Differentiate from first principle

1. y= x^2 + 3x

2. y= x^2 + 3x + 8

Answer:

9.4(3.5 - 2.6x) = -0.4(5.5 + 4.85x)​

Step-by-step explanation:

x = 1.56

Sorry I didn't show my work, my computer won't let me upload pictures right now. I hope this helps!

Answer:

Time left for Madison for other activities is [tex]\frac{5x}{12}[/tex] h .

Step-by-step explanation:

Given as :

The time reserved by Madison for activities = x hours

The time uses for basketball = [tex]\frac{1}{4}[/tex] of x = [tex]\frac{x}{4}[/tex] h

The time uses for playing saxophone = [tex]\frac{1}{3}[/tex] of x = [tex]\frac{x}{3}[/tex] h

So , The total time used by him = [tex]\frac{x}{4}[/tex] h +  [tex]\frac{x}{3}[/tex] h

I.e The total time used by him =  [tex]\frac{7x}{12}[/tex] h

Now, The time left for other activities = x h -   [tex]\frac{7x}{12}[/tex] h

I.e  The time left for other activities =  [tex]\frac{12x - 7x}{12}[/tex] h

or,  The time left for other activities =  [tex]\frac{5x}{12}[/tex] h

Hence Time left for Madison for other activities is [tex]\frac{5x}{12}[/tex] h . Answer

Answer:

-2.96 , -2 11/12, 2.95

Step-by-step explanation:

To find the sum of 3.14 and 4.83, simply add the two numbers together: 3.14 + 4.83 equals 7.97.

The sum of 3.14 and 4.83 can be calculated by performing a simple addition of the two numbers:

3.14

+ 4.83

-------

 7.97

So, the sum of 3.14 and 4.83 is 7.97.

Answer:

The diameter of the circle is B) 24 inches.

Step-by-step explanation:

The value given (12 inches) is the radius of the circle. The diameter of a circle is equal to 2 * radius. 2 * 12 = 24.

The diameter of the circle is 24 inches.

Option B is the correct answer.

We have,

The diameter of a circle is a line segment that passes through the center of the circle and connects two points on its circumference.

It is the longest chord of the circle and divides the circle into two equal halves.

The diameter is commonly denoted by the symbol "d" and is related to the radius of the circle (denoted by "r") by the equation:

d = 2r

Now,

r = 12 inches

So,

d = 2r = 2 x 12 inches

d = 24 inches

d = 24 inches

Thus,

The diameter of the circle is 24 inches.

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594.15

Step-by-step explanation:

To find the sale price of the iPhone 11, we first calculate the amount of discount which comes to $104.85 and subtract this from the original price. The sale price of the iPhone 11 is therefore $594.15.

The question is about computing the sale price of an iPhone 11 which originally costs $699.00, given that a discount of 15 percent is provided. In mathematical terms, you would be required to find 15% of $699.00 and subtract that amount from the original price to get the sale price.

So, first, determine the amount of discount: 15 / 100 * $699.00 = $104.85. Next, subtract this discount from the original price: $699.00 - $104.85 = $594.15. So, the sale price of the iPhone 11 would be $594.15.

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Answer:

36

Step-by-step explanation:

171/(4+0.75) =36

you want it to be in minutes, so calculate the 45 seconds over 60 seconds, which is 0.75. Add that to the 4 minutes, and divide the total number of copies over the time used, and you have speed/minute.

To find how many copies the machine makes per minute, we convert the total time to minutes (4 minutes and 45 seconds equals 4.75 minutes) and then divide the number of copies (171) by this time, resulting in 36 copies per minute.

To calculate how many copies the machine makes per minute, we need to convert 4 minutes and 45 seconds into minutes. Since there are 60 seconds in a minute, 45 seconds is the same as 0.75 minutes (45/60). Adding this to 4 minutes gives us a total time of 4.75 minutes for the machine to make 171 copies. Now, to find the copies made per minute, we divide the number of copies by the number of minutes:

Copies per minute = Total copies / Total time in minutes

= 171 copies / 4.75 minutes

= 36 copies per minute.

Answer:

$40

Step-by-step explanation:

3 hours x 10= 30 hours

$4 x 10= $40

Number of adult tickets sold = 17

Number of student tickets sold =32

Number of senior citizen tickets sold = 51

Given that a certain school sells:

adult tickets = $ 8 ; student tickets = $ 5 and senior citizen tickets = $ 6

Let the number of adult tickets sold be "a"

Let the number of student tickets sold be "b"

Let the number of senior citizen tickets sold be "c"

For one game 100 tickets were sold for $ 600

Number of adult tickets sold + number of student tickets sold + number of senior citizen tickets sold = 100

a + b + c = 100 ------ eqn 1

Number of adult tickets sold  x price of one adult ticket +  number of student tickets sold x  price of one student tickets +  number of senior citizen tickets sold x price of one senior citizen tickets = 600

8a + 5b + 6c = 600  ----- eqn 2

There are 3 times as many adult tickets sold as senior citizen tickets

Hence we get,

3a = c  -------- eqn 3

Put eqn 3 in eqn 1 we get,

a + b + 3a = 100

4a + b = 100

b = 100 - 4a  ----- eqn 4

Substitute eqn 3 and eqn 4 in eqn 2, we get

8a + 5(100 - 4a) + 6(3a) = 600

8a + 500 - 20a + 18a = 600

6a = 600 - 500

a = 16.67 that is approximately 17

a = 17

Substitute a = 17 in eqn 3,

3(17) = c

c = 51

Substitute a = 17 in eqn 4,

b = 100 - 4(17) = 100 - 68 = 32

b = 32

Thus we get:

number of adult tickets sold = a = 17

number of student tickets sold = b = 32

number of senior citizen tickets sold = c = 51

The second graph, on the right side is a straight line without any gap or break so it is a graph of continuous data.

Step-by-step explanation:

A continuous data s the type of data which contains real values also. the continuous data is measured.

The graph of a continuous data is a continuous line without any breaks. The graph starts and ends only on one note. Not having any breaks or gaps.

In the given diagram, we can observe the both graphs.

The first graph is a scatter plot which only shows points on the graph. It is graph of some discrete data.

The second graph, on the right side is a straight line without any gap or break so it is a graph of continuous data.

Keywords: Discrete data, continuous data

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Answer:

The explicit rule is Ak = 1 + 2 * (k - 1)

Step-by-step explanation:

1. Let's review the information provided to us for finding the explicit rule for the sequence.

The arithmetic sequence 1, 3, 5, 7, 9, . . . represents the set of odd natural numbers.

2. Let's find the solution:

Ak = 1 + 2 * (k - 1)

For k = 1 ⇒ Ak = 1 + 2 * (1 - 1) = 1 + 2 * 0 = 1 + 0 = 1

For k = 2 ⇒ Ak = 1 + 2 * (2 - 1) = 1 + 2 * 1 = 1 + 2 = 3

For k = 3 ⇒ Ak = 1 + 2 * (3 - 1) = 1 + 2 * 2 = 1 + 4 = 5

For k = 4 ⇒ Ak = 1 + 2 * (4 - 1) = 1 + 2 * 3 = 1 + 6 = 7

For k = 5 ⇒ Ak = 1 + 2 * (5 - 1) = 1 + 2 * 4 = 1 + 8 = 9

For k = 6 ⇒ Ak = 1 + 2 * (6 - 1) = 1 + 2 * 5 = 1 + 10 = 11

For k = 7 ⇒ Ak = 1 + 2 * (7 - 1) = 1 + 2 * 6 = 1 + 12 = 13

Answer:

1st: 1+(k-1)2

2nd: 399

3rd: C

4th: 40,000

explanation:

just did it :)

Answer:

The probability that Aaron goes to the gym on exactly one of the two days is 0.74

Step-by-step explanation:

Let P(Aaron goes to the gym on exactly one of the two days) be the probability that Aaron goes to the gym on exactly one of the two days.

Then

P(Aaron goes to the gym on exactly one of the two days) =

P(Aaron goes to the gym on Saturday and doesn't go on Sunday) +

P(Aaron doesn't go to the gym on Saturday and goes on Sunday)

P(Aaron goes to the gym on Saturday and doesn't go on Sunday) =

P(the probability that Aaron goes to the gym on Saturday)×P(If Aaron goes to the gym on Saturday the probability that he does not go on Sunday)

=0.8×0.7=0.56

Thus, P(Aaron doesn't go to the gym on Saturday and goes on Sunday) = P(The probability that Aaron doesn't go to the gym on Saturday)×P(if Aaron does not go to the gym on Saturday the probability he goes on Sunday)

=0.2×0.9=0.18

Then

P(Aaron goes to the gym on exactly one of the two days) =0.56 + 0.18 =0.74

Answer:

0.74

Step-by-step explanation:

i just did it now on my maths-watch homework

Answer:

51/44 OR 1 7/44

Step-by-step explanation:

In adding fractions with unlike denominators, you have to find a common factor. In this case, I'll choose 44 because 11 times 4 is 44. So, whatever you do to the bottom must be done to the top as well. 11 times 4 is 44, so 10 times 4 is 40. The new fraction is 40/44. We'll do the same for the other fraction. 4 times 11 is 44, so 1 times 11 is 11. The new fraction is 11/44. Now we can add since we have common factors. 40/44 plus 11/44 is 51/44, which can be simplified to 1 7/44.

Required polynomial of degree four having zeros as -2 , 4 , 4 , 8 is [tex]f(x)=x^{4}-14 x^{3}+48 x^{2}+32 x-256[/tex]

Need to determine a polynomial of degree 4 and the zeros are -2, 4 , 4 and 8

Let the required polynomial be represented by f(x)

The factor theorem describes the relationship between the root of a polynomial and a factor of the polynomial.

If the polynomial p(x) is divided by cx−d and the remainder, given by p(d/c), is equal to zero, then cx−d is a factor of p(x).

-2 is zero of a polynomial means when x = -2, f(-2) = 0, so from factor theorem we can say that  

=> x = -2 that is x + 2 = 0 is factor of polynomial f(x)

4 is zero of a polynomial means when x = 4, f(4) = 0 , so from factor theorem we can say that  

=> x = 4 that is x -4 = 0 is factor of polynomial f(x)

4 is zero of a polynomial means when x = 4, f(4) = 0 , so from factor theorem we can say that  

=> x = 4 that is x -4 = 0 is factor of polynomial f(x)

8 is zero of a polynomial means when x = 8, f(8) = 0 , so from factor theorem we can say that  

=> x = 8 that is x -8 = 0 is factor of polynomial f(x)

So now we have four factors of polynomial f(x) that are (x + 2), (x -4) , (x -4) and (x – 8)

And as given that degree of polynomial f(x) is 4  

Now f(x) is equal to product of factors

[tex]\begin{array}{l}{\Rightarrow f(x)=(x+2)(x-4)^{2}(x-8)} \\\\ {=>f(x)=(x+2)\left(x^{2}-8 x+16\right)(x-8)} \\\\ {=>f(x)=(x+2)\left(x^{3}-8 x^{2}+16 x-8 x^{2}+64 x-128\right)} \\\\ {=>f(x)=(x+2)\left(x^{3}-16 x^{2}+80 x-128\right)} \\\\ {=>f(x)=x\left(x^{3}-16 x^{2}+80 x-128\right)+2\left(x^{3}-16 x^{2}+80 x-128\right)} \\\\ {=>f(x)=x^{4}-16 x^{3}+80 x^{2}-128 x+2 x^{3}-32 x^{2}+160 x-256} \\\\ {=>f(x)=x^{4}-14 x^{3}+48 x^{2}+32 x-256}\end{array}[/tex]

Hence required polynomial of degree four having zeros as -2 , 4 , 4 , 8 is [tex]f(x)=x^{4}-14 x^{3}+48 x^{2}+32 x-256[/tex]

Answer:

The correct answer is A)-27,618 feet because -29,029 Subtract by -1,411 is -27,618 far from each other

The answer is D the other guy is wrong, trust me I just got that question wrong lol

Answer:

See explanation

Step-by-step explanation:

Consider triangles ACM and BCM. In these triangles,

So,

[tex]\triangle ACM\cong \triangle BCM[/tex] by ASA postulate (if one side and two angles adjacent to this side of one triangle are congruent to one side and two angles adjacent to this side of another triangle, then two triangles are congruent).

Two-column proof:

      Statement                                 Reason

1. [tex]m\angle 3=m\angle 4[/tex]                          Given

2. [tex]CM\perp AB[/tex]                        Given

3. [tex]m\angle 1=m\angle 2=90^{\circ}[/tex]       Definition of perpendicular lines CM and AB

4. [tex]\overline{CM}\cong \overline{CM}[/tex]          Reflexive property

5. [tex]\triangle ACM\cong \triangle BCM[/tex]                       ASA postulate

Answer:

-2/3 (fixed it)

Step-by-step explanation:

Answer:

6.83 miles

Step-by-step explanation:

The length of the third side is approximately: [tex]\[\boxed{2.256 \, \text{miles}}\][/tex]

To find the length of the third side of a triangular course with a given angle between two sides, we can use the Law of Cosines.

[tex]\[c^2 = a^2 + b^2 - 2ab \cos(\gamma)\][/tex]

We want to find the length of the third side c

First, we need to plug in the values into the Law of Cosines formula:

[tex]\[c^2 = (3.5)^2 + (2.5)^2 - 2 \cdot 3.5 \cdot 2.5 \cdot \cos(40^\circ)\][/tex]

Calculate each term:

[tex]\[(3.5)^2 = 12.25\][/tex]

[tex]\[(2.5)^2 = 6.25\][/tex]

[tex]\[2 \cdot 3.5 \cdot 2.5 = 17.5\][/tex]

Using a calculator, we find:

[tex]\[\cos(40^\circ) \approx 0.7660\][/tex]

Substitute all the values into the equation:

[tex]\[c^2 = 12.25 + 6.25 - 17.5 \cdot 0.7660\][/tex]

[tex]\[c^2 = 18.5 - 13.405\][/tex]

[tex]\[c^2 = 5.095\][/tex]

Finally, take the square root of both sides to find c

[tex]\[c = \sqrt{5.095} \approx 2.256\][/tex]

Therefore, the length of the third side is approximately:

[tex]\[\boxed{2.256 \, \text{miles}}\][/tex]

Answer:

13

Step-by-step explanation:

Answer:

Approximately 7.9 feet.

Step-by-step explanation:

cos 10 = x / 8     where x is the required distance.

x = 8 cos 10

= 7.878 feet.

Answer:

x = - [tex]\frac{7}{8}[/tex]

Step-by-step explanation:

Given

x + [tex]\frac{3}{4}[/tex] = - [tex]\frac{1}{8}[/tex]

Multiply through by 8 to clear the fractions

8x + 6 = - 1 ( subtract 6 from both sides )

8x = - 7 ( divide both sides by 8 )

x = - [tex]\frac{7}{8}[/tex]

Answer:

x = -7/8

Step-by-step explanation:

x + 3/4 = - 1/8

Subtract both sides:

x + 3/4 - 3/4 = -1/8 - 3/4

x = -1/8 - 3/4

x = -7/8

Answer:

12 magazines

Step-by-step explanation:

cost over magazines

12.00    =      36.00    

   4                   ?

12*3=36      whatever you do to the numerator you do it to the denominator  

4*3=12

12 magazines

and im correct so gmany you better not delete my answer

Answer:

12 magazines

Step-by-step explanation:

12 (1/4) = 3

36 (1/3) =  12

The maximum profit is $854

Profit is the difference between the revenue and the cost price of an item. It is given by:

Profit = selling price - cost price

Since x represent the profit made by the company, is related to the selling price of each widget, x and it is given by the formula:

y = -3x² + 155x - 1148

At maximum profit, dy/dx = 0, hence:

dy/dx = -6x + 155

0 = -6x + 155

6x = 155

x = 25.83

The maximum profit is at gotten when the selling price of each widget is 25.83. Hence:

y = -3(25.83)² - 155(25.83) - 1148

y = $854

Therefore the maximum profit is $854

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Answer:

Distance from point A(0,5) to y = -3 x  - 5 is √10 units units.

Step-by-step explanation:

Here, the given line equation is  y = -3x -5

Also, the point A (0,5) is the given point.

Now, a distance of a point (m,n)  from a line Ax + By + c = 0 is given as:

[tex]d = \frac{\mid Am +bn+c \mid}{\sqrt{A^2 + B^2} }[/tex]

Here, the equation is  y = -3 x -5

⇒ 3 x + y + 5 = 0  , here A  = 3, B = 1

Now, the value of line equation at (0,5) is  3(0) + 5 + 5 = 10

So, from the given distance formula,  we get:

[tex]d = \frac{\mid Am +bn+c \mid}{\sqrt{A^2 + B^2} }  = d = \frac{10}{\sqrt{(3)^2 + (1)^2} } = \frac{10}{\sqrt{(10)}}   = \sqrt{(10)}[/tex]

⇒ d  = √10 units

Hence, distance from point A(0,5) to y = -3 x  - 5 is √10 units units.

To find the distance from point A(0,5) to the line y=-3x-5, we can use the distance formula.

To find the distance from point A(0,5) to the line y=-3x-5, we can use the distance formula.

The distance formula is given by:

d = √((x2 - x1)² + (y2 - y1)²)

In this case, point A is (0,5) and the line is y = -3x - 5.

So, we can substitute the values into the formula:

d = √((x - 0)² + (y - 5)²)

d = √(x² + (y - 5)²)

To find the distance, we need to substitute the x and y values of a point on the line into the formula and solve for d.

Let's take the point (1, -8) as an example:

d = √((1)² + (-8 - 5)²)

d = √(1 + 169)

d = √170

So, the distance from point A(0,5) to the line y=-3x-5 is √170.

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Answer:

step by step explanation:64^3x=512^2x+12

64^3x-512^2x=12

2^18x-2^18x=12

0=12

There is no solution for x in the given quadratic equation.

The equation which is of 2nd degree is known as quadratic equation.

Example: ax^2 + bx + c = 0 (quadratic equation)

               Here a, b, c are known quantities and x is variable.

               Here a can't be 0.

The equation given in the question is:

  64^3x =512^2x+12

 (8^2)^3x = (8^3)^2x + 12

 (8)^6x = (8)^6x + 12

There is no value of x, which will satisfy the equation hence it has no solution.

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Answer:

57

Step-by-step explanation:

The bottom line of the triangle is 180 degrees. Therefore, 2y + 4y - 36 has to equal 180. So, once you solve this linear equation, you will find that y equals 36. A triangle's angles always equal a total of 180 degrees. So, x + 51 + 2y has to equal 180, as well. Since we know y, substitute in 36 for 2y. Now the equation is 51 + 72 + x = 180. Solve for x. X is 57.

Answer:

57°

Step-by-step explanation:

The angles that are at the bottom middle are on a straight line, so they must add up to 180°. In order to determine y, use the equation 180 = 2y + 4y -36. After solving for y, you should be left with 36 = y. Now, we can fill in the bottom right angle in the left triangle. This would be 36 times 2, or 72. In triangles, all angles always add up to 180°, so, we can use the equation 180 = x + 51 + 72. Once solved for x, this will leave you with 57 = x, our final answer.

Answer:

Step-by-step explanation:

10/12 divide by 2= 5/6

Answer:

54 cm on the blueprint represents actual distance of 27 m.

Step-by-step explanation:

Scale on the blue print drawing of a house show 6 cm represents 3 m.

So, the proportion is [tex]\frac{6}{300} = \frac{1}{50}[/tex] {Since, 3 m = 300 cm.}

Hence, the original dimensions of the house is reduced in the ratio [tex]\frac{1}{50}[/tex] in the blue print drawing.

Then, 27 m i.e. 2700 cm will be represented in the drawing by [tex]2700 \times \frac{1}{50} = 54[/tex] cm.

Therefore, 54 cm on the blueprint represents actual distance of 27 m. (Answer)

Answer:

j=-37

Step-by-step explanation:

step 1

Find the slope of the given line

we have

[tex]2x+3y=21[/tex]

Convert to slope intercept form

Isolate the variable y

subtract 2x both sides

[tex]3y=-2x+21[/tex]

divide by 3 both sides

[tex]y=-\frac{2}{3}x+7[/tex]

The slope is

[tex]m=-\frac{2}{3}[/tex]

step 2

we have the points

(2,-9) and (j,17)

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{17+9}{j-2}[/tex]

[tex]m=\frac{26}{j-2}[/tex]

Remember that

If two lines are parallel then their slope are equal

therefore

[tex]\frac{26}{j-2}=-\frac{2}{3}[/tex]

[tex]26(3)=-2(j-2)\\78=-2j+4\\2j=4-78\\2j=-74\\j=-37[/tex]

The chemist should use 86.13 liters of the 15% solution,

47.29 liters of the 35% solution,

94.58 liters of the 65% solution to obtain a mixture of 228 liters containing 25% acid, using 2 times as much of the 65% solution as the 35% solution.

To solve this problem, we need to find how many liters of each solution should be used to obtain a mixture of 228 liters containing 25% acid, using 2 times as much of the 65% solution as the 35% solution. Here's how we can approach the problem:

Let's assume that we need to use x liters of the 15% solution, y liters of the 35% solution, and z liters of the 65% solution.

From the problem statement, we know that:

x + y + z = 228 (since we need a total of 228 liters of the mixture)

z = 2y (since we need to use 2 times as much of the 65% solution as the 35% solution)

0.15x + 0.35y + 0.65z = 0.25(228) (since we need the final mixture to contain 25% acid)

We can use these equations to solve for x, y, and z. Here's how:

Substitute z = 2y into the first equation to get x + y + 2y = 228, which simplifies to x + 3y = 228.

Rearrange this equation to get x = 228 - 3y.

Substitute z = 2y into the second equation to get 0.15x + 0.35y + 0.65(2y) = 0.25(228), which simplifies to 0.15x + 1.15y = 74.4.

Substitute x = 228 - 3y into this equation to get 0.15(228 - 3y) + 1.15y = 74.4, which simplifies to 34.2 - 0.3y = 74.4 - 1.15y.

Rearrange this equation to get 0.85y = 40.2, which simplifies to y = 47.29.

Substitute y = 47.29 into z = 2y to get z = 94.58.

Substitute y = 47.29 and z = 94.58 into x + 3y = 228 to get x = 86.13.

Therefore, the chemist should use 86.13 liters of the 15% solution, 47.29 liters of the 35% solution, and 94.58 liters of the 65% solution to obtain a mixture of 228 liters containing 25% acid, using 2 times as much of the 65% solution as the 35% solution.

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