At The Local Golf Court, Tom has 8 of the 25 best course ever recorded what percent of the best Scores does Tom have?
Answers
The 25 best course represent the 100%
If tom has 8 of the 25
Make a rule of three:
25---------100%
8------------ x
x= (8*100)/25
x= 32%
Related Questions
Three quarters of the circumference of a circle equals how many degrees ?A.45B.90C.180D.270E.360
Answers
Three quarters is equivalent to 3/4.
The total degrees of a circle is equal to 360°
Determining three quarters of the circumference, we get:
[tex](\frac{\text{ 3}}{\text{ 4}})(360^{\circ})[/tex]We get,
[tex](\frac{\text{ 3}}{\text{ 4}})(360^{\circ})[/tex][tex]=\frac{3\text{ x 360}}{\text{ 4}}[/tex][tex]\text{ }=\frac{1080\text{ }}{4}[/tex][tex]=270^{\circ}[/tex]Therefore, three quarters of the circumference of a circle is 270°
The answer is letter D.
Use the box plot to answer the following questions.22 2311 1224 25 261318 19 20 2114 15 16 17Cost of DVDs (in dollars)a) The minimum price ise) The median isb) The maximum price isf)75% of the DVDs cost at leastandg) The cheapest 25% of DVDs cost betweenc) The first quartile isd) The third quartile is
Answers
From the box plot:
a) The minimum price is $11
b) The maximum price is $25
c) The first quartile is $14
d) The third quartile is $20
e) The median is $16
f) 75% of the DVDs cost at least $14
g) The cheapest 25% of DVDs cost between $11 and $14
At the movie theatre, child admission is $6.30 and adult admission is $9.60 on Monday, 139 tickets were sold for a total sales of $1136.40 how many child tickets were sold that day
Answers
Solution:
Take x as the number of child tickets sold, and y as the number of adult tickets sold.
so the equations will be:
6.30x+9.60y=1136.40 Equation 1 : Total sale.
x + y = 139 Equation 2: Total amount of tickets sold.
From equation 2, we obtain:
x = 139-y Equation 3
replacing this into equation 1, we get:
[tex]6.30\mleft(139-y\mright)+9.60y=1136.40[/tex]applying the distributive property, this is equivalent to:
[tex]875.7-6.30y+9.60y=1136.40[/tex]this is equivalent to:
[tex]-6.30y+9.60y=1136.40-\text{ }875.7[/tex]this is equivalent to:
[tex]3.3\text{ y = 260.7}[/tex]solving for y, this is equivalent to:
[tex]y\text{ =}\frac{260.7}{3.3}=79[/tex]now, replacing this into equation 3, we obtain:
[tex]x=139-y=\text{ 139-79=60}[/tex]So that, we can conclude that the correct answer is:
the number of child tickets sold is x= 60
How to write a quadratic equation using the turning point and one other coordinate. Turning point (2.247,0.665) other coordinate ( 1.27,0.32)
Answers
The turning point of a parabola is the same as the vertex of the parabola. This means that the coordinate of the turning point is also the coordinate of the vertex. Recall, the vertex form of a quadratic equation is expressed as
y = a(x - h)^2 + k
where
a is the leading coefficient
h and k are the x and y coordinates of the vertex.
From the information given,
Coordinate of turning point or vertex is (2.247,0665). This means that
h = 2.247
k = 0.665
Coordinate of other point is (1.27, 0.32). This means that
x = 1.27
y = 0.32
By substituting these values into the equation, we have
0.32 = a(1.27 - 2.247)^2 + 0.665
0.32 = 0.954529a + 0.665
Substracting 0.665 from both sides, it becomes
0.954529a = 0.32 - 0.665 = - 0.345
Dividing both sides by 0.954529, it becomes
0.954529a/0.954529 = - 0.345/0.954529
a = - 0.361
By substituting these values into the equation, the quadratic equation is
y = - 0.361(x - 2.247)^2 + 0.665
Find the volume of this cylinder. Use 3 for a.3 in.V = tr2h=7 in.V ~ [?]in3Ñ
Answers
The formula to find the volume of a cylinder is:
[tex]\begin{gathered} V=\pi r^2h \\ \text{ Where} \\ V\text{ is the volume} \\ r\text{ is the radius} \\ h\text{ is the height} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} r=3in^{} \\ h=7in \\ \pi\approx3\Rightarrow\text{ The symbol }\approx\text{ is read 'approximately'} \end{gathered}[/tex][tex]\begin{gathered} V=\pi r^2h \\ V\approx3(3in)^2(7in) \\ V\approx3(9in^2)^{}(7in) \\ V\approx189in^3 \end{gathered}[/tex]Therefore, the volume of the cylinder is approximately 189
Determine whether the given ordered pair is a solution to the system of equations. 6x−2y =34−3x+3y =15 and (11,16) ____Yes, it is a solution.____ No, it is not a solution.
Answers
Given:
[tex]\begin{gathered} 6x-2y=34\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ -3x+3y=15\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]Sol:.
Mutiply by 2 in equation (2) then.
[tex]\begin{gathered} -3x+3y=15 \\ 2(-3x+3y)=2\times15 \\ -6x+6y=30 \end{gathered}[/tex]Add both equation then:
[tex]\begin{gathered} 6x-2y=34 \\ -6x+6y=30 \\ \text{Add both equation:} \\ 6x-2y+(-6x)+6y=34+30 \\ 6x-6x+6y-2y=34+30 \\ 6y-2y=64 \\ 4y=64 \\ y=\frac{64}{4} \\ y=16 \end{gathered}[/tex]Put the value of y for find the value od "x"
[tex]\begin{gathered} 6x-2y=34 \\ y=16 \\ 6x-2(16)=34 \\ 6x-32=34 \\ 6x=34+32 \\ 6x=66 \\ x=\frac{66}{6} \\ x=11 \end{gathered}[/tex]So the value of "x" is 11 and value of "y" is 16 then:
[tex]\text{solution =(11,16)}[/tex]12in represent 25 miles information to match each distance on the map
Answers
Answer"
8inches = 100miles
18inches = 225miles
12inches = 150miles
Explanation
Given the conversion rate;
2inches = 25miles
For 8 inches;
2inches = 25miles
8inches = x
Cross mutlply
2x = 8 * 25
2x = 200
x = 200/2
x = 100miles
Hence 8inches = 100miles
For 18inches
2inches = 25miles
18inches = y
Cross multiply
2y = 25* 18
2y = 450
y = 450/2
y = 225miles
Hence 18inches = 225miles
For 12inches;
2inches = 25miles
12inches = z
Cross multiply
2z = 12 * 25
2z = 300
z = 300/2
z = 150miles
Hence 12inches = 150miles
4x3-12x2 + 8x Find the quotient of -4x O x² – 3x+2 O x2 + 12x - 4 O -x² + 3x-2 Ox2 - 12x + 4
Answers
Given
[tex]\frac{4x^3-12x^2+8x}{-4x}[/tex]Procedure
[tex]\begin{gathered} \frac{4x^3}{-4x}-\frac{12x^2}{-4x}+\frac{8x}{-4x} \\ -x^2+3x-2 \end{gathered}[/tex]The answer is
[tex]-x^2+3x-2[/tex]need help trying to solve problem. I do not understand the step process.
Answers
it is a right triangle ebcase an angle is 90°
so, we can use trigonometric ratios
we will use sine
[tex]\sin (\alpha)=\frac{O}{H}[/tex]where alpha is the angle, O the opposite side from the angle and H the hypotenuse o the triangle
then, replacing
[tex]\sin (66)=\frac{x}{4}[/tex]we use the angle 66° becase we need to find x and x is the opposite side from it
now solve the expression for x
[tex]\begin{gathered} x=4\sin (66) \\ \end{gathered}[/tex]and calculate
[tex]x=3.65[/tex]The value of x is 3.65m
Which of the following sets of numbers could represent the three sides of a righttriangle?{54, 72, 91} {5, 12, 14) {20, 22, 29} {48, 64, 80}
Answers
To answer this question, we can use the Pythagorean Theorem in each case to determine if each of the sides represents a side of a right triangle.
[tex]h^2=a^2+b^2[/tex]This is the algebraic expression of the Pythagorean Theorem. The hypotenuse is the largest side of the triangle.
First case{54, 72, 91}
Hypotenuse = 91
Then, we have:
[tex]91^2=54^2+72^2\Rightarrow8281=2916+5184\Rightarrow8281\ne8100[/tex]They do not represent the sides of a right triangle.
Second case{5, 12, 14)
Hypotenuse = 14
[tex]14^2=5^2+12^2\Rightarrow196=25+144\Rightarrow196\ne169[/tex]They do not represent the sides of a right triangle.
Third case{20, 22, 29}
[tex]29^2=20^2+22^2\Rightarrow841=400+484\Rightarrow841\ne884[/tex]They do not represent the sides of a right triangle.
Fourth case{48, 64, 80}
[tex]80^2=48^2+64^2\Rightarrow6400=2304+4096\Rightarrow6400=6400[/tex]This triple represents the sides of a right triangle.
In summary, the answer is {48, 64, 80} (last option).
Choose the shape that matches the definition a three dimensional shape with a circular base and a vertex opposite base.
Answers
We need to identify which is the correct shape. We are told that it has a vertex. A vertex is a point where two or more lines, curves or edges met. In three dimensional shapes a vertex is a corner of the shape. As you can see, from the three shapes we have in the picture the only one with a corner is the cone. It is also important to note that this corner is in the opposite side of the base and this base has a circular shape.
AnswerAs we discussed above the shape that meets these characteristics is the cone. Therefore the answer is the cone.
Find the missing side. Round to thenearest tenth.A) 7.1B) 24.7D) 4.9C) 3.6
Answers
From the provided image, we are provided with the opposite side, which is 11, and the adjacent side which is x.
The suitable trigonometry ratio for this is the Tangent.
[tex]\begin{gathered} \text{Tan 66}^0=\text{ }\frac{opposite}{\text{adjacent}} \\ \text{Tan 66}^0=\frac{11}{x} \\ 2.246=\frac{11}{x} \\ x=\frac{11}{2.246} \\ x=4.89 \\ To\text{ the nearest tenth, x = 4.9} \end{gathered}[/tex]Hence, the missing side is 4.9
A regular heptagon with 7 sides is inscribed in a circle with radius 10 millimeters. What is the area of the figure? 273.641 mm.2 234.549 mm.2 39.092 mm.2 321.311 mm.2
Answers
Given:
A regular heptagon with 7 sides is inscribed in a circle.
The radius is 10 mm.
The inscribed angle in the regular heptagon is 51.43 degrees.
Consider,
[tex]\begin{gathered} a^2=10^2+10^2-2(10)(10)\cos 51.43^{\circ} \\ a^2=200-200(0.6235) \\ a=8.68 \end{gathered}[/tex]The area of the heptagon is,
[tex]\begin{gathered} A=\frac{7}{4}a^2\cot (\frac{180^{\circ}}{7}) \\ =\frac{7}{4}(8.68)^2\cot (\frac{180^{\circ}}{7}) \\ =273.7\operatorname{mm} \end{gathered}[/tex]
Answer: option a) 273.641 mm² ( approximately)
Answer:
273.641 mm²
Step-by-step explanation:
Ramsay cuts out a piece from a circular cardboard for a school project. The radius of the cardboard is 14 inches and the measure of the central angle is 54 degrees, as shown
Answers
Given the figure, we can deduce the following information:
1. The radius of the cardboard is 14 inches.
2. The measure of the central angle is 54 degrees.
To determine the length of the curve boundary of the piece of the cardboard, we use the formula:
[tex]\text{Arc Length}=2\pi r(\frac{\theta}{360})[/tex]where:
θ=central angle
r=radius
We plug in what we know:
[tex]\begin{gathered} \text{Arc Length}=2\pi r(\frac{\theta}{360}) \\ =2\pi(14)(\frac{54}{360}) \\ \text{Simplify} \\ \text{Arc Length}=4.2\pi\text{ inches} \end{gathered}[/tex]Therefore, the answer is 4.2π inches.
The preimage was (5, 4) and after the rotation the image was (4, 5). What many degrees counterclockwise did the point rotate?a. none of the above.b. 270c.180d.90
Answers
Answer:
a. none of the above.
Explanation:
The transformation
[tex](x,y)\rightarrow(y,x)[/tex]is a 270-degree rotation clockwise NOT counterclockwise; therefore, none of the choices given is correct.
what is the inverse of the following condition?if it is not trudy's birthday,then she is not going to eat rocky road ice cream
Answers
You have a statement in the form:
If not p, then not q
p: is trudy's birthday
q: she is going to eat rocky road ice cream
The inversion of a negation is a affirmation:
If p, then q
Then, the inverse of given conditional is:
If is trudy's birthday, then she is going to eat rocky road ice creamDetermine roots Describeend BehaviorDraw Quich Sketch.of polymonialf(x) =-77"+ 2X
Answers
The equation is:
[tex]f(x)=7x^4+2x^3[/tex]So to made an sketch of the polynomial we can us a grapher so:
So the roots will be a range that is:
[tex](0,0)\text{ and (}-\frac{2}{7},0)[/tex]solve the equation for x, and enter your answer in the box
Answers
Given the equation:
[tex]8x-36=-12[/tex]We will solve the equation to find (x) as follows:
First, add 36 to both sides
[tex]\begin{gathered} 8x-36+36=-12+36 \\ 8x=24 \end{gathered}[/tex]Then, divide both sides by 8
[tex]\begin{gathered} \frac{8x}{8}=\frac{24}{8} \\ \\ x=3 \end{gathered}[/tex]So, the answer will be x = 3
2.54 * 10 to the 5[tex]41.222[/tex]Please I need help with question number 5.
Answers
We are going to solve question 5.
To answer this question, we have:
To
2g - 4f = 6f Solve for g.
Answers
The expression we have is:
[tex]2g-4f=6f[/tex]Step 1. To solve for g, we need to have the term that contains "g" alone on one side of the equation. For that reason the first step will be to add 4f to both sides of the equation:
[tex]2g-4f+4f=6f+4f[/tex]And as we can see, on the left side we get -4f+4f which cancel each other:
[tex]2g=6f+4f[/tex]Step 2. Combine the like terms on the right side of the equation.
We can combine 6f+4f because the two terms have the same variable, and the result is 10f:
[tex]2g=10f[/tex]Step 3. The last step to solve for g is to divide both sides of the equation by 2:
[tex]\frac{2g}{2}=\frac{10f}{2}[/tex]On the left side we get g:
[tex]g=\frac{10f}{2}[/tex]and on the right side, 10f/2 is equal to 5f:
[tex]g=5f[/tex]Answer:
[tex]g=5f[/tex]Convert 6 2/3cups to pints, Express your answer in simplest form,
Answers
Express the relation between cups and pints.
1 cup= 1/2 pint.
Convert 6 2/3 cups to pints.
Convert 6 2/3 mixed fraction to normal fraction implies,
[tex]6\frac{2}{3}=\frac{20}{3}[/tex]Thus,
[tex]\begin{gathered} \frac{20}{3}\text{ cups=}\frac{1}{2}\times\frac{20}{3} \\ =\frac{10}{3} \\ =3\frac{1}{3} \end{gathered}[/tex]Therefore, 6 2/3 cups is 3 1/3 pints.
Convert: 10 gallonsParagraphliters (Round your answer to the nearest tenth.)
Answers
1 Gallon = 3.785 Liters
10Gallons = x
using the rule of three:
[tex]\begin{gathered} 1Gallon*x=3.785Liters*10Gallons \\ \end{gathered}[/tex]Solving for x:
[tex]x=\frac{3.785Liters*10Gallons}{1Gallon}=37.85Liters\approx\text{ 38Liters}[/tex]The answer is 38 Liters
Which linear equations have an infinite number of solutions? Check all that apply. (x – ) = (x – )8(x + 2) = 5x – 1412.3x – 18 = 3(–6 + 4.1x)(6x + 10) = 7(x – 2)4.2x – 3.5 = 2.1 (5x + 8)
Answers
To know if a expression have infinite solution we replace x for the same values in bot sides so I will replace x=0 in all option so:
a)
[tex]\begin{gathered} (0-\frac{3}{7})=\frac{2}{3}(\frac{3}{2}(0)-\frac{9}{14}) \\ -\frac{3}{7}=-\frac{18}{42} \\ -\frac{3}{7}=-\frac{3}{7} \end{gathered}[/tex]So there are infinit solutions.
b)
[tex]\begin{gathered} 8(0+2)=5(0)-14 \\ 16=-14 \end{gathered}[/tex]so this do NOT have infinite solutions.
c)
[tex]\begin{gathered} 12.3(0)-18=3(-6+4.1(0)) \\ -18=-18 \end{gathered}[/tex]SO it has infinite solutions
d)
[tex]\begin{gathered} \frac{1}{2}(6(0)+10)=7(\frac{3}{7}(0)-2) \\ 5=-14 \end{gathered}[/tex]So this do NOT have infinit solutions
e)
[tex]\begin{gathered} 4.2(0)-3.5=2.1(5(0)+8) \\ -3.5=18.8 \end{gathered}[/tex]SO it do NOT have infinite solutions
So A) and C) have infinite solutions
Hi, can you help me answer this question please, thank you!
Answers
The formula for a margin error is given by
[tex]ME=z\frac{\sigma}{\sqrt[]{n}}[/tex]Where z is the z-critical(associated with the confidence), sigma is the standard deviation, n is the sample size, and ME is the interval.
From the text, we know the desired margin error is 25(ME = 25), the standard deviation is 300, and using our confidence of 95% we can calculate the z-critical value. For a 95% confidence, we have a z-critical of 1.96.
Using those values in our equation, we have
[tex]25=1.96\times\frac{300}{\sqrt[]{n}}[/tex]Solving for n, we get our sample size.
[tex]\begin{gathered} 25=1.96\times\frac{300}{\sqrt[]{n}} \\ \sqrt[]{n}=1.96\times\frac{300}{25} \\ \sqrt[]{n}=1.96\times12 \\ \sqrt[]{n}=23.52 \\ n=553.1904 \end{gathered}[/tex]We would need 554 students.
The decibel rating D is related to the sound intensity I by the formula D=10log(I/(10^-16)) for the noise in decibels. a) let D and d represent the decibel ratings of sounds of intensity I and i, respectively. Using properties of logarithms, find a simplified formula for the difference between the two ratings, D-d, in terms of the two intensities I and i. b) If a sounds intensity quadruples, how many decibels louder does the sound become?
Answers
The decibel D is related by the formula:
[tex]D=10\log _{10}(\frac{l}{10^{-16}})[/tex]Now, let's find a simplified formula between the two rating D and I using properties of logarithms:
We are going to use the same formula but changing D by d and I by i, then subtract both formulas:
[tex]d=10\log _{10}(\frac{i}{10^{-16}})[/tex]D-d:
[tex]D-d=10\log _{10}(\frac{I}{10^{-16}})\text{ - 10}\log _{10}(\frac{i}{10^{-16}})[/tex]Factorize the number 10:
[tex]D-d=10\lbrack\log _{10}(\frac{I}{10^{-16}})-\log _{10}(\frac{i}{10^{-16}})\rbrack[/tex]Use the next rule of logarithms:
[tex]\log _a(\frac{m}{n})=\log _am-\log _an[/tex]So:
[tex]D-d=10\lbrack\log _{10}I-\log _{10}10^{-16}-\log _{10}i+\log _{10}10^{-16}\rbrack[/tex]Operate the common terms:
[tex]D-d=10\lbrack\log _{10}I-\log _{10}i\rbrack[/tex]Now, we are going to use the same rule presented before by changing the rest by a division:
[tex]D-d=10\log _{10}(\frac{I}{i})[/tex]With the before formula you can solve the difference between two ratings.
b)The sound intensity now quadruples, using the first given formula find the decibels louder:
So I = 4, replace this value and solve:
[tex]D=10\log _{10}(\frac{4}{10^{-16}})[/tex]We use the same property changing the division by a subtraction:
[tex]D=10\log _{10}4-10\log _{10}10^{-16}[/tex]Now, we are going to use the next property:
[tex]\log _{}a^b=b\cdot\log _{}a[/tex][tex]D=10\log _{10}4-(10\cdot-16\log _{10}10)[/tex]The dollar value v (t) of a certain car model that is t years old given by the following exponential function. v(t) =19,900(0.90) tFind the initial value if the car and the value after 12 years. Round your answers to the nearest dollar as necessary.
Answers
Given
[tex]v(t)=19,900(0.90)^t[/tex]
Procedure
Initial value
[tex]\begin{gathered} v(0)=19,900(0.90)^0 \\ v(0)=19,900 \end{gathered}[/tex]19,900 initial value of the car
value after 12 years
[tex]\begin{gathered} v(12)=19,900(0.90)^{12} \\ v(12)=19,900\cdot0.2824 \\ v(12)=5,620.34 \end{gathered}[/tex]$5,620.34 value of the car after 12 years
Which of the following equations describes the line shown below? Check allthat apply.(-2,6)(4,3)A. y-3 = -1/2 (x-4)B. y-6 = -1/2 (x+2)C. y-3 = -2 (x-4)D. y-6 = -1/2 (x-2)E. y-4 = -1/2 (x-3)F. y-6 = -2 (x+2)
Answers
To find the equation of the line, we will use the formula;
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_{1)}[/tex]The points given are;
(-2, 6) and (4, 3)
x₁ = -2 y₁=6 x₂=4 y₂=3
Substitute the value into the formula
[tex]y-6=\text{ }\frac{3-6}{4+2}(x+2)[/tex]Evaluate
[tex]y-6=\frac{-3}{6}(x+2)[/tex][tex]y-6=-\frac{1}{2}(x+2)[/tex]The correct option is B
What is the slope of the line that goes through (5, -1) and is perpendicular to a line with slope 2/5.
Answers
-5/2
Explanation
Step 1
find the slope of the line :
when 2 lines are perpendicular the product of their slopes equals -1,so
[tex]\begin{gathered} if\text{ line 1}\perp\text{ line 2} \\ then \\ slope_1*slope_2=-1 \end{gathered}[/tex]then, let
[tex]\begin{gathered} slope_1=given=\frac{2}{5} \\ slope_2=slope_2 \\ hence \\ \frac{2}{5}*slope_2=-1 \\ to\text{ solve, multiply both sides by 5/2} \\ \frac{2}{5}slope_2*\frac{5}{2}=-1*\frac{5}{2} \\ slope_2=-\frac{5}{2} \end{gathered}[/tex]therefore, the slope of the line we are looking for is -5/2
Step 2
now, use the point-slope formula to find the equation of the line, it says
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where\text{ m is the slope } \\ (x_1,y_1)\text{ is a point from the line} \end{gathered}[/tex]a)let
[tex]\begin{gathered} slope=slope_2=-\frac{5}{2} \\ point=(5,-1) \end{gathered}[/tex]b) replace and solve for y to find the equation
[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-(-1)=-\frac{5}{2}(x-5) \\ y+1=-\frac{5}{2}x+\frac{25}{2} \\ subtract\text{ 1 in both sides} \\ y+1-1=-\frac{5}{2}x+\frac{25}{2}-1 \\ y=-\frac{5}{2}x+\frac{23}{2} \end{gathered}[/tex]therefore, the equation of the line is
[tex]y=-\frac{5}{2}x+\frac{23}{2}[/tex]
and the slope is
[tex]-\frac{5}{2}[/tex]the slope of the line we are looking for is -5/2
Select all of the equations below that are equivalent to p + q = -48
Answers
We want to find the equivalents from the options to the following equation
[tex]p+q=-48[/tex]If we divide both sides by - 3, we're going to have
[tex]\begin{gathered} \frac{p+q}{-3}=-\frac{48}{-3} \\ \frac{p+q}{-3}=16 \end{gathered}[/tex]Since this result is different from the first option, the first option is not equivalent to the initial equaiton.
Doing the same for the others, dividing by - 2 we have
[tex]\begin{gathered} \frac{p+q}{-2}=-\frac{48}{-2} \\ \frac{p+q}{-2}=24 \end{gathered}[/tex]dividing by - 12 we have
[tex]\begin{gathered} \frac{p+q}{-12}=-\frac{48}{-12} \\ \frac{p+q}{-12}=4 \end{gathered}[/tex]dividing by 8 we have
[tex]\begin{gathered} \frac{p+q}{8}=-\frac{48}{8} \\ \frac{p+q}{8}=-6 \end{gathered}[/tex]The only equivalent expression through the options is
[tex]\frac{p+q}{8}=-6[/tex]91 pointSimplify the following function4.222-25 12-36O4(x+6(22-25)(4x+6)+ +5,0(x+5)(8-5) 2 + +6, +5,0O4(x+6)(3-5)(x+5)*7 +5, +6,0(2+5)27-5,0O
Answers
ANSWER
[tex]\begin{gathered} -\frac{4(x+6)}{(x-5)(x+5)} \\ x\ne\pm5,\pm6,0 \end{gathered}[/tex]EXPLANATION
We want to simplify the expression:
[tex]-\frac{4x}{x^2-25}\div\frac{(x^2-6x)}{x^2-36}[/tex]To do this, first change the sign to a multiplication sign and flip the fraction on the right:
[tex]-\frac{4x}{x^2-25}\cdot\frac{x^2-36}{(x^2-6x)}[/tex]Now, simplify the expression by applying the difference of two squares and factorization:
[tex]\begin{gathered} -\frac{4x}{(x-5)(x+5)}\cdot\frac{(x-6)(x+6)}{x(x-6)} \\ \Rightarrow-\frac{4}{(x-5)(x+5)}\cdot\frac{(x+6)}{1} \\ \Rightarrow-\frac{4(x+6)}{(x-5)(x+5)} \end{gathered}[/tex]The expression will be invalid when x is:
[tex]\pm5,\pm6,0[/tex]Therefore, the answer is option C.