Please show the work. 5256÷52, 5624÷46, 756÷36, 2760÷12. It's a lot to do, so I'm making this 40 points.
Use the 1st derivative test to find the intervals where the function is increasing or decreasing. Please show your work so I can get a better understanding on how you achieved the solution. Thank you.
As the name of the test suggests, you have to compute the derivative:
[tex]f(x) = \dfrac1{2x+3} \implies f'(x) = -\dfrac2{(2x+3)^2}[/tex]
Find where, if at all, the derivative vanishes or is undefined - these are the critical points of f(x).
In this case, the derivative is never 0 since the numerator is constant and the denominator is non-negative. You also see that f '(x) is negative over its entire domain.
The denominator goes to 0 when 2x + 3 = 0, or x = -3/2.
Now split up the domain of f(x) into intervals with endpoints at the critical points. Here, we consider the two intervals, (-∞, -3/2) and (-3/2, ∞).
Take any point from either interval and check the sign of f '(x) at that point. Any points will do, but you should strive to pick one that makes calculations simple.
• From (-∞, -3/2), take x = -2; then f ' (-2) = -2 < 0. Since f '(x) is negative over this interval, f(x) is decreasing over it.
• From (-3/2, ∞), take x = 0; then f ' (0) = -2/9 < 0. Again, this means f(x) is decreasing over this interval.
So, the first derivative test tells us that f(x) = 1/(2x + 3) is decreasing over the intervals (-∞, -3/2) and (-3/2, ∞); in other words, over its entire domain.
For the second function, we have
[tex]f(x) = \dfrac{x+1}{x+3} \implies f'(x) = \dfrac{(x+3)-(x+1)}{(x+3)^2} = \dfrac2{(x+3)^2}[/tex]
Again, there's only one critical point, this time at x = -3 where the derivative is undefined.
• From the interval (-∞, -3), take x = -4; then f ' (-4) = 2 > 0, so f(x) is increasing.
• From the interval (-3, ∞), take x = 0; then f ' (0) = 2/9 > 0, so f(x) is increasing.
Evaluate the expression ab2 + 2ab + a2 for a = 6 and b = 3.
a) 128
b) 126
c) 130
c) 124
Answer:
I believe there is an error with the problem
Step-by-step explanation:
3*6*2 + 2*6*3 + 6*2 = 36+36+12 = 84
The answer of the expression ab² + 2ab + a² for a = 6 and b = 3 will be 126 so option (b) will be correct.
What is an expression?
A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
Given the expression
ab² + 2ab + a²
Now,
a = 6 and b= 3
So,
⇒ 6(3)² + 2(6)(3) + 6²
⇒ 36 + 54 + 36
⇒ 126
Hence "The answer of the expression ab² + 2ab + a² for a = 6 and b = 3 will be 126".
To learn more about expression,
https://brainly.com/question/14083225
#SPJ5
A jewelry store bought a gold necklace and marked it up 110% from the original cost of $23.52. Later on, Dean purchased the gold necklace and paid 14.75% sales tax. How much, including tax, did he pay for the gold
necklace?
9514 1404 393
Answer:
$56.68
Step-by-step explanation:
The final price is ...
(cost price) × (1 +110%) × (1 +14.75%) = (cost price)×2.10×1.1475
= $23.52×2.40975 ≈ $56.68
Dean paid $56.68 for the necklace.
Explain the three different ways of writing a ratio and provide an example
Answer: The most common way to write a ratio is as a fraction, 3/6. We could also write it using the word "to," as "3 to 6."
Step-by-step explanation:
you can write ratios as 3/6 , 3 to 6, or 3:6
3. For the pair of polynomials given, select all points of intersection.
f(x) = (x + 7)(x – 5)
g(x) = x-5
a. (-8, -13)
b. (-7,0)
C. (-5, -10)
d. (-6, -11)
e. (5,0)
Answer:
-6, -11 and 5, 0
Step-by-step explanation:
Graphing calculators can help you a lot with this type of Algebra. I suggest GeoGebra.org
help me figure this out.
Answer:
30; -5 is 5 units away from 0 and V is 25 units away from 0, and 5 + 25 = 30.
Step-by-step explanation:
To find the distance between point T, which has a value of -5, and V, which has a value of 25, we should find the absolute value of each number and then add those numbers together.
So, the absolute value of -5 is 5 and the absolute value of 25 is 25. 25 + 5 = 30, and this is the length of TV.
If you have any further questions or need clarification on anything, let me know!
Rocco loves making spaghetti with his grandmother. They make homemade tomato sauce by adding pureed tomatoes, sugar, salt, olive oil, and water. He notices that after he stops stirring, he sees a greasy film at the top of the red liquid. What does this tell you about his sauce mixture?
Oil floats on water because it is less dense I believe. So that would be the oil on top of the sauce(the oil is on top because of the water that was also added).
HELP PLEASE. which equation describes a line parallel to line g that has a y-intercept at (0, -1)
Answer:
Line C is parallel to the given line.
Step-by-step explanation:
The given graph slopes down, and thus has a negative slope: m = -1/2.
Of the possible choices, only C has this slope: y = (-1/2)x + b. The y-intercepts b and (0, 6) need not be the same, as the quality of parallelness is all that we care about here.
f(x) = 732
g(x) = 3x + 2
Find
(1) (a). Include any restrictions on the domain.
, 3 > 0
OA () (x) = 0 + 0
B. (4) (z) = 2, 3
c. (4) (x) = x +
OD. () () + -1
Answer:
Option DStep-by-step explanation:
Given:
[tex]f(x) = \sqrt[3]{3x}[/tex][tex]g(x)=3x+2[/tex]Find (f/g)(x):
[tex](f/g)(x)=f(x)/g(x)=\sqrt[3]{3x}/(3x+2)[/tex]The restriction is, the denominator can't be zero:
3x + 2 ≠ 0 ⇒ 3x ≠ -2 ⇒ x ≠ -2/3Correct choice is D
A line passes through the point (6,-4) and has a slope of - 4/3.
Write an equation in point-slope form for this line.
Answer:
Step-by-step explanation:
In point-slope form,
y - y1 = m(x - x1)
m = -4/3
x1 = 6
y1 = -3
y + 3 = (-4/3)(x - 6)
Write 5288 as a product of its prime factors
Answer:677
Step-by-step explanation i dont know
Whats the answer? ( BRANLIEST )
Answer:
14/2 i think
Step-by-step explanation:
Please help me with this problem.
Answer:
yes
no
yes
no
Step-by-step explanation:
You can tell it's negation when the word "not" is used.
Solve the system of equations by using substitution.
6r + 7s = –1
2r + 4s = –12
1) (–4, –8)
2) (–8, –4)
3) (–7, 8)
4) (8, –7)
Answer:
r = 8 and
s = -7
Step-by-step explanation:
(2r + 4s = - 12)/2 =
r +2s = -6
r = -2s - 6
Substitution:
6 (-2s -6) + 7s = -1
-12s - 36 + 7s = -1
-5s = 36-1
s = 35/-5
s = -7
6r + 7(-7) = -1
6r - 49 = -1
6r = 49-1
r = 48/6
r = 8
solve pls brainliest
Here it should be this
a) 300
b) 1732
a
1
=
3
and
a
n
=
a
n
−
1
−
1
a
1
=3 and a
n
=a
n−1
−1
Answer:????????
Step-by-step explanation:?
What is the equation of a line parallel to y= -1/2x+6 that passes through (-4, 1)?
Simplify:
3 square root 216/343
Answer:
answer is .........6/7....
Answer: 6/7
Step-by-step explanation:
Kristen babysits 38 hours a week for $6.80 per hour. She earns an additional $224.00 in tips . How much did she make in 1 week?
Answer:
$502.40
Step-by-step explanation:
Kristen works 38 hours for $6.80 per hour.
We multiply her pay and the hours she worked:
38 × 6.8 = 258.4
Thus, she makes $258.40/week
Now we add her tips, which would be the equation 258.4 + 224
258.4 + 224 = 502.4
So, she made $502.40 in 1 week
Solve for h in the mathematical formula A=1/2(a+b)h
Step-by-step explanation:
Since we arent given enough information to SOLVE for h, I will get as close as I can by rearranging the equation for h
Convert the fraction to a decimal for simplicity
A = 0.5(a + b)h
Divide both sides of the equals by 0.5
A/0.5 = (a + b)h
We can convert A/0.5 into its reciprocal
2 A = (a + b)h
Divide both sides of the equation by the bracketed (a + b)
(2 A) / (a + b) = h
Rewritten
h = [tex]\frac{2A}{(a + b)}[/tex]Which graph and equation shows a proportional relationship between and y? NEED HELP ASAP!!!
Answer:
y = 0.45x
Step-by-step explanation:
proportional relationships must pass through the point 0,0
both the x and y intercepts must equal 0
A duck is 2 feet below the surface of a pond. If its position can be recorded as −2 feet, what would the position of 0 represent?
A 2 feet below water
B 2 feet above water
C The bottom of the pond
D On the surface of the pond
Answer:
0 will be the right answer
Step-by-step explanation:
so im guessing either 2 feet below or the bottom of the pond
d. What is the number sentence?
Answer:
Combination of numbers and mathematical operations that children are often required to solve
Fishing Hook G is let down 2 times its present depth. Where is Fishing Hook G?
Answer:
[tex]2g[/tex]
Step-by-step explanation:
In other words, this problem is asking where Fishing Hook G is after it's 2 times deeper. Let g = its previous depth. We do 2 * g = 2g.
Subtract the linear expressions.
(−7.6x+7.4)−(3.5x+6.5)
What is the difference?
Enter your answer in the box.
Step-by-step explanation:
-7.6x+7.4-3.5x-6.5
-7.6x-3.5x+7.4-6.5
-11.1x+0.9
Last winter, the ratio of days with snow to days with no snow was 1.12. Write this ratio as a fraction in simplest form? PLS HELP
9514 1404 393
Answer:
28/25
Step-by-step explanation:
To make the number into a fraction, multiply and divide by 100:
1.12 × 100/100 = 112/100
Recognize that numerator and denominator have a factor of 4 in common:
112/100 = 28×4/(25×4) = 28/25
(6-9d4)-(3d4+4) polynomials
Answer:
2(1 - 6d⁴)
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
Identify
(6 - 9d⁴) - (3d⁴ + 4)
Step 2: Simplify
(Parenthesis) Distribute negative: 6 - 9d⁴ - 3d⁴ - 4Combine like terms: 2 - 12d⁴Factor: 2(1 - 6d⁴)A line passes through the point (−3,−10) , and it’s perpendicular to the line y=0 . Find an equation for this line.
Answer:
Step-by-step explanation:
y = 0 is actually the x axis.
All the points on the line you want have an x value of - 3
-3,-10 is actually one of those points
The equation you want is x = - 3
A store owner had nine employees and bought nine hundred fifty-one uniforms for them. If he wanted to give each employee the same number of uniforms, how many more should he buy so he doesn’t have any extra?
Answer:
105
Step-by-step explanation:
Divide 951 by 9