Why is implicit differentiation necessary in order to find derivatives of curves which do not represent functions?
Come up with your own implicitly defined function. What is its first, second, and third derivative?

Answer:

No

Step-by-step explanation:

A function is a relation in which no two ordered pairs have the same first element.

A function associates each element in its domain with one and only one element in its range.

Answer:

18) If ∠1 = 124° , then ∠4 = 56°.

19) if ∠2 = 48°, then ∠3 = 132°.

20) if ∠4 = 55°, then ∠2 = 55°.

21) if ∠6 = 120° , then ∠8= 120°.

22) if ∠7 = 50.5 , then ∠6= 50.5°.

23) if ∠3 = 118.7°, then ∠2= 61.3°

Step-by-step explanation:

Given two parallel lines a and b.

And other line, which is called transversal line cuts these two parallel lines to make 8 angles.

Now,

18) Given, ∠1 = 124°

 Now, sum of consecutive interior angles made by transversal line with parallel lines = 180° .

⇒∠1 + ∠4 = 180°

⇒∠a = 180° - 124° = 56°.

19) ∠2 = 48°.

as sum of consecutive interior angles made by transversal line with parallel lines = 180° .

∠2 + ∠3 = 180°.

⇒ ∠3 = 180° - 48° = 132°.

20) ∠4 = 55°

Alternate angles made by transversal line with parallel lines are equal .

⇒∠2 = ∠4 = 55°.

21) ∠6 = 120°

As corresponding angles made by transversal line with parallel lines are equal. ∠6 = ∠3 = 120°.

now, also opposite angles are equal

⇒ ∠3 = ∠8 = 120°.

22) ∠7 = 50.5

As corresponding angles made by transversal line with parallel lines are equal. ∠7 = ∠2 = 50.5°.

now, also opposite angles are equal

⇒ ∠2 = ∠6 = 50.5°.

23) ∠3 = 118.7°

as sum of consecutive interior angles made by transversal line with parallel lines = 180° .

∠3 + ∠2 = 180°.

⇒ ∠2 = 180° - 118.7° = 61.3°

Answer:

77.78

Step-by-step explanation:

Answer:

77.78

Step-by-step explanation:

i had this ? on rsm student portal.

Answer:

[tex]\frac{78}{25}[/tex]

Step-by-step explanation:

A rational number has the form

[tex]\frac{a}{b}[/tex] ← where a and b are integers

3.12 = [tex]\frac{312}{100}[/tex] ← divide numerator/denominator by 4, thus

3.12 = [tex]\frac{78}{25}[/tex] ← in simplest form

Answer:

3.3 x - (3.3*8) - x = 1.2

2.3 x - (3.3*8) = 1.2

2.3 x - 26.4 = 1.2

2.3 x - 26.4 + 26.4 = 1.2 + 26.4

2.3 x = 27.6

2.3 x / 2.3 = 27.6 / 2.3

x = 12

Answer:

12

Step-by-step explanation:

2/3 x + x = 20

2/3 x + 3/3x = 20

5/3 x = 20   ... times 3/5 both sides

x = 12

check: 2/3 x 12 + 12 = 8 + 12 = 20

Answer:

4

Step-by-step explanation:

first add up the xs that gives you 5x because first 3x+4x gives you 7 then minus that with 2x that gives you five,

now add the numbers -76+96 that gives you 20 now the equation becomes

5x=20

now divide 20 by 5 that gives you 4

Answer:

[tex]4.624[/tex]

Step-by-step explanation:

[tex]y=0.043x+0.324\\given \ miles \ x=100\\y= 0.043\times100+0.324\\=4.3+0.324\\=4.624[/tex]

Answer:

16 serving.

Step-by-step explanation:

Given: 3/4 cup servings.

Now, computing the number of serving in 12 cups of cherries.

Using unitary method to solve.

∴ Number of serving= [tex]total\ cups \times number\ of\ serving\ per\ cup[/tex]

Number of serving in one cup is [tex]\frac{4}{3}[/tex]

Number of serving in 12 cups = [tex]12\times \frac{4}{3} = 16 \ serving[/tex]

Number of serving in 12 cups= [tex]16\ serving[/tex]

∴ There are 16 serving is possible in 12 cups of cherries.

Final answer:

To calculate the number of 3/4 cup servings in 12 cups of cherries, divide 12 by 3/4, which equals 16 servings.

Explanation:

To determine how many 3/4 cup servings are in 12 cups of cherries, we can divide the total number of cups by the size of one serving.

First, we express the serving size and the total amount in the same units: 3/4 cup and 12 cups.

Next, we divide the total amount of cherries by the serving size: 12 cups ÷ 3/4 cup.

To perform the division, we can multiply 12 by the reciprocal of 3/4, which is 4/3 (12 × 4/3 = 16).

The result is that there are 16 servings of 3/4 cup in 12 cups of cherries.

Answer:

See explanation

Step-by-step explanation:

1. Lines l and k are parallel. These lines are cut be transversal n. Angles 2 and 7 are corresponding angles when parallel lines l and k are cut by transversal n. By Corresponding Angles Ttheorem, angles 2 and 7 are congruent.

2. Lines m and n are parallel. These lines are cut be transversal k. Angles 2 and 10 are alternate interior angles when parallel lines m and n are cut by transversal k. By Alternate Interior Angles Theorem, angles 2 and 10 are congruent.

3. Angles 2 and 7 are congruent (see 1)

   Angles 2 and 10 are congruent (see 2)

  Hence, angles 7 and 10 are congruent by transitive property.

Answer:

[tex]x>22.5[/tex]

Step-by-step explanation:

Given linear inequality:

[tex]2x+5>50[/tex]

Solving for [tex]x[/tex]

Subtracting both sides by 5.

[tex]2x+5-5>50-5[/tex]

[tex]2x>45[/tex]

Dividing both sides by 2.

[tex]\frac{2x}{2}>\frac{45}{2}[/tex]

∴ [tex]x>22.5[/tex]

The graph of the inequality is shown below.

The line is represented by dotted line because the inequality sign is only greater than which means 22.5 is not included in the solution.  

After 16 hours, the charges will be same.

Step-by-step explanation:

Given,

Janet's upfront fee = $20

Charges per hour = $7.50

Let,

x be the number of hours.

J(x) = 7.50x+20

Lisa has no upfront fee.

Charges per hour = $8.75

L(x) = 8.75x

For the charges to be equal;

J(x) = L(x)

[tex]7.50x+20=8.75x\\20=8.75x-7.50x\\20=1.25x\\1.25x=20[/tex]

Dividing both sides by 1.25

[tex]\frac{1.25x}{1.25}=\frac{20}{1.25}\\x=16[/tex]

After 16 hours, the charges will be same.

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Answer:

No.

Step-by-step explanation: Assuming you mean x^3*x-7, these two equations do not produce the same line.

Answer:

Step-by-step explanation:

[tex]x^3\cdot x^{-7}=x^{3+(-7)}=x^{-4}\\\\\text{used}\ a^n\cdot a^m=a^{n+m}\\\\\text{Other way}\\\\a^{-n}=\dfrac{1}{a^n}\\\\x^3\cdot x^{-7}=x^3\cdot\dfrac{1}{x^7}=\dfrac{x^3}{x^7}=\dfrac{x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1}{x\!\!\!\!\diagup_1\cdot x\!\!\!\!\diagup_1 \cdot x\!\!\!\!\diagup_1 \cdot x\cdot x\cdot x\cdot x}=\dfrac{1}{x^4}=x^{-4}[/tex]

Answer:

Step-by-step explanation:

an = 6n - 13

If n  = 10  ,  a10 = 6*10 - 13 = 60-13 = 47

If n  = 11 ,  a11 = 6*11 - 13 = 66-13 = 53

If n  = 12  ,  a12 = 6*12 - 13 = 72-13 =  59

The formula to find the nth term of the sequence an, is a(n) = -13 + 6n

From the question, we have the following parameters that can be used in our computation:

a(10) = 47

a(11) = 53

a(12) = 59

a(13) = 65

The nth term of an arithmetic sequence can be represented as

a(n) = a(1) + (n - 1) * d

Where,

common difference,

d = 6

So, we have

a(n) = a(1) + (n - 1) * 6

Using the 12th term, we have

a(1) + (12 - 1) * 6 = 59

a(1)  = 59 - 66

a(1)  = -7

So,, we have

a(n) = -7 + (n - 1) * 6

Expand

a(n) = -13 + 6n

Hence, the formula to find an is a(n) = -13 + 6n

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Answer:

16.00

Step-by-step explanation:

When you divide twenty percent(0.20) to 20.00 you will get sixteen or 4.00 dollars off

135 cubes are required to fill the prism

Solution:

Given that a rectangular prism with volume of 5 cubic units is filled with cubes with side lengths of [tex]\frac{1}{3}[/tex] units

Then the number of cubes required to fill the prism will be given by:

[tex]\text { number of cubes }=\frac{\text {volume of rectangular prism}}{\text {volume of cube}}[/tex]

Volume of rectangular prism = 5 cubic units

[tex]\text{ Volume of cube}=(\text { side })^{3}$[/tex]

[tex]\text { Volume of cube }=\left(\frac{1}{3}\right)^{3}=\frac{1}{27}[/tex]

Therefore number of cubes required to fill the prism are:

[tex]\text { number of cubes }=\frac{5}{\frac{1}{27}}=5 \times 27=135[/tex]

Therefore 135 cubes are required to fill the prism

Answer:

135

Step-by-step explanation:

Answer:

A) The increase population of town after 3 years is 1.2 times initial population

B) The increase population of town after 5 years is 1.4 times initial population .

Step-by-step explanation:

Given as :

The rate of growth of population of a town = r = 7.5%

Let The initial population of town = p

A ) Let The increase population of town after 3 years = P

The time period = n = 3 years

Now, According to question

The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]

Or, The increase population of town after 3 years  = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 3}[/tex]

Or, P = p × [tex](1.075)^{3}[/tex]

Or, P = p × 1.242

So, The increase population of town after 3 years = P = 1.2 times initial population

Hence,The increase population of town after 3 years is 1.2 times initial population .  Answer

B )  Let The increase population of town after 5 years = P'

The time period = n = 5 years

Now, According to question

The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]

Or,  The increase population of town after 5 years = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 5}[/tex]

Or, P' = p × [tex](1.075)^{5}[/tex]

Or, P' = p × 1.4356

So, The increase population of town after 5 years = P' = 1.4 times initial population

Hence,The increase population of town after 5 years is 1.4 times initial population . Answer

Answer:

answer is y-5=-3(x-3)

Step-by-step explanation:

your y-coordinate is 5 s you would write y-5 and your slope is -3 with your x-coordinate as 3 so that would be written as -3(x-3).  The equation put together correctly would be y-5=-3(x-3)

Answer:

y-5=-3(x-3)

Step-by-step explanation:

y-y1=m(x-x1)

y-5=-3(x-3)

The y-intercept of [tex]\(12x + y^3 = 2\) is at \((0, \sqrt[3]{2})\).[/tex]

To find the y-intercept of the equation [tex]\(12x + y^3 = 2\)[/tex], we first need to understand what the y-intercept represents. The y-intercept is the point where the graph intersects the y-axis, which means the x-coordinate of this point is 0.

To find the y-intercept, we set [tex]\(x = 0\)[/tex] in the equation and solve for y:

[tex]\[12(0) + y^3 = 2\][/tex]

[tex]\[y^3 = 2\][/tex]

To solve for y, we take the cube root of both sides:

[tex]\[y = \sqrt[3]{2}\][/tex]

So, the y-intercept of the equation is [tex]\((0, \sqrt[3]{2})\).[/tex]

Answer:

The number of dimes is 14 and the number of quarters is 7.

Step-by-step explanation:

Given:

Emily has $3.15 worth of dimes and quarters.

She has twice as many dimes as quarters.

Now, to determine the number of dimes and the number of quarters.

Let the number of quarters be [tex]x.[/tex]

And the number of dimes be  [tex]2x.[/tex]

So, the total worth of dimes and quarters = $3.15.

Now, to get the number of dimes and quarters:

According to question:

[tex]0.10(2x)+0.25x=3.15[/tex]

[tex]0.20x+0.25x=3.15[/tex]

[tex]0.45x=3.15[/tex]

Dividing both sides by 0.45 we get:

[tex]x=7.[/tex]

Thus, the number of quarters = 7.

So, the number of dimes = [tex]2x=2\times 7=14.[/tex]

Therefore, the number of dimes is 14 and the number of quarters is 7.

7/19

bc 2 5/7 = 19/7. the reciprocal is a fraction reversed. or upside down that is. So, your answer is 7/19

Answer:

7/19

Step-by-step explanation:

2 5/7=19/7

Answer:

x>5

Step-by-step explanation:

-3(2x+5)<-45

2x+5<-45/-3

2x+5<15

2x<15-5

2x<10

x<10/2

x<5

x>5

The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.

Step-by-step explanation:

Given,

Cost of one pound of Caramels = $10.28

Cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel = [tex]10.28*1\frac{3}{4}[/tex]

Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]10.28*\frac{7}{4}=\frac{71.96}{4}= \$17.99[/tex]

Cost of one pound of chocolate milk = $13.85

Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]13.85*1\frac{3}{4}=13.85*\frac{7}{4}[/tex]

Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]\frac{96.95}{4}=\$24.24[/tex]

Difference = 24.24 - 17.99 = $6.25

The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.

Keywords: difference, multiplication

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Final answer:

The cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels, after calculating the total cost of each based on their per pound price.

Explanation:

To find out how much more the cost for 1 3/4 pounds of milk chocolate is than the cost for 1 3/4 pounds of caramels, we first need to calculate the cost of 1 3/4 pounds of each type of candy. Since the cost per pound of caramels is $10.28 and the cost per pound of milk chocolate is $13.85, we can set up our calculations as follows:

Total cost of caramels = 1.75 (pounds) * $10.28 (per pound) = $17.99

Total cost of milk chocolate = 1.75 (pounds) * $13.85 (per pound) = $24.24

Now, we subtract the total cost of caramels from the total cost of milk chocolate to find the difference:

Cost difference = $24.24 - $17.99 = $6.25

So, the cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels.

For this case we must simplify the following expression:

[tex](2a ^ 3-5a) - (7a+ 3a ^ 2) =[/tex]

By definition of the law of multiplication signs we have to:

[tex]- * + = -[/tex]

Rewriting the expression we have:

[tex]2a ^ 3-5a-7a-3a ^ 2 =[/tex]

We add similar terms taking into account that:

Equal signs are added and the same sign is placed.

[tex]2a ^ 3-3a ^ 2-12a[/tex]

ANswer:

[tex]2a ^ 3-3a ^ 2-12a[/tex]

Answer:

It would be (3,5)

Step-by-step explanation:

On a coordinate plane it would be changed in which the 2nd number becomes first & the + or - changes. Same for the first number.

Answer:

200g of sugar, 600g of flour, 400g of butter

Step-by-step explanation:

50g sugar = 15 biscuits

3 x 50g = flour --) 150g = flour

2 x 50g = butter --) 100g = butter

60/15 = 4; 4 times as much

4 x 50g = 200g of sugar

4 x 150g = 600g of flour

4 x 100g = 400g of butter

The amount of flour she needed is 600g.

Given that,

Based on the above information, the calculation is as follows:

50g sugar = 15 biscuits

[tex]= 3 \times 50g\\\\ = 150g\ flour[/tex]

And.  

[tex]= 2 \times 50g \\\\= 100g \ butter[/tex]

Now  

[tex]= 60\div15[/tex]

= 4 times

Therefore, the amount of floor should be

[tex]= 150 \times 4[/tex]

= 600 grams.

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225

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Answer: 3x-x+2=4

Step-by-step explanation:

absolute value of 225 = | 225 | = 225    

Answer:5x+7y

Step-by-step explanation:

Your welcome

Note: As you missed to mention the graph for f(x) = x + 1 from where we had to check which option defines the accurate graph. But, after a little research, I was able to get the graph of this question, and hence attaching the graph. So, I am answering based on that graph which, anyways, would clear your concept about determining the domain of the function that shows in a graph.

Answer:

x > 1 is the domain of the f(x) = x + 1.

Step-by-step explanation:

A domain is the set of all x values that a function passes through. It means a domain is set of all input values where the function is defined, meaning whatever you input the x value, for every x-value there is only one y-value that corresponds to it.

So, now lets talk about the given function f(x) = x + 1 and its graph as shown in attached figure. Carefully observe the top right part of the graph of f(x) = x + 1. It is validating the condition of x > 1.

For example,

Just input some x values, greater than 1 i.e. x > 1, in f(x) = x + 1 to determine the output values.

For example, for x > 1

and so on.

So, the top right part of the graph of f(x) = x + 1 is validating the condition of x > 1 as it is passing through P(2, 3), P(3, 4) and P(4, 5) etc. and so on.

So, x > 1 is the domain of the f(x) = x + 1.

Keywords: domain, function

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Answer:

"D"  X > 1

Step-by-step explanation:

HOPE THIS HELPS!!!

25% off means it would be selling for 75% of the original price ( 100% - 25% = 75%).

To find the sale price you would multiply the regular price by 75%:

The equation would be y = 0.75x