93[/tex]Amount of salt will be 11.93 lb
d
From the graph, for large t the value Q(t) the amount of salt approaches to 21 lb.
The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system if it exists. Write an exact answer in simplified form. If there are infinitely many solutions, write an expression involving z for each coordinate where z represents all real numbers.
ANSWER:
[tex]\begin{gathered} x+2z=1 \\ y-5z=3 \end{gathered}[/tex]The solution is:
[tex]\begin{gathered} x=1-2z \\ y=3+5z \\ z=z \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We must convert the matrix into a system of linear equations.
Each vertical represents the letters x, y and z, the first the x, the second y and the third the z. The fourth value is the value of the independent term that would be equal to the other expression, just like this:
[tex]\begin{gathered} 1x+0y+2z=1 \\ 0x+1y-5z=3 \\ 0x+0y+0z=0 \end{gathered}[/tex]We operate and the system will finally be like this
[tex]\begin{gathered} x+2z=1 \\ y-5z=3 \end{gathered}[/tex]let's solve the system and we have:
[tex]\begin{gathered} x=1-2z \\ y=3+5z \\ z=z \end{gathered}[/tex]supposed that there are two types of tickets to a show: Advance and same-day. Advance tickets cost $25 and same-day tickets cost $40.For one performance, there were 60 tickets sold in all, and the total amount paid for them was $205. How many tickets of each type were sold?number of advanced tickets sold:number of same-day tickets sold:
For the show there are two types of tickets:
Advance tickets, that cost $25
Same-day tickets, that cost $40
We know that for one function there were 60 tickets sold for a total amount of $205.
Let "a" represent the number of advanced tickets sold and "s" represent the number of same-day tickets sold.
The total number of tickets sold for the function can be expressed as the sum of the number of advance tickets (a) sold and the number of same-day tickets sold (s)
[tex]60=a+s[/tex]If each advance ticket costs $25 and there were "a" advance tickets sold, the total earnings for advance tickets can be expressed as 25a
And if each same-day ticket costs $40 and there were "s" same-day tickets sold, the earnings for selling same-day tickets can be expressed as 40s
The total earnings for the performance can be expressed as the sum of the earnings for selling advance tickets and the earnings for selling same-day tickets:
[tex]205=25a+40s[/tex]Both equations established form an equation system and we can use them to determine the number of advance and same-day tickets sold:
-First, write the first equation for one of the variables, I will write it for "a"
[tex]\begin{gathered} 60=a+s \\ a=60-s \end{gathered}[/tex]-Second, replace the expression obtained for "a" into the second equation:
[tex]\begin{gathered} 205=25a+40s \\ 205=25(60-s)+40s \end{gathered}[/tex]From this expression, we can calculate the value of "s", first, you have to distribute the multiplication on the parentheses term, which means that you have to multiply both terms by 25:
[tex]\begin{gathered} 205=25\cdot60-25\cdot s+40s \\ 205=1500-25s+40s \end{gathered}[/tex]Next, simplify the like terms
[tex]205=1500+15s[/tex]Pass "1500" to the other side by applying the inverse operation to both sides of it, which means that you have to subtract 1500 to both sides of the equal sign:
[tex]\begin{gathered} 205-1500=1500-1500+15s \\ -1295=15s \end{gathered}[/tex]And finally divide both sides by 15 to reach the value of s
[tex]\begin{gathered} -\frac{1295}{15}=\frac{15s}{15} \\ -86.33=s \end{gathered}[/tex]With the value of s calculated, you can replace it into the expression obtained for a and calculate its value:
[tex]\begin{gathered} a=60-s \\ a=60-(-86.33) \\ a=146.33 \end{gathered}[/tex]So with the information given, the number of advanced and same-day tickets sold are:
a=146.33
s=-86.33
Which of the equations below represent exponential decay? Select all that apply. • y= (6.35)^x• y= (0.01)^ x• y= (3/4) 2^x• y= 700 (1-0.35)^x • y= (4/3) ^x
The equation is that represent exponential decay is:
[tex]y=700(1-0.35)^x[/tex]Explanation:The rate in the equation of an exponential decay is negative, this would make it reduce expentially, rather than grow.
The best equation that demonstrate this is:
[tex]y=700(1-0.35)^x[/tex]Where the rate is 0.35
Find the term named in the problem,and the explicit formula. -32,-132,-232,-332,… find a40
We need to find the n term formula:
The given sequence represents an arithmetic sequence and it follows the next form:
[tex]a_n=a+(n-1)d[/tex]Where a represents the first term, in this case, a= -31
n is the term of the sequence
And d is the constant:
Let's find the constant
a1 to a2 =
-32 to -132, then, -32 needs -100 units bo equal to -132.
Now, -132 need -100 units to be equal to -232.
-232 needs -100 units to be equal to -332
Therefore, the constant d is equal to -100, d=-100
Replacing these values:
[tex]a_n=-32+(n-1)(-100)[/tex]Then:
[tex]a_n=-32-(n-1)(100)[/tex]With this n formula, we can replace n=40, then, we will find a40:
[tex]a_{40}=-32-(40-1)100[/tex]Therefore:
[tex]a_{40}=-3932[/tex]what is 1.8333333 as a fraction
This is a periodic decimal, which means a fixed part of the number will repeat forever, this part is called period. In this case the period is equal to 3. To convert a periodic decimal to a fraction we need to do as below.
We need to subtract the part of the number that doesn't repeat with one period of that part that repeats without the dot, which would be "183" and subtract it with the part that doesn't repeat without the dot "18". This would be "183 - 18 = 165". We then count the number of algarisms in the period of the number, in this case we only have one, which is "3". For every algarism in the period we add a "9" to the denominator. If there are numbers on the decimal part that don't repeat we add "0" after the 9. So we have the following fraction.
[tex]1.833333\ldots\text{ = }\frac{183-18}{90}\text{ = }\frac{165}{90}[/tex]I need help with number part a and bThank you very much
PART A
For our beautiful sun, we'll have that:
[tex]b=1.4\cdot10^3[/tex]This way,
[tex]\begin{gathered} M=-2.5\log (\frac{1.4\cdot10^3}{2.84\cdot10^{-8}}) \\ \\ \Rightarrow M=-9.74 \end{gathered}[/tex]PART B
We'll have the equation:
[tex]-0.27=-2.5\log (\frac{b}{2.84\cdot10^{-8}})[/tex]Solving for b,
[tex]\begin{gathered} -0.27=-2.5\log (\frac{b}{2.84\cdot10^{-8}})\rightarrow0.27=2.5\log (\frac{b}{2.84\cdot10^{-8}}) \\ \\ \rightarrow\frac{0.27}{2.5}=\log (\frac{b}{2.84\cdot10^{-8}})\rightarrow0.108=\log (\frac{b}{2.84\cdot10^{-8}}) \end{gathered}[/tex]Now we'll use the following property:
[tex]c=\log _a(b)\Leftrightarrow b=a^c[/tex]This way,
[tex]\begin{gathered} 0.108=\log (\frac{b}{2.84\cdot10^{-8}})\rightarrow e^{0.108}=\frac{b}{2.84\cdot10^{-8}} \\ \\ \Rightarrow b=2.84\cdot10^{-8}e^{0.108} \\ \\ \Rightarrow b=3.16\cdot10^{-8} \end{gathered}[/tex]Find the value of x that will make L||M.2x - 3MX + 4x = [?]
We can say that Line L and Line M are parallel to each other if, when cut by a transversal line, the corresponding angles, the alternate exterior angles, and the alternate interior angles are congruent.
In the figure shown, we have a pair of alternate exterior angles. Therefore, the two angles must be equal to each other. With that, we have the following equation:
[tex]2x-3=x+4[/tex]From that equation, we can solve x by joining like terms on either side of the equation.
[tex]\begin{gathered} 2x-x=4+3 \\ x=7 \end{gathered}[/tex]Therefore, x = 7. When asked, the measure of the two angles are 11 degrees.
Which expression is equivalent to -1/2(6x - 12)A. 6x + 6B. 3x - 12C. 3X-6D. 3x + 6
The expression is 3x-6
From the question, we have
1/2(6x - 12)
=1/2*6x-1/2*12
=3x-6
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
To learn more about multiplication visit: https://brainly.com/question/5992872
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Answer:
The expression is 3x-6
From the question, we have
1/2(6x - 12)
=1/2*6x-1/2*12
=3x-6
Step-by-step explanation:
17 ohms to kilohms (Round answer to the nearest thousandth.)
In converting measurements, you must take note of the prefixes.
Note that a kilo is 1000 times the base measurement.
Example :
1 kilometer = 1000 meter
1 kilogram = 1000 gram
From the given problem :
1 kiloohm = 1000 ohm
17 ohms will be :
[tex]17\cancel{\text{ohms}}\times\frac{1\text{kiloohm}}{1000\cancel{\text{ohm}}}=\frac{17}{1000}=0.017\text{kiloohm}[/tex]The answer is 0.017 kiloohm
With the points (8,4) (-6,-6) (-10, 12) (2,-4). What are the new points if thescale factor of dilation is 4?*
The transformation for a points using a dilation factor k follows the rule:
[tex](x,y)\Rightarrow k(x,y)\Rightarrow(kx,ky)[/tex]Applying this to the points given
[tex](8,4)\Rightarrow(8\cdot4,4\cdot4)\Rightarrow(32,16)[/tex][tex](-6,-6)\Rightarrow(4\cdot-6,4\cdot-6)\Rightarrow(-24,-24)[/tex][tex](-10,12)\Rightarrow(4\cdot-10,12\cdot4)\Rightarrow(-40,48)[/tex][tex](2,-4)\Rightarrow(4\cdot2,4\cdot-4)\Rightarrow(8,-16)[/tex]Find the absolute value|9\5|
Absolute value simply means the number must be made positive. Since 9/5 is positive already the absolute value remains 9/5
A city currently has 129 streetlights. As part of a urban renewal program, the city council has decided to install 3 additional streetlights at the end of each week for the next 52 weeks.How many streetlights will the city have at the end of 45 weeks?—————
Solution
Step 1
Current number of streetlights = 129
Step 2
Number installed per week = 3
[tex]\begin{gathered} Number\text{ of straightlights installed in 45 weeks = 3 }\times\text{ 45} \\ =\text{ 135} \end{gathered}[/tex]Step 3
Number of straightlights at the end of 45 weeks = 129 + 135 = 264
Final answer
256
The sales S (in billions of dollars) for Starbucks from 2009 through 2014 can be modeled by the exponential functionS(t) = 3.71(1.112)twhere t is the time in years, with t = 9 corresponding to 2009.† (Round your answers to two decimal places.)a) Use the model to estimate the sales in 2015 in billions of dollars.b) Use the model to estimate the sales in 2024 in billions of dollars.
a) Use the model to estimate the sales in 2015 in billions of dollars
Evaluate the function for t=15
[tex]\begin{gathered} S(15)=3.71(1.112)\placeholder{⬚}^{15} \\ \\ S(15)\approx18.24 \end{gathered}[/tex]The sales in 2015 will be $18.24 billionb) Use the model to estimate the sales in 2024 in billions of dollars
Evaluate the function for t=24
[tex]\begin{gathered} S(24)=3.71(1.112)\placeholder{⬚}^{24} \\ \\ S(24)=47.41 \end{gathered}[/tex]The sales in 2024 will be $47.41 billionThe perimeter of a rectangular goat pen is 28 meters. The area is 45 square meters. Whatare the dimensions of the pen?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given information
[tex]\begin{gathered} Perimeter=2l+2b=28m \\ Area=lb=45m^2 \\ \\ where\text{ l is the length, b is the breadth} \end{gathered}[/tex]STEP 2: Label the two equations
[tex]\begin{gathered} 2l+2b=28------equation\text{ 1} \\ lb=45----equation\text{ 2} \end{gathered}[/tex]STEP 3: Solve for the missing values
Isolate l in equation 1
[tex]\begin{gathered} 2(l+b)=28 \\ l+b=\frac{28}{2}=14 \\ l=14-b-----equation\text{ 3} \end{gathered}[/tex]Substitute 14-b for l in equation 2
[tex]\begin{gathered} (14-b)\cdot b=45 \\ 14b-b^2=45 \\ We\text{ have the quadratic equation} \\ -b^2+14b-45=0 \end{gathered}[/tex]Solve the equation quadratically
[tex]\begin{gathered} -b^{2}+14b-45=0 \\ -b^2+9b+5b-45=0 \\ -b(b-9)+5(b-9)=0 \\ (-b+5)(b-9)=0 \\ -b+5=0,b=5 \\ b-9=0,b=9 \\ \\ b=5,b=9 \end{gathered}[/tex]Substitute the values into equation 3,
[tex]\begin{gathered} l=14-b \\ when\text{ b = 5} \\ l=14-5=9 \\ When\text{ b = 9} \\ l=14-9=5 \end{gathered}[/tex]Hence, the dimensions of the pen is given as:
[tex]9m\text{ }by\text{ }5m[/tex]Write an equation in slope-intercept form with aslope of 10 that passes through (0,6)A.x + y = 6B. y + 10x + 6C. 7x + y = 10D. y = 10x + 6
What is the amplitude and period of F(t) = sin 2t?a. amplitude: 1; period, pib. amplitude: -1; period: pic. amplitude: 1; period: 2pid. amplitude: -1; period: 2piPlease select the best answer from the choices provided
Answer:
[tex]\text{amplitude: 1, period: }\pi[/tex]Explanation:
Given the function in the attached image;
[tex]f(t)=\sin 2t[/tex]Comparing to the general form of periodic equations.
[tex]f(t)=A\sin B(t+C)+D[/tex][tex]\begin{gathered} A=\text{ Amplitude} \\ A=1 \end{gathered}[/tex][tex]\begin{gathered} \text{Period =}\frac{2\pi}{B} \\ \text{ from the equation B = 2;} \\ \text{ Period = }\frac{2\pi}{2}=\pi \end{gathered}[/tex]Therefore;
[tex]\text{amplitude: 1, period: }\pi[/tex]After graduating from college, Carlos receives two different job offers. Both pay a starting salary of $65000 per year, but one job promises a $3250 raise per year, while the other guarantees a 4% raise each year. Complete the tables below to determine what his salary will be after t years. Round your answers to the nearest dollar.
Given:
• Starting salary of each Job = $65000
,• Job 1 promises a $3250 raise per year
,• Job 2 promises a 4% raise each year.
Let's complete the given tables.
The equation to represent job 1 will be a linear equation:
y = 3250t + 65000
The equation which represents job 2 will be an exponential equation:
[tex]\begin{gathered} y=65000\mleft(1+0.04\mright)^t \\ \\ y=65000(1.04)^t \end{gathered}[/tex]Now, to complete the tables, input the different values of t into the equation and solve for y.
• For Job 1, we have the following:
• When t = 1:
y = 3250(1) + 65000 = 68250
• When t = 5:
y = 3250(5) + 65000
y = 16250 + 65000
y = 81250
• When t = 10:
y = 3250(10) + 65000
y = 32500 + 65000
y = 97500
• When t = 15:
y = 3250(15) + 65000
y =48750 + 65000
y = 113750
• When t = 20:
y = 3250(20) + 65000
y = 65000 + 65000
y = 130000
• For Job 2, we have the folllowing:
• When t = 1:
y = 65000(1.04)¹
y = 67600
• When t = 5
y = 65000(1.04)⁵
y = 65000(1.216652902)
y = 79082
• When t = 10:
y = 65000(1.04)¹⁰
y = 65000(1.480244285)
y = 96216
• When t = 15:
y = 65000(1.04)¹⁵
y = 65000(1.800943506)
y = 117061
• When t = 20
y = 65000(1.04)²⁰
y = 65000(2.191123143)
y = 142423
Therefore, we have the complete table below:
Simplify the expression. 1 3 3 m +8 4 3m 3 2 3 1 3 3 +8 4 2 (Use the operation symbols in the math palette as ne any numbers in the expression.)
We need to simplify the following expression
[tex]\frac{3}{4}m^3+8-\frac{1}{2}m^3[/tex]We first group the similar terms, they are the first and the third one
[tex](\frac{3}{4}m^3-\frac{1}{2}m^3)+8[/tex]then we use common factor to take out the m^3 of the parenthesis
[tex]m^3(\frac{3}{4}-\frac{1}{2})+8=\frac{1}{4}m^3+8=4(m^3+2)^{}[/tex]Write the equation of the function in vertex form, then convert to standard form.
The equation of the parabola in vertex form is
[tex]y=a(x-h)^2+k[/tex]where the point (h,k) is the coordinate of the vertex. From our picture, we can note that (h,k)=(-6,-4).
By substituting these values into our first equation, we have
[tex]y=a(x-(-6))^2-4[/tex]which gives
[tex]y=a(x+6)^2-4[/tex]Now, we can find the constant a by substituting one of the other given point. If we choose point (0,-2) into this last equation, we get
[tex]-2=a(0+6)^2-4[/tex]which gives
[tex]\begin{gathered} -2=a(6^2)-4 \\ -2=36a-4 \end{gathered}[/tex]then, by moving -4 to the left hand side, we have
[tex]\begin{gathered} -2+4=36a \\ 2=36a \\ or\text{ equivalently,} \\ 36a=2 \end{gathered}[/tex]and finally, a is equal to
[tex]\begin{gathered} a=\frac{2}{36} \\ a=\frac{1}{18} \end{gathered}[/tex]hence, the equation of the parabola in vertex form is
[tex]y=\frac{1}{18}(x+6)^2-4[/tex]Now, lets convert this equation into a standrd form. This can be done by expanding the quadratic term and collecting similar term. That is, by expanding the quadratic terms, we obtain
[tex]y=\frac{1}{18}(x^2+12x+36)-4[/tex]now, by distributing 1/18, we have
[tex]y=\frac{1}{18}x^2+\frac{12}{18}x+\frac{36}{18}-4[/tex]which is equivalent to
[tex]y=\frac{1}{18}x^2+\frac{1}{3}x+2-4[/tex]and finally, the parabola equation in standard form is
[tex]y=\frac{1}{18}x^2+\frac{1}{3}x-2[/tex]The distance from Boston, Massachusetts to Little Rock, Arkansas is 1,452.8 miles. How many ft/min would you have to drive to get there in 20 hours and 45 minutes?
First we find the speed in mi/h.
We know that 20 h 45 min is equal to 20.75 hours, then the speed is
[tex]\frac{1452.8\text{ mi}}{20.75\text{ h}}=70.01\text{ mi/h}[/tex]Now we convert the speed to ft/min:
[tex]70.01\text{ mi/h}\cdot\frac{1\text{ h}}{60\text{ min}}\cdot\frac{5280\text{ ft}}{1\text{ mi}}=6161.27\text{ ft/min}[/tex]Therefore you would have to drive at a speed of 6161.27 ft/min
Find the vertical asymptotes of the graph of the rational function. y= x-15 / x + 6 The equation (s) of the vertical asymptotes is/are x= _____. (Use a comma to separate the answers as needed.)
Solution
The vertical asymptotes
[tex]\begin{gathered} y=\frac{x-15}{x+6}= \\ \end{gathered}[/tex]setting the denominator to 0
=> x + 6 = 0
=> x = - 6
The equation (s) of the vertical asymptotes is/are x = - 6