In order to find \( f(x+h) \) given the function \( f(x) = \fraction{x²}{x+3} \), we need to replace every instance of \( x \) in the function with \( x+h \). Here are the steps to do so:
1. Write down the original function:
\( f(x) = \fraction{x²}{x+3} \)
2. Substitute \( x+h \) for \( x \) in the function to get \( f(x+h) \):
\( f(x+h) = \fraction{(x+h)²}{(x+h)+3} \)
3. Now expand the numerator and simplify the expression:
\( (x+h)² = x² + 2xh + h² \)
Therefore, \( f(x+h) = \fraction{x² + 2xh + h²}{x+h+3} \)
That is the expression for \( f(x+h) \) given the function \( f(x) = \fraction{x²}{x+3} \). Note that you could further simplify the expression depending on the context or the specific question asked, but as it stands, this is the correct substitution and form of \( f(x+h) \).
Which description best represents the equation 25x + 50 = y?
Answer:
see the explanation
Step-by-step explanation:
we know that
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate of the linear equation
b is the y-intercept or initial value of the linear equation
In this problem we have
[tex]y=25x+50[/tex]
This is the equation of a line in slope intercept form
so
Is a linear equation (the graph is a line)
The slope is positive and is equal to [tex]m=25[/tex]
The y-intercept is the point (0,50) (y-intercept is the value of y when the value of x is equal to zero)
The value of b is [tex]b=50[/tex] (y-coordinate of the y-intercept)
The x-intercept is the point (-2,0) (x-intercept is the value of x when the value of y is equal to zero)
The linear function is a increasing function (the slope is positive)
ANYONE GOOD IN MATH TRANSLATIONS??
Answer:
(x, y ) → (x + 2, y - 4 )
Step-by-step explanation:
Compare the coordinates of 2 corresponding points in the original and the image, that is
B(- 5, 4 ) → B'(- 3, 0 )
To translate from B → B'
We require a shift of 2 units right in the x direction and 4 units down in the y direction, that is
(x, y ) → (x + 2, y - 4 ) ← translation rule
One day,students in Mr. Tate’s science lab noticed a strange moss growing on a cabinet. During the next few days, the moss grew quickly, covering desks,chairs,and the floor. Each day, the class recorded the growth of the moss. 1 on the first day, the moss covered 1 1/2 square feet. On the second day, it covered a total of 3 3/4 square feet.how much more surface did the moss cover on the second day?
Answer:
[tex]\frac{9}{4}\ or\ 2\frac{1}{4}\ square feet[/tex]
Step-by-step explanation:
On the first day the moss covered
[tex]=1\frac{1}{2}\ square feet[/tex]
[tex]=\frac{3}{2}\ square\ feet[/tex]
One the second day the moss covered [tex]=3\frac{3}{4}[/tex] square feet
[tex]=\frac{15}{4}\ square\ feet[/tex]
Extension of moss cover on second day
= Moss covered second day - Moss covered first day
[tex]=\frac{15}{4}-\frac{3}{2}\\=\frac{15}{4}-\frac{3\times2}{2\times2} \\=\frac{15}{4}-\frac{6}{4}\\=\frac{9}{4} \\=2\frac{1}{4}\ square\ feet[/tex]
OMGGGG PLZZZZZ HELP!!!!!URGENT DUE TODAY OR IM DEAD!!
Which equation is equivalent to6 + 3(x + 4) = 13?
√−100 = ___ +_____i
...
The square root of -100 is 0 + 10i or simply 10i in the form of a complex number, representing the imaginary part along the complex plane's imaginary axis.
Explanation:The square root of a negative number is not a real number, but rather a complex number denoted by the imaginary unit i for the square root of -1. To find the square root of -100, express -100 as the product of its prime factors: [tex]\(-100 = -1 \times 2^2 \times 5^2\)[/tex]. Then, applying the properties of square roots, break it down: [tex]\(\sqrt{-1} \times \sqrt{2^2} \times \sqrt{5^2}\)[/tex].
The square root of -1 is represented as i, while the square roots of [tex]\(2^2\)[/tex] and [tex]\(5^2\)[/tex] are 2 and 5, respectively. Combining these results, the square root of -100 is 0 + 10i, or simply 10i in complex number form, indicating that it lies on the imaginary axis of the complex plane.
It's important to note that the square root of a negative number results in a complex number with a real part of 0 and an imaginary part that represents the square root of the positive value of the number. In this case, the square root of -100 yields an imaginary component of 10i, indicating the distance from 0 along the imaginary axis in the complex plane, demonstrating the nature of complex numbers when dealing with square roots of negative values.
Chandler is walking 1/16 km every 10 minutes. How many kilometers will he walk in 1 hour?!
Answer:
[tex]\frac{3}{8} or\ 0.375\ km[/tex]
Step-by-step explanation:
Given: Chandler walk 1/16 km every 10 minutes.
First, lets find how many 10 minutes in one hours or convert minutes in hours.
∴ Time= [tex]\frac{60}{10} \ h[/tex]
Now, finding kilometres travelled in 1 hour.
Distance travelled= [tex]\frac{1}{16} \times \frac{60}{10} = \frac{1}{16} \times 6[/tex]
Distance travelled = [tex]\frac{3}{8}[/tex]
Converting [tex]\frac{3}{8} \ km[/tex] into decimal will have 0.375 km.
∴ [tex]\frac{3}{8} or\ 0.375\ km[/tex] will chandler walk in 1 hour.
missy sold between seven and 12 glasses of lemonade every hour at her lemonade stand. If she sold lemonade for two hours how many glasses could she have sold?
Answer:
24
Step-by-step explanation:
she sold 12 glasses of lemonade in one our times by two and you get 24
Missy could have sold between 14 and 24 glasses of lemonade in two hours, given that she sold between 7 and 12 glasses per hour.
To find out the range of glasses Missy could have sold in two hours, we need to calculate the minimum and maximum number of glasses sold per hour and then find the totals for two hours:
Step-by-Step Explanation
Minimum glasses per hour: 7 glassesMaximum glasses per hour: 12 glassesTotal for two hours (minimum): 7 glasses/hour * 2 hours = 14 glassesTotal for two hours (maximum): 12 glasses/hour * 2 hours = 24 glassesHence, Missy could have sold between 14 and 24 glasses of lemonade in the two hours.
A principal of $4000 is invested at 8.75% interest, compounded annually. How many years will it take to accumulate $14,000 or more in the account?
Answer:
The number of years will it take to accumulate the amount in the account is 15 years .
Step-by-step explanation:
Given as :
The principal invested = p = $4000
The rate of interest = r = 8.75% compounded annually
The amount accumulate after t years = A = $14,000
Let The years of accumulation = t years
From Compounded Interest
Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, $14000 = $4000 × [tex](1+\dfrac{\textrm 8.75}{100})^{\textrm t}[/tex]
Or, [tex]\dfrac{14000}{4000}[/tex] = [tex](1.0875)^{\textrm t}[/tex]
Or, 3.5 = [tex](1.0875)^{\textrm t}[/tex]
Taking log both side
[tex]Log_{10}[/tex]3.5 = [tex]Log_{10}[/tex] [tex](1.0875)^{\textrm t}[/tex]
Or, 0.54 = t [tex]Log_{10}[/tex]1.0875
or, 0.54 = t × 0.036
∴ t = [tex]\dfrac{0.54}{0.036}[/tex]
I.e t = 15
So, The number of years will it take = t = 15 years
Hence, The number of years will it take to accumulate the amount in the account is 15 years . Answer
Please help!!!!!!.....
Answer:
The diagonals ZX and YW are perpendicular to each other.
Step-by-step explanation:
We have to prove diagonal ZX is perpendicular to diagonal YW.
Now, the coordinates of Z(0,b), and X(2a,b)
Hence, slope of ZX is m = [tex]\frac{b - b}{2a - 0} = 0[/tex]
Therefore, ZX is parallel to x-axis.
Now, the coordinates of Y(a,0) and W(a,4b)
Hence, slope of YW is n = [tex]\frac{4b - 0}{a - a} = \infty[/tex]
Therefore, YW is parallel to y-axis.
Hence, the diagonals ZX and YW are perpendicular to each other. (Proved)
Solve for Y
-5y + 8 = -3y + 10?
Answer:
y=-1
Step-by-step explanation:
-5y+8=-3y+10
-5y-(-3y)+8=10
-5y+3y=10-8
-2y=2
y=2/-2
y=-1
Ralph and Homer read a total of 33 books over the summer. Ralph read three more than four times as many as Homer. How many books did each person read?
Help Please! Add work.
Ralph read 27 books and Homer read 6 books.
Step-by-step explanation:
Given,
Total books read = 33
Let,
Books read by Ralph = x
Books read by Homer = y
According to given statement;
x+y=33 Eqn 1
Ralph read three more than four times as many as Homer.
x = 4y+3 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex](4y+3)+y=33\\4y+3+y=33\\5y=33-3\\5y=30[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{30}{5}\\y=6[/tex]
Putting y=6 in Eqn 2
[tex]x=4(6)+3\\x=24+3\\x=27[/tex]
Ralph read 27 books and Homer read 6 books.
Keywords: linear equation, substitution method
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a line parallel to y=3x+2 and intersects the points (1,9).What is the equation of this parallel line
Answer:
y=3x+6
Step-by-step explanation:
Parallel means same slope.
y-y1=m(x-x1)
y-9=3(x-1)
y=3x-3+9
y=3x+6
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line will be y=3x+6.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.
The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is constant.
Since the line is parallel to y=3x+2, the slope of the line will be the same as this line, therefore, will be equal to 3. The equation of the required line will be,
y = 3x + c
Now, the value of constant, c can be found by substituting the point in the equation of the line, therefore,
9 = 3(1) + c
9 = 3 + c
c = 6
Hence, the equation of the line will be y=3x+6.
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Randy went shopping and bought 1.8 pounds of grapes and 3.47 pounds of bananas.how many pounds of fruit did randy buy in all
Answer:
3.47 + 1.8 = 5.27 lbs of fruit Randy bought in all
Between 4:00 p.m. and 7:00 p.m. the temperature in Boxerville dropped 18
degrees. If the temperature at 7:00p.m. is 64 degrees, what was the
temperature in degrees at 4:00 p.m.?
Answer here
SUBMIT
To find the temperature in Boxerville at 4:00 p.m. after a drop of 18 degrees by 7:00 p.m. (with a 7:00 p.m. temperature of 64 degrees), we add the dropped degrees back to find the original temperature was 82 degrees.
The question asks to find the temperature at 4:00 p.m. in Boxerville given that it dropped 18 degrees by 7:00 p.m., and the temperature at 7:00 p.m. is 64 degrees. To solve this, we simply need to add the 18-degree drop back to the 7:00 p.m. temperature to find the original temperature at 4:00 p.m.
To find the temperature at 4:00 p.m., we calculate:
Temperature at 7:00 p.m.: 64 degrees
Temperature drop: 18 degrees
Original temperature at 4:00 p.m.: 64 degrees + 18 degrees = 82 degrees
Therefore, the temperature at 4:00 p.m. was 82 degrees.
which rate describes a unit price?
$1.00 for 2 lemons
3.00 for every pound
$4.00 for 3 slices of pizza
$6.00 for every 6 bottles
I'm assuming there should be a dollar sign here. This is the same as saying "$3 for one pound". A unit rate has some amount per 1 unit of something else. In this case, the 1 unit is 1 pound.
A different example of a unit rate is writing 40 miles per hour. This is the same as saying the car drives 40 miles in 1 hour. The unit here is the "1 hour".
Answer:
Given: $1.00 for 2 lemons $3.00 for every pound $4.00 for 3 slices of pizza $6.0
Step-by-step explanation:
Which line most accurately represents the line of best fit for the scatter plot?
A graph shows numbers from 0 to 14 on the x axis at increments of 2 and the numbers 0 to 112 on the y axis at increments of 16. Scatter plot shows ordered pairs 0, 32 and 2, 48 and 3.5, 56 and 4, 72 and 6, 75 and 8, 90 and 9, 96 and 10, 110. A line labeled A joins ordered pair 0, 32 and 4, 112. A line labeled B joins the ordered pairs 0, 32 and 10.5, 112. A line labeled C joins the ordered pairs 0, 32 and 14, 96. A line labeled D joins the ordered pairs 0, 32 and 14, 64.
Line A
Line B
Line C
Line D
Answer:
Hence two ordered pairs can be joined to best draw the line of best fit for this scatter plot are (0, 14) and (10, 1)
Option B is correct.
Step-by-step explanation:
Find the result when 28 is decreased by 25%
Answer: 21
Step-by-step explanation:
28-(28/100)*25=28-7=21
PLZ help me super really really fast
Answer:
A. 3 cm
Step-by-step explanation:
The smallest face has the sides 4 cm and 8 cm. If the water is 4 cm from its top, then the height of the water is [tex]16-4=12[/tex] cm and the volume of the water is
[tex]V_{water}=4\cdot 8\cdot 12=384\ cm^3[/tex]
The largest face has the sides 8 cm and 16 cm. If the container is placed on its largest face, then the volume of the water is
[tex]V_{water}=8\cdot 16\cdot h \ cm^3,[/tex]
where h is the height of the water.
Equate volumes of the water:
[tex]8\cdot 16\cdot h=384\\ \\h=\dfrac{384}{8\cdot 16}=3\ cm[/tex]
Therefore, the water is 3 cm from the bottom.
Make a conjecture about two different non vertical lines in the same plane that have the same slope
Two different non-vertical lines in the same plane with the same slope are parallel to each other. The slope determines the angle of the line with respect to the x-axis, and lines with the same slope do not intersect if they have different y-intercepts.
Explanation:When making a conjecture about two different non-vertical lines in the same plane that have the same slope, one can conclude that these two lines are parallel to each other. This is because the slope of a line represents the steepness and direction of the line, and lines with the same slope will never intersect and are hence parallel. The slope is determined by the ratio of the rise (change in y) over the run (change in x), and as illustrated in Figure A1, the slope is consistent along the entire length of a straight line. If two lines have the same slope but different y-intercepts, they will maintain the same angle with respect to the x-axis but will be positioned at different locations in the plane.
An example is given in Figure A1, where a line has a y-intercept of 9 and a slope of 3. The slope and y-intercept are represented by the 'm' and 'b' terms in the linear equation y = mx + b. Therefore, even if two lines have the same 'm' value, if their 'b' values are different, the lines will be parallel but not coincident (overlapping).
-16/1296 in simplest form
Pls someone help!
Answer:
-1/81
Step-by-step explanation:
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Answer:
-1/81
Step-by-step explanation:
What is the slope of the line with equation Y -3 equals -1/2(X -2)?
Answer:
The slope is dy/dx= -1/2
Step-by-step explanation:
Y-3= -1/2(X -2)
Y= -1/2x +2/2 +3
Y= -1/2x +1+3
Y= - 1/2x +4
The slope dy/dx= -1/2
3. Put the polynomial in standard form.
5x-3x + 1+ 6x?
1+ 6x² + 5x+3x?
6x² + 5x - 3x +1
-3x? + 5x+ 6x² + 1
-3x2 + 6x² + 5x + 1
The polynomial in standard form is [tex]\( -3x^3 + 6x^2 + 5x + 1 \)[/tex], which corresponds to option A.
Here are the step-by-step instructions to put the given polynomial in standard form:
1. Rearrange the terms by descending order of exponents: Start by rewriting the polynomial with the terms arranged from highest degree to lowest degree.
[tex]$$ -3x^3 + 6x^2 + 5x + 1 $$[/tex]
2. Check for any missing terms: Make sure that each degree of x from highest to lowest is represented. In this case, all terms are present.
3. Double check the arrangement: Ensure that the terms are arranged correctly with respect to their exponents.
[tex]$$ -3x^3 + 6x^2 + 5x + 1 $$[/tex]
Thus, the polynomial in standard form is:
[tex]\[ -3x^3 + 6x^2 + 5x + 1 \][/tex]
Therefore, the correct answer is option A.
Complete Question:
Put the polynomial in standard form
[tex]$$5 x-3 x^3+1+6 x^2$$[/tex]
Choose the correct option
A: [tex]$-3 x^3+6 x^2+5 x+1$[/tex]
B: [tex]$1+6 x^2+5 x-3 x^3$[/tex]
C: [tex]$6 x^2+5 x-3 x^3+1$[/tex]
D: [tex]$-3 x^3+5 x+6 x^2+1$[/tex]
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Subtracting 3x2 + 4x – 5 from 7x2 + x + 9 results in a polynomial. After subtracting 4x2 – 3x from this polynomial, the difference is ____________.
Answer:
14
Step-by-step explanation:
To subtract 3x2 + 4x – 5 from 7x2 + x + 9, we will take the difference of the two polynomials to have;
7x2 + x + 9 -(3x2 + 4x – 5)
= 7x²+x+9-3x²-4x+5
= 7x²-3x²+x-4x+9+5
= 4x²-3x+14
Further subtracting 4x²-3x from the resulting polynomial will give us;
4x²-3x+14 - (4x²-3x)
= 4x²-3x+14-4x²+3x
= 4x²-4x²-3x+3x+14
= 14
Therefore the final answer is 14
Subtracting 3x^2 + 4x - 5 from 7x^2 + x + 9 yields the polynomial 4x^2 - 3x + 14. The difference polynomial is 4x^2 - 3x + 14.
When subtracting 3x^2 + 4x - 5 from 7x^2 + x + 9, you need to subtract the coefficients of like terms.
Starting with 7x^2 + x + 9 - (3x^2 + 4x - 5), you subtract the corresponding coefficients:
(7x^2 - 3x^2) + (x - 4x) + (9 + 5)
This simplifies to:
4x^2 - 3x + 14
So, the resulting polynomial is 4x^2 - 3x + 14 after subtracting.
In this polynomial, the highest degree term is 4x^2, the linear term is -3x, and the constant term is 14. The difference is a quadratic polynomial with a leading coefficient of 4, a linear term with a coefficient of -3, and a constant term of 14.
This polynomial represents the result of subtracting 3x^2 + 4x - 5 from 7x^2 + x + 9.
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complete the missing value in y - 4 = -2(x + 3)
Answer:
y=-2x-2
Step-by-step explanation:
y-4=-2(x+3)
y=-2x-6+4
y=-2x-2
A large crane used at a construction site has a
253 foot reel of cable. A 3-foot section of
cable weighs 2 pounds. What is the weight of
the cable on the reel? Write your answer as a
fraction.
Answer:
168.67 lbs
Step-by-step explanation:
given that a 3 foot section of cable weights 2 lbs, i.e
3 feet ---> weighs 2 lbs
1 foot (i.e unit weight) -----> weighs 2/3 lbs
253 feet ------> weighs (2/3) x 253 = 168.67 lbs
Solve this math problem
Ranking the three from best to worst will be: point, line, plane. The justification is that, the starting concept determines the next one.
Step-by-step explanation:
The connection can be described by starting with the fundamental concept,procedure or strategy that give rise to the others. In this case, to form a line, you need to have points that join to extend infinitely in different directions. This means the point, is the fundamental concept, that will give the line.A plane is an infinite set of points that form a connected flat surface extending infinitely far in all direction. So here again, the plane exist where there is a set of points. However, a plane is named by three points that are in the plane but not in the same line. Hence, before naming a plane, the concept of a line should be considered. Ranking the three from best to worst will be: point, line, plane. The justification is that, the starting concept determines the next one.
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which expression is equivalent to 2/5(4x+9)
Answer:
d
Step-by-step explanation:
because 2/5 × 4x=8/5 and 2/5×9=18/5
ita in d
Find the time required for an investment of $6000 to triple if the interest rate of 5.5% is compounded continuously.
Answer: t ≈ 20 years
Step-by-step explanation:
Since it is compounded continuously , we will use the compound interest formula:
A = P[tex]e^{rt}[/tex]
Where A is the amount when tripled
P is the initial amount
r is the rate
t is the time
since the investment is tripled , it means the A = 3P.
From the question:
A = 3P
P = $6000
r = 5.5%
t = ?
Substituting into the formula , we have
3P = P[tex]e^{rt}[/tex] , that is
3(6000) = 6000[tex]e^{0.055t}[/tex]
Dividing through by 6000 , we have
3 = [tex]e^{0.055t}[/tex]
Take the In of both sides in order to remove the exponential , that is
In 3 = 0.055t
divide through by 0.055
t = In 3 / 0.055
Therefore :
t = 19.97476888
t≈ 20 years
Question 5) Which of the following equations is equivalent to 5 - 2x + 7y = 4 ?
abel
Aly- - Ex-1
labey
Bv=zx -
sebep
Cy=x+
adol
y = 2
PLEASE HELP!!!!!
Answer:
B
Step-by-step explanation:
Given
5 - 2x + 7y = 4 ( subtract 5 from both sides )
- 2x + 7y = - 1 ( add 2x to both sides )
7y = 2x - 1 ( divide all terms by 7 )
y = [tex]\frac{2}{7}[/tex] x - [tex]\frac{1}{7}[/tex] → B
Answer:
B. [tex]y=\frac{2}{7}x-\frac{1}{7}[/tex]
Step-by-step explanation:
We have been given an equation [tex]5-2x+7y=4[/tex]. We are asked to choose the equation that is equivalent to our given equation.
We will convert our given equation in point-slope form of equation.
[tex]5-2x+2x+7y=4+2x[/tex]
[tex]5+7y=4+2x[/tex]
[tex]5-5+7y=4-5+2x[/tex]
[tex]7y=-1+2x[/tex]
[tex]7y=2x-1[/tex]
Divide both sides by 7:
[tex]\frac{7y}{7}=\frac{2x}{7}-\frac{1}{7}[/tex]
[tex]y=\frac{2}{7}x-\frac{1}{7}[/tex]
Therefore, equation [tex]y=\frac{2}{7}x-\frac{1}{7}[/tex] is equivalent to our given equation and option B is the correct choice.