Answers
Answer:
-12x²
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Function NotationCombining Like TermsFactoringExpanding by FOIL (First Outside Inside Last)Calculus
Evaluating LimitsDefinition of a Derivative: [tex]f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]Step-by-step explanation:
Step 1: Define
[tex]f(x) = 1 - 4x^3[/tex]
Step 2: Differentiate
Substitute [DOD]: [tex]f'(x)= \lim_{h \to 0} \frac{[1-4(x+h)^3]-(1-4x^3)}{h}[/tex]Expand: [tex]f'(x)= \lim_{h \to 0} \frac{[1-4(x^3+3hx^2+3h^2x+h^3)]-(1-4x^3)}{h}[/tex]Distribute: [tex]f'(x)= \lim_{h \to 0} \frac{1-4x^3-12hx^2-12h^2x-4h^3-1+4x^3}{h}[/tex]Combine like terms: [tex]f'(x)= \lim_{h \to 0} \frac{-12h^2x-4h^3-12hx^2}{h}[/tex]Factor: [tex]f'(x)= \lim_{h \to 0} \frac{h(-12hx-4h^2-12x^2)}{h}[/tex]Divide: [tex]f'(x)= \lim_{h \to 0} -12hx-4h^2-12x^2[/tex]Evaluate: [tex]f'(x)= \-12x^2[/tex]Related Questions
One species of fish in a fishery had an initial population
of 255 fish and after 9 seasons, the population had grown to
480 fish. A second species that was being overfished started
with an initial population of 450 fish, and after the same 9
seasons, it had a new population of 90 fish. Assuming a
linear growth, write the equations for the population of
•each species. Graph your equations in the coordinate plane.
Find the point in the graph which represents when the two
populations will have the same number of fish. After how
many seasons will the second population be eliminated?
Answers
9514 1404 393
Answer:
y = 25x +255y = -40x +450(3, 330)11 1/4 seasonsStep-by-step explanation:
The 2-point form of the equation of a line is useful for these problems. It is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
__
a) The two points are (0, 255) and (9, 480). The equation is ...
y = (480 -255)/(9 -0)(x -0) +255
y = 25x +255
__
b) The two points are (0, 450), (9, 90). The equation is ...
y = (90 -450)/(9 -0)(x -0) +450
y = -40x +450
__
c) The point where both populations are the same is (3, 330).
__
d) The second population will be eliminated after 11 1/4 seasons.
F F 2 X LIGI OM -8 What is the slope of a line parallel to line ? O A. A line parallel to line r has an undefined slope. OB. OC. -1 OD. 1
Answers
it would be 0 as its a 0 slope, hence forth the parallel line would also be 0!
(3 + 6)2 + ((17 + 8) - 42)
Answers
Answer:
1 I think.
Step-by-step explanation:
Answer: 1
Step-by-step explanation:
Given Equation
(3 + 6)2 + ((17 + 8) - 42)
We will simplify to get the answer.
[tex]= (9)[/tex] × [tex](2) + 17 + 8 - 42[/tex]
= [tex]18+17+8-42[/tex]
= [tex]18 + 25 - 42[/tex]
= [tex]18 + -17[/tex]
= 1
The answer to the question is 1.
in 2011, there were 3223 sea otters in monterey Bay is approximately 77 square miles. to the nearest whole number, what was the density of the sea otter population? (explain your answer)
Answers
Answer:
42 sea otters per mi2
Solve the equation for x.
logs (3x + 5) = log5 (2x + 8)
x = 7/3
x = 3
O
x = 0
O
No solution
Answers
what is the slope of this line? please please help me
Answers
Answer:
its 0 slope
Step-by-step explanation:
Write a Proof statement,
Answers
Answer:
Step-by-step explanation:
Given:
MO bisects ∠KMN and LO bisects ∠KLN
To prove:
LK ≅ LN
Statements Reasons
1). MO bisects ∠KMN 1). Given
2). LO bisects ∠KLN 2). Given
3). ∠KLM ≅ ∠NLM 3). Definition of angle bisector
4). ∠KMO ≅∠NMO 4). Definition of angle bisector
5). ∠KMO + ∠KML = 180° 5). Linear pair postulate
6). ∠NMO + ∠NML = 180° 6). Linear pair postulate
7). ∠KMO + ∠KML = ∠NMO + ∠NML 7). Transitive property of equality
8). ∠KMO + ∠KML = ∠KMO + ∠NML 8). Substitution property
9). ∠KML = ∠NML 9). Subtraction property of equaity
10). LM ≅ LM 10). Reflexive property
11). ΔLKM ≅ ΔLNM 11). ASA property of congruence
12). LK ≅ LN 12). CPCTC
As Jupiter revolves around the sun, it travels at a speed of approximately 8 miles per second. Convert this speed to kilometers per second. At this speed, how
many kilometers will Jupiter travel in 15 seconds? In your computations, assume that I mile is equal to 1.6 kilometers. Do not round your answers
Answers
Answer:
Speed is 12.8km/sec. Jupiter will travel 192km in 15 sec.
Step-by-step explanation:
[tex]\frac{8mi}{1sec} * \frac{1.6km}{1mi} = 12.8km/sec[/tex]
[tex]\frac{12.8km}{1sec} * 15sec = 192km[/tex]
4x – 2y = 14
z = 2y - 1
Answers
Answer: x
=
7
y
z
+
1
2
y
+
−
1
4
Step-by-step explanation:
From each of the following sets make all possible ordered pairs,
(a) P= {x,y)
(b) X= {1, 2, 3)
Answers
Answer:
All possible ordered pairs are as follows:
{(x, 1), (x, 2), (x, 3), (y, 1), (y, 2), (y, 3)}Step-by-step explanation:
In an ordered pair (x, y),
x is called the first component y is called the second component.Let
P = {x, y}
X = {1, 2, 3}
The number of elements in the set P = n(P) = 2The number of elements in the set X = n(X) = 3So, the number of possible ordered pairs = 2 × 3 = 6
Therefore, all possible ordered pairs are as follows:
{(x, 1), (x, 2), (x, 3), (y, 1), (y, 2), (y, 3)}Last month you spent $40 on clothing. This month you spent 120% of what you spent last month. Set up a proportion to model this situation. How much did you spend this month?
Answers
Answer:
$48
Step-by-step explanation:
Given that:
Money spent on clothing last month = $40
Money spent this month is 120% of the spending of the last month.
To find:
A proportion to model this situation.
And the spending done this month?
Solution:
Let us have a look at 120% first.
[tex]120\%= \dfrac{120}{100} = \dfrac{6}{5}[/tex]
[tex]\frac{6}{5}[/tex] of [tex]x[/tex] can be found by comparing [tex]x[/tex] with 5, then we have to find the equivalent of 6.
Here, [tex]x[/tex] is 40.
5 parts are equivalent to 40
1 part is equivalent to [tex]\frac{40}{5} = 8[/tex]
6 parts are equivalent to [tex]8\times 6 = 48[/tex]
OR
simply:
[tex]40 \times \dfrac{120}{100} = 48[/tex]
Which ordered pair would form a proportional relationship with the point graphed below? 40 (-20,40) 30 20 10 -40-30-20-190 10 20 30 40 x -20 -30 -40 0 (-40, 20) 0 (-10.-20) O (15, -30) O (5, -15)
Answers
Answer:
(15,-30)
Step-by-step explanation:
By forming a proportional relationship with the marked point, what we are saying is that the same dilation if applied to each coordinates of the marked point will form the new point
The marked point is given as (-20,40)
If we dilate this by -0.75 units
That will give (15, -30)
So this forms a proportional relationship with the marked point
find the profit or loss of the following:
CP=Rs 300, SP= Rs 832
Answers
Answer:
Profit of 532
Step-by-step explanation:
Since the SP is more than the CP then there is a profit
profit = SP - CP = 832 - 300 = 532
Naomi surveyed 480 of the students in her school about their favorite color. 95% said their favorite color was red. How many students' favorite color was red?
Answers
Answer:
456 students
Step-by-step explanation:
In order to find 95% of the 480 students, you can set up the equation below:
[tex]\frac{students}{total} = \frac{percent}{100percent}[/tex]
[tex]\frac{x}{480students} =\frac{95percent}{100 percent}[/tex]
x * 100 = 480 * 95
x = 45600 / 100 = 456
95% of 480 students is 456 students.
HELPPP PLEASE ASAP!!!!!!
Answers
Answer:
with what......
Step-by-step explanation:
..........
Answer:
with what?
Step-by-step explanation:
what what what
If the principal is $612 and the rate of interest is 2.85%, what is the amount of interest after eight years?
Answers
Answer:
$766.28
Step-by-step explanation:
The equation for interest rate is as follows:
[tex]A = P(1 + r)^t\\[/tex]
A = The total amount
P = Initial amount
R = The interest rate
T = Time
Let's plug everything into the equation that is given in the question:
The initial amount = 612
Interest rate = 2.85
Time = 8 years
[tex]A = 612(1+.0285)^8[/tex]
***Just a reminder we move the decimal over twice when working with percents***
Now, lets solve for the total amount:
[tex]A = 612(1.0285)^8\\A = 612(1.252086602)\\A = 766.28[/tex]
Therefore, after 8 years the principal is $766.28.
I hope this helps!!
If you have any questions feel free to ask!
- Kay :)
Question 12(Multiple Choice Worth 5 points)
(02.03 MC)
Which sequence of transformations will change figure PQRS to figure P′Q′R′S′?
A coordinate grid is labeled from negative 5 to 0 to 5 on both x and y axes at increments of 1. Figure PQRS has P at ordered pair 1, 2, Q at 2,1, R at 3,2, S at 3,3. Figure P prime Q prime R prime S prime has P prime at ordered pair 1,negative 2, Q prime at 2,negative 1, R prime at 3,negative 2 and S prime at 3,negative 3.
Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis
Counterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axis
Counterclockwise rotation about the origin by 270 degrees followed by reflection about the x-axis
Counterclockwise rotation about the origin by 270 degrees followed by reflection about the y-axis
Answers
Step-by-step explanation:
answer: counterclockwise rotation about the origin by 90degrees followed by reflection about the x-axis.
please give me brainliest:)
The longer leg of a 30°-60°-90° triangle measures
[tex]8 \sqrt{3} [/tex]
inches. What is the length of the shorter leg?
Answers
Answer:
Length of shorter leg is 8 inches
Step-by-step explanation:
Here, we want to calculate the length of the shorter leg of a 30-60-90 triangle
In a 30-60-90 triangle, the sides are in the ratio;
1: √3 : 2
So the ratio of the length of the shorter and longer leg is;
1 : √3
So in this case let the shorter leg be x
x/8 √3 = 1/√3
8 √3 * 1 = √3 * x
x = 8 √3/√3
x = 8 inches
can someone plz help me with this question ASAP. drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. the organizers of a founders day festival on main street surveyed local businesses to see if they would be offering any promotions to customers during the festival. the table contains the data gathered.
Answers
Answer:
hello the geinus has arrived
Which equation represents a line which is perpendicular to the line y = 4/3x-6
Answers
what is the derivative of ( 2w^2+1 ) ?
Answers
If you know about the power rule,
d/dw (2w² + 1) = 2 d/dw (w²) = 2 • 2w = 4w
If you have to use the limit definition of the derivative, let f(w) = 2w² + 1. Then
[tex]f'(w)=\displaystyle\lim_{h\to0}\frac{f(w+h)-f(w)}h[/tex]
[tex]f'(w)=\displaystyle\lim_{h\to0}\frac{(2(w+h)^2+1)-(2w^2+1)}h[/tex]
[tex]f'(w)=\displaystyle\lim_{h\to0}\frac{2(w^2+2wh+h^2)-2w^2}h[/tex]
[tex]f'(w)=\displaystyle\lim_{h\to0}\frac{4wh+2h^2}h[/tex]
[tex]f'(w)=\displaystyle\lim_{h\to0}(4w+2h)=\boxed{4w}[/tex]
Solve the system by substitution.
y = 3x + 14
y = X
Answers
Answer:
[tex]\boxed{x = -7~~and~~ y =-7}[/tex]
Step-by-step explanation:
y = 3x + 14
y = x
.
x = 3x + 14
3x - x = -14
2x = -14
[tex]x = \frac{-14}{2}[/tex]
x = -7
.
y = x
y = -7
Answer:
x = 7 and y = -7
Step-by-step explanation:
use substitution method
If (2x+10°) and (3x+10°) from a linear pair,find the angles.
Answers
Step-by-step explanation:
2x+10+3x+10=180
5x=160
x=32
2x+10
2×32+10
74
3x+10
3×32+10
106
Use an equation to find the value of k so that the line that passes through (k,4) and (3,-2) has a slope of m=-1
K=
Answers
Plug in what you know
-1 = (-2-4)/(3-k)
-1 = -6/(3-k)
-6/6 = -1, so 3-k = 6
3-k = 6, -k = 3, k = -3
Answer: k = -3
Which of the following functions best describes this graph?
A. y = x^2 - 8x +18
B. y = (x+4)(x+5)
C. y = x^2 -9x +20
D. y = (x-3)(x+4)
Answers
Answer:
C
Step-by-step explanation:
Looking at the graph, we can see the roots at two points
these are points x = 4 and x = 5
This can be written in their linear forms as;
x-4 and x-5
Finding the products of both, we have
x(x-5) -4(x-5)
= x^2 -5x -4x + 20
= x^2 - 9x + 20
Please answer correctly !!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
BF = 24
BH = ?
BH = 2/3 BF
BH = 2/3 24
BH = 16
| 18| - | - 10| what is the absolute value
Answers
Answer:
16
Step-by-step explanation:
Answer:
Step-by-step explanation:
the absolute value of 18 is 18 because absolute value is the distance from zero. the calculate value of -10 is 10. 18-10=8
|18| - |-10| =
18 - 10 = 8
ANSWER PLSSS!!!!!!
What is Ann's speed at 7 mins? give a reason to support your answer
Answers
Answer:
She drove 4 minutes
Step-by-step explanation:
116 is 35% of what number?
Answers
Answer:
Step-by-step explanation:
we use the formula
(116*100)/35=331.43
Answer:
about 331.43
Step-by-step explanation:
116(100)/35=331.43
Javier often orders party trays from his favorite Mexican food restaurant for company events. For a recent company event, he spent $259 on 4 burrito platters and 2 taco platters. For a company meeting, he spent $284 on 4 burrito platters and 4 taco platters. How much does each type of platter cost?
and
Jeff is a shoe salesman, and he works on commission. This week, there is a special incentive to sell shoes and boots by a certain company. Yesterday, Jeff sold 8 pairs of shoes and 7 pairs of boots, earning $188 in commission. Today, he sold 8 pairs of shoes and 6 pairs of boots, earning a total commission of $168. How much does Jeff earn for the sale of each type of footwear?
Answers
Answer:
1. 1 Burrito Platter = $58.50 , 1 Taco platter = $12.50
2. One pair of boots = $20 , One pair of shoes = $6
Step-by-step explanation:
1. Let the cost of one burrito platter be x and one taco platter be y.
4x + 2y = 259 --- Equation 1
4x + 4y = 284 --- Equation 2
Equations 2-1: 4x + 4y - 4x - 2y = 284 - 259
2y = 25
y = 25 ÷ 2
y = 12.50 (Taco platter)
Substitute y = 12.50 into Equation 1:
4x + 2y = 259
4x + 2(12.50) = 259
4x + 25 = 259
4x = 259 - 25
= 234
x = 234 ÷ 4
x = 58.50 (Burrito platter)
2. Let the cost of one pair of boots be x and one pair of shoes be y.
7x + 8y = 188 --- Equation 1
6x + 8y = 168 --- Equation 2
Equations 1-2: 7x + 8y - 6x - 8y = 188 - 168
x = 20 (Boots)
Substitute x = 20 into Equation 2:
6x + 8y = 168
6(20) + 8y = 168
120 + 8y = 168
8y = 168 - 120
= 48
y = 48 ÷ 8
y = 6 (Shoes)