The average rate of change of the function is -59.4
The formula for calculating the rate of change of the function is expressed as:
[tex]f'(x)=\frac{f(b)-f(a)}{b-a}[/tex]
Given the function
[tex]f(x)=120(0.1)^x\\f(0) = 120(0.1)^0\\f(0)=120\\[/tex]
Get the value of f(2)
[tex]f(2)=120(0.1)^2\\f(2) = 120(0.1)^2\\f(2)=1.2\\[/tex]
Substitute into the formula to have:
[tex]f'(x)=\frac{1.2-120}{2-0}\\f'(x)=\frac{118.8}{2} \\f'(x)= -59.4[/tex]
Hence the average rate of change of the function is -59.4
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Suppose the graph of y = f(x) is translated left 2 units, and up 8 units, then stretched vertically by a
factor of 3.
The new graph will have equation y =
Answer: f(x)=3(x+4)+ 8
Step-by-step explanation:
Stretch vertically by a factor of 3: y = 3x
Then, translate two units leftward: y = 3(x+2)
Then, translate 8 units upward: y = 3(x+4)+ 8
Which division problem is modeled
Answer:
The first one
Step-by-step explanation:
if you count, there are five full rows, and two extra, so 52/100. then you count the sections that the colored area is: 4. then count how many squares are in each colored section: 13.
a.
Write the equation in slope intercept form of a line that goes through the points
(-7, 10) and (1,4). Hint: once you find m, you will need to solve for b
Answer:
y= -¾x + 19/4
Step-by-step explanation:
get gradient and substitute
1) An airplane is at 10,000 feet above the ground. It needs to fly higher to reach the regular flying height. It increases its height at a constant rate of 2,000 feet per minute. How high will the plane be in 10 minutes?
Answer:
20000
Step-by-step explanation:
Answer: 30,000 feet
Step-by-step explanation: We start with the 10,000 feet original height. From there, we can take 2,000 feet per minute and multiply it by 10 minutes. That gets us 20,000 feet. Add 20,000 to our original 10,000 and we get 30,000.
what is a trinomial?
Answer:
In elementary algebra, a trinomial is a polynomial consisting of three terms or monomials.
Answer:
An algebraic expression of three terms
Step-by-step explanation:
A trinomial consists of 3 terms connected to one another by + or - sign(s).
Examples: x^2 - 2x - 5 is a trinomial: Its 3 terms are arranged in descending order by powers of x.
Please help me with this
HELP 35 POINTS
State the domain and range to each of these functions and determine function or not.
Answer:
see below
Step-by-step explanation:
2.x<1, y=all real numbers
3. -1<=x<=3 -3<=y<=2
4. x= all real numbers, y>-2
5. 7<=x<5, 3<=y<1
6.x>-4, y>-1
Expand & simplify 4 ( p + 3 ) + 4 ( p − 6 )
Answer:
8p -12Step-by-step explanation:
Expand & simplify 4 ( p + 3 ) + 4 ( p − 6 )
4(p + 3) +4(p - 6) =
4p + 12 + 4p - 24 =
8p -12
it takes clay 1/2 hour to mow his lawn how much of the yard will be mowed after 1/3 hour
Answer:
Step-by-step explanation:
Clays rate is 1/2 hour per lawn. We can write this as Rate = 3/2 hr/lawn.
If Clay mows for 1/3 hour, we can determine the amount of lawn mowed by dividing the 1/3 hour by the rate:
(1/3 hr)/(3/2 hr/lawn) = (1/3)*(2/3) = 2/9 of a lawn.
solve |8y+4|=2|y-1|
please show the work!
HELLO PLEASE GIVE ME THE RIGHT ANSWER ASAP THANK YOU !
[tex]\large\underline{\sf{Solution-}}[/tex]
[tex]\textsf{Given expression;}\\[/tex]
[tex] \rm{23 = \frac{7}{9}(6x - 36) + 9 } \\ [/tex]
[tex] \rm{\longmapsto} \: 23 = \frac{(42x - 256)}{9} + 9 \\ [/tex]
[tex] \rm{\longmapsto} \: 23 = \frac{(42x - 256 + 81)}{9} \\ [/tex]
[tex] \rm{\longmapsto} \: 23 = \frac{(42x - 175)}{9} \\ [/tex]
[tex] \rm{\longmapsto} \: \frac{23}{1} = \frac{(42x - 175)}{9} \\ [/tex]
[tex]\textsf{By doing cross multiplication, we get}\\[/tex]
[tex] \rm{\longmapsto}23(9) = 1(42x - 175) \\ [/tex]
[tex] \rm{\longmapsto}207 =42x - 175\\ [/tex]
[tex]\rm{\longmapsto} \: 42x = - 175 - 207 \\ [/tex]
[tex]\rm{\longmapsto} \: 42x = - 379 \\ [/tex]
[tex]\rm \therefore \: x = - \frac{375}{42} \\ [/tex]
[tex]\textsf{Hence, the value of x will be -375/42 respectively.}\\[/tex]
[tex]\textbf{Read more:}[/tex]
[tex]\textsf{Similar Questions}[/tex]
Solve the expression and find the value of x. [tex] \frac{x…
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The density of glass in a bottle is 2.4gcm^3. The volume of glass used to make the bottle is 13.4cm^3. Calculate the mass of the glass bottle.
Answer:
Density is g/cm^3, not gcm^3
Mass = 32.16 grams [32.2 grams for 3 sig figs)
Step-by-step explanation:
Density = Mass/Volume
Density = 2.4g/cm^3
Volume = 13.4cm^3
---
2.4g/cm^3 = Mass/13.4cm^3
Mass = (2.4g/cm^3)*(13.4cm^3)
Mass = 32.16 grams [32.2 grams for 3 sig figs)
The mass of the glass-bottle is 32.16 grams.
What is volume?Space occupied by an object in three-dimensional space is called as volume of an object. In simple words, space is taken by object.
Given:
The density of glass in a bottle is 2.4 grams per cubic centimeters.
The volume of glass used to make the bottle is 13.4 grams per cubic centimeters.
Density = Mass/Volume
Density = 2.4 grams per cubic centimeters.
Volume = 13.4 cubic centimeters.
Substituting all the values,
2.4 = Mass / 13.4
Mass = 13.4 x 2.4
Mass = 32.16
Therefore, mass = 322.16 grams.
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Dante argues that point P is the circumcenter of the triangle. Determine if
Dante is correct and justify your answer.
Dante is incorrect because point P is not the circumcenter of the triangle.
What is the circumcenter of a triangle?The circumcenter of a triangle is a specific point or location either inside or outside the triangle that represents the center if a circumcircle is drawn or if a circle that touches all the vertices of a triangle is drawn.
How to identify a circumcenter?There are some simple characteristics to determine if a circumcenter is correct.
All the vertices of a triangle have the same distance from the circumcenter.In obtuse triangles like the one shown in the image, this point is located outside the triangle.Based on these characteristics we can conclude Dante is incorrect because the distance from point P to the three vertices is not the same and this point should be located outside not inside the triangle.
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1) what is the area (square units)
Twelve square tiles, each measuring 5 inches
on a side, are laid side by side. What is the total
width of the tiles?
Answer:
pretty sure 60, 5 x 12
Step-by-step explanation:
just do 5 x 12 if there's 12 tiles and their measurement is 5 inches each
What is meaning of irrational exponents.
Answer:
Here
Step-by-step explanation:
Irrational exponents are non repeating or infinite decimals while rational exponents are rational numbers. The value of an irrational exponent when calculated is approximate in nature while the value of rational exponent is exact.
Write an equation in point-slope form of
the line that has a slope of 2 and passes
through point (5,-3).
Answer:
(y+3)=2(x-5)
Step-by-step explanation:
find the missing triangle measurements. I WILL GIVE BRAINLIEST! PLEASE
Answer:
ABC= 60
DCE= 65
DEF= 105
Step-by-step explanation:
Answer:
60°; 65°; 115°Step-by-step explanation:
ΔABC is equilateral since all sides marked as congruent. Therefore:
m∠ABC = 60°ΔCDE is isosceles since two sides marked as congruent:
m∠DCE = m∠DEC = 1/2(180° - 50°) = 1/2(130°) = 65°∠DEF forms a linear pair with ∠DEC, so they sum to 180°:
m∠DEF = 180° - 65° = 115°There are 22 tables in the cafeteria. Each table can seat 8 students.There are 4 lunch periods each day.How many students can the cafeteria seat each day?
Answer:
704 students can fit in the cafeteria a day
please dont give a useless answer
Answer:
[tex]\frac{7}{10} ,0.7[/tex]
Reasoning:
Do the inverse of adding 4/5 to isolate and find a.
[tex]1\frac{1}{2} - \frac{4}{5} =\frac{7}{10}[/tex]
Decimal Form:
[tex]1.5-0.8=0.7[/tex]
Answer:
a = 0.7 = 7/10
Step-by-step explanation:
Subtract 4/5 from both sides.
a + 4/5 = 1 1/2
a + 0.8 = 1.5
a + 0.8 -0.8 = 1.5 -0.8 . . . . subtract 4/5 from both sides
a = 0.7 = 7/10
_____
If you like, you can solve this a couple of other ways:
1) Solve it as an integer problem.
10a +8 = 15 . . . . . . multiply the given equation by 10 to clear fractions
10a = 7 . . . . . . . . subtract 8
a = 7/10 . . . . . . divide by 10
2) Use a common denominator
a +8/10 = 1 5/10
a = 1 5/10 -8/10 . . . . . subtract 8/10
a = 15/10 -8/10 = (15 -8)/10 = 7/10 . . . . . convert to improper fraction
__
Additional comment
It is a good idea to get comfortable working with numbers in any form in which they are presented: decimal, fraction, mixed number, scientific notation, percentage. Knowing how to convert between forms is essential.
A retirement account was opened with a $900 deposit. If the account earns 4.25% interest compounded continuously and has no other deposits or withdrawals, how long will it take the value to double?
It will take 16.66years long for the money to double
The formula for calculating the compound amount is expressed as:
A = P(1+r)^t
A is the amount after t years = 2(900) = $1800P is the amount invested = $900r is the rate in decimal = 4.25% = 0.0425Substitute into the formula to have:
1800 = 900(1+0.0425)^t
2 =(1+0.0425)^t
2 = 1.0425^t
ln2 = tln1.0425
t = ln2/ln1.0425
t = 0.6931/0.0416
t = 16.66years
This shows that it will take 16.66years long for the money to double
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[tex]\sf 78-2x=87-3x[/tex]
Answer:
x = 9
Step-by-step explanation:
78 - 2x = 87 - 3x
3x - 2x = 87 - 78
x = 9
x = 9
Step-by-step explanation:
=> 78-2x= 87 -3x
=> 78-87=-3x+2x
=> -9 = -x
=> x = 9
In two or more complete sentences describe how to determine if the function, f(x) =3cos(x) is even by looking at a graph
Answer:
You know that a cosine graph is a sine graph moved to the left by pi/2, therefore, like a linear equation, you need to make the cosine graph 3 times less width.
Step-by-step explanation:
the point (-2,6) is on a line with a slope of 3/4. If the point -8,k) is also on the same line what is the value of k
For a point with a slope 3/4 and which passes through the points (-2, 6) and (-8, k), the value of k is 1.5
The line passes through the points (-2, 6) and (-8, k)
That is, [tex]x_1=-2, y_1=6, x_2=-8, y_2=k[/tex]
The slope of the line, m = 3/4
The formula for calculating the slope of a line is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute [tex]x_1=-2, y_1=6, x_2=-8, y_2=k, m = \frac{3}{4}[/tex] into the formula above
[tex]\frac{3}{4} = \frac{k-6}{-8-(-2)} \\\\\frac{3}{4} = \frac{k-6}{-8+2}\\\\\frac{3}{4} = \frac{k-6}{-6}\\\\-6(3)=4(k-6)\\\\-18=4k-24\\\\4k=-18+24\\\\4k=6\\\\k=\frac{6}{4} \\\\k=1.5[/tex]
Therefore, the value of k is 1.5
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Which ordered pairs in the form (x, y) are solutions to the equation 3x−4y=21? select each correct answer. (−1, −6) (7, 0) (11, 3) (−3, 3).
Answer:
(-1, -6), (7, 0) , and (11, 3)
Step-by-step explanation:
3x - 4y = 21 Solve the equation for y
3x - 21 = 4y
(3x - 21)/4 = y
Now use the ordered pair and find the true ordered pair
(-1, -6) [ (3)(-1) - 21]/ 4 ; (-3 -21)/4 ; (-24)/4 = -6 True
(7, 0) [(3)(7) -21]/4 ; (21 - 21)/4; 0/4 = 0 True
(11, 3) [(3)(11) - 21]/4; (33 - 21)/4; 12/4 = 3 True
(-3 ,3) [(3)(-3) - 21]/4 (-9 -21)/4 ; -30/4 = -7.5 No
Please help me and
explain how you got the answer
Answer:
x = 7°
Step-by-step explanation:
∠WST is an exterior angle of the triangle
The two interior angles (5x - 1) and (57) add up to WST ( 12x + 7) because they are the non-adjacent interior angles
Solve:
(5x - 1) + (57) = (12x + 7)
5x - 1 = 12x - 50
-1 = 7x - 50
49 = 7x
x = 7
-Chetan K
Owen had 8,452 books donated to our school. If he shares with with 23 classes about how many books does each class get? Again assesment due tom :,)
Answer:
327.5
Step-by-step explanation:
8452/23 = 327.478
Round to about 327.5 books per class
Answer:
each class gets 367 books
100 points if you get this
Answer:
....
Step-by-step explanation:
Answer:
I AGREE
Step-by-step explanation:
Use the model to find the missing number in the pair of equivalent expressions.
15 + 9 = ?(5 + 3)
What number is missing from the expression?
Answer:
3
Reasoning:
[tex]3(5+3)=15+9[/tex]
Distribute three to the numbers to get 15+9.
what is 18 kg in grams
Answer:
18 000
Step-by-step explanation:
One kg is 1000 grams. 18 kg are 18 x 1000 = 18 0000 grams.
