We need to find g(x)/f(x) so we will put them over each other as a fraction
[tex]\frac{g(x)}{f(x)}=\frac{x^2-5}{4x+1}\text{ , x}\ne\frac{-1}{4}[/tex]In any algebraic fraction, denominators can not be zero, so we avoid any values make it equal to zero like -1/4 in our question
What is the solution to the equation 3^x = 10?
Start by applying the log on both sides wi
Consider the function f defined by:f(x)=4x-12 FIND: The value of f at x=-7The value of f when x=1
Answer:
• f(-7)=-40
,• f(1)=-8
Explanation:
Given the function f(x) defined below:
[tex]f(x)=4x-12[/tex](a)The value of f at x=-7
When x=-7
Substitute -7 for x:
[tex]\begin{gathered} f(-7)=4(-7)-12 \\ =-28-12 \\ =-40 \end{gathered}[/tex]The value of f at x=-7 is -40.
(b)The value of f when x=1
When x=1
Substitute 1 for x:
[tex]\begin{gathered} f(1)=4(1)-12 \\ =4-12 \\ =-8 \end{gathered}[/tex]The value of f at x=1 is -8.
THE FIRST ONE TO ANSWER GETS 50 POINTS !!!!!!!!!!!!!!!!!!!!!!!!!
There are 27 students in Mr. Mello's class. Find the total number of pages the students read by the end of November.
BEST ANSWER PLS !!!
If there are 27 students in Mr. Mello's class then the total number of pages the students read by the end of November will be 1350.
Given that there are 27 students in Mr. Mello's class.
We are required to find the total number of pages that the students read by the end of November.
Assume that there are 50 pages in the book and all the pages are read in the month of November.
Total number of pages read by all the students by the end of November=27*50
(Product of number of pages in the book and the number of students)
= 1350 pages
Answer:
810
Step-by-step explanation:
Based on the given conditions, formulate: 30x27
Calculate the product or quotient:810
I got this off of another answer site that had 4.6 star answers. the other person who answered got it off another person who asked the same thing in this website they got a high star too so I dont know which is correct
Solve forx: 3x - 5 = 2x + 6.1-111-11
To solve the equation we need to isolate the "x" variable on the left side. This is done step-by-step below:
3x - 5 = 2x + 6
3x - 2x -5 = 6
x = 6 + 5
x = 11
Let E be the event where the sum of two rolled dice is less than 8. List the outcomes in Ec.
Explanations:
Answer:
Suppose that the functions f and g are defined as follows F(x)=5/x+7g(x)=2/xFind f/g then give its domain using an interval or union of intervals Simplify your answer as much as possible (f/g)(x)=Domain of f/g:
Given the functions:
[tex]\begin{gathered} f(x)=\frac{5}{x+7} \\ \text{AND} \\ g(x)=\frac{2}{x} \end{gathered}[/tex]Let's solve for the following:
• (a) f/g
To solve for f/g let's divide f(x) by g(x).
We have:
[tex]\frac{f}{g}=\frac{f(x)}{g(x)}=(\frac{f}{g})(x)=\frac{\frac{5}{x+7}}{\frac{2}{x}}[/tex]Solving further, we have:
[tex]\begin{gathered} (\frac{f}{g})(x)=\frac{5}{x+7}\ast\frac{x}{2} \\ \\ (\frac{f}{g})(x)=\frac{5x}{2(x+7)} \end{gathered}[/tex]Therefore, the function f/g is:
[tex](\frac{f}{g})(x)=\frac{5x}{2(x+7)}[/tex]• (b) Domain of f/g.
The domain is the set of all possible x-values where the function is defined.
To find the domain, set the denominator to zero and solve for x.
We have:
[tex]2(x+7)=0[/tex]Divide both sides by 2:
[tex]\begin{gathered} \frac{2(x+7)}{2}=\frac{0}{2} \\ \\ (x+7)=0 \end{gathered}[/tex]Subtract 7 from both sides:
[tex]\begin{gathered} x+7-7=0-7 \\ \\ x=-7 \end{gathered}[/tex]Therefore, the domian is:
[tex]\mleft(-\infty,-7\mright)\cup(-7,\infty)[/tex]ANSWER:
[tex](a)\text{ ( }\frac{f}{g})(x)=\frac{5x}{2(x+7)}[/tex][tex](b)\text{ Domain: }(-\infty,-7)\cup(-7,\infty)[/tex]Yolanda is preparing a liquid fertilizer that she will use on her lawn. She mixes 4 tablespoons of liquid fertilizer with 6 gallons of water.Using this ratio, how many gallons of water should be mixed with each tablespoon of liquid fertilizer?
Given data:
The given amount of liquid fertilizer is f=4.
The given water is w=6 gallons.
4 tablespoons= 6 gallons of water
1 tablespoon= 1.5 gallons of water.
Thus, 1.5 gallons of water is mix with each tablespoon.
Write an equation of the line passes through (-4,4) y=1/2x+1
Answer: y = -2x - 4
The equation of the line given is
[tex]\frac{1}{2}x\text{ + 1}[/tex]The slope - intercept form of equation is written as
y = mx + b
Where m = slope and b = intercept
From the above equation
m = 1/2
For a perpendicular line
[tex]\begin{gathered} For\text{ perpendicular line} \\ m1\text{ x m2 = -1} \\ m1\text{ = }\frac{1}{2} \\ \text{Therefore,} \\ \frac{1}{2}\text{ x m2 = -1} \\ \text{Make m2 the subject of the formula} \\ m2\text{ = }\frac{-1}{\frac{1}{2}} \\ m2\text{ = -1 x }\frac{2}{1} \\ m2\text{ = -2} \end{gathered}[/tex]Since m2 = -2
Hence, the perpendicular equation can be calculated
(y - y1) = m(x - x1)
The given point is ( -4, 4)
x1 = -4 and y1 = 4, and m = -2
(y - 4) = -2(x - (-4)
(y - 4) = -2(x + 4)
Open the parenthesis
y - 4 = -2x - 2*4
y - 4 = -2x - 8
y = -2x -8 + 4
y = -2x - 4
is 2017, mass uit snacks O) A bottle contains 2 liters of soda. Chris and his friends drink 985 milliliters of soda. How much soda is left? 1 99 tolomL 985 mL 1 DISME
ANSWER
1.015 L = 1,015 mL
EXPLANATION
To solve this we have to keep the relation 1 L = 1000mL in mind.
So if the soda bottle contains 2L, that is the same as 2000 mL. When we have to subtract two amounts (or add them) we always have to put them in the same units, so we either have to use them all in milliliters or in liters. Since the amount of soda they drank is less than 1000mL, it is better if we use milliliters:
[tex]2000mL-985mL=1015mL[/tex]The amount of soda left is 1015mL or, what is the same, 1.015 L
Subtract. x^2−x+3/x^2+2x−8 − x^2−3x−5/x^2+2x−8
The value after subtraction will be;
⇒ 2 / (x - 2)
What is mean by Subtraction?
Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The expression is,
⇒ (x² - 3x - 5) / (x² + 2x - 8) - (x² - 3x - 5) / (x² + 2x - 8)
Now,
Subtract the expression as;
The expression is,
⇒ (x² - x + 3) / (x² + 2x - 8) - (x² - 3x - 5) / (x² + 2x - 8)
⇒ (x² - x + 3) - (x² - 3x - 5) / (x² + 2x - 8)
⇒ x² - x + 3 - x² + 3x + 5 / (x² + 2x - 8)
⇒ 2x + 8 / (x² + (4-2)x - 8)
⇒ 2x + 8 / (x² + 4x - 2x - 8)
⇒ 2x + 8 / (x (x + 4) - 2 (x + 4))
⇒ 2(x + 4) / (x + 4) (x- 2)
⇒ 2 / (x - 2)
Thus, The value after subtraction will be;
⇒ 2 / (x - 2)
Learn more about the subtraction visit:
https://brainly.com/question/28467694
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can you please help me?
Answer : The linear function of the graph when move down 3 units is y = x - 3
The graph shift vertically because it is down 3 units
The standard equation of a linear function is
y = mx + b
Where b = intercept and m = slope
Move 3 unit down means b = -3
Hence, y = x-3
Answer is y = x - 3
Joshua is going to invest $9,000 and leave it in an account for 5 years. Assuming theinterest is compounded continuously, what interest rate, to the nearest tenth of apercent, would be required in order for Joshua to end up with $12,500?
Let r be the percent annual interest rate of the account. Since $9000 are left for 5 years, for an outcome of $12,500, then:
[tex]9000\times(1+\frac{r}{100})^5=12,500[/tex]Divide both sides by 9000:
[tex](1+\frac{r}{100})^5=\frac{12500}{9000}=\frac{25}{18}[/tex]Take the 5th root to both sides:
[tex]\begin{gathered} 1+\frac{r}{100}=\sqrt[5]{\frac{25}{18}} \\ \Rightarrow\frac{r}{100}=\sqrt[5]{\frac{25}{18}}-1 \\ \Rightarrow r=100(\sqrt[5]{\frac{25}{18}}-1) \end{gathered}[/tex]Use a calculator to find the decimal expression for r:
[tex]r=6.790716585\ldots[/tex]Therefore, to the nearest tenth:
[tex]r=6.8[/tex]This means that Joshua would need to invest his money on a 6.8% annual interest account.
What is the value of m ? How do you solve it ?
We have a parallelogram.
The diagonals of a parallelogram bisect each other. This means that each diagonal is divided in two equal segments by the other diagonal.
This let us write:
[tex]9=2n-1[/tex]and
[tex]m+8=3m[/tex]We can solve for n as:
[tex]\begin{gathered} 9=2n-1 \\ 9+1=2n \\ 10=2n \\ n=\frac{10}{2} \\ n=5 \end{gathered}[/tex]and for m as:
[tex]\begin{gathered} m+8=3m \\ m-3m=-8 \\ -2m=-8 \\ m=\frac{-8}{-2} \\ m=4 \end{gathered}[/tex]Answer: the value of m is 4.
There was a survey taken to see which types of pets people prefer. Out of 11 participents, 5 said they prefer dogs, 4 said they prefer cats, and 3 said they prefer birds. What is the percentages of people that prefer dogs, cats, and birds?
To find the percentages of people that prefer dogs, cats or birds, divide the corresponding amount of people that likes each pet by the total amount of people in the survey, and then multiply that quantity by 100.
Since there are 11 participants, we should divide each quantity by 11.
Dogs:
There are 5 people who prefer dogs. The percentage is:
[tex]\frac{5}{11}\times100\text{ \%}=45.4545\ldots\text{ \%}[/tex]Cats:
There are 4 people who prefer cats. The percentage is:
[tex]\frac{4}{11}\times100\text{ \%=36.3636}\ldots\text{ \%}[/tex]Birds:
There are 3 people who prefer birds. The percentage is:
[tex]\frac{3}{11}\times100\text{ \%=27.2727}\ldots\text{ \%}[/tex]solve for y and simplify your answer5/4y = -9
ok heres my problem,on average, a refrigerator door is opened 68 times each day.Len has 2 refrigerators in his house.based on this average,about how many times ina 1 week period are the refrigerator doors opened?
68 times / day
ok
If he open only one refrigerator per day
68 x 7 = 476
He opens the refrigerator 476 times per week
But he has 2 refrigerators
476 x 2 = 952 times
Result, Len open the doors of both refreigerators 952 times per week
Done
Do you have any question?
-2 5/7 x (-4 2/3). with steps
We want to do the following multiplication:
[tex](-2\frac{5}{7})\cdot(-4\frac{2}{3})[/tex]Let's transform that into a normal fraction:
[tex]\begin{gathered} 2\frac{5}{7}=2+\frac{5}{7}=\frac{14+5}{7}=\frac{19}{7} \\ \\ 2\frac{5}{7}=\frac{19}{7} \end{gathered}[/tex]and the other fraction
[tex]\begin{gathered} \text{ 4}\frac{2}{3}=4+\frac{2}{3}=\frac{12+2}{3}=\frac{14}{3} \\ \\ 4\frac{2}{3}=\frac{14}{3} \end{gathered}[/tex]Therefore we can multiply the following fractions:
[tex]\begin{gathered} (-\frac{19}{7})\cdot(-\frac{14}{3}) \\ \\ \end{gathered}[/tex]The result is
[tex](-\frac{19}{7})(-\frac{14}{3})=\frac{19}{7}\cdot\frac{14}{3}=\frac{19}{1}\cdot\frac{2}{3}=\frac{38}{3}[/tex]Therefore
[tex](-2\frac{5}{7})\cdot(-4\frac{2}{3})=\frac{38}{3}[/tex]if we want we can write it in the same form as the others
Final answer
[tex]\frac{38}{3}=12\frac{2}{3}[/tex]Find all values of X,where |x| = 11.
The equation to solve is:
[tex]|x|=11[/tex]From basic definition of absolute value, we can say,
If
[tex]|x|=a[/tex]Then,
[tex]x=a,-a[/tex]Using this definition of absolute value, we can solve this equation:
[tex]\begin{gathered} |x|=11 \\ x=-11,11 \end{gathered}[/tex]Answer:
[tex]x=-11,11[/tex]choose the correct statement of the rule; then complete the table for missing values. A merchant adds $3.00 to his cost to determine his selling price.
We have to find a relation between selling price in function of cost C.
If C is the cost, then the selling price is a function of C: f(
a basketball court is 94 ft long and 50 ft wide Ryan used long steps to estimate the length of the Court as 93 ft and a width as 48 what is the percent error of Ryan's measure area round to your nearest hundred
5.02%
Explanation:Percentage error formula = |(approximate value - Exact value)|/(exact value) × 100
Area of the court = length × width
length = 94 ft
width = 50 ft
Exact area = 94ft × 50 ft
Exact area = 4700 ft²
length = 93 ft
width = 48 ft
Approximate area = 93 ft × 48 ft
Approximate area = 4464 ft²
[tex]\begin{gathered} \text{percent error = }\frac{|4464\text{ - 4700|}}{4700}\times\text{ 100} \\ \text{percent error = }\frac{|-236|}{4700}\times100 \\ \text{percent error = }\frac{236}{4700}\times100 \end{gathered}[/tex][tex]\begin{gathered} \text{Percent error = }0.0502\text{ }\times\text{ 100} \\ \text{Percent error = 5.02\%} \end{gathered}[/tex]choose all that apply 3/4 ÷ 1/81/66243/4•1/83/4•8/14/3•8/1
Explanation:
The steps to divide fractions are KCF:
• K,eep the first fraction as it is
,• C,hange the division sign to a multiplication sign
,• F,lip the second fraction:
[tex]\begin{gathered} \frac{3}{4}\div\frac{1}{8}= \\ \frac{3}{4}\times\frac{8}{1}= \\ \frac{3\times8}{4\times1}=\frac{24}{4}=6 \end{gathered}[/tex]Here we can see which ones apply
Answer:
• 6
,• 3/4 • 8/1
3 Step Problem: Erik is building a cubby bookshelf, that is, a bookshelf divided into storage holes (cubbies) instead of shelves. He wants the height of the bookshelf to be x^2 - 2x - 3 and the width to be x^2 + 4x + 3. Each cubby hole in the bookshelf will have a height of x + 3 and width of x - 3.STEP 1 of 3: Write a rational expression to determine how many cubbies high the book shelf will be.
Step 1:
In order to determine the number of cubbies high, we just need to divide the total height x² - 2x - 3 by the height of one cubby x + 3:
x² divided by x: x
x multiplied by (x + 3): x² + 3x
x² - 2x - 3 minus x² + 3x: -5x - 3
-5x divided by x: -5
-5 multiplied by (x + 3): -5x - 15
-5x - 3 minus -5x - 15: 12
The division doesn't have remainder 0, so let's write the division as a fraction:
[tex]\text{number of cubbies}=\frac{x^2-2x-3}{x+3}[/tex]4) Select all ordered pairs that satisfy thefunction: y=-3x + 4A.(-2,10)B. (-1,1)C. (5,-11)D. (6,-22)
To know if an ordered pair satisfy an equation we have to substitute the values in it and see if the left side is equatl to the right side.
Pair (-2,10)
In this case x=-2 and y=10. Plugging the values in the equation:
[tex]\begin{gathered} 10=-3(-2)+4 \\ 10=6+4 \\ 10=10 \end{gathered}[/tex]since both sides have the same value, this paired satisfy the equation.
Pair (-1,1)
In this case x=-1 and y=1. Then
[tex]\begin{gathered} 1=-3(-1)+4 \\ 1=3+4 \\ 1=7 \end{gathered}[/tex]since this is not true, this ordered pair don't satisfy the equation.
Pair (5,-11)
In this case x=5 and y=-11. Then
[tex]\begin{gathered} -11=-3(5)+4 \\ -11=-15+4 \\ -11=-11 \end{gathered}[/tex]since this is true the ordered pair satisfy the equation.
Pair (6,-22)
In this case x=6 and y=-22. Then
[tex]\begin{gathered} -22=-3(6)+4 \\ -22=-18+4 \\ -22=-14 \end{gathered}[/tex]since this is not true, this ordered pair don't satisfy the equation.
Therefore the ordered pairs that satisfy the equation are the points A and C.
The angle between 0 degrees and 60 degrees that is coterminal with the 1993 angle is degrees.Please show work neatly
Given:
[tex]1993^0[/tex]To Determine: The coterminal angle of the given angle
Solution
Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side. For example 30° , −330° and 390° are all coterminal
[tex]\begin{gathered} 1993^0-360^0=1633^0 \\ 1633^0-360^0=1273^0 \\ 1273^0-360^0=913^0 \\ 913^0-360^0=553^0 \\ 553^0-360^0=193^0 \end{gathered}[/tex]Hence, the angle that coterminal with 1993 degrees is 193⁰
help me pleaae im a starr.
Answer: the value of m+n must equal 225.
Step-by-step explanation: If all the classroom crayons are accounted for in the table above, you can add all of the remaining crayons togeher which would get you to 65. 290 - 65 = 225.
This is the best answer I can come up with. I hope this helps.
Hello,Can you please help me with question# 11 ? it is express each sum using summation notation. Use 'i' as the index of th sum
Given:
The sum of terms
[tex]4^3+5^3+6^3..........+13^3[/tex]Required:
Find sum.
Explanation:
We know sum of cube of first n terms of natural numbers
[tex]\sum_{n\mathop{=}1}^{\infty}n^3=[\frac{n(n+1)}{2}]^2[/tex]Now,
[tex]\begin{gathered} =(1^3+2^3+....+13^3)-(1^3+2^3+3^3) \\ =[\frac{13(13+1)}{2}]^2-36 \\ =8281-36 \\ =8245 \end{gathered}[/tex]Answer:
The sum of terms is 8245.
what is volume of sphere if it is 1ft?
a haunted house found that it number of Halloween weekend customers can be modeled by
You have the following equation for the number N of halloween weekend customers in terms of the entrance price p (in dollars).
Consider that for each dollar p, there are 15 halloween weekend customers less. That is the meaning of the factor -15 in the given function for N(p). As p increases, the term -15p is lower and lower, which means that N is lower.
5 centimeters by 3 centimetres and a height of 2 centimetres
firstly you have to calculate the volume of the rectangular prism
volume = base area x height
since it is a rectangular prism
then the area = length x breath
length = 5cm , breath = 3cm
therefore
[tex]\begin{gathered} \text{Area = l }\times b \\ =\text{ 5 }\times3 \\ =15cm^2 \end{gathered}[/tex]volume = base area x height
volume = 15 x 2
[tex]\text{volume = 15}\times2=30cm^3[/tex][tex]^{}\text{thus, the cameron fills }\frac{1}{2}cm^3[/tex]so the amount of the cameron fills that can fill up the prism is
[tex]\frac{30}{\frac{1}{2}}\text{ = 30 }\times\frac{2}{1}=60cm^3[/tex]the answer is D
what is the slope and y-intercept of negative 3x + 5y equals -15
-3x + 5y = -15
The general form of a line using slope and y intercept is: y = mx + b
where m is the slope and b is the y intercept
So we have to write the original equation in this form:
-3x + 5y = -15
5y = 3x - 15
y = (3/5)x - 15/5
y = (3/5)x - 3
In this case, m= 3/5 and b = -3
Therefore m = 3/5
Therefore the y intercept (when x = 0) is -3
Answer:
slope is 3/5
y intercept -3