Answer:
[tex]\fbox {See below} \downarrow[/tex]
Step-by-step explanation:
Question 1 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(4x^{3})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 4(3)x^{3-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 12x^{2}}[/tex]
Question 2 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{2}{x^{4}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(2x^{-4})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 2(-4)x^{-4-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -8x^{-5}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -\frac{8}{x^{5}}}[/tex]
Question 3 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3\sqrt{x})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3(x)^{\frac{1}{2}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 3(\frac{1}{2})x^{\frac{1}{2}-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{3}{2}x^{-\frac{1}{2}}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{3}{2\sqrt{x}}}[/tex]
Question 4 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{3}{\sqrt{x}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{-\frac{1}{2}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 3(-\frac{1}{2})x^{-\frac{1}{2}-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -\frac{3}{2}x^{-\frac{3}{2}}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -\frac{3}{2x\sqrt{x}}}[/tex]
Question 5 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{x^{3}}{4})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{1}{4}(3)x^{3-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{3}{4}x^{2}}[/tex]
Question 6 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{5})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 3(5)x^{5-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 15x^{4}}[/tex]
Question 3 of 32
Which of the following could be the equation for a parabola that opens to the
left with vertex (-17, 2)?
A. x=-3(y-2)² - 17
OB. x-3(y +17)² +2
OC. y-3(x-2)² - 17
D. y=3(x+17)² +2
Answer:
A
Step-by-step explanation:
The parabola opens to the left, so this eliminates C and D.
Also, the vertex is at (-17, 2), and out of A and B, the only parabola with this vertex is A.
what’s the inverse of f(x)=(x+3)^3-1
Answer:
cbrt(x+1)-3=y
Step-by-step explanation:
The inverse of a function is when the domain and range are swapped. So to find the inverse simply swap the x and y in the equation and then solve for y.
[tex]y = (x+3)^3-1\\x=(y+3)^3-1\\x+1=(y+3)^3\\\sqrt[3]{x+1}=y+3\\\sqrt[3]{x+1}-3=y[/tex]
i need a little help -
A cube has a side length x and an each dimension is being increased by y, guys. :)
A). Write an expression for the surface area of the new cube, and then expand, and simplify, guys. :)
B). Please find the difference of the surface areas of the new cube and the original cube, guys. :)
Surface area of old cube
6(side)²6x²Side of new cube
x+ySurface area
6(x+y)²6(x²+y²+2xy)6x²+6y²+12xyDifference
6y²+12xyAnswer:
A) 6(x + y)² = 6x² + 12xy +6y²
B) 12xy +6y²
Step-by-step explanation:
Surface area of a cube = 6s² (where s is the side length)
Part A
Given:
x = side length of original cube⇒ Surface area of the original cube = 6x²
If the side length of the cube is increased by y, then:
(x + y) = side length of new cube⇒ Surface area of the new cube = 6(x + y)²
Expand and simplify:
⇒ 6(x + y)²
⇒ 6(x + y)(x + y)
⇒ 6(x² + xy + xy + y²)
⇒ 6x² + 12xy +6y²
Part B
To find the difference between the surface areas of the new and original cubes, subtract the surface area of the original cube from the surface area of the new cube:
⇒ SA of new cube - SA of original cube
⇒ 6x² + 12xy +6y² - 6x²
⇒ 12xy +6y²
The area of a rectangular piece of land is 2/3 square mile.
One dimension is 1 1⁄2 miles.
Answer:
4/9 miles
Step-by-step explanation:
[tex]\sf Area = \dfrac{2}{3} \ square \ miles\\[/tex]
[tex]\sf length = 1\dfrac{1}{2}=\dfrac{3}{2} \ miles[/tex]
[tex]\sf Width \ of \ rectangle = \dfrac{Area}{length}[/tex]
[tex]\sf = \dfrac{2}{3} \div \ \dfrac{3}{2}\\\\ =\dfrac{2}{3}*\dfrac{2}{3}\\\\ =\dfrac{4}{9} \ miles\\[/tex]
Use KCF method for faction division.
K- Keep the first fraction.
C - Change the division to multiplication.
F - Flip the second fraction.
Find the value of x.
A. 6.6
B. 5.5
C. 8.8
D. 1.1
Answer:
the answer is D
Step-by-step explanation:
the answer is D because the
Answer: d
Step-by-step explanation:
Suppose that F(x) = x² and G(x) = 3x^2 + 8. Which statement best compares the graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units to the left.
B. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units to the left.
C. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units up.
D. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units up.
Answer:
The graph of G(x) is the graph of F(x) stretched vertically and shifted 8 units up.
On a coordinate plane, a circle has a center at (0, 0). Point (3, 0) lies on the circle.
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
Does the point (2, StartRoot 6 EndRoot) lie on the circle shown? Explain.
Yes, the distance from (3, 0) to (0, 0) is 3 units.
Yes, the distance from (0, 0) to (2, StartRoot 6 EndRoot) is 3 units.
No, the distance from (3, 0) to (2, StartRoot 6 EndRoot) is not 3 units.
No, the distance from (0, 0) to (2, StartRoot 6 EndRoot) is not 3 units.
Answer: Option (4)
Step-by-step explanation:
We know that the radius of the circle is 3.
Using the distance formula, the distance from the given point to the center is
[tex]\sqrt{(\sqrt{6}-0)^{2}+(2-0)^{2}} = \sqrt{10} \neq 3[/tex]
Answer:d
Step-by-step explanation:
Pls someone help me on this question
Answer: [tex]x=65^{\circ}, y=65^{\circ}, z=65^{\circ}[/tex]
Step-by-step explanation:
All radii of a circle are congruent, so by the base angles theorem
z = y = (180-50)/2 = 65.Also, angles x and y are inscribed in the same arc, and they are thus congruent, meaning x = 65.
What are the zeros of this function?
I need these answers ASAP would be very grateful for these if you would like to help me out I would appreciate it and give a good amount of points!
Answer:
5. 8π 6. 18π 7. 8.6π 8. 11/4π
Step-by-step explanation:
8. 2 3/4
2*4+3 = 11/4
Given f(x) = (x - 1)(x + 2)(x − 3), what are the zeros and end behavior of the function?
A function assigns the value of each element of one set to the other specific element of another set. The zeroes of the functions are -2, 1, and 3.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given f(x) = (x - 1)(x + 2)(x − 3), therefore, the zeroes of the functions are -2, 1, and 3. The end behavior of the function is that if x approaches ∞ then f(x) approaches ∞, while if x approaches -∞ then f(x) approaches -∞, as can be observed from the given graph.
Hence, the zeroes of the functions are -2, 1, and 3.
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Answer:
−1, 2, −3; continues downward to the left and upward to the right
Step-by-step explanation:
P(x) Q(x) = R(x); if P(x)
72 Am
R(x); if P(x)=x+2 and R(x) = x³ - 3x² - 6x-2, what is Q(x)?
Answer:
Q(x) is = to 11x² that's my answer
Simplify 8 − (14). plsss help
Answer:
(-6)
Step-by-step explanation:
Integer subtraction:
If two numbers have different sign, subtract and the result will have the sign of the bigger number.
8 - 14 = (-6)
Subtract 8 from 14 and the bigger number is 14 and sign of 14 is (-).
So, the answer is (-6)
Raj correctly determined that ray LH is the bisector of AngleGLI. Which information could he have used to determine this?
AngleGLH Is-congruent-to AngleILM
mAngleKLM = 5mAngleILM
mAngleGLI = 2mAngleGLH
mAngleGLI = mAngleGLH + mAngleHLI
The information could he have used to determine this is C. ∠GLI = 2∠GLH.
What is an angle?An angle is formed from the intersection of two lines. The types of angles are acute, obtuse, and scalene.
∠GLI is bisected by LH, hence:
∠GLH = ∠HLI (definition of bisection)
∠GLI = ∠GLH + ∠HLI (angle addition)
∠GLI = 2∠GLH
The information that can be used to determine this is ∠GLI = 2∠GLH.
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Answer: its C
Step-by-step explanation: on edge
Triangle ABC is a right triangle with CD | AB. Angle C is a right angle.
(BC)²+(AC)² = (AB)(BD + AD). Using
gives Blank space for answering Question.
(BC)²+(AC)=(AB) (AB), which simplifies to (BC)2 + (AC)2 = (AB)2
Possible answers
CPCTC
Side-Angle-Side Similarity Postulate
congruent
Side-Side-Side Similarity Postulate
segment addition postulate
proportional
First blank: Side-Angle-Side similarity postulate
Second blank: proportional
PLEASE HELP - mid term review question!
The isosceles triangle theorem states that if two sides of a triangle are _________, then the angles opposite those sides are congruent.
A. similar
B. adjacent
C. congruent
D. proportional
The isosceles triangle theorem states that if two sides of a triangle are congruent then the angles opposite those sides are congruent. The correct answer is option c.
What is the isosceles triangle?The triangle is having three sides in an isosceles triangle the two opposite sides are equal and the two adjacent angles with similar sides are equal.
The isosceles triangle theorem states that if two sides of a triangle are congruent then the angles opposite those sides are congruent.
Therefore the isosceles triangle theorem states that if two sides of a triangle are congruent then the angles opposite those sides are congruent. The correct answer is option c.
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Please help with this question
Answer:
4
Step-by-step explanation:
the second column and the second row so, the answer is 4
Isabella has a dozen apples of the same size and a dozen
watermelons of the same size. Isabella uses her juicer to extract 15
ounces of watermelon juice from 3 watermelons and 5 ounces of
apple juice from 9 apples. She makes a watermelon-apple juice
blend from an equal number of watermelons and apples. What
percent of the blend is watermelon juice?
90 per cent of the blend is watermelon juice.
Given that, Isabella has a dozen apples of the same size and a dozen watermelons of the same size.
Isabella uses her juicer to extract 15 ounces of watermelon juice from 3 watermelons and 5 ounces of apple juice from 9 apples.
We need to find what per cent of the blend is watermelon juice.
What is per cent?The percentage is a relative value indicating the hundredth part of any quantity. One per cent (symbolized 1%) is the hundredth part; thus, 100 per cent represents the entirety and 200 per cent specifies twice the given quantity.
Given that, she makes a watermelon-apple juice blend from an equal number of watermelons and apples.
So if she takes 9 apples, she can extract 5 ounces of juice.
By taking the same number of watermelons, that is 9 she can extract 15×3=45 ounces of juice.
Per cent of watermelon juice in the blend=45/50 ×100= 90%
Therefore, 90 per cent of the blend is watermelon juice.
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For every pound a company spends on advertising, it spends £0.80 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.
The ratio of amount spent on advertising to the amount spent on its website in its simplest form is 0.5 : 0.4
RatioAmount spent on advertising = £1Amount spent on website = £0.80Ratio of amount spent on advertising to the amount spent on its website
= £1 : £0.80
= 1 / 0.80
= 0.5 / 0.4
= 0.5 : 0.4
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disributivity of multiplication over addition for rational numbers solve : -3/4 , 2/3 and -5/6 = 1/8 ? how ?
The distributive property of multiplication over addition for rational numbers is (a) -3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]
Complete questionWhich of the following is an example of distributive property of multiplication over addition for rational numbers
(a) -3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]
(b) -3/4 × {2/3 + (-5/6)} = [3/4 × 2/3] - (-5/6)
(c) -3/4 × {2/3 + (-5/6)} = 2/3 + (-3/4) × -5/6
(d) -3/4 × {2/3 + (-5/6)} = {2/3 + (-5/6)} - 3/4
How to determine the correct distributive property?The distributive property of multiplication states that:
a * (b + c) = (a * b) + (a * c)
From the given question, we have:
-3/4 × {2/3 + (-5/6)}
This means that:
a = -3/4
b = 2/3
c = -5/6
Recall that a * (b + c) = (a * b) + (a * c)
So, we have:
-3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]
Hence, the distributive property of multiplication over addition for rational numbers is (a) -3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]
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8x3+70÷7-7
tell accordingly the correct answer will be marked as brainliest
Answer:
27
Step-by-step explanation:
When solving complicated equations like this, we need to remember the order of operations (PEMDAS), which is the order that we solve an equation
P arentheses
E xponents
M ultiplication
D ivision
A ddition
S ubtraction
now, here's the thing: we actually to multiplication/division at the same time, and the same thing with addition/subtraction
(as in, adding -4 is the same thing as subtracting 4, so we can't truly make a distinction between the two)
so, when we have multiple instances of multiplication/division , we solve left to right
(and then the same thing for addition/subtraction)
8 × 3 + 70 ÷ 7 - 7
so, we first need to multiply 8 by 3
8 × 3 = 24
next, we move to the right:
and we divide 70 by 7
70 ÷ 7 = 10
let's rewrite our equation:
(24) + (10) - 7
24 + 10 - 7 = 27
so, the answer to this expression is 27
hope this helps!! have a lovely day :)
9.
Let f(x) = 2x + 2. Solve f−1(x) when x = 4. (1 point)
Answer:
1
Step-by-step explanation:
The value of the output given by the inverse for a given input is the same as the input of the original function that results in the output equal to the given input.
So, 2x + 2 = 4, meaning the answer is 1
Given that x is an even number, express, in terms of x, the product of the next two odd numbers.
Answer:
Odd is the answer.
Step-by-step explanation:
An even number can be written in the form 2x, where x is an integer.
An odd number can be written in the form 2x + 1, where x is an integer.
So two odd numbers can be represented by 2a +1 and 2b +1, the product would be:
(2a + 1)(2b +1) = 4ab + 2a + 2b + 1 = which can be written as 2(2ab + a +b) + 1, but 2ab +a + b represents some integer, so 2ab + a + b = x.
So (2a + 1)(2b + 1) = 2(2ab + a + b ) + 1 = 2x +1 which is odd.
(11-8)x3+7+27-3
(18÷3)+6+(14-8)x5
(11-7)x6+4+32-4
The results of the arithmetic evaluations as given in the task content are; 40,42 and 62.
What are the results of the arithmetic evaluations?The arithmetic operations above can be evaluated and simplified as follows;
(11-8)x3+7+27-3 = (3×3)+7+27-3 = 40.
(18÷3)+6+(14-8)x5 = (6)+6+(6)x5 = 42.
(11-7)x6+4+32-4 = (5×6) +4 +32-4 = 62.
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True or false? Any fraction made up of two natural numbers is a rational number. Explain your answer.
Rational numbers are numbers that can be written in the form of a/b where a and b are integers.
What are Rational and Irrational numbers?Rational numbers are numbers that can be written in the form of a/b where a and b are integers.
Example: 1/2, 3.5 (which is writable as 7/5), 2(which is writable as 4/2), etc.
Irrational numbers are those real numbers that are not rational numbers.
For example √2, π, √13, etc.
It is an important thing to Know that all natural numbers are integers, and all integers are rational numbers. That means natural numbers are not irrational.
The given statement that any fraction is made up of two natural numbers is a rational number is true.
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Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution.
-3x+3y=9
2x-7y=-14
Alse please don't take long
Choices are attached
Answer:
[tex]\sf C) \ x = -1\dfrac{2}{5} , \ y = \ 1\dfrac{3}{5}[/tex]
Given equations:
a) -3x + 3y = 9b) 2x - 7y = -14Make x the subject in equation 1:
-3x + 3y = 9-3x = 9 - 3yx = y - 3Substitute this into equation 2:
2(y - 3) - 7y = -14
2y - 7y = -14 + 6
-5y = -8
y = -8/-5
y = 1.6
Then x = y - 3
= 1.6 - 3
= -1.4
Solution: (x, y) ⇒ (-1.4, 1.6)
Peter's dog weighs 12 pounds more than Joe's dog. The dogs weigh 36
pounds all together. Write an equation to find the weight of Joe's dog.
Subtract (0.95x minus -0.04) minus (0.99x minus 0.13).
Sparky bought a rare Mickey Mantle baseball card for $16,500 that is increasing 8% in value every year. How much will the card be worth in 7 years?
Answer: 28,278.10
Step-by-step explanation:
[tex]a_{7} =16500(1.08)^7[/tex]
[tex]a_{7} =28278.1[/tex]
