Answers
Step 1:
Write the function
[tex]f(x)\text{ = }\frac{x^2+\text{ 7x + 10}}{x^2\text{ + 9x + 20}}\text{ }[/tex]Step 2:
Factorize both the numerator and the denominator.
[tex]\begin{gathered} f(x)\text{ = }\frac{x^2\text{ + 2x + 5x + 10}}{x^2\text{ + 4x + 5x + 20}} \\ f(x)\text{ = }\frac{x(x\text{ + 2) + 5(x + 2)}}{x(x\text{ + 4) + 5 (x + 4)}} \\ f(x)\text{ = }\frac{(x\text{ + 5)(x +2)}}{(x\text{ + 5)(x + 4)}} \end{gathered}[/tex]Step 3:
A hole is a common factor between the numerator and the denominator.
Hole: x + 5 = 0
x = -5
Final answer
Hole is -5
Related Questions
Mark noticed the probability that a certain player hits a home run in a single game is 0.175. Mark interested in the variability of the number of home runs if this player plays 200 games. If Mark uses the normal approximation of the binomial distribution to model the number of home runs, what is the standard deviation for a total of 200 games?
Answers
The standard deviation for a total of 200 games is 5.3735.
How to calculate the standard deviation?Let X = number of home runs of this player in 200 games played by him.
p = probability that a this player hits a home run in a single game and this is given to be 0.175.
Where np = Mean of X and √{np(1 - p)} is the standard deviation of X.
Here n = 200 and p = 0.175. So, the standard deviation for a total of 200 games is the standard deviation for a total of X
= √(200 x 0.175 x 0.825) / 2
= 5.3735
The value is 5.3735.
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What is the axis of symmetry for the following quadratic?(x-3)(x+7)
Answers
The symmetry of a quadratic equation is given by the line that passes through its vertex, so in order to find the axis of symmetry we need to find the coordinate of the vertex, which is done below.
[tex]x_{\text{vertex}}=\frac{-b}{2a}[/tex]Where "a" is the number multiplying the square factor and "b" is the number multiplying the factor that isn't squared. To find these two constants we need to expand the equation given.
[tex]\begin{gathered} (x-3)\cdot(x+7) \\ x^2+7x-3x-21 \\ x^2+4x-21 \end{gathered}[/tex]We have that a = 1 and b = 4, therefore:
[tex]x_{\text{vertex}}=\frac{-4}{2\cdot1}=-2[/tex]The axis of symmetry for this quadratic equation is x=-2.
There are 9,321 leaves on a tree. Explain why the digit 3 stays the same when9,321 is rounded to the nearest hundred.
Answers
To round the nearest hundred the digit in the hundred column and test digit in the tens column.
To round the nearest hundred the digit in the hundred column is rounding digit and the digit in the tens column is test digit.
We find the rounding digit in hundred column is 3. Then we look out the test digit 2 to the right of the 3 in the tens column. Because 2<5 we round down and leave the 3 in the hundred column. Then replace the two rightmost digits with 0's.
The 9,321 rounded to the nearest hundred is 9,300.
A restaurant offers a $12 dinner special that has 4 choices for an appetizer, 11 choices for an entree, and 3 choices for a dessert. How many different meals are available when you select an appetizer, an entree, and a dessert?
Answers
the probability that DeAndre missed at least 1 day of school in a given week is
Answers
Probability that Deandre missed at least 1 day is;
[tex]Pr(x\ge1)=Pr(1)+Pr(2)+Pr(3)+Pr(4)+Pr(5)[/tex]Write out the values of each probability and sum them
[tex]\begin{gathered} Pr(x\ge1)=0.25+0.18+0.34+0.12+0.04 \\ =0.93 \end{gathered}[/tex]Hence,
The probability that Deandre missed at least 1 day is 0.93
e costs 7 dollars. Lamar buys p pounds. Write an equation to represent the total00XХ$?
Answers
Given:
A pound of chocolate costs 7 dollars.
To find:
The equation represents the total cost c for buying p pounds of chocolate.
Solution:
It is given that a pound of chocolate costs 7 dollars. So,
[tex]\begin{gathered} 1\text{ pound}=7\text{ dollars} \\ 1\times p\text{ pounds}=7\times p\text{ dollars} \\ p\text{ pounds}=7p\text{ dollars} \end{gathered}[/tex]Since the cost of p pounds of chocolate is c. So,
[tex]c=7p[/tex]Thus, the answer is c = 7p.
laws of exponent : multiplication and power to a power5x3 • 2 x ²
Answers
Multiplication of coefficients and variable
It's given the expression:
[tex]5x^3\cdot2x^2[/tex]Solve for x. Round to the nearest tenth ofa degree, if necessary.5.3HGto8.5F
Answers
We have a rigth triangle, where we have to find the measure of x.
We can use trigonometric ratios to relate the lengths of the sides and the measure of x.
The lengths we know are from the hypotenuse and the adyacent side of x, so we can use the following trigonometric ratio:
[tex]\begin{gathered} \cos (x)=\frac{\text{Adyacent}}{\text{Hypotenuse}} \\ \cos (x)=\frac{5.3}{8.5} \\ x=\arccos (\frac{5.3}{8.5})\approx\arccos (0.623)\approx51.4\degree \end{gathered}[/tex]Answer: x = 51.4°
A is in the shape of a quarter circle of radius 15 cm.
B is in the shape of a circle.
A
15 cm
The area of A is 9 times the area of B.
Work out the radius of B.
B
Answers
Answer:
[tex]\frac{5}{2}[/tex] or 2.5cm
Step-by-step explanation:
Hello! Let's help you with your question here!
Let's start by working out what we know and what we need. So, we know that P is a circle and Q is the shape of a quarter circle with a radius of 20cm. The area of Q is 9 times the area of P and we must find the radius of P.
To start, we're looking for area, so we should at least start looking at the area of a circle, given radius, which is:
[tex]A=\pi r^2[/tex]
Now, we don't necessarily know r (radius) and the area either. However, we can try to use the quarter circle as our guide for the full circle. So, we want to find the area of the quarter circle, we can do that by using this formula!
[tex]A=\frac{1}{4} \pi r^2[/tex]
The reason why we put a [tex]\frac{1}{4}[/tex] at the front of [tex]\pi r^{2}[/tex] is because we're only solving for a quarter of a circle instead of the entire circle.
Now that we have our formula! We can calculate the area of the quarter circle as follows:
[tex]A=\frac{1}{4}\pi 15^2[/tex]
[tex]A=\frac{\pi 15^2}{4}[/tex] -We combine the fraction [tex]\frac{1}{4}[/tex] into the rest of the equation.
[tex]A=\frac{225\pi }{4}[/tex] - Evaluating [tex]15^2[/tex]
Now that we have the area of the quarter circle, we can now work on the full circle. What we know is that the area of A is 9 times of B, since we're finding the radius of B, we can essentially plug in the area and solve for the radius of the full circle. That would be as such:
[tex]A=9\pi r^2[/tex] -We're using the area of circle A to find the radius of B.
[tex]\frac{225\pi }{4} =9\pi r^2[/tex] - Plugging in the area of the quarter circle.
[tex]\frac{225\pi }{4}/9\pi =\frac{9\pi r^2}{9\pi }[/tex] - We divide [tex]9\pi[/tex] to get rid of it on the right side.
[tex]\frac{25}{4} =r^2[/tex] - When dividing by [tex]\pi[/tex], the numerator [tex]\pi[/tex] gets cancelled out.
[tex]\sqrt{\frac{25}{4} }=r[/tex] -We square root to get rid of the squared.
[tex]\frac{5}{2}=r[/tex] - Square rooted both numerator and denominator.
And there we have it! We finally get a radius of [tex]\frac{5}{2}[/tex] or 2.5cm.
How do you find the square root of -6 by imaginary numbers
Answers
To find the square root of a negative number use the next:
[tex]\sqrt{-1}=i[/tex]For -6:
You can write -6 as the product of 6 and -1:
[tex]\sqrt{\left(6\right)*\left(-1\right)}[/tex]The square root of a product is the same as the product of the square root if each of the factors:
[tex]=\sqrt{6}*\sqrt{-1}[/tex]As the square root of 6 is not a exact number (it has many decimals) you leave the square root of 6 as it is. The square root of -1 is i; then, the square root of -6 is:
[tex]\begin{gathered} =\sqrt{6}*i \\ =\sqrt{6}i \end{gathered}[/tex]Then, the square root of -6 is: (√6)iHELP PLEASEEEEE!!!!!!
Answers
A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
The visual depiction of numbers, such as fractions, integers, and whole numbers, spread out uniformly along a single horizontal line is known as a number line. A number line can be used as a tool for operations like addition and subtraction as well as comparison and sorting of numbers.
Given:
As from the Figure we have
-1 3/4 = -7/4 = -1.75, which is represented by point 1 on the number line.
and, 14/8 = 1.75, which is represented by point 7 on the number line.
and, 1.125, which is represented by point 6 on the number line.
and, -0.875, which is represented by point 4 on the number line.
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help meee pleaseeee pleasee
Answers
Answer:
Step-by-step explanation:
Which choice could be used in proving that the given triangles are similar? A) PO 6 DE 4 II B) PO 4 EF 9 PO 4 DE 6 D) PR 6 DE 6 allo
Answers
1. Knowledge: Use your Factoring Flowchart or Concept Map to factor the following Quadratic Polynomials. Copy down the question and show any necessary steps if it is a multi-step factoring process (not just a single-step solution). Question F to I
Answers
Solution
We are asked to factorize the following questions
Question F:
[tex]\begin{gathered} 4+6x+2x^2 \\ \text{ 2 is common among the terms, so we can factorize it out} \\ \\ 2(2+3x+x^2) \\ \text{ The term }3x\text{ can also be written as }2x+x.\text{ And the terms }2x\text{ and }x\text{ multiply to get }2x^2 \\ \text{ Thus, we have,} \\ \\ 2(2+3x+x^2)=2(2+2x+x+x^2) \\ \text{ In this new expression, }2\text{ is common to }2+2x\text{ while }x\text{ is common to }x+x^2 \\ \text{ Thus, we can factorize them out} \\ \\ 2(2+2x+x+x^2)=2(2(1+x)+x(1+x)) \\ \text{ Lastly, }(1+x)\text{ is common to }2(1+x)\text{ and }x(1+x) \\ \\ 2(2(1+x)+x(1+x))=2((2+x)(1+x)) \\ \\ \therefore4+6x+2x^2=2(2+x)(1+x) \end{gathered}[/tex]Question G:
[tex]\begin{gathered} 3x^2-1x-10 \\ \text{ The term }-1x\text{ can also be written as }-6x+5x\text{ and the terms }-6x\text{ and }5x\text{ multiply to get} \\ -30x^2.\text{ Thus, we have,} \\ \\ 3x^2-1x-10=3x^2-6x+5x-10 \\ 3x\text{ is common to }(3x^2-6x)\text{ and }5\text{ is common to \lparen}5x-10) \\ \text{ Thus, we can factor them out} \\ \\ 3x^2-6x+5x-10=3x(x-2)+5(x-2) \\ (x-2)\text{ is common to both terms, so we can factor again} \\ \\ 3x(x-2)+5(x-2)=(x-2)(3x+5) \\ \\ \therefore3x^2-1x-10=(x-2)(3x+5) \end{gathered}[/tex]Final Answer
The answers to questions F and G are:
[tex]\begin{gathered} 4+6x+2x^2=2(2+x)(1+x) \\ \\ 3x^2-1x-10=(x-2)(3x+5) \end{gathered}[/tex]
You have a piggy bank containing a total of 66 coins in dimes and quarters. If the piggy bank contains $10.20, how many dimes are there in the piggy bank?
Answers
I have 42 dimes in my piggy bank according to the given condition of 66 coins and amount $10.20 and used the system of equation as well as substitution method.
What is system of equation?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system. A group of two or more equations that share the same variables is known as a system of equations. A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations.
What is substitution method?Finding the value of any variable from one equation in terms of another variable is the first step in the substitution method. For instance, if there are two equations, x+y=7 and x-y=8, we can deduce that x=7-y from the first equation. Applying the substitution method begins with this.
Here,
x+y=66 ......(1)
1 dime values 10 cents.
1 quarter values 25 cents.
10x+25y=1020 ........(2)
x=66-y
10(66-y)+25y=1020
660-10y+25y=1020
15y=360
y=360/15
y=24
x=66-24
x=42
I used the system of equations and the substitution method to determine that I have 42 dime coins in my piggy bank in accordance with the requirement of 66 coins totaling $10.20.
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The length of each side of a square is extended 5 in. The area of the resulting square is 64 in,2 Find the length of a side of the
original square.
Answers
Answer: i donno
Step-by-step explanation:
ask Professor Ahmad Shaoki
For the function f(x). describe, in words, the effects of each variable alb,h,k on the graph of a*f(bx+h)+k
Answers
Answer:
a: a produces vertical stretch
b: b produces a horizontal stretch
h: h produces a translation to the left of the X-axis
k: k produces a translation on the new function upward of the Y-axis
Step-by-step explanation:
An intermediate function is produced by adding each variable in the following order:
1) f(x) to f(bx):
Effect:
the horizontal stretch of f(x) along the x-axis with stretch factor b
2) f(bx) to f(bx+h):
Effect:
translation of f(bx) to the left of the X-axis by h units
3) f(bx+h) to a*f(bx+h):
Effect:
vertical stretching of f(bx+h) by a factor equal to a
4) Finally, a*f(bx+h) to a*f(bx+h)+k:
Effect:
vertical translation of a*f(bx+h) by h units upwards along the Y-axis.
Blaise M.
Determine whether or not the digits below are divisible by: 2,3,4,5,6,8,9,or, 10 a. 897 b. 12,000 c. 8190 d. 327
Answers
You have the following numbrs:
897
12,000
8190
327
In order to determine if the previous numbers are divisibles for numbers between 2 and 10, you take into account the following points:
- If last two digits are divisible by a number, and the part of the number without the last units is divisible too, you can consider that the complete number is divisible too.
- If the last digit is 0, then the number is divisible by 2 and 5 and 10.
- If the number is even, it is dividible by 2.
- In case a number ends in varios zeros you can consider if the digits before the zeros are divisible by a specific number.
- 897 is divisible by 3, because 97 is divisible by 3 and 800 too.
- 12,000 is divisible by 2, 3, 4, 5, 6, 8 and 10, because it is an even number, ends in 0 and the first digits are divisible by 3, 4, 6.
- 8190 is divisible by 2, 3, 5, 6, and 10, becaues it is even, ends in 0 and the number of last two digits is divisible by 3 and 6 and 8100 too.
- 327 is divisible by 3, because number of last two digits is divisible by 3 and 300 too.
A squirrel is perched in a tree 50 feet above sea level. Directly below the squirrel, a bird is flying 17 feet above sea level. Directly below the bird is a trout, swimming 23 feet below seal level.how far apart are the squirrel and bird?
Answers
Solution
We can do the following operation_
17-50 = -33 ft
And that represent the distance between te heron and the squirrel
And since the actual height is -23 ft
Then the answer would be given by:
17 -(-23) = 40 ft
The distance from the squirrel and the bird is 40 ft
a computer program is in Shannon's computer carries out a single mathematical operation in 1.5 * 10 over 6 seconds how much time would the program take to complete 2.5 * 10/3 mathematical operations
Answers
Question:
Solution:
This computer program carries out a single mathematical operation in
[tex]1.5x10^{-6}\text{ seconds}[/tex]then, to complete 2.5 x 10^3 mathematical operations the program will take a time of:
[tex](1.5x10^{-6})(2.5x10^3)=3.75x10^{-3}[/tex]thus, the correct answer is:
[tex]3.75x10^{-3}[/tex]given that f(x)=3x-6, determine f(8)
Answers
According to the given data we have the following function:
f(x)=3x-6
To determine f(8) we would have to plug in into the equation the 8 and then proceed to calculate it, so:
If f(x)=3x-6
Then, f(8)=3(8)-6
f(8)=24-6
f(8)=18
Please help and answer this question ASAP! :)
Answers
Answer:
Odd, Even, Even, Neither=========================
The difference between odd and even functions is that:
f(-x) = f(x) for even functions,f(-x) = - f(x) for odd functions.Let's test this property for the given functions.
Function f(x)f(-4) = - f(4) = 8 and f(-2) = - f(2) = 1, so this is an odd functionFunction g(x)g(4) = g(-4) = -4 and g(2) = g(-2) = 2, so this is an even functionFunction j(x)j(2) = j(-2) = 2 and j(1) = (j-1) = - 4, so this is an even functionFunction k(x)k(-4) = 9, k(4) = 1 and k(-2) = 4, k(2) = 0, since each value is different this is neither odd nor even functionIf A={a,c} and B={d,g,w} then complete the Following:a. Find AxBb. Find n(AxB)c. write a multiplication equation involving numerals related to the parts in (a) and (b)...a. AxB = {____} Type an ordered pair. Use commas to separate answers as needed
Answers
Given the two sets:
[tex]\begin{gathered} A=\mleft\lbrace a,c\mright\rbrace \\ B=\mleft\lbrace d,g,w\mright\rbrace \end{gathered}[/tex]we can write the product set of A and B in the following form:
[tex]AxB=\mleft\lbrace(a,d\mright),(a,g),(a,w),(c,d),(c,g),(c,w)\}[/tex]next, we have that the number of elements in A is 2 and the number of elements in B is 3, then, we have:
[tex]n(AxB)=2\cdot3=6[/tex]finally, the equation that involves the numerals of the previous parts is:
[tex]n(AxB)=n(A)\cdot n(B)[/tex]where n(A) and n(B) represents the number of elements in A and B respectively.
In general, what points can have coordinates reversed and still have the same location?Choose the correct answer below.O the points with x-coordinates 0o the points with y-coordinates 0o the points with the same x- and y-coordinatesO the points with opposite coordinates
Answers
SOLUTION
The Point of a co-ordinate is always written as
[tex](x,y)[/tex]Giving a point
[tex]\begin{gathered} A(x,y) \\ \text{if the coordinates of x and y are the same } \end{gathered}[/tex]For instance x=2 and y=2, the point will be
[tex](2,2)[/tex]If the coordinate of x and y are reversed, the point will remain the same
Hence
the points with the same x- and y-coordinates will give the same location if the coordinate is reversed.
Therefore The Third option is correct (c)
a gallon of ice cream costs $4.76. How much does it cost per quart? There are 4 qts per gallon.
Answers
There are 4 quarts in a gallon so the price of one gallon that they have given us has to be split into four so $4.76/4 =$1. 19/quart
3 ftFind the outer perimeter ofthis figure. Round youranswer to the nearesthundredth. Use 3.14 toapproximate .4 ft5 ft5 ftP = [ ? ] ftNotice that only half of the circle is included in the figure!Enter
Answers
Perimeter = sum of outer lengths
Lenght of the triangle sides = 5ft
perimeter of a semicircle = π d; half = π d / 2
5 ft + 5ft + π r
5 + 5 + (3.14*3) = 19.42 ft
What’s the volume and surface area of the object shown ?
Answers
Volume of object = 42 cubic cm
Surface area of object = 96 square cm
Explanations:The given figure is a triangular prism.The formula for calculating its volume is expressed as:
[tex]volume\text{ }of\text{ prism}=BH[/tex]where:
B is the base area
H is the height of prism
[tex]\begin{gathered} volume\text{ of }prism=(\frac{1}{2}\times4\times3)\times7 \\ volume\text{ of }prism=6\times7 \\ volume\text{ of }prism=42cm^3 \end{gathered}[/tex]Determine the surface area of the prism
The surface area if the sum of all the faces of the prism.The faces consists of 3 rectangles and 2 triangles. The surface area is calculated as:
[tex]\begin{gathered} Surface\text{ area}=2(0.5\times3\times4)+(7\times4)+(3\times7)+(5\times7) \\ Surface\text{ area}=12cm^2+28cm^2+21cm^2+35cm^2 \\ Surface\text{ area}=96cm^2 \end{gathered}[/tex]Hence the surface area of the object shown is 96 square cm
I need help finding the passing adjusted grade of 70A=10R^1/2
Answers
Given:
Passing grade = 70
Formula for adjusted grade, A:
[tex]A=10R^{\frac{1}{2}}[/tex]Given a passing adjusted grade of 70, let's find the raw score, R.
To solve for R, substitute 70 for A and solve for R.
We have:
[tex]\begin{gathered} 70=10R^{\frac{1}{2}} \\ \end{gathered}[/tex]Divide both sides by 10:
[tex]\begin{gathered} \frac{70}{10}=\frac{10R^{\frac{1}{2}}}{10} \\ \\ 7=R^{\frac{1}{2}} \end{gathered}[/tex]Take the square of both sides:
[tex]\begin{gathered} 7^2=(R^{\frac{1}{2}})^2 \\ \\ 7^2=R^{\frac{1}{2}\times2} \\ \\ 49=R^1 \\ \\ 49=R \\ \\ R=49 \end{gathered}[/tex]Therefore, the raw score a student would need to have a passing adjusted grade of 70 is 49
ANSWER:
49
Which angle is coterminal to 128°?A. -52°B. 308C. 232°D. 488°
Answers
The coterminal of angle with measure x is x + 360 degrees
Example:
If x = 30 degrees, then
The coterminal of x is 30 + 360 = 390 degrees
The coterminal of 128 degrees is 128 + 360 = 488 degrees
Then the answer is D
A graph the line that passes through the points (1,-5) and (5,7)and determine the equation of the line
Answers
Answer:
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Class 11
>>Applied Mathematics
>>Straight lines
>>Various forms of the equation of a line
>>Find the equation of the line that passe
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Find the equation of the line that passes through the points (7,5) and (−9,5)
Hard
Updated on : 2022-09-05
Solution
verified
Verified by Toppr
Correct option is A)
Since slope of line passing through two points (x
1
,y
1
) and (x
2
,y
2
) is m=
x
2
−x
1
y
2
−y
1
We now find the slope of the line passing through the points (7,5) and (−9,5) as shown below:
m=
−9−7
5−5
=
−16
0
=0
Therefore, the slope of the line is 0.
Now use the slope and either of the two points to find the y-intercept.
y=mx+b
5=(0)(7)+b
b=5
Write the equation in slope intercept form as:
y=mx+b
y=(0)x+5
y=5
Hence, the equation of the line is y=5.