[tex]\stackrel{de finition \textit{ of a derivative as a limit}}{\lim\limits_{h\to 0}~\cfrac{f(x+h)-f(x)}{h}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[-4(x+h)^3-1]~~ - ~~[-4x^3-1]}{h} \\\\\\ \cfrac{[-4(x^3+3x^2h+3xh^2+h^3)-1]~~ ~~+4x^3+1}{h} \\\\\\ \cfrac{[-4x^3-12x^2h-12xh^2-4h^3-1]~~ ~~+4x^3+1}{h} \\\\\\ \cfrac{-4x^3-12x^2h-12xh^2-4h^3-1+4x^3+1}{h}\implies \cfrac{-12x^2h-12xh^2-4h^3}{h}[/tex]
[tex]\cfrac{h(-12x^2-12xh-4h^2)}{h}\implies -12x^2-12xh-4h^2 \\\\\\ \lim\limits_{h\to 0}~-12x^2-12xh-4h^2\implies \lim\limits_{h\to 0}~-12x^2-12x(0)-4(0)^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \lim\limits_{h\to 0}~-12x^2~\hfill[/tex]
If ∠JAM and ∠JAK are supplementary angles, then what is the measure of ∠KAL?
A.
60°
B.
33°
C.
55°
D.
57°
Answer:
D) 57
Step-by-step explanation:
180 - 123
Question 1 options:
What is the length of MN¯¯¯¯¯¯¯ ? Important to have calculator in degree mode. Round answer to tenths.
The radius of a semicircle is 1 kilometer. What is the semicircle's area?
Answer:
1.6
Step-by-step explanation:
area of a semicircle is A = pi * r^2/2
So pi*1^2/2
3.14/2
1.57079632679
Rounded to the nearest tenth
1.6
Help help ASAP please
Answer:
y = -4x + 15
Step-by-step explanation:
slope of y = x/4 - 2 is 1/4
slope of line perpendicular to above line is -4
so y = -4x + b
use (4, -1)
-1 = -4(4) + b
b = 16 - 1 = 15
so
y = -4x + 15
You roll a six sided die. Find the probability of 1) event A rolling a 3.
2) event B rolling a 7 3) event C rolling a number less than 5.
Answer:
total sum (s)= 6
probability of getting a 3 = 3÷6
= 1÷2
Step-by-step explanation:
probability of getting a 7 =0÷7
=0
probability of getting less than 5 =4÷6
2÷3
y=x+2
y+1= – 4x
Is this ordered pair a solution of the system of equations? Help:(
Put value of y in Equation 1 in Equation 2.
[tex] \looparrowright \sf y + 1 = - 4x[/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf (x + 2) + 1 = - 4x[/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf x + 2 + 1 = - 4x[/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf x +3= - 4x[/tex]
[tex] \\ \\ [/tex]
[tex] \looparrowright \sf x + 4x= - 3[/tex]
[tex] \\ \\ [/tex]
[tex]\looparrowright \sf 5x= - 3[/tex]
[tex] \\ \\ [/tex]
[tex]\looparrowright \sf x= \dfrac{ - 3}{5} [/tex]
[tex] \\ \\ [/tex]
Let's find value of y :
[tex] \\ \\ [/tex]
[tex]\looparrowright \sf y=x+2[/tex]
[tex] \\ \\ [/tex]
[tex]\looparrowright \sf y= \dfrac{ - 3}{5} +2[/tex]
[tex] \\ \\ [/tex]
[tex]\looparrowright \sf y= \dfrac{ - 3 + 10}{5} [/tex]
[tex] \\ \\ [/tex]
[tex]\looparrowright \sf y= \dfrac{7}{5} [/tex]
Solution:
[tex]\looparrowright \sf \bigg( \dfrac{ - 3}{5} , \dfrac{7}{5} \bigg)[/tex]
pls can u gus tell me the ans and explanation
Step-by-step explanation:
the volume of the tank is
80×50×45 = 180,000 cm³
3/4 of that volume is
180000 × 3/4 = 135,000 cm³
so, we want to know how long it takes to fill 135,000 cm³.
the water intake flow is 9 l / minute.
now we need to know that a cube of 10 cm side length contains exactly 1 liter of water.
such a cube has the volume
10×10×10 = 10³ = 1000 cm³
so, 1000 cm³ = 1 liter.
and we need to fill 135,000 cm³.
how many times fit 1000 cm³ into 135,000 cm³ ?
135000/1000 = 135 times.
and that means it would take 135 minutes to fill it, if the flow was 1 l / minute.
but it is faster (9 times faster) : 9 l / minute
so, how many minutes ?
135 / 9 = 15 minutes
it takes 15 minutes to fill 3/4 of the tank.
Answer:
15 minutes
Step-by-step explanation:
The volume (V) of the tank is calculated as
V = lbh (l is the length, b the breadth and h the height (
here l = 80, b = 50, h = 45 , then
V = 80 × 50 × 45 = 180000 cm³
1 litre = 1000 cm³ , then
9 litres = 9 × 1000 = 9000 cm³
Divide the volume of the tank by 9000 for time in minutes
180000 ÷ 9000 = 20 minutes
It takes [tex]\frac{3}{4}[/tex] × 20 = 15 minutes to fill [tex]\frac{3}{4}[/tex] of the tank
90 kids in the band 20% of the kids own their own instruments how many kids own their own instruments
Answer:
18
Step-by-step explanation:
20% = .20
90 x .20=18
Hence, 18 kids own their own instruments
[RevyBreeze]
Find all integers greater than 3 but less than 10
____________________________________
Step-by-step explanation:
Set up: 3<x<10
An integer is a positive or negative number that doesn't include a fraction, or decimal.
Fun Fact: 0 can be an integer too!
x represents the unknown integer.
Integers greater than 3, but less than 10 are:
3<4<103<5<103<6<103<7<103<8<103<9<104, 5, 6, 7, 8, and 9 work as possible integers.
Lesson 13 Exit Ticket 5.4
Name
Date
1. Solve. Draw a rectangular fraction model, and write a number sentence to show your thinking.
I do not know how to do this
A rectangular fraction model can be drawn based on this idea: Annie had a total of cookies 20 but she gave 9 cookies to her friends, how many cookies does she have?
What is a rectangular fraction model?A rectangular fraction model refers to using a rectangle and dividing it to represent and understand fractions. This might be easier than representing fractions by only using numbers.
How to draw a rectangular fraction model?The first step is to think about a possible situation or word problem. After this, you can draw the fraction model. For example:
Annie had a total of 20 cookies but she gave 9 cookies to her friends, how many cookies does she have?For this, divide a rectangle in the total of parts (20) and color the total of parts that Annie has (11). This means the total of cookies she has is 11/20.
Learn more about rectangles in: https://brainly.com/question/10046743
Solve for x.
−4/5x+3/10<8/10
Answer:
x > -5/8
Step-by-step explanation:
Simplify by combining x and 4/5 and then moving 4 to the left side of x
-x * 4/5 + 3/10 < 8/10
-4x/5 + 3/10 < 8/10
Now we cancel the common factor of 8 and 10.
Factor 2 out of 8
-4x/5 + 3/10 < 2(4)/10
2 from 10
-4x/5 + 3/10 < 4/5
Now move all the terms not containing x to the right side
Lets subtract 3/10 from both sides
-4x/5 < 4/5 - 3/10
Now we multiply by 2/2 to write 4/5 with a common denomi.
-4x/5 < 4/5 * 2/2 - 3/10
Now write with a common denom of 10 and multiply by 1
-4x/5 < 4*2/5 * 2 - 3/10
5 by 2
-4x/5 < 4 * 2/10 - 3/10
Combine
-4x/5 < 4 * 2 - 3/10
Simplify the numerator by multiplying then subtracting
-4x/5 < 8 - 3/10
-4x/5 < 5/10
Cancel the common factor of 5 and 10...
-4x/5 < 5(1)/10
-4x/5 5* 1/5 * 2
-4x/5 < 1/2
Now we divide by -1
-4x/5)/-1 > 1/2)/-1
4x/5 > 1/2)-1
4x/5 > -1/2
Multiply both sides by 5 and cancel common factors. (5)
4x * 5 > -1/2 * 5
4x > -1/2 * 5
4x > -5/2
Now divide by 4 in each term
4x/4 > -5/2)/4
x > -5/2)/4
Multiply the numer by the reciprocal of the denom
x > -5/1 * 1/4
x > -5/4 * 2
x > -5/8
PLEASE HELP, Will give brainliest
Answer:
the first four terms are 2, 4, 6, and 8
Step-by-step explanation:
the y intercept becomes the first term. the for each value y increases by 2, this is the common difference.there are two ways you can get it. the by using equation of linear graphs y=mx+c and another by using the formula of AP Tn=a+(n-1)d.
both m(slope) and common difference(d) means the same thing.
Two pools are being filled with water. To start, the first pool contains 2164 liters of water and the second pool contains 2500 liters of water. Water is being added to the first pool at a rate of 31.75 liters per minute. Water is being added to the second pool at a rate of 21.25 liters per minute.
After how many minutes will the two pools have the same amount of water?
How much water will be in each pool when they have the same amount?
The amount of water in each pool at a particular time are illustrations of linear functions
Both pools will have the same amount of water after 32 minutesBoth pools will have 3180 liters at 32 minutesHow to determine the time they have the same amountFor the first pool, we have the following parameters
Initial amount = 2164 litersRate = 31.75 liters per minuteSo, the equation of the amount of water in the pool is:
y = 2164 + 31.75x
For the second pool, we have the following parameters
Initial amount = 2500 litersRate = 21.25 liters per minuteSo, the equation of the amount of water in the pool is:
y = 2500 + 21.25x
When both pools have the same amount of water, we have:
2164 + 31.75x = 2500 + 21.25x
Collect like terms
31.75x - 21.25x = 2500 - 2164
Evaluate the like terms
10.5x = 336
Solve for x
x = 32
This means that they will have the same amount of water after 32 minutes
Substitute 32 for x in y = 2164 + 31.75x
This gives
y = 2164 + 31.75 * 32
y = 3180
Both pools will have 3180 liters at 32 minutes
Read more about linear functions at:
https://brainly.com/question/15602982
Hello, pls help on these exercises
Answer:
c.p= R.s 75 ,loss=R.s 9 solve it
answer this please? :)
Answer:
yes
Step-by-step explanation:
see the attachement
The population of a Midwest industrial town decreased from 213,000 to 209,000 in just 2years. Assuming that this trend continues, what will the population be after an additional 3 years?
Answer:
203,000
Step-by-step explanation:
You need to find the pattern first, so you need to subtract 213,000 from 209,000 to get 4,000. Now that is the pattern for 2 years we need it for 1 year. So divide 4,000÷2=2,000 for 1 year. Next, you need to multiply 2,000×3=6,000. That is the decrease of the population for 3 years. Finally, subtract 6,000 from 209,000.
Hope you get an A! <3
There's a positive correlation between the amount of fertilizer a homeowner uses
and the height of the plants in her garden.
Which statement is true?
The correlation is most likely a causation.
The correlation is most likely a coincidence.
The correlation is most likely due to a lurking variable.
Answer:
The correlation is most likely a causation
Step-by-step explanation:
Causation
A change in one variable causes a change in another variable
Coincidence
The two variables are not related at all, but correlate by chance.
Lurking variable
A variable that is not measured in the study (i.e. it's a third variable that is neither the explanatory nor the response variable)
As fertilizer directly affects plant growth, then the correlation is most likely a causation
12. Find one solution for each equation. Assume all angles are acute angles
a. cos(0 + 4°) = sin(30 +2°)
Answer:
21 degrees
Step-by-step explanation:
I'm assuming that the 0 is supposed to be theta, which I'm replacing with x to make it easier for me to type.
Because these angles are acute, we can use the fact that if two angles A and B are complementary, then sinA = cosB.
So we can get that x+4+3x+2=90
4x+6=90
4x=84
x=21
Choose the equation of the line in slope-intercept form.
Perpendicular to y = 2x + 9 and has the point (4,-1).
A. y = 2x + 3
B. y = 2x + 9
C. y = -1/2x + 1
D. y = -1/2x + 3
answer:
c. y = -1/2x + 1
steps-explanation:
given sample equation:
y = 2x + 9comparing to the formula of slope intercept form: y = mx + b
[ where m is the slope and b is the y-intercept ]
we can determine here that the slope is 2 and 9 is the y-intercept.
but here we need only the slope.
making the slope perpendicular using: -1/m → 1/-2 → -1/2
formula:
y - y1 = m(x - x1)using the formula: [ here known that y1 is -1 and x1 is 4 ]
y - -1 = -1/2(x - 4)y + 1 = -1/2 x + 2y = -1/2 x + 2 - 1y = -1/2 x + 1Answer:
C) y = -1/2x + 1
Step-by-step explanation:
Equation of a line in slope-intercept form: y = mx + b
(where m is the slope (gradient) and b is the y-intercept)
The slopes of two perpendicular lines are negative reciprocals of each other. So, if the line is perpendicular to y = 2x + 9, then the slope m of the new line will be -1/2.
Therefore, y = -(1/2)x + b
We are told that the line passes through point (4, -1).
Substituting the found value for m the the point (4, -1) into point-slope form:
y - y1 = m(x - x1)
y - -1 = -(1/2)(x -4)
y = -(1/2)x + 1
What is the solution to the equation below?
4 + square root 6x + 4 = 8
[tex]4+ \sqrt{6x + 4 = 8} [/tex]
[tex] \sqrt{6x + 4 = 4}[/tex]
[tex]6x + 4 = 16[/tex]
[tex]6x = 12[/tex]
[tex]x = \frac{12}{6} = 2[/tex]
Option C is correct, x=2 is the solution to the equation 4+√(6x+4)=8
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 4+√(6x+4)=8
We have to solve for x
Subtract 4 from both sides
√(6x+4)=4
Square on both sides
6x+4=16
Subtract 4 from both sides
6x=12
Divide both sides by 6
x=2
Hence, Option C is correct, x=2 is the solution to the equation 4+√(6x+4)=8
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
x/5+7=3
tellme fastplease
Answer:
-20
Step-by-step explanation:
x/5=3-7
x/5=-4
x=-4×5
x=-20
An article reports that men over 6 feet tall earn more than men under 6 feet, with these numbers: average 6 foot plus male’s salary $55,000, average male’s salary under 6 foot tall of $47,000, with a p-value of 0.45. Based on that reported p-value, and using the common definition of "statistical significance," which is the case?
Answer:
D
Step-by-step explanation:
as the p value is 0.45 > 0.05 so the report that men over 6 feet tall earn more then men under 6 feet tall is accepted. So the salary differences are statistically signifcant
in the sequence 5,11,19,29,41
find the 25th term
Answer:
25th term = 701
Step-by-step explanation:
see attached
have a great day :)
I WILL GIVE BRAINLIEST
please help i’m so tired i’m gonna cry
1)) Select the expressions that
are equivalent to 5(7m + 7) - 9.
35m + 26
5(-9m + 16m + 7) - 9
7m + 26
(7m + 7)5 - 9
Answer:
a) 35m+26
Step-by-step explanation:
5(7m+7)-9
= 35m+35-9
=35m+26
Hope this helps!
Answer:
Step-by-step explanation:
5(7m + 7) - 9
= 5*7m + 5 * 7 - 9
= 35m + 35 - 9
= 35m + 26
answers: 1st, 2nd, and 4th choices
A radioactive material has a half life of 7 minutes, how long until there is 5% of the material remaining?
Can some pls help me with this problem?
Answer:
1.05 sorry it took so long.
Step-by-step explanation:
15 3 ones x 5 hundredths = 15 hundredths
+ 90 3 ones x 3 tenths = 9 tenths = 90 hundredths
105 hundredths = 1.05
this is what i got from the example on the top. Compare the example with number 2.
Error Analysis A math test asks the students to solve the inequality X-2511, and then graph the
solutions. Mason said the solutions are x s9 and graphed the solutions as shown below. Solve the
inequality and graph the solutions. What error might Mason have made?
What are the solutions?
X
Answer: x < 18
Step-by-step explanation:
x - 2 < 16
We eliminate 2 to isolate the variable, x by adding 2 to both sides. -2 + 2 = 0.
x < 18
We can test this because 17 is less than 18. Pretend x = 17
17 < 18✅
Mason subtracted 2, instead of adding 2.
In order to graph this, put an open circle at 18, and the arrow should point to the left.
calculate without using calculate 25/√37-12
Answer:
5
Step-by-step explanation:
[tex]\frac{25}{\sqrt{37-12} }[/tex]
= [tex]\frac{25}{\sqrt{25} }[/tex]
= [tex]\frac{25}{5}[/tex]
= 5
You and eight friends plan a surprise party. Each of you contributes the same amount of
money m for food. Their mom also contributes $20.
a. Write an algebraic expression for the total amount of money contributed for food.
b. Evaluate your expression if each person contributed $10.50
Answer:
a. 9m + 8×$20 = $340
b. 9×$10.50 + 8×$10.50 = $178.50
Step-by-step explanation:
Its self-explanatory
A bakery give me three options 12 cupcakes for $29 24 cupcakes for $56 50 cupcakes for $129 find each unit price to the nearest cent
a = 29 / 12
b = 56 / 24
c = 129 / 50
a = 2.42
b = 2.33
c = 2.58
b is cheapest, 24 for $56